Zvyagin37 LHCb Collaboration 1 Centro Brasileiro de Pesquisas Físicas CBPF, Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro UFRJ, Rio de Janeiro, Brazil 3 Center for High
Trang 1Measurement of CP Violation in the Phase Space
of B → KþK−π and B → πþπ−π Decays
R Aaij,40B Adeva,36M Adinolfi,45C Adrover,6A Affolder,51Z Ajaltouni,5J Albrecht,9F Alessio,37M Alexander,50S Ali,40G Alkhazov,29P Alvarez Cartelle,36 A A Alves Jr.,24 S Amato,2 S Amerio,21 Y Amhis,7 L Anderlini,17,a J Anderson,39R Andreassen,56J E Andrews,57R B Appleby,53O Aquines Gutierrez,10F Archilli,18A Artamonov,34M Artuso,58E Aslanides,6 G Auriemma,24,bM Baalouch,5S Bachmann,11 J J Back,47A Badalov,35C Baesso,59V Balagura,30W Baldini,16R J Barlow,53C Barschel,37S Barsuk,7 W Barter,46Th Bauer,40A Bay,38J Beddow,50F Bedeschi,22I Bediaga,1S Belogurov,30K Belous,34I Belyaev,30E Ben-Haim,8G Bencivenni,18S Benson,49J Benton,45
A Berezhnoy,31R Bernet,39M.-O Bettler,46M van Beuzekom,40A Bien,11S Bifani,44T Bird,53A Bizzeti,17,cP.M Bjørnstad,53T Blake,37F Blanc,38 J Blouw,10S Blusk,58 V Bocci,24A Bondar,33N Bondar,29 W Bonivento,15S Borghi,53A Borgia,58T J V Bowcock,51E Bowen,39C Bozzi,16T Brambach,9J van den Brand,41J Bressieux,38D Brett,53M Britsch,10T Britton,58N H Brook,45H Brown,51A Bursche,39G Busetto,21,dJ Buytaert,37S Cadeddu,15O Callot,7 M Calvi,20,e M Calvo Gomez,35,fA Camboni,35 P Campana,18,37D Campora Perez,37A Carbone,14,g G Carboni,23,hR Cardinale,19,iA Cardini,15H Carranza-Mejia,49L Carson,52K Carvalho Akiba,2G Casse,51L Castillo Garcia,37M Cattaneo,37 Ch Cauet,9R Cenci,57M Charles,54Ph Charpentier,37 S.-F Cheung,54N Chiapolini,39M Chrzaszcz,39,25K Ciba,37X Cid Vidal,37G Ciezarek,52P E L Clarke,49M Clemencic,37H V Cliff,46J Closier,37C Coca,28V Coco,40J Cogan,6E Cogneras,5P Collins,37A Comerma-Montells,35A Contu,15,37A Cook,45M Coombes,45
S Coquereau,8 G Corti,37B Couturier,37G A Cowan,49D C Craik,47M Cruz Torres,59S Cunliffe,52R Currie,49C
D’Ambrosio,37
P David,8P N Y David,40A Davis,56I De Bonis,4K De Bruyn,40S De Capua,53M De Cian,11J M De Miranda,1L De Paula,2 W De Silva,56P De Simone,18D Decamp,4M Deckenhoff,9 L Del Buono,8N Déléage,4 D Derkach,54O Deschamps,5F Dettori,41A Di Canto,11H Dijkstra,37M Dogaru,28S Donleavy,51F Dordei,11A Dosil Suárez,36D Dossett,47A Dovbnya,42F Dupertuis,38P Durante,37R Dzhelyadin,34A Dziurda,25A Dzyuba,29S Easo,48
U Egede,52V Egorychev,30S Eidelman,33D van Eijk,40S Eisenhardt,49U Eitschberger,9R Ekelhof,9L Eklund,50,37I
El Rifai,5 Ch Elsasser,39A Falabella,14,jC Färber,11C Farinelli,40S Farry,51D Ferguson,49V Fernandez Albor,36F Ferreira Rodrigues,1M Ferro-Luzzi,37S Filippov,32M Fiore,16,jC Fitzpatrick,37M Fontana,10F Fontanelli,19,iR Forty,37
O Francisco,2M Frank,37C Frei,37M Frosini,17,37,aE Furfaro,23,hA Gallas Torreira,36D Galli,14,gM Gandelman,2P Gandini,58Y Gao,3J Garofoli,58P Garosi,53J Garra Tico,46L Garrido,35C Gaspar,37R Gauld,54E Gersabeck,11M Gersabeck,53 T Gershon,47Ph Ghez,4 V Gibson,46L Giubega,28V V Gligorov,37C Göbel,59 D Golubkov,30A Golutvin,52,30,37A Gomes,2 P Gorbounov,30,37 H Gordon,37M Grabalosa Gándara,5R Graciani Diaz,35L.A Granado Cardoso,37E Graugés,35G Graziani,17A Grecu,28E Greening,54S Gregson,46P Griffith,44L Grillo,11O Grünberg,60B Gui,58E Gushchin,32Yu Guz,34,37 T Gys,37C Hadjivasiliou,58G Haefeli,38C Haen,37S C Haines,46S Hall,52B Hamilton,57T Hampson,45S Hansmann-Menzemer,11N Harnew,54S T Harnew,45J Harrison,53T Hartmann,60J He,37
T Head,37V Heijne,40K Hennessy,51P Henrard,5J.A Hernando Morata,36E van Herwijnen,37M Heß,60A Hicheur,1E Hicks,51D Hill,54M Hoballah,5C Hombach,53W Hulsbergen,40P Hunt,54T Huse,51N Hussain,54D Hutchcroft,51D Hynds,50V Iakovenko,43M Idzik,26P Ilten,12R Jacobsson,37A Jaeger,11E Jans,40P Jaton,38A Jawahery,57F Jing,3M John,54D Johnson,54C R Jones,46C Joram,37B Jost,37M Kaballo,9S Kandybei,42W Kanso,6M Karacson,37T M Karbach,37I R Kenyon,44T Ketel,41B Khanji,20O Kochebina,7I Komarov,38R F Koopman,41P Koppenburg,40M Korolev,31A Kozlinskiy,40 L Kravchuk,32K Kreplin,11M Kreps,47G Krocker,11P Krokovny,33F Kruse,9 M Kucharczyk,20,25,37,eV Kudryavtsev,33K Kurek,27T Kvaratskheliya,30,37V N La Thi,38D Lacarrere,37G Lafferty,53A Lai,15D Lambert,49R W Lambert,41E Lanciotti,37G Lanfranchi,18C Langenbruch,37T Latham,47C Lazzeroni,44R Le Gac,6J van Leerdam,40J.-P Lees,4 R Lefèvre,5A Leflat,31J Lefrançois,7 S Leo,22O Leroy,6 T Lesiak,25B Leverington,11Y Li,3 L Li Gioi,5 M Liles,51R Lindner,37C Linn,11B Liu,3G Liu,37S Lohn,37I Longstaff,50J H Lopes,2N Lopez-March,38H Lu,3D Lucchesi,21,dJ Luisier,38H Luo,49O Lupton,54F Machefert,7I V Machikhiliyan,30
F Maciuc,28O Maev,29,37S Malde,54G Manca,15,kG Mancinelli,6J Maratas,5U Marconi,14P Marino,22,lR Märki,38J Marks,11G Martellotti,24A Martens,8A Martín Sánchez,7M Martinelli,40D Martinez Santos,41,37D Martins Tostes,2A Martynov,31A Massafferri,1 R Matev,37Z Mathe,37C Matteuzzi,20E Maurice,6 A Mazurov,16,37,jJ McCarthy,44 A McNab,53R McNulty,12B McSkelly,51 B Meadows,56,54F Meier,9 M Meissner,11M Merk,40D A Milanes,8 M.-N Minard,4J Molina Rodriguez,59S Monteil,5D Moran,53P Morawski,25A Mordà,6M J Morello,22,lR Mountain,58I Mous,40F Muheim,49K Müller,39R Muresan,28B Muryn,26B Muster,38P Naik,45T Nakada,38R Nandakumar,48I PRL 112, 011801 (2014)
Trang 2Nasteva,1M Needham,49S Neubert,37N Neufeld,37A D Nguyen,38T D Nguyen,38C Nguyen-Mau,38,mM Nicol,7V Niess,5R Niet,9N Nikitin,31T Nikodem,11A Nomerotski,54A Novoselov,34A Oblakowska-Mucha,26V Obraztsov,34S Oggero,40S Ogilvy,50O Okhrimenko,43R Oldeman,15,kM Orlandea,28J.M Otalora Goicochea,2 P Owen,52A Oyanguren,35B K Pal,58A Palano,13,nM Palutan,18J Panman,37A Papanestis,48M Pappagallo,50C Parkes,53C J Parkinson,52G Passaleva,17 G D Patel,51M Patel,52G N Patrick,48C Patrignani,19,iC Pavel-Nicorescu,28A Pazos Alvarez,36A Pearce,53A Pellegrino,40G Penso,24,oM Pepe Altarelli,37S Perazzini,14,gE Perez Trigo,36A Pérez-Calero Yzquierdo,35P Perret,5M Perrin-Terrin,6L Pescatore,44E Pesen,61G Pessina,20K Petridis,52A Petrolini,19,iA Phan,58
E Picatoste Olloqui,35B Pietrzyk,4 T Pilař,47
D Pinci,24S Playfer,49M Plo Casasus,36F Polci,8 G Polok,25A Poluektov,47,33 E Polycarpo,2 A Popov,34 D Popov,10B Popovici,28 C Potterat,35A Powell,54J Prisciandaro,38 A Pritchard,51C Prouve,7 V Pugatch,43 A Puig Navarro,38G Punzi,22,pW Qian,4 B Rachwal,25 J H Rademacker,45 B Rakotomiaramanana,38M S Rangel,2I Raniuk,42N Rauschmayr,37G Raven,41S Redford,54S Reichert,53M M Reid,47
A C dos Reis,1 S Ricciardi,48A Richards,52K Rinnert,51V Rives Molina,35D A Roa Romero,5 P Robbe,7 D A Roberts,57A B Rodrigues,1E Rodrigues,53P Rodriguez Perez,36S Roiser,37V Romanovsky,34A Romero Vidal,36M Rotondo,21J Rouvinet,38T Ruf,37F Ruffini,22H Ruiz,35P Ruiz Valls,35G Sabatino,24,hJ J Saborido Silva,36N Sagidova,29P Sail,50B Saitta,15,kV Salustino Guimaraes,2B Sanmartin Sedes,36R Santacesaria,24C Santamarina Rios,36
E Santovetti,23,hM Sapunov,6 A Sarti,18C Satriano,24,b A Satta,23M Savrie,16,jD Savrina,30,31M Schiller,41H Schindler,37M Schlupp,9M Schmelling,10B Schmidt,37O Schneider,38A Schopper,37M.-H Schune,7R Schwemmer,37
B Sciascia,18A Sciubba,24M Seco,36A Semennikov,30K Senderowska,26I Sepp,52N Serra,39J Serrano,6P Seyfert,11
M Shapkin,34I Shapoval,16,42,jY Shcheglov,29T Shears,51L Shekhtman,33O Shevchenko,42V Shevchenko,30A Shires,9 R Silva Coutinho,47M Sirendi,46 N Skidmore,45T Skwarnicki,58N A Smith,51E Smith,54,48 E Smith,52J Smith,46M Smith,53 M D Sokoloff,56 F J P Soler,50F Soomro,38D Souza,45B Souza De Paula,2 B Spaan,9 A Sparkes,49P Spradlin,50F Stagni,37S Stahl,11O Steinkamp,39S Stevenson,54S Stoica,28S Stone,58B Storaci,39M Straticiuc,28U Straumann,39V K Subbiah,37L Sun,56W Sutcliffe,52S Swientek,9V Syropoulos,41M Szczekowski,27P Szczypka,38,37D Szilard,2 T Szumlak,26S T’Jampens,4
M Teklishyn,7 E Teodorescu,28F Teubert,37C Thomas,54E Thomas,37J van Tilburg,11 V Tisserand,4 M Tobin,38 S Tolk,41D Tonelli,37S Topp-Joergensen,54N Torr,54E Tournefier,4,52S Tourneur,38M T Tran,38 M Tresch,39A Tsaregorodtsev,6 P Tsopelas,40N Tuning,40,37M Ubeda Garcia,37A Ukleja,27A Ustyuzhanin,52,q U Uwer,11V Vagnoni,14G Valenti,14A Vallier,7 R Vazquez Gomez,18P Vazquez Regueiro,36C Vázquez Sierra,36S Vecchi,16J J Velthuis,45M Veltri,17,rG Veneziano,38M Vesterinen,37B Viaud,7D Vieira,2X Vilasis-Cardona,35,fA Vollhardt,39D Volyanskyy,10D Voong,45A Vorobyev,29V Vorobyev,33C Voß,60H Voss,10R Waldi,60C Wallace,47R Wallace,12S Wandernoth,11J Wang,58D R Ward,46N K Watson,44A D Webber,53D Websdale,52M Whitehead,47J Wicht,37J Wiechczynski,25D Wiedner,11L Wiggers,40G Wilkinson,54M
P Williams,47,48M Williams,55F F Wilson,48J Wimberley,57J Wishahi,9W Wislicki,27M Witek,25G Wormser,7S A Wotton,46S Wright,46S Wu,3K Wyllie,37Y Xie,49,37Z Xing,58Z Yang,3X Yuan,3O Yushchenko,34M Zangoli,14M Zavertyaev,10,sF Zhang,3L Zhang,58W C Zhang,12Y Zhang,3A Zhelezov,11A Zhokhov,30L Zhong,3A Zvyagin37
(LHCb Collaboration)
1
Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3
Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5
Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7
LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France
9
Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institutfür Kernphysik (MPIK), Heidelberg, Germany
11
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
12School of Physics, University College Dublin, Dublin, Ireland
13
Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15
Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17
Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
PRL 112, 011801 (2014)
Trang 319Sezione INFN di Genova, Genova, Italy
20
Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Padova, Padova, Italy
22
Sezione INFN di Pisa, Pisa, Italy
23Sezione INFN di Roma Tor Vergata, Roma, Italy
24
Sezione INFN di Roma La Sapienza, Roma, Italy
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
26
AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland
27National Center for Nuclear Research (NCBJ), Warsaw, Poland
28
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
32
Institute 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
34
Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Redfsearch (CERN), Geneva, Switzerland
38
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, Switzerland
40
Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
41Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands
42
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
43Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
44
University of Birmingham, Birmingham, United Kingdom
45H.H Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
46
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
47Department of Physics, University of Warwick, Coventry, United Kingdom
48
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
49School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
50
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
51Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
52
Imperial College London, London, United Kingdom
53School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
54
Department of Physics, University of Oxford, Oxford, United Kingdom
55Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
56
University of Cincinnati, Cincinnati, Ohio, USA
57University of Maryland, College Park, Maryland, USA
58
Syracuse University, Syracuse, New York, USA
59Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil [associated
with Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil]
60Institutfür Physik, Universität Rostock, Rostock, Germany (associated with Physikalisches
Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,Germany)
61Celal Bayar University, Manisa, Turkey [associated with European Organization
for Nuclear Research (CERN), Geneva, Switzerland]
(Received 18 October 2013; published 7 January 2014) The charmless decays B→ KþK−π and B→ πþπ−π are reconstructed in a data set of pp
collisions with an integrated luminosity of1.0 fb−1and center-of-mass energy of 7 TeV, collected by LHCb
in 2011 The inclusive charge asymmetries of these modes are measured to beACPðB→KþK−πÞ¼
−0.1410.040ðstatÞ0.018ðsystÞ0.007ðJ=ψ KÞ and ACPðB→ πþπ−πÞ ¼ 0.117 0.021 ðstatÞ
0.009 ðsystÞ 0.007ðJ=ψ KÞ, where the third uncertainty is due to the CP asymmetry of the B→
J=ψKreference mode In addition to the inclusiveCP asymmetries, larger asymmetries are observed in
localized regions of phase space
Published by the American Physical Society under the terms of theCreative Commons Attribution 3.0 License Further distribution of this work must maintain attribution to the author(s) and the published articles title, journal citation, and DOI
Trang 4The noninvariance of the combined asymmetry of charge
conjugation and parity, known asCP violation, is described
in the standard model by the Cabibbo-Kobayashi-Maskawa
quark-mixing matrix [1,2] CP violation is established
experimentally in theK0[3],B0[4,5], andB[6]systems.
Charmless decays ofB mesons to three hadrons offer the
possibility to investigateCP asymmetries that are localized
in phase space [7,8], as these decays are dominated by
intermediate two-body resonant states In previous
mea-surements of this type, the phase spaces of B→
KKþK− and B→ Kπþπ− decays were observed to
have regions of large local asymmetries[9–12] Concerning
baryonic modes, no significant effects have been observed
in either B→ p ¯pK orB → p ¯pπ decays [13] Large
CP-violating asymmetries have also been observed in
charmless two-body B-meson decays such as B0→
Kþπ− and B0
s → K−πþ (and the corresponding ¯B0 and
¯B0
s decays)[14–16]
Some recent effort has been made to understand the origin
of the large asymmetries For directCP violation to occur,
two interfering amplitudes with different CP-violating
and CP-conserving phases must contribute to the decay
process [17] 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 [18,19] Another explanation focuses on final-state
KK↔ππ rescattering, which can occur between decay
channels with the same flavor quantum numbers[9,19,20]
Invariance ofCPT 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 theS
matrix, must be equal for charge-conjugated decays Effects
of SU(3) flavor symmetry breaking have also been
inves-tigated and partially explain the observed patterns[19,21,22]
The B→ KþK−π decay is interesting because s¯s
resonant contributions are strongly suppressed [23–25]
Recently, LHCb reported an upper limit on the ϕ
contri-bution to be BðB → ϕπÞ < 1.5 × 10−7 at the 90%
confidence level [26] The lack of KþK− resonant
con-tributions makes theB→ KþK−π decay a good probe
for rescattering from decays with pions The B→
πþπ−π mode, on the other hand, has large resonant
contributions, as shown in an amplitude analysis by the
BABAR Collaboration, which measured the inclusive CP
asymmetry to be (0.03 0.06) [27] For B → KþK−π
decays, the inclusive CP-violating asymmetry was
mea-sured by the BABAR Collaboration to be (0.00 0.10)
[28], from a comparison of Bþ andB− sample fits Both
results are compatible with the noCP-violation hypothesis
In this Letter we report measurements of the inclusive
CP-violating asymmetries for B → πþπ−π and B→
KþK−π decays The CP asymmetry in B decays to a
final state f is defined as
ACPðB→ fÞ ≡ Φ½ΓðB−→ f−Þ; ΓðBþ→ fþÞ; (1)
whereΦ½X; Y ≡ ðX − YÞ=ðX þ YÞ is the asymmetry func-tion, Γ is the decay width, and the final states f are
πþπ−π orKþK−π The asymmetry distributions across
the phase space are also investigated
The LHCb detector [29] is a single-arm forward spec-trometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containingb or c quarks The analysis is based onpp collision data, corresponding
to an integrated luminosity of1.0 fb−1, collected in 2011 at
a center-of-mass energy of 7 TeV
The simulated events, used in this analysis to determine some of the fit parameters, are generated using PYTHIA 6.4[30]with a specific LHCb configuration[31] Decays
of hadronic particles are produced by EVTGEN [32], in which final-state radiation is generated using PHOTOS
[33] The interaction of the generated particles with the detector and its response are implemented using the GEANT4 toolkit[34]as described in Ref.[35]
Events are selected by a trigger [36] 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 soft-ware trigger requires a two-, three-, or four-track secondary vertex with a high sum of the transverse momentapT of the
tracks and significant displacement from the primarypp interaction vertices (PVs) At least one track should have
pT > 1.7 GeV=c and χ2
IPwith respect to any PV greater
than 16, whereχ2
IPis defined as the difference between the
χ2 of a given PV reconstructed with and without the
considered track, and IP is the impact parameter A multi-variate algorithm [37] is used for the identification of secondary vertices consistent with the decay of ab hadron Further criteria are applied off-line to select B mesons and suppress the combinatorial background TheB decay
products are required to satisfy a set of selection criteria on the momenta,pT andχ2
IPof the final-state tracks, and the
distance of closest approach between any two tracks TheB candidates are required to havepT > 1.7 GeV=c, χ2
IP<
10 (defined by projecting the B-candidate trajectory back-wards from its decay vertex), decay vertex χ2< 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 θ between theB-candidate momentum and the direction of flight from the primary vertex to the decay vertex, cosðθÞ > 0.999 98 Final-state kaons and pions are further selected using particle identification information, provided
by two ring-imaging Cherenkov detectors [38], and are required to be incompatible with muons [39] Charm contributions are removed by excluding the regions of
30 MeV=c2 around the world average value of the D0
mass[40]in the two-body invariant massesmπ þ π −,mK π ∓, andmK þ K −
PRL 112, 011801 (2014)
Trang 5Unbinned extended maximum likelihood fits to the
invariant-mass spectra of the selected B candidates are
performed to obtain the signal yields and raw asymmetries
The B → KþK−π and B → πþπ−π signal
compo-nents are parametrized by a Cruijff function[41]with equal
left and right widths and different radiative tails to account
for the asymmetric effect of final-state radiation 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
expo-nential 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[42]
convolved with a Gaussian resolution function ForB→
πþπ−π decays, the shape and yield parameters describing
the four-body backgrounds are varied in the fit, while for
B → KþK−π decays they are taken from simulation,
due to a further contribution from B0
s decays such as
B0
s → D−
sðKþK−π−Þπþ We define peaking backgrounds
as decay modes with one misidentified particle, namely the
channelsB → Kπþπ−for theB → πþπ−πmode and
B → Kπþπ− and B → KKþK− for the B→
KþK−π 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 forBþandB−decays The invariant
mass spectra of the B → KþK−π and B → πþπ−π
candidates are shown in Fig 1 The signal yields obtained
are NðKKπÞ ¼ 1870 133 and NðπππÞ ¼ 4904 148,
and the raw asymmetries areArawðKKπÞ ¼ −0.143 0.040
andArawðπππÞ ¼ 0.124 0.020, where the uncertainties are
statistical
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
deter-mined by the ratio between the B− and Bþ average
efficiencies in simulated events, reweighted to reproduce
the population of signal data over the phase space TheCP
asymmetries are obtained from the acceptance-corrected raw asymmetries Aacc
raw, by subtracting the asymmetry induced by the detector acceptance and interactions
of final-state pions with matter ADðπÞ, as well as the B-meson production asymmetry APðBÞ,
ACP¼ Aacc
raw− ADðπÞ − APðBÞ: (2)
The pion detection asymmetry,ADðπÞ ¼ 0.0000 0.0025, has previously been measured by LHCb[43] The production asymmetry APðBÞ is measured from a data sample of approximately 6.3 × 104 B→ J=ψ ðμþμ−ÞK decays.
The B→ J=ψ K sample passes the same trigger,
kin-ematic, and kaon particle identification selection criteria as the signal samples, and it has a similar event topology The
APðBÞ term is obtained from the raw asymmetry of the
B→ J=ψ K mode as
APðBÞ ¼ ArawðJ=ψKÞ − ACPðJ=ψKÞ − ADðKÞ; (3)
whereACPðJ=ψ KÞ ¼ 0.001 0.007[40]is the world aver-ageCPasymmetryofB → J=ψ Kdecays, andADðKÞ ¼
−0.010 0.003 is the kaon interaction asymmetry obtained fromD0→ Kπ∓ andD0→ KþK−decays[44], and
cor-rected forADðπÞ
The detector acceptance and reconstruction depend on the trigger selection The efficiency of the hadronic hard-ware 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
APðBÞ term is performed separately for each trigger configuration The trigger-averaged value of the production asymmetry isAPðBÞ ¼ −0.004 0.004, where the uncer-tainty is statistical only The integratedCP asymmetries are then the weighted averages of theCP asymmetries for the two trigger samples
] 2
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] 2
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→
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] 2
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] 2
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±
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→
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−
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+
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±
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→
±
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−
π
+
π
±
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→
±
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FIG 1 (color online) Invariant mass spectra of (a)B→ πþπ−πdecays and (b)B→ KþK−πdecays The left-hand panel in each
figure shows theB−modes and the right-hand panel shows theBþmodes The results of the unbinned maximum likelihood fits are
overlaid The main components of the fit are also shown
Trang 6The methods used in estimating the systematic
uncer-tainties of the signal model, combinatorial background,
peaking background, and acceptance correction are the
same as those used in Ref [9] For B → KþK−π
decays, we also evaluate a systematic uncertainty due to
the four-body-decay background component taken from
simulation, by varying the Gaussian mean and resolution
according to the difference between simulation and data
The ADðπÞ and ADðKÞ uncertainties are included as
systematic uncertainties related to the procedure The
ADðπÞ value is largely independent of pion kinematics
[43] and thus no further systematic uncertainty is
assigned A systematic uncertainty is evaluated to
account for the difference in kaon kinematics between
B → J=ψ K decays and D0 decays from which
ADðKÞ is obtained For B → KþK−π decays, the
residual interaction asymmetry due to the possible
differences in K− and Kþ momenta was found to be
negligible The systematic uncertainties are summarized
in Table I
The results obtained for the inclusiveCP asymmetries of theB → KþK−π and B → πþπ−π decays are
ACPðB → KþK−πÞ ¼ −0.141 0.040 0.018 0.007;
ACPðB → πþπ−πÞ ¼ 0.117 0.021 0.009 0.007; where the first uncertainty is statistical, the second is the experimental systematic, and the third is due to the CP asymmetry of theB→ J=ψ Kreference mode[40] The
significances of the inclusive charge asymmetries, calcu-lated by dividing the central values by the sum in quad-rature of the statistical and both systematic uncertainties, are 3.2 standard deviations (σ) for B → KþK−π and
4.9σ for B → πþπ−π decays.
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 Bþ samples.
Figure 2 shows the raw asymmetries (not corrected for efficiency), AN
raw¼ Φ½N−; Nþ, computed using the num-bers ofB−(N−) andBþ(Nþ) candidates in each bin of the
B→ πþπ−π and B → KþK−π Dalitz plots The
B→ πþπ−π Dalitz plot is symmetrized and its
two-body invariant mass squared variables are defined as
m2
π þ π −low< m2
π þ π −high The AN
raw distribution in the Dalitz plot of the B → πþπ−π mode reveals an asymmetry
concentrated at low values ofm2
π þ π −low and high values of
m2
π þ π −high The distribution of the projection of the number
of events onto them2
π þ π −lowinvariant mass [inset in Fig.2(a)] shows that this asymmetry is located in the region
m2
π þ π −low<0.4GeV2=c4 and m2
π þ π −high>15GeV2=c4 For
B→ KþK−π we identify a negative asymmetry located
TABLE I Systematic uncertainties onACPðB→ KþK−πÞ
andACPðB→ πþπ−πÞ The total systematic uncertainties are
the sum in quadrature of the individual contributions
Systematic uncertainty ACPðKKπÞ ACPðπππÞ
Combinatorial background 0.003 0.0008
Four-body-decay
background
ADðπÞ uncertainty 0.003 0.0025
ADðKÞ uncertainty 0.003 0.0032
ADðKÞ kaon kinematics 0.008 0.0075
]
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− π + π 2
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-0.6 -0.4 -0.2 0 0.2 0.4 0.6
] 4
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/ 2 [GeV low
−
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+
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m
Candidates/(0.10 GeV 0
20 40 60 80 100
-+ B
(a) LHCb
]
4
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/
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[GeV
− K + K 2
m
0 5 10 15 20 25 30 35 40
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
] 4
c
/ 2 [GeV
-K
+
K 2
m
Candidates/(0.10 GeV 0
10 20 30 40 50 60
B + B
(b) LHCb
FIG 2 (color online) Asymmetries of the number of events (including signal and background, not corrected for efficiency) in bins of the Dalitz plotAN
rawfor (a)B→ πþπ−πand (b)B→ KþK−πdecays The inset figures show the projections of the number of
events in bins of (a) them2
π þ π −low variable form2
π þ π −high> 15 GeV2=c4 and (b) them2
K þ K − variable
PRL 112, 011801 (2014)
Trang 7in the lowKþK− invariant mass region This can be seen
also in the inset figure of the KþK− invariant mass
projection, where there is an excess of Bþ candidates for
m2
K þ K − < 1.5 GeV2=c4 Although B→ KþK−π is not
expected to have KþK− resonant contributions such as
φð1020Þ [45], a clear structure is observed This structure
was also seen by the BABAR Collaboration[28]but was not
studied separately forB− andBþ components No
signifi-cant asymmetry is present in the low-mass region of the
Kπ∓ invariant mass projection.
The CP asymmetries are further studied in the regions
where large raw asymmetries are found The regions are
defined as m2
π þ π −high> 15 GeV2=c4 and m2
π þ π −low <
0.4 GeV2=c4 for the B → πþπ−π mode and m2
K þ K − <
1.5 GeV2=c4 for the B → KþK−π 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 NregðKKπÞ ¼ 342 28 and
Areg
rawðKKπÞ ¼ −0.658 0.070 for the B → KþK−π
mode and NregðπππÞ ¼ 229 20 and Areg
rawðπππÞ ¼ 0.555 0.082 for the B→ πþπ−π mode The CP
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, the ADðπÞ and APðBÞ
statistical uncertainties, and theADðKÞ kaon kinematics
The local charge asymmetries for the two regions are
measured to be
Areg
CPðB→ KþK−πÞ ¼ −0.648 0.070 0.013 0.007;
Areg
CPðB→ πþπ−πÞ ¼ 0.584 0.082 0.027 0.007;
where the first uncertainty is statistical, the second
is the experimental systematic, and the third is due to
the CP asymmetry of the B→ J=ψ K reference
mode[40]
In conclusion, we have found the first evidence of inclusive CP asymmetries of the B→ KþK−π and
B→ πþπ−π modes with significances of 3.2σ and 4.9σ, respectively The results are consistent with those measured by the BABAR Collaboration [27,28] These charge asymmetries are not uniformly distributed in phase space For B → KþK−π 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 lowKþK−invariant mass ForB →
πþπ−πdecays, a large positive asymmetry is measured in
the lowm2
π þ π −low and high m2
π þ π −high phase-space region, not clearly associated with a resonant state The evidence presented here for CP violation in B→ KþK−π and
B→ πþπ−π decays, along with the recent evidence for
CP violation in B → Kπþπ− and B → KKþK−
decays [9] and recent theoretical developments [18–21], indicates new mechanisms for CP asymmetries, which should be incorporated in models for future amplitude analyses of charmless three-bodyB decays
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent perfor-mance of the LHC We thank the technical and admin-istrative staff at the LHCb institutes We acknowledge support from CERN and from the following 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 (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 (U.S.) We also acknowledge the support received from the ERC under FP7 The Tier1 computing centers are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (Netherlands), PIC (Spain),
] 2
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→
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] 2
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−
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0 10 20 30 40 50 60 70
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] 2
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+
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−
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+
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m
model
±
π
−
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+
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→
±
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combinatorial 4-body
→
s 0
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4-body
→
B
−
K
+
K
±
K
→
±
B
−
π
+
π
±
K
→
±
B
FIG 3 (color online) Invariant mass spectra of (a)B→ πþπ−πdecays in the regionm2
π þ π −low< 0.4 GeV2=c4andm2
π þ π −high>
15 GeV2=c4 and (b) B→ KþK−π decays in the region m2
K þ K − < 1.5 GeV2=c4 The left-hand panel in each figure shows the
B− modes and the right-hand panel shows theBþ modes The results of the unbinned maximum likelihood fits are overlaid.
Trang 8and 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
aAlso at LIFAELS, La Salle, Universitat Ramon Llull,
Barcelona, Spain
bAlso at Hanoi University of Science, Hanoi, Vietnam
c
Also at Università di Roma Tor Vergata, Roma, Italy
dAlso at Institute of Physics and Technology, Moscow,
Russia
eAlso at Università di Ferrara, Ferrara, Italy
f
Also at Università di Bari, Bari, Italy
gAlso at Università di Modena e Reggio Emilia, Modena,
Italy
hAlso at Università di Cagliari, Cagliari, Italy
i
Also at Università di Genova, Genova, Italy
jAlso at Università di Milano Bicocca, Milano, Italy
k
Also at Università di Padova, Padova, Italy
lAlso at P.N Lebedev Physical Institute, Russian Academy
of Science (LPI RAS), Moscow, Russia
mAlso at Università di Roma La Sapienza, Roma, Italy
n
Also at Università della Basilicata, Potenza, Italy
oAlso at Scuola Normale Superiore, Pisa, Italy
p
Also at Università di Urbino, Urbino, Italy
qAlso at Università di Pisa, Pisa, Italy
r
Also at Università di Bologna, Bologna, Italy
sAlso at Università di Firenze, Firenze, Italy
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