EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2011-214 LHCb-PAPER-2011-021 March 13, 2012
Measurement of the CP -violating phase φ
s
in the decay B
s
0
→ J/ψ φ
The LHCb Collaboration
R. Aaij23, C. Abellan Beteta35,n, B. Adeva36, M. Adinolfi42, C. Adrover6, A. Affolder48, Z. Ajaltouni5,
J. Albrecht37, F. Alessio37, M. Alexander47, G. Alkhazov29, P. Alvarez Cartelle36, A.A. Alves Jr22, S. Amato2,
Y. Amhis38, J. Anderson39, R.B. Appleby50, O. Aquines Gutierrez10, F. Archilli18,37, L. Arrabito53,
A. Artamonov34, M. Artuso52,37, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back44, D.S. Bailey50,
V. Balagura30,37, W. Baldini16, R.J. Barlow50, C. Barschel37, S. Barsuk7, W. Barter43, A. Bates47, C. Bauer10, Th. Bauer23, A. Bay38, I. Bediaga1, S. Belogurov30, K. Belous34, I. Belyaev30,37, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson46, J. Benton42, R. Bernet39, M.-O. Bettler17, M. van Beuzekom23, A. Bien11, S. Bifani12, T. Bird50, A. Bizzeti17,h, P.M. Bjørnstad50, T. Blake37, F. Blanc38, C. Blanks49, J. Blouw11, S. Blusk52,
A. Bobrov33, V. Bocci22, A. Bondar33, N. Bondar29, W. Bonivento15, S. Borghi47,50, A. Borgia52, T.J.V. Bowcock48, C. Bozzi16, T. Brambach9, J. van den Brand24, J. Bressieux38, D. Brett50, M. Britsch10, T. Britton52, N.H. Brook42,
H. Brown48, A. B¨uchler-Germann39, I. Burducea28, A. Bursche39, J. Buytaert37, S. Cadeddu15, O. Callot7,
M. Calvi20,j, M. Calvo Gomez35,n, A. Camboni35, P. Campana18,37, A. Carbone14, G. Carboni21,k,
R. Cardinale19,i,37, A. Cardini15, L. Carson49, K. Carvalho Akiba2, G. Casse48, M. Cattaneo37, Ch. Cauet9,
M. Charles51, Ph. Charpentier37, N. Chiapolini39, K. Ciba37, X. Cid Vidal36, G. Ciezarek49, P.E.L. Clarke46,37,
M. Clemencic37, H.V. Cliff43, J. Closier37, C. Coca28, V. Coco23, J. Cogan6, P. Collins37, A. Comerma-Montells35,
F. Constantin28, A. Contu51, A. Cook42, M. Coombes42, G. Corti37, G.A. Cowan38, R. Currie46, C. D’Ambrosio37,
P. David8, P.N.Y. David23, I. De Bonis4, S. De Capua21,k, M. De Cian39, F. De Lorenzi12, J.M. De Miranda1,
L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H. Degaudenzi38,37, L. Del Buono8, C. Deplano15,
D. Derkach14,37, O. Deschamps5, F. Dettori24, J. Dickens43, H. Dijkstra37, P. Diniz Batista1, F. Domingo Bonal35,n,
S. Donleavy48, F. Dordei11, A. Dosil Su´arez36, D. Dossett44, A. Dovbnya40, F. Dupertuis38, R. Dzhelyadin34, A. Dziurda25, S. Easo45, U. Egede49, V. Egorychev30, S. Eidelman33, D. van Eijk23, F. Eisele11, S. Eisenhardt46, R. Ekelhof9, L. Eklund47, Ch. Elsasser39, D. Elsby55, D. Esperante Pereira36, L. Est`eve43, A. Falabella16,14,e, E. Fanchini20,j, C. F¨arber11, G. Fardell46, C. Farinelli23, S. Farry12, V. Fave38, V. Fernandez Albor36,
M. Ferro-Luzzi37, S. Filippov32, C. Fitzpatrick46, M. Fontana10, F. Fontanelli19,i, R. Forty37, M. Frank37, C. Frei37, M. Frosini17,f,37, S. Furcas20, A. Gallas Torreira36, D. Galli14,c, M. Gandelman2, P. Gandini51, Y. Gao3,
J-C. Garnier37, J. Garofoli52, J. Garra Tico43, L. Garrido35, D. Gascon35, C. Gaspar37, N. Gauvin38,
M. Gersabeck37, T. Gershon44,37, Ph. Ghez4, V. Gibson43, V.V. Gligorov37, C. G¨obel54, D. Golubkov30,
A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa G´andara35, R. Graciani Diaz35,
L.A. Granado Cardoso37, E. Graug´es35, G. Graziani17, A. Grecu28, E. Greening51, S. Gregson43, B. Gui52,
E. Gushchin32, Yu. Guz34, T. Gys37, G. Haefeli38, C. Haen37, S.C. Haines43, T. Hampson42,
S. Hansmann-Menzemer11, R. Harji49, N. Harnew51, J. Harrison50, P.F. Harrison44, T. Hartmann56, J. He7,
V. Heijne23, K. Hennessy48, P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37, E. Hicks48, K. Holubyev11,
ii P. Hopchev4, W. Hulsbergen23, P. Hunt51, T. Huse48, R.S. Huston12, D. Hutchcroft48, D. Hynds47, V. Iakovenko41, P. Ilten12, J. Imong42, R. Jacobsson37, A. Jaeger11, M. Jahjah Hussein5, E. Jans23, F. Jansen23, P. Jaton38, B. Jean-Marie7, F. Jing3, M. John51, D. Johnson51, C.R. Jones43, B. Jost37, M. Kaballo9, S. Kandybei40, M. Karacson37, T.M. Karbach9, J. Keaveney12, I.R. Kenyon55, U. Kerzel37, T. Ketel24, A. Keune38, B. Khanji6,
Y.M. Kim46, M. Knecht38, P. Koppenburg23, A. Kozlinskiy23, L. Kravchuk32, K. Kreplin11, M. Kreps44,
G. Krocker11, P. Krokovny11, F. Kruse9, K. Kruzelecki37, M. Kucharczyk20,25,37,j, T. Kvaratskheliya30,37,
V.N. La Thi38, D. Lacarrere37, G. Lafferty50, A. Lai15, D. Lambert46, R.W. Lambert24, E. Lanciotti37,
G. Lanfranchi18, C. Langenbruch11, T. Latham44, C. Lazzeroni55, R. Le Gac6, J. van Leerdam23, J.-P. Lees4,
R. Lef`evre5, A. Leflat31,37, J. Lefran¸cois7, O. Leroy6, T. Lesiak25, L. Li3, L. Li Gioi5, M. Lieng9, M. Liles48,
R. Lindner37, C. Linn11, B. Liu3, G. Liu37, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar35, N. Lopez-March38,
H. Lu38,3, J. Luisier38, A. Mac Raighne47, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc10, O. Maev29,37,
J. Magnin1, S. Malde51, R.M.D. Mamunur37, G. Manca15,d, G. Mancinelli6, N. Mangiafave43, U. Marconi14,
R. M¨arki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51, A. Mart´ın S´anchez7, D. Martinez Santos37,
A. Massafferri1, Z. Mathe12, C. Matteuzzi20, M. Matveev29, E. Maurice6, B. Maynard52, A. Mazurov16,32,37,
G. McGregor50, R. McNulty12, M. Meissner11, M. Merk23, J. Merkel9, R. Messi21,k, S. Miglioranzi37,
D.A. Milanes13,37, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran12, P. Morawski25, R. Mountain52, I. Mous23, F. Muheim46, K. M¨uller39, R. Muresan28,38, B. Muryn26, B. Muster38, M. Musy35, J. Mylroie-Smith48, P. Naik42, T. Nakada38, R. Nandakumar45, I. Nasteva1, M. Nedos9, M. Needham46, N. Neufeld37,
C. Nguyen-Mau38,o, M. Nicol7, V. Niess5, N. Nikitin31, A. Nomerotski51, A. Novoselov34, A. Oblakowska-Mucha26,
V. Obraztsov34, S. Oggero23, S. Ogilvy47, O. Okhrimenko41, R. Oldeman15,d, M. Orlandea28,
J.M. Otalora Goicochea2, P. Owen49, K. Pal52, J. Palacios39, A. Palano13,b, M. Palutan18, J. Panman37,
A. Papanestis45, M. Pappagallo47, C. Parkes50,37, C.J. Parkinson49, G. Passaleva17, G.D. Patel48, M. Patel49,
S.K. Paterson49, G.N. Patrick45, C. Patrignani19,i, C. Pavel-Nicorescu28, A. Pazos Alvarez36, A. Pellegrino23,
G. Penso22,l, M. Pepe Altarelli37, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo36, A. P´erez-Calero Yzquierdo35,
P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrella16,37, A. Petrolini19,i, A. Phan52, E. Picatoste Olloqui35,
B. Pie Valls35, B. Pietrzyk4, T. Pilaˇr44, D. Pinci22, R. Plackett47, S. Playfer46, M. Plo Casasus36, G. Polok25,
A. Poluektov44,33, E. Polycarpo2, D. Popov10, B. Popovici28, C. Potterat35, A. Powell51, J. Prisciandaro38,
V. Pugatch41, A. Puig Navarro35, W. Qian52, J.H. Rademacker42, B. Rakotomiaramanana38, M.S. Rangel2,
I. Raniuk40, G. Raven24, S. Redford51, M.M. Reid44, A.C. dos Reis1, S. Ricciardi45, K. Rinnert48,
D.A. Roa Romero5, P. Robbe7, E. Rodrigues47,50, F. Rodrigues2, P. Rodriguez Perez36, G.J. Rogers43, S. Roiser37, V. Romanovsky34, M. Rosello35,n, J. Rouvinet38, T. Ruf37, H. Ruiz35, G. Sabatino21,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail47, B. Saitta15,d, C. Salzmann39, M. Sannino19,i, R. Santacesaria22, C. Santamarina Rios36, R. Santinelli37, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina30, P. Schaack49, M. Schiller24, S. Schleich9, M. Schlupp9, M. Schmelling10, B. Schmidt37, O. Schneider38,
A. Schopper37, M.-H. Schune7, R. Schwemmer37, B. Sciascia18, A. Sciubba18,l, M. Seco36, A. Semennikov30,
K. Senderowska26, I. Sepp49, N. Serra39, J. Serrano6, P. Seyfert11, M. Shapkin34, I. Shapoval40,37, P. Shatalov30,
Y. Shcheglov29, T. Shears48, L. Shekhtman33, O. Shevchenko40, V. Shevchenko30, A. Shires49, R. Silva Coutinho44,
T. Skwarnicki52, A.C. Smith37, N.A. Smith48, E. Smith51,45, K. Sobczak5, F.J.P. Soler47, A. Solomin42,
F. Soomro18, B. Souza De Paula2, B. Spaan9, A. Sparkes46, P. Spradlin47, F. Stagni37, S. Stahl11, O. Steinkamp39,
S. Stoica28, S. Stone52,37, B. Storaci23, M. Straticiuc28, U. Straumann39, V.K. Subbiah37, S. Swientek9,
M. Szczekowski27, P. Szczypka38, T. Szumlak26, S. T’Jampens4, E. Teodorescu28, F. Teubert37, C. Thomas51,
E. Thomas37, J. van Tilburg11, V. Tisserand4, M. Tobin39, S. Topp-Joergensen51, N. Torr51, E. Tournefier4,49,
M.T. Tran38, A. Tsaregorodtsev6, N. Tuning23, M. Ubeda Garcia37, A. Ukleja27, P. Urquijo52, U. Uwer11,
V. Vagnoni14, G. Valenti14, R. Vazquez Gomez35, P. Vazquez Regueiro36, S. Vecchi16, J.J. Velthuis42, M. Veltri17,g, B. Viaud7, I. Videau7, X. Vilasis-Cardona35,n, J. Visniakov36, A. Vollhardt39, D. Volyanskyy10, D. Voong42, A. Vorobyev29, H. Voss10, S. Wandernoth11, J. Wang52, D.R. Ward43, N.K. Watson55, A.D. Webber50,
D. Websdale49, M. Whitehead44, D. Wiedner11, L. Wiggers23, G. Wilkinson51, M.P. Williams44,45, M. Williams49, F.F. Wilson45, J. Wishahi9, M. Witek25, W. Witzeling37, S.A. Wotton43, K. Wyllie37, Y. Xie46, F. Xing51, Z. Xing52, Z. Yang3, R. Young46, O. Yushchenko34, M. Zavertyaev10,a, F. Zhang3, L. Zhang52, W.C. Zhang12,
Y. Zhang3, A. Zhelezov11, L. Zhong3, E. Zverev31, A. Zvyagin37. 1Centro Brasileiro de Pesquisas F´ısicas (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, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
iii 7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨at 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 Roma Tor Vergata, Roma, Italy 22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, The Netherlands 25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krac´ow, Poland 26AGH University of Science and Technology, Krac´ow, Poland
27Soltan Institute for Nuclear Studies, 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 F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 39Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 44Department of Physics, University of Warwick, Coventry, United Kingdom 45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 47School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 55University of Birmingham, Birmingham, United Kingdom
56Physikalisches Institut, Universit¨at Rostock, Rostock, Germany, associated to11
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia bUniversit`a di Bari, Bari, Italy
cUniversit`a di Bologna, Bologna, Italy dUniversit`a di Cagliari, Cagliari, Italy eUniversit`a di Ferrara, Ferrara, Italy fUniversit`a di Firenze, Firenze, Italy gUniversit`a di Urbino, Urbino, Italy
hUniversit`a di Modena e Reggio Emilia, Modena, Italy iUniversit`a di Genova, Genova, Italy
jUniversit`a di Milano Bicocca, Milano, Italy kUniversit`a di Roma Tor Vergata, Roma, Italy lUniversit`a di Roma La Sapienza, Roma, Italy mUniversit`a della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain oHanoi University of Science, Hanoi, Viet Nam
We present a measurement of the time-dependent CP -violating asymmetry in Bs0→ J/ψ φ decays,
using data collected with the LHCb detector at the LHC. The decay time distribution of B0
s→ J/ψ φ
is characterized by the decay widths ΓHand ΓLof the heavy and light mass eigenstates of the B0
s-B0s
system and by a CP -violating phase φs. In a sample of about 8500 Bs0→ J/ψ φ events isolated from
0.37 fb−1of pp collisions at√s = 7 TeV we measure φs = 0.15 ± 0.18 (stat) ± 0.06 (syst) rad. We
also find an average B0
s decay width Γs≡ (ΓL+ ΓH)/2 = 0.657 ± 0.009 (stat) ± 0.008 (syst) ps
−1
and a decay width difference ∆Γs ≡ ΓL− ΓH = 0.123 ± 0.029 (stat) ± 0.011 (syst) ps−1. Our
measurement is insensitive to the transformation (φs, ∆Γs) 7→ (π − φs, −∆Γs).
To be submitted to Physical Review Letters
In the Standard Model (SM) CP violation arises through a single phase in the CKM quark mixing matrix [1]. In neutral B meson decays to a final state which is ac-cessible to both B and B mesons, the interference be-tween the amplitude for the direct decay and the ampli-tude for decay after oscillation, leads to a time-dependent CP -violating asymmetry between the decay time distri-butions of B and B mesons. The decay B0
s → J/ψ φ
allows the measurement of such an asymmetry, which can be expressed in terms of the decay width differ-ence of the heavy (H) and light (L) B0
s mass
eigen-states ∆Γs ≡ ΓL − ΓH and a single phase φs [2]. In
the SM, the decay width difference is ∆ΓSMs = 0.087 ± 0.021 ps−1 [3], while the phase is predicted to be small, φSMs = −2 arg (−VtsVtb∗/VcsVcb∗) = −0.036 ± 0.002 rad [4].
This value ignores a possible contribution from sub-leading decay amplitudes [5]. Contributions from physics beyond the SM could lead to much larger values of φs[6].
In this Letter we present measurements of φs, ∆Γsand
the average decay width Γs ≡ (ΓL+ ΓH)/2. Previous
measurements of these quantities have been reported by the CDF and DØ collaborations [7]. We use an integrated luminosity of 0.37 fb−1 of pp collision data recorded at a centre-of-mass energy√s = 7 TeV by the LHCb experi-ment during the first half of 2011. The LHCb detector is a forward spectrometer at the Large Hadron Collider and is described in detail in Ref. [8].
We look for Bs0 → J/ψ φ candidates in decays to J/ψ → µ+µ− and φ → K+K−. Events are selected by a trigger system consisting of a hardware trigger, which selects muon or hadron candidates with high transverse momentum with respect to the beam direction (pT),
fol-lowed by a two stage software trigger. In the first stage a simplified event reconstruction is applied. Events are required to either have two well-identified muons with invariant mass above 2.7 GeV, or at least one muon or one high-pT track with a large impact parameter to any
primary vertex. In the second stage a full event recon-struction is performed and only events with a muon can-didate pair with invariant mass within 120 MeV of the nominal J/ψ mass [9] are retained. We adopt units such that c = 1 and ~ = 1.
For the final event selection muon candidates are re-quired to have pT > 0.5 GeV. J/ψ candidates are
cre-ated from pairs of oppositely charged muons that have a common vertex and an invariant mass in the range 3030 − 3150 MeV. The latter corresponds to about eight times the µ+µ−invariant mass resolution and covers part
of the J/ψ radiative tail. The φ selection requires two oppositely charged particles that are identified as kaons, form a common vertex and have an invariant mass within ±12 MeV of the nominal φ mass [9]. The pT of the φ
candidate is required to exceed 1 GeV. The mass window covers approximately 90% of the φ → K+K− lineshape.
We select B0
s candidates from combinations of a J/ψ
and a φ with invariant mass mB in the range 5200 −
5550 MeV. The latter is computed with the invariant mass of the µ+µ− pair constrained to the nominal J/ψ mass. The decay time t of the B0s is obtained from a
ver-tex fit that constrains the Bs0→ µ+µ−K+K− candidate
to originate from the primary vertex [10]. The χ2of the
fit, which has 7 degrees of freedom, is required to be less than 35. In the small fraction of events with more than one candidate, only the candidate with the smallest χ2
is kept. B0
s candidates are required to have a decay time
within the range 0.3 < t < 14.0 ps. Applying a lower bound on the decay time suppresses a large fraction of the prompt combinatorial background whilst having a small effect on the sensitivity to φs. From a fit to the
mB distribution, shown in Fig. 1, we extract a signal of
8492 ± 97 events.
The B0s→ J/ψ φ → µ+µ−K+K− decay proceeds via
two intermediate spin-1 particles (i.e. with the K+K− pair in a P-wave). The final state can be CP -even or CP -odd depending upon the relative orbital angular mo-mentum between the J/ψ and the φ. The same final state can also be produced with K+K− pairs with zero
relative orbital angular momentum (S-wave) [11] . This S-wave final state is CP -odd. In order to measure φs
it is necessary to disentangle the CP -even and CP -odd components. This is achieved by analysing the distribu-tion of the reconstructed decay angles Ω = (θ, ψ, ϕ) in the transversity basis [12, 13]. In the J/ψ rest frame we define a right-handed coordinate system such that the x axis is parallel to the direction of the φ momentum and the z axis is parallel to the cross-product of the K− and K+ momenta. In this frame θ and ϕ are the azimuthal and polar angles of the µ+. The angle ψ is the angle
[MeV] B m 5300 5350 5400 Events / 2 MeV 0 500 1000 data signal background sum
LHCb
FIG. 1. Invariant mass distribution for B0
s → µ+µ −
K+K−
candidates with the mass of the µ+µ− pair constrained to
the nominal J/ψ mass. Curves for fitted contributions from signal (dashed), background (dotted) and their sum (solid) are overlaid.
between the K− momentum and the J/ψ momentum in the rest frame of the φ.
We perform an unbinned maximum likelihood fit to the invariant mass mB, the decay time t, and the three decay
angles Ω. The probability density function (PDF) used in the fit consists of signal and background components which include detector resolution and acceptance effects. The PDFs are factorised into separate components for the mass and for the remaining observables.
The signal mB distribution is described by two
Gaus-sian functions with a common mean. The mean and width of the narrow Gaussian are fit parameters. The
fraction of the second Gaussian and its width relative to the narrow Gaussian are fixed to values obtained from simulated events. The mB distribution for the
combina-torial background is described by an exponential func-tion with a slope determined by the fit. Possible peaking background from decays with similar final states such as B0 → J/ψ K∗0 is found to be negligible from studies
using simulated events.
The distribution of the signal decay time and angles is described by a sum of ten terms, corresponding to the four polarization amplitudes and their interference terms. Each of these is the product of a time-dependent function and an angular function [12]
d4Γ(Bs0→ J/ψ φ) dt dΩ ∝ 10 X k=1 hk(t) fk(Ω) . (1)
The time-dependent functions hk(t) can be written as
hk(t) = Nke−Γst [ckcos(∆mst) + dksin(∆mst)
+akcosh 12∆Γst + bksinh 12∆Γst . (2)
where ∆ms is the Bs0 oscillation frequency. The
coeffi-cients Nk and ak, . . . , dk can be expressed in terms of φs
and four complex transversity amplitudes Ai at t = 0.
The label i takes the values {⊥, k, 0} for the three P-wave amplitudes and S for the S-P-wave amplitude. In the fit we parameterize each Ai(0) by its magnitude squared
|Ai(0)|2and its phase δi, and adopt the convention δ0= 0
and P |Ai(0)|2 = 1. For a particle produced in a B0s
flavour eigenstate the coefficients in Eq. 2 and the angu-lar functions fk(Ω) are then, see [13, 14], given by
k fk(θ, ψ, ϕ) Nk ak bk ck dk
1 2 cos2ψ 1 − sin2θ cos2φ |A0(0)|2 1 − cos φs 0 sin φs
2 sin2ψ 1 − sin2θ sin2φ
|Ak(0)|2 1 − cos φ
s 0 sin φs
3 sin2ψ sin2θ |A⊥(0)|2 1 cos φs 0 − sin φs
4 − sin2ψ sin 2θ sin φ |Ak(0)A⊥(0)| 0 − cos(δ⊥− δk) sin φs sin(δ⊥− δk) − cos(δ⊥− δk) cos φs
5 12√2 sin 2ψ sin2θ sin 2φ |A0(0)Ak(0)| cos(δk− δ0) − cos(δk− δ0) cos φs 0 cos(δk− δ0) sin φs
6 1
2
√
2 sin 2ψ sin 2θ cos φ |A0(0)A⊥(0)| 0 − cos(δ⊥− δ0) sin φs sin(δ⊥− δ0) − cos(δ⊥− δ0) cos φs
7 23(1 − sin2θ cos2φ) |A
S(0)|2 1 cos φs 0 − sin φs
8 1
3
√
6 sin ψ sin2θ sin 2φ |AS(0)Ak(0)| 0 − sin(δk− δS) sin φs cos(δk− δS) − sin(δk− δS) cos φs
9 13√6 sin ψ sin 2θ cos φ |AS(0)A⊥(0)| sin(δ⊥− δS) sin(δ⊥− δS) cos φs 0 − sin(δ⊥− δS) sin φs
10 43√3 cos ψ(1 − sin2θ cos2φ) |AS(0)A0(0)| 0 − sin(δ0− δS) sin φs cos(δ0− δS) − sin(δ0− δS) cos φs
We neglect CP violation in mixing and in the decay amplitudes. The differential decay rates for a B0
s meson
produced at time t = 0 are obtained by changing the sign of φs, A⊥(0) and AS(0), or, equivalently, the sign
of ck and dk in the expressions above. The PDF is
in-variant under the transformation (φs, ∆Γs, δk, δ⊥, δS) 7→
(π − φs, −∆Γs, −δk, π − δ⊥, −δS) which gives rise to a
two-fold ambiguity in the results.
We have verified that correlations between decay time and decay angles in the background are small enough to be ignored. Using the data in the mB sidebands, which
we define as selected events with mB outside the range
5311 − 5411 MeV, we determine that the background decay time distribution can be modelled by a sum of two exponential functions. The lifetime parameters and the relative fraction are determined by the fit. The decay angle distribution is modelled using a histogram obtained from the data in the mBsidebands. The normalisation of
the background with respect to the signal is determined by the fit.
The measurement of φs requires knowledge of the
flavour of the Bs0 meson at production. We exploit the following flavour specific features of the accompanying (non-signal) b-hadron decay to tag the Bs0 flavour: the
charge of a muon or an electron with large transverse mo-mentum produced by semileptonic decays, the charge of a kaon from a subsequent charmed hadron decay and the momentum-weighted charge of all tracks included in the inclusively reconstructed decay vertex. These signatures are combined using a neural network to estimate a per-event mistag probability, ω, which is calibrated with data from control channels [15]. The fraction of tagged events in the signal sample is εtag= (24.9 ± 0.5)%. The dilution
of the CP asymmetry due to the mistag probability is D = 1 − 2ω. The effective dilution in our signal sample is D = 0.277 ± 0.006 (stat) ± 0.016 (syst), resulting in an effective tagging efficiency of εtagD2 = (1.91 ± 0.23)%.
The uncertainty in ω is taken into account by allowing calibration parameters described in Ref. [15] to vary in the fit with Gaussian constraints given by their estimated uncertainties. Both tagged and untagged events are used in the fit. The untagged events dominate the sensitivity to the lifetimes and amplitudes.
To account for the decay time resolution, the PDF is convolved with a sum of three Gaussian functions with a common mean and different widths. Studies on simulated data have shown that selected prompt J/ψ K+K−
combi-nations have nearly identical resolution to signal events. Consequently, we determine the parameters of the res-olution model from a fit to the decay time distribution of such prompt combinations in the data, after subtract-ing non-J/ψ events with the sPlot method [16] ussubtract-ing the µ+µ− invariant mass as discriminating variable. The re-sulting dilution is equivalent to that of a single Gaussian with a width of 50 fs. The uncertainty on the decay time resolution is estimated to be 4% by varying the selection of events and by comparing in the simulation the reso-lutions obtained for prompt combinations and B0
s signal
events. This uncertainty is accounted for by scaling the widths of the three Gaussians by a common factor of 1.00 ± 0.04, which is varied in the fit subject to a Gaus-sian constraint. In similar fashion the uncertainty on the mixing frequency is taken into account by varying it within the constraint imposed by the LHCb measurement
∆ms= 17.63 ± 0.11 (stat) ± 0.02 (syst) ps−1 [17].
The decay time distribution is affected by two accep-tance effects. First, the efficiency decreases approxi-mately linearly with decay time due to inefficiencies in the reconstruction of tracks far from the central axis of the detector. This effect is parameterized as (t) ∝ (1 − βt) where the factor β = 0.016 ps−1 is determined from simulated events. Second, a fraction of approxi-mately 14% of the events has been selected exclusively by a trigger path that exploits large impact parameters of the decay products, leading to a drop in efficiency at small decay times. This effect is described by the empiri-cal acceptance function (t) ∝ (at)c/ [1 + (at)c], applied
only to these events. The parameters a and c are deter-mined in the fit. As a result, the events selected with impact parameter cuts do effectively not contribute to the measurement of Γs.
The uncertainty on the reconstructed decay angles is small and is neglected in the fit. The decay angle accep-tance is determined using simulated events. The devia-tion from a flat acceptance is due to the LHCb forward geometry and selection requirements on the momenta of final state particles. The acceptance varies by less than 5% over the full range for all three angles.
The results of the fit for the main observables are shown in Table I. The likelihood profile for δk is not
parabolic and we therefore quote the 68% confidence level (CL) range 3.0 < δk < 3.5. The correlation coefficients
for the statistical uncertainties are ρ(Γs, ∆Γs) = −0.30,
ρ(Γs, φs) = 0.12 and ρ(∆Γs, φs) = −0.08. Figure 2 shows
the data distribution for decay time and angles with the projections of the best fit PDF overlaid. To assess the overall agreement of the PDF with the data we calculate the goodness of fit based on the point-to-point dissimilar-ity test [18]. The p-value obtained is 0.68. Figure 3 shows the 68%, 90% and 95% CL contours in the ∆Γs-φsplane.
These contours are obtained from the likelihood profile after including systematic uncertainties, and correspond to decreases in the natural logarithm of the likelihood, with respect to its maximum, of 1.15, 2.30 and 3.00 re-spectively.
TABLE I. Fit results for the solution with ∆Γs > 0 with
statistical and systematic uncertainties.
parameter value σstat. σsyst.
Γs[ps−1] 0.657 0.009 0.008 ∆Γs [ps−1] 0.123 0.029 0.011 |A⊥(0)|2 0.237 0.015 0.012 |A0(0)|2 0.497 0.013 0.030 |AS(0)|2 0.042 0.015 0.018 δ⊥[rad] 2.95 0.37 0.12 δS [rad] 2.98 0.36 0.12 φs[rad] 0.15 0.18 0.06 3
decay time [ps] 2 4 6 8 Events / 0.2 ps 1 10 2 10 3 10 LHCb θ cos -1 -0.5 0 0.5 1 Events / 0.1 0 200 400 600 LHCb ψ cos -1 -0.5 0 0.5 1 Events / 0.1 0 200 400 600 LHCb [rad] ϕ -2 0 2 Events / 0.31 rad 0 200 400 600 LHCb
FIG. 2. Projections for the decay time and transversity angle
distributions for events with mB in a ± 20 MeV range around
the Bs0 mass. The points are the data. The dashed, dotted
and solid lines represent the fitted contributions from signal, background and their sum. The remaining curves correspond to different contributions to the signal, namely the CP -even P-wave (dashed with single dot), the CP -odd P-wave (dashed with double dot) and the S-wave (dashed with triple dot).
The sensitivity to φs stems mainly from its
appear-ance as the amplitude of the sin(∆mst) term in Eq. 1,
which is diluted by the decay time resolution and mistag probability. Systematic uncertainties from these sources and from the mixing frequency are absorbed in the sta-tistical uncertainties as explained above. Other system-atic uncertainties are determined as follows, and added in quadrature to give the values shown in Table I.
To test our understanding of the decay angle accep-tance we compare the rapidity and momentum distribu-tions of the kaons and muons of selected B0
s candidates
in data and simulated events. Only in the kaon momen-tum distribution do we observe a significant discrepancy. We reweight the simulated events to match the data, red-erive the acceptance corrections and assign the resulting difference in the fit result as a systematic uncertainty. This is the dominant contribution to the systematic un-certainty on all parameters except Γs. The limited size
of the simulated event sample leads to a small additional uncertainty. The systematic uncertainty due to the back-ground decay angle modelling was found to be negligible by comparing with a fit where the background was re-moved statistically using the sPlot method [16].
In the fit each |Ai(0)|2 is constrained to be greater
than zero, while their sum is constrained to unity. This can result in a bias if one or more of the amplitudes is small. This is the case for the S-wave amplitude, which is compatible with zero within 3.2 standard deviations. The resulting biases on the |Ai(0)|2have been determined
using simulations to be less than 0.010 and are included
[rad] s φ 0 2 4 ] -1 [ pss Γ∆ -0.2 -0.1 0 0.1 0.2 best fit 68% CL 90% CL 95% CL Standard Model LHCb
FIG. 3. Likelihood confidence regions in the ∆Γs-φs plane.
The black square and error bar corresponds to the Standard Model prediction [3, 4].
as systematic uncertainties.
Finally, a systematic uncertainty of 0.008 ps−1 was as-signed to the measurement of Γs due to the uncertainty
in the decay time acceptance parameter β. Other sys-tematic uncertainties, such as those from the momentum scale and length scale of the detector, were found to be negligible.
In summary, in a sample of 0.37 fb−1 of pp collisions at√s = 7 TeV collected with the LHCb detector we ob-serve 8492 ± 97 Bs0 → J/ψ K+K− events with K+K−
invariant mass within ± 12 MeV of the φ mass. With these data we perform the most precise measurements of φs, ∆Γs and Γs in Bs0→ J/ψ φ decays, substantially
improving upon previous measurements [7] and provid-ing the first direct evidence for a non-zero value of ∆Γs.
Two solutions with equal likelihood are obtained, related by the transformation (φs, ∆Γs) 7→ (π − φs, −∆Γs). The
solution with positive ∆Γs is
φs = 0.15 ± 0.18 (stat) ± 0.06 (syst) rad,
Γs = 0.657 ± 0.009 (stat) ± 0.008 (syst) ps−1,
∆Γs= 0.123 ± 0.029 (stat) ± 0.011 (syst) ps−1,
and is in agreement with the Standard Model predic-tion [3, 4]. Values of φs in the range 0.52 < φs < 2.62
and −2.93 < φs < −0.21 are excluded at 95%
confi-dence level. In a future publication we shall differentiate between the two solutions by exploiting the dependence of the phase difference between the P-wave and S-wave contributions on the K+K− invariant mass [14].
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 CERN and at the LHCb institutes, and acknowledge support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN, Xun-taGal and GENCAT (Spain); SNSF and SER (Switzer-land); NAS Ukraine (Ukraine); STFC (United King-dom); NSF (USA). We also acknowledge the support received from the ERC under FP7 and the Region Au-vergne.
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