EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2012-247 LHCb-PAPER-2012-019 August 28, 2012

Measurement of the ratio of branching fractions ${\cal B}(B^{0}\\!\rightarrow
K^{*0}\gamma)$/${\cal B}(B^{0}_{s}\\!\rightarrow\phi\gamma)$ and the direct
$C\\!P$ asymmetry in $B^{0}\\!\rightarrow K^{*0}\gamma$

The LHCb collaboration†††Authors are listed on the following pages.

The ratio of branching fractions of the radiative $B$ decays
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$ has
been measured using an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$ of $pp$
collision data collected by the LHCb experiment at a centre-of-mass energy of
$\sqrt{s}$ $=7$$\mathrm{\,Te\kern-1.00006ptV}$. The value obtained is

$\frac{{\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)}{{\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)}=1.23\pm 0.06\mathrm{\,(stat.)}\pm
0.04\mathrm{\,(syst.)}\pm 0.10\,(f_{s}/f_{d})\,,$

where the first uncertainty is statistical, the second is the experimental
systematic uncertainty and the third is associated with the ratio of
fragmentation fractions $f_{s}/f_{d}$. Using the world average value for
${\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)$, the branching fraction ${\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)$ is measured to be $(3.5\pm 0.4)\times
10^{-5}$.

The direct $C\\!P$ asymmetry in $B^{0}\\!\rightarrow K^{*0}\gamma$ decays has
also been measured with the same data and found to be

$\mathcal{A}_{C\\!P}(B^{0}\\!\rightarrow K^{*0}\gamma)=(0.8\pm
1.7\mathrm{\,(stat.)}\pm 0.9\mathrm{\,(syst.)})\%\,.$

Both measurements are the most precise to date and are in agreement with the
previous experimental results and theoretical expectations.

Submitted to Nuclear Physics B

LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C.
Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M.
Alexander48, S. Ali38, G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22,
S. Amato2, Y. Amhis36, L. Anderlini17,f, J. Anderson37, R.B. Appleby51, O.
Aquines Gutierrez10, F. Archilli18,35, A. Artamonov 32, M. Artuso53, E.
Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, C. Baesso54, V.
Balagura28, W. Baldini16, R.J. Barlow51, C. Barschel35, S. Barsuk7, W.
Barter44, A. Bates48, C. Bauer10, Th. Bauer38, A. Bay36, J. Beddow48, I.
Bediaga1, S. Belogurov28, K. Belous32, I. Belyaev28, E. Ben-Haim8, M.
Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, A. Berezhnoy29, R.
Bernet37, M.-O. Bettler44, M. van Beuzekom38, A. Bien11, S. Bifani12, T.
Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50,
J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W.
Bonivento15, S. Borghi48,51, A. Borgia53, T.J.V. Bowcock49, C. Bozzi16, T.
Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10, T.
Britton53, N.H. Brook43, H. Brown49, A. Büchler-Germann37, I. Burducea26, A.
Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo
Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14,c, G. Carboni21,k, R.
Cardinale19,i,35, A. Cardini15, L. Carson50, K. Carvalho Akiba2, G. Casse49,
M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph. Charpentier35, P. Chen3,36, N.
Chiapolini37, M. Chrzaszcz 23, K. Ciba35, X. Cid Vidal34, G. Ciezarek50,
P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J. Closier35, C. Coca26, V.
Coco38, J. Cogan6, E. Cogneras5, P. Collins35, A. Comerma-Montells33, A.
Contu52, A. Cook43, M. Coombes43, G. Corti35, B. Couturier35, G.A. Cowan36, D.
Craik45, S. Cunliffe50, R. Currie47, C. D’Ambrosio35, P. David8, P.N.Y.
David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, M. De Cian37, J.M. De
Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9, H.
Degaudenzi36,35, L. Del Buono8, C. Deplano15, D. Derkach14,35, O. Deschamps5,
F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1, F. Domingo
Bonal33,n, S. Donleavy49, F. Dordei11, A. Dosil Suárez34, D. Dossett45, A.
Dovbnya40, F. Dupertuis36, R. Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S.
Easo46, U. Egede50, V. Egorychev28, S. Eidelman31, D. van Eijk38, F. Eisele11,
S. Eisenhardt47, R. Ekelhof9, L. Eklund48, I. El Rifai5, Ch. Elsasser37, D.
Elsby42, D. Esperante Pereira34, A. Falabella14,e, C. Färber11, G. Fardell47,
C. Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, F. Ferreira
Rodrigues1, M. Ferro-Luzzi35, S. Filippov30, C. Fitzpatrick47, M. Fontana10,
F. Fontanelli19,i, R. Forty35, O. Francisco2, M. Frank35, C. Frei35, M.
Frosini17,f, S. Furcas20, A. Gallas Torreira34, D. Galli14,c, M. Gandelman2,
P. Gandini52, Y. Gao3, J-C. Garnier35, J. Garofoli53, J. Garra Tico44, L.
Garrido33, D. Gascon33, C. Gaspar35, R. Gauld52, E. Gersabeck11, M.
Gersabeck35, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V. Gligorov35, C.
Göbel54, D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H. Gordon52, M.
Grabalosa Gándara33, R. Graciani Diaz33, L.A. Granado Cardoso35, E. Graugés33,
G. Graziani17, A. Grecu26, E. Greening52, S. Gregson44, O. Grünberg55, B.
Gui53, E. Gushchin30, Yu. Guz32, T. Gys35, C. Hadjivasiliou53, G. Haefeli36,
C. Haen35, S.C. Haines44, S. Hall50, T. Hampson43, S. Hansmann-Menzemer11, N.
Harnew52, S.T. Harnew43, J. Harrison51, P.F. Harrison45, T. Hartmann55, J.
He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando Morata34, E. van
Herwijnen35, E. Hicks49, D. Hill52, M. Hoballah5, P. Hopchev4, W.
Hulsbergen38, P. Hunt52, T. Huse49, N. Hussain52, R.S. Huston12, D.
Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12, J. Imong43, R.
Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F. Jansen38, P.
Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R. Jones44, B.
Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35, T.M. Karbach9, J.
Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36, B. Khanji20,
Y.M. Kim47, M. Knecht36, O. Kochebina7, I. Komarov29, R.F. Koopman39, P.
Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M.
Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, M. Kucharczyk20,23,35,j, V.
Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36, D. Lacarrere35, G.
Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G.
Lanfranchi18,35, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J.
van Leerdam38, J.-P. Lees4, R. Lefèvre5, A. Leflat29,35, J. Lefrançois7, O.
Leroy6, T. Lesiak23, L. Li3, Y. Li3, L. Li Gioi5, M. Lieng9, M. Liles49, R.
Lindner35, C. Linn11, B. Liu3, G. Liu35, J. von Loeben20, J.H. Lopes2, E.
Lopez Asamar33, N. Lopez-March36, H. Lu3, J. Luisier36, A. Mac Raighne48, F.
Machefert7, I.V. Machikhiliyan4,28, F. Maciuc10, O. Maev27,35, J. Magnin1, S.
Malde52, R.M.D. Mamunur35, G. Manca15,d, G. Mancinelli6, N. Mangiafave44, U.
Marconi14, R. Märki36, J. Marks11, G. Martellotti22, A. Martens8, L. Martin52,
A. Martín Sánchez7, M. Martinelli38, D. Martinez Santos35, A. Massafferri1, Z.
Mathe12, C. Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35, J.
McCarthy42, G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9,
D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran51,
P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. Müller37, R.
Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T.
Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35, A.D.
Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29, T. Nikodem11,
A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S.
Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26, J.M.
Otalora Goicochea2, P. Owen50, B.K. Pal53, A. Palano13,b, M. Palutan18, J.
Panman35, A. Papanestis46, M. Pappagallo48, C. Parkes51, C.J. Parkinson50, G.
Passaleva17, G.D. Patel49, M. Patel50, G.N. Patrick46, C. Patrignani19,i, C.
Pavel-Nicorescu26, A. Pazos Alvarez34, A. Pellegrino38, G. Penso22,l, M. Pepe
Altarelli35, S. Perazzini14,c, D.L. Perego20,j, E. Perez Trigo34, A. Pérez-
Calero Yzquierdo33, P. Perret5, M. Perrin-Terrin6, G. Pessina20, A.
Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pie Valls33, B.
Pietrzyk4, T. Pilař45, D. Pinci22, S. Playfer47, M. Plo Casasus34, F. Polci8,
G. Polok23, A. Poluektov45,31, E. Polycarpo2, D. Popov10, B. Popovici26, C.
Potterat33, A. Powell52, J. Prisciandaro36, V. Pugatch41, A. Puig Navarro33,
W. Qian3, J.H. Rademacker43, B. Rakotomiaramanana36, M.S. Rangel2, I.
Raniuk40, N. Rauschmayr35, G. Raven39, S. Redford52, M.M. Reid45, A.C. dos
Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, D.A. Roa Romero5, P.
Robbe7, E. Rodrigues48,51, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35,
V. Romanovsky32, A. Romero Vidal34, M. Rosello33,n, J. Rouvinet36, T. Ruf35,
H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48,
B. Saitta15,d, C. Salzmann37, B. Sanmartin Sedes34, M. Sannino19,i, R.
Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M.
Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D.
Savrina28, P. Schaack50, M. Schiller39, H. Schindler35, S. Schleich9, M.
Schlupp9, M. Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H.
Schune7, R. Schwemmer35, B. Sciascia18, A. Sciubba18,l, M. Seco34, A.
Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P.
Seyfert11, M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T.
Shears49, L. Shekhtman31, O. Shevchenko40, V. Shevchenko28, A. Shires50, R.
Silva Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K.
Sobczak5, F.J.P. Soler48, A. Solomin43, F. Soomro18,35, D. Souza43, B. Souza
De Paula2, B. Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O.
Steinkamp37, S. Stoica26, S. Stone53, B. Storaci38, M. Straticiuc26, U.
Straumann37, V.K. Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36,35,
T. Szumlak24, S. T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C.
Thomas52, E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39,
S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S. Tourneur36, M.T.
Tran36, A. Tsaregorodtsev6, N. Tuning38, M. Ubeda Garcia35, A. Ukleja25, U.
Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34,
S. Vecchi16, J.J. Velthuis43, M. Veltri17,g, G. Veneziano36, M. Vesterinen35,
B. Viaud7, I. Videau7, D. Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A.
Vollhardt37, D. Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31, C.
Voß55, H. Voss10, R. Waldi55, R. Wallace12, S. Wandernoth11, J. Wang53, D.R.
Ward44, N.K. Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, J.
Wicht35, D. Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M.
Williams50, F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A.
Wotton44, S. Wright44, S. Wu3, K. Wyllie35, Y. Xie47, F. Xing52, Z. Xing53, Z.
Yang3, R. Young47, X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a,
F. Zhang3, L. Zhang53, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A.
Zvyagin35.

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
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
24AGH University of Science and Technology, Kraków, Poland
25Soltan Institute for Nuclear Studies, Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
32Institute for High Energy Physics (IHEP), Protvino, Russia
33Universitat de Barcelona, Barcelona, Spain
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain
35European Organization for Nuclear Research (CERN), Geneva, Switzerland
36Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
37Physik-Institut, Universität Zürich, Zürich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
45Department of Physics, University of Warwick, Coventry, United Kingdom
46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
48School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
55Institut für Physik, 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

##  1 Introduction

In the Standard Model (SM), the decays111Unless stated otherwise, charge
conjugated modes are implicitly included throughout this paper.
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$
proceed at leading order through the electromagnetic penguin transitions,
$b\\!\rightarrow s\gamma$. At one-loop level these transitions are dominated
by a virtual intermediate top quark coupling to a $W$ boson. Extensions of the
SM predict additional one-loop contributions that can introduce sizeable
changes to the dynamics of the transition [1, *Gershon:th-null-tests:2006,
*Mahmoudi:th-msugra:2006, *Altmannshofer:2011gn].

Radiative decays of the $B^{0}$ meson were first observed by the CLEO
collaboration in 1993 in the decay mode $B^{0}\\!\rightarrow K^{*0}\gamma$
[2]. In 2007 the Belle collaboration reported the first observation of the
analogous decay in the $B^{0}_{s}$ sector, $B^{0}_{s}\\!\rightarrow\phi\gamma$
[3]. The current world averages of the branching fractions of
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$ are
$(4.33\pm 0.15)\times 10^{-5}$ and $(5.7^{+2.1}_{-1.8})\times 10^{-5}$,
respectively [4, 5, *belle:exp-b2kstgamma:2004, *cleo:exp-excl-radiative-
decays:1999]. These results are in agreement with the latest theoretical
predictions from NNLO calculations using soft-collinear effective theory [8],
${\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)=(4.3\pm 1.4)\times 10^{-5}$ and
${\cal B}(B^{0}_{s}\\!\rightarrow\phi\gamma)=(4.3\pm 1.4)\times 10^{-5}$,
which suffer from large uncertainties from hadronic form factors. A better-
predicted quantity is the ratio of branching fractions, as it benefits from
partial cancellations of theoretical uncertainties. The two branching fraction
measurements lead to a ratio ${\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)/{\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)$=$0.7\pm 0.3$, while the SM prediction
is $1.0\pm 0.2$ [8]. When comparing the experimental and theoretical branching
fraction for the $B^{0}_{s}\\!\rightarrow\phi\gamma$ decay, it is necessary to
account for the large decay width difference in the $B^{0}_{s}-\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}_{s}$ system. This can give rise to
a correction on the theoretical branching fraction as large as $9\%$ as
described in [9].

The direct $C\\!P$ asymmetry in the $B^{0}\\!\rightarrow K^{*0}\gamma$ decay
is defined as $\mathcal{A}_{C\\!P}=[\Gamma(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\overline{f})-\Gamma(B^{0}\rightarrow
f)]/[\Gamma(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\overline{f})+\Gamma(B^{0}\rightarrow
f)]$. The SM prediction,
$\mathcal{A}^{\mathrm{SM}}_{C\\!P}(B^{0}\\!\rightarrow K^{*0}\gamma)=(-0.61\pm
0.43)\%$ [10], is affected by a smaller theoretical uncertainty from the
hadronic form factors than the branching fraction calculation. The precision
on the current experimental value, $\mathcal{A}_{C\\!P}(B^{0}\\!\rightarrow
K^{*0}\gamma)=(-1.6\pm 2.2\pm 0.7)\%$ [5, 11], is statistically limited and
more precise measurements would constrain contributions from beyond the SM
scenarios, some of which predict that this asymmetry could be as large as
$-15\%$ [12, *Aoki:SUSY, *Aoki:SUSY-CP, *Kagan:NP].

This paper presents a measurement of ${\cal B}(B^{0}\\!\rightarrow
K^{*0}\gamma)$/${\cal B}(B^{0}_{s}\\!\rightarrow\phi\gamma)$ using
1.0$\mbox{\,fb}^{-1}$ of data taken with the LHCb detector. The measured ratio
and the world average value of ${\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)$
are then used to determine ${\cal B}(B^{0}_{s}\\!\rightarrow\phi\gamma)$. This
result supersedes a previous LHCb measurement based on an integrated
luminosity of 0.37$\mbox{\,fb}^{-1}$ of data at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ [16]. A measurement of the direct
$C\\!P$ asymmetry of the decay $B^{0}\\!\rightarrow K^{*0}\gamma$ is also
presented.

##  2 The LHCb detector and dataset

The LHCb detector [17] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream. The
combined tracking system has a momentum resolution $\Delta p/p$ that varies
from 0.4% at 5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ to 0.6% at
100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$, and an impact parameter (IP)
resolution of 20$\,\upmu\rm m$ for tracks with high transverse momentum
($p_{\rm T}$). Charged hadrons are identified using two ring-imaging Cherenkov
detectors (RICH). Photon, electron and hadron candidates are identified by a
calorimeter system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers. The trigger consists of a hardware stage, based on information from
the calorimeter and muon systems, followed by a software stage which applies a
full event reconstruction.

Decay candidates are required to have triggered on the signal photon and the
daughters of the vector meson. At the hardware stage, the decay candidates
must have been triggered by an electromagnetic candidate with transverse
energy ($E_{\rm T}$) $>2.5\mathrm{\,Ge\kern-1.00006ptV}$. The software stage
is divided into two steps. The first one performs a partial event
reconstruction and reduces the rate such that the second can perform full
event reconstruction to further reduce the data rate. At the first software
stage, events are selected when a charged track is reconstructed with IP
$\chi^{2}$ $>16$. The IP $\chi^{2}$ is defined as the difference between the
$\chi^{2}$ of the $pp$ interaction vertex (PV) fit reconstructed with and
without the considered track. Furthermore, a charged track is required to have
either $p_{\rm T}$ $>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ for a photon
with $E_{\rm T}$ $>2.5\mathrm{\,Ge\kern-1.00006ptV}$ or $p_{\rm T}$
$>1.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ when the photon has $E_{\rm T}$
$>4.2\mathrm{\,Ge\kern-1.00006ptV}$. At the second software stage, a track
passing the previous criteria must form a $K^{*0}$ or $\phi$ candidate when
combined with an additional track, and the invariant mass of the combination
of the $K^{*0}$ ($\phi$) candidate and the photon candidate that triggered the
hardware stage is required to be within
1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ of the world average $B^{0}$
($B^{0}_{s}$) mass. The data used for this analysis correspond to
1.0$\mbox{\,fb}^{-1}$ of $pp$ collisions collected in 2011 at the LHC with a
centre-of-mass energy of $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$.

Large samples of $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ Monte Carlo simulated events are used to
optimise the signal selection and to parametrise the invariant-mass
distribution of the $B$ meson. Possible contamination from specific background
channels has also been studied using dedicated simulated samples. For the
simulation, $pp$ collisions are generated using Pythia 6.4 [18] with a
specific LHCb configuration [19]. Decays of hadronic particles are described
by EvtGen [20] in which final state radiation is generated using Photos [21].
The interaction of the generated particles with the detector and its response
are implemented using the Geant4 toolkit [22, *Agostinelli:geant4:2003] as
described in Ref. [24].

##  3 Offline event selection

The selection of $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ decays is designed to maximise the
cancellation of uncertainties in the ratio of their selection efficiencies.

The charged tracks used to build the vector mesons are required to have
$p_{\rm T}$ $>500{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, with at least one of
them having $p_{\rm T}$ $>1.2{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. In
addition, a requirement of IP $\chi^{2}>25$ means that they must be
incompatible with coming from any PV. The charged tracks are identified as
either kaons or pions using information provided by the RICH system. This is
based on the comparison between the two particle hypotheses. Kaons (pions) in
the studied $B\\!\rightarrow V\gamma$ decays, where $V$ stands for the vector
meson, are identified with a $\sim 70\,(83)\,\%$ efficiency for a $\sim
3\,(2)\,\%$ pion (kaon) contamination.

Photon candidates are required to have $E_{\rm T}$
$>2.6\mathrm{\,Ge\kern-1.00006ptV}$. Neutral and charged clusters in the
electromagnetic calorimeter are separated based on their compatibility with
extrapolated tracks [25] while photon deposits are distinguished from
$\pi^{0}$ deposits using the shape of the showers in the electromagnetic
calorimeter.

Oppositely-charged kaon-pion (kaon-kaon) combinations are accepted as $K^{*0}$
($\phi$) candidates if they form a good quality vertex and have an invariant
mass within $\pm 50\,(\pm 10){\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
world average $K^{*0}$ ($\phi$) mass [11]. The resulting vector meson
candidate is combined with the photon candidate to make a $B$ candidate. The
invariant-mass resolution of the selected $B$ candidate is
$\approx$100${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for the decays
presented in this paper.

The $B$ candidates are required to have an invariant mass within
1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ of the world average $B$ mass [11]
and to have $p_{\rm T}$ $>3{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. They must
also point to a PV, with IP $\chi^{2}$ $<9$, and the angle between the $B$
candidate momentum direction and the $B$ line of flight has to be less than
20$\rm\,mrad$. In addition, the vertex separation $\chi^{2}$ between the $B$
meson vertex and its related PV must be larger than 100. The distribution of
the helicity angle $\theta_{\mathrm{H}}$, defined as the angle between the
momentum of any of the daughters of the vector meson and the momentum of the
$B$ candidate in the rest frame of the vector meson, is expected to follow a
$\sin^{2}\theta_{\mathrm{H}}$ function for $B\\!\rightarrow V\gamma$, and a
$\cos^{2}\theta_{\mathrm{H}}$ function for the $B\\!\rightarrow V\pi^{0}$
background. A requirement of $|\cos\theta_{\mathrm{H}}|<0.8$ is therefore made
to reduce $B\\!\rightarrow V\pi^{0}$ background, where the neutral pion is
misidentified as a photon. Background coming from partially reconstructed
$B$-hadron decays is reduced by requiring the $B$ vertex to be isolated: its
$\chi^{2}$ must increase by more than two units when adding any other track in
the event.

##  4 Signal and background description

The signal yields of the $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ decays are determined from an extended
unbinned maximum-likelihood fit performed simultaneously to the invariant-mass
distributions of the $B^{0}$ and $B^{0}_{s}$ candidates. A constraint on the
$B^{0}$ and $B^{0}_{s}$ masses is included in the fit which requires the
difference between them to be consistent with the LHCb measurement of $87.3\pm
0.4$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [26]. The $K^{*0}$ and $\phi$
resonances are described by a relativistic $P$-wave Breit-Wigner distribution
[27] convoluted with a Gaussian distribution to take into account the detector
resolution. The natural width of the resonances is fixed to the world average
value [11]. A polynomial line shape is added to describe the background. The
resulting distribution is fitted to the vector meson invariant-mass
distribution, as shown in Fig. 1.

Figure 1: Invariant-mass distributions of the (a) $K^{*0}$ and (b) $\phi$
resonance candidates. The black points represent the data and the fit result
is represented as a solid blue line. The fit is described in the text. The
regions outside the vector meson invariant-mass window are shaded. The Poisson
$\chi^{2}$ residuals [28] are shown below the fits with the $\pm 2\,\sigma$
confidence-level interval delimited by solid red lines.

The fit to the invariant mass of the vector-meson candidates yields a
resonance mass of $895.7\pm 0.4$$\mathrm{\,Me\kern-1.00006ptV}$ and
$1019.42\pm 0.09$$\mathrm{\,Me\kern-1.00006ptV}$ for the $K^{*0}$ and $\phi$,
respectively, in agreement with the world average values [11]. The detector
resolution extracted from the fit is $5\pm 4$$\mathrm{\,Me\kern-1.00006ptV}$
for the $K^{*0}$ resonance and $1.3\pm 0.1$$\mathrm{\,Me\kern-1.00006ptV}$ for
the $\phi$. The effect of taking the value found in data or the world average
as the central value of the vector meson mass window is negligible. In
addition no systematic uncertainty due to the choice of the line shape of the
resonances is assigned.

Both $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ signal distributions are parametrised with
a two-sided Crystal Ball distribution [29]. In the low mass region, there can
be possible losses in the photon energy due to the fiducial volume of the
calorimeter. A tail at high masses is also observed and can be explained by
the spread in the error of the reconstructed $B$ mass and pile-up effects in
the photon deposition. The parameters describing the tails on both sides are
fixed to the values determined from simulation. The width of each signal peak
is left as a free parameter in the fit.

The reconstructed mass distribution of the combinatorial background has been
determined from the low-mass sideband of the $K^{*0}$ mass distribution as an
exponential function with different attenuation constants for the two decay
channels. Additional contamination from several exclusive background decays is
studied using simulated samples. The irreducible $B^{0}_{s}\rightarrow
K^{*}\gamma$ decays, the $\mathchar 28931\relax^{0}_{b}\rightarrow\mathchar
28931\relax^{*}(pK^{-})\gamma$ decays222$\mathchar 28931\relax^{*}$ stands for
$\mathchar 28931\relax(1520)$ and other b-baryon resonances promptly decaying
into a $pK^{-}$ final state., and the charmless $B^{0}_{(s)}\rightarrow
h^{+}h^{\prime-}\pi^{0}$ decays produce peaked contributions under the
invariant-mass peak of $B^{0}\\!\rightarrow K^{*0}\gamma$. As the experimental
branching fractions of the charmless $B^{0}_{s}$ and $\mathchar
28931\relax^{0}_{b}$ decays are unknown, the corresponding contamination rates
are estimated either using the predicted branching fraction in the case of
$B_{s}^{0}\rightarrow K^{*0}\gamma$ decays, assuming SU(3) symmetry for
$B^{0}_{s}\rightarrow h^{+}h^{\prime-}\pi^{0}$ decays, or by directly
estimating the signal yield from an independent sample as in $\mathchar
28931\relax^{0}_{b}\rightarrow\mathchar 28931\relax^{*}\gamma$ decays. The
overall contribution from these decays is estimated to represent $(2.6\pm
0.4)$% and $(0.9\pm 0.6)$% of the $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ yields, respectively. Each of these
contributions is modelled with a Crystal Ball function determined from a
simulated sample and their yields are fixed in the fit.

The partial reconstruction of the charged $B\rightarrow h^{+}h^{\prime-}\gamma
X$ or $B\rightarrow h^{+}h^{\prime-}\pi^{0}X$ decays gives a broad
contribution at lower candidate masses, with a high-mass tail that extends
into the signal region. The partially reconstructed $B^{+}\rightarrow
K^{*0}\pi^{+}\gamma$ and $B^{+}\rightarrow\phi K^{+}\gamma$ radiative decays
produce a peaking contribution in the low-mass sideband at around
5.0${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ for $B^{0}\\!\rightarrow
K^{*0}\gamma$ and around 4.5${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ for
$B^{0}_{s}\\!\rightarrow\phi\gamma$. The corresponding contamination has been
estimated to be $(3.3\pm 1.1)\%$ and $(1.8\pm 0.3)$% for the
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$
decays, respectively. The partially reconstructed neutral $B$ meson decays
also contribute at the same level and several other channels exhibit a similar
final state topology. These contributions are described by a Crystal Ball
function and the yields are left to vary in the fit. The parameters of the
Crystal Ball function are determined from the simulation. Additional
contributions from the partial reconstruction of multi-body charmed decays and
$B\rightarrow V\pi^{0}\mathrm{X}$ have been added to the simultaneous fit in
the same way. The shape of these contributions, again determined from the
simulation, follows an ARGUS function [30] peaking around
$4.0$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$. The various background
contributions included in the fit model are summarised in Table 1.

Table 1: Expected contributions to the $B^{0}\\!\rightarrow K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$ yields in the $\pm$1${\mathrm{\,Ge\kern-0.90005ptV\\!/}c^{2}}$ mass window from the exclusive background channels: radiative decays, $h^{+}h^{\prime-}\gamma$ (top), charmless b decays involving energetic $\pi^{0}$, $h^{+}h^{\prime-}\pi^{0}$ (middle) and partially reconstructed decays (bottom). The average measurement (exp.) or theoretical (theo.) branching fraction is given where available. Each exclusive contribution above 0.1% is included in the fit model, with a fixed shape determined from simulation. The amplitude of the partially reconstructed backgrounds is left to vary in the fit while the $h^{+}h^{\prime-}\gamma$ and $h^{+}h^{\prime-}\pi^{0}$ contributions are fixed to their expected level. Decay | Branching fraction | Relative contribution to
---|---|---
| ($\times 10^{6}$) | $B^{0}\\!\rightarrow K^{*0}\gamma$ |  $B^{0}_{s}\\!\rightarrow\phi\gamma$
$\mathchar 28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{*}\gamma$ | estimated from data | ($1.0\pm 0.3$)% | ($0.4\pm 0.3$)%
$B^{0}_{s}\\!\rightarrow K^{*0}\gamma$ |  $1.26\pm 0.31$ (theo. [31]) | ($0.8\pm 0.2$)% | $\mathcal{O}(10^{-4})$
$B^{0}\\!\rightarrow K^{+}\pi^{-}\pi^{0}$ |  $35.9^{\,+\,2.8}_{\,-\,2.4}$ (exp. [4]) | ($0.5\pm 0.1$)% | $\mathcal{O}(10^{-4})$
$B^{0}_{s}\\!\rightarrow K^{+}\pi^{-}\pi^{0}$ | estimated from SU(3) symmetry | ($0.2\pm 0.2$)% | $\mathcal{O}(10^{-4})$
$B^{0}_{s}\\!\rightarrow K^{+}K^{-}\pi^{0}$ | estimated from SU(3) symmetry | $\mathcal{O}(10^{-4})$ | ($0.5\pm 0.5$)%
$B^{+}\\!\rightarrow K^{*0}\pi^{+}\gamma$ |  $20^{\,+\,7}_{\,-\,6}$ (exp. [4]) | ($3.3\pm 1.1$)% | $<6\times 10^{-4}$
$B^{0}\\!\rightarrow K^{+}\pi^{-}\pi^{0}\gamma$ |  $41\pm 4$ (exp. [4]) |  $(4.5\pm 1.7)$% | $\mathcal{O}(10^{-4})$
$B^{+}\\!\rightarrow\phi K^{+}\gamma$ |  $3.5\pm 0.6$ (exp. [4]) | $3\times 10^{-4}$ |  $(1.8\pm 0.3)$%
$B\rightarrow V\pi^{0}\mathrm{X}$ |  $\mathcal{O}(10\%)$ (exp. [4]) | $\mathrm{a~{}few}\%$ | $\mathrm{a~{}few}\%$

At the trigger level, the electromagnetic calorimeter calibration is different
from that in the offline analysis. Therefore, the
$\pm$1${\mathrm{\,Ge\kern-1.00006ptV\\!/}c^{2}}$ mass window requirement
imposed by the trigger causes a bias in the $B$ meson acceptance to appear
near the limits of this window. The inefficiency at the edges of the mass
window is modelled by including a three-parameter threshold function in the
fit model

$T(m_{B})=\left(1-\mathrm{erf}\left(\frac{m_{B}-t_{\mathrm{L}}}{\sqrt{2}\mathrm{\sigma_{d}}}\right)\right)\times\left(1-\mathrm{erf}\left(\frac{t_{\mathrm{U}}-m_{B}}{\sqrt{2}\mathrm{\sigma_{d}}}\right)\right)\,,$
(1)

where erf is the Gauss error function. The parameter
$\mathrm{t_{L}}$($\mathrm{t_{U}}$) represents the actual lower (upper) mass
threshold and $\mathrm{\sigma_{d}}$ is the resolution.

##  5 Measurement of the ratio of branching fractions

The ratio of branching fractions is measured as

$\frac{{\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)}{{\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)}=\frac{N_{B^{0}\\!\rightarrow
K^{*0}\gamma}}{N_{B^{0}_{s}\\!\rightarrow\phi\gamma}}\times\frac{{\cal
B}(\phi\rightarrow K^{+}K^{-})}{{\cal B}(K^{*0}\rightarrow
K^{+}\pi^{-})}\times\frac{f_{s}}{f_{d}}\times\frac{\epsilon_{B^{0}_{s}\\!\rightarrow\phi\gamma}}{\epsilon_{B^{0}\\!\rightarrow
K^{*0}\gamma}}\,,$ (2)

where $N$ are the observed yields of signal candidates, $\mathrm{{\cal
B}(\phi\rightarrow K^{+}K^{-})/{\cal B}(K^{*0}\rightarrow
K^{+}\pi^{-})}=0.735\pm 0.008$ [11] is the ratio of branching fractions of the
vector mesons, $f_{s}/f_{d}=0.267^{+0.021}_{-0.020}$ [32] is the ratio of the
$B^{0}$ and $B_{s}^{0}$ hadronization fractions in $pp$ collisions at
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and
$\epsilon_{B^{0}_{s}\\!\rightarrow\phi\gamma}/\epsilon_{B^{0}\\!\rightarrow
K^{*0}\gamma}$ is the ratio of total reconstruction and selection efficiencies
of the two decays.

The results of the fit are shown in Fig. 2. The number of $B^{0}\\!\rightarrow
K^{*0}\gamma$ and $B^{0}_{s}\\!\rightarrow\phi\gamma$ candidates is $5279\pm
93$ and $691\pm 36$, respectively, corresponding to a yield ratio of $7.63\pm
0.38$. The relative contamination from partially reconstructed radiative
decays is fitted to be $(15\pm 5)\%$ for $B^{0}\\!\rightarrow K^{*0}\gamma$
and $(5\pm 3)\%$ for $B^{0}_{s}\\!\rightarrow\phi\gamma$, in agreement with
the expected rate from $B^{+(0)}\rightarrow K^{*0}\pi^{+(0)}\gamma$ and
$B^{+(0)}\rightarrow\phi K^{+(0)}\gamma$, respectively. The contribution from
partial reconstruction of charmed decays at low mass is fitted to be $(5\pm
4)\%$ and $(0^{+9}_{-0})$% of the $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ yields, respectively.

Figure 2: Invariant-mass distributions of the (a) $B^{0}\\!\rightarrow
K^{*0}\gamma$ and (b) $B^{0}_{s}\\!\rightarrow\phi\gamma$ candidates. The
black points represent the data and the fit result is represented as a solid
blue line. The signal is fitted with a double-sided Crystal Ball function
(short-dashed green line). The combinatorial background is modelled with an
exponential function (long-dashed red line). In decreasing amplitude order,
the exclusive background contributions to $B^{0}\\!\rightarrow K^{*0}\gamma$
are $B^{+(0)}\\!\rightarrow K^{*0}\pi^{+(0)}\gamma$ (short-dotted black),
$B\rightarrow K^{*0}(\phi)\pi^{0}X$ (long-dashed blue),
$B^{0}_{s}\\!\rightarrow K^{*0}\gamma$ (dotted short-dashed green), $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{*}\gamma$ (double-
dotted dashed pink), $B^{0}\\!\rightarrow K^{+}\pi^{-}\pi^{0}$ (dotted long-
dashed black) and $B^{0}_{s}\\!\rightarrow K^{+}\pi^{-}\pi^{0}$ (long-dotted
blue). The background contributions to $B^{0}_{s}\\!\rightarrow\phi\gamma$ are
$B^{+(0)}\\!\rightarrow\phi K^{+(0)}\gamma$ (dotted black), $\mathchar
28931\relax^{0}_{b}\\!\rightarrow\mathchar 28931\relax^{*}\gamma$ (double-
dotted dashed pink) and $B^{0}_{s}\\!\rightarrow K^{+}K^{-}\pi^{0}$ (dotted-
dashed black). No significant contribution to
$B^{0}_{s}\\!\rightarrow\phi\gamma$ is found from partially reconstructed
$B\rightarrow K^{*0}(\phi)\pi^{0}X$ decays. The Poisson $\chi^{2}$ residuals
[28] are shown below the fit with the $\pm 2\,\sigma$ confidence-level
interval delimited by solid red lines.

The systematic uncertainty from the background modelling is determined by
varying the parameters that have been kept constant in the fit of the
invariant-mass distribution within their uncertainty. The 95% CL interval of
the relative variation on the yield ratio is determined to be $[-1.2,+1.4]\%$
and is taken as a conservative estimate of the systematic uncertainty
associated with the background modelling. The relative variation is dominated
by the effect from the partially reconstructed background. This procedure is
repeated to evaluate the systematic uncertainty from the signal-shape
modelling, by varying the parameters of the Crystal-Ball tails within their
uncertainty. A relative variation of $[-1.3,+1.4]\%$ on the yield ratio is
observed and added to the systematic uncertainty. As a cross-check of the
possible bias introduced on the ratio by the modelling of the mass window
thresholds and the partially reconstructed background that populates the low
mass region, the fit is repeated in a reduced mass window of $\pm
700$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ around the world average $B$
meson mass. The result is found to be statistically consistent with the
nominal fit. Combining these systematic effects, an overall
$({}_{-1.8}^{+2.0})$% relative uncertainty on the yield ratio is found.

The efficiency ratio can be factorised as

$\frac{\epsilon_{B^{0}_{s}\\!\rightarrow\phi\gamma}}{\epsilon_{B^{0}\\!\rightarrow
K^{*0}\gamma}}=r_{\text{reco\&sel}}\times r_{\text{PID}}\times
r_{\text{trigger}}\,,$ (3)

where $r_{\text{reco\&sel}}$, $r_{\text{PID}}$ and $r_{\text{trigger}}$ are
the efficiency ratios due to the reconstruction and selection requirements,
the particle identification (PID) requirements and the trigger requirements,
respectively.

The correlated acceptance of the kaons due to the limited phase-space in the
$\phi\\!\rightarrow K^{+}K^{-}$ decay causes the $\phi$ vertex to have a worse
spatial resolution than the $K^{*0}$ vertex. This affects the
$B^{0}_{s}\\!\rightarrow\phi\gamma$ selection efficiency through the IP
$\chi^{2}$ and vertex isolation cuts, while the common track cut $p_{\rm T}$
$>500{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ is less efficient on the softer
pion from the $K^{*0}$ decay. These effects partially cancel and the
reconstruction and selection efficiency ratio is found to be
$r_{\text{reco\&sel}}=0.906\pm 0.007\,\text{(stat.)}\pm
0.017\,\text{(syst.)}$. The majority of the systematic uncertainties also
cancel, since the kinematic selections are almost identical for both decays.
The remaining systematic uncertainties include the hadron reconstruction
efficiency, arising from differences in the interaction of pions and kaons
with the detector and uncertainties in the description of the detector
material. The reliability of the simulation in describing the
$\text{IP}\,\chi^{2}$ of the tracks and the isolation of the $B$ vertex is
also included in the systematic uncertainty on the $r_{\text{reco\&sel}}$
ratio. The simulated samples are weighted for each signal and background
contribution to reproduce the reconstructed mass distribution seen in data. No
further systematic uncertainties are associated with the use of the
simulation, since kinematic properties of the decays are observed to be well
modelled. Uncertainties associated with the photon are negligible, because the
reconstruction is identical in both decays.

The PID efficiency ratio is determined from data by means of a calibration
procedure using pure samples of kaons and pions from $D^{*\pm}\\!\rightarrow
D^{0}(K^{+}\pi^{-})\pi^{\pm}$ decays selected without PID information. This
procedure yields $r_{\text{PID}}=0.839\pm 0.005\,\text{(stat.)}\pm
0.010\,\text{(syst.)}$.

The trigger efficiency ratio $r_{\text{trigger}}=1.080\pm
0.009\,\text{(stat.)}$ is obtained from the simulation. The systematic
uncertainty due to any difference in the efficiency of the requirements made
at the trigger level is included as part of the selection uncertainty.

Finally, the ratio of branching fractions is obtained using Eq. 2,

$\frac{{\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)}{{\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)}=1.23\pm 0.06\,\mathrm{(stat.)}\pm
0.04\,\mathrm{(syst.)}\pm 0.10\,(f_{s}/f_{d})\,,$

where the first uncertainty is statistical, the second is the experimental
systematic uncertainty and the third is due to the uncertainty on
$f_{s}/f_{d}$. The contributions to the systematic uncertainty are summarised
in Table 2.

Table 2: Summary of the individual contributions to the relative systematic uncertainty on the ratio of branching fractions as defined in Eq. 2. Uncertainty source | Systematic uncertainty
---|---
$r_{\mathrm{reco\&sel.}}$ | 2.0%
$r_{\mathrm{PID}}$ | 1.3%
$r_{\mathrm{trigger}}$ | 0.8%
$\mathrm{{\cal B}(\phi\rightarrow K^{+}K^{-})/{\cal B}(K^{*0}\rightarrow K^{+}\pi^{-})}$ | 1.1%
Signal and background modelling |  ${}^{+2.0}_{-1.8}$%
Total | 3.4%

##  6 Measurement of the $C\\!P$ asymmetry in $B^{0}\\!\rightarrow
K^{*0}\gamma$ decays

The $B^{0}\\!\rightarrow K^{*0}\gamma$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}\gamma$ invariant mass
distributions are fitted simultaneously to measure a raw asymmetry defined as

$\mathcal{A}_{\mathrm{RAW}}=\frac{N(K^{-}\pi^{+}\gamma)-N(K^{+}\pi^{-}\gamma)}{N(K^{-}\pi^{+}\gamma)+N(K^{+}\pi^{-}\gamma)}\,,$
(4)

where $N(X)$ is the signal yield measured in the final state $X$. This
asymmetry must be corrected for detection and production effects to measure
the physical $C\\!P$ asymmetry. The detection asymmetry arises mainly from the
kaon quark content giving a different interaction rate with the detector
material depending on its charge. The $B^{0}$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ mesons may also not be produced
with the same rate in the region covered by the LHCb detector, inducing the
$B^{0}$ meson production asymmetry. The physical $C\\!P$ asymmetry and these
two corrections are related through

${\cal A}_{CP}(B^{0}\\!\rightarrow K^{*0}\gamma)={\cal
A}_{\mathrm{RAW}}(B^{0}\\!\rightarrow K^{*0}\gamma)-{\cal
A}_{\mathrm{D}}(K\pi)-\kappa{\cal A}_{\mathrm{P}}(B^{0})\,,$ (5)

where ${\cal A}_{\mathrm{D}}(K\pi)$ and ${\cal A}_{\mathrm{P}}(B^{0})$
represent the detection asymmetry of the kaon and pion pair and $B^{0}$ meson
production asymmetry, respectively. The dilution factor $\kappa$ arises from
the oscillations of neutral $B$ mesons.

To determine the raw asymmetry, the fit keeps the same signal mean and width,
as well as the same mass-window threshold parameters for the $B^{0}$ and
$\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ signal. The yields of the
combinatorial background and partially reconstructed decays are allowed to
vary independently. The relative amplitudes of the exclusive peaking
backgrounds, $\mathchar 28931\relax^{0}_{b}\rightarrow\mathchar
28931\relax^{*}\gamma$, $B^{0}_{s}\rightarrow K^{*0}\gamma$ and
$B^{0}_{(s)}\rightarrow K^{+}\pi^{-}\pi^{0}$, are fixed to the same values for
both $B$ flavours.

Figure 3: Invariant-mass distributions of the (a) $\kern
1.61993pt\overline{\kern-1.61993ptB}{}^{0}$ $\rightarrow$$\kern
1.79997pt\overline{\kern-1.79997ptK}{}^{*0}$ $\gamma$ and (b)
$B^{0}\\!\rightarrow K^{*0}\gamma$ decay candidates. The black points
represent the data and the fit result is represented as a solid blue line. The
different background components are also shown. The Poisson $\chi^{2}$
residuals [28] are shown below the fits with the $\pm 2\,\sigma$ confidence-
level interval delimited by solid red lines.

Figure 3 shows the result of the simultaneous fit. The yields of the
combinatorial background across the entire mass window are compatible within
statistical uncertainty. The number of combinatorial background candidates is
$2070\pm 414$ and $1552\pm 422$ in the full mass range for the
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}\gamma$ decays, respectively. The
contribution from the charmless partially reconstructed decay
$B^{+}\\!\rightarrow K^{*0}\pi^{+}\gamma$ to $B^{0}\\!\rightarrow
K^{*0}\gamma$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}\gamma$ is $(10\pm 6)\,\%$ and
$(24\pm 7)\,\%$ of the signal yield, respectively. Furthermore, the charmed
partially reconstructed decays $B\rightarrow K^{*0}\pi^{0}\mathrm{X}$
contribute with $(7\pm 8)\,\%$ and $(9\pm 8)\,\%$ of the signal yield to the
$B^{0}\\!\rightarrow K^{*0}\gamma$ and $\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptK}{}^{*0}\gamma$ decays, respectively. The
latter decays give contributions that are mainly located outside the signal
invariant-mass region, as can be seen from Fig. 3.

The value of the raw asymmetry determined from the fit is
$\mathcal{A}_{\mathrm{RAW}}=(0.3\pm 1.7)\,\%$, where the uncertainty is
statistical only.

The systematic uncertainty from the background modelling is determined as
explained in Sect. 4. To address the systematic uncertainty from the possible
$C\\!P$ asymmetry in the background, the yield of the $B^{0}\rightarrow
K^{+}\pi^{-}\pi^{0}$ decay is varied within its measured $C\\!P$ asymmetry
$\mathcal{A}_{C\\!P}(B^{0}\rightarrow K^{*0}\pi^{0})=(-15\pm 12)\%$ [4]. For
the other decays, a measurement of the $C\\!P$ asymmetry has not been made.
The variation is therefore performed over the full $\pm 100\%$ range. The
effect of these variations on $\mathcal{A}_{\mathrm{RAW}}$ gives rise to a
Gaussian distribution centred at $-0.2\%$ with a standard deviation of 0.7%,
thus a correction of $\Delta{\cal A}_{\mathrm{bkg}}=(-0.2\pm 0.7)\%$ is
applied. The systematic uncertainty from the signal modelling is evaluated
using a similar procedure and is found to be negligible. The possible double
misidentification ($K^{-}\pi^{+}\rightarrow\pi^{-}K^{+}$) in the final state
would induce a dilution of the measured raw asymmetry. This is evaluated using
simulated events and is also found to be negligible.

An instrumental bias can be caused by the vertical magnetic field, which
deflects oppositely-charged particles into different regions of the detector.
Any non-uniformity of the instrumental performance could introduce a bias in
the asymmetry measurement. This potential bias is experimentally reduced by
regularly changing the polarity of the magnetic field during data taking. As
the integrated luminosity is slightly different for the “up” and “down”
polarities, a residual bias could remain. This bias is studied by comparing
the $C\\!P$ asymmetry measured separately in each of the samples collected
with opposite magnet polarity, up or down. Table 3 summarises the $C\\!P$
asymmetry and the number of signal candidates for the two magnet polarities.
The asymmetries with the two different polarities are determined to be
compatible within the statistical uncertainties and the luminosity-weighted
average, ${\cal A}_{\mathrm{RAW}}=(0.4\pm 1.7)\%$, is in good agreement with
the $C\\!P$ asymmetry measured in the full data sample.

Table 3:  $C\\!P$ asymmetry and total number of signal candidates measured for each magnet polarity. | Magnet Up | Magnet Down
---|---|---
$\int{\cal L}dt$ ($\mbox{\,pb}^{-1}$) | $432\pm 15$ |  $588\pm 21$
${\cal A}^{\mathrm{RAW}}$ (%) | $1.3\pm 2.6$ |  $-0.4\pm 2.2$
Signal candidates | $2189\pm 65$ |  $3103\pm 71$

The residual bias can be extracted from the polarity-split asymmetry as

$\Delta{\cal
A}_{\mathrm{M}}=\left(\frac{\mathcal{L}^{\mathrm{up}}-\mathcal{L}^{\mathrm{down}}}{\mathcal{L}^{\mathrm{up}}+\mathcal{L}^{\mathrm{down}}}\right)\left(\frac{\mathcal{A}^{\mathrm{down}}_{\mathrm{RAW}}-\mathcal{A}^{\mathrm{up}}_{\mathrm{RAW}}}{2}\right)\,,$
(6)

which is found to be consistent with zero $\Delta{\cal
A}_{\mathrm{M}}=(+0.1\pm 0.2)\,\%$. The raw asymmetry obtained from the fit is
corrected by $\Delta{\cal A}_{\mathrm{bkg}}$ and $\Delta{\cal
A}_{\mathrm{M}}$.

The detection asymmetry can be defined in terms of the detection efficiencies
of the charge-conjugate final states by

${\cal
A}_{\mathrm{D}}(K\pi)=\frac{\epsilon(K^{-}\pi^{+})-\epsilon(K^{+}\pi^{-})}{\epsilon(K^{-}\pi^{+})+\epsilon(K^{+}\pi^{-})}\,.$
(7)

The related asymmetries have been studied at LHCb using control samples of
charm decays [33]. It has been found that for $K\pi$ pairs in the kinematic
range relevant for our analysis the detection asymmetry is ${\cal
A}_{\mathrm{D}}(K\pi)=(-1.0\pm 0.2)\%$.

The $B$ production asymmetry is defined in terms of the different production
rates

${\cal A}_{\mathrm{P}}(B^{0})=\frac{R(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0})-R(B^{0})}{R(\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0})+R(B^{0})}$ (8)

and has been measured at LHCb to be ${\cal A}_{\mathrm{P}}(B^{0})=(1.0\pm
1.3)\%$ using large samples of
$B^{0}\\!\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$ decays
[33]. The contribution of the production asymmetry to the measured $C\\!P$
asymmetry is diluted by a factor $\kappa$, defined as

$\kappa=\frac{\int^{\infty}_{0}\cos(\Delta
m_{d}t)e^{-\Gamma_{d}t}\epsilon(t)dt}{\int^{\infty}_{0}\cosh(\frac{\Delta\Gamma_{d}t}{2})e^{-\Gamma_{d}t}\epsilon(t)dt}\,,$
(9)

where $\Delta m_{d}$ and $\Delta\Gamma_{d}$ are the mass difference and the
decay width difference between the mass eigenstates of the $B^{0}-\kern
1.79993pt\overline{\kern-1.79993ptB}{}^{0}$ system, $\Gamma_{d}$ is the
average of their decay widths and $\epsilon(t)$ is the decay-time acceptance
function of the signal selection. The latter has been determined from data
using the decay-time distribution of background-subtracted signal candidates,
the known $B^{0}$ lifetime and assuming $\Delta\Gamma_{d}=0$. The dilution
factor is found to be $\kappa=0.41\pm 0.04$, where the uncertainty comes from
knowledge of the acceptance function parameters as well as $\Gamma_{d}$ and
$\Delta m_{d}$.

Table 4: Corrections to the raw asymmetry and corresponding systematic uncertainties. Correction to $A_{RAW}$ |  | Value [%]
---|---|---
Background model |  $\Delta{\cal A}_{bkg}$ | $-0.2\pm 0.7$
Magnet polarity |  $\Delta{\cal A}_{\mathcal{M}}$ | $+0.1\pm 0.3$
Detection |  $-{\cal A}_{\mathrm{D}}(K\pi)$ | $+1.0\pm 0.2$
$B^{0}$ production |  $-\kappa{\cal A}_{\mathrm{P}}(B^{0})$ | $-0.4\pm 0.5$
Total |  |  $+0.5\pm 0.9$

Adding the above corrections, which are summarised in Table 4, to the raw
asymmetry, the direct $C\\!P$ asymmetry in $B^{0}\\!\rightarrow K^{*0}\gamma$
decays is measured to be

${\cal A}_{CP}(B^{0}\\!\rightarrow K^{*0}\gamma)=(0.8\pm
1.7\,(\mathrm{stat.})\pm 0.9\,(\mathrm{syst.}))\%\,.$

##  7 Results and conclusions

Using an integrated luminosity of 1.0$\mbox{\,fb}^{-1}$ of $pp$ collision data
collected by the LHCb experiment at a centre-of-mass energy of
$\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$, the ratio of branching fractions
between $B^{0}\\!\rightarrow K^{*0}\gamma$ and
$B^{0}_{s}\\!\rightarrow\phi\gamma$ has been measured to be

$\frac{{\cal B}(B^{0}\\!\rightarrow K^{*0}\gamma)}{{\cal
B}(B^{0}_{s}\\!\rightarrow\phi\gamma)}=1.23\pm 0.06\,\mathrm{(stat.)}\pm
0.04\,\mathrm{(syst.)}\pm 0.10\,(f_{s}/f_{d})\,,$

which is the most precise measurement to date and is in good agreement with
the SM prediction of $1.0\pm 0.2$ [8].

Using the world average value ${\cal B}(B^{0}\\!\rightarrow
K^{*0}\gamma)=(4.33\pm 0.15)~{}\times 10^{-5}$ [4], the
$B^{0}_{s}\\!\rightarrow\phi\gamma$ branching fraction is determined to be

${\cal B}(B^{0}_{s}\\!\rightarrow\phi\gamma)=(3.5\pm 0.4)\times 10^{-5}\,,$

in agreement with the previous measurement [3]. This is the most precise
measurement to date and is consistent with, but supersedes, a previous LHCb
result using an integrated luminosity of 0.37$\mbox{\,fb}^{-1}$ [16].

The direct $C\\!P$ asymmetry in $B^{0}\\!\rightarrow K^{*0}\gamma$ decays has
also been measured with the same data sample and found to be

${\cal A}_{C\\!P}(B^{0}\\!\rightarrow K^{*0}\gamma)=(0.8\pm
1.7\,\mathrm{(stat.)}\pm 0.9\,\mathrm{(syst.)})\%\,,$

in agreement with the SM expectation of $(-0.61\pm 0.43)$ % [10]. This is
consistent with previous measurements [5, *belle:exp-b2kstgamma:2004,
*cleo:exp-excl-radiative-decays:1999], and is the most precise result of the
direct $C\\!P$ asymmetry in $B^{0}\\!\rightarrow K^{*0}\gamma$ decays to date.

## 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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