Differential branching fraction and angular analysis of the - arXiv.org

34 Pages·2013·0.86 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2013-074
LHCb-PAPER-2013-019
8 July 2013
3
1
0 Differential branching fraction
2

t
c and angular analysis of
O
0 ∗0 + −
3 the decay B → K µ µ
2

]
x
e
-
p
e
h
[ The LHCb collaboration†

2
v Abstract
5
2 The angular distribution and differential branching fraction of the decay
3 B0 K∗0µ+µ− are studied using a data sample, collected by the LHCb experi-
6 →
ment in pp collisions at √s = 7TeV, corresponding to an integrated luminosity of
.
4 1.0fb−1. Several angular observables are measured in bins of the dimuon invariant
0
mass squared, q2. A first measurement of the zero-crossing point of the forward-
3
1 backward asymmetry of the dimuon system is also presented. The zero-crossing
v: point is measured to be q2 = 4.9 0.9GeV2/c4, where the uncertainty is the sum of
0 ±
i statistical and systematic uncertainties. The results are consistent with the Standard
X
Model predictions.
r
a
Submitted to JHEP
c CERN on behalf of the LHCb collaboration, license CC-BY-3.0.
(cid:13)
†Authors are listed on the following pages.
ii
LHCb collaboration
R. Aaij40, C. Abellan Beteta35,n, 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 Jr24,37, S. Amato2, S. Amerio21, Y. Amhis7, L. Anderlini17,f,
J. Anderson39, R. Andreassen56, R.B. Appleby53, O. Aquines Gutierrez10, F. Archilli18,
A. Artamonov 34, M. Artuso58, E. Aslanides6, G. Auriemma24,m, S. Bachmann11, J.J. Back47,
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. Blouw11, 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, I. Burducea28, 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, M. Charles54, Ph. Charpentier37,
P. Chen3,38, N. Chiapolini39, M. Chrzaszcz 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, 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 Cian39, J.M. De Miranda1, L. De Paula2, W. De Silva56,
P. De Simone18, D. Decamp4, M. Deckenhoff9, L. Del Buono8, N. D´el´eage4, D. Derkach14,
O. Deschamps5, F. Dettori41, A. Di Canto11, F. Di Ruscio23,k, H. Dijkstra37, M. Dogaru28,
S. Donleavy51, F. Dordei11, A. Dosil Su´arez36, D. Dossett47, A. Dovbnya42, F. Dupertuis38,
R. Dzhelyadin34, A. Dziurda25, A. Dzyuba29, S. Easo48,37, U. Egede52, V. Egorychev30,
S. Eidelman33, D. van Eijk40, S. Eisenhardt49, U. Eitschberger9, R. Ekelhof9, L. Eklund50,37,
I. El Rifai5, Ch. Elsasser39, D. Elsby44, A. Falabella14,e, C. Fa¨rber11, G. Fardell49, C. Farinelli40,
S. Farry12, V. Fave38, D. Ferguson49, V. Fernandez Albor36, F. Ferreira Rodrigues1,
M. Ferro-Luzzi37, S. Filippov32, M. Fiore16, C. Fitzpatrick37, M. Fontana10, F. Fontanelli19,i,
R. Forty37, O. Francisco2, M. Frank37, C. Frei37, M. Frosini17,f, S. Furcas20, 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. Gershon47,37, Ph. Ghez4, V. Gibson46, V.V. Gligorov37, C. G¨obel59,
D. Golubkov30, A. Golutvin52,30,37, A. Gomes2, H. Gordon54, M. Grabalosa G´andara5,
R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graug´es35, G. Graziani17, A. Grecu28,
E. Greening54, S. Gregson46, P. Griffith44, O. Gru¨nberg60, B. Gui58, E. Gushchin32, Yu. Guz34,37,
T. Gys37, C. Hadjivasiliou58, G. Haefeli38, C. Haen37, S.C. Haines46, S. Hall52, T. Hampson45,
S. Hansmann-Menzemer11, N. Harnew54, S.T. Harnew45, J. Harrison53, T. Hartmann60, J. He37,
V. Heijne40, K. Hennessy51, P. Henrard5, J.A. Hernando Morata36, E. van Herwijnen37,
E. Hicks51, D. Hill54, M. Hoballah5, C. Hombach53, P. Hopchev4, 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,
iii
D. Johnson54, C.R. Jones46, C. Joram37, B. Jost37, M. Kaballo9, S. Kandybei42, M. Karacson37,
T.M. Karbach37, I.R. Kenyon44, U. Kerzel37, T. Ketel41, A. Keune38, 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,j, V. Kudryavtsev33, 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. Lef`evre5, A. Leflat31, J. Lefranc¸ois7, 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, E. Lopez Asamar35, N. Lopez-March38, H. Lu3,
D. Lucchesi21,q, J. Luisier38, H. Luo49, F. Machefert7, I.V. Machikhiliyan4,30, F. Maciuc28,
O. Maev29,37, S. Malde54, G. Manca15,d, G. Mancinelli6, U. Marconi14, R. M¨arki38, J. Marks11,
G. Martellotti24, A. Martens8, L. Martin54, A. Mart´ın S´anchez7, M. Martinelli40,
D. Martinez Santos41, D. Martins Tostes2, A. Massafferri1, R. Matev37, Z. Mathe37,
C. Matteuzzi20, E. Maurice6, A. Mazurov16,32,37,e, J. McCarthy44, A. McNab53, R. McNulty12,
B. Meadows56,54, F. Meier9, M. Meissner11, M. Merk40, D.A. Milanes8, M.-N. Minard4,
J. Molina Rodriguez59, S. Monteil5, D. Moran53, P. Morawski25, M.J. Morello22,s,
R. Mountain58, I. Mous40, F. Muheim49, K. Mu¨ller39, R. Muresan28, B. Muryn26, B. Muster38,
P. Naik45, T. Nakada38, R. Nandakumar48, I. Nasteva1, M. Needham49, N. Neufeld37,
A.D. Nguyen38, T.D. Nguyen38, C. Nguyen-Mau38,p, 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. Oyanguren 35,o, 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. Pellegrino40, G. Penso24,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, K. Petridis52, A. Petrolini19,i, A. Phan58, E. Picatoste Olloqui35, B. Pietrzyk4,
T. Pilaˇr47, 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, V. Pugatch43, A. Puig Navarro38, G. Punzi22,r, W. Qian4, J.H. Rademacker45,
B. Rakotomiaramanana38, M.S. Rangel2, I. Raniuk42, N. Rauschmayr37, G. Raven41,
S. Redford54, M.M. Reid47, A.C. dos Reis1, S. Ricciardi48, A. Richards52, K. Rinnert51,
V. Rives Molina35, D.A. Roa Romero5, P. Robbe7, E. Rodrigues53, P. Rodriguez Perez36,
S. Roiser37, V. Romanovsky34, A. Romero Vidal36, J. Rouvinet38, T. Ruf37, F. Ruffini22,
H. Ruiz35, P. Ruiz Valls35,o, G. Sabatino24,k, J.J. Saborido Silva36, N. Sagidova29, P. Sail50,
B. Saitta15,d, V. Salustino Guimaraes2, C. Salzmann39, B. Sanmartin Sedes36, M. Sannino19,i,
R. Santacesaria24, C. Santamarina Rios36, E. Santovetti23,k, M. Sapunov6, A. Sarti18,l,
C. Satriano24,m, A. Satta23, M. Savrie16,e, D. Savrina30,31, P. Schaack52, 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, P. Shatalov30, Y. Shcheglov29, T. Shears51,37, L. Shekhtman33, O. Shevchenko42,
V. Shevchenko30, A. Shires52, R. Silva Coutinho47, T. Skwarnicki58, N.A. Smith51, E. Smith54,48,
M. Smith53, M.D. Sokoloff56, F.J.P. Soler50, F. Soomro18, D. Souza45, B. Souza De Paula2,
B. Spaan9, A. Sparkes49, P. Spradlin50, F. Stagni37, S. Stahl11, O. Steinkamp39, S. Stoica28,
iv
S. Stone58, B. Storaci39, M. Straticiuc28, U. Straumann39, V.K. Subbiah37, L. Sun56,
S. Swientek9, V. Syropoulos41, M. Szczekowski27, P. Szczypka38,37, 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, M. Ubeda Garcia37, A. Ukleja27, D. Urner53, U. Uwer11, V. Vagnoni14,
G. Valenti14, R. Vazquez Gomez35, P. Vazquez Regueiro36, 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, 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. Wishahi9,
M. Witek25, S.A. Wotton46, S. Wright46, S. Wu3, K. Wyllie37, Y. Xie49,37, F. Xing54, Z. Xing58,
Z. Yang3, R. Young49, 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 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
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 Universita¨t Dortmund, Dortmund, Germany
10Max-Planck-Institut fu¨r 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 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, Krak´ow, Poland
26AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science,
Krak´ow, 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
v
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 Zu¨rich, Zu¨rich, 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
59Pontif´ıcia Universidade Cato´lica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2
60Institut fu¨r Physik, Universit¨at Rostock, Rostock, Germany, associated to 11
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
oIFIC, Universitat de Valencia-CSIC, Valencia, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversit`a di Padova, Padova, Italy
rUniversit`a di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
vi
1 Introduction
The B0 K∗0µ+µ− decay,1 where K∗0 K+π−, is a b s flavour changing neutral
→ → →
current process that is mediated by electroweak box and penguin type diagrams in the
Standard Model (SM). The angular distribution of the K+π−µ+µ− system offers particular
sensitivity to contributions from new particles in extensions to the SM. The differential
branching fraction of the decay also provides information on the contribution from those
new particles but typically suffers from larger theoretical uncertainties due to hadronic
form factors.
The angular distribution of the decay can be described by three angles (θ ,θ and
(cid:96) K
φ) and by the invariant mass squared of the dimuon system (q2). The B0 K∗0µ+µ−
→
decay is self-tagging through the charge of the kaon and so there is some freedom in the
choice of the angular basis that is used to describe the decay. In this paper, the angle θ is
(cid:96)
defined as the angle between the direction of the µ+ (µ−) and the direction opposite that
of the B0 (B0) in the dimuon rest frame. The angle θ is defined as the angle between the
K
direction of the kaon and the direction of opposite that of the B0 (B0) in in the K∗0 (K∗0)
rest frame. The angle φ is the angle between the plane containing the µ+ and µ− and the
plane containing the kaon and pion from the K∗0 (K∗0) in the B0 (B0) rest frame. The
basis is designed such that the angular definition for the B0 decay is a CP transformation
of that for the B0 decay. This basis differs from some that appear in the literature. A
graphical representation, and a more detailed description, of the angular basis is given in
Appendix A.
Using the notation of Ref. [1], the decay distribution of the B0 corresponds to
d4Γ 9 (cid:104)
= Issin2θ +Iccos2θ +
dq2dcosθ dcosθ dφ 32π 1 K 1 K
(cid:96) K
Issin2θ cos2θ +Iccos2θ cos2θ +
2 K (cid:96) 2 K (cid:96)
I sin2θ sin2θ cos2φ+I sin2θ sin2θ cosφ +
3 K (cid:96) 4 K (cid:96)
(1)
I sin2θ sinθ cosφ+I sin2θ cosθ +
5 K (cid:96) 6 K (cid:96)
I sin2θ sinθ sinφ+I sin2θ sin2θ sinφ +
7 K (cid:96) 8 K (cid:96)
(cid:105)
I sin2θ sin2θ sin2φ ,
9 K (cid:96)
where the 11 coefficients, I , are bilinear combinations of K∗0 decay amplitudes, , and
j m
A
vary with q2. The superscripts s and c in the first two terms arise in Ref. [1] and indicate
either a sin2θ or cos2θ dependence of the corresponding angular term. In the SM,
K K
there are seven complex decay amplitudes, corresponding to different polarisation states
of the K∗0 and chiralities of the dimuon system. In the angular coefficients, the decay
amplitudes appear in the combinations 2, Re( ∗) and Im( ∗). Combining
|Am| AmAn AmAn
1Charge conjugation is implied throughout this paper unless stated otherwise.
1
B0 and B0 decays, and assuming there are equal numbers of each, it is possible to build
angular observables that depend on the average of, or difference between, the distributions
for the B0 and B0 decay,
(cid:30) (cid:30)
(cid:0) ¯(cid:1) dΓ (cid:0) ¯(cid:1) dΓ
S = I +I or A = I I . (2)
j j j dq2 j j − j dq2
These observables are referred to below as CP averages or CP asymmetries and are
normalised with respect to the combined differential decay rate, dΓ/dq2, of B0 and B0
decays. The observables S , S and S depend on combinations Im( ∗) and are
7 8 9 AmAn
suppressed by the small size of the strong phase difference between the decay amplitudes.
They are consequently expected to be close to zero across the full q2 range not only in
the SM but also in most extensions. However, the corresponding CP asymmetries, A , A
7 8
and A , are not suppressed by the strong phases involved [2] and remain sensitive to the
9
effects of new particles.
If the B0 and B0 decays are combined using the angular basis in Appendix A, the
resulting angular distribution is sensitive to only the CP averages of each of the angular
terms. Sensitivity to A , A and A is achieved by flipping the sign of φ (φ φ) for the
7 8 9
→ −
B0 decay. This procedure results in a combined B0 and B0 angular distribution that is
sensitive to the CP averages S S and the CP asymmetries of A , A and A .
1 6 7 8 9
−
Inthelimitthatthedimuonmassislargecomparedtothemassofthemuons,q2 4m2,
(cid:29) µ
the CP average of Ic, Is, Ic and Is (Sc, Ss, Sc and Ss) are related to the fraction of
1 1 2 2 1 1 2 2
longitudinal polarisation of the K∗0 meson, F (Sc = Sc = F and 4Ss = 4Ss = 1 F ).
L 1 − 2 L 3 1 2 − L
The angular term, I in Eq. 1, which has a sin2θ cosθ dependence, generates a forward-
6 K (cid:96)
backward asymmetry of the dimuon system, A [3] (A = 3S ). The term S is related
FB FB 4 6 3
to the asymmetry between the two sets of transverse K∗0 amplitudes, referred to in
literature as A2 [4], where S = 1 (1 F )A2.
T 3 2 − L T
In the SM, A varies as a function of q2 and is known to change sign. The q2
FB
dependence arises from the interplay between the different penguin and box diagrams that
contribute to the decay. The position of the zero-crossing point of A is a precision test
FB
of the SM since, in the limit of large K∗0 energy, its prediction is free from form-factor
uncertainties [3]. At large recoil, low values of q2, penguin diagrams involving a virtual
photon dominate. In this q2 region, A2 is sensitive to the polarisation of the virtual photon
T
which, in the SM, is predominately left-handed, due to the nature of the charged-current
interaction. In many possible extensions of the SM however, the photon can be both left-
or right-hand polarised, leading to large enhancements of A2 [4].
T
The one-dimensional cosθ and cosθ distributions have previously been studied by
(cid:96) K
the LHCb [5], BaBar [6], Belle [7] and CDF [8] experiments with much smaller data
samples. The CDF experiment has also previously studied the φ angle. Even with the
larger dataset available in this analysis, it is not yet possible to fit the data for all 11
angular terms. Instead, rather than examining the one dimensional projections as has
been done in previous analyses, the angle φ is transformed such that
2
(cid:40)
φ+π if φ < 0
ˆ
φ = (3)
φ otherwise
to cancel terms in Eq. 1 that have either a sinφ or a cosφ dependence. This provides a
simplified angular expression, which contains only F , A , S and A ,
L FB 3 9
(cid:20)
1 d4Γ 9 3
= F cos2θ + (1 F )(1 cos2θ )
dΓ/dq2dq2dcosθ dcosθ dφˆ 16π L K 4 − L − K −
(cid:96) K
F cos2θ (2cos2θ 1) +
L K (cid:96)
−
1
(1 F )(1 cos2θ )(2cos2θ 1) +
L K (cid:96)
4 − − − (4)
S (1 cos2θ )(1 cos2θ )cos2φˆ +
3 K (cid:96)
− −
4
A (1 cos2θ )cosθ +
FB K (cid:96)
3 −
(cid:105)
A (1 cos2θ )(1 cos2θ )sin2φˆ .
9 K (cid:96)
− −
This expression involves the same set of observables that can be extracted from fits to the
one-dimensional angular projections.
At large recoil it is also advantageous to reformulate Eq. 4 in terms of the observables
A2 and ARe, where A = 3 (1 F )ARe. These so called “transverse” observables only
T T FB 4 − L T
depend on a subset of the decay amplitudes (with transverse polarisation of the K∗0) and
are expected to come with reduced form-factor uncertainties [4,9]. A first measurement of
A2 was performed by the CDF experiment [8].
T
This paper presents a measurement of the differential branching fraction (d /dq2),
B
A , F , S and A of the B0 K∗0µ+µ− decay in six bins of q2. Measurements of the
FB L 3 9
→
transverse observables A2 and ARe are also presented. The analysis is based on a dataset,
T T
corresponding to 1.0fb−1 of integrated luminosity, collected by the LHCb detector in
√s = 7TeV pp collisions in 2011. Section 2 describes the experimental setup used in the
analyses. Section 3 describes the event selection. Section 4 discusses potential sources of
peaking background. Section 5 describes the treatment of the detector acceptance in the
analysis. Section 6 discusses the measurement of d /dq2. The angular analysis of the
ˆ B
decay, in terms of cosθ , cosθ and φ, is described in Sec. 7. Finally, a first measurement
(cid:96) K
of the zero-crossing point of A is presented in Sec. 8.
FB
2 The LHCb detector
The LHCb detector [10] is a single-arm forward spectrometer, covering the pseudorapidity
range 2 < η < 5, that is designed to study b and c hadron decays. A dipole magnet with a
bending power of 4Tm and a large area tracking detector provide momentum resolution
ranging from 0.4% for tracks with a momentum of 5GeV/c to 0.6% for a momentum
3
of 100GeV/c. A silicon microstrip detector, located around the pp interaction region,
provides excellent separation of B meson decay vertices from the primary pp interaction
and impact parameter resolution of 20µm for tracks with high transverse momentum (p ).
T
Two ring-imaging Cherenkov (RICH) detectors [11] provide kaon-pion separation in the
momentum range 2 100GeV/c. Muons are identified based on hits created in a system
−
of multiwire proportional chambers interleaved with layers of iron. The LHCb trigger [12]
comprises a hardware trigger and a two-stage software trigger that performs a full event
reconstruction.
Samples of simulated events are used to estimate the contribution from specific sources
of exclusive backgrounds and the efficiency to trigger, reconstruct and select the B0
K∗0µ+µ− signal. The simulated pp interactions are generated using Pythia 6.4 [13] wi→th
a specific LHCb configuration [14]. Decays of hadronic particles are then described by
EvtGen Photos
[15] in which final state radiation is generated using [16]. Finally, the
Geant4
toolkit [17] is used to simulate the detector response to the particles produced
Pythia EvtGen
by / , as described in Ref. [18]. The simulated samples are corrected
for known differences between data and simulation in the B0 momentum spectrum, the
detector impact parameter resolution, particle identification [11] and tracking system
performance using control samples from the data.
3 Selection of signal candidates
The B0 K∗0µ+µ− candidates are selected from events that have been triggered by a
→
muon with p > 1.5GeV/c, in the hardware trigger. In the first stage of the software
T
trigger, candidates are selected if there is a reconstructed track in the event with high
impact parameter (> 125µm) with respect to one of the primary pp interactions and
p > 1.5GeV/c. In the second stage of the software trigger, candidates are triggered on
T
the kinematic properties of the partially or fully reconstructed B0 candidate [12].
Signal candidates are then required to pass a set of loose (pre-)selection requirements.
Candidates are selected for further analysis if: the B0 decay vertex is separated from
the primary pp interaction; the B0 candidate impact parameter is small, and the impact
parameters of the charged kaon, pion and muons are large, with respect to the primary pp
interaction; and the angle between the B0 momentum vector and the vector between the
primary pp interaction and the B0 decay vertex is small. Candidates are retained if their
K+π− invariant mass is in the range 792 < m(K+π−) < 992MeV/c2.
A multivariate selection, using a boosted decision tree (BDT) [19] with the AdaBoost
algorithm[20], isappliedtofurtherreducethelevelofcombinatorialbackground. TheBDT
isidenticaltothatdescribedinRef.[5]. Ithasbeentrainedonadatasample, corresponding
to 36pb−1 of integrated luminosity, collected by the LHCb experiment in 2010. A sample
of B0 K∗0J/ψ (J/ψ µ+µ−) candidates is used to represent the B0 K∗0µ+µ− signal
→ → →
in the BDT training. The decay B0 K∗0J/ψ is used throughout this analysis as a
→
control channel. Candidates from the B0 K∗0µ+µ− upper mass sideband (5350 <
→
m(K+π−µ+µ−) < 5600MeV/c2) are used as a background sample. Candidates with
4