The LHCb collaboration

# Evidence for $C\\!P$ violation in time-integrated $\bm{D^{0}\rightarrow
h^{-}h^{+}}$ 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. Büchler-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
Suárez36, 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. Estève43, A.
Falabella16,14,e, E. Fanchini20,j, C. Färber11, 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. Göbel54, D.
Golubkov30, A. Golutvin49,30,37, A. Gomes2, H. Gordon51, M. Grabalosa
Gándara35, R. Graciani Diaz35, L.A. Granado Cardoso37, E. Graugés35, 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. Lefèvre5, A. Leflat31,37, J. Lefrançois7, 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. Märki38, J. Marks11, G. Martellotti22, A. Martens8, L. Martin51, A. Martín
Sánchez7, 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.
Müller39, 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. Pérez-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. Pilař44, 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 Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di 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, Kraców, Poland
26AGH University of Science and Technology, Kraców, 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 Fédérale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universität Zürich, Zürich, 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
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55University of Birmingham, Birmingham, United Kingdom
56Physikalisches Institut, Universität Rostock, Rostock, Germany, associated
to 11

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

###### Abstract

A search for time-integrated $C\\!P$ violation in $D^{0}\rightarrow
h^{-}h^{+}$ ($h=K$, $\pi$) decays is presented using 0.62 $\mbox{\,fb}^{-1}$
of data collected by LHCb in 2011. The flavor of the charm meson is determined
by the charge of the slow pion in the $D^{*+}\rightarrow D^{0}\pi^{+}$ and
$D^{*-}\rightarrow\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\pi^{-}$
decay chains. The difference in $C\\!P$ asymmetry between $D^{0}\rightarrow
K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$, $\Delta A_{C\\!P}\equiv
A_{C\\!P}(K^{-}K^{+})\,-\,A_{C\\!P}(\pi^{-}\pi^{+})$, is measured to be
$\left[-0.82\pm 0.21(\mathrm{stat.})\pm 0.11(\mathrm{syst.})\right]\%$. This
differs from the hypothesis of $C\\!P$ conservation by $3.5$ standard
deviations.

###### pacs:

11.30.Er, 13.25.Ft

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

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

The charm sector is a promising place to probe for the effects of physics
beyond the Standard Model (SM). There has been a resurgence of interest in the
past few years since evidence for $D^{0}$ mixing was first seen
bib:babar_mixing_moriond ; bib:belle_mixing_moriond . Mixing is now well-
established bib:hfag  at a level which is consistent with, but at the upper
end of, SM expectations falk_grossman_ligeti_nir_petrov . By contrast, no
evidence for $C\\!P$ violation in charm decays has yet been found.

The time-dependent $C\\!P$ asymmetry $A_{C\\!P}(f;\,t)$ for $D^{0}$ decays to
a CP eigenstate $f$ (with $f=\bar{f}$) is defined as

$A_{C\\!P}(f;\,t)\equiv\frac{\Gamma(D^{0}(t)\rightarrow f)-\Gamma(\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(t)\rightarrow
f)}{\Gamma(D^{0}(t)\rightarrow f)+\Gamma(\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(t)\rightarrow f)},$ (1)

where $\Gamma$ is the decay rate for the process indicated. In general
$A_{C\\!P}(f;\,t)$ depends on $f$. For $f=K^{-}K^{+}$ and $f=\pi^{-}\pi^{+}$,
$A_{C\\!P}(f;\,t)$ can be expressed in terms of two contributions: a direct
component associated with $C\\!P$ violation in the decay amplitudes, and an
indirect component associated with $C\\!P$ violation in the mixing or in the
interference between mixing and decay. In the limit of U-spin symmetry, the
direct component is equal in magnitude and opposite in sign for $K^{-}K^{+}$
and $\pi^{-}\pi^{+}$, though the size of U-spin breaking effects remains to be
quantified precisely bib:grossman_kagan_nir . The magnitudes of $C\\!P$
asymmetries in decays to these final states are expected to be small in the SM
bib:cicerone ; bib:lenz ; bib:grossman_kagan_nir ; bib:petrov , with
predictions of up to $\mathcal{O}(10^{-3})$. However, beyond the SM the rate
of $C\\!P$ violation could be enhanced bib:grossman_kagan_nir ;
bib:littlest_higgs .

The asymmetry $A_{C\\!P}(f;\,t)$ may be written to first order as
bib:cdf_paper ; bib:bigi_d2hh

$A_{C\\!P}(f;\,t)=a^{\mathrm{dir}}_{C\\!P}(f)\,+\,\frac{t}{\tau}a^{\mathrm{ind}}_{C\\!P},$
(2)

where $a^{\mathrm{dir}}_{C\\!P}(f)$ is the direct $C\\!P$ asymmetry, $\tau$ is
the $D^{0}$ lifetime, and $a^{\mathrm{ind}}_{C\\!P}$ is the indirect $C\\!P$
asymmetry. To a good approximation this latter quantity is universal
bib:grossman_kagan_nir ; bib:kagan_sokoloff . The time-integrated asymmetry
measured by an experiment, $A_{C\\!P}(f)$, depends upon the time-acceptance of
that experiment. It can be written as

$A_{C\\!P}(f)=a^{\mathrm{dir}}_{C\\!P}(f)\,+\,\frac{\langle
t\rangle}{\tau}a^{\mathrm{ind}}_{C\\!P},$ (3)

where $\langle t\rangle$ is the average decay time in the reconstructed
sample. Denoting by $\Delta$ the differences between quantities for
$D^{0}\rightarrow K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$ it is then
possible to write

$\displaystyle\Delta A_{C\\!P}$ $\displaystyle\equiv$ $\displaystyle
A_{C\\!P}(K^{-}K^{+})\,-\,A_{C\\!P}(\pi^{-}\pi^{+})$ $\displaystyle=$
$\displaystyle\left[a^{\mathrm{dir}}_{C\\!P}(K^{-}K^{+})\,-\,a^{\mathrm{dir}}_{C\\!P}(\pi^{-}\pi^{+})\right]\,+\,\frac{\Delta\langle
t\rangle}{\tau}a^{\mathrm{ind}}_{C\\!P}.$

In the limit that $\Delta\langle t\rangle$ vanishes, $\Delta A_{C\\!P}$ is
equal to the difference in the direct $C\\!P$ asymmetry between the two
decays. However, if the time-acceptance is different for the $K^{-}K^{+}$ and
$\pi^{-}\pi^{+}$ final states, a contribution from indirect $C\\!P$ violation
remains.

The most precise measurements to date of the time-integrated $C\\!P$
asymmetries in $D^{0}\rightarrow K^{-}K^{+}$ and
$D^{0}\rightarrow\pi^{-}\pi^{+}$ were made by the CDF, BaBar, and Belle
collaborations bib:cdf_paper ; bib:babar_paper2008 ; bib:belle_paper2008 . The
Heavy Flavor Averaging Group (HFAG) has combined time-integrated and time-
dependent measurements of $C\\!P$ asymmetries, taking account of the different
decay time acceptances, to obtain world average values for the indirect
$C\\!P$ asymmetry of $a_{C\\!P}^{\mathrm{ind}}=(-0.03\pm 0.23)\%$ and the
difference in direct $C\\!P$ asymmetry between the final states of $\Delta
a_{C\\!P}^{\mathrm{dir}}=(-0.42\pm 0.27)\%$ bib:hfag .

In this Letter, we present a measurement of the difference in time-integrated
$C\\!P$ asymmetries between $D^{0}\rightarrow K^{-}K^{+}$ and
$D^{0}\rightarrow\pi^{-}\pi^{+}$, performed with 0.62 $\mbox{\,fb}^{-1}$ of
data collected at LHCb between March and June 2011. The flavor of the initial
state ($D^{0}$ or $\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}$) is
tagged by requiring a $D^{*+}\rightarrow D^{0}\pi_{\mathrm{s}}^{+}$ decay,
with the flavor determined by the charge of the slow pion
($\pi_{\mathrm{s}}^{+}$). The inclusion of charge-conjugate modes is implied
throughout, except in the definition of asymmetries.

The raw asymmetry for tagged $D^{0}$ decays to a final state $f$ is given by
$A_{\mathrm{raw}}(f)$, defined as

$A_{\mathrm{raw}}(f)\equiv\frac{N(D^{*+}\rightarrow
D^{0}(f)\pi_{s}^{+})\,-\,N(D^{*-}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(f)\pi_{s}^{-})}{N(D^{*+}\rightarrow
D^{0}(f)\pi_{s}^{+})\,+\,N(D^{*-}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(f)\pi_{s}^{-})},$ (5)

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

To first order the raw asymmetries may be written as a sum of four components,
due to physics and detector effects:

$A_{\mathrm{raw}}(f)=A_{C\\!P}(f)\,+\,A_{\mathrm{D}}(f)\,+\,A_{\mathrm{D}}(\pi_{\mathrm{s}}^{+})\,+\,A_{\mathrm{P}}(D^{*+}).$
(6)

Here, $A_{\mathrm{D}}(f)$ is the asymmetry in selecting the $D^{0}$ decay into
the final state $f$, $A_{\mathrm{D}}(\pi_{\mathrm{s}}^{+})$ is the asymmetry
in selecting the slow pion from the $D^{*+}$ decay chain, and
$A_{\mathrm{P}}(D^{*+})$ is the production asymmetry for $D^{*+}$ mesons. The
asymmetries $A_{\mathrm{D}}$ and $A_{\mathrm{P}}$ are defined in the same
fashion as $A_{\mathrm{raw}}$. The first-order expansion is valid since the
individual asymmetries are small.

For a two-body decay of a spin-0 particle to a self-conjugate final state
there can be no $D^{0}$ detection asymmetry, i.e.
$A_{\mathrm{D}}(K^{-}K^{+})=A_{\mathrm{D}}(\pi^{-}\pi^{+})=0.$ Moreover,
$A_{\mathrm{D}}(\pi_{\mathrm{s}}^{+})$ and $A_{\mathrm{P}}(D^{*+})$ are
independent of $f$ and thus in the first-order expansion of equation 5 those
terms cancel in the difference
$A_{\mathrm{raw}}(K^{-}K^{+})\,-\,A_{\mathrm{raw}}(\pi^{-}\pi^{+})$, resulting
in

$\Delta
A_{C\\!P}=A_{\mathrm{raw}}(K^{-}K^{+})\,-\,A_{\mathrm{raw}}(\pi^{-}\pi^{+}).$
(7)

To minimize second-order effects that are related to the slightly different
kinematic properties of the two decay modes and that do not cancel in $\Delta
A_{C\\!P}$, the analysis is performed in bins of the relevant kinematic
variables, as discussed later.

The LHCb detector is a forward spectrometer covering the pseudorapidity range
$2<\eta<5$, and is described in detail in Ref. LHCb . The Ring Imaging
Cherenkov (RICH) detectors are of particular importance to this analysis,
providing kaon-pion discrimination for the full range of track momenta used.
The nominal downstream beam direction is aligned with the $+z$ axis, and the
field direction in the LHCb dipole is such that charged particles are
deflected in the horizontal ($xz$) plane. The field polarity was changed
several times during data taking: about 60% of the data were taken with the
down polarity and 40% with the other.

Selections are applied to provide samples of $D^{*+}\rightarrow
D^{0}\pi_{\mathrm{s}}^{+}$ candidates, with $D^{0}\rightarrow K^{-}K^{+}$ or
$\pi^{-}\pi^{+}$. Events are required to pass both hardware and software
trigger levels. A loose $D^{0}$ selection is applied in the final state of the
software trigger, and in the offline analysis only candidates that are
accepted by this trigger algorithm are considered. Both the trigger and
offline selections impose a variety of requirements on kinematics and decay
time to isolate the decays of interest, including requirements on the track
fit quality, on the $D^{0}$ and $D^{*+}$ vertex fit quality, on the transverse
momentum ($\mbox{$p_{\mathrm{T}}$}>2$ GeV$/c$) and decay time
($ct>100\,\,\upmu\rm m$) of the $D^{0}$ candidate, on the angle between the
$D^{0}$ momentum in the lab frame and its daughter momenta in the $D^{0}$ rest
frame ($|\cos\theta|<0.9$), that the $D^{0}$ trajectory points back to a
primary vertex, and that the $D^{0}$ daughter tracks do not. In addition, the
offline analysis exploits the capabilities of the RICH system to distinguish
between pions and kaons when reconstructing the $D^{0}$ meson, with no tracks
appearing as both pion and kaon candidates.

A fiducial region is implemented by imposing the requirement that the slow
pion lies within the central part of the detector acceptance. This is
necessary because the magnetic field bends pions of one charge to the left and
those of the other charge to the right. For soft tracks at large angles in the
$xz$ plane this implies that one charge is much more likely to remain within
the 300 mrad horizontal detector acceptance, thus making
$A_{\mathrm{D}}(\pi_{\mathrm{s}}^{+})$ large. Although this asymmetry is
formally independent of the $D^{0}$ decay mode, it breaks the assumption that
the raw asymmetries are small and it carries a risk of second-order systematic
effects if the ratio of efficiencies of $D^{0}\rightarrow K^{-}K^{+}$ and
$D^{0}\rightarrow\pi^{-}\pi^{+}$ varies in the affected region. The fiducial
requirements therefore exclude edge regions in the slow pion $(p_{x},p)$
plane. Similarly, a small region of phase space in which one charge of slow
pion is more likely to be swept into the beampipe region in the downstream
tracking stations, and hence has reduced efficiency, is also excluded. After
the implementation of the fiducial requirements about 70% of the events are
retained.

The invariant mass spectra of selected $K^{-}K^{+}$ and $\pi^{-}\pi^{+}$ pairs
are shown in Fig. 1. The half-width at half-maximum of the signal lineshape is
8.6 MeV$/c^{2}$ for $K^{-}K^{+}$ and 11.2 MeV$/c^{2}$ for $\pi^{-}\pi^{+}$,
where the difference is due to the kinematics of the decays and has no
relevance for the subsequent analysis. The mass difference ($\delta m$)
spectra of selected candidates, where $\delta m\equiv
m(h^{-}h^{+}\pi_{\mathrm{s}}^{+})-m(h^{-}h^{+})-m(\pi^{+})$ for $h=K,\pi$, are
shown in Fig. 2.

Figure 1:  Fits to the (a) $m(K^{-}K^{+})$ and (b) $m(\pi^{-}\pi^{+})$ spectra
of $D^{*+}$ candidates passing the selection and satisfying $0<\delta m<15$
MeV$/c^{2}$. The dashed line corresponds to the background component in the
fit, and the vertical lines indicate the signal window of 1844–1884
MeV$/c^{2}$.

Candidates are required to lie inside a wide $\delta m$ window of 0–15
MeV$/c^{2}$, and in Fig. 2 and for all subsequent results candidates are in
addition required to lie in a mass signal window of 1844–1884 MeV$/c^{2}$. The
$D^{*+}$ signal yields are approximately $1.44\times 10^{6}$ in the
$K^{-}K^{+}$ sample, and $0.38\times 10^{6}$ in the $\pi^{-}\pi^{+}$ sample.
Charm from $b$-hadron decays is strongly suppressed by the requirement that
the $D^{0}$ originate from a primary vertex, and accounts for only 3% of the
total yield. Of the events that contain at least one $D^{*+}$ candidate, 12%
contain more than one candidate; this is expected due to background soft pions
from the primary vertex and all candidates are accepted. The background-
subtracted average decay time of $D^{0}$ candidates passing the selection is
measured for each final state, and the fractional difference $\Delta\langle
t\rangle/\tau$ is obtained. Systematic uncertainties on this quantity are
assigned for the uncertainty on the world average $D^{0}$ lifetime $\tau$
$(0.04\%)$, charm from $b$-hadron decays $(0.18\%$), and the background-
subtraction procedure $(0.04\%)$. Combining the systematic uncertainties in
quadrature, we obtain $\Delta\langle t\rangle/\tau=\left[9.83\pm
0.22(\mathrm{stat.})\pm 0.19(\mathrm{syst.})\right]\%$. The $\pi^{-}\pi^{+}$
and $K^{-}K^{+}$ average decay time is $\langle t\rangle=\left(0.8539\pm
0.0005\right)$ ps, where the error is statistical only.

Figure 2:  Fits to the $\delta m$ spectra, where the $D^{0}$ is reconstructed
in the final states (a) $K^{-}K^{+}$ and (b) $\pi^{-}\pi^{+}$, with mass lying
in the window of 1844–1884 MeV$/c^{2}$. The dashed line corresponds to the
background component in the fit.

Fits are performed on the samples in order to determine
$A_{\mathrm{raw}}(K^{-}K^{+})$ and $A_{\mathrm{raw}}(\pi^{-}\pi^{+})$. The
production and detection asymmetries can vary with $p_{\mathrm{T}}$ and
pseudorapidity $\eta$, and so can the detection efficiency of the two
different $D^{0}$ decays, in particular through the effects of the particle
identification requirements. The analysis is performed in 54 kinematic bins
defined by the $p_{\mathrm{T}}$ and $\eta$ of the $D^{*+}$ candidates, the
momentum of the slow pion, and the sign of $p_{x}$ 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 magnet polarities. Second, the first
60% of data are processed separately from the remainder, with the division
aligned with a break in data taking due to an LHC technical stop. In total,
216 statistically independent measurements are considered for each decay mode.

In each bin, one-dimensional unbinned maximum likelihood fits to the $\delta
m$ spectra are performed. The signal is described as the sum of two Gaussian
functions with a common mean $\mu$ but different widths $\sigma_{i}$,
convolved with a function $B(\delta m;s)=\Theta(\delta m)\,\delta m^{s}$
taking account of the asymmetric shape of the measured $\delta m$
distribution. Here, $s\simeq-0.975$ is a shape parameter fixed to the value
determined from the global fits shown in Fig. 2, $\Theta$ is the Heaviside
step function, and the convolution runs over $\delta m$. The background is
described by an empirical function of the form $1-e^{-(\delta m-\delta
m_{0})/\alpha}$, where $\delta m_{0}$ and $\alpha$ are free parameters
describing the threshold and shape of the function, respectively. The $D^{*+}$
and $D^{*-}$ samples in a given bin are fitted simultaneously and share all
shape parameters, except for a charge-dependent offset in the central value
$\mu$ and an overall scale factor in the mass resolution. The raw asymmetry in
the signal yields is extracted directly from this simultaneous fit. No fit
parameters are shared between the 216 subsamples of data, nor between the
$K^{-}K^{+}$ and $\pi^{-}\pi^{+}$ final states.

The fits do not distinguish between the signal and backgrounds that peak in
$\delta m$. Such backgrounds can arise from $D^{*+}$ decays in which the
correct slow pion is found but the $D^{0}$ is partially mis-reconstructed.
These backgrounds are suppressed by the use of tight particle identification
requirements and a narrow $D^{0}$ mass window. From studies of the $D^{0}$
mass sidebands (1820–1840 and 1890–1910 MeV$/c^{2}$), this contamination is
found to be approximately 1% of the signal yield and to have small raw
asymmetry (consistent with zero asymmetry difference between the $K^{-}K^{+}$
and $\pi^{-}\pi^{+}$ final states). Its effect on the measurement is estimated
in an ensemble of simulated experiments and found to be negligible; a
systematic uncertainty is assigned below based on the statistical precision of
the estimate.

A value of $\Delta A_{C\\!P}$ is determined in each measurement bin as the
difference between $A_{\mathrm{raw}}(K^{-}K^{+})$ and
$A_{\mathrm{raw}}(\pi^{-}\pi^{+})$. Testing these 216 measurements for mutual
consistency, we obtain $\chi^{2}/\mathrm{ndf}=211/215$ ($\chi^{2}$ probability
of 56%). A weighted average is performed to yield the result $\Delta
A_{C\\!P}=(-0.82\pm 0.21)\%$, where the uncertainty is statistical only.

Numerous robustness checks are made. The value of $\Delta A_{C\\!P}$ is
studied as a function of the time at which the data were taken (Fig. 3) and
found to be consistent with a constant value ($\chi^{2}$ probability of 57%).
The measurement is repeated with progressively more restrictive RICH particle
identification requirements, finding values of $(-0.88\pm 0.26)\%$ and
$(-1.03\pm 0.31)\%$; both of these values are consistent with the baseline
result when correlations are taken into account. Table 1 lists $\Delta
A_{C\\!P}$ for eight disjoint subsamples of data split according to magnet
polarity, the sign of $p_{x}$ of the slow pion, and whether the data were
taken before or after the technical stop. The $\chi^{2}$ probability for
consistency among the subsamples is 45%. The significances of the differences
between data taken before and after the technical stop, between the magnet
polarities, and between $p_{x}>0$ and $p_{x}<0$ are $0.4$, $0.6$, and $0.7$
standard deviations, respectively. Other checks include applying electron and
muon vetoes to the slow pion and to the $D^{0}$ daughters, use of different
kinematic binnings, validation of the size of the statistical uncertainties
with Monte Carlo pseudo-experiments, tightening of kinematic requirements,
testing for variation of the result with the multiplicity of tracks and of
primary vertices in the event, use of other signal and background
parameterizations in the fit, and imposing a full set of common shape
parameters between $D^{*+}$ and $D^{*-}$ candidates. Potential biases due to
the inclusive hardware trigger selection are investigated with the subsample
of data in which one of the signal final-state tracks is directly responsible
for the hardware trigger decision. In all cases good stability is observed.
For several of these checks, a reduced number of kinematic bins are used for
simplicity. No systematic dependence of $\Delta A_{C\\!P}$ is observed with
respect to the kinematic variables.

Figure 3:  Time-dependence of the measurement. The data are divided into 19 disjoint, contiguous, time-ordered blocks and the value of $\Delta A_{C\\!P}$ measured in each block. The horizontal red dashed line shows the result for the combined sample. The vertical dashed line indicates the technical stop referred to in Table 1.  Table 1:  Values of $\Delta A_{C\\!P}$ measured in subsamples of the data, and the $\chi^{2}/\mathrm{ndf}$ and corresponding $\chi^{2}$ probabilities for internal 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 $p_{x}$ for the slow pion (left, right). The consistency among the eight subsamples is $\chi^{2}/\mathrm{ndf}=6.8/7$ (45%).  Subsample | $\Delta A_{C\\!P}~{}[\%]$ | $\chi^{2}/\mathrm{ndf}$
---|---|---
Pre-TS, up, left | $-1.22\pm 0.59$ | $13/26~{}(98\%)$
Pre-TS, up, right | $-1.43\pm 0.59$ | $27/26~{}(39\%)$
Pre-TS, down, left | $-0.59\pm 0.52$ | $19/26~{}(84\%)$
Pre-TS, down, right | $-0.51\pm 0.52$ | $29/26~{}(30\%)$
Post-TS, up, left | $-0.79\pm 0.90$ | $26/26~{}(44\%)$
Post-TS, up, right | $+0.42\pm 0.93$ | $21/26~{}(77\%)$
Post-TS, down, left | $-0.24\pm 0.56$ | $34/26~{}(15\%)$
Post-TS, down, right | $-1.59\pm 0.57$ | $35/26~{}(12\%)$
All data | $-0.82\pm 0.21$ | $211/215~{}(56\%)$

Systematic uncertainties are assigned by: loosening the fiducial requirement
on the slow pion; assessing the effect of potential peaking backgrounds in
Monte Carlo pseudo-experiments; repeating the analysis with the asymmetry
extracted through sideband subtraction in $\delta m$ instead of a fit;
removing all candidates but one (chosen at random) in events with multiple
candidates; and comparing with the result obtained without kinematic binning.
In each case the full value of the change in result is taken as the systematic
uncertainty. These uncertainties are listed in Table 2. The sum in quadrature
is $0.11\%$. Combining statistical and systematic uncertainties in quadrature,
this result is consistent at the $1\sigma$ level with the current HFAG world
average bib:hfag .

Table 2:  Summary of absolute systematic uncertainties for $\Delta A_{C\\!P}$.  Source | Uncertainty
---|---
Fiducial requirement | 0.01%
Peaking background asymmetry | 0.04%
Fit procedure | 0.08%
Multiple candidates | 0.06%
Kinematic binning | 0.02%
Total | 0.11%

In conclusion, the time-integrated difference in $C\\!P$ asymmetry between
$D^{0}\rightarrow K^{-}K^{+}$ and $D^{0}\rightarrow\pi^{-}\pi^{+}$ decays has
been measured to be

$\Delta A_{C\\!P}=\left[-0.82\pm 0.21(\mathrm{stat.})\pm
0.11(\mathrm{syst.})\right]\%$

with 0.62 $\mbox{\,fb}^{-1}$ of 2011 data. Given the dependence of $\Delta
A_{C\\!P}$ on the direct and indirect $C\\!P$ asymmetries, shown in Eq.
(Evidence for $C\\!P$ violation in time-integrated $\bm{D^{0}\rightarrow
h^{-}h^{+}}$ decay rates), and the measured value $\Delta\langle
t\rangle/\tau=\left[9.83\pm 0.22(\mathrm{stat.})\pm
0.19(\mathrm{syst.})\right]\%$, the contribution from indirect $C\\!P$
violation is suppressed and $\Delta A_{C\\!P}$ is primarily sensitive to
direct $C\\!P$ violation. Dividing the central value by the sum in quadrature
of the statistical and systematic uncertainties, the significance of the
measured deviation from zero is $3.5\sigma$. This is the first evidence for
$C\\!P$ violation in the charm sector. To establish whether this result is
consistent with the SM will require the analysis of more data, as well as
improved theoretical understanding.

## 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, XuntaGal and GENCAT
(Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United
Kingdom); NSF (USA). We also acknowledge the support received from the ERC
under FP7 and the Region Auvergne.

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