EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

LHCb-PAPER-2011-023CERN-PH-EP-2011-208

March 19, 2012

Evidence for CP violation in time-integrated D0 → h−h+ decay rates

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. Artamonov 34, 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. Buchler-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 Suarez36, 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. Esteve43, A. Falabella16,14,e,

E. Fanchini20,j , C. Farber11, 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. Gobel54, D. Golubkov30,

A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa Gandara35, R. Graciani Diaz35,

L.A. Granado Cardoso37, E. Grauges35, 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,

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, R. Koopman24, 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. Lefevre5, A. Leflat31,37, J. Lefrancois7, 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,

arX

iv:1

112.

0938

v2 [

hep-

ex]

16

Mar

201

2

2

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. Marki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51, A. Martın Sanchez7,

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. Muller39, 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. Perez-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. Pilar44, 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 Fısicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China4LAPP, Universite de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France

5Clermont Universite, Universite Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France6CPPM, Aix-Marseille Universite, CNRS/IN2P3, Marseille, France

7LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay, France8LPNHE, Universite Pierre et Marie Curie, Universite Paris Diderot, CNRS/IN2P3, Paris, France

9Fakultat Physik, Technische Universitat Dortmund, Dortmund, Germany10Max-Planck-Institut fur Kernphysik (MPIK), Heidelberg, Germany

11Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg, Germany12School of Physics, University College Dublin, Dublin, Ireland

13Sezione INFN di Bari, Bari, Italy14Sezione INFN di Bologna, Bologna, Italy

3

15Sezione INFN di Cagliari, Cagliari, Italy16Sezione INFN di Ferrara, Ferrara, Italy17Sezione INFN di Firenze, Firenze, Italy

18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy19Sezione INFN di Genova, Genova, Italy

20Sezione INFN di Milano Bicocca, Milano, Italy21Sezione INFN di Roma Tor Vergata, Roma, Italy22Sezione INFN di Roma La Sapienza, Roma, Italy

23Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands24Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, The Netherlands25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kracow, Poland

26AGH University of Science and Technology, Kracow, Poland27Soltan Institute for Nuclear Studies, Warsaw, Poland

28Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia

30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia

34Institute for High Energy Physics (IHEP), Protvino, Russia35Universitat de Barcelona, Barcelona, Spain

36Universidad de Santiago de Compostela, Santiago de Compostela, Spain37European Organization for Nuclear Research (CERN), Geneva, Switzerland38Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland

39Physik-Institut, Universitat Zurich, Zurich, Switzerland40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine

41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom44Department of Physics, University of Warwick, Coventry, United Kingdom

45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom

47School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

49Imperial College London, London, United Kingdom50School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

51Department of Physics, University of Oxford, Oxford, United Kingdom52Syracuse University, Syracuse, NY, United States

53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member54Pontifıcia Universidade Catolica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

55University of Birmingham, Birmingham, United Kingdom56Physikalisches Institut, Universitat Rostock, Rostock, Germany, associated to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, RussiabUniversita di Bari, Bari, Italy

cUniversita di Bologna, Bologna, ItalydUniversita di Cagliari, Cagliari, ItalyeUniversita di Ferrara, Ferrara, ItalyfUniversita di Firenze, Firenze, ItalygUniversita di Urbino, Urbino, Italy

hUniversita di Modena e Reggio Emilia, Modena, ItalyiUniversita di Genova, Genova, Italy

jUniversita di Milano Bicocca, Milano, ItalykUniversita di Roma Tor Vergata, Roma, ItalylUniversita di Roma La Sapienza, Roma, ItalymUniversita della Basilicata, Potenza, Italy

nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, SpainoHanoi University of Science, Hanoi, Viet Nam

(The LHCb collaboration)

A search for time-integrated CP violation in D0 → h−h+ (h = K, π) decays is presented using0.62 fb−1 of data collected by LHCb in 2011. The flavor of the charm meson is determined by thecharge of the slow pion in the D∗+ → D0π+ and D∗− → D0π− decay chains. The difference inCP asymmetry between D0 → K−K+ and D0 → π−π+, ∆ACP ≡ ACP (K−K+) − ACP (π−π+),is measured to be [−0.82± 0.21(stat.)± 0.11(syst.)] %. This differs from the hypothesis of CPconservation by 3.5 standard deviations.

4

The charm sector is a promising place to probe forthe effects of physics beyond the Standard Model (SM).There has been a resurgence of interest in the past fewyears since evidence for D0 mixing was first seen [1, 2].Mixing is now well-established [3] at a level which is con-sistent with, but at the upper end of, SM expectations [4].By contrast, no evidence for CP violation in charm de-cays has yet been found.

The time-dependent CP asymmetry ACP (f ; t) for D0

decays to a CP eigenstate f (with f = f) is defined as

ACP (f ; t) ≡ Γ(D0(t)→ f)− Γ(D0(t)→ f)

Γ(D0(t)→ f) + Γ(D0(t)→ f), (1)

where Γ is the decay rate for the process indicated. Ingeneral ACP (f ; t) depends on f . For f = K−K+ andf = π−π+, ACP (f ; t) can be expressed in terms of twocontributions: a direct component associated with CPviolation in the decay amplitudes, and an indirect com-ponent associated with CP violation in the mixing or inthe interference between mixing and decay. In the limitof U-spin symmetry, the direct component is equal inmagnitude and opposite in sign for K−K+ and π−π+,though the size of U-spin breaking effects remains to bequantified precisely [5]. The magnitudes of CP asymme-tries in decays to these final states are expected to besmall in the SM [5–8], with predictions of up to O(10−3).However, beyond the SM the rate of CP violation couldbe enhanced [5, 9].

The asymmetry ACP (f ; t) may be written to first orderas [10, 11]

ACP (f ; t) = adirCP (f) +t

τaindCP , (2)

where adirCP (f) is the direct CP asymmetry, τ is theD0 lifetime, and aindCP is the indirect CP asymmetry.To a good approximation this latter quantity is uni-versal [5, 12]. The time-integrated asymmetry mea-sured by an experiment, ACP (f), depends upon the time-acceptance of that experiment. It can be written as

ACP (f) = adirCP (f) +〈t〉τaindCP , (3)

where 〈t〉 is the average decay time in the reconstructedsample. Denoting by ∆ the differences between quanti-ties for D0 → K−K+ and D0 → π−π+ it is then possibleto write

∆ACP ≡ ACP (K−K+) − ACP (π−π+) (4)

=[adirCP (K−K+) − adirCP (π−π+)

]+

∆〈t〉τ

aindCP .

In the limit that ∆〈t〉 vanishes, ∆ACP is equal to thedifference in the direct CP asymmetry between the twodecays. However, if the time-acceptance is different forthe K−K+ and π−π+ final states, a contribution fromindirect CP violation remains.

The most precise measurements to date of the time-integrated CP asymmetries in D0 → K−K+ and D0 →π−π+ were made by the CDF, BaBar, and Belle col-laborations [10, 13, 14]. The Heavy Flavor AveragingGroup (HFAG) has combined time-integrated and time-dependent measurements of CP asymmetries, taking ac-count of the different decay time acceptances, to ob-tain world average values for the indirect CP asymme-try of aindCP = (−0.03 ± 0.23)% and the difference in di-rect CP asymmetry between the final states of ∆adirCP =(−0.42± 0.27)% [3].

In this Letter, we present a measurement of the differ-ence in time-integrated CP asymmetries between D0 →K−K+ and D0 → π−π+, performed with 0.62 fb−1 ofdata collected at LHCb between March and June 2011.The flavor of the initial state (D0 or D0) is tagged byrequiring a D∗+ → D0π+

s decay, with the flavor deter-mined by the charge of the slow pion (π+

s ). The inclusionof charge-conjugate modes is implied throughout, exceptin the definition of asymmetries.

The raw asymmetry for tagged D0 decays to a finalstate f is given by Araw(f), defined as

Araw(f) ≡ N(D∗+ → D0(f)π+s ) − N(D∗− → D0(f)π−

s )

N(D∗+ → D0(f)π+s ) + N(D∗− → D0(f)π−

s ),

(5)where N(X) refers to the number of reconstructed eventsof decay X after background subtraction.

To first order the raw asymmetries may be written asa sum of four components, due to physics and detectoreffects:

Araw(f) = ACP (f) + AD(f) + AD(π+s ) + AP(D∗+). (6)

Here, AD(f) is the asymmetry in selecting the D0 de-cay into the final state f , AD(π+

s ) is the asymmetry inselecting the slow pion from the D∗+ decay chain, andAP(D∗+) is the production asymmetry for D∗+ mesons.The asymmetries AD and AP are defined in the samefashion as Araw. The first-order expansion is valid sincethe individual asymmetries are small.

For a two-body decay of a spin-0 particle to a self-conjugate final state there can be no D0 detection asym-metry, i.e. AD(K−K+) = AD(π−π+) = 0. Moreover,AD(π+

s ) and AP(D∗+) are independent of f and thus inthe first-order expansion of equation 5 those terms cancelin the difference Araw(K−K+) − Araw(π−π+), resultingin

∆ACP = Araw(K−K+) − Araw(π−π+). (7)

To minimize second-order effects that are related to theslightly different kinematic properties of the two decaymodes and that do not cancel in ∆ACP , the analysis isperformed in bins of the relevant kinematic variables, asdiscussed later.

The LHCb detector is a forward spectrometer coveringthe pseudorapidity range 2 < η < 5, and is described in

5

detail in Ref. [15]. The Ring Imaging Cherenkov (RICH)detectors are of particular importance to this analysis,providing kaon-pion discrimination for the full range oftrack momenta used. The nominal downstream beamdirection is aligned with the +z axis, and the field direc-tion in the LHCb dipole is such that charged particles aredeflected in the horizontal (xz) plane. The field polar-ity was changed several times during data taking: about60% of the data were taken with the down polarity and40% with the other.

Selections are applied to provide samples of D∗+ →D0π+

s candidates, with D0 → K−K+ or π−π+. Eventsare required to pass both hardware and software triggerlevels. A loose D0 selection is applied in the final state ofthe software trigger, and in the offline analysis only can-didates that are accepted by this trigger algorithm areconsidered. Both the trigger and offline selections imposea variety of requirements on kinematics and decay time toisolate the decays of interest, including requirements onthe track fit quality, on the D0 and D∗+ vertex fit qual-ity, on the transverse momentum (pT > 2 GeV/c) anddecay time (ct > 100 µm) of the D0 candidate, on theangle between the D0 momentum in the lab frame and itsdaughter momenta in the D0 rest frame (| cos θ| < 0.9),that the D0 trajectory points back to a primary vertex,and that the D0 daughter tracks do not. In addition,the offline analysis exploits the capabilities of the RICHsystem to distinguish between pions and kaons when re-constructing the D0 meson, with no tracks appearing asboth pion and kaon candidates.

A fiducial region is implemented by imposing the re-quirement that the slow pion lies within the central partof the detector acceptance. This is necessary because themagnetic field bends pions of one charge to the left andthose of the other charge to the right. For soft tracks atlarge angles in the xz plane this implies that one charge ismuch more likely to remain within the 300 mrad horizon-tal detector acceptance, thus making AD(π+

s ) large. Al-though this asymmetry is formally independent of the D0

decay mode, it breaks the assumption that the raw asym-metries are small and it carries a risk of second-order sys-tematic effects if the ratio of efficiencies of D0 → K−K+

and D0 → π−π+ varies in the affected region. The fidu-cial requirements therefore exclude edge regions in theslow pion (px, p) plane. Similarly, a small region of phasespace in which one charge of slow pion is more likely tobe swept into the beampipe region in the downstreamtracking stations, and hence has reduced efficiency, isalso excluded. After the implementation of the fiducialrequirements about 70% of the events are retained.

The invariant mass spectra of selected K−K+ andπ−π+ pairs are shown in Fig. 1. The half-width athalf-maximum of the signal lineshape is 8.6 MeV/c2 forK−K+ and 11.2 MeV/c2 for π−π+, where the differ-ence is due to the kinematics of the decays and hasno relevance for the subsequent analysis. The mass

)2c) (MeV/+K-K(m1820 1840 1860 1880 1900

)2 cEn

trie

s / (

0.5

MeV

/

0

20000

40000

60000 LHCb

)2c) (MeV/+π-π(m1820 1840 1860 1880 1900

)2 cEn

trie

s / (

0.5

MeV

/

0

5000

10000

LHCb

a)

b)

FIG. 1. Fits to the (a) m(K−K+) and (b) m(π−π+) spec-tra of D∗+ candidates passing the selection and satisfying0 < δm < 15 MeV/c2. The dashed line corresponds to thebackground component in the fit, and the vertical lines indi-cate the signal window of 1844–1884 MeV/c2.

difference (δm) spectra of selected candidates, whereδm ≡ m(h−h+π+

s ) − m(h−h+) − m(π+) for h = K,π,are shown in Fig. 2. Candidates are required to lie in-side a wide δm window of 0–15 MeV/c2, and in Fig. 2and for all subsequent results candidates are in addi-tion required to lie in a mass signal window of 1844–1884 MeV/c2. The D∗+ signal yields are approximately1.44 × 106 in the K−K+ sample, and 0.38 × 106 in theπ−π+ sample. Charm from b-hadron decays is stronglysuppressed by the requirement that the D0 originatefrom a primary vertex, and accounts for only 3% ofthe total yield. Of the events that contain at least oneD∗+ candidate, 12% contain more than one candidate;this is expected due to background soft pions from theprimary vertex and all candidates are accepted. Thebackground-subtracted average decay time of D0 can-didates passing the selection is measured for each finalstate, and the fractional difference ∆〈t〉/τ is obtained.Systematic uncertainties on this quantity are assignedfor the uncertainty on the world average D0 lifetime

6

)2c (MeV/mδ0 5 10 15

)2 cEn

trie

s / (

0.1

MeV

/

0

20000

40000

60000

80000

)2c (MeV/mδ0 5 10 15

)2 cEn

trie

s / (

0.1

MeV

/

0

5000

10000

15000

20000

a)

b)

LHCb

LHCb

FIG. 2. Fits to the δm spectra, where the D0 is reconstructedin the final states (a) K−K+ and (b) π−π+, with mass ly-ing in the window of 1844–1884 MeV/c2. The dashed linecorresponds to the background component in the fit.

τ (0.04%), charm from b-hadron decays (0.18%), andthe background-subtraction procedure (0.04%). Com-bining the systematic uncertainties in quadrature, weobtain ∆〈t〉/τ = [9.83± 0.22(stat.)± 0.19(syst.)] %.The π−π+ and K−K+ average decay time is 〈t〉 =(0.8539± 0.0005) ps, where the error is statistical only.

Fits are performed on the samples in order to deter-mine Araw(K−K+) and Araw(π−π+). The productionand detection asymmetries can vary with pT and pseu-dorapidity η, and so can the detection efficiency of thetwo different D0 decays, in particular through the effectsof the particle identification requirements. The analy-sis is performed in 54 kinematic bins defined by the pTand η of the D∗+ candidates, the momentum of the slowpion, and the sign of px of the slow pion at the D∗+

vertex. The events are further partitioned in two ways.First, the data are divided between the two dipole mag-net polarities. Second, the first 60% of data are processedseparately from the remainder, with the division alignedwith a break in data taking due to an LHC technical stop.

In total, 216 statistically independent measurements areconsidered for each decay mode.

In each bin, one-dimensional unbinned maximum like-lihood fits to the δm spectra are performed. The signalis described as the sum of two Gaussian functions witha common mean µ but different widths σi, convolvedwith a function B(δm; s) = Θ(δm) δms taking accountof the asymmetric shape of the measured δm distribu-tion. Here, s ' −0.975 is a shape parameter fixed to thevalue determined from the global fits shown in Fig. 2, Θis the Heaviside step function, and the convolution runsover δm. The background is described by an empiricalfunction of the form 1− e−(δm−δm0)/α, where δm0 and αare free parameters describing the threshold and shape ofthe function, respectively. The D∗+ and D∗− samples ina given bin are fitted simultaneously and share all shapeparameters, except for a charge-dependent offset in thecentral value µ and an overall scale factor in the massresolution. The raw asymmetry in the signal yields isextracted directly from this simultaneous fit. No fit pa-rameters are shared between the 216 subsamples of data,nor between the K−K+ and π−π+ final states.

The fits do not distinguish between the signal andbackgrounds that peak in δm. Such backgrounds canarise from D∗+ decays in which the correct slow pion isfound but the D0 is partially mis-reconstructed. Thesebackgrounds are suppressed by the use of tight particleidentification requirements and a narrow D0 mass win-dow. From studies of the D0 mass sidebands (1820–1840and 1890–1910 MeV/c2), this contamination is found tobe approximately 1% of the signal yield and to have smallraw asymmetry (consistent with zero asymmetry differ-ence between the K−K+ and π−π+ final states). Itseffect on the measurement is estimated in an ensembleof simulated experiments and found to be negligible; asystematic uncertainty is assigned below based on thestatistical precision of the estimate.

A value of ∆ACP is determined in each measure-ment bin as the difference between Araw(K−K+) andAraw(π−π+). Testing these 216 measurements for mutualconsistency, we obtain χ2/ndf = 211/215 (χ2 probabilityof 56%). A weighted average is performed to yield theresult ∆ACP = (−0.82 ± 0.21)%, where the uncertaintyis statistical only.

Numerous robustness checks are made. The value of∆ACP is studied as a function of the time at which thedata were taken (Fig. 3) and found to be consistent witha constant value (χ2 probability of 57%). The mea-surement is repeated with progressively more restrictiveRICH particle identification requirements, finding valuesof (−0.88 ± 0.26)% and (−1.03 ± 0.31)%; both of thesevalues are consistent with the baseline result when cor-relations are taken into account. Table I lists ∆ACP foreight disjoint subsamples of data split according to mag-net polarity, the sign of px of the slow pion, and whetherthe data were taken before or after the technical stop.

7

Run block0 5 10 15 20

(%

)C

PA∆

-6

-4

-2

0

2

4

6

LHCb

FIG. 3. Time-dependence of the measurement. The data aredivided into 19 disjoint, contiguous, time-ordered blocks andthe value of ∆ACP measured in each block. The horizontalred dashed line shows the result for the combined sample.The vertical dashed line indicates the technical stop referredto in Table I.

The χ2 probability for consistency among the subsam-ples is 45%. The significances of the differences betweendata taken before and after the technical stop, betweenthe magnet polarities, and between px > 0 and px < 0are 0.4, 0.6, and 0.7 standard deviations, respectively.Other checks include applying electron and muon vetoesto the slow pion and to the D0 daughters, use of differentkinematic binnings, validation of the size of the statisti-cal uncertainties with Monte Carlo pseudo-experiments,tightening of kinematic requirements, testing for varia-tion of the result with the multiplicity of tracks and ofprimary vertices in the event, use of other signal andbackground parameterizations in the fit, and imposing afull set of common shape parameters between D∗+ andD∗− candidates. Potential biases due to the inclusivehardware trigger selection are investigated with the sub-sample of data in which one of the signal final-state tracksis directly responsible for the hardware trigger decision.In all cases good stability is observed. For several of thesechecks, a reduced number of kinematic bins are used forsimplicity. No systematic dependence of ∆ACP is ob-served with respect to the kinematic variables.

Systematic uncertainties are assigned by: loosening thefiducial requirement on the slow pion; assessing the effectof potential peaking backgrounds in Monte Carlo pseudo-experiments; repeating the analysis with the asymmetryextracted through sideband subtraction in δm instead ofa fit; removing all candidates but one (chosen at random)in events with multiple candidates; and comparing withthe result obtained without kinematic binning. In eachcase the full value of the change in result is taken as thesystematic uncertainty. These uncertainties are listed inTable II. The sum in quadrature is 0.11%. Combin-

TABLE I. Values of ∆ACP measured in subsamples of thedata, and the χ2/ndf and corresponding χ2 probabilities forinternal consistency among the 27 bins in each subsample.The data are divided before and after a technical stop (TS),by magnet polarity (up, down), and by the sign of px forthe slow pion (left, right). The consistency among the eightsubsamples is χ2/ndf = 6.8/7 (45%).

Subsample ∆ACP [%] χ2/ndfPre-TS, up, left −1.22± 0.59 13/26 (98%)Pre-TS, up, right −1.43± 0.59 27/26 (39%)Pre-TS, down, left −0.59± 0.52 19/26 (84%)Pre-TS, down, right −0.51± 0.52 29/26 (30%)Post-TS, up, left −0.79± 0.90 26/26 (44%)Post-TS, up, right +0.42± 0.93 21/26 (77%)Post-TS, down, left −0.24± 0.56 34/26 (15%)Post-TS, down, right −1.59± 0.57 35/26 (12%)All data −0.82± 0.21 211/215 (56%)

TABLE II. Summary of absolute systematic uncertainties for∆ACP .

Source UncertaintyFiducial requirement 0.01%Peaking background asymmetry 0.04%Fit procedure 0.08%Multiple candidates 0.06%Kinematic binning 0.02%Total 0.11%

ing statistical and systematic uncertainties in quadra-ture, this result is consistent at the 1σ level with thecurrent HFAG world average [3].

In conclusion, the time-integrated difference in CPasymmetry between D0 → K−K+ and D0 → π−π+ de-cays has been measured to be

∆ACP = [−0.82± 0.21(stat.)± 0.11(syst.)] %

with 0.62 fb−1 of 2011 data. Given the dependenceof ∆ACP on the direct and indirect CP asymmetries,shown in Eq. (4), and the measured value ∆〈t〉/τ =[9.83± 0.22(stat.)± 0.19(syst.)] %, the contribution fromindirect CP violation is suppressed and ∆ACP is primar-ily sensitive to direct CP violation. Dividing the centralvalue by the sum in quadrature of the statistical and sys-tematic uncertainties, the significance of the measureddeviation from zero is 3.5σ. This is the first evidence forCP violation in the charm sector. To establish whetherthis result is consistent with the SM will require the anal-ysis of more data, as well as improved theoretical under-standing.

8

ACKNOWLEDGEMENTS

We express our gratitude to our colleagues in the CERNaccelerator departments for the excellent performance ofthe LHC. We thank the technical and administrative staffat CERN and at the LHCb institutes, and acknowledgesupport 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 supportreceived from the ERC under FP7 and the Region Au-vergne.

[1] BaBar collaboration, B. Aubert et al., Evidence forD0–D0 Mixing, Phys. Rev. Lett. 98 (2007) 211802,[arXiv:hep-ex/0703020].

[2] Belle collaboration, M. Staric et al., Evidence for D0–D0 Mixing, Phys. Rev. Lett. 98 (2007) 211803,[arXiv:hep-ex/0703036].

[3] Heavy Flavor Averaging Group, D. Asner et al., Aver-ages of b-hadron, c-hadron, and tau-lepton Properties,arXiv:1010.1589.

[4] A. F. Falk, Y. Grossman, Z. Ligeti, Y. Nir, andA. A. Petrov, D0–D0 mass difference from a dis-

persion relation, Phys. Rev. D69 (2004) 114021,[arXiv:hep-ph/0402204].

[5] Y. Grossman, A. L. Kagan, and Y. Nir, New physics andCP violation in singly Cabibbo suppressed D decays,Phys. Rev. D75 (2007) 036008, [arXiv:hep-ph/0609178].

[6] S. Bianco, F. L. Fabbri, D. Benson, and I. Bigi, A Ci-cerone for the physics of charm, Riv. Nuovo Cim. 26N7(2003) 1, [arXiv:hep-ex/0309021].

[7] M. Bobrowski, A. Lenz, J. Riedl, and J. Rohrwild, Howlarge can the SM contribution to CP violation in D0−D0

mixing be?, JHEP 1003 (2010) 009, [arXiv:1002.4794].[8] A. A. Petrov, Searching for New Physics with Charm,

PoS BEAUTY2009 (2009) 024, [arXiv:1003.0906].[9] I. I. Bigi, M. Blanke, A. J. Buras, and S. Recksiegel,

CP Violation in D0–D0 Oscillations: General Consider-ations and Applications to the Littlest Higgs Model withT-Parity, JHEP 0907 (2009) 097, [arXiv:0904.1545].

[10] CDF collaboration, T. Aaltonen et al., Measurement ofCP–violating asymmetries in D0 → π+π− and D0 →K+K− decays at CDF, arXiv:1111.5023. (submittedto Phys. Rev. D).

[11] I. I. Bigi, A. Paul, and S. Recksiegel, Conclusionsfrom CDF Results on CP Violation in D0 → π+π−,K+K− and Future Tasks, JHEP 1106 (2011) 089,[arXiv:1103.5785].

[12] A. L. Kagan and M. D. Sokoloff, On Indirect CP Viola-

tion and Implications for D0–D0 and B0s–B

0s mixing,

Phys. Rev. D80 (2009) 076008, [arXiv:0907.3917].

[13] BaBar collaboration, B. Aubert et al., Search for CPviolation in the decays D0 → K−K+ and D0 → π−π+,Phys. Rev. Lett. 100 (2008) 061803, [arXiv:0709.2715].

[14] Belle collaboration, M. Staric et al., Measurement of CPasymmetry in Cabibbo suppressed D0 decays, Phys. Lett.B670 (2008) 190, [arXiv:0807.0148].

[15] LHCb collaboration, A. A. Alves Jr et al., The LHCbDetector at the LHC, JINST 3 (2008) S08005.