# Accumulating Hints for Flavour Violating Higgses at the Electroweak Scale

Andreas Crivellin<EMAIL_ADDRESS>Physik-Institut, Universität
Zürich, Winterthurerstrasse 190, CH–8057 Zürich, Switzerland  Paul Scherrer
Institut, CH–5232 Villigen PSI, Switzerland  Syuhei Iguro
<EMAIL_ADDRESS>Institute for Theoretical Particle Physics (TTP),
Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131
Karlsruhe, Germany  Institute for Astroparticle Physics (IAP), KIT, Hermann-
von-Helmholtz-Platz 1,
76344 Eggenstein-Leopoldshafen, Germany

###### Abstract

A combined explanation of the deviations from Standard Model predictions in
$h\to e\tau$, $h\to\mu\tau$, $b\to s\ell^{+}\ell^{-}$, the $W$ mass and
$R({D^{(*)}})$ as well as the excess in $t\to bH^{+}(130\,{\rm GeV})\to
b\overline{b}c$ is proposed: We show that a Two-Higgs-Doublet Model with non-
minimal flavour violation can simultaneously explain these hints for new
physics without violating the stringent bounds from e.g. $\mu\to e\gamma$,
$\tau\to\mu\gamma$, $B_{s}-\bar{B}_{s}$ mixing, $b\to s\gamma$, low mass di-
jet and $pp\to H^{+}H^{-}\to\tau^{+}\tau^{-}\nu\bar{\nu}$ searches.
Furthermore, a shift in the SM Higgs coupling strength to tau leptons as well
as a non-zero $t\to hc$ rate is predicted, as preferred by recent
measurements. We propose three benchmark points providing such a simultaneous
explanation and calculate their predictions, including collider signatures
which can be tested with upcoming LHC run-3 data.

††preprint: PSI-PR-23-41, ZU-TH 73/23, P3H-23-078, TTP23-051

##  I Introduction

The Standard Model (SM) describes the known fundamental constituents of matter
and their interactions at sub-atomic scales. It has been extensively tested
and verified by a plethora of measurements ParticleDataGroup:2022pth  and the
discovery of the Brout-Englert-Higgs boson Higgs:1964ia ; Englert:1964et ;
Higgs:1964pj ; Guralnik:1964eu  at the LHC ATLAS:2012yve ; CMS:2012qbp , which
has, in fact, properties Langford:2021osp ; ATLAS:2021vrm ; CMS:2022dwd ;
ATLAS:2022vkf  in agreement with the SM expectations, provided its last
missing puzzle piece.

However, these results do not exclude the existence of additional scalars, if
the SM-Higgs signal strengths are not significantly altered (i.e. the mixing
with the new scalars is sufficiently small) and their contribution to the
$\rho$ parameter ($\rho=m_{Z}^{2}\cos^{2}\theta_{W}/m_{W}^{2}$) does not
violate the experimental bounds. In fact, several indirect and direct hints
suggest the existence of new Higgses (see Ref. Crivellin:2023zui  for a recent
review). In this article, we will focus on flavour violating signatures
motivated by the indications for non-zero rates of $t\to bH^{+}(130)\to
b\overline{b}c$, $h\to e\tau$ and $h\to\mu\tau$ as well as the deviations from
the SM predictions in $b\to s\ell^{+}\ell^{-}$, the $W$ mass and
$R({D^{(*)}})$. While for the latter three anomalies many viable NP options
exist, the first three hints point towards new scalars coupling (directly) to
SM fermions. This singles out $SU(2)_{L}$ doublets with hypercharge 1/2.
Since, except for the $W$ mass, flavour violation is clearly required, we will
study the two-Higgs-doublet model (2HDM) with generic Yukawa couplings
Hou:1991un ; Chang:1993kw ; Liu:1987ng ; Cheng:1987rs ; Savage:1991qh ;
Antaramian:1992ya ; Hall:1993ca ; Luke:1993cy ; Atwood:1995ud ; Atwood:1996vj
as a minimal model with the potential of explaining these measurements.

The layout of this article is given as follows: In Sec. II we introduce our
model. Then in Sec. III we consider the status of the anomalies and the
relevant bounds together with our NP contributions. In Sec. IV we propose the
benchmark points that can resolve the anomalies and calculate their
predictions before we conclude in Sec. V.

##  II G2HDM

In the 2HDM with generic Yukawa couplings (G2HDM), also called the type-III
2HDM, one can work in the so-called Higgs basis where only one Higgs doublet
acquires a nonzero vacuum expectation value (VEV) Davidson:2005cw  such that

$\displaystyle H_{1}=\left(\begin{array}[]{c}G^{+}\\\
\frac{v+\phi_{1}+iG^{0}}{\sqrt{2}}\end{array}\right),~{}~{}~{}H_{2}=\left(\begin{array}[]{c}H^{+}\\\
\frac{\phi_{2}+iA}{\sqrt{2}}\end{array}\right).$ (5)

Here, $G^{+}$ and $G^{0}$ are would-be Goldstone bosons, and $H^{+}$ and $A$
are the charged Higgs and the CP-odd Higgs boson, respectively, with $v\approx
246\,$GeV. The Yukawa couplings can then be written as

$\displaystyle\mathcal{L}_{Y}=$
$\displaystyle-\overline{Q}_{L}^{i}\\!\left({{H_{1}}y_{d}^{i}+{H_{2}}\rho_{d}^{ij}}\right)\\!d_{R}^{i}-\overline{L}_{L}^{i}\\!\left({{H_{1}}y_{\ell}^{i}+{H_{2}}\rho_{\ell}^{ij}}\right)\\!e_{R}^{i}$
$\displaystyle-\overline{Q}_{L}^{i}{({V^{\dagger}})^{ij}}\left({{{\tilde{H}}_{1}}y_{u}^{j}+{{\tilde{H}}_{2}}\rho_{u}^{jk}}\right)u_{R}^{j},$
(6)

where $i$, $j$ and $k$ are flavour indices, and
$\tilde{H}_{1,2}=i\tau_{2}H^{*}_{1,2}$ with $\tau_{2}$ being the second Pauli
matrix. We now perform the rotation

$\displaystyle\begin{pmatrix}\phi_{1}\\\
\phi_{2}\end{pmatrix}=\begin{pmatrix}\cos\theta_{\beta\alpha}&\sin\theta_{\beta\alpha}\\\
-\sin\theta_{\beta\alpha}&\cos\theta_{\beta\alpha}\end{pmatrix}\begin{pmatrix}H\\\
h\end{pmatrix},$ (7)

to go to the mass eigenstates $h$ and $H$ for the neutral Higgses, where $h$
is SM-like. Furthermore, writing and $Q=(V^{\dagger}u_{L},d_{L})^{T}$, where
$V$ is the Cabbibo-Kobayashi-Maskawa (CKM) matrix Cabibbo:1963yz ;
Kobayashi:1973fv , we arrive at the mass eigenbasis for the fermions with
$y_{i}^{f}=\sqrt{2}m_{f_{i}}/v$ ($m_{f_{i}}$ denoting the fermion masses).

Note that $\rho_{f}^{ij}$ is independent of the fermion masses, i.e. contains
9 complex parameters each for $f=u,d,\ell$. The off-diagonal elements of
$\rho_{d}$ are stringently constrained by meson mixing and decays and we will
thus disregard them. We will rather consider the minimal scenario where
$\rho_{u}^{tt}$, $\rho_{u}^{tc}$, $\rho_{\ell}^{\tau\tau}$,
$\rho_{\ell}^{\mu\tau}$, and $\rho_{\ell}^{e\tau}$ are the only nonzero
entries. In addition, we consider $m_{H^{\pm}}$, $m_{H}$, $m_{A}$ and Higgs
mixing parameter $c_{\beta\alpha}\equiv\cos\theta_{\beta\alpha}$ as free
parameters (with relevant impact on the phenomenology) while we disregard CP-
violation in the Higgs potential.

##  III Observables

Let us now discuss the different anomalies, the corresponding contributions in
the G2HDM as well as the constraints from various other observables.

###  III.1 $t\to bH^{+}(130)\to b\overline{b}c$

The ATLAS run-2 analysis ATLAS:2023bzb  reported an excess in $t\to bH^{+}\to
b\overline{b}c$ with a global (local) significance of $2.5\,(3.0)\sigma$ at
$m_{H^{+}}\approx 130\,{\rm GeV}$ with Br$(t\to bH^{+})\times{\rm
Br}(H^{+}\to\overline{b}c)=(0.16\pm 0.06)\%$.#1#1#1The analogous CMS result is
available only with run-1 data CMS:2018dzl  and hence the sensitivity is not
competitive. See Refs. Akeroyd:2022ouy ; Bernal:2023aai  for alternative
explanations of the $m_{H^{+}}\approx 130\,{\rm GeV}$ excess. In our model we
have

$\displaystyle{\rm{Br}}(t\to
bH^{+})=\frac{m_{t}|\rho_{u}^{tt}|^{2}}{16\pi\Gamma_{t}}\\!\left(1-\frac{m_{H^{+}}^{2}}{m_{t}^{2}}\right)^{\\!2}\\!\\!\approx
0.16\left(\frac{|\rho_{u}^{tt}|}{0.06}\right)^{\\!2}{\\!\%}\,,$ (8)

where we set $m_{H^{+}}=130\,{\rm GeV}$ on the right-handed side of the
equation. As we will see later, the numerically relevant couplings for the
decay of $H^{+}$ are $\rho_{u}^{tc}$ and $\rho_{\ell}^{\ell\tau}$, with
$\ell=e,\,\mu,\,\tau$, such that

${\rm Br}(H^{+}\to
c\overline{b})\approx\frac{3|\rho_{u}^{tc}|^{2}}{3|\rho_{u}^{tc}|^{2}+\sum\limits_{\ell^{\prime}}|\rho_{\ell}^{\ell^{\prime}\tau}|^{2}}\,.$
(9)

###  III.2 $h\to e\tau,\mu\tau$

While the previous run-1 excess in $h\to\mu\tau$ CMS:2015qee ; ATLAS:2015cji
was not confirmed by run-2 data, the latest ATLAS and CMS results show again
indications for nonzero $h\to e\tau$ and $h\to\mu\tau$ rates CMS:2021rsq ;
ATLAS:2023mvd . The combined significance is $2.4\sigma$ ($\Delta\chi^{2}=8.3$
with dof=2) with the best fit values Br$(h\to
e\tau)\simeq{\rm{Br}}(h\to\mu\tau)\approx 0.08\%$ while 2.3$\sigma$ for $h\to
e\tau$ and 1.3$\sigma$ for $h\to\mu\tau$ are obtained for the separated
measurements.

We have at tree-level

$\displaystyle{\rm{Br}}(h\to l\tau)$
$\displaystyle=\frac{c_{\beta\alpha}^{2}m_{h}}{16\pi^{2}\Gamma_{h}}\left(|\rho_{\ell}^{l\tau}|^{2}+|\rho_{\ell}^{\tau
l}|^{2}\right)$ $\displaystyle\approx
0.06\left(\frac{c_{\beta\alpha}\sqrt{|\rho_{\ell}^{l\tau}|^{2}+|\rho_{\ell}^{\tau
l}|^{2}}}{10^{-3}}\right)^{2}\%,$ (10)

where $l=e,\,\mu$.

###  III.3 $b\to s\ell^{+}\ell^{-}$

Recent global $b\to s\ell^{+}\ell^{-}$ fits favour $C_{9}^{U}\approx-1$ at the
$5\sigma$ level Buras:2022qip ; Neshatpour:2022pvg ; Gubernari:2022hxn ;
Ciuchini:2022wbq ; Alguero:2023jeh ; Wen:2023pfq ; Capdevila:2023yhq #2#2#2The
main drivers for this preference for NP are $P_{5}^{\prime}$ Descotes-
Genon:2012isb ; LHCb:2015svh ; LHCb:2020lmf ; LHCb:2020gog , the total
branching ratio and angular observables in $B_{s}\to\phi\mu^{+}\mu^{-}$
LHCb:2015wdu ; LHCb:2021zwz ; LHCb:2021xxq  as well as the Br$(B\to
K\mu^{+}\mu^{-})$ LHCb:2014cxe ; LHCb:2016ykl ; Parrott:2022zte , which are
fully compatible with semi-inclusive observables Isidori:2023unk .. This means
that lepton flavour universal NP with vectorial couplings to lepton and left-
handed couplings to bottom and strange is required.

In our model the charm loop contributes to $C_{9}^{U}$ via an off-shell photon
penguin Jager:2017gal ; Bobeth:2014rda ; Iguro:2018qzf ; Crivellin:2019dun ;
Kumar:2022rcf ; Iguro:2023jju ; Crivellin:2023saq  and we obtain
Crivellin:2019dun ,

$\displaystyle\Delta C_{9}^{U}(\mu_{b})\approx$
$\displaystyle-0.52\left(\frac{|\rho_{u}^{tc}|^{2}-|\rho_{u}^{cc}|^{2}}{0.5^{2}}\right)+0.50\left(\frac{\rho_{u}^{tc*}\rho_{u}^{cc}}{0.01}\right).$
(11)

We see that a sizable coupling $\rho_{u}^{tc}$ is necessary if
$\rho_{u}^{cc}\approx 0$ is assumed while the product
$\rho_{u}^{tc*}\rho_{u}^{cc}$ has a CKM enhancement w.r.t. the SM.

###  III.4 $R({D^{(*)}})$

The long-standing $3\sigma$–$4\sigma$ discrepancy in $B\to D^{(*)}\tau\nu$
HFLAV:2022pwe  can be solved by a charged Higgs contribution Crivellin:2012ye
; Crivellin:2013wna ; Cline:2015lqp ; Crivellin:2015hha ; Lee:2017kbi ;
Iguro:2017ysu ; Martinez:2018ynq ; Fraser:2018aqj ; Athron:2021auq ;
Iguro:2022uzz ; Blanke:2022pjy ; Ezzat:2022gpk ; Fedele:2022iib ; Das:2023gfz
if $m_{H^{\pm}}\lesssim 400\,{\rm GeV}$ avoiding the constraints from
$\tau\nu$ searches Iguro:2018fni ; Iguro:2022uzz .#3#3#3Note that the bound
from Br($B_{c}\to\tau\nu$) is relaxed once the charm mass uncertainty and
considerable $p_{T}$ dependence of fragmentation function of $b\to B_{c}$ is
taken into account Alonso:2016oyd ; Celis:2016azn ; Blanke:2018yud ;
Aebischer:2021ilm  such that our model can explain the central value of
$R(D^{(*)})$. While in principle, the scalar operator changes the differential
distributions in $B\to D^{(*)}\tau\nu$ Sakaki:2014sea ; Celis:2016azn ;
Iguro:2017ysu , we will not consider these constraints since the theory
prediction significantly depends on the form-factors used. In fact, recent
lattice results from HPQCD Harrison:2023dzh  and Fermi-MILC
FermilabLattice:2021cdg  have a mild tension with Belle (II) data
Fedele:2023ewe ; Penalva:2023snz  while JLQCD agrees with the measurement
Aoki:2023qpa . Furthermore, correlations among the bins of the differential
distributions are not provided in both Belle and BaBar papers. Our NP
contribution is given by

$\displaystyle C_{S_{L}}^{\ell^{\prime}\ell}(\mu_{b})=$ $\displaystyle
F_{RG}\left(\frac{\rho_{u}^{tc*}\rho_{\ell}^{\ell\ell^{\prime}*}}{m_{H^{+}}^{2}}\right)\bigl{/}\left(\frac{4G_{F}V_{cb}}{\sqrt{2}}\right)$
$\displaystyle\approx$ $\displaystyle
0.67\left(\frac{\rho_{u}^{tc*}\rho_{\ell}^{\ell\ell^{\prime}*}}{0.01}\right)\left(\frac{130\,{\rm
GeV}}{m_{H^{+}}}\right)^{2},$ (12)

where $F_{RG}\approx 1.5$ accounts for the renormalization running effect
(RGE) Alonso:2013hga ; Jenkins:2013wua ; Gonzalez-Alonso:2017iyc ;
Aebischer:2017gaw . For the numerical analysis we use Ref. Blanke:2018yud  to
calculate $R(D^{(*)})$, which is consistent with the recent update of Ref.
Iguro:2022yzr ; Iguro:2020cpg , and use the HFLAV SM prediction HFLAV:2022pwe
. Note that in order to explain $R({D^{(*)}})$ at the 1$\sigma$ level and non-
interfering effect, either via an imaginary part of $C_{S_{L}}^{\tau\tau}$
and/or $C_{S_{L}}^{\tau l}$ is needed.

###  III.5 Charged-lepton flavour violation

The product $\rho_{\ell}^{e\tau}\rho_{\ell}^{\mu\tau}$ induces potentially
dangerous $\mu\to e$ transitions at the one-loop level. Furthermore, if in
addition $\rho_{\ell}^{\tau e}$ and $\rho_{\ell}^{\tau\mu}$ were nonzero large
$\tau$-mass enhanced contributions to the magnetic operator would arise.
However, even if $\rho_{\ell}^{\tau l}$ is set to zero we have for
$c_{\beta\alpha}=0.1$, $m_{\phi}=200\,{\rm GeV}$ and $m_{H^{+}}=130\,{\rm
GeV}$ Omura:2015xcg #4#4#4We checked that the $\rho_{u}^{tt}$ induced two-loop
Barr-Zee contribution is negligible in our scenario.

$\displaystyle{\rm Br}(\mu\to e\gamma)\approx 2.8\times
10^{-13}\left(\frac{|\rho_{\ell}^{e\tau}\rho_{\ell}^{\mu\tau*}|}{7\times
10^{-5}}\right)^{2},$ (13)

where $\phi=H,\,A$ which can be compared with the current upper limit of ${\rm
Br}(\mu\to e\gamma)\leq 3.1\times 10^{-13}$ at $90\,\%$ Cattaneo:2023iua .
Note that the $c_{\beta\alpha}$ dependence is mild for $c_{\beta\alpha}\ll 1$.
Moreover, a correlation among $\mu\to e\gamma$, $\mu\to 3e$ and $\mu\to e$
conversion Crivellin:2014cta ; Calibbi:2017uvl  can be found

$\displaystyle{\rm{Br}}(\mu\to e\gamma)\approx 140\\!\times\\!{\rm{Br}}(\mu\to
3e)\approx 420\\!\times\\!{\rm{Cr}}(\mu\rm{Al}\to e\rm{Al}),$ (14)

where Cr corresponds to the conversion rate for which improved measurements
are foreseen in the near future Blondel:2013ia ; Baldini:2013ke ; Mu2e:2014fns
; COMET:2018auw . Similarly $\tau\to l\gamma$ is induced by the product
$\rho_{\ell}^{\tau\tau}\rho_{\ell}^{l\tau}$, but the predicted Br is at least
one order smaller than the projected Belle II sensitivity Belle-II:2018jsg .

###  III.6 $b\to s\gamma$ and $B_{s}-\bar{B}_{s}$ mixing

$b\to s\gamma$ and $B_{s}-\bar{B}_{s}$ mixing give relevant constraints on
$\rho_{u}^{tc}$ and $\rho_{u}^{tt}$. Adopting the global fit of Ref.
Wen:2023pfq  we find $-0.035\lesssim{\rm{Re}}\Delta C_{7}(\mu_{b})\lesssim
0.037$ at the $2\sigma$ level.#5#5#5Reference Alguero:2021anc  finds allowed
values down to $-0.04$ at $2\sigma$ level. We obtain the semi-analytic formula
for one-loop charged Higgs contribution Crivellin:2019dun

$\displaystyle\Delta
C_{7}(\mu_{b})\approx-0.03\left(\frac{|\rho_{u}^{tc}|}{0.5}\right)^{2}-0.008\left(\frac{|\rho_{u}^{tt}|}{0.5}\right)^{2},$
(15)

meaning that the G2HDM interferes constructively with the SM.

Using the input of Ref. Crivellin:2023saq  we obtain the allowed range of
$-0.09\leq R_{B_{s}}\equiv\Delta M_{B_{s}}^{\rm{G2HDM}}/\Delta
M_{B_{s}}^{\rm{SM}}\leq 0.07$. This has to be compared to Iguro:2017ysu

$\displaystyle R_{B_{s}}\approx
0.05\left(\frac{|\rho_{u}^{tc}|}{0.5}\right)^{2}+0.002\left(\frac{|\rho_{u}^{tt}|}{0.05}\right)^{2}-0.01\biggl{|}\frac{\rho_{u}^{tc*}\rho_{u}^{tt}}{0.025}\biggl{|}\,,$
(16)

for $m_{H^{\pm}}=130$ GeV. Similarly, we can consider $\Delta M_{B_{d}}$ and
$\Delta\Gamma_{B_{s(d)}}$ (see, e.g. the online update of Ref. UTfit:2007eik
), however, the constraints are less stringent and also $D^{0}-\bar{D}^{0}$
and kaon mixing are not relevant for our minimal coupling structure
Iguro:2019zlc .

###  III.7 $t\to ch(A,H)$

For the the decay of a top to a charm quark and SM Higgs, we have

$\displaystyle{\rm Br}(t\to hc)$
$\displaystyle=\frac{m_{t}c_{\beta\alpha}^{2}(|\rho_{u}^{tc}|^{2}+|\rho_{u}^{ct}|^{2})}{64\pi\Gamma_{t}}\left(1-\frac{m_{h}^{2}}{m_{t}^{2}}\right)^{2}$
$\displaystyle\approx 2.4\times
10^{-4}\left(\frac{\rho_{u}^{tc}c_{\beta\alpha}}{0.05}\right)^{2}.$ (17)

Similarly, the rates for $A$ and $H$ are obtained by replacing $m_{h}$ and
$c_{\beta\alpha}$ with $s_{\beta\alpha}$ and $m_{H,A}$, respectively. The
current ATLAS upper limit is set as ${\rm Br}(t\to hc)\leq 4.0\times 10^{-4}$
at 95$\%\;$CL ATLAS:2023ujo . Note that this is weaker than the expected limit
of $2.4\times 10^{-4}$ at $95\%$ such that a non-zero rate is in fact
preferred. Moreover CMS finds ${\rm Br}(t\to hc)\leq 3.7\times 10^{-4}$ at
$95\%\;$CL, compared to an expected sensitivity of $3.5\times 10^{-4}$
CMS:2023ufv . The high-luminosity LHC (HL-LHC) can probe Br$(t\to hc)\leq
1.1\times 10^{-4}$ TheATLAScollaboration:2013nbo ; ATLAS:2016qxw .

Figure 1:  Upper left: Predicted values of $\Delta C_{9}^{U}$ and preferred
regions for ${\rm Br}(t\to bH^{+})$ in the $\rho_{u}^{tc}$-$\rho_{u}^{tt}$
plane along with constraints from $b\to s\gamma$ (lighter gray) and
$B_{s}-\bar{B}_{s}$ mixing (darker gray) assuming Br$(H^{+}\to bc)\approx
100\%$. The HL-LHC sensitivity to Br$(t\to hc)$ is shown for
$c_{\beta\alpha}=0.085$ (orange-dashed line). The red cross and the blue
diamond indicate our two benchmark points BM1 and BM2, respectively. Upper
right: Preferred regions ($1\sigma$ and $2\sigma$) from $h\to l\tau$ for
$c_{\beta\alpha}=0.085$, $c_{\beta\alpha}=0.1$ and $c_{\beta\alpha}=0.15$, in
the $\rho_{\ell}^{e\tau}$-$\rho_{\ell}^{\mu\tau}$ plane as well as the
exclusion region from $\mu\to e\gamma$ which, in a linear approximation, is
independent of $c_{\beta\alpha}$. Bottom left (right): Preferred regions from
$R({D^{(*)}})$ ($1\sigma$ and $2\sigma$) as well as the exclusion region from
$\mu\to e\gamma$ (gray), $\kappa_{\tau}$ (blue) and $B_{c}\to\tau\nu$ (red) in
the $\rho_{\ell}^{\tau\tau}$-$\overline{\rho_{\ell}^{l\tau}}$ plane assuming
all Yukawa couplings to be real. The up-quark Yukawa couplings are set to the
values of BM1 (BM2) given in the upper figures while the benchmark value of
$\overline{\rho_{\ell}^{l\tau}}$ is indicated by the orange line. The current
measured central value of $\kappa_{\tau}$ is shown as a dashed blue line.

###  III.8 Collider searches

Search for the supersymmetric partners of the tau lepton at LHC can constrain
$R({D^{(*)}})$ explanations with light charged Higgses Iguro:2022uzz .
However, for the coupling hierarchy $\rho_{u}^{tc}\gg\rho_{\ell}^{\ell\tau}$,
$H^{+}$ dominantly decays into $c\overline{b}$. In this case, di-jet searches,
especially bottom flavoured ones, are relevant. However, the current upper
limit on $\rho_{u}^{tc}$ is a factor 2 weaker than the one favoured by $\Delta
C_{9}^{U}$ Iguro:2022uzz ; Desai:2022zig  once the $b\to s\gamma$ and
$B_{s}-\bar{B}_{s}$ mixing constraints are taken into account.

Recently, ATLAS and CMS released the result of a same-sign top search
targeting a G2HDM ATLAS:2023tlp ; CMS:2023fod . They do not find a significant
excess in mass range of our interest and set the upper limit, assuming a
single scalar particle as a mediator, of $|\rho_{u}^{tc}|\lesssim
0.3$.#6#6#6This constraint could be potentially extrapolated to lower masses.
However, this needs detailed experimental analysis since a top quark will be
less boosted and this would make the detection more difficult. However, in the
limit of $m_{H}=m_{A}$ the effect is suppressed due to destructive
interference.

For $m_{\phi}\lesssim m_{t}+m_{c}$, neutral scalars produced via an EW Drell-
Yan process (i.e. $pp\to Z^{*}\to AH$) could in principle have sizable decays
to $\ell\tau$. This setup would then be stringently constrained by chargino
and neutralino searches CMS:2021edw ; ATLAS:2022nrb ; Iguro:2023jkf .
Therefore, these searches can exclude regions in parameter space in which both
neutral scalar masses are lighter than $m_{t}+m_{c}$ and where Br$(H,A\to
l\tau)\sim 1$. However, note that in our setup
Br$(H^{+}\to\overline{\tau}\nu)\approx 0$ due to the large
$H^{+}\to\overline{b}c$ width.

###  III.9 Higgs coupling strength

Although both ATLAS ATLAS:2022vkf  and CMS CMS:2022dwd  found that the
$h\tau\overline{\tau}$ coupling is consistent with the SM prediction within
uncertainties, their central value is slightly smaller than the SM one,
resulting in a coupling strength relative to the SM one of

$\displaystyle\kappa_{\tau}=0.93\pm
0.07\,({\rm{ATLAS}}),~{}~{}\kappa_{\tau}=0.92\pm 0.08\,({\rm{CMS}}).$ (18)

Since nonzero $c_{\beta\alpha}$ and $\rho_{\ell}^{\tau\tau}$ are necessary for
$h\to l\tau$ and $R({D^{(*)}})$, a deviation in $\kappa_{\tau}$ is inevitable.

In our model, the signal strength $\kappa_{\tau}$ is given as

$\displaystyle\kappa_{\tau}=\biggl{|}\frac{\frac{\sqrt{2}m_{\tau}}{v}s_{\beta\alpha}+\rho_{\ell}^{\tau\tau}c_{\beta\alpha}}{\frac{\sqrt{2}m_{\tau}}{v}}\biggl{|}.$
(19)

Remarkably $c_{\beta\alpha}=0.1$ and $\rho_{\ell}^{\tau\tau}=-0.01$ give
$\kappa_{\tau}=0.90$ which improves the fit.

###  III.10 Oblique correction (ST parameters)

The mass differences between new Higgses induce deviations of the S and T
parameters from 0, i.e. their SM values. Lead by the CDF-II measurement
CDF:2022hxs  we have

$\displaystyle{\rm{S}}=0.086\pm 0.077,~{}~{}{\rm{T}}=0.177\pm 0.070,$ (20)

with the correlation of $\rho=0.89$ based on the global fit deBlas:2022hdk .

##  IV Phenomenological Analysis

We can now consider the preferred size of the relevant free parameters
$\rho_{u}^{tc},\,\rho_{\ell}^{\tau\tau},\,\rho_{\ell}^{\mu\tau}$,
$\rho_{\ell}^{e\tau}$, $c_{\beta\alpha}$, $m_{H,A}$ and $m_{H^{+}}$, assuming
in the first step that all couplings are real and that the other new Yukawa
couplings are negligibly small.

Concerning observables that are only sensitive to the charged Higgs
contribution, we first use the excess in $t\to H^{+}b\to b\overline{b}c$ to
fix $m_{H^{+}}\approx 130\,$GeV. Furthermore, $b\to s\ell^{+}\ell^{-}$ favors
sizable and negative $\Delta C_{9}^{U}$ which can be obtained via
$\rho_{u}^{tc}$, such that for Br$(H^{+}\to c\bar{b})\approx 100\%$, i.e.
$|\rho_{\ell}^{\ell\tau}|,|\rho_{u}^{cc}|\ll|\rho_{u}^{tc}|$, leading to
$\rho_{u}^{tt}\approx 0.06$. However, the possible effect in $\Delta
C_{9}^{U}$ is limited to $\approx-0.6$ by the constraints from $b\to s\gamma$
and $B_{s}-\bar{B}_{s}$ mixing. This is illustrated in Fig. 1 (upper left).
Note that the impact of the neutral Higgses can be disregarded for these
observables, such that we can choose two benchmark (BM) points for the
couplings $\rho_{u}^{tc}$, i.e. $\rho_{u}^{tc}=0.53$ and $\rho_{u}^{tc}=0.5$
for BM1 and BM2, respectively for $\rho_{u}^{cc}\approx 0$.

Turning to observables sensitive to lepton couplings, the excesses in $h\to
e\tau$ and $h\to\mu\tau$ lead to a preference of nonzero values of
$\rho_{\ell}^{e\tau}$, $\rho_{\ell}^{\mu\tau}$ and $c_{\beta\alpha}$.#7#7#7In
principle also $\rho_{\ell}^{\tau e}$, $\rho_{\ell}^{\tau\mu}$ could explain
$h\to e\tau$ and $h\to\mu\tau$. However, in order to avoid chirally enhanced
effects in $\mu\to e\gamma$ it is important that both $\rho_{\ell}^{\tau
e}\rho_{\ell}^{\mu\tau}$ and $\rho_{\ell}^{e\tau}\rho_{\ell}^{\tau\mu}$ are
not sizable. Furthermore, to avoid effects in $b\to cl\nu$, we will opt for
$\rho_{\ell}^{l\tau}\neq 0$ and $\rho_{\ell}^{\tau l}=0$. This at the same
time leads to an effect in $\mu\to e\gamma$ as illustrated in Fig. 1 (upper
right). Note the mild dependence on the neutral Higgs masses which we set for
definiteness to $200\,$GeV, and that explaining both $h\to e\tau$ and
$h\to\mu\tau$ at the same time is possible with a Higgs mixing of
$c_{\beta\alpha}\gtrsim 0.08$. Since the significance of excesses in $h\to
e\tau$ and $h\to\mu\tau$ are slightly different, the contours are not
symmetric in the $\rho_{\ell}^{e\tau}$-$\rho_{\ell}^{\mu\tau}$ plane. To
maximize the contribution to $R({D^{(*)}})$ while explaining $h\to l\tau$ at
$1\sigma$ we fixed the $r_{\mu
e}\equiv\rho_{\ell}^{\mu\tau}/\rho_{\ell}^{e\tau}=2.7$ and
$\overline{\rho_{\ell}^{l\tau}}\equiv|\rho_{\ell}^{e\tau}|+|\rho_{\ell}^{\mu\tau}|\approx
0.019$ (BM1). In a more conservative setup we use and $r_{\mu e}=1$ and
$\overline{\rho_{\ell}^{l\tau}}=0.015$ (BM2). Finally, since
$|\rho_{\ell}^{l\tau}|\ll|\rho_{u}^{tc}|$ the results discussed in the
previous paragraph are not affected.

Let us now consider $R({D^{(*)}})$ in the lower panel in Fig. 1 for BM1 (left)
and BM2 (right) where we also show the $\mu\to e\gamma$ exclusion region in
the $\rho_{\ell}^{\tau\tau}$-$\overline{\rho_{\ell}^{l\tau}}$ plane. The red
and blue regions are excluded by the $B_{c}\to\tau\nu$ lifetime and
$\kappa_{\tau}$, respectively. Note that the minimal deviation of
$\kappa_{\tau}$ from unity is $4\,\%$ for BM1 since
$|\rho_{\ell}^{\tau\tau}|\gtrsim 5\times 10^{-3}$ and $c_{\beta\alpha}\gtrsim
0.08$ are necessary to explain $h\to l\tau$ and $R({D^{(*)}})$ simultaneously.

Figure 2: Preferred regions (green: $1\sigma$, yellow: $2\sigma$) from
electroweak precision data along with exclusion regions from multi-tau and
same-sign top searches as well as $\mu\to e\gamma$ in the $m_{A}$-$m_{H}$
plane.

Parameters
---
$m_{H^{+}}=130\,{\rm{GeV}},\,m_{\phi}=200\,{\rm{GeV}},\,c_{\beta\alpha}=0.1,\,\rho_{u}^{tt}=0.06$,
$\rho_{u}^{tc}=0.45,\,\rho_{\ell}^{\tau\tau}=-0.01(1\pm
i),\,\rho_{\ell}^{\mu\tau}=0.01,\,\rho_{\ell}^{e\tau}=0.006$
Predictions
${\rm{Br}}(t\to b\overline{b}c)=0.16\%,\,\Delta
C_{9}^{U}=-0.43,\,{\rm{Br}}(h\to\mu\tau)=0.061\%$,
${\rm{Br}}(h\to e\tau)=0.022\%,\,R(D)=0.375,\,R(D^{*})=0.272,$
$\kappa_{\tau}=0.90,\,\chi^{2}_{\rm{SM}}-\chi^{2}_{\rm{G2HDM}}({\rm{ST}},\,2023)=10.4,$
${\rm{Br}}(\mu\to e\gamma)=2.0\times 10^{-13},$ $\Delta
C_{7}=-0.025,\,R_{B_{s}}=0.03,$
${\rm{Br}}(B_{c}\to\tau\overline{\nu})=31\,\%,\,{\rm{Br}}(t\to ch)=2.0\times
10^{-4}$

Table 1: The value of the parameters for BM3 and the corresponding predictions
for the observables.

Note that BM1 is on the edge of the current constraints such that it can
explain all anomalies within $1\sigma$ while BM2 is more conservative w.r.t.
the experimental bounds but is only in agreement with $R({D^{(*)}})$ at the
$2\sigma$ level. The reason for this is that $\rho_{\ell}^{e\tau}$ and
$\rho_{\ell}^{\mu\tau}$ are smaller which reduces the non-interfering effect
NP with the SM. Since also an imaginary part of
$\rho_{u}^{tc}\rho_{\ell}^{\tau\tau}$ leads to an amplitude which does not
interfere with the SM this can help to explain $R({D^{(*)}})$.#8#8#8Note that
electroweak baryogenesis could be realized with complex Yukawa couplings
Fuyuto:2017ewj ; Kanemura:2023juv . We can write
$\overline{\rho_{\ell}^{l\tau}}$ effectively as
$\overline{\rho_{\ell}^{l\tau}}=|\rho_{\ell}^{e\tau}|+|\rho_{\ell}^{\mu\tau}|+{\rm{Im}}[\rho_{\ell}^{\tau\tau}]$.
Note that $\rho_{\ell}^{\tau\tau}$ does not contribute to $\mu\to
e\gamma$.#9#9#9For simplicity we consider the complex $\rho_{\ell}^{\tau\tau}$
and assume that $\rho_{u}^{tc}$ remains to be real. However, $\rho_{u}^{tc}$
could be complex as well without conflicting $\Delta\Gamma_{B}$. Once we
consider complex $\rho_{\ell}^{\tau\tau}$, we can generate an imaginary value
of the $h\tau\overline{\tau}$ coupling (for $c_{\beta\alpha}\neq 0$). Since
the ATLAS measurement of the SM-Higgs CP properties only starts to constrain
this ATLAS:2022akr , the resulting bound is too weak to be relevant.
Therefore, $|\rho_{\ell}^{\tau\tau}|$ can be bigger than in the case
$\rho_{\ell}^{\tau\tau}$ is real and thus explain $R({D^{(*)}})$ with smaller
$|\rho_{u}^{tc}|$ and hence yields smaller $\Delta C_{7}$, alleviating the
$b\to s\gamma$ bound. The corresponding benchmark point (BM3) is given in Tab.
1 which explains $t\to bH^{+}\to b\overline{b}c$, $h\to l\tau$ and
$R({D^{(*)}})$ within $1\sigma$ with $\Delta C_{9}^{U}=-0.4$ and moderate
$\Delta C_{7}$ and Br$(\mu\to e\gamma)$.

Figure 3: Diagram showing the correlations between the free parameters
(circles) of our model (except the Higgs masses) and the observables.
Observables providing strong constraints are shown as red hexagons while the
ones pointing towards a NP effect are shown as black rectangles.

Finally, we consider the impact of varying $m_{A}$ and $m_{H}$ in Fig. 2 for
BM3. Multi-tau final state searches exclude the bottom-left#10#10#10Note that
the inclusive di-$\tau$ resonance search CMS:2022goy  will be able to cover
the region where either $H$ or $A$ is lighter than $m_{t}+m_{c}$ in future.
while smaller values of $m_{A}$ and $m_{H}$ are also disfavoured by Br$(\mu\to
e\gamma)$. Same-sign top searches provide constraints if $m_{H},\,m_{A}\gtrsim
200\,$GeV. However, because of the cancellation between the amplitudes from
$A$ and $H$, $m_{H}\simeq m_{A}$ can evade this bound. Furthermore, once
$\phi\to W^{\pm}H^{\mp}$ becomes kinematically allowed, same-sign top searches
lose their constraining power. Note that top associated Higgs production
Iguro:2023jju  and bottom associated $H^{+}$ production Blanke:2022pjy  as
well as lowering the threshold of same-sign top searches ATLAS:2023tlp ;
CMS:2023fod  are crucial to probe this scenario.

##  V Conclusions and discussion

Motivated the hints for NP in $t\to bH^{+}$, $b\to s\ell^{+}\ell^{-}$, $h\to
e\tau$, $h\to\mu\tau$, $m_{W}$ and $R({D^{(*)}})$ we revisited a the 2HDM with
generic sources of flavour violation. We found a minimal set of parameters
that can address these deviations from the SM predictions without violating
any other constraint (see, BM points for the favored coupling structure). The
correlation between the free parameters (except the Higgs masses) and the
observables in Fig. 3. Furthermore, a mild mass difference between the charged
and additional neutral Higgs mass is necessary to evade the LHC constraint
which at the same time improves the EW global fit by shifting the prediction
for the $W$ mass. Furthermore, a deviation in the SM Higgs coupling strength
to tau leptons $\kappa_{\tau}$ and a non-zero rate for $t\to hc$ are
predicted, both welcomed by current data.

While we assumed the other Yukawa coupling to be negligible,
$\rho_{d}^{bb}\approx\mathcal{O}(10^{-2})$ could be helpful to reduce the
effect in $\Delta C_{7}$ while allowing for $b$-associated production of the
new neutral scalars at the LHC. Adding a small $\rho_{u}^{cc}$ would induce
$\Delta C_{9}^{U}$ (see Eq. (11)).#11#11#11It would be important to comment on
that an additional $\rho_{u}^{cc}$ does not induce $D-\bar{D}$ mixing since
$H^{+}$ does not couple to up quark in our setup. Note that once we give up
either $h\to\mu\tau$ or $h\to e\tau$, the $\mu\to e\gamma$ constraint can be
relaxed such that $R({D^{(*)}})$ could be fully explained. This is because
$\rho_{\ell}^{e\tau}$ or $\rho_{\ell}^{\mu\tau}$ can be larger and hence the
smaller $c_{\beta\alpha}$ is allowed. Then larger $\rho_{\ell}^{\tau\tau}$ and
smaller $\rho_{u}^{tc}$ can explain $R({D^{(*)}})$. While a smaller
$\rho_{u}^{tc}$ would lead to a smaller contribution to $\Delta C_{9}^{U}$, a
tiny $\rho_{u}^{cc}$ can already regenerate a sizable value. Note that a
smaller $\rho_{u}^{tc}$ would also be beneficial to avoid tuning the neutral
Higgs masses while still avoiding collider constraints. To assess the validity
of such a more complicated scenario, a global fit, e.g. with the public tool
GAMBIT Athron:2021auq , is desirable for future research.

###### Acknowledgements.

We are very grateful to Lisong Chen, Marco Fedele, Ulrich Nierste, Teppei
Kitahara, Hiroyasu Yonaha and Martin Lang for enlightening discussions and
encouraging this work. The work of A. C. is supported by a professorship grant
from the Swiss National Science Foundation (No. PP00P21_76884). S. I. would
like to thank PSI for the worm hospitality where he stayed during the initial
stage of this project. S. I. is supported by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under grant
396021762-TRR 257.

## References

  * (1) Particle Data Group Collaboration, R. L. Workman et al., “Review of Particle Physics,” PTEP 2022 (2022) 083C01.
  * (2) P. W. Higgs, “Broken symmetries, massless particles and gauge fields,” Phys. Lett. 12 (1964) 132–133.
  * (3) F. Englert and R. Brout, “Broken Symmetry and the Mass of Gauge Vector Mesons,” Phys. Rev. Lett. 13 (1964) 321–323.
  * (4) P. W. Higgs, “Broken Symmetries and the Masses of Gauge Bosons,” Phys. Rev. Lett. 13 (1964) 508–509.
  * (5) G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, “Global Conservation Laws and Massless Particles,” Phys. Rev. Lett. 13 (1964) 585–587.
  * (6) ATLAS Collaboration, G. Aad et al., “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B 716 (2012) 1–29, arXiv:1207.7214 [hep-ex].
  * (7) CMS Collaboration, S. Chatrchyan et al., “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC,” Phys. Lett. B 716 (2012) 30–61, arXiv:1207.7235 [hep-ex].
  * (8) ATLAS, CMS Collaboration, J. M. Langford, “Combination of Higgs measurements from ATLAS and CMS : couplings and $\kappa-$ framework,” PoS LHCP2020 (2021) 136.
  * (9) ATLAS Collaboration, “Combined measurements of Higgs boson production and decay using up to $139$ fb-1 of proton-proton collision data at $\sqrt{s}=13$ TeV collected with the ATLAS experiment,”.
  * (10) CMS Collaboration, A. Tumasyan et al., “A portrait of the Higgs boson by the CMS experiment ten years after the discovery,” Nature 607 no. 7917, (2022) 60–68, arXiv:2207.00043 [hep-ex].
  * (11) ATLAS Collaboration, “A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery,” Nature 607 no. 7917, (2022) 52–59, arXiv:2207.00092 [hep-ex]. [Erratum: Nature 612, E24 (2022)].
  * (12) A. Crivellin and B. Mellado, “Anomalies in Particle Physics,” arXiv:2309.03870 [hep-ph].
  * (13) W.-S. Hou, “Tree level $t\to ch$ or $h\to tc$ decays,” Phys. Lett. B 296 (1992) 179–184.
  * (14) D. Chang, W. S. Hou, and W.-Y. Keung, “Two loop contributions of flavor changing neutral Higgs bosons to $\mu\to e\gamma$,” Phys. Rev. D 48 (1993) 217–224, arXiv:hep-ph/9302267.
  * (15) J. Liu and L. Wolfenstein, “Spontaneous CP Violation in the $SU(2)_{L}\times U(1)_{Y}$ Model with Two Higgs Doublets,” Nucl. Phys. B 289 (1987) 1.
  * (16) T. P. Cheng and M. Sher, “Mass Matrix Ansatz and Flavor Nonconservation in Models with Multiple Higgs Doublets,” Phys. Rev. D 35 (1987) 3484.
  * (17) M. J. Savage, “Constraining flavor changing neutral currents with $B\to\mu^{+}\mu^{-}$,” Phys. Lett. B 266 (1991) 135–141.
  * (18) A. Antaramian, L. J. Hall, and A. Rasin, “Flavor changing interactions mediated by scalars at the weak scale,” Phys. Rev. Lett. 69 (1992) 1871–1873, arXiv:hep-ph/9206205.
  * (19) L. J. Hall and S. Weinberg, “Flavor changing scalar interactions,” Phys. Rev. D 48 (1993) R979–R983, arXiv:hep-ph/9303241.
  * (20) M. E. Luke and M. J. Savage, “Flavor changing neutral currents in the Higgs sector and rare top decays,” Phys. Lett. B 307 (1993) 387–393, arXiv:hep-ph/9303249.
  * (21) D. Atwood, L. Reina, and A. Soni, “Probing flavor changing top - charm - scalar interactions in $e^{+}e^{-}$ collisions,” Phys. Rev. D 53 (1996) 1199–1201, arXiv:hep-ph/9506243.
  * (22) D. Atwood, L. Reina, and A. Soni, “Phenomenology of two Higgs doublet models with flavor changing neutral currents,” Phys. Rev. D 55 (1997) 3156–3176, arXiv:hep-ph/9609279.
  * (23) S. Davidson and H. E. Haber, “Basis-independent methods for the two-Higgs-doublet model,” Phys. Rev. D 72 (2005) 035004, arXiv:hep-ph/0504050. [Erratum: Phys.Rev.D 72, 099902 (2005)].
  * (24) N. Cabibbo, “Unitary Symmetry and Leptonic Decays,” Phys. Rev. Lett. 10 (1963) 531–533.
  * (25) M. Kobayashi and T. Maskawa, “CP Violation in the Renormalizable Theory of Weak Interaction,” Prog. Theor. Phys. 49 (1973) 652–657.
  * (26) ATLAS Collaboration, “Search for a light charged Higgs boson in $t\rightarrow H^{\pm}b$ decays, with $H^{\pm}\rightarrow cb$, in the lepton+jets final state in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector,” arXiv:2302.11739 [hep-ex].
  * (27) CMS Collaboration, A. M. Sirunyan et al., “Search for a charged Higgs boson decaying to charm and bottom quarks in proton-proton collisions at $\sqrt{s}=8$ TeV,” JHEP 11 (2018) 115, arXiv:1808.06575 [hep-ex].
  * (28) A. G. Akeroyd, S. Moretti, and M. Song, “Slight excess at 130 GeV in search for a charged Higgs boson decaying to a charm quark and a bottom quark at the Large Hadron Collider,” J. Phys. G 49 no. 8, (2022) 085004, arXiv:2202.03522 [hep-ph].
  * (29) N. Bernal, M. Losada, Y. Nir, and Y. Shpilman, “The flavor of a light charged Higgs,” arXiv:2307.11813 [hep-ph].
  * (30) CMS Collaboration, V. Khachatryan et al., “Search for Lepton-Flavour-Violating Decays of the Higgs Boson,” Phys. Lett. B 749 (2015) 337–362, arXiv:1502.07400 [hep-ex].
  * (31) ATLAS Collaboration, G. Aad et al., “Search for lepton-flavour-violating $H\to\mu\tau$ decays of the Higgs boson with the ATLAS detector,” JHEP 11 (2015) 211, arXiv:1508.03372 [hep-ex].
  * (32) CMS Collaboration, A. M. Sirunyan et al., “Search for lepton-flavor violating decays of the Higgs boson in the $\mu\tau$ and e$\tau$ final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” Phys. Rev. D 104 no. 3, (2021) 032013, arXiv:2105.03007 [hep-ex].
  * (33) ATLAS Collaboration, “Searches for lepton-flavour-violating decays of the Higgs boson into $e\tau$ and $\mu\tau$ in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector,” arXiv:2302.05225 [hep-ex].
  * (34) A. J. Buras, “Standard Model predictions for rare K and B decays without new physics infection,” Eur. Phys. J. C 83 no. 1, (2023) 66, arXiv:2209.03968 [hep-ph].
  * (35) S. Neshatpour, T. Hurth, F. Mahmoudi, and D. Martinez Santos, “Neutral Current B-Decay Anomalies,” Springer Proc. Phys. 292 (2023) 11–21, arXiv:2210.07221 [hep-ph].
  * (36) N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, “Improved theory predictions and global analysis of exclusive $b\to s\mu^{+}\mu^{-}$ processes,” JHEP 09 (2022) 133, arXiv:2206.03797 [hep-ph].
  * (37) M. Ciuchini, M. Fedele, E. Franco, A. Paul, L. Silvestrini, and M. Valli, “Constraints on lepton universality violation from rare B decays,” Phys. Rev. D 107 no. 5, (2023) 055036, arXiv:2212.10516 [hep-ph].
  * (38) M. Algueró, A. Biswas, B. Capdevila, S. Descotes-Genon, J. Matias, and M. Novoa-Brunet, “To (b)e or not to (b)e: no electrons at LHCb,” Eur. Phys. J. C 83 no. 7, (2023) 648, arXiv:2304.07330 [hep-ph].
  * (39) Q. Wen and F. Xu, “The Global Fits of New Physics in $b\to s$ after $R_{K^{(*)}}$ 2022 Release,” arXiv:2305.19038 [hep-ph].
  * (40) B. Capdevila, A. Crivellin, and J. Matias, “Review of Semileptonic $B$ Anomalies,” arXiv:2309.01311 [hep-ph].
  * (41) S. Descotes-Genon, J. Matias, M. Ramon, and J. Virto, “Implications from clean observables for the binned analysis of $B\to K^{*}\mu^{+}\mu^{-}$ at large recoil,” JHEP 01 (2013) 048, arXiv:1207.2753 [hep-ph].
  * (42) LHCb Collaboration, R. Aaij et al., “Angular analysis of the $B^{0}\to K^{*0}\mu^{+}\mu^{-}$ decay using 3 fb-1 of integrated luminosity,” JHEP 02 (2016) 104, arXiv:1512.04442 [hep-ex].
  * (43) LHCb Collaboration, R. Aaij et al., “Measurement of $CP$-Averaged Observables in the $B^{0}\rightarrow K^{*0}\mu^{+}\mu^{-}$ Decay,” Phys. Rev. Lett. 125 no. 1, (2020) 011802, arXiv:2003.04831 [hep-ex].
  * (44) LHCb Collaboration, R. Aaij et al., “Angular Analysis of the $B^{+}\rightarrow K^{\ast+}\mu^{+}\mu^{-}$ Decay,” Phys. Rev. Lett. 126 no. 16, (2021) 161802, arXiv:2012.13241 [hep-ex].
  * (45) LHCb Collaboration, R. Aaij et al., “Angular analysis and differential branching fraction of the decay $B^{0}_{s}\to\phi\mu^{+}\mu^{-}$,” JHEP 09 (2015) 179, arXiv:1506.08777 [hep-ex].
  * (46) LHCb Collaboration, R. Aaij et al., “Branching Fraction Measurements of the Rare $B^{0}_{s}\rightarrow\phi\mu^{+}\mu^{-}$ and $B^{0}_{s}\rightarrow f_{2}^{\prime}(1525)\mu^{+}\mu^{-}$\- Decays,” Phys. Rev. Lett. 127 no. 15, (2021) 151801, arXiv:2105.14007 [hep-ex].
  * (47) LHCb Collaboration, R. Aaij et al., “Angular analysis of the rare decay ${B}_{s}^{0}\to\phi\mu^{+}\mu^{-}$,” JHEP 11 (2021) 043, arXiv:2107.13428 [hep-ex].
  * (48) LHCb Collaboration, R. Aaij et al., “Differential branching fractions and isospin asymmetries of $B\to K^{(*)}\mu^{+}\mu^{-}$ decays,” JHEP 06 (2014) 133, arXiv:1403.8044 [hep-ex].
  * (49) LHCb Collaboration, R. Aaij et al., “Measurements of the S-wave fraction in $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$ decays and the $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ differential branching fraction,” JHEP 11 (2016) 047, arXiv:1606.04731 [hep-ex]. [Erratum: JHEP 04, 142 (2017)].
  * (50) HPQCD Collaboration, W. G. Parrott, C. Bouchard, and C. T. H. Davies, “Standard Model predictions for $B\to K\ell^{+}\ell^{-}$, $B\to K\ell_{1}\ell_{2}$ and $B\to K\nu\nu$ using form factors from Nf=2+1+1 lattice QCD,” Phys. Rev. D 107 no. 1, (2023) 014511, arXiv:2207.13371 [hep-ph]. [Erratum: Phys.Rev.D 107, 119903 (2023)].
  * (51) G. Isidori, Z. Polonsky, and A. Tinari, “Semi-inclusive $b\to s\bar{\ell}\ell$ transitions at high $q^{2}$,” arXiv:2305.03076 [hep-ph].
  * (52) S. Jäger, M. Kirk, A. Lenz, and K. Leslie, “Charming new physics in rare $B$-decays and mixing?,” Phys. Rev. D 97 no. 1, (2018) 015021, arXiv:1701.09183 [hep-ph].
  * (53) C. Bobeth, U. Haisch, A. Lenz, B. Pecjak, and G. Tetlalmatzi-Xolocotzi, “On new physics in $\Delta\Gamma_{d}$,” JHEP 06 (2014) 040, arXiv:1404.2531 [hep-ph].
  * (54) S. Iguro and Y. Omura, “Status of the semileptonic $B$ decays and muon $g-2$ in general 2HDMs with right-handed neutrinos,” JHEP 05 (2018) 173, arXiv:1802.01732 [hep-ph].
  * (55) A. Crivellin, D. Müller, and C. Wiegand, “$b\to s\ell^{+}\ell^{-}$ transitions in two-Higgs-doublet models,” JHEP 06 (2019) 119, arXiv:1903.10440 [hep-ph].
  * (56) G. Kumar, “Interplay of the charged Higgs boson effects in $R_{D^{(*)}}$, $b\rightarrow s\ell^{+}\ell^{-}$, and $W$ mass,” Phys. Rev. D 107 no. 7, (2023) 075016, arXiv:2212.07233 [hep-ph].
  * (57) S. Iguro, “Conclusive probe of the charged Higgs solution of $P_{5}^{\prime}$ and $R_{{D^{(*)}}}$ discrepancies,” Phys. Rev. D 107 no. 9, (2023) 095004, arXiv:2302.08935 [hep-ph].
  * (58) A. Crivellin and M. Kirk, “Diquark Explanation of $b\to s\ell^{+}\ell^{-}$,” arXiv:2309.07205 [hep-ph].
  * (59) Heavy Flavor Averaging Group, HFLAV Collaboration, Y. S. Amhis et al., “Averages of b-hadron, c-hadron, and $\tau$-lepton properties as of 2021,” Phys. Rev. D 107 no. 5, (2023) 052008, arXiv:2206.07501 [hep-ex].
  * (60) A. Crivellin, C. Greub, and A. Kokulu, “Explaining $B\to D\tau\nu$, $B\to D^{*}\tau\nu$ and $B\to\tau\nu$ in a 2HDM of type III,” Phys. Rev. D 86 (2012) 054014, arXiv:1206.2634 [hep-ph].
  * (61) A. Crivellin, A. Kokulu, and C. Greub, “Flavor-phenomenology of two-Higgs-doublet models with generic Yukawa structure,” Phys. Rev. D 87 no. 9, (2013) 094031, arXiv:1303.5877 [hep-ph].
  * (62) J. M. Cline, “Scalar doublet models confront $\tau$ and b anomalies,” Phys. Rev. D 93 no. 7, (2016) 075017, arXiv:1512.02210 [hep-ph].
  * (63) A. Crivellin, J. Heeck, and P. Stoffer, “A perturbed lepton-specific two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model,” Phys. Rev. Lett. 116 no. 8, (2016) 081801, arXiv:1507.07567 [hep-ph].
  * (64) J.-P. Lee, “$B\to D^{(*)}\tau\nu_{\tau}$ in the 2HDM with an anomalous $\tau$ coupling,” Phys. Rev. D 96 no. 5, (2017) 055005, arXiv:1705.02465 [hep-ph].
  * (65) S. Iguro and K. Tobe, “$R(D^{(*)})$ in a general two Higgs doublet model,” Nucl. Phys. B 925 (2017) 560–606, arXiv:1708.06176 [hep-ph].
  * (66) R. Martinez, C. F. Sierra, and G. Valencia, “Beyond $\mathcal{R}(D^{(*)})$ with the general type-III 2HDM for $b\to c\tau\nu$,” Phys. Rev. D 98 no. 11, (2018) 115012, arXiv:1805.04098 [hep-ph].
  * (67) S. Fraser, C. Marzo, L. Marzola, M. Raidal, and C. Spethmann, “Towards a viable scalar interpretation of $R_{D^{(*)}}$,” Phys. Rev. D 98 no. 3, (2018) 035016, arXiv:1805.08189 [hep-ph].
  * (68) P. Athron, C. Balazs, T. E. Gonzalo, D. Jacob, F. Mahmoudi, and C. Sierra, “Likelihood analysis of the flavour anomalies and g – 2 in the general two Higgs doublet model,” JHEP 01 (2022) 037, arXiv:2111.10464 [hep-ph].
  * (69) S. Iguro, “Revival of $H^{-}$ interpretation of $R_{D^{(*)}}$ anomaly and closing low mass window,” Phys. Rev. D 105 no. 9, (2022) 095011, arXiv:2201.06565 [hep-ph].
  * (70) M. Blanke, S. Iguro, and H. Zhang, “Towards ruling out the charged Higgs interpretation of the ${R}_{D^{\left(\ast\right)}}$ anomaly,” JHEP 06 (2022) 043, arXiv:2202.10468 [hep-ph].
  * (71) K. Ezzat, G. Faisel, and S. Khalil, “Investigating $R_{D}$ and $R_{D^{*}}$ anomalies in a Left-Right model with an Inverse Seesaw,” arXiv:2204.10922 [hep-ph].
  * (72) M. Fedele, M. Blanke, A. Crivellin, S. Iguro, T. Kitahara, U. Nierste, and R. Watanabe, “Impact of $\Lambda_{b}\to\Lambda_{c}\tau\nu$ measurement on new physics in $b\to c\ell\nu$ transitions,” Phys. Rev. D 107 no. 5, (2023) 055005, arXiv:2211.14172 [hep-ph].
  * (73) N. Das, A. Adhikary, and R. Dutta, “Revisiting $b\to c\tau\nu$ anomalies with charged Higgs boson,” arXiv:2305.17766 [hep-ph].
  * (74) S. Iguro, Y. Omura, and M. Takeuchi, “Test of the $R(D^{(*)})$ anomaly at the LHC,” Phys. Rev. D 99 no. 7, (2019) 075013, arXiv:1810.05843 [hep-ph].
  * (75) R. Alonso, B. Grinstein, and J. Martin Camalich, “Lifetime of $B_{c}^{-}$ Constrains Explanations for Anomalies in $B\to D^{(*)}\tau\nu$,” Phys. Rev. Lett. 118 no. 8, (2017) 081802, arXiv:1611.06676 [hep-ph].
  * (76) A. Celis, M. Jung, X.-Q. Li, and A. Pich, “Scalar contributions to $b\to c(u)\tau\nu$ transitions,” Phys. Lett. B 771 (2017) 168–179, arXiv:1612.07757 [hep-ph].
  * (77) M. Blanke, A. Crivellin, S. de Boer, T. Kitahara, M. Moscati, U. Nierste, and I. Nišandžić, “Impact of polarization observables and $B_{c}\to\tau\nu$ on new physics explanations of the $b\to c\tau\nu$ anomaly,” Phys. Rev. D 99 no. 7, (2019) 075006, arXiv:1811.09603 [hep-ph].
  * (78) J. Aebischer and B. Grinstein, “Standard Model prediction of the $B_{c}$ lifetime,” JHEP 07 (2021) 130, arXiv:2105.02988 [hep-ph].
  * (79) Y. Sakaki, M. Tanaka, A. Tayduganov, and R. Watanabe, “Probing New Physics with $q^{2}$ distributions in $\bar{B}\to D^{(*)}\tau\bar{\nu}$,” Phys. Rev. D 91 no. 11, (2015) 114028, arXiv:1412.3761 [hep-ph].
  * (80) J. Harrison and C. T. H. Davies, “$B\rightarrow D^{*}$ vector, axial-vector and tensor form factors for the full $q^{2}$ range from lattice QCD,” arXiv:2304.03137 [hep-lat].
  * (81) Fermilab Lattice, MILC, Fermilab Lattice, MILC Collaboration, A. Bazavov et al., “Semileptonic form factors for $B\rightarrow D^{*}\ell\nu$ at nonzero recoil from $2+1$-flavor lattice QCD: Fermilab Lattice and MILC Collaborations,” Eur. Phys. J. C 82 no. 12, (2022) 1141, arXiv:2105.14019 [hep-lat]. [Erratum: Eur.Phys.J.C 83, 21 (2023)].
  * (82) M. Fedele, M. Blanke, A. Crivellin, S. Iguro, U. Nierste, S. Simula, and L. Vittorio, “Discriminating $B\to D^{*}\ell\nu$ form factors via polarization observables and asymmetries,” Phys. Rev. D 108 no. 5, (2023) 055037, arXiv:2305.15457 [hep-ph].
  * (83) N. Penalva, J. M. Flynn, E. Hernández, and J. Nieves, “Study of new physics effects in $\bar{B}_{s}\to D^{(*)}_{s}\tau^{-}\bar{\nu}_{\tau}$ semileptonic decays using Standard Model lattice QCD form factors and heavy quark effective theory,” arXiv:2304.00250 [hep-ph].
  * (84) JLQCD Collaboration, Y. Aoki, B. Colquhoun, H. Fukaya, S. Hashimoto, T. Kaneko, R. Kellermann, J. Koponen, and E. Kou, “$B\to D^{*}\ell\nu_{\ell}$ semileptonic form factors from lattice QCD with Möbius domain-wall quarks,” arXiv:2306.05657 [hep-lat].
  * (85) R. Alonso, E. E. Jenkins, A. V. Manohar, and M. Trott, “Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology,” JHEP 04 (2014) 159, arXiv:1312.2014 [hep-ph].
  * (86) E. E. Jenkins, A. V. Manohar, and M. Trott, “Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence,” JHEP 01 (2014) 035, arXiv:1310.4838 [hep-ph].
  * (87) M. González-Alonso, J. Martin Camalich, and K. Mimouni, “Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays,” Phys. Lett. B 772 (2017) 777–785, arXiv:1706.00410 [hep-ph].
  * (88) J. Aebischer, M. Fael, C. Greub, and J. Virto, “B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale,” JHEP 09 (2017) 158, arXiv:1704.06639 [hep-ph].
  * (89) S. Iguro, T. Kitahara, and R. Watanabe, “Global fit to $b\to c\tau\nu$ anomalies 2022 mid-autumn,” arXiv:2210.10751 [hep-ph].
  * (90) S. Iguro and R. Watanabe, “Bayesian fit analysis to full distribution data of $\bar{B}\to D^{(*)}\ell\bar{\nu}$: $|V_{cb}|$ determination and New Physics constraints,” JHEP 08 (2020) 006, arXiv:2004.10208 [hep-ph].
  * (91) Y. Omura, E. Senaha, and K. Tobe, “$\tau$\- and $\mu$-physics in a general two Higgs doublet model with $\mu-\tau$ flavor violation,” Phys. Rev. D 94 no. 5, (2016) 055019, arXiv:1511.08880 [hep-ph].
  * (92) P. W. Cattaneo, “A search for $\mu^{+}\to e^{+}\gamma$ with the first dataset of the MEG II experiment,” arXiv:2310.12614 [hep-ex].
  * (93) A. Crivellin, M. Hoferichter, and M. Procura, “Improved predictions for $\mu\to e$ conversion in nuclei and Higgs-induced lepton flavor violation,” Phys. Rev. D 89 (2014) 093024, arXiv:1404.7134 [hep-ph].
  * (94) L. Calibbi and G. Signorelli, “Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction,” Riv. Nuovo Cim. 41 no. 2, (2018) 71–174, arXiv:1709.00294 [hep-ph].
  * (95) A. Blondel et al., “Research Proposal for an Experiment to Search for the Decay $\mu\to eee$,” arXiv:1301.6113 [physics.ins-det].
  * (96) A. M. Baldini et al., “MEG Upgrade Proposal,” arXiv:1301.7225 [physics.ins-det].
  * (97) Mu2e Collaboration, L. Bartoszek et al., “Mu2e Technical Design Report,” arXiv:1501.05241 [physics.ins-det].
  * (98) COMET Collaboration, R. Abramishvili et al., “COMET Phase-I Technical Design Report,” PTEP 2020 no. 3, (2020) 033C01, arXiv:1812.09018 [physics.ins-det].
  * (99) Belle-II Collaboration, W. Altmannshofer et al., “The Belle II Physics Book,” PTEP 2019 no. 12, (2019) 123C01, arXiv:1808.10567 [hep-ex]. [Erratum: PTEP 2020, 029201 (2020)].
  * (100) M. Algueró, B. Capdevila, S. Descotes-Genon, J. Matias, and M. Novoa-Brunet, “$b\rightarrow s\ell^{+}\ell^{-}$ global fits after $R_{K_{S}}$ and $R_{K^{*+}}$,” Eur. Phys. J. C 82 no. 4, (2022) 326, arXiv:2104.08921 [hep-ph].
  * (101) UTfit Collaboration, M. Bona et al., “Model-independent constraints on $\Delta F=2$ operators and the scale of new physics,” JHEP 03 (2008) 049, arXiv:0707.0636 [hep-ph].
  * (102) S. Iguro and Y. Omura, “The direct $CP$ violation in a general two Higgs doublet model,” JHEP 08 (2019) 098, arXiv:1905.11778 [hep-ph].
  * (103) ATLAS Collaboration, G. Aad et al., “Search for flavor-changing neutral $tqH$ interactions with $H\rightarrow\gamma\gamma$ in $pp$ collisions at $\sqrt{s}$ = 13 TeV using the ATLAS detector,” arXiv:2309.12817 [hep-ex].
  * (104) CMS Collaboration, “Search for flavor-changing neutral current interactions of the top quark and Higgs boson in proton-proton collisions at $\sqrt{s}=13$ TeV,”.
  * (105) “Sensitivity of ATLAS at HL-LHC to flavour changing neutral currents in top quark decays $t\to cH$, with $H\to\gamma\gamma$,”.
  * (106) ATLAS Collaboration, “Expected sensitivity of ATLAS to FCNC top quark decays $t\rightarrow Zu$ and $t\rightarrow Hq$ at the High Luminosity LHC,”.
  * (107) N. Desai, A. Mariotti, M. Tabet, and R. Ziegler, “The charged Higgs from the Bottom-Up: probing flavor at the LHC,” JHEP 11 (2022) 112, arXiv:2206.01761 [hep-ph].
  * (108) ATLAS Collaboration, G. Aad et al., “Search for heavy Higgs bosons with flavour-violating couplings in multi-lepton plus $b$-jets final states in $pp$ collisions at 13 TeV with the ATLAS detector,” arXiv:2307.14759 [hep-ex].
  * (109) CMS Collaboration, “Search for new Higgs bosons through same-sign top quark pair production in association with a jet in proton-proton collisions at $\sqrt{s}=13~{}\mathrm{TeV}$,”.
  * (110) CMS Collaboration, A. Tumasyan et al., “Search for supersymmetry in final states with two or three soft leptons and missing transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” JHEP 04 (2022) 091, arXiv:2111.06296 [hep-ex].
  * (111) ATLAS-CONF-2022-042.
  * (112) S. Iguro, T. Kitahara, M. S. Lang, and M. Takeuchi, “Current Status of the Muon $g-2$ Interpretations within Two-Higgs-Doublet Models,” arXiv:2304.09887 [hep-ph].
  * (113) CDF Collaboration, T. Aaltonen et al., “High-precision measurement of the $W$ boson mass with the CDF II detector,” Science 376 no. 6589, (2022) 170–176.
  * (114) J. de Blas, M. Pierini, L. Reina, and L. Silvestrini, “Impact of the Recent Measurements of the Top-Quark and $W$-Boson Masses on Electroweak Precision Fits,” Phys. Rev. Lett. 129 no. 27, (2022) 271801, arXiv:2204.04204 [hep-ph].
  * (115) K. Fuyuto, W.-S. Hou, and E. Senaha, “Electroweak baryogenesis driven by extra top Yukawa couplings,” Phys. Lett. B 776 (2018) 402–406, arXiv:1705.05034 [hep-ph].
  * (116) S. Kanemura and Y. Mura, “Electroweak baryogenesis via top-charm mixing,” JHEP 09 (2023) 153, arXiv:2303.11252 [hep-ph].
  * (117) ATLAS Collaboration, G. Aad et al., “Measurement of the CP properties of Higgs boson interactions with $\tau$-leptons with the ATLAS detector,” Eur. Phys. J. C 83 no. 7, (2023) 563, arXiv:2212.05833 [hep-ex].
  * (118) CMS Collaboration, A. Tumasyan et al., “Searches for additional Higgs bosons and for vector leptoquarks in $\tau\tau$ final states in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” JHEP 07 (2023) 073, arXiv:2208.02717 [hep-ex].


# Context-Aware Change Detection With Semi-Supervised Learning

###### Abstract

Change detection using earth observation data plays a vital role in
quantifying the impact of disasters in affected areas. While data sources like
Sentinel-2 provide rich optical information, they are often hindered by cloud
cover, limiting their usage in disaster scenarios. However, leveraging pre-
disaster optical data can offer valuable contextual information about the area
such as landcover type, vegetation cover, soil types, enabling a better
understanding of the disaster’s impact. In this study, we develop a model to
assess the contribution of pre-disaster Sentinel-2 data in change detection
tasks, focusing on disaster-affected areas. The proposed Context-Aware Change
Detection Network (CACDN) utilizes a combination of pre-disaster Sentinel-2
data, pre and post-disaster Sentinel-1 data and ancillary Digital Elevation
Models (DEM) data. The model is validated on flood and landslide detection and
evaluated using three metrics: Area Under the Precision-Recall Curve (AUPRC),
Intersection over Union (IoU), and mean IoU. The preliminary results show
significant improvement (4%, AUPRC, 3-7% IoU, 3-6% mean IoU) in model’s change
detection capabilities when incorporated with pre-disaster optical data
reflecting the effectiveness of using contextual information for accurate
flood and landslide detection.

Index Terms—  Change Detection, Deep Learning, Residual Fusion, Floods,
Landslides, Context-aware Models, Semi-Supervised Learning.

##  1 Introduction

Climate change is leading to an increase in the frequency of natural hazards,
with more and more people being affected by disasters [1] such as floods,
landslides, wildfires and many others. An efficient evaluation of affected
areas after and during a disaster event can help with quick and reliable
emergency response and future action plans. Earth observations, such as
multispectral and Synthetic Aperture Radar (SAR) imaging, are valuable tools
for assessing and mitigating the negative impacts of natural hazards.

Sentinel satellites, such as Sentinel-2, are widely used for different
classification, mapping, and monitoring tasks because of their openly
accessible high spatial and temporal resolution data. Sentinel-2 is rich in
information due to its multispectral imaging capabilities, which capture
imagery in a wide range of visible and infrared wavelengths, providing
detailed information about the earth’s surface. However, most natural hazards
are highly correlated with environmental conditions such as clouds, haze, and
smoke, and Sentinel-2 is vulnerable to these associated artifacts. Sentinel-1,
on the other hand, is a radar satellite that acquires imagery regardless of
weather or lighting conditions. Hence, primarily used in many research for
monitoring changes in the earth’s surface caused by natural disasters [2, 3,
4]. However, the side-looking geometry and inherent characteristics of SAR
images, such as speckle and layover/foreshortening, pose challenges in
learning discriminative features. Consequently, SAR images generally exhibit
lower classification accuracy compared to clear optical images in most common
remote sensing datasets [5]. Some existing works focused on combining the SAR
and optical data [6, 7, 8]. Most of the disaster change detection works use
post-disaster optical data which is often partially hindered by the clouds or
smoke [9] affecting the impact assessment capability. However, we can easily
obtain clear pre-disaster optical images. Our aim is to utilize clear
Sentinel-2 pre-disaster images to learn about the area context before the
disaster, which can be used to improve the accuracy of post-disaster
assessments. In this study, we propose a model that can detect changes more
efficiently by learning from more contextual information. We use sentinel-1
pre and post-disaster images along with Sentinel-2 pre-disaster images, DEM
and derived slope features so that model can correlate the disaster-affected
area with superior spatial features and physical properties of the area.

Fig. 1: CACDN Architecture. The three autoencoders are pretrained on
corresponding Sentinel data with self-supervision.

##  2 Data Preparation

We tested our context-aware change detection approach on two types of disaster
events namely flood detection and landslide detection. For the flood detection
task, we utilized an existing dataset called Sen1floods11 [5] and expanded it
by incorporating additional data. The original dataset consisted of 446
Sentinel-1 post-flood patches, each measuring 512x512 pixels, along with
corresponding ground truth labels. We divided each sample into smaller 256x256
pixel tiles and extended the dataset by adding Sentinel-1 Ground Range
Detected (GRD) pre-flood images, cloud-free Sentinel-2 MSI Level-2A pre-flood
images, DEM SRTM and it is derived data. We downloaded additional data using
Google Earth Engine python API [10]. The Sentinel-1 images consisted of two
polarization bands (VV, VH), while Sentinel-2 had four bands (Red, Green,
Blue, NIR). The DEM data provided elevation information, and we also utilized
it’s derived products such as slope and aspect. To maintain consistency in
evaluation, we followed the data division guidelines established by the
Sen1Floods11 dataset. For the landslide detection task, we collected a small
dataset encompassing two landslides one in Hokkaido, Japan (Sep 2018) and
another in Mt Talakmau, Indonesia (Feb 2022). Ground truth maps for these
landslides were obtained from UNOSAT. To organize the data, we divided the
area of interest into tiles of size 128x128 pixels. Corresponding Sentinel-1
GRD pre-landslide images, Sentinel-1 GRD post-landslide images, Sentinel-2 MSI
Level-2A pre-landslide images, DEM SRTM data, and derived products such as
slope and aspect were processed and downloaded at 10m spatial resolution using
Google Earth Engine python API. The dataset was split into training and test
sets, with an 80-20 ratio, resulting in 227 training samples and 57 test
samples.

##  3 Proposed Method

###  3.1 CACDN Architecture

Figure 1 shows the architecture of the proposed Context Aware Change Detection
Network (CACDN), consisting of four branches to learn features separately from
Sentinel-2 pre-disaster image, Sentinel-1 pre-disaster image, DEM data and
Sentinel-1 post-image. The four branches take different size inputs specified
network diagram where p represents patch size (width and height both). The
sentinel image features are learned using autoencoders (see Figure 2) as our
foundation model. We used autoencoder with a Resnet50 encoder and a decoder
containing four upsampling blocks (convolutional, Batchnormalization amd
upsampling layer) reconstructing input. The fourth branch takes DEM input and
passes through two sets of convolutional and batch normalization layers.

Fig. 2: Foundation model. Autoencoder pretrained on reconstruction task.

Fig. 3: Residual Fusion block.

Multi-scale feature maps from the three reconstruction networks and output DEM
feature maps from the fourth branch are fused together. We propose a residual
fusion technique (see Figure 3) to fuse the feature maps from the four
branches, enabling model to get benefit from Sentinel-2 pre-image without
introducing extra errors in training. The concept is inline with the residual
networks [11] using identity blocks. The fusion takes place in three steps
with different scale features (p/8 x p/8), (p/4 x p/4) and (p/2 x p/2). The
fused features are then fed to a set of layers (see Figure 1 for details)
generating a binary change map of size (pxp).

###  3.2 Implementation and Training

The three autoencoders are first pretrained on reconstruction tasks with self-
supervision. The reconstruction losses used are cross-entropy and mean square
error with equal weight i.e. 0.5. The pretrained autoencoders are combined
with the DEM processing branch and the remaining network. The full network is
then trained using a weighted combination of supervised segmentation losses
and self-supervised reconstruction losses given in equation Eq. 1. The
supervised losses are focal loss ($L_{focal}$) and dice loss ($L_{dice}$). The
self-supervised reconstruction losses are cross-entropy ($L_{ce}$) and mean
square error $L_{mse}$).

$\displaystyle Loss=0.6*(L_{focal}+L_{dice})+0.4*(L_{ce}+\beta*L_{mse})$ (1)

Our proposed CACDN model is evaluated on two change detection tasks namely
flood detection and landslide detection. For flood detection, we trained the
model on tiles of size 256 x 256 and for landslides, we used smaller tiles 128
x128 pixels. Since our landslide data is comparatively small, we trained a
smaller version of the CACDN model. To reduce the model size we used Resnet50
encoder with three downsampling levels and decoder with three upsampling
blocks. Also, the features are fused at two scales (p/4 x p/4) and (p/2 x p/2
) with the same number of channels i.e. 384 and 128. Training images are
augmented using Gaussian blur and gamma contrast augmentation methods. We pre-
trained each autoencoder for 50 epochs with batch size 4, adam optimizer and
0.0001 as the initial learning rate. The end-to-end network is trained for 300
epochs with batch size 4, adam optimizer and a smaller initial learning rate
of 0.00001. For better convergence, the learning rate is decayed until
0.000001. The decay steps are controlled with the ”reduce on plateau” method.

##  4 Results and Evaluation

We evaluated CACDN model on flood detection and landslide detection using
three metrics; IoU to measure overlap between the predicted change areas and
the ground truth change areas, mean IoU to calculate the average IoU across
all predicted and ground truth change areas, and AUPRC to assess the trade-off
between precision and recall. AUPRC metric is important here because of
imbalanced change detection datasets. IoU and mean IoU focus on the spatial
accuracy and overlap between predicted and ground truth change areas, while
AUPRC evaluates the classification performance and the balance between
precision and recall.

The qualitative results on flood detection and landslide detection are given
in Table 1 and 2 respectively. To show the impact of using Sentinel-2 pre-
disaster images, We present a comparison of our CACDN model with Sentinel-2
pre-disaster images and CACDN model without Sentinel-2 pre-disaster images.

Table 1: CACDN evaluation results on Floods test set.

Method | AUPRC | IoU | Mean IoU
---|---|---|---
CACDN with S2 Pre-Image | 0.838 | 0.738 | 0.50
CACDN w/o S2 Pre-Image | 0.801 | 0.712 | 0.47

On the flood detection task, all three metric scores are good ensuring highly
accurate flood detection both in terms of pixel-wise overlapping with ground
truth and in terms of precision-recall balance. When trained with Sentinel-2
pre-flood image our model gave a lead of 3 to 4 % in all three metrics (see
Table 1). The gain in mean IoU score indicates an improvement across test
samples and a better AUPRC score shows model’s ability to correctly identify
positive changes. The metric scores are supported by the qualitative results
in Figure 4, where the model gave better detections (overlap with ground truth
and low false detection rate) when trained with Sentinel-2 pre-flood image. On
further evaluation, we see that Sentinel-2 helps to reduce confusion caused by
similar features of shallow water vegetation and floods in Sentinel-1 imagery.
Using Sentinel-2 pre-images, land covers are better differentiated and
waterbodies, particularly narrow rivers, are better detected, leading to
improved flood detection. Additionally, incorporating DEM data allows the
model to learn the correlation between surface slope and flood possibility,
enabling the identification of areas with high-slope surfaces that are less
likely to be flooded.

Table 2: CACDN evaluation results on Landslide test set.

Method | AUPRC | IoU | Mean IoU
---|---|---|---
CACDN with S2 Pre-Image | 0.746 | 0.453 | 0.363
CACDN w/o S2 Pre-Image | 0.708 | 0.380 | 0.301

Fig. 4: Result Samples. Two sample results are visualized in 2 rows. The first
sample is from the flood test set and the second sample is from the landslide
test set.

Similar to the flood detection task, our model shows better landslide
detection when trained with Sentinel-2 pre-landslide images (see Table 2). The
gain of 5 to 7 % across three metric scores. Sentinel-1 often suffers from
foreshortening and shadow effects especially in mountain areas, making it
challenging to accurately detect and characterize landslides. Whereas,
Sentinel-2 is less affected by the foreshortening allowing a better
representation of the landscape. Furthermore, DEM and slope data provide
valuable physical properties for the model to learn the correlation with the
landslide event and enhance landslide detection.

##  5 Conclusion

In this study, we developed a context aware change detection model that learns
contextual features from multi-source data such as surface texture features
from Sentinel-1 SAR data, landcover features from Sentinel-2 MSI data, and
correlation of physical properties (elevation, slope) with the type of
disaster event. Since clear MSI data is not available in most of the disaster
scenarios, we incorporate pre-disaster MSI data to learn from the optical
features (pre-disaster) of the affected area. We study the impact of using
Sentinel-2 pre-disaster images on the model’s change detection capabilities.
We identified that incorporating contextual information from pre-disaster
optical images helps model to learn specific characteristics and
vulnerabilities of the region, leading to more accurate and reliable
detection. Our model gained 4 to 7 % IoU when training the model with
Sentinel-2 pre-disaster images for flood and landslide detection tasks. Moving
forward, our future work aims to validate our approach on larger datasets and
several other types of disaster events. This will allow us to develop a more
generalized model that can offer a more effective and reliable approach for
quantifying the disaster impact. Ultimately, our research contributes to the
advancement of disaster management and mitigation efforts.

## References

  * [1] UNDRR,  “2021 disasters in numbers,”  2022,  Accessed: 2022-06-30.
  * [2] Ritu Yadav, Andrea Nascetti, Hossein Azizpour, and Yifang Ban,  “Unsupervised flood detection on sar time series,”  arXiv preprint arXiv:2212.03675, 2022.
  * [3] Prosper Washaya and Timo Balz,  “Sar coherence change detection of urban areas affected by disasters using sentinel-1 imagery,”  Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci, 2018.
  * [4] Ritu Yadav, Andrea Nascetti, and Yifang Ban,  “Deep attentive fusion network for flood detection on uni-temporal sentinel-1 data,”  Frontiers in Remote Sensing, 2022.
  * [5] D. Bonafilia, B. Tellman, T. Anderson, and E. Issenberg,  “Sen1floods11: a georeferenced dataset to train and test deep learning flood algorithms for sentinel-1,”  in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2020.
  * [6] Yifang Ban, Puzhao Zhang, Andrea Nascetti, Alexandre R Bevington, and Michael A Wulder,  “Near real-time wildfire progression monitoring with sentinel-1 sar time series and deep learning,”  Scientific reports, 2020.
  * [7] Bipendra Basnyat, Nirmalya Roy, and Aryya Gangopadhyay,  “Flood detection using semantic segmentation and multimodal data fusion,”  in 2021 IEEE International Conference on Pervasive Computing and Communications Workshops and other Affiliated Events (PerCom Workshops), 2021, pp. 135–140.
  * [8] Simon Plank, Andre Twele, and Sandro Martinis,  “Landslide mapping in vegetated areas using change detection based on optical and polarimetric sar data,”  Remote Sensing, 2016.
  * [9] Victor HR Prudente, ID Sanches, Marcos Adami, Sergii Skakun, LV Oldoni, Haron Abrahim Magalhães Xaud, MR Xaud, and Y Zhang,  “Sar data for land use land cover classification in a tropical region with frequent cloud cover,”  in IGARSS 2020-2020 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2020, pp. 4100–4103.
  * [10] Noel Gorelick, Matt Hancher, Mike Dixon, Simon Ilyushchenko, David Thau, and Rebecca Moore,  “Google earth engine planetary-scale geospatial analysis for everyone,”  Remote Sensing of Environment, 2017,  Big Remotely Sensed Data: tools, applications and experiences.
  * [11] K. He, X. Zhang, S. Ren, and J. Sun,  “Deep residual learning for image recognition,”  in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016.