# Measurement of $C\\!P$ violation in the phase space of
$B^{\pm}\rightarrow K^{+}K^{-}\pi^{\pm}$ and
$B^{\pm}\rightarrow\pi^{+}\pi^{-}\pi^{\pm}$ decays

LHCb collaboration
R. Aaij40, B. Adeva36, M. Adinolfi45, C. Adrover6, A. Affolder51, Z.
Ajaltouni5, J. Albrecht9, F. Alessio37, M. Alexander50, S. Ali40, G.
Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr24, S. Amato2, S. Amerio21, Y.
Amhis7, L. Anderlini17,f, J. Anderson39, R. Andreassen56, J.E. Andrews57, R.B.
Appleby53, O. Aquines Gutierrez10, F. Archilli18, A. Artamonov34, M. Artuso58,
E. Aslanides6, G. Auriemma24,m, M. Baalouch5, S. Bachmann11, J.J. Back47, A.
Badalov35, C. Baesso59, V. Balagura30, W. Baldini16, R.J. Barlow53, C.
Barschel37, S. Barsuk7, W. Barter46, Th. Bauer40, A. Bay38, J. Beddow50, F.
Bedeschi22, I. Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30, E. Ben-
Haim8, G. Bencivenni18, S. Benson49, J. Benton45, A. Berezhnoy31, R. Bernet39,
M.-O. Bettler46, M. van Beuzekom40, A. Bien11, S. Bifani44, T. Bird53, A.
Bizzeti17,h, P.M. Bjørnstad53, T. Blake37, F. Blanc38, J. Blouw10, S. Blusk58,
V. Bocci24, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi53, A.
Borgia58, T.J.V. Bowcock51, E. Bowen39, C. Bozzi16, T. Brambach9, J. van den
Brand41, J. Bressieux38, D. Brett53, M. Britsch10, T. Britton58, N.H. Brook45,
H. Brown51, A. Bursche39, G. Busetto21,q, J. Buytaert37, S. Cadeddu15, O.
Callot7, M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, D.
Campora Perez37, A. Carbone14,c, G. Carboni23,k, R. Cardinale19,i, A.
Cardini15, H. Carranza-Mejia49, L. Carson52, K. Carvalho Akiba2, G. Casse51,
L. Castillo Garcia37, M. Cattaneo37, Ch. Cauet9, R. Cenci57, M. Charles54, Ph.
Charpentier37, S.-F. Cheung54, N. Chiapolini39, M. Chrzaszcz39,25, K. Ciba37,
X. Cid Vidal37, G. Ciezarek52, P.E.L. Clarke49, M. Clemencic37, H.V. Cliff46,
J. Closier37, C. Coca28, V. Coco40, J. Cogan6, E. Cogneras5, P. Collins37, A.
Comerma-Montells35, A. Contu15,37, A. Cook45, M. Coombes45, S. Coquereau8, G.
Corti37, B. Couturier37, G.A. Cowan49, D.C. Craik47, M. Cruz Torres59, S.
Cunliffe52, R. Currie49, C. D’Ambrosio37, P. David8, P.N.Y. David40, A.
Davis56, I. De Bonis4, K. De Bruyn40, S. De Capua53, M. De Cian11, J.M. De
Miranda1, L. De Paula2, W. De Silva56, P. De Simone18, D. Decamp4, M.
Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach54, O. Deschamps5, F.
Dettori41, A. Di Canto11, H. Dijkstra37, M. Dogaru28, S. Donleavy51, F.
Dordei11, A. Dosil Suárez36, D. Dossett47, A. Dovbnya42, F. Dupertuis38, P.
Durante37, R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48, U. Egede52,
V. Egorychev30, S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U.
Eitschberger9, R. Ekelhof9, L. Eklund50,37, I. El Rifai5, Ch. Elsasser39, A.
Falabella14,e, C. Färber11, C. Farinelli40, S. Farry51, D. Ferguson49, V.
Fernandez Albor36, F. Ferreira Rodrigues1, M. Ferro-Luzzi37, S. Filippov32, M.
Fiore16,e, C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,i, R. Forty37, O.
Francisco2, M. Frank37, C. Frei37, M. Frosini17,37,f, E. Furfaro23,k, A.
Gallas Torreira36, D. Galli14,c, M. Gandelman2, P. Gandini58, Y. Gao3, J.
Garofoli58, P. Garosi53, J. Garra Tico46, L. Garrido35, C. Gaspar37, R.
Gauld54, E. Gersabeck11, M. Gersabeck53, T. Gershon47, Ph. Ghez4, V. Gibson46,
L. Giubega28, V.V. Gligorov37, C. Göbel59, D. Golubkov30, A. Golutvin52,30,37,
A. Gomes2, P. Gorbounov30,37, H. Gordon37, M. Grabalosa Gándara5, R. Graciani
Diaz35, L.A. Granado Cardoso37, E. Graugés35, G. Graziani17, A. Grecu28, E.
Greening54, S. Gregson46, P. Griffith44, L. Grillo11, O. Grünberg60, B. Gui58,
E. Gushchin32, Yu. Guz34,37, T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C.
Haen37, S.C. Haines46, S. Hall52, B. Hamilton57, T. Hampson45, S. Hansmann-
Menzemer11, N. Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37,
T. Head37, V. Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E.
van Herwijnen37, M. Heß60, A. Hicheur1, E. Hicks51, D. Hill54, M. Hoballah5,
C. Hombach53, W. Hulsbergen40, P. Hunt54, T. Huse51, N. Hussain54, D.
Hutchcroft51, D. Hynds50, V. Iakovenko43, M. Idzik26, P. Ilten12, R.
Jacobsson37, A. Jaeger11, E. Jans40, P. Jaton38, A. Jawahery57, F. Jing3, M.
John54, D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S.
Kandybei42, W. Kanso6, M. Karacson37, T.M. Karbach37, I.R. Kenyon44, T.
Ketel41, B. Khanji20, O. Kochebina7, I. Komarov38, R.F. Koopman41, P.
Koppenburg40, M. Korolev31, A. Kozlinskiy40, L. Kravchuk32, K. Kreplin11, M.
Kreps47, G. Krocker11, P. Krokovny33, F. Kruse9, M. Kucharczyk20,25,37,j, V.
Kudryavtsev33, K. Kurek27, T. Kvaratskheliya30,37, V.N. La Thi38, D.
Lacarrere37, G. Lafferty53, A. Lai15, D. Lambert49, R.W. Lambert41, E.
Lanciotti37, G. Lanfranchi18, C. Langenbruch37, T. Latham47, C. Lazzeroni44,
R. Le Gac6, J. van Leerdam40, J.-P. Lees4, R. Lefèvre5, A. Leflat31, J.
Lefrançois7, S. Leo22, O. Leroy6, T. Lesiak25, B. Leverington11, Y. Li3, L. Li
Gioi5, M. Liles51, R. Lindner37, C. Linn11, B. Liu3, G. Liu37, S. Lohn37, I.
Longstaff50, J.H. Lopes2, N. Lopez-March38, H. Lu3, D. Lucchesi21,q, J.
Luisier38, H. Luo49, O. Lupton54, F. Machefert7, I.V. Machikhiliyan30, F.
Maciuc28, O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, J. Maratas5,
U. Marconi14, P. Marino22,s, R. Märki38, J. Marks11, G. Martellotti24, A.
Martens8, A. Martín Sánchez7, M. Martinelli40, D. Martinez Santos41,37, D.
Martins Tostes2, A. Martynov31, A. Massafferri1, R. Matev37, Z. Mathe37, C.
Matteuzzi20, E. Maurice6, A. Mazurov16,37,e, J. McCarthy44, A. McNab53, R.
McNulty12, B. McSkelly51, B. Meadows56,54, F. Meier9, M. Meissner11, M.
Merk40, D.A. Milanes8, M.-N. Minard4, J. Molina Rodriguez59, S. Monteil5, D.
Moran53, P. Morawski25, A. Mordà6, M.J. Morello22,s, R. Mountain58, I. Mous40,
F. Muheim49, K. Müller39, R. Muresan28, B. Muryn26, B. Muster38, P. Naik45, T.
Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, S. Neubert37, N.
Neufeld37, A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,o, M. Nicol7, V.
Niess5, R. Niet9, N. Nikitin31, T. Nikodem11, A. Nomerotski54, A. Novoselov34,
A. Oblakowska-Mucha26, V. Obraztsov34, S. Oggero40, S. Ogilvy50, O.
Okhrimenko43, R. Oldeman15,d, M. Orlandea28, J.M. Otalora Goicochea2, P.
Owen52, A. Oyanguren35, B.K. Pal58, A. Palano13,b, M. Palutan18, J. Panman37,
A. Papanestis48, M. Pappagallo50, C. Parkes53, C.J. Parkinson52, G.
Passaleva17, G.D. Patel51, M. Patel52, G.N. Patrick48, C. Patrignani19,i, C.
Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pearce53, A. Pellegrino40, G.
Penso24,l, M. Pepe Altarelli37, S. Perazzini14,c, E. Perez Trigo36, A. Pérez-
Calero Yzquierdo35, P. Perret5, M. Perrin-Terrin6, L. Pescatore44, E. Pesen61,
G. Pessina20, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste
Olloqui35, B. Pietrzyk4, T. Pilař47, D. Pinci24, S. Playfer49, M. Plo
Casasus36, F. Polci8, G. Polok25, A. Poluektov47,33, E. Polycarpo2, A.
Popov34, D. Popov10, B. Popovici28, C. Potterat35, A. Powell54, J.
Prisciandaro38, A. Pritchard51, C. Prouve7, V. Pugatch43, A. Puig Navarro38,
G. Punzi22,r, W. Qian4, B. Rachwal25, J.H. Rademacker45, B.
Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N. Rauschmayr37, G. Raven41,
S. Redford54, S. Reichert53, M.M. Reid47, A.C. dos Reis1, S. Ricciardi48, A.
Richards52, K. Rinnert51, V. Rives Molina35, D.A. Roa Romero5, P. Robbe7, D.A.
Roberts57, A.B. Rodrigues1, E. Rodrigues53, P. Rodriguez Perez36, S. Roiser37,
V. Romanovsky34, A. Romero Vidal36, M. Rotondo21, J. Rouvinet38, T. Ruf37, F.
Ruffini22, H. Ruiz35, P. Ruiz Valls35, G. Sabatino24,k, J.J. Saborido Silva36,
N. Sagidova29, P. Sail50, B. Saitta15,d, V. Salustino Guimaraes2, B. Sanmartin
Sedes36, R. Santacesaria24, C. Santamarina Rios36, E. Santovetti23,k, M.
Sapunov6, A. Sarti18, C. Satriano24,m, A. Satta23, M. Savrie16,e, D.
Savrina30,31, M. Schiller41, H. Schindler37, M. Schlupp9, M. Schmelling10, B.
Schmidt37, O. Schneider38, A. Schopper37, M.-H. Schune7, R. Schwemmer37, B.
Sciascia18, A. Sciubba24, M. Seco36, A. Semennikov30, K. Senderowska26, I.
Sepp52, N. Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I.
Shapoval16,42,e, Y. Shcheglov29, T. Shears51, L. Shekhtman33, O. Shevchenko42,
V. Shevchenko30, A. Shires9, R. Silva Coutinho47, M. Sirendi46, N. Skidmore45,
T. Skwarnicki58, N.A. Smith51, E. Smith54,48, E. Smith52, J. Smith46, M.
Smith53, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro38, D. Souza45, B. Souza De
Paula2, B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S. Stahl11, O.
Steinkamp39, S. Stevenson54, S. Stoica28, S. Stone58, B. Storaci39, M.
Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56, W. Sutcliffe52, S.
Swientek9, V. Syropoulos41, M. Szczekowski27, P. Szczypka38,37, D. Szilard2,
T. Szumlak26, S. T’Jampens4, M. Teklishyn7, E. Teodorescu28, F. Teubert37, C.
Thomas54, E. Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin38, S. Tolk41,
D. Tonelli37, S. Topp-Joergensen54, N. Torr54, E. Tournefier4,52, S.
Tourneur38, M.T. Tran38, M. Tresch39, A. Tsaregorodtsev6, P. Tsopelas40, N.
Tuning40,37, M. Ubeda Garcia37, A. Ukleja27, A. Ustyuzhanin52,p, U. Uwer11, V.
Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P. Vazquez
Regueiro36, C. Vázquez Sierra36, S. Vecchi16, J.J. Velthuis45, M. Veltri17,g,
G. Veneziano38, M. Vesterinen37, B. Viaud7, D. Vieira2, X. Vilasis-
Cardona35,n, A. Vollhardt39, D. Volyanskyy10, D. Voong45, A. Vorobyev29, V.
Vorobyev33, C. Voß60, H. Voss10, R. Waldi60, C. Wallace47, R. Wallace12, S.
Wandernoth11, J. Wang58, D.R. Ward46, N.K. Watson44, A.D. Webber53, D.
Websdale52, M. Whitehead47, J. Wicht37, J. Wiechczynski25, D. Wiedner11, L.
Wiggers40, G. Wilkinson54, M.P. Williams47,48, M. Williams55, F.F. Wilson48,
J. Wimberley57, J. Wishahi9, W. Wislicki27, M. Witek25, G. Wormser7, S.A.
Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, Z. Xing58, Z. Yang3,
X. Yuan3, O. Yushchenko34, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L.
Zhang58, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, A. Zhokhov30, L. Zhong3, A.
Zvyagin37.
1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
42NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
44University of Birmingham, Birmingham, United Kingdom
45H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
46Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
50School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
54Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, MA, United States
56University of Cincinnati, Cincinnati, OH, United States
57University of Maryland, College Park, MD, United States
58Syracuse University, Syracuse, NY, United States
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
60Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
61Celal Bayar University, Manisa, Turkey, associated to 37

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
bUniversità di Bari, Bari, Italy
cUniversità di Bologna, Bologna, Italy
dUniversità di Cagliari, Cagliari, Italy
eUniversità di Ferrara, Ferrara, Italy
fUniversità di Firenze, Firenze, Italy
gUniversità di Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam
pInstitute of Physics and Technology, Moscow, Russia
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy

###### Abstract

The charmless decays $B^{\pm}\rightarrow K^{+}K^{-}\pi^{\pm}$ and
$B^{\pm}\rightarrow\pi^{+}\pi^{-}\pi^{\pm}$ are reconstructed in a data set,
corresponding to an integrated luminosity of 1.0 fb-1 of $pp$ collisions at a
center-of-mass energy of 7 TeV, collected by LHCb in 2011. The inclusive
charge asymmetries of these modes are measured to be
$A_{C\\!P}(B^{\pm}\rightarrow K^{+}K^{-}\pi^{\pm})=-0.141\pm
0.040\mathrm{\,(stat)}\pm 0.018\mathrm{\,(syst)}\pm
0.007({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm})$ and
$A_{C\\!P}(B^{\pm}\rightarrow\pi^{+}\pi^{-}\pi^{\pm})=0.117\pm
0.021\mathrm{\,(stat)}\pm 0.009\mathrm{\,(syst)}\pm
0.007({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm})$, where the third
uncertainty is due to the $C\\!P$ asymmetry of the
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ reference
mode. In addition to the inclusive $C\\!P$ asymmetries, larger asymmetries are
observed in localized regions of phase space.

###### pacs:

13.25.Hw,11.30.Er

The LHCb collaboration

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 |  |
---|---|---
|  | CERN-PH-EP-2013-190
|  | LHCb-PAPER-2013-051
|  | 17 October 2013

© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.

Submitted to Phys. Rev. Lett.

Charmless decays of $B$ mesons to three hadrons are dominated by quasi-two-
body processes involving intermediate resonant states. The rich interference
pattern present in such decays makes them favorable for the investigation of
charge asymmetries that are localized in the phase space Miranda1 ; Miranda2 .
The large samples of charmless $B$ decays collected by the LHCb experiment
allow direct $C\\!P$ violation to be measured in regions of phase space. In
previous measurements of this type, the phase spaces of ${B^{\pm}\to
K^{\pm}K^{+}K^{-}}$ and ${B^{\pm}\to K^{\pm}\pi^{+}\pi^{-}}$ decays were
observed to have regions of large local asymmetries LHCb-PAPER-2013-027 .
Concerning baryonic modes, no significant effects have been observed in either
${B^{\pm}\to p\bar{p}K^{\pm}}$ or ${B^{\pm}\to p\bar{p}\pi^{\pm}}$ decays
LHCB-PAPER-2013-031 . Large $C\\!P$-violating asymmetries have also been
observed in charmless two-body $B$ meson decays such as $B^{0}\to
K^{+}\pi^{-}$ and $B^{0}_{s}\to K^{-}\pi^{+}$ (and the corresponding $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ decays) LHCb-PAPER-2013-018 .

Some recent efforts have been made to understand the origin of the large
asymmetries. For direct $C\\!P$ violation to occur, two interfering amplitudes
with different weak and strong phases must be involved in the decay process
BSS1979 . Interference between intermediate states of the decay can introduce
large strong phase differences, and is one mechanism for explaining local
asymmetries in the phase space PhysRevD.87.076007 ; Bhattacharya:2013cvn .
Another explanation focuses on final-state $KK\leftrightarrow\pi\pi$
rescattering, which can occur between decay channels with the same flavor
quantum numbers LHCb-PAPER-2013-027 ; Bhattacharya:2013cvn ; IgnacioCPT .
Invariance of $C\\!PT$ symmetry constrains hadron rescattering so that the sum
of the partial decay widths, for all channels with the same final-state
quantum numbers related by the S matrix, must be equal for charge-conjugated
decays. Effects of SU(3) flavor symmetry breaking have also been investigated
and partially explain the observed patterns Xu:2013dta ; Bhattacharya:2013cvn
; Gronau:2013mda .

The ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ decay is interesting because $s\bar{s}$
resonant contributions are strongly suppressed ozzi1 ; ozzi2 ; ozzi4 .
Recently, LHCb reported an upper limit on the $\phi$ contribution to be
$\mathcal{B}(B^{\pm}\to\phi\pi^{\pm})<1.5\times 10^{-7}$ at the 90% confidence
level LHCB-PAPER-2013-048 . The lack of $K^{+}K^{-}$ resonant contributions
makes the ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ decay a good probe for
rescattering from decays with pions. The ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$
mode, on the other hand, has large resonant contributions, as shown in an
amplitude analysis by the BaBar collaboration, which measured the inclusive
$C\\!P$ asymmetry to be $(0.03\pm 0.06)$ BaBarpipipi . For ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays, the inclusive $C\\!P$-violating asymmetry was
measured by the BaBar collaboration to be ($0.00\pm 0.10$) BaBarkkpi , from a
comparison of $B^{+}$ and $B^{-}$ sample fits. Both results are compatible
with the no $C\\!P$-violation hypothesis.

In this Letter we report measurements of the inclusive $C\\!P$-violating
asymmetries for ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ and ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays. The $C\\!P$ asymmetry in $B^{\pm}$ decays to a
final state $f^{\pm}$ is defined as

$A_{C\\!P}(B^{\pm}\to f^{\pm})\equiv\Phi[\Gamma(B^{-}\to
f^{-}),\Gamma(B^{+}\to f^{+})],$ (1)

where $\Phi[X,Y]\equiv(X-Y)/(X+Y)$ is the asymmetry function, $\Gamma$ is the
decay width, and the final states $f^{\pm}$ are $\pi^{+}\pi^{-}\pi^{\pm}$ or
$K^{+}K^{-}\pi^{\pm}$. The asymmetry distributions across the phase space are
also investigated.

The LHCb detector Alves:2008zz  is a single-arm forward spectrometer covering
the pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The analysis is based on $pp$ collision data,
corresponding to an integrated luminosity of 1.0 fb-1, collected in 2011 at a
center-of-mass energy of 7 TeV.

Figure 1: Invariant mass spectra of (a) ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$
decays and (b) ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ decays. The left panel in
each figure shows the $B^{-}$ modes and the right panel shows the $B^{+}$
modes. The results of the unbinned maximum likelihood fits are overlaid. The
main components of the fit are also shown.

Events are selected by a trigger LHCb-DP-2012-004  that consists of a hardware
stage, based on information from a calorimeter system and five muon stations,
followed by a software stage, which applies a full event reconstruction.
Candidate events are first required to pass the hardware trigger, which
selects particles with a large transverse energy. The software trigger
requires a two-, three- or four-track secondary vertex with a high sum of the
transverse momenta, $p_{\rm T}$, of the tracks and significant displacement
from the primary $pp$ interaction vertices (PVs). At least one track should
have $\mbox{$p_{\rm T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and
$\chi^{2}_{\rm IP}$ with respect to any primary interaction greater than 16,
where $\chi^{2}_{\rm IP}$ is defined as the difference between the $\chi^{2}$
of a given PV reconstructed with and without the considered track, and IP is
the impact parameter. A multivariate algorithm BBDT  is used for the
identification of secondary vertices consistent with the decay of a $b$
hadron.

Further criteria are applied offline to select $B$ mesons and suppress the
combinatorial background. The $B^{\pm}$ decay products are required to satisfy
a set of selection criteria on their momenta, their $p_{\rm T}$, the
$\chi^{2}_{\rm IP}$ of the final-state tracks, and the distance of closest
approach between any two tracks. The $B$ candidates are required to have
$\mbox{$p_{\rm T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, $\chi^{2}_{\rm
IP}<10$ (defined by projecting the $B$ candidate trajectory backwards from its
decay vertex), decay vertex $\chi^{2}<12$, and decay vertex displacement from
any PV greater than 3 mm. Additional requirements are applied to variables
related to the $B$-meson production and decay, such as the angle $\theta$
between the $B$-candidate momentum and the direction of flight from the
primary vertex to the decay vertex, $\cos(\theta)>0.99998$. Final-state kaons
and pions are further selected using particle identification information,
provided by two ring-imaging Cherenkov detectors LHCb-DP-2012-003 , and are
required to be incompatible with a muon LHCb-DP-2013-001 . The kinematic
selection is common to both decay channels, while the particle identification
selection is specific to each final state. Charm contributions are removed by
excluding the regions of $\pm 30{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
around the world average value of the $D^{0}$ mass PDG2012  in the two-body
invariant masses $m_{\pi^{+}\pi^{-}}$, $m_{K^{\pm}\pi^{\mp}}$ and
$m_{K^{+}K^{-}}$.

The simulated events used in this analysis are generated using Pythia 6.4
Sjostrand:2006za  with a specific LHCb configuration LHCb-PROC-2010-056 .
Decays of hadronic particles are produced by EvtGen Lange:2001uf , in which
final-state radiation is generated using Photos Golonka:2005pn . The
interaction of the generated particles with the detector and its response are
implemented using the Geant4 toolkit Allison:2006ve ; *Agostinelli:2002hh as
described in Ref. LHCb-PROC-2011-006 .

Unbinned extended maximum likelihood fits to the mass spectra of the selected
$B^{\pm}$ candidates are performed to obtain the signal yields and raw
asymmetries. The ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ and
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ signal components are parametrized by a
Cruijff function Cruijff  with equal left and right widths and different
radiative tails to account for the asymmetric effect of final-state radiation
on the signal shape. The means and widths are left to float in the fit, while
the tail parameters are fixed to the values obtained from simulation. The
combinatorial background is described by an exponential distribution whose
parameter is left free in the fit. The backgrounds due to partially
reconstructed four-body $B$ decays are parametrized by an ARGUS distribution
Argus  convolved with a Gaussian resolution function. For
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ decays the shape and yield parameters
describing the backgrounds are varied in the fit, while for ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays they are taken from simulation, due to a further
contribution from four-body $B^{0}_{s}$ decays such as $B^{0}_{s}\to
D^{-}_{s}(K^{+}K^{-}\pi^{-})\pi^{+}$. We define peaking backgrounds as decay
modes with one misidentified particle, namely the channels ${B^{\pm}\to
K^{\pm}\pi^{+}\pi^{-}}$ for the ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ mode,
and ${B^{\pm}\to K^{\pm}\pi^{+}\pi^{-}}$ and ${B^{\pm}\to K^{\pm}K^{+}K^{-}}$
for the ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ mode. The shapes and yields of the
peaking backgrounds are obtained from simulation. The yields of the peaking
and partially reconstructed background components are constrained to be equal
for $B^{+}$ and $B^{-}$ decays. The invariant mass spectra of the ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ and ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ candidates are
shown in Fig. 1.

The signal yields obtained are $N(KK\pi)=1870\pm 133$ and
$N(\pi\pi\pi)=4904\pm 148$, and the raw asymmetries are $A_{\rm
raw}(K\\!K\pi)=-0.143\pm 0.040$ and $A_{\rm raw}(\pi\pi\pi)=0.124\pm 0.020$,
where the uncertainties are statistical. The $C\\!P$ asymmetries are expressed
in terms of the measured raw asymmetries, corrected for effects induced by the
detector acceptance and interactions of final-state pions with matter $A_{\rm
D}(\pi^{\pm})$, as well as for a possible $B$-meson production asymmetry
$A_{\rm P}(B^{\pm})$,

$\\!\\!\\!A_{C\\!P}\\!=\\!A_{\rm raw}\\!-\\!A_{\rm D}(\pi^{\pm})\\!-\\!A_{\rm
P}(B^{\pm}).$ (2)

The pion detection asymmetry, $A_{\rm D}(\pi^{\pm})=0.0000\pm 0.0025$, has
been previously measured by LHCb LHCb-PAPER-2012-009 . The production
asymmetry $A_{\rm P}(B^{\pm})$ is measured from a data sample of approximately
$6.3\times 10^{4}$ $B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}(\mu^{+}\mu^{-})K^{\pm}$ decays. The
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ sample
passes the same trigger, kinematic, and kaon particle identification selection
criteria as the signal samples, and it has a similar event topology. The
$A_{\rm P}(B^{\pm})$ term is obtained from the raw asymmetry of the
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ mode as

$A_{\rm P}(B^{\pm})=A_{\rm raw}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K)-A_{C\\!P}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K)-A_{\rm
D}(K^{\pm}),$ (3)

where $A_{C\\!P}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K)=0.001\pm
0.007$ PDG2012  is the world average $C\\!P$ asymmetry of
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ decays, and
$A_{\rm D}(K^{\pm})=-0.010\pm 0.003$ is the kaon interaction asymmetry
obtained from $D^{0}\to K^{\pm}\pi^{\mp}$ and $D^{0}\to K^{+}K^{-}$ decays
LHCb-PAPER-2011-029 , and corrected for $A_{\rm D}(\pi^{\pm})$. The $C\\!P$
asymmetries of the ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ and
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ channels are then determined using Eqs.
2 and 3.

Figure 2:  Asymmetries of the number of events (including signal and
background) in bins of the Dalitz plot, $A_{\rm raw}^{N}$, for (a)
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ and (b) ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays. The inset figures show the projections of the
number of events in bins of (a) the $m^{2}_{\pi^{+}\pi^{-}\,{\rm low}}$
variable for $m^{2}_{\pi^{+}\pi^{-}\,{\rm
high}}>15{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and (b) the
$m^{2}_{K^{+}K^{-}}$ variable. The distributions are not corrected for
efficiency.

Since the detector efficiencies for the signal modes are not uniform across
the Dalitz plot, and the raw asymmetries are also not uniformly distributed,
an acceptance correction is applied to the integrated raw asymmetries. It is
determined by the ratio between the $B^{-}$ and $B^{+}$ average efficiencies
in simulated events, reweighted to reproduce the population of signal data
over the phase space. Furthermore, the detector acceptance and reconstruction
depend on the trigger selection. The efficiency of the hadronic hardware
trigger is found to have a small charge asymmetry for kaons. Therefore, the
data are divided into two samples: events with candidates selected by the
hadronic trigger and events selected by other triggers independently of the
signal candidate. The acceptance correction and subtraction of the $A_{\rm
P}(B^{\pm})$ term is performed separately for each trigger configuration. The
trigger-averaged value of the production asymmetry is $A_{\rm
P}(B^{\pm})=-0.004\pm 0.004$, where the uncertainty is statistical only. The
integrated $C\\!P$ asymmetries are then the weighted averages of the $C\\!P$
asymmetries for the two trigger samples.

The methods used in estimating the systematic uncertainties of the signal
model, combinatorial background, peaking background, and acceptance correction
are the same as those used in Ref. LHCb-PAPER-2013-027 . For ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays, we also evaluate a systematic uncertainty due to
the partially reconstructed background model by varying the mean and
resolution according to the difference between simulation and data obtained
from the signal component. The $A_{\rm D}(\pi^{\pm})$ and $A_{\rm D}(K^{\pm})$
uncertainties are included as systematic uncertainties related to the
procedure. A systematic uncertainty is also evaluated to account for the
difference in kaon kinematics between the $B^{\pm}$ and $D^{0}$ decays. The
systematic uncertainties for the measurements of $A_{C\\!P}({B^{\pm}\to
K^{+}K^{-}\pi^{\pm}})$ and $A_{C\\!P}({B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}})$
are summarized in Table 1.

The results obtained for the inclusive $C\\!P$ asymmetries of the ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ and ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ decays are

$\displaystyle A_{C\\!P}({B^{\pm}\to K^{+}K^{-}\pi^{\pm}})\\!$
$\displaystyle=$ $\displaystyle\\!-0.141\pm 0.040\pm 0.018\pm 0.007,$
$\displaystyle A_{C\\!P}({B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}})\\!$
$\displaystyle=$ $\displaystyle\\!0.117\pm 0.021\pm 0.009\pm 0.007,$

where the first uncertainty is statistical, the second is the experimental
systematic, and the third is due to the $C\\!P$ asymmetry of the
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ reference
mode PDG2012 . The significances of the inclusive charge asymmetries,
calculated by dividing the central values by the sum in quadrature of the
statistical and both systematic uncertainties, are 3.2 standard deviations
($\sigma$) for ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ and $4.9\sigma$ for
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ decays.

Table 1:  Systematic uncertainties on $A_{C\\!P}({B^{\pm}\to K^{+}K^{-}\pi^{\pm}})$ and $A_{C\\!P}({B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}})$. The total systematic uncertainties are the sum in quadrature of the individual contributions. Systematic uncertainty | $A_{C\\!P}(K\\!K\pi)$ | $A_{C\\!P}(\pi\pi\pi)$
---|---|---
Signal model |  0.001 |  0.0005
Combinatorial background |  0.003 |  0.0008
Peaking background | $\;\;\;\,0.001$ | $\;\;\;\,0.0025$
Acceptance |  0.014 |  0.0032
Part. rec. background |  0.005 |  –
$A_{\rm D}(\pi^{\pm})$ uncertainty |  0.003 |  0.0025
$A_{\rm D}(K^{\pm})$ uncertainty |  0.003 |  0.0032
$A_{\rm D}(K^{\pm})$ kaon kinematics |  0.008 |  0.0075
Total |  0.018 |  0.0094

Figure 3: Invariant mass spectra of (a) ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$
decays in the region $m^{2}_{\pi^{+}\pi^{-}\,{\rm
low}}<0.4{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and
$m^{2}_{\pi^{+}\pi^{-}\,{\rm
high}}>15{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$, and (b) ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays in the region
$m^{2}_{K^{+}K^{-}}<1.5{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$. The left
panel in each figure shows the $B^{-}$ modes and the right panel shows the
$B^{+}$ modes. The results of the unbinned maximum likelihood fits are
overlaid.

In addition to the inclusive charge asymmetries, we study the asymmetry
distributions in the two-dimensional phase space of two-body invariant masses.
The Dalitz plot distributions in the signal region, defined as the three-body
invariant mass region within two Gaussian widths from the signal peak, are
divided into bins with approximately equal numbers of events in the combined
$B^{-}$ and $B^{+}$ samples. Figure 2 shows the raw asymmetries (not corrected
for efficiency), $A_{\rm raw}^{N}=\Phi[N^{-},N^{+}]$, computed using the
number of negative ($N^{-}$) and positive ($N^{+}$) entries in each bin of the
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ and ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$
Dalitz plots. The ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ Dalitz plot is
symmetrized and its two-body invariant mass squared variables are defined as
$m^{2}_{\pi^{+}\pi^{-}\,{\rm low}}<m^{2}_{\pi^{+}\pi^{-}\,{\rm high}}$. The
$A_{\rm raw}^{N}$ distribution in the Dalitz plot of the
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ mode reveals an asymmetry concentrated
at low values of $m^{2}_{\pi^{+}\pi^{-}\,{\rm low}}$ and high values of
$m^{2}_{\pi^{+}\pi^{-}\,{\rm high}}$. The distribution of the projection of
the number of events onto the $m^{2}_{\pi^{+}\pi^{-}\,{\rm low}}$ invariant
mass (inset in Fig. 2(a)) shows that this asymmetry is located in the region
$m^{2}_{\pi^{+}\pi^{-}\,{\rm
low}}<0.4{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and
$m^{2}_{\pi^{+}\pi^{-}\,{\rm
high}}>15{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$. For ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ we identify a negative asymmetry located in the low
$K^{+}K^{-}$ invariant mass region. This can be seen also in the inset figure
of the $K^{+}K^{-}$ invariant mass projection, where there is an excess of
$B^{+}$ candidates for
$m^{2}_{K^{+}K^{-}}<1.5{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$. Although
${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ has no $\phi(1020)$ contribution LHCB-
PAPER-2013-048 ; phiBR , a clear structure is observed. This structure was
also seen by the BaBar collaboration BaBarkkpi  but was not studied separately
for $B^{-}$ and $B^{+}$ components. No significant asymmetry is present in the
low-mass region of the ${K^{\pm}\pi^{\mp}}$ invariant mass projection.

The $C\\!P$ asymmetries are further studied in the regions where large raw
asymmetries are found. The regions are defined as $m^{2}_{\pi^{+}\pi^{-}\,{\rm
high}}>15{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ and
$m^{2}_{\pi^{+}\pi^{-}\,{\rm
low}}<0.4{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ for the
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ mode, and
$m^{2}_{K^{+}K^{-}}<1.5{\mathrm{\,Ge\kern-1.00006ptV^{2}\\!/}c^{4}}$ for the
${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ mode. Unbinned extended maximum likelihood
fits are performed to the mass spectra of the candidates in these regions,
using the same models as for the global fits. The spectra are shown in Fig. 3.
The resulting signal yields and raw asymmetries for the two regions are
${N^{\mathrm{reg}}(K\\!K\pi)=342\pm 28}$ and ${A_{\rm
raw}^{\mathrm{reg}}(K\\!K\pi)=-0.658\pm 0.070}$ for the ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ mode, and ${N^{\mathrm{reg}}(\pi\pi\pi)=229\pm 20}$ and
${A_{\rm raw}^{\mathrm{reg}}(\pi\pi\pi)=0.555\pm 0.082}$ for the
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ mode. The $C\\!P$ asymmetries are
obtained from the raw asymmetries using Eqs. 2 and 3 and applying an
acceptance correction. Systematic uncertainties are estimated due to the
signal models, acceptance correction and binning choice in the region, the
$A_{\rm D}(\pi^{\pm})$ and $A_{\rm P}(B^{\pm})$ statistical uncertainties and
the $A_{\rm D}(K^{\pm})$ kaon kinematics. The local charge asymmetries for the
two regions are measured to be

$\displaystyle A_{C\\!P}^{\mathrm{reg}}({B^{\pm}\to K^{+}K^{-}\pi^{\pm}})\\!$
$\displaystyle=$ $\displaystyle\\!-0.648\pm 0.070\pm 0.013\pm 0.007,$
$\displaystyle
A_{C\\!P}^{\mathrm{reg}}({B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}})\\!$
$\displaystyle=$ $\displaystyle\\!0.584\pm 0.082\pm 0.027\pm 0.007,$

where the first uncertainty is statistical, the second is the experimental
systematic and the third is due to the $C\\!P$ asymmetry of the
${B^{\pm}\to{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{\pm}}$ reference
mode PDG2012 .

In conclusion, we have found the first evidence of inclusive $C\\!P$
asymmetries of the ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ and
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ modes with significances of $3.2\sigma$
and $4.9\sigma$, respectively. The results are consistent with those measured
by the BaBar collaboration BaBarkkpi ; BaBarpipipi . These charge asymmetries
are not uniformly distributed in the phase space. For ${B^{\pm}\to
K^{+}K^{-}\pi^{\pm}}$ decays, where no significant resonant contribution is
expected, we observe a very large negative asymmetry concentrated in a
restricted region of the phase space in the low $K^{+}K^{-}$ invariant mass.
For ${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ decays, a large positive asymmetry
is measured in the low $m^{2}_{\pi^{+}\pi^{-}\,{\rm low}}$ and high
$m^{2}_{\pi^{+}\pi^{-}\,{\rm high}}$ phase-space region, not clearly
associated to a resonant state. The evidence presented here for $C\\!P$
violation in ${B^{\pm}\to K^{+}K^{-}\pi^{\pm}}$ and
${B^{\pm}\to\pi^{+}\pi^{-}\pi^{\pm}}$ decays, along with the recent evidence
for $C\\!P$ violation in ${B^{\pm}\to K^{\pm}\pi^{+}\pi^{-}}$ and ${B^{\pm}\to
K^{\pm}K^{+}K^{-}}$ decays LHCb-PAPER-2013-027  and recent theoretical
developments Bhattacharya:2013cvn ; IgnacioCPT ; Xu:2013dta ;
PhysRevD.87.076007 , indicate new mechanisms for $C\\!P$ asymmetries, which
should be incorporated in models for future amplitude analyses of charmless
three-body $B$ decays.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC
(China); CNRS/IN2P3 and Region Auvergne (France); BMBF, DFG, HGF and MPG
(Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR
(Poland); MEN/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov
Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER
(Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We
also acknowledge the support received from the ERC under FP7. The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by
Yandex LLC (Russia), as well as to the communities behind the multiple open
source software packages that we depend on.

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