aainstitutetext: Instituto de Física Corpuscular, Parque Científico,
C/Catedrático José Beltrán, 2, E-46980 Paterna, Spain

# Constraints on coloured scalars from global fits

Otto Eberhardt<EMAIL_ADDRESS>a Víctor Miralles
<EMAIL_ADDRESS>a Antonio Pich<EMAIL_ADDRESS>
###### Abstract

We consider a simple extension of the electroweak theory, incorporating one
$SU(2)_{L}$ doublet of colour-octet scalars with Yukawa couplings satisfying
the principle of minimal flavour violation. Using the HEPfit package, we
perform a global fit to the available data, including all relevant theoretical
constraints, and extract the current bounds on the model parameters. Coloured
scalars with masses below 1.05 TeV are already excluded, provided they are not
fermiophobic. The mass splittings among the different (charged and CP-even and
CP-odd neutral) scalars are restricted to be smaller than 20 GeV. Moreover,
for scalar masses smaller than 1.5 TeV, the Yukawa coupling of the coloured
scalar multiplet to the top quark cannot exceed the one of the SM Higgs
doublet by more than 80%. These conclusions are quite generic and apply in
more general frameworks (without fine tunings). The theoretical requirements
of perturbative unitarity and vacuum stability enforce relevant constraints on
the quartic scalar potential parameters that are not yet experimentally
tested.

††preprint: IFIC/21-24

##  1 Introduction

The main focus of the first LHC run was on the search for the Standard Model
(SM) Higgs boson and culminated in its spectacular discovery in 2012
Aad:2012tfa ; Chatrchyan:2012xdj . After the conclusion of the run 2, the
properties of this new scalar are much better known, and they seem to agree
very well with the SM predictions. In combination with direct LHC searches for
additional spin-$0$ particles, they put strong bounds on extensions of the
scalar sector of the SM, as for example the Two-Higgs-Doublet model
Eberhardt:2020dat . On the other hand, new physics beyond the Standard Model
(BSM) is needed to fix the shortcomings of the current theoretical framework,
and many BSM scenarios could manifest themselves through the appearance of
additional scalars at the LHC. Most of these SM extensions contain scalar
fields which transform as singlets under the $SU(3)_{C}$ group of QCD and,
therefore, do not carry colour charge. But coloured scalars are less
constrained than one might naively think: they do not mix with the SM Higgs
and contribute to its signal strengths only at the loop level. However, recent
LHC searches for scalar resonances are expected to yield strong constraints on
their properties.

Here we want to study a simple extension of the SM scalar sector with one
$SU(2)_{L}$ doublet of scalar fields that transforms as an octet under the
colour $SU(3)_{C}$ group. In some sense, one can think of it as a Two-Higgs-
Doublet model in which one of the doublets is coloured. Scalars of this type
with masses around the electroweak scale could emerge naturally from $SU(5)$
or $SO(10)$ unification theories at high energy scales Georgi:1979df ;
Dorsner:2006dj ; Perez:2016qbo ; Bertolini:2013vta . As this model was first
proposed by Manohar and Wise Manohar:2006ga , we will refer to it as the
Manohar-Wise (MW) model in the following. Several phenomenological aspects of
this dynamical scenario have been studied in the literature Gresham:2007ri ;
Gerbush:2007fe ; Burgess:2009wm ; Degrassi:2010ne ; He:2011ti ;
Dobrescu:2011aa ; Bai:2011aa ; Arnold:2011ra ; Kribs:2012kz ; Reece:2012gi ;
Cao:2013wqa ; He:2013tla ; Cheng:2015lsa ; Cheng:2016tlc ; Martinez:2016fyd ;
Hayreter:2017wra ; Cheng:2018mkc ; Hayreter:2018ybt ; Gisbert:2019ftm ;
Miralles:2019uzg ; Miralles:2020tei , yet a comprehensive analysis including
all relevant up-to-date constraints has not been performed.

In this article we will present such an analysis. After defining the MW model
in Section 2, we briefly describe in Section 3 the HEPfit package
deBlas:2019okz  that we employ to perform the global fits. This section
explains in detail the various constraints on the parameter space of the
model, which come from theoretical considerations (Section 3.1), Higgs
measurements (Section 3.2), direct LHC searches (Section 3.3) and flavour
observables (Section 3.4). Putting all pieces together, we show the results of
our fits in Section 4. Finally, Section 5 contains a summary of our findings
and a brief outlook on future prospects.

##  2 The scalar colour-octet model

The MW model extends the SM with one electroweak doublet of colour-octet
scalar fields with hypercharge $Y=\frac{1}{2}$. Since it has colour charge,
the new scalar multiplet does not mix with the SM Higgs doublet. Furthermore,
the coloured particles cannot acquire a vacuum expectation value (vev) because
colour must be conserved. Therefore, only the SM Higgs boson will acquire a
vev which will minimise the most general potential that can be built with this
scalar sector:

$\displaystyle V_{\text{\tiny{MW}}}$
$\displaystyle=m_{\Phi}^{2}\Phi^{\dagger}\Phi+\tfrac{1}{2}\lambda\left(\Phi^{\dagger}\Phi\right)^{2}+2m_{S}^{2}{\rm
Tr}\left(S^{\dagger i}S^{\phantom{\dagger}}_{i}\right)+\mu_{1}{\rm
Tr}\left(S^{\dagger i}S^{\phantom{\dagger}}_{i}S^{\dagger
j}S^{\phantom{\dagger}}_{j}\right)+\mu_{2}{\rm Tr}\left(S^{\dagger
i}S^{\phantom{\dagger}}_{j}S^{\dagger j}S^{\phantom{\dagger}}_{i}\right)$
$\displaystyle\phantom{{}={}}+\mu_{3}{\rm Tr}\left(S^{\dagger
i}S^{\phantom{\dagger}}_{i}\right){\rm Tr}\left(S^{\dagger
j}S^{\phantom{\dagger}}_{j}\right)+\mu_{4}{\rm Tr}\left(S^{\dagger
i}S^{\phantom{\dagger}}_{j}\right){\rm Tr}\left(S^{\dagger
j}S^{\phantom{\dagger}}_{i}\right)+\mu_{5}{\rm
Tr}\left(S^{\phantom{\dagger}}_{i}S^{\phantom{\dagger}}_{j}\right){\rm
Tr}\left(S^{\dagger i}S^{\dagger j}\right)$
$\displaystyle\phantom{{}={}}+\mu_{6}{\rm
Tr}\left(S^{\phantom{\dagger}}_{i}S^{\phantom{\dagger}}_{j}S^{\dagger
j}S^{\dagger i}\right)+\nu_{1}\Phi^{\dagger i}\Phi_{i}{\rm Tr}\left(S^{\dagger
j}S^{\phantom{\dagger}}_{j}\right)+\nu_{2}\Phi^{\dagger i}\Phi_{j}{\rm
Tr}\left(S^{\dagger j}S^{\phantom{\dagger}}_{i}\right)$
$\displaystyle\phantom{{}={}}+\left[\nu_{3}\Phi^{\dagger i}\Phi^{\dagger
j}{\rm
Tr}\left(S^{\phantom{\dagger}}_{i}S^{\phantom{\dagger}}_{j}\right)+\nu_{4}\Phi^{\dagger
i}{\rm Tr}\left(S^{\dagger
j}S^{\phantom{\dagger}}_{j}S^{\phantom{\dagger}}_{i}\right)+\nu_{5}\Phi^{\dagger
i}{\rm Tr}\left(S^{\dagger
j}S^{\phantom{\dagger}}_{i}S^{\phantom{\dagger}}_{j}\right)+{\rm
h.c.}\right],$ (1)

where $\Phi=(\phi^{+},\phi^{0})^{T}$ is the usual SM doublet, the traces are
taken in colour space, and $i$ and $j$ denote $SU(2)_{L}$ indices. The
additional $(8,2)_{1/2}$ scalar fields $S^{A}=(S^{A,+},S^{A,0})^{T}$ are
contained in the multiplet $S=S^{A}T^{A}$ with $T^{A}$ the generators of the
$SU(3)_{C}$ group. All potential parameters are real except $\nu_{3}$,
$\nu_{4}$ and $\nu_{5}$, but performing a phase rotation we can always take
$\nu_{3}$ to be also real.

From Eq. (1) we can derive the masses of the physical neutral octet scalar
($m_{R}$), the neutral octet pseudoscalar ($m_{I}$) and the charged octet
($m_{S^{\pm}}$), which are split by the Higgs vev,
$\langle\phi^{0}\rangle=v/\sqrt{2}$:

$m^{2}_{S^{\pm}}=m^{2}_{S}+\nu_{1}\,\frac{v^{2}}{4}\,,\qquad\qquad
m^{2}_{R,I}=m^{2}_{S}+(\nu_{1}+\nu_{2}\pm 2\,\nu_{3})\,\frac{v^{2}}{4}\,.$ (2)

The kinetic term (the factor two gives the correct canonical normalisation for
the fields)

$\mathcal{L}_{K}\,=\,2\,\mathrm{Tr}[(D_{\mu}S)^{\dagger}D^{\mu}S]$ (3)

generates the interaction of the octet scalars with the gauge bosons through
the covariant derivative

$D_{\mu}S\,=\,\partial_{\mu}S+ig_{s}\,[G_{\mu},S]+ig\,\frac{\sigma^{i}}{2}\,W_{\mu}^{i}S+\frac{i}{2}\,g^{\prime}B_{\mu}S\,,$
(4)

with $G_{\mu}=G_{\mu}^{A}T^{A}$ the octet gluon field. Thus, these
interactions are determined by the gauge symmetry and do not introduce
additional free parameters.

The coloured scalars can also couple to the quarks through the Yukawa
interaction. In order to guarantee the suppression of unwanted flavour-
changing neutral currents, which are extremely suppressed experimentally, we
will assume the principle of Minimal Flavour Violation (MFV) Chivukula:1987py
; DAmbrosio:2002vsn , which is based on the hypothesis that all Yukawa
matrices are proportional to the same flavour structures that break the
$SU(3)_{Q_{L}}\otimes SU(3)_{u_{R}}\otimes SU(3)_{d_{R}}$ symmetry in the SM.
This is in fact one of the main motivations of the MW model because the only
scalar representations that can couple to quarks and be compatible with this
principle are the colour octet or singlet electroweak doublets Manohar:2006ga
. With this assumption, the Yukawa couplings of the coloured scalars take the
form

$\displaystyle{\cal
L}_{Y}\supset-\sum^{3}_{i,j=1}\left[\eta_{D}Y^{d}_{ij}\,\bar{Q}_{L_{i}}Sd_{R_{j}}+\eta_{U}Y^{u}_{ij}\,\bar{Q}_{L_{i}}\tilde{S}u_{R_{j}}+\text{h.c.}\right].$
(5)

Here, $i$ and $j$ are family indices, $Y^{q}=\sqrt{2}M_{q}/v$ ($q=u,d$) denote
the up and down SM Yukawa matrices and the tilde in the $S$ field indicates
charge conjugation. The proportionality constants $\eta_{U}$ and $\eta_{D}$
are, in general, complex parameters.

Looking at Eqs. (1) and (5), we observe that the MW model contains 18 more
parameters than the SM, 14 of which are real while the other 4 are imaginary
phases. In order to simplify the phenomenological analysis and to reduce the
total number of free parameters we will only work in the CP-conserving limit.
This assumption removes the imaginary parts of $\nu_{4}$, $\nu_{5}$,
$\eta_{U}$ and $\eta_{D}$ and we end up with only 14 new free parameters.

##  3 Fit constraints

Our statistical data analysis will be based on a global Bayesian fit. We make
use of the public HEPfit package deBlas:2019okz , which is interfaced with the
Bayesian Analysis Toolkit Caldwell:2008fw . This code has been already applied
to several BSM analyses, including the Two-Higgs-Doublet model Cacchio:2016qyh
; Gori:2017tvg ; Chowdhury:2017aav ; Eberhardt:2020dat  and the Georgi-
Machacek model Chiang:2018cgb . We have adapted the code, including the
additional routines needed to study the MW model. These routines are also
public and can be extended in future works to incorporate additional
observables. In our fit we have only included observables that have been
directly calculated with this model. Constraints obtained from existing bounds
on higher-dimension operators111See for instance Ref. Farina:2018lqo  (and
references therein) where some particular colour-octet models are analysed.
Owing to the MFV assumption which strongly suppresses the scalar couplings to
light quarks, the $pp\to t\bar{t}$ analysis of Ref. Farina:2018lqo  is not
relevant for the MW model. are omitted, since we prefer to directly include in
the fit the observables used to derive those constraints. Indeed, HEPfit has
also been proven to be extremely reliable to constrain higher-dimension
operators deBlas:2018tjm ; Durieux:2019rbz ; Miralles:2021dyw . One of the key
features of HEPfit is its independence of other codes at runtime, which
provides a very fast framework for statistical analyses.

Since we will try to use in our fit all the available information, we did not
have any previous constraints on the MW parameters. Therefore we decided to
use a uniform distribution as a prior for the 14 free parameters of the MW
model. The ranges adopted are shown in Table 1. The range taken for $\eta_{U}$
follows from the assumption of a perturbative top Yukawa coupling, while
larger values of $\eta_{D}$ are possible since $m_{b}\ll m_{t}$. The
dependence of our results on the priors used turns out to be small, as long as
these priors are reasonable. For instance, increasing the range of $m_{S}^{2}$
up to $2^{2}$ TeV2 leads to the same limits, but we do not gain any further
information since many of the direct-searches analyses included do not go
beyond $1.5$ TeV. For $\nu_{n}$, $\mu_{n}$ and $\eta_{U}$ the posterior
probabilities are basically zero in the limits of the ranges considered and
the same constraints are always found if this (reasonable) condition is
satisfied. The only exception is $\eta_{D}$ which could not be constrained
within the range considered. However, higher values of $\eta_{D}$ will always
bring stronger limits on the other parameters. The parameter space is
constrained by the theoretical and experimental requirements that we now
discuss.

Parameters | ${\color[rgb]{0,0,0}m_{S}^{2}}$ | ${\color[rgb]{0,0,0}\nu_{n}}$ | ${\color[rgb]{0,0,0}\mu_{n}}$ | ${\color[rgb]{0,0,0}\eta_{U}}$ | ${\color[rgb]{0,0,0}\eta_{D}}$
---|---|---|---|---|---
Priors |  ${\color[rgb]{0,0,0}(0.4^{2},1.5^{2})}$ TeV2 | (-10, 10) | (-10, 10) | (-5, 5) | (-20, 20)
Table 1: Prior values of the fitted parameters.

###  3.1 Theoretical constraints

Since we are interested in the LHC phenomenology, we will assume that the MW
model is well defined up to the few TeV scale. As a consequence, the
renormalisation group (RG) evolution should be stable between the electroweak
scale and 5 TeV. By RG stability we mean the absence of Landau poles as well
as the fact that the scalar potential $V_{\text{\tiny{MW}}}$ should be bounded
from below at any of the considered scales. The RG equations (without Yukawa
and gauge couplings) were taken from Ref. He:2013tla  and a set of necessary
positivity bounds was derived in Ref. Cheng:2018mkc .

Another strong constraint on the quartic couplings of $V_{\text{\tiny{MW}}}$
is the unitarity requirement that the two-to-two scattering processes of the
scalar particles should not have a probability larger than $1$. This condition
is usually expressed in terms of the partial wave amplitudes $a_{j}$. Using
their LO ($a_{j}^{(0)}$) and NLO ($a_{j}^{(1)}$) expressions Cheng:2018mkc ,
perturbative unitarity can be imposed at LO, NLO and at the so-called NLO+
approximation Murphy:2017ojk  that includes the square of the NLO correction
and therefore contains some, but not all, NNLO terms Cheng:2018mkc :

$\left|a_{j}^{(0)}+\mathrm{Re}\\!\left(a_{j}^{(1)}\right)\right|^{2}\,\leq\,\frac{1}{4}\,.$
(6)

Note also that the LO and NLO expressions for the partial wave amplitudes are
only available in the large–$s$ approximation and should not be applied below
a certain scale $\mu_{u}$, which we choose to be $\mu_{u}=1.5$ TeV as the
current limits on the mass of the colour-octet scalars are around 1 TeV
Miralles:2019uzg .

On top of these unitarity bounds, we also impose perturbative behaviour of the
quantum corrections and allow only for scenarios in which the NLO
contributions to the partial wave amplitudes are smaller in magnitude than the
LO term.

In the fits, we run up to 3 or 5 TeV each parameter set, sampled at the
electroweak scale, and control at each intermediate step if the parameters
still comply with positivity and (above $\mu_{u}$) perturbative unitarity. If
this is not the case, the running is stopped and the corresponding cut-off
scale is returned as an output.

###  3.2 Higgs constraints

Production | Decay | Reference | $L$ | $\sqrt{s}$ | Reference | $L$ | $\sqrt{s}$
---|---|---|---|---|---|---|---
|  |  | [fb-1] | [TeV] |  | [fb-1] | [TeV]
|  | ATLAS | CMS
ggF | $h\to\gamma\gamma$ | Aad:2014eha  | 4.5/20.3 | 7/8 | Khachatryan:2014ira  | 5.1/19.7 | 7/8
VBF
VH | ATLAS:2020pvn  | 139 | 13 | Sirunyan:2021ybb  | 137 | 13
ttH
ggF | $\mu^{+}\mu^{-}$ | - | - | - | Khachatryan:2016vau  | 5/20 | 7/8
Aad:2020xfq  | 139 | 13 | Sirunyan:2020two  | 137 | 13
$\tau^{+}\tau^{-}$ | Aad:2015vsa  | 4.5/20.3 | 7/8 | Chatrchyan:2014nva  | 4.9/19.7 | 7/8
ATLAS:2020qdt  | 139 | 13 | CMS:2020gsy  | 137 | 13
$WW$ | ATLAS:2014aga ; Aad:2015ona  | 25, 4.5/20.3 | 7/8 | Chatrchyan:2013iaa  | 4.9/19.4 | 7/8
ATLAS:2020qdt  | 139 | 13 | CMS:2020gsy  | 137 | 13
$Z\gamma$ | Aad:2015gba  | 4.7/20.3 | 7/8 | Chatrchyan:2013vaa  | 5/19.6 | 7/8
Aad:2020plj  | 139 | 13 | Sirunyan:2018tbk  | 35.9 | 13
$ZZ$ | Aad:2014eva  | 4.5/20.3 | 7/8 | Khachatryan:2014jba  | 5.1/19.7 | 7/8
Aad:2020mkp  | 139 | 13 | CMS:2020gsy  | 137 | 13
Table 2: Higgs signal strengths measured by ATLAS and CMS.

In the MW model there are additional contributions to some of the production
and decay channels of the SM Higgs boson, due to the presence of the colour-
octet scalars. At the LHC, the SM Higgs boson is produced mainly through gluon
fusion (ggF), vector boson fusion (VBF), associated production with a
$t\bar{t}$ pair (tth) and associated production with vector bosons (Wh/Zh).
The LO contribution to the first process is a one-loop amplitude already in
the SM. As the coloured scalars couple to gluons and to the SM Higgs boson,
they will contribute to the gluon-fusion production mode at the same order
than the SM. Similarly, the decay of the SM Higgs boson to photons is also a
one-loop process in the SM to which the new scalars contribute.

The LHC data for the Higgs physics are parametrized in terms of the Higgs
signal strengths, which are defined as the measured cross section times
branching ratio for a given production and decay Higgs channel, in units of
the SM prediction. Table 2 compiles the experimental papers from which we have
taken the values of the different Higgs signal strengths. Comparing the
measured values of these observables with their theoretical predictions
Cheng:2016tlc , we will try to constrain the parameters $\nu_{1}$, $\nu_{2}$
and $\nu_{3}$, which are directly related with the mass splittings of the new
scalars in Eq. (2).

###  3.3 Constraints from direct searches

In order to find constraints from direct experimental searches of additional
scalars, we will compare the theoretical prediction of the production cross-
section times branching ratio of a given process, $\sigma\cdot\mathcal{B}$,
with the experimental upper limits of the ATLAS and CMS collaborations. The
channels that we have included in the fit are shown in Table 3. Since decays
of the colour-octet scalars into purely electroweak bosons are forbidden, we
have only considered their decays into gluons and quarks. Furthermore, in
order to be sure that the decay modes studied are indeed the dominant ones, we
impose for each search that the mass difference between the coloured scalar we
are analysing and the lightest member of the $S$ multiplet is smaller than the
$W^{\pm}$ mass Miralles:2019uzg . In this way, we forbid kinematically the
decays into another coloured scalar and a gauge boson, which can become the
dominant decay modes for some configurations of the parameter space. As we
will show later, this assumption is well justified, given the constraints that
perturbative unitarity enforce on the mass splittings of the new scalars.

Channel | Experiment | Mass range | ${\cal L}$
---|---|---|---
|  |  | [TeV] | [fb-1]
$pp\to S_{R,I}\to tt$ | ATLAS | Aaboud:2018mjh  | [0.4;3] | 36.1
$bb\to S_{R,I}\to tt$ | ATLAS | ATLAS-CONF-2016-104  | [0.4;1] | 13.2
$pp\to S_{R,I}tt\to(tt)(tt)$ | ATLAS | Aaboud:2018xpj  | [0.4,1] | 36.1
$pp\to S^{+}b\bar{t}\to t\bar{b}b\bar{t}$ | ATLAS | Aad:2021xzu  | [0.2;2] | 139.1
$bb\to S_{R,I}\to bb$ | CMS8 | Khachatryan:2015tra  | [0.1;0.9] | 19.7
$gg\to S_{R,I}\to bb$ | CMS8 | Sirunyan:2018pas  | [0.325;1.2] | 19.7
$pp\to S_{R,I}\to bb$ | CMS | CMS-PAS-HIG-16-025  | [0.55;1.2] | 2.69
$bb\to S_{R,I}\to bb$ | CMS | Sirunyan:2018taj  | [0.3;1.3] | 35.7
$pp\to S_{R,I}\to gg$ | CMS | Sirunyan:2018xlo  | [0.5,8] | 27 & 36
$pp\to S_{R,I}S_{R,I}\to(gg)(gg)$ | ATLAS | Aaboud:2017nmi  | [0.5,1.75] | 36.7
Table 3: Data from direct searches included in the fit. CMS8 means CMS at 8
TeV, the rest is at 13 TeV.

Since HEPfit cannot generate events by itself, the theoretical predictions for
$\sigma\cdot\mathcal{B}$ must be provided with other tools. We have used
MadGraph Alwall:2014hca  to create tables with the values of
$\sigma\cdot\mathcal{B}$ for different input choices of the parameters on
which these observables depend: $\eta_{U}$, $\eta_{D}$, $(\nu_{4}+\nu_{5})$
and $m_{S}$. These tables are read by HEPfit, which performs a linear
interpolation to obtain the value of the observables at any point. The error
of the linear interpolation is estimated to be 10% or less for
$\log(\sigma\cdot\mathcal{B})$.

The experimental data are also provided in the form of tables, which compile
the values of the 95% upper limits on $\sigma\cdot\mathcal{B}$, as a function
of the resonance mass. In these tables, HEPfit also performs a linear
interpolation if needed.

In order to compare the theoretical results with the experimental data, we
define the ratio of the theoretical prediction over the experimental upper
limit. To this ratio we will assign a Gaussian distribution (restricted to
positive values) centered at 0 such that the value 1 is excluded with a 95%
probability.

###  3.4 Flavour constraints

Regarding flavour transitions, we have included in the analysis the
$B^{0}_{s}-\bar{B}^{0}_{s}$ mixing and the decay
$B^{0}_{s}\rightarrow\mu^{+}\mu^{-}$, which are the most constraining
observables. The expressions for the relevant Wilson coefficients were taken
from Ref. Cheng:2015lsa , where a complete one-loop calculation was performed.
Only the charged scalars contribute to these processes at the one-loop level,
and the corresponding amplitudes involve the parameters $\eta_{U}$ and
$\eta_{D}$. The leading $\eta_{U}$ contributions are proportional to the top-
quark mass, while the $\eta_{D}$ terms are weighted by the bottom-quark mass.
Therefore, the transition amplitudes are mainly governed by the parameter
$\eta_{U}$.

These observables strongly depend on the numerical values of the relevant
quark mixings. We cannot use the standard determinations of the CKM entries,
since they assume the validity of the SM. In order to obtain non-contaminated
values, we perform a specific CKM fit using HEPfit, which only includes
observables that are not affected by the coloured scalars. The inputs of this
CKM fit, shown in Table 4, are taken from the PDG 2020 Zyla:2020zbs  except
$|V_{cs}|$, for which we have adopted the more recent result of Ref.
Chakraborty:2021qav . The value of $|V_{ud}|$ has been considerably shifted
with respect to the one quoted in the PDG 2018 Tanabashi:2018oca . Combined
with the reduction of its uncertainty, this generates a violation of unitarity
in the first row of the CKM matrix at the $3\sigma$ level. Since there is no
full consensus in the community, we have adopted a conservative attitude,
increasing the error of $|V_{ud}|$ by a factor $2.4$ so that CKM unitarity is
recovered at 2$\sigma$, without modifying any central values. The results of
this CKM fit, shown in Table 5, are then used as inputs in our analysis of the
MW parameter space.

CKM Parameter | Input Value | Source
---|---|---
$|V_{ud}|$ | $0.97370\pm 0.00033$ |  Superallowed $0^{+}\to 0^{+}$ nuclear $\beta$
decays
$|V_{us}|$ | $0.2245\pm 0.0008$ |  Kaon and pion semileptonic and leptonic decays
$|V_{cd}|$ | $0.221\pm 0.004$ |  Semileptonic and leptonic charm decays
$|V_{cs}|$ | $0.966\pm 0.008$
$|V_{cb}|$ | $(41.0\pm 1.4)\times 10^{-3}$ |  Exclusive and inclusive semileptonic decays of $B$ mesons
$|V_{ub}|$ | $(3.82\pm 0.24)\times 10^{-3}$
$|V_{td}/V_{ts}|$ | $0.205\pm 0.006$ |  $B^{0}-\overline{B}^{0}$ mixing
Table 4: Inputs Zyla:2020zbs ; Chakraborty:2021qav  used for the CKM fit and processes from which they are obtained. The error of $|V_{ud}|$ has been increased by a factor 2.4. | Value | Correlation
---|---|---
$\lambda$ | $A$ | $\overline{\rho}$ | $\overline{\eta}$
$\lambda$ | $0.22518\pm 0.00069$ | 1 | $-0.18$ | 0.08 | $-0.084$
$A$ | $0.808\pm 0.028$ | $-0.18$ | 1 | $-0.22$ | $-0.41$
$\overline{\rho}$ | $0.181\pm 0.026$ | 0.08 | $-0.22$ | 1 | 0.039
$\overline{\eta}$ | $0.360\pm 0.029$ | $-0.084$ | $-0.41$ | 0.039 | 1
Table 5: Wolfenstein parameters obtained from a fit to the CKM entries in
Table 4.

###  3.5 Electroweak precision data

In this work, we are studying the most general CP-conserving MW model, so we
have not imposed any additional assumptions such as Custodial Symmetry.
Therefore, the coloured scalars generate non-vanishing contributions to the
oblique parameters Peskin:1990zt ; Peskin:1991sw  that can be used to
constrain the parameter space of the model. The standard bounds on $S$, $T$
and $U$ Zyla:2020zbs  include in the global fit the ratio $R_{b}=\Gamma(Z\to
b\bar{b})/\Gamma(Z\to\mathrm{hadrons})$, which incorporates quantum
corrections to $\Gamma(Z\to b\bar{b})$ that are enhanced by the large value of
the top quark mass Bernabeu:1987me ; Bernabeu:1990ws . Since the ratio $R_{b}$
receives also sizeable corrections from the additional scalars, we cannot use
these bounds. Similarly to what has been done before for the CKM matrix, we
first determine the oblique parameters, performing a combined fit with HEPfit
of electroweak precision observables without $R_{b}$ Eberhardt:2020dat , and
then use the resulting values as inputs in our analysis of the MW model. The
values of the oblique parameters that we have obtained from this fit are shown
in Table 6.

| Value | Correlation
---|---|---
$S$ | $T$ | $U$
$S$ | 0.093$\pm$ 0.101 | 1.00 | 0.86 | -0.54
$T$ | 0.111$\pm$0.116 | 0.86 | 1.00 | -0.83
$U$ | -0.016$\pm$0.088 | -0.54 | -0.83 | 1.00
Table 6: Results for the fit of the oblique parameters $S$, $T$ and $U$,
excluding the information from $R_{b}$.

The theoretical predictions for $S$, $T$ and $U$ in the MW model have been
taken from Ref. Burgess:2009wm . The oblique parameters depend on the masses
of the new scalars and, therefore, provide important constraints on $m_{S}$,
$\nu_{1}$, $\nu_{2}$ and $\nu_{3}$. Once, the oblique parameters have been
fixed, we also include $R_{b}$ in the fit to the MW parameter space. The
theoretical prediction of this observable, including the QCD corrections, has
been taken from Ref. Degrassi:2010ne . The ratio $R_{b}$ will basically
constrain $\eta_{U}$ because, like for the flavour observables, the new
physics contribution comes from one-loop diagrams involving virtual charged
scalars, coupled to heavy quarks.

##  4 Results

###  4.1 Theoretical constraints

As mentioned before, we have imposed that this model should satisfy
perturbative unitarity and be well defined up to, at least, 3 TeV. These
conditions generate bounds on all the parameters of the scalar potential that,
in some cases, can be stronger than the ones obtained from experimental data.
For instance, the quartic couplings are not constrained experimentally but the
theoretical requirements imply that none of them can be, in modulus, higher
than 6. The theoretical constraints can be translated to physical observables
like the mass differences, which depend on these parameters. In Fig. 1 we show
the theoretical constraints on the scalar mass differences for two choices of
the UV scale, 3 TeV and 5 TeV. Obviously, requiring the model to be valid up
to a higher scale results in stronger bounds. The figure exhibits also the
importance of perturbative unitarity, showing how the limits get weakened if
the scale above which we impose it is chosen to be higher.

Figure 1: Theoretical constraints on the mass splittings, as functions of the
scalar masses. The different coloured regions correspond to imposing RG
stability up to an UV mass scale of 3 or 5 TeV, and imposing perturbative
unitarity conditions above 2.5 TeV or 1.5 TeV.

The large impact of these theoretical constraints can be better appreciated in
Fig. 8, which displays the bounds they impose on the $\mu_{n}$ and $\nu_{n}$
potential parameters, in the form of two-dimensional correlated plots,
compared with the final results from the global fit, including all
constraints, that we will later discuss.

###  4.2 Experimental constraints

Figure 2: Two-dimensional constraints on $\nu_{1}$, $\nu_{2}$ and $\nu_{3}$
from Higgs signal strengths (red), compared with the theoretically allowed
regions (green), assuming RG stability up to 3 TeV.

As we have shown before, using theoretical arguments we can constrain the
parameter space of all the new quartic couplings that appear in the scalar
potential. In this section we will use experimental measurements in order to
constrain the masses of the coloured scalars and their Yukawa couplings. But
first of all let us consider the observables that constrain also the
parameters of the potential and let us compare the results with the ones
obtained from theoretical requirements.

In Fig. 2 we show the constraints on $\nu_{1}$, $\nu_{2}$ and $\nu_{3}$
emerging from the Higgs signal strengths and compare them with the
theoretically allowed regions, imposing RG stability up to 3 TeV. Clearly the
theoretical restrictions are much stronger than the Higgs constraints so, a
priori, one could think that the latter will be irrelevant in the global fit.
However, the addition of these experimental observables will have some effect
on the global fit, as we will show later. The fact that the constraints from
the Higgs signal strengths, alone, are so weak is an expected behaviour, given
that the coloured scalars only start to contribute to them at the one-loop
level.

The oblique parameters constrain the scalar mass splittings, bounding the
combinations of quartic couplings $\nu_{2}\pm 2\nu_{3}$ that appear in Eq.
(2). This is clearly seen in the narrow allowed regions (orange) displayed in
Fig. 3. At large values of $\nu_{2,3}$, the oblique parameters impose that
$\nu_{2}\approx\pm 2\nu_{3}$ in order to reduce the splitting between the
charged scalar and either the CP-odd or CP-even neutral scalars. The oblique
bounds are relevant even when we consider the theoretical constraints up to 5
TeV, but they are specially important when we only require RG stability up to
3 TeV. Indeed, combining both constraints we can obtain a harder restriction
on these parameters for the 3 TeV case.

Figure 3: Allowed two-dimensional regions of $\nu_{2}$ and $\nu_{3}$ from the
oblique parameters (orange, 95% probability) and from theoretical constraints
(green) with the NLO+ approximation. The darker and lighter green areas
correspond to requiring RG stability up to 3 and 5 TeV, respectively.

The absolute mass scale $m_{S}$ is constrained by the electroweak ratio
$R_{b}$, which is also sensitive to the Yukawa alignment parameter $\eta_{U}$.
The $m_{S}$-$\eta_{U}$ plane is also constrained by the two flavour
observables that we have considered: $B^{0}_{s}-\bar{B}^{0}_{s}$ mixing and
$\text{Br}(B_{s}\rightarrow\mu^{+}\mu^{-})$. The left panel of Fig. 4 displays
the regions allowed by each of these observables, individually, at 95%
probability. The mass difference between $B^{0}_{s}$ and $\bar{B}^{0}_{s}$
turns out to provide the strongest bounds, although they are quite similar to
the ones from $\text{Br}(B_{s}\rightarrow\mu^{+}\mu^{-})$. Furthermore, since
the three observables exhibit a similar dependence on these parameters, the
combined constraints obtained with the three observables together are not much
better than the ones given by just $\Delta M_{B_{s}}$ or
$\text{Br}(B_{s}\rightarrow\mu^{+}\mu^{-})$.

The $m_{S}$-$\eta_{U}$ plane is also constrained by the direct searches, as
shown in the right panel of Fig. 4. In this figure we have only included
searches with at least one top quark in the final state because those are the
channels generating the most interesting constraints. Since the figure does
not include any observable constraining the scalar mass differences, we have
set these mass splittings to zero. Doing so, we are able to totally exclude
values of $m_{S}$ (equal in this case to the physical scalar masses) smaller
than 1.1 TeV, for any value of the other parameters, with a probability of
95%. The plot shows also the additional constraints obtained on this plane
from flavour observables.

In Fig. 5 we display the analogous constraints emerging from direct searches
in channels without top quarks in the final state. Relevant bounds are only
obtained at small values of $\eta_{U}$ or for high values of $\eta_{D}$. This
is to be expected because those are the parameter regions where the scalar
decays into top quarks are suppressed and, therefore, the branching ratios for
the other channels are increased. The decay channels to top quarks are of
course the dominant ones outside these particular regions of the parameter
space, and decay modes without top quarks become irrelevant for large values
of $\eta_{U}$ or small values of $\eta_{D}$.

Similar features are found in the $m_{S}$-$\eta_{D}$ plane, where the bound
$m_{S}>1.1$ TeV is also obtained with a 95% probability from direct searches
in channels with top-quark production. This could be, in principle, a bit
surprising because one could naively expect that for very small values of
$\eta_{U}$ those searches should not generate any constraint. This is true for
the channels in which a neutral scalar decays to a $t\bar{t}$ pair, but not
for a charged scalar decaying to $t\bar{b}$, a process which also depends on
$\eta_{D}$. Indeed, in the right panel of Fig. 4, one observes that the lower
bound on $m_{S}$ decreases when $\eta_{U}$ approaches zero. This is because
all channels with neutral scalars become irrelevant in that limit, but the
information from charged-scalar channels is still good enough to generate a
quite strong constraint. Therefore, as long as $\eta_{U}$ and $\eta_{D}$ are
not both extremely close to zero, we obtain good constraints on $m_{S}$. Since
the MW model is motivated by MFV, the particular region where the two quark
Yukawa couplings are both zero does not seem to have much theoretical
interest.

Figure 4: Experimental constraints on the $m_{S}$-$\eta_{U}$ plane. Left
panel: allowed regions at 95% probability obtained from $R_{b}$ (blue),
$\text{Br}(B_{s}\rightarrow\mu^{+}\mu^{-})$ (yellow) and $\Delta M_{B_{s}}$
(magenta). Right panel: combined flavour constraints, compared with the limits
from direct searches including top quarks, at 95% probability. Figure 5:
Constraints on the $m_{S}$-$\eta_{U}$ (left) and $m_{S}$-$\eta_{D}$ (right)
planes, obtained from direct searches in channels without top quarks in the
final state.

###  4.3 All constraints

Once we have analysed the constraints emerging from individual observables, we
can combine all of them into a global fit. The first interesting result is
that we are able to find lower limits for the physical masses of our scalars
and constraints on their mass splittings, as shown in Fig. 6. Note that the
mass differences between the different scalars are now restricted to be
smaller than 25 GeV with a 99.7% probability, if we impose RG stability and
perturbative unitarity up to 3 TeV, and to be smaller than 20 GeV, with the
same probability, when we go up to 5 TeV. This justifies a posteriori our
approximation of not including in the analysis of direct searches the decays
of the coloured scalars into another scalar plus a weak boson.

Figure 6: Comparison of theoretical and global constraints on the mass
splittings, as a function of the different scalar masses, imposing RG
stability and perturbative unitarity up to 3 and 5 TeV. For the global fit we
plot the 95% and 99.7% regions.

Another interesting result is shown in Fig. 7, where we plot again the
constraints on the $m_{S}$-$\eta_{U}$ and $m_{S}$-$\eta_{D}$ planes. We can
clearly see how $\eta_{D}$ is not constrained. On the other hand, $|\eta_{U}|$
cannot take values higher than 1.8, for masses of the scalars smaller than 1.5
TeV, within a probability of 95%. The constraint on the scalar mass scale is
mainly coming from direct searches including decays to top quarks. This is why
for values of $\eta_{U}$ close to zero the lower bounds on $m_{S}$ are weaker.
However, as mentioned before, even for very small values of $|\eta_{U}|$ the
constraints remain strong. We have also performed some global fits in which we
set $\eta_{U}=0$ or $\eta_{D}=0$. For the first case we found that the limits
on the scalar masses are roughly 100 GeV smaller, while for the second we
found the same result than for the global fit in which we vary both
parameters. Therefore, even in the hypothetical case that some symmetry would
force one of the Yukawa couplings to vanish, one would still find important
constraints on the scalar masses.

Figure 7: Allowed regions on the $m_{S}$-$\eta_{U}$ (left) and
$m_{S}$-$\eta_{D}$ (right) planes from the global fit, at 95% and 99.7%
probability, imposing RG stability up to 3 TeV and perturbative unitarity at
NLO+. Quite similar results are obtained, requiring RG stability up to only 1
TeV.

The two-dimensional correlations among the quartic potential parameters are
displayed in Fig. 8, which compares the limits emerging from the global fit
with those obtained with only theoretical constraints, imposing RG stability
and perturbative unitarity up to 3 and 5 TeV. The allowed regions from
theoretical constraints must be understood as having 100% probability because
they correspond to a discrete condition: a given point of the parameter space
is either allowed or not. This introduces a small difference when comparing
the theoretical and global limits, since the latter ones refer to a slightly
smaller probability. Taking this into account, we can still see that $\nu_{1}$
and $\nu_{2}$ are slightly more constrained in the global fit, if RG stability
is only imposed up to 3 TeV. Nevertheless, for the other observables the
allowed regions remain almost invariant when including the experimental
information. This is not a surprise because the measured observables depend on
$\nu_{1}$, $\nu_{2}$ and $\nu_{3}$. The improvements introduced by the global
fit are a consequence of adding the oblique parameters and, specially, the
Higgs signal strengths. In order to check this, we performed a fit with only
theory and the Higgs signal strengths and the results for $\nu_{1}$ and
$\nu_{2}$ were basically identical to the ones of the global fit. Indeed,
although the Higgs signal strengths alone do not produce strong limits,
combining them with the theoretical constraints, which reduce the allowed
range of $\nu_{3}$, results in very good bounds on $\nu_{1}$ and $\nu_{2}$.

If RG stability is imposed up to 5 TeV, the current experimental measurements
have a quite small impact in the allowed regions in Fig. 8, which are mainly
governed by the much stronger theoretical constraints.

Finally, in Table 7 we present the marginalised allowed ranges for the
parameters of the potential, from the global fit, with a probability of 95%.
As can be seen there, none of the quartic couplings can be, in modulus, higher
than 5 within this probability.

Figure 8: Two-dimensional correlations among the quartic couplings of the scalar potential. The allowed (99.7% probability) regions from the global fit are compared with the results obtained with only theoretical constraints, imposing perturbative unitarity and RG stability up to 3 and 5 TeV. Variables | All 3TeV | All 5TeV
---|---|---
$\mu_{1}$ | (-2.9, 2.3) | (-1.3, 1.5)
$\mu_{2}$ | (-2.7, 2.6) | (-1.8, 1.8)
$\mu_{3}$ | (-1.6, 2.4) | (-1.0, 1.6)
$\mu_{4}$ | (-0.60, 1.35) | (-0.44, 0.90)
$\mu_{5}$ | (-1.0, 1.9) | (-0.7, 1.3)
$\mu_{6}$ | (-4.6, 3.5) | (-2.9, 2.4)
$\nu_{1}$ | (-0.8, 1.4) | (-0.66, 0.97)
$\nu_{2}$ | (-1.2, 2.0) | (-0.95, 1.47)
$\nu_{3}$ | (-0.65, 0.70) | (-0.45, 0.49)
$\nu_{4}$ | (-2.4, 2.4) | (-1.7, 1.6)
$\nu_{5}$ | (-1.6, 1.5) | (-1.7, 1.6)
Table 7: Allowed ranges for the quartic potential parameters from the global
fit, at 95% probability.

##  5 Summary

In this work, we have presented the first global fit of the MW model. We have
combined the more relevant theoretical and experimental constraints, including
flavour and electroweak precision observables, Higgs signal strengths and
direct searches. The theoretical constraints have a quite large impact on the
scalar parameter space, specially when RG stability is imposed up to 5 TeV,
providing bounds on all the scalar potential parameters. The current
experimental information on the Higgs signal strengths and the oblique
parameters gives an improved sensitivity to $\nu_{1}$, $\nu_{2}$ and
$\nu_{3}$, which becomes relatively more important if RG stability is only
imposed up to 3 TeV. This allows for more stringent constraints on the scalar
mass splittings.

The flavour observables and $R_{b}$ constrain the $m_{S}$-$\eta_{U}$ plane,
but all of them in the same direction. The strongest limits come from $\Delta
M_{B_{s}}$ and $\text{Br}(B_{s}\rightarrow\mu^{+}\mu^{-})$, which combined,
require that

$|\eta_{U}|\,<\,1.8$ (7)

for scalar masses smaller than 1.5 TeV, within a probability of 95%.

A quite strong bound on the absolute mass scale $m_{S}$ emerges from the LHC
data on direct searches for new scalars. The more sensitive channels, which
involve the production of top quarks in the final state, imply that the masses
of all coloured scalars must satisfy the bound

$m_{S^{\pm}},m_{S_{R}},m_{S_{I}}\,>\,1.05\;\mathrm{TeV}$ (8)

for any value of the other parameters, with a 95% probability. The global fit
also restricts the scalar mass splittings to be smaller than 20 GeV, with a
95% probability, even when RG stability is only imposed up to 3 TeV.

As shown in Ref. Miralles:2019uzg , even for tiny values of
$|\eta_{U}|>10^{-7}$, one still finds a strong lower bound on the scalar
masses, provided $|\eta_{D}|>10^{-5}$. These bounds can only be avoided for
fermiophobic scalars with $\eta_{U}\approx\eta_{D}\approx 0$, such that their
decay into a fermion-antifermion pair is highly suppressed. In that case, they
would have a completely different experimental signature, since they would
either decay into a lighter coloured scalar and a gauge boson or would behave
as strongly-interacting long-lived particles. Although fermiophobic scalars
are not compelling from the MFV point of view of the MW model, their
phenomenology could be interesting by itself, but requires a more specific
analysis that we postpone to future works.

The forthcoming Run3 of the LHC and its subsequent high-luminosity phase will
provide much larger data samples, substantially increasing the sensitivity to
coloured scalar particles. Mass scales up to 1.3 TeV seem to be reachable with
the expected luminosity of 3 $\text{ab}^{-1}$. The constraints on those
potential parameters not related to scalar masses will remain, however,
largely dependent on theoretical considerations, unless a real discovery of a
colourful scalar state emerges from the data.

## Acknowledgements

This work has been supported in part by the Spanish Government and ERDF funds
from the EU Commission [grant FPA2017-84445-P], by the Generalitat Valenciana
[grant Prometeo/2017/053] and by the COST Action CA16201 PARTICLEFACE. The
work of V.M. is supported by the FPU doctoral contract FPU16/0191, funded by
the Spanish Ministry of Universities.

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License Attribution 4.0 International (CC BY 4.0).

HASOC (2021) Hate Speech and Offensive Content Identification in English and
Indo-Aryan Languages

<EMAIL_ADDRESS>]<EMAIL_ADDRESS>]
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<EMAIL_ADDRESS>]

# Battling Hateful Content in Indic Languages
HASOC ’21

Aditya Kadam  Anmol Goel  Jivitesh Jain  Jushaan Singh Kalra  Mallika
Subramanian  Manvith Reddy  Prashant Kodali  T.H. Arjun  Manish Shrivastava
Ponnurangam Kumaraguru  International Institute of Information Technology,
Hyderabad, India  Delhi Technological University, Delhi, India

(2020)

###### Abstract

The extensive rise in consumption of online social media (OSMs) by a large
number of people poses a critical problem of curbing the spread of hateful
content on these platforms. With the growing usage of OSMs in multiple
languages, the task of detecting and characterizing hate becomes more complex.
The subtle variations of code-mixed texts along with switching scripts only
add to the complexity. This paper presents a solution for the HASOC 2021
Multilingual Twitter Hate-Speech Detection challenge by team PreCog IIIT
Hyderabad. We adopt a multilingual transformer based approach and describe our
architecture for all 6 subtasks as part of the challenge. Out of the 6 teams
that participated in all the subtasks, our submissions rank 3rd overall.

###### keywords:

Hate Speech Social Media Code Mixed Indic Languages Transformer Architecture

##  1 Introduction

Dissemination of hateful content on nearly all social media is increasingly
becoming an alarming concern. In the research community as well, this is a
heavily studied research problem [1, 2, 3, 4, 5]. Misconduct such as bullying,
derogatory comments based on gender, race, religion, threatening remarks etc.
are more prevalent today than ever before. The repercussions that such content
can have is profound and can result in increased mental stress, emotional
outburst and negative psychological impacts [6]. Hence, curbing the
proliferation of this hate speech is imperative. Furthermore, the massive
scale at which online social media platforms function makes it an even more
pressing issue, which needs to be addressed in a robust manner. Most online
social media platforms have imposed strict guidelines
111https://help.twitter.com/en/rules-and-policies/hateful-conduct-policy
222https://transparency.fb.com/en-gb/policies/community-standards/hate-speech/
333https://support.google.com/youtube/answer/2801939 to help prevent the
spread of hate. In spite of these platform regulations, the dynamics of user-
interaction influence the diffusion of (and hence increase in) hate to a large
extent [1].

The problem of hate speech has been addressed by several researchers, but the
rise in multilingual content has added to the complexity of identification of
hateful content. Majority of these studies deal with high-resource languages
such as English, and only recently have low-resource languages – such as
several Indic Languages – been more deeply explored [7]. In a country like
India, with multitude of regional languages, the phenomenon of Code
Mixing/Switching (wherein linguistic units such as phrases/words of two
languages occur in a single utterance) is also pervasive.

In this paper we elucidate our approach in solving the six downstream tasks of
hate speech identification and characterization in Indian languages as a part
of the  ‘HASOC ’21 Hate Speech and Offensive Content Identification in English
and Indo-Aryan Languages’ challenge [8]. Motivated by existing architectures,
we curate our own pipeline by fusing fine-tuned transformer based models with
additional features to solve this challenge and highlight the different
methodologies that were adopted for the three languages – English, Hindi,
Marathi, and Code Mixed Hindi - English. We also make our code, methodology
and approach public to the research community.
444https://github.com/Adi2K/Precog-HASOC-2021

##  2 Literature Review

Discerning hateful content on social media is an already tricky problem given
the challenges associated with it, for instance disrespectful/abusive words
could be censored in text, some expressions may not be inherently offensive,
however they can be so in the right context [9]. Owing to the conversational
design of social media wherein users can reply to a given comment (either
support, refute or irrelevant to the original message), the build-up of
threads in response to a hateful message can also intensify hate even if the
reply is not hateful on its own. The evolution of such hate intensity has
shown diverse patterns and no direct correlation to the parent tweet which
makes the task of hate speech detection more difficult [10].

Significant amount of research has been conducted to evaluate traditional NLP
approaches such as character level CNNs, word embedding based approaches and
the myriad of variations with LSTMs (sub-word level, hierarchical, BiLSTMs)
[11]. Likewise, Machine Learning algorithms including SVMs, K-Nearest
Neighbours, Multinomial Naive Bayes (MNB) and their respective performances in
multilingual text settings have also been explored [12, 7, 13]. Investigating
categories of profane words that are commonly used in hate speech is another
non-trivial subtask under the hate detection umbrella, primarily because of
the different interpretations of words in different cultures/demographics,
adaptation of slangs in newer generations etc [14].

In recent times however, with the introduction of Transformer based models and
their performance in Natural Language Understanding (NLU) tasks, significant
work has been done in order to adapt these for multilingual texts as well to
leverage transfer between languages. Models such as XLMR, mBERT, MuRIL,
RemBERT have gained much popularity and have shown promising results [15, 16,
17]. Transfer learning based approaches that leverage performance of high
resource languages accompanied with CNN classification heads have also shown
significant improvements in capturing hateful content on social media
platforms [18, 19]. Sharing and re-utilizing the model weights learnt whilst
training on a corpus for a high resource language can aid the process of
training for languages that are still under explored [20].

##  3 Dataset

###  3.1 Dataset & Task Description

Subtask 1 consisted of data for 3 languages, namely – English, Hindi and
Marathi [21, 22]. For English and Hindi, the task was further subdivided into
2 sub-parts: a) Identification of hateful v/s non-hateful content and b)
Characterizing the kind of hate present in a tweet – either Profane, Hateful,
Offensive or None. The distribution of the different data classes for each of
the three languages is shown in Table 1.

Table 1: Distribution of the HASOC 2021 dataset for each task and its associated subtasks. For each language and task, the corresponding number of tweets per class is shown below. Tweets pertaining to Subtask 1 are in three languages – English, Hindi, Marathi. | Task A |  | Task B
---|---|---|---
Language | Non-Hateful | Hateful |  | None | Offensive | Hate | Profane
English | 1342 | 2501 |  | 1342 | 1196 | 683 | 622
Hindi | 3161 | 1433 |  | 3161 | 654 | 566 | 213
Marathi | 1205 | 669 |  | - | - | - | -
Subtask 2 | 2899 | 2841 |  | - | - | - | -

The focus of Subtask 2 was binary classification: Hate & Offensive or Non
Hate-Offensive. The given dataset distribution for this task is shown in Table
1. This data was accompanied by the following additions [23]:

  * •

Tweets are English - Hindi Code Mix sentences, and

  * •

Classification should not be based on the tweet alone, but should also account
for the context as well.
For example : Consider that in a tweet thread, tweet A is a reply to tweet B.
For classifying tweet A, the model can leverage the information from the
parent tweet - tweet B.

Figure 3(b) demonstrates the relationship between the tweets to be classified
and their contexts.

###  3.2 Preprocessing Data

As a precursor to applying any NLP models on text data, we pre-processed the
dataset with standard techniques. Given that the data from Twitter is bound to
have certain amount of noise and unwanted elements such as – URLs, mentions
etc, these were removed from the tweet texts. Hashtags have a slightly
different contribution to analysis of the tweet since they may or may not
contribute positively in the classification task. Through the results from our
experiments, we observed that omitting the hashtags proved to work better, and
hence they were cleaned from the tweet as well.

Since the data is code mixed, not only in terms of the combination of
languages but also with respect to scripts (some English text is written in
Roman script, whereas some Hindi text is written in Devanagari apart from
Roman), we also normalize the Indic language scripts for Marathi and Hindi. In
addition to that, we removed stop words for the Marathi dataset using this
list. 555https://github.com/stopwords-iso/stopwords-mr Finally, punctuations
were also removed from the dataset texts.

An interesting observation was that for the task of hate detection, the
presence of emojis converted to text in the tweets did not improve the
performance of our models significantly (rather it reduced the scores by some
margin). However, including emojis along with text while classifying hate did
have a positive impact since the emoji-text conversion was able to capture
hints of sentiment and indirect offensive/profane content.

##  4 Methodology

###  4.1 Subtask 1: Identifying Hate, offensive and profane content from the
post

(a) Using BerTweet model with a MLP classifier head.

(b) Combining CNN features over XLM-R output and manually generated feature
vectors.

Figure 1: Architecture and pipeline for the models used for the downstream
task of hate detection and classification for the English language for Subtask
1.

####  4.1.1 English Classifiers

For the English Subtask 1, the architecture that resulted in the best
performance is an ensemble of the following models:

  * •

Fine-tuned BERTweet model [24]

  * •

Fine-tuned XLM-Roberta [16] with CNN Head

We use XLM-R, a multilingual model, along with the monolingual model in the
ensemble as we found that some of the text in the training set has
transliterated Hindi along with some Devanagari text. We extracted textual
features such as distribution of ‘?’, ‘!’, capital letters etc. We also use
the percentage of profane words and sentiment of the text as a feature. We use
profane words list curated from various sources such as words/cuss
666https://github.com/words/cuss, zacanger/profane-words
777https://github.com/zacanger/profane-words, t-davison/lexicons.
888https://github.com/t-davidson/hate-speech-and-offensive-
language/tree/master/lexicons For sentiment analysis we use the TweetEval [25]
model and use its softmax output as a feature to our models.

Inspired by Kim [26] we pass the embedding (concatenated last 4 hidden layers)
to a CNN and max-pool convolution layers of various widths to a fully
connected layer of size 128 with dropout. We concatenate this 128 dimensional
vector with our feature vector. We pass this output onto a dense output layer
with softmax activation and cross entropy loss as shown in Figure 1.

Along with the previous models, we fine-tune BERTweet, a pre-trained language
model for English tweets. BERTweet has the same architecture as BERT and is
trained on the pre-training procedure of RoBERTa, but it is trained solely on
tweets, thus, making it a viable alternative and suitable for our task. This
model has shown state-of-the-art results on tasks based on tweets [24]. We use
the encoder architecture and pass the pooled output through a linear layer for
the classification which uses softmax activation and cross-entropy loss as
shown in the Figure 1.

We also train the models on the previous years datasets but notice that this
does not increase the performance of the models but actually degrades the
performance in Task 1B due to skewed distribution of classes. Transliteration
of emojis didn’t improve the performance. The class imbalance in Subtask 1-B
degraded the performance of our models hence we tried to improve upon it by
using a weighted loss function but we notice that this decreases the
performance and that the domain specific distribution is actually helping the
models. We also perform K-Fold Validation and use early stopping to avoid
over-fitting. We average the probabilities of each class across folds and the
two models in our ensemble.

(a) The base architecture for Hindi & Marathi languages for Subtask 1 using
XLM-R with CNN augmented with textual features vector followed by a softmax
layer.

(b) Multilingual MiniLM architecture adopted to overcome class imbalance while
characterizing hate for the Hindi Subtask 1-B.

Figure 2: Architecture and pipeline for the models used for the downstream
task of hate detection and classification for the Hindi & Marathi language for
Subtask 1.

####  4.1.2 Hindi & Marathi Classifier

For both the Hindi and Marathi language, the architecture that performed the
best utilized the XLM-R transformer model. This model was able to capture the
code-mixed and multilingual nature of the tweets dataset. To amplify the
results, we leveraged intermediary representations of the language model as
well as textual features that were extracted from the tweets. In particular,
we utilized the Multilingual MiniLM language model for fine-tuning on Hindi
Subtask 1-B. We observed that MiniLM with Focal Loss instead of Cross Entropy
Loss performed better than other baselines in the imbalanced multi-class
setting of Hindi Subtask 1-B. Focal Loss compensates for class imbalance with
a factor that increases the network’s sensitivity towards mis-classified
samples.

Inspired by Mozafari et al. [18] we use the pre-trained representations of the
text from 12 hidden layer of XLM-R model (each of 768 dimensions) and then
apply a CNN layer with a kernel size of 3. The output is then passed through a
soft-max following which the cross-entropy loss is computed whilst training.
This model architecture is represented in Figure 2. Tuning hyperparameters
such as optimizers, loss functions and dropout layers, we experiment with
different options. For the optimizers we try Adadelta and Adam optimizers with
Adam working out better. Amongst all loss functions, the Cross Entropy Loss
performed the best. As for the dropout layers we explore dropouts in the range
0.1-0.5 and use 0.5 as the final dropout for the model architecture.

We further augment the model features, with two kinds of textual features –
fraction of profane words and sentiment of the tweet. Due to lack of resources
for Marathi we catalogue 999https://github.com/Adi2K/MarathiSwear a list of
profane words in Marathi and use this to find the fraction of profane words in
a tweet. For Hindi, we curate a list of profane words by collating and
appending to existing lists 101010https://github.com/neerajvashistha/online-
hate-speech-recog/blob/master/data/hi/Hinglish-Offensive-Text-
Classification/Hinglish_Profanity_List.csv, and use this to score each tweet.
As for the sentiment of the tweet, we incorporated off-the-shelf HuggingFace
models to obtain the positive, negative and neutral scores for a tweet
111111https://huggingface.co/l3cube-pune/MarathiSentiment
121212https://huggingface.co/cardiffnlp/twitter-xlm-roberta-base-sentiment.
Although the textual features improved the performance for Hindi only by a
small margin, for Marathi, manually extracted textual features helped in
achieving a significant boost.

For the Marathi Subtask 1, we experimented with a voting ensemble of the XLM-
Roberta with CNN Head using the following features:

  * •

Word Embedding + Fraction of Profane Words + Sentiment Polarity

  * •

Word Embedding + Sentiment Polarity

  * •

Word Embedding

However we noticed that the base model with the embedding and the textual
features performed better on the leaderboard.

(a) Model pipeline for hate detection in conversational threads for Subtask 2.

(b) Hierarchy of a conversation thread and its associated comments.

Figure 3: Model Pipeline and tweet conversation thread example for Subtask 2.

###  4.2 Subtask 2 : Identification of Conversational Hate-Speech in Code-
Mixed Languages (ICHCL)

The tweets for Subtask 2 are code mixed. While the Transformer based encoder
models have performed well on various monolingual NLU tasks, their performance
does not reach the same level on code mixed sentences. Multilingual
transformer based models, have been applied for various code mixed NLU tasks,
and have performed better than monolingual transformer based models [27]. For
this task, we use XLM-RoBERTa [16]. To capture the context and the tweet
itself, we modify the input in the following manner, where [CLS] , [SEP] are
part of the vocabulary of model, and are used to classify and take multiple
sentences as input, respectively.

[CLS] <Tweet text to be classified> [SEP] <context of parent tweet> [SEP]

Here, <Tweet text to be classified> is the text of the tweet/comment/reply
that is being classified, while <Context of parent tweet> is either just the
parent tweet or concatenation of parent tweet and comment, depending on
weather the text to be classified is a tweet or a comment or a reply. While
classifying a standalone tweet, the context is left empty. The Hindi corpus
used to train XLM-Roberta is in Devanagari script, while there is only a small
portion of the corpus which is in Romanised form. With the hypothesis that the
performance of model will improve if the Hindi tokens are in Devanagari
script, we used CSNLI tool 131313https://github.com/irshadbhat/csnli to
convert the Romanised tokens to Devanagari script. However, this normalisation
only had a marginal impact on the final performance of the model. We used
Huggingface’s Trainer API to train the XLM-R model, and the hyperparameters
were chosen using the hyperparameter search functionality offered by Trainer
API.

Table 2: Performance scores for each of the six subtasks in terms of their test accuracy percentage and Macro F1 scores. All the architectures that were experimented and tested out are tabulated here. We can observe form the results that XLM-R combined with CNN classifier head works best across the languages of Subtask 1, while for Subtask 2, XLM-R with normalised input text performs the best in our experiments. Language | Subtask | Method | Accuracy | Macro F1
---|---|---|---|---
English | A | XLM-R + CNN | 62.30 | 0.62
Ensemble | 79.94 | 0.78
XLM-R + CNN + Sentiment Scores | 81.03 | 0.79
English | B | XLM-R + CNN + Weighted loss | 60.50 | 0.53
Ensemble | 65.18 | 0.59
Hindi | A | MuRIL | 68.90 | 0.60
XLM-R Base | 74.00 | 0.76
XLM-R + CNN | 80.09 | 0.77
Hindi | B | MiniLM with Focal Loss | 72.64 | 0.51
Marathi | A | XLM-R Base | 84.16 | 0.86
Ensemble | 88.48 | 0.87
XLM-R + CNN | 88.64 | 0.87
Hi-En Code mix | 2 | XLM-R without norm | 67.58 | 0.67
XLM-R with norm | 69.36 | 0.70

###  4.3 Experiments

We used Huggingface Transformers [28] library for implementing the
classifiers. For hyper parameter tuning we use Optuna Framework
141414https://optuna.org/ library. Exploring multiple architectures
simultaneously, we also tried ensembling an odd number of models following a
majority rule based selection. For the English Subtask 1 we also did
ensembling with averaged softmax probabilities. However, the increase in
complexity of the classification pipeline did not necessarily improve
performance scores, considering the size and the distribution of the dataset
for Hindi and Marathi but helped in English. Table 2 captures the Accuracies
and F1 scores (corresponding to submissions made on the leaderboard) of all
our models for each of the subtasks.

##  5 Conclusion

In this paper, we presented our approaches for Hate Speech detection on Indian
Languages and code mix between Hindi-English using multilingual transformer
based encoder models. Although, in this work we have employed different models
to address individual language specific subtasks, a multi-task single model
based approach, which performs well across all the language pairs, would be an
interesting challenge, which we wish to explore as a future work. In addition
to this, as part of future work, we would like to improve the performance by
carrying out an additional step of domain adaptive pre-training of the encoder
models, and an efficient ensemble of multilingual encoder models.

###### Acknowledgements.

We would like to thank the organisers of HASOC’21 Shared task for addressing a
crucial problem of hate speech in Indian languages by releasing data
resources, and for the smooth conduct of the competition. We would also like
to specially thank all members of our research lab, PreCog, for the
constructive suggestions during the whole process.

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