Time-Dependent {\boldmath CP }-Violating Asymmetry in B 0 → ρ 0 γ Decays
aa r X i v : . [ h e p - e x ] F e b Belle Preprint 2007-40KEK Preprint 2007-43
Time-Dependent
C P -Violating Asymmetry in B → ρ γ Decays
Y. Ushiroda, K. Sumisawa, N. Taniguchi, I. Adachi, H. Aihara, K. Arinstein, T. Aushev,
18, 12
S. Bahinipati, A. M. Bakich, V. Balagura, E. Barberio, K. Belous, U. Bitenc, A. Bondar, A. Bozek, M. Braˇcko,
20, 13
T. E. Browder, P. Chang, Y. Chao, A. Chen, W. T. Chen, B. G. Cheon, R. Chistov, I.-S. Cho, Y. Choi, J. Dalseno, M. Dash, S. Eidelman, D. Epifanov, N. Gabyshev, B. Golob,
19, 13
H. Ha, J. Haba, K. Hara, T. Hara, K. Hayasaka, M. Hazumi, D. Heffernan, T. Hokuue, Y. Hoshi, W.-S. Hou, H. J. Hyun, K. Inami, A. Ishikawa, H. Ishino, R. Itoh, Y. Iwasaki, D. H. Kah, J. H. Kang, H. Kawai, T. Kawasaki, H. Kichimi, Y. J. Kim, K. Kinoshita, S. Korpar,
20, 13
P. Kriˇzan,
19, 13
P. Krokovny, R. Kumar, C. C. Kuo, A. Kuzmin, Y.-J. Kwon, M. J. Lee, S. E. Lee, T. Lesiak, S.-W. Lin, D. Liventsev, F. Mandl, S. McOnie, T. Medvedeva, K. Miyabayashi, H. Miyake, H. Miyata, Y. Miyazaki, R. Mizuk, D. Mohapatra, G. R. Moloney, Y. Nagasaka, M. Nakao, H. Nakazawa, S. Nishida, O. Nitoh, S. Noguchi, T. Nozaki, S. Ogawa, T. Ohshima, S. Okuno, S. L. Olsen,
6, 9
P. Pakhlov, G. Pakhlova, C. W. Park, H. Park, L. S. Peak, L. E. Piilonen, H. Sahoo, Y. Sakai, O. Schneider, J. Sch¨umann, A. J. Schwartz, K. Senyo, M. E. Sevior, M. Shapkin, C. P. Shen, H. Shibuya, J.-G. Shiu, B. Shwartz, J. B. Singh, A. Sokolov, A. Somov, S. Staniˇc, M. Stariˇc, T. Sumiyoshi, O. Tajima, F. Takasaki, K. Tamai, M. Tanaka, Y. Teramoto, I. Tikhomirov, K. Trabelsi, S. Uehara, K. Ueno, T. Uglov, Y. Unno, S. Uno, P. Urquijo, Y. Usov, G. Varner, K. Vervink, S. Villa, C. C. Wang, C. H. Wang, M.-Z. Wang, P. Wang, X. L. Wang, Y. Watanabe, E. Won, B. D. Yabsley, A. Yamaguchi, Y. Yamashita, M. Yamauchi, Z. P. Zhang, A. Zupanc, and O. Zyukova (The Belle Collaboration) Budker Institute of Nuclear Physics, Novosibirsk Chiba University, Chiba University of Cincinnati, Cincinnati, Ohio 45221 The Graduate University for Advanced Studies, Hayama Hanyang University, Seoul University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba Hiroshima Institute of Technology, Hiroshima Institute of High Energy Physics, Chinese Academy of Sciences, Beijing Institute of High Energy Physics, Vienna Institute of High Energy Physics, Protvino Institute for Theoretical and Experimental Physics, Moscow J. Stefan Institute, Ljubljana Kanagawa University, Yokohama Korea University, Seoul Kyoto University, Kyoto
Typeset by REVTEX 1 Kyungpook National University, Taegu ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne University of Ljubljana, Ljubljana University of Maribor, Maribor University of Melbourne, School of Physics, Victoria 3010 Nagoya University, Nagoya Nara Women’s University, Nara National Central University, Chung-li National United University, Miao Li Department of Physics, National Taiwan University, Taipei H. Niewodniczanski Institute of Nuclear Physics, Krakow Nippon Dental University, Niigata Niigata University, Niigata University of Nova Gorica, Nova Gorica Osaka City University, Osaka Osaka University, Osaka Panjab University, Chandigarh Saga University, Saga University of Science and Technology of China, Hefei Seoul National University, Seoul Sungkyunkwan University, Suwon University of Sydney, Sydney, New South Wales Toho University, Funabashi Tohoku Gakuin University, Tagajo Tohoku University, Sendai Department of Physics, University of Tokyo, Tokyo Tokyo Institute of Technology, Tokyo Tokyo Metropolitan University, Tokyo Tokyo University of Agriculture and Technology, Tokyo Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul (Dated: November 4, 2018)
Abstract
We report the first measurement of CP -violation parameters in B → ρ γ decays based on adata sample of 657 × B ¯ B pairs collected with the Belle detector at the KEKB asymmetric-energy e + e − collider. We obtain the time-dependent and direct CP -violating parameters, S ρ γ = − . ± . ± . A ρ γ = − . ± . ± . PACS numbers: 11.30.Er, 13.25.Hw W tb γs ( d ) V ∗ ts ( V ∗ td ) FIG. 1: Feynman diagram for radiative b decay in the SM. Radiative decay processes are sensitive to physics beyond the standard model (SM). Fig-ure 1 shows the lowest order Feynman diagram for radiative b decay in the SM. The heavySM particles in the loop can be replaced by new physics (NP) particles. Hence the corre-sponding physics observables may deviate from SM expectations. Recently, the possibility oftime-dependent CP asymmetries in b → sγ from NP have drawn much theoretical and ex-perimental interest [1, 2, 3, 4]. Both Belle [3] and BaBar [4] have measured time-dependent CP -violating parameters in B → K S π γ decay. The results so far are consistent with theSM.Signals for B → ρ γ have been established by Belle [5] and BaBar [6], which enablesus to measure CP asymmetries in the b → dγ process. As in b → sγ , the photon emittedin b → dγ (¯ b → ¯ dγ ) is predominantly left-handed (right-handed), and hence the finalstate is flavor specific [1]. In the decay B → ρ γ , the SM predicts no time-dependent CP asymmetry ( S ) and − . CP asymmetry ( A ) [2, 7]. In particular, assuming thetop quark is the dominant contribution in the loop shown in Fig. 1, the decay amplitude hasa weak phase φ that cancels the phase in the mixing; consequently S vanishes. Observinga non-zero value of S would indicate effects of NP [8]. In this Letter, we present the firstmeasurements of S and A for the B → ρ ( → π + π − ) γ transition based on 657 × B ¯ B pairs collected with the Belle detector [9] at the KEKB asymmetric-energy e + e − (3.5 on8.0 GeV) collider [10].The Belle detector is a large-solid-angle magnetic spectrometer that consists of a sili-con vertex detector (SVD), a 50-layer central drift chamber, an array of aerogel thresholdCherenkov counters, a barrel-like arrangement of time-of-flight scintillation counters, andan electromagnetic calorimeter (ECL) comprised of CsI(Tl) crystals located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return locatedoutside of the coil is instrumented to detect K L mesons and to identify muons.At the KEKB, the Υ(4 S ) is produced with a Lorentz boost of βγ = 0 .
425 along the z axis, which is defined as the direction antiparallel to the e + beam direction. In the decaychain Υ(4 S ) → B B → f rec f tag , where one of the B mesons decays at time t rec to a finalstate f rec , which is our signal mode, and the other decays at time t tag to a final state f tag B and B , the decay rate has a time dependence given by P (∆ t ) = e −| ∆ t | /τ B τ B (cid:26) q h S sin(∆ m d ∆ t )+ A cos(∆ m d ∆ t ) i(cid:27) . (1)Here τ B is the B lifetime, ∆ m d is the mass difference between the two B mass eigenstates,∆ t is the time difference t rec − t tag , and the b -flavor charge q = +1 ( −
1) when the tagging B meson is a B ( B ). Since the B and B mesons are approximately at rest in the Υ(4 S )center-of-mass system (c.m.s.), ∆ t can be determined from the displacement in z betweenthe f rec and f tag decay vertices: ∆ t ≃ ( z rec − z tag ) / ( βγc ) ≡ ∆ z/ ( βγc ).We reconstruct B → ρ γ , as well as a control sample of B → K ∗ ( → K + π − ) γ [11]. Forhigh energy prompt photons, we select the cluster in the ECL with the highest energy in thec.m.s. from clusters that have no associated charged track. We require 1 . < E c . m . s .γ < . E /E > .
95, where E /E is the ratioof energies summed in 3 × × π → γγ or η → γγ decays, photons fromthese decays are rejected as described in [12]; this retains 97% of the signal and rejects 20%of the background events. The polar angle of the photon direction in the laboratory frameis restricted to the barrel region of the ECL (33 ◦ < θ γ < ◦ ).Charged tracks are required to originate from the vicinity of the interaction point (IP),within 3 cm in z and 0.5 cm in r - φ ; their transverse momenta are required to be greater than0 .
22 GeV /c . Charged tracks from K S decays as well as positively identified protons, muonsand electrons are excluded. Finally, candidate tracks are classified as pion candidates andkaon candidates according to the ratio of kaon and pion particle identification likelihoods.This selection retains 87% of pions while rejecting 92% of kaons. Pairs of oppositely chargedpions are combined to form ρ candidates. Oppositely charged kaon and pion candidatesare combined to form K ∗ candidates. We form the invariant mass M Kπ for K ∗ and ρ candidates. To obtain M Kπ for ρ candidates, we assign the kaon mass to each pion in turn,and take the lower of the two values. We use M Kπ rather than M ππ since it gives a betterseparation of the ρ γ signal from the K ∗ γ background.We form two kinematic variables: the energy difference ∆ E ≡ ( P i E ∗ i ) − E ∗ beam andthe beam-energy constrained mass M bc ≡ p ( E ∗ beam ) − ( P i p ∗ i ) , where E ∗ beam is the beamenergy in the c.m.s., E ∗ i and p ∗ i are the energy and momentum of the i -th final state particlein the c.m.s., and the summation is taken over all the final state particles of the candidate B meson. Unlike M Kπ , we do not assign the kaon mass but instead assign the pion mass toform the energy and the momentum of ρ γ candidates. The signal box in ∆ E , M bc and M Kπ ,which is used for the measurements of CP -violating parameters, is defined as − .
15 GeV ≤ ∆ E ≤ . .
27 GeV /c ≤ M bc ≤ .
29 GeV /c and 0 . /c < M Kπ < . /c .A larger region in ∆ E and M bc , − . < ∆ E < . . /c < M bc is usedto determine the signal and background fractions.In order to suppress the background contribution from q ¯ q ( e + e − → q ¯ q with q = u, d, s, c ),an event likelihood ratio R is formed from likelihood variables for signal ( L sig ) and back-ground ( L bkg ) as R ≡ L sig / ( L sig + L bkg ). These likelihood variables are obtained by com-bining three variables: a Fisher discriminant F [13] that uses modified Fox-Wolfram mo-ments [14] as discriminating variables, the polar angle of the B meson candidate momentumin the c.m.s. (cos θ B ), and the cosine of the helicity angle (cos θ H ) defined as the momentum4irection of the π + with respect to the opposite of the B momentum in the ρ rest frame(similary for K ∗ γ ). We also require | cos θ H | < .
75 in order to suppress background fromrandom low momentum pions. R is also used to determine the best candidate when mul-tiple candidates are found in a single event, although the fraction of events with multiplecandidates is small (0.7%).There is a large background from B → K ∗ γ , which has a branching fraction forty timeslarger than that of B → ρ γ . When a kaon is misidentified as a pion, the K ∗ γ events easilymimic the ρ γ signal. This background peaks at K ∗ mass in M Kπ , and distributes in low∆ E region because the pion mass is assigned to the kaon. However, this is still acceptablesince the CP asymmetries in the B → K ∗ γ decay are known with good precision. Thereare several background contributions from B decays that could have finite CP asymmetries, ρ + π − , ρ π , and π + π − η ; however the contributions from these modes are small and thustheir impact on our measurement is tiny.The b -flavor of the accompanying B meson is identified from inclusive properties of par-ticles that are not associated with the reconstructed signal decay. The algorithm for flavortagging is described in detail elsewhere [15]. We use two parameters, q defined in Eq. (1) and r , to represent the tagging information. The parameter r is an event-by-event flavor-taggingquality factor that ranges from 0 to 1: r = 0 when there is no flavor discrimination and r = 1 when the flavor assignment is unambiguous. The value of r is determined by usingMonte Carlo (MC) and is used to sort data into seven r intervals. Events with r > . r intervals; for each interval, the wrong-tag fraction w and the difference ∆ w in w between the B and B decays are determined from high-statistics control samples ofsemi-leptonic and hadronic b → c decays. For events with r ≤ .
1, there is negligible flavordiscrimination available and we set w to 0.5.The vertex position of the signal-side decay of B → ρ γ and the control sample B → K ∗ γ is reconstructed from one or two charged track trajectories that have enough hits inthe SVD, with a constraint on the IP. The IP profile ( σ x ≃ µ m, σ y ≃ µ m) is smearedby the finite B flight length in the plane perpendicular to the z axis (21 µm ). The other(tag-side) B vertex is determined from well reconstructed tracks that are not assigned tothe signal side. A constraint to the IP profile is also imposed. The resolution of the distanceof the two B vertices is typically 160 µ m.After all the selections are applied, we obtain 5362 candidates in the ∆ E - M bc - M Kπ fitregion, of which 410 are in the signal box. We perform an extended unbinned maximumlikelihood (UML) fit to the ∆ E - M bc - M Kπ distribution in order to resolve the ρ γ , K ∗ γ ,other B ¯ B and q ¯ q components.The probability density function (PDF) for ρ γ and K ∗ γ are obtained from MC. Weuse a two-dimensional histogram for M bc -∆ E , and two one-dimensional histograms for M Kπ depending on ∆ E . For these PDFs, the peak position and the width are corrected using the B → K ∗ γ control sample in order to account for differences between data and simulation.The PDF for the other B ¯ B background component, which populates the lower ∆ E region,is also obtained from MC. For q ¯ q background, we use the product of one dimensional PDFs:the ARGUS parameterization [16] for M bc , a first-order polynomial for ∆ E , and a 20 binhistogram for M Kπ . The shape parameters (one ARGUS coefficient, one polynomial coeffi-cient, and fractions of 19 bin contents) are determined in the fit. Together with the yield ofthe four components, we have 25 free parameters in the fit.From the fit, we find 48 . ± . ρ γ candidates, 180 . ± . K ∗ γ background candi-dates, 10 . ± . B ¯ B background candidates, and 168 . ± . q ¯ q background candi-5 E (GeV) E v en t s / ( . G e V ) M K π (GeV/c ) E v en t s / ( . G e V / c ) FIG. 2: ∆ E (left) and M Kπ (right) distributions for signal enhanced samples. The followingselections are applied: 5 .
27 GeV /c ≤ M bc ≤ .
29 GeV /c and 0 .
92 GeV /c ≤ M Kπ (left), and5 .
27 GeV /c ≤ M bc ≤ .
29 GeV /c and − .
05 GeV ≤ ∆ E ≤ . B → K ∗ γ , B → ρ γ , and other B ¯ B and q ¯ q components. Notethat the other B ¯ B component is too small to be visible in the plot on the right. dates inside the signal box. Figure 2 shows the ∆ E and M Kπ projections of the fit result forthe signal enhanced samples. The observed M Kπ distribution is described well by our PDF,which implies there is no significant contribution from non-resonant π + π − γ or K + π − γ .We determine S and A from an UML fit to the observed ∆ t distribution. For each event,the following likelihood function is evaluated: P i =(1 − f ol ) Z + ∞−∞ d (∆ t ′ ) (cid:20)X j f j P j (∆ t ′ ) R j (∆ t i − ∆ t ′ ) (cid:21) + f ol P ol (∆ t i ) , (2)where j runs over four components ( B → ρ γ , B → K ∗ γ , other B ¯ B and q ¯ q ). The prob-ability of each component ( f j ) is calculated using the result of the M bc -∆ E - M Kπ fit on anevent-by-event basis. We also incorporate the flavor tagging quality r distribution. The r distributions for K ∗ γ and q ¯ q are obtained by repeating the M bc -∆ E - M Kπ fit procedure tothe signal sample and also to the control sample for each r interval with yield parametersfloated. We found consistent distributions for the signal sample and the control sample.The r distribution for ρ γ is expected to be consistent with K ∗ γ , since the flavor is deter-mined only by the tag side; this is confirmed by MC. The distribution of B ¯ B background isestimated from MC.The PDF expected for the ρ γ distribution, P ρ γ , is given by the time-dependent decayrate [Eq. (1)], modified to incorporate the effect of incorrect flavor assignment; the param-eters τ B and ∆ m d are fixed to their world-average values [17]. The distribution is then6 t (ps) E v en t s / ( . p s ) q= + − ∆ t (ps) R a w a sy mm e t r y / ( . p s ) -1-0.75-0.5-0.2500.250.50.751-7.5 -5 -2.5 0 2.5 5 7.5 FIG. 3: (Left) ∆ t distributions for B → ρ γ for q = +1 (light solid) and q = − . < r ≤ .
0. The thin curve is the fit projection while the thick curve shows the signalcomponent. Points with error bars are data. (Right) Raw asymmetry in each ∆ t bin with 0 . 0. The solid curve shows the result of the UML fit. convolved with the proper-time interval resolution function R ρ γ , which takes into accountthe finite vertex resolution. The parameterization of R ρ γ is the same as the one used in the B → φK [18] analysis. The same functional forms for the PDF and resolution are used forthe K ∗ γ and other B ¯ B components, but with separate lifetime and CP -violating param-eters. We assume no CP asymmetry in K ∗ γ and other B ¯ B background events; possibledeviations from this assumption are taken into account in the systematic error. The lifetimeof B → K ∗ γ is the same as B → ρ γ . The effective lifetime of B ¯ B background is obtainedfrom a fit to the MC sample; the result is 1 . ± . 06 ps. The PDF for q ¯ q background events, P q ¯ q , is modeled as a sum of exponential and delta function components, and is convolvedwith a double Gaussian which represents the resolution function R q ¯ q . All parameters in P q ¯ q and R q ¯ q are determined by a fit to the ∆ t distribution in the ∆ E - M bc sideband region(∆ E > . M bc − . < (∆ E − . 2) with ∆ E in GeV and M bc in GeV /c ). P ol is aGaussian function that represents a small outlier component with fraction f ol [19].The only free parameters in the CP fit to B → ρ γ are S ρ γ and A ρ γ , which aredetermined by maximizing the likelihood function L = Q i P i (∆ t i ; S , A ), where the productis over all events. We obtain S ρ γ = − . ± . ± . , and (3) A ρ γ = − . ± . ± . , (4)where the systematic errors are obtained as discussed below.We define the raw asymmetry in each ∆ t bin by ( N q =+1 − N q = − ) / ( N q =+1 + N q = − ), where N q =+1 ( − is the number of observed candidates with q = +1 ( − t distributions and the raw asymmetry for events with 0 . < r ≤ . → K ∗ γ control sample, the K ∗ γ component in the B → ρ γ sample and the ρ γ candidates gives 1 . ± . 04 ps, 1 . ± . 16 ps and 1 . +0 . − . ps, respectively. These resultsare all consistent with the nominal B lifetime (1 . ± . 009 ps [17]). A CP asymme-try fit for the control sample gives an asymmetry consistent with zero ( S = +0 . ± . A = − . ± . CP asymmetry fit to the K ∗ γ component in the B → ρ γ samplealso gives a consistent result ( S = +0 . ± . A = − . ± . σ error. The largest contribution to the systematic erroris from the uncertainty in the probability of each component ( f j ), because of the limitedstatistics; we find an uncertainty of 0.16 on S and 0.09 on A . The CP asymmetry in K ∗ γ has a direct impact on the measurement. Based on the fit result from the control sample,we vary A K ∗ γ from zero up to ± . 05, and find an error of 0.04 on A . The CP asymmetryin other B ¯ B backgrounds has less impact on the measurement. This asymmetry is variedby the weighted average of possible maximum CP asymmetries ( ± S , 0.09 on A ); we find an error of 0.01 or less on both S and A . The uncertainty from the resolution function parameters is 0.06 on S and 0.07 on A . In addition to the above mentioned categories, we also take the following small sourcesof uncertainty into account: the uncertainty in the vertex reconstruction and flavor tagging,uncertainty due to the tag-side interference effect [20], uncertainty in the knowledge of the q ¯ q background ∆ t PDF, uncertainty in the physics parameters such as ∆ m d , τ B , possibleeffect of correlations between M bc , ∆ E and M Kπ and other possible biases. Adding thesecontributions in quadrature, we obtain a systematic error of 0.18 on S and 0.14 on A .In summary, we have measured the time-dependent CP asymmetry in the decay B → ρ γ using a sample of 657 × B ¯ B pairs. We obtain CP -violation parameters S ρ γ = − . ± . ± . A ρ γ = − . ± . ± . CP asymmetry and therefore no in-dication of NP is found. This is the first measurement of CP asymmetry parameters in a b → dγ process.We thank the KEKB group for excellent operation of the accelerator, the KEK cryogenicsgroup for efficient solenoid operations, and the KEK computer group and the NII for valuablecomputing and Super-SINET network support. We acknowledge support from MEXT andJSPS (Japan); ARC and DEST (Australia); NSFC and KIP of CAS (China); DST (India);MOEHRD, KOSEF and KRF (Korea); KBN (Poland); MES and RFAAE (Russia); ARRS(Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE (USA). REFERENCES [1] D. Atwood, M. Gronau and A. Soni, Phys. Rev. Lett. , 185 (1997);[2] P. Ball, G. W. Jones and R. Zwicky, Phys. Rev. D , 054004 (2007).[3] Belle Collaboration, Y. Ushiroda et al. , Phys. Rev. D , 111104 (2006).[4] BaBar Collaboration, B. Aubert et al. , Phys. Rev. D , 051103 (2005).[5] Belle Collaboration, D. Mohapatra et al. , Phys. Rev. Lett. , 221601 (2006).[6] BaBar Collaboration, B. Aubert et al. , Phys. Rev. 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