Search for CP Violation in the Decay $D^+\rightarrow K^0_S K^+$
Abstract
We search for violation in the decay using a data sample with an integrated luminosity of 977 fb collected with the Belle detector at the KEKB asymmetric-energy collider. No violation has been observed and the asymmetry in decay is measured to be , which is the most sensitive measurement to date. After subtracting violation due to mixing, the asymmetry in decay is found to be .
Belle Collaboration 21]B. R. Ko 21]E. Won 9]I. Adachi 51]H. Aihara 3]K. Arinstein 41]D. M. Asner 16]T. Aushev 45]A. M. Bakich 14]K. Belous 33]V. Bhardwaj 12]B. Bhuyan 3]A. Bondar 56]G. Bonvicini 37]A. Bozek 26,17]M. Bračko 8]T. E. Browder 27]V. Chekelian 34]A. Chen 36]P. Chen 7]B. G. Cheon 16]K. Chilikin 16]R. Chistov 20]K. Cho 6]S.-K. Choi 44]Y. Choi 56]D. Cinabro 27,47]J. Dalseno 4]Z. Doležal 12]D. Dutta 3]S. Eidelman 5]S. Esen 56]H. Farhat 41]J. E. Fast 46]V. Gaur 3]N. Gabyshev 56]S. Ganguly 56]R. Gillard 7]Y. M. Goh 24,17]B. Golob 32]K. Hayasaka 33]H. Hayashii 49]Y. Hoshi 36]W.-S. Hou 22]H. J. Hyun 32,31]T. Iijima 50]A. Ishikawa 9]Y. Iwasaki 28]T. Julius 58]J. H. Kang 50]E. Kato 27]C. Kiesling 22]H. O. Kim 21]J. B. Kim 21]K. T. Kim 22]M. J. Kim 20]Y. J. Kim 5]K. Kinoshita 17]J. Klucar 26,17]S. Korpar 41]R. T. Kouzes 24,17]P. Križan 3]P. Krokovny 19]T. Kuhr 53]T. Kumita 3]A. Kuzmin 58]Y.-J. Kwon 55]Y. Li 43]C. Liu 9]D. Liventsev 23]R. Louvot 33]K. Miyabayashi 39]H. Miyata 16,29]R. Mizuk 46]G. B. Mohanty 27,47]A. Moll 42]N. Muramatsu 10]Y. Nagasaka 40]E. Nakano 9]M. Nakao 27]E. Nedelkovska 51]C. Ng 46]N. Nellikunnummel 9]S. Nishida 8]K. Nishimura 54]O. Nitoh 48]S. Ogawa 31]T. Ohshima 18]S. Okuno 2]C. Oswald 16,29]P. Pakhlov 16]G. Pakhlova 22]H. Park 22]H. K. Park 25]T. K. Pedlar 17]R. Pestotnik 17]M. Petrič 55]L. E. Piilonen 27,47]K. Prothmann 27]M. Ritter 19]M. Röhrken 8]H. Sahoo 50]T. Saito 9]Y. Sakai 46]S. Sandilya 17]L. Santelj 50]T. Sanuki 50]Y. Sato 23]O. Schneider 1,11]G. Schnell 15]C. Schwanda 5]A. J. Schwartz 57]K. Senyo 31]O. Seon 28]M. E. Sevior 14]M. Shapkin 31]C. P. Shen 52]T.-A. Shibata 36]J.-G. Shiu 45]A. Sibidanov 27,47]F. Simon 17]P. Smerkol 58]Y.-S. Sohn 16]E. Solovieva 17]M. Starič 53]T. Sumiyoshi 41]G. Tatishvili 40]Y. Teramoto 9]K. Trabelsi 9]T. Tsuboyama 52]M. Uchida 16,30]T. Uglov 7]Y. Unno 9]S. Uno 1]C. Van Hulse 27]P. Vanhoefer 8]G. Varner 35]C. H. Wang 36]M.-Z. Wang 13]P. Wang 18]Y. Watanabe 55]K. M. Williams 38]Y. Yamashita 13]C. C. Zhang 3]V. Zhilich 19]A. Zupanc \affiliation[1]University of the Basque Country UPV/EHU, 48080 Bilbao, Spain \affiliation[2]University of Bonn, 53115 Bonn, Germany \affiliation[3]Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630090, Russian Federation \affiliation[4]Faculty of Mathematics and Physics, Charles University, 121 16 Prague, The Czech Republic \affiliation[5]University of Cincinnati, Cincinnati, OH 45221, USA \affiliation[6]Gyeongsang National University, Chinju 660-701, South Korea \affiliation[7]Hanyang University, Seoul 133-791, South Korea \affiliation[8]University of Hawaii, Honolulu, HI 96822, USA \affiliation[9]High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan \affiliation[10]Hiroshima Institute of Technology, Hiroshima 731-5193, Japan \affiliation[11]Ikerbasque, 48011 Bilbao, Spain \affiliation[12]Indian Institute of Technology Guwahati, Assam 781039, India \affiliation[13]Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, PR China \affiliation[14]Institute for High Energy Physics, Protvino 142281, Russian Federation \affiliation[15]Institute of High Energy Physics, Vienna 1050, Austria \affiliation[16]Institute for Theoretical and Experimental Physics, Moscow 117218, Russian Federation \affiliation[17]J. Stefan Institute, 1000 Ljubljana, Slovenia \affiliation[18]Kanagawa University, Yokohama 221-8686, Japan \affiliation[19]Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany \affiliation[20]Korea Institute of Science and Technology Information, Daejeon 305-806, South Korea \affiliation[21]Korea University, Seoul 136-713, South Korea \affiliation[22]Kyungpook National University, Daegu 702-701, South Korea \affiliation[23]École Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland \affiliation[24]Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia \affiliation[25]Luther College, Decorah, IA 52101, USA \affiliation[26]University of Maribor, 2000 Maribor, Slovenia \affiliation[27]Max-Planck-Institut für Physik, 80805 München, Germany \affiliation[28]School of Physics, University of Melbourne, Victoria 3010, Australia \affiliation[29]Moscow Physical Engineering Institute, Moscow 115409, Russian Federation \affiliation[30]Moscow Institute of Physics and Technology, Moscow Region 141700, Russian Federation \affiliation[31]Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan \affiliation[32]Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan \affiliation[33]Nara Women’s University, Nara 630-8506, Japan \affiliation[34]National Central University, Chung-li 32054, Taiwan \affiliation[35]National United University, Miao Li 36003, Taiwan \affiliation[36]Department of Physics, National Taiwan University, Taipei 10617, Taiwan \affiliation[37]H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland \affiliation[38]Nippon Dental University, Niigata 951-8580, Japan \affiliation[39]Niigata University, Niigata 950-2181, Japan \affiliation[40]Osaka City University, Osaka 558-8585, Japan \affiliation[41]Pacific Northwest National Laboratory, Richland, WA 99352, USA \affiliation[42]Research Center for Electron Photon Science, Tohoku University, Sendai 980-8578, Japan \affiliation[43]University of Science and Technology of China, Hefei 230026, PR China \affiliation[44]Sungkyunkwan University, Suwon 440-746, South Korea \affiliation[45]School of Physics, University of Sydney, NSW 2006, Australia \affiliation[46]Tata Institute of Fundamental Research, Mumbai 400005, India \affiliation[47]Excellence Cluster Universe, Technische Universität München, 85748 Garching, Germany \affiliation[48]Toho University, Funabashi 274-8510, Japan \affiliation[49]Tohoku Gakuin University, Tagajo 985-8537, Japan \affiliation[50]Tohoku University, Sendai 980-8578, Japan \affiliation[51]Department of Physics, University of Tokyo, Tokyo 113-0033, Japan \affiliation[52]Tokyo Institute of Technology, Tokyo 152-8550, Japan \affiliation[53]Tokyo Metropolitan University, Tokyo 192-0397, Japan \affiliation[54]Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan \affiliation[55]CNP, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA \affiliation[56]Wayne State University, Detroit, MI 48202, USA \affiliation[57]Yamagata University, Yamagata 990-8560, Japan \affiliation[58]Yonsei University, Seoul 120-749, South Korea
1 Introduction
Studies of violation in charmed meson decays provide a promising
opportunity to search for new physics beyond the standard model
(SM) [1] in the absence of disagreement between experimental
measurements and the SM interpretation of violation in and
meson decays [2, 3, 4].
Recently, the LHCb collaboration has reported [5] where is the asymmetry difference between
(1) |
where and denote direct and indirect violation, respectively, and is the mean proper decay time of the selected signal sample in units of the lifetime [9]. The factor in eq. (1) depends on the experimental conditions and the largest value reported to date is from the CDF measurement [6]. Therefore, reveals a significant direct violation difference between the two decays. Within the SM, direct violation in the charm sector is expected to be present only in singly Cabibbo-suppressed (SCS) decays, and even there is expected to be small, [10]. Hence, the current measurements engender questions of whether the origin of the asymmetry lies within [11, 12, 13, 14] or beyond [15, 16, 17, 18] the SM. The origin of calls for the precise measurements of in and . A complementary test is a precise measurement of in another SCS charmed hadron decay, , as suggested in ref. [13].
As shown in figures 1(a) and 1(b),
the decay shares the same decay diagrams
with by exchanging the spectator quarks,
. Although there are additional contributions to
the two decays as shown in figures 1(c)
and 1(d), these are expected to be small due to
helicity- and color-suppression considerations
In this paper, we report results from a search for violation in the decay that originates from decay, where decays to . The asymmetry in the decay, , is then defined as
(2) | |||||
where is the partial decay width. In eq. (2), is the asymmetry in the decay and is that in decay induced by mixing in the SM [19, 20, 21] in which the decay arises from together with a small contribution from , where the latter is known precisely from semileptonic decays, % [2]. As shown in eq. (2), the product of the two small asymmetries is neglected. The decaying to the final state proceeds from decay, which is SCS. In the SM, direct violation in SCS charmed meson decays is predicted to occur with a non-vanishing phase that enters the diagram shown in figure 1(b) in the Kobayashi-Maskawa ansatz [22]. The current average of favors a negative value of direct violation in decay. Correspondingly, the asymmetry in decays is more likely to have a negative value since the two asymmetry terms shown in eq. (2) are negative.
2 Methodology
We determine by measuring the asymmetry in the signal yield
(3) |
where is the number of reconstructed decays. The asymmetry in eq. (3) includes the forward-backward asymmetry () due to - interference and higher order QED effects in [23, 24, 25], and the detection efficiency asymmetry between and () as well as . In addition, ref. [26] calculates another asymmetry source, denoted , due to the differences in interactions of and mesons with the material of the detector. Since we reconstruct the with combinations, the detection asymmetry cancels out for . The asymmetry of eq. (3) can be written as
(4) | |||||
by neglecting the terms involving the product of asymmetries. In eq. (4), is the sum of and as stated in eq. (2), where the former is independent of all kinematic variables while the latter is known to depend on the decay time according to ref. [27], and is an odd function of the cosine of the polar angle of the momentum in the center-of-mass system (c.m.s.). depends on the transverse momentum and the polar angle of the in the laboratory frame (lab). Here, is a function of the lab momentum of the . To correct for in eq. (4), we use the technique developed in our previous publication [28]. We use and decays where the is reconstructed with combinations and hence the detection asymmetry nearly cancels out [29] (the residual small effect is included in the systematic error). Since these are Cabibbo-favored decays for which the direct asymmetry is expected to be negligible, in analogy to eq. (4), and can be written as
(5) | |||||
(6) | |||||
Thus, with the additional term in
, one can measure
by subtracting
from , assuming the same for and
mesons. We also obtain according to
ref. [26]. After these and
corrections
(7) |
We subsequently extract and as a function of by taking sums and differences: {subequations}
(8) |
(9) |
Note that extracting in eq. (7) using eq. (8) is crucial here to cancel out the Belle detector’s asymmetric acceptance in .
3 Data and event selections
The data used in this analysis were recorded at the resonances or near the resonance with the Belle detector at the asymmetric-energy collider KEKB [30]. The data sample corresponds to an integrated luminosity of 977 fb. The Belle detector is a large solid angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprising CsI(Tl) crystals located inside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux return located outside the coil is instrumented to detect mesons and to identify muons. A detailed description of the Belle detector can be found in ref. [31].
Except for the tracks from decays we require charged tracks to originate from the vicinity of the interaction point (IP) by limiting the impact parameters along the beam direction (-axis) and perpendicular to it to less than 4 cm and 2 cm, respectively. All charged tracks other than those from decays are identified as pions or kaons by requiring the ratio of particle identification likelihoods, , constructed using information from the CDC, TOF, and ACC, to be larger or smaller than 0.6, respectively [32]. For both kaons and pions, the efficiencies and misidentification probabilities are about 90% and 5%, respectively.
We form candidates adopting the standard Belle criteria [33], requiring the invariant mass of the charged track pair to be within GeV/. The “loose” candidates not satisfying these standard selections are also used in this analysis with additional requirements described later.
The and candidates are combined to form a candidate by fitting their tracks to a common vertex; the candidate is fitted to the independently measured IP profile to give the production vertex. To remove combinatorial background as well as mesons that are produced in possibly -violating meson decays, we require the meson momentum calculated in the c.m.s. () to be greater than 2.5 and 3.0 GeV/ for the data taken at the and resonances, respectively. For the data taken below , where no mesons are produced, we apply the requirement 2.0 GeV/. In addition to the selections described above, we further optimize the signal sensitivity with four variables: the goodness-of-fit values of the decay- and production-vertex fits and , the transverse momentum of the in the lab , and the angle between the momentum vector (as reconstructed from its daughters) and the vector joining the production and decay vertices. We optimize the requirement on these four variables with the standard and loose selections by maximizing , where and are the yields in the invariant mass signal ( GeV/) and sideband ( and GeV/) regions, respectively. The optimal set of (, , , ) requirements are found to be (100, 10, 0.30 GeV/, 40), (100, 10, 0.25 GeV/, 115), and (100, 10, 0.20 GeV/, 125) for the data taken below the , at the , and at the , respectively. Note that is highly correlated with and ; hence, a tighter requirement on the sample results in looser and requirements and vice versa for the data taken below the . The candidates with the loose requirement are further optimized with two additional variables: the of the fit of tracks from the decay and the kaon from the meson decay to a single vertex () and the angle between the momentum vector (as reconstructed from its daughters) and the vector joining the and decay vertices. The two variables are again varied simultaneously and the optimum is found to be 6 and 3 for all data. The inclusion of candidates with the loose requirement improves the statistical sensitivity by approximately 5%. After the final selections described above, we find no significant peaking backgrounds—for example, decays—in the Monte Carlo (MC) simulated events [34]. Figure 2 shows the distributions of and together with the results of the fits described below.
Each signal is parameterized as two Gaussian distributions with a common mean. The combinatorial background is parameterized with the unnormalized form , where and are fit parameters. The asymmetry and the sum of the and yields are directly obtained from a simultaneous fit to the and candidate distributions. Besides the asymmetry and the sum of the and yields, the common parameters in the simultaneous fit are the widths of the two Gaussians and the ratio of their amplitudes. The asymmetry and the sum of the and yields from the fit are and , respectively, where the errors are statistical.
In order to measure the asymmetry in decays, we must also reconstruct and decays: see eqs. (4), (5), and (6). For the reconstruction of the and decays, we require the same track quality, particle identification, vertex fit quality, and requirements as used for the reconstruction of the decays, where the mass window for the is 16 MeV/ [29] of the nominal mass [2].
4 Extraction of in the decay
To obtain , we first extract from a simultaneous fit to the mass distributions of and candidates with similar parameterizations as for decays except that, for the signal description, a single Gaussian is used. The values of are evaluated in 101010 bins of the three-dimensional (3D) phase space (, , ). Each and candidate is then weighted with a factor of and , respectively, in the corresponding bin of this space. After this weighting, the asymmetry in the decay sample becomes . The detector asymmetry, , is measured from simultaneous fits to the weighted distributions in 1010 bins of the 2D phase space (, ) with similar parameterizations as used for decays except that, for the signal description, a sum of a Gaussian and bifurcated Gaussian is used. Figure 3 shows the measured in bins of and together with for comparison; we observe that shows a dependency that is inherited from while does not. The average of over the phase space is , where the error is due to the limited statistics of the sample.
Based on a recent study of [26], we obtain the dilution asymmetry in bins of lab momentum. For the present analysis, is approximately 0.1% after integrating over the phase space of the two-body decay.
The data samples shown in figure 2 are divided into 101016 bins of the 3D phase space (, , ). Each candidate is then weighted with a factor of in this space. The weighted distributions in bins of are fitted simultaneously to obtain the corrected asymmetry. We fit the linear component in to determine ; the component is uniform in . Figure 4 shows and as a function of . From a weighted average over the bins, we obtain , where the error is statistical.
5 Systematic uncertainty
The entire analysis procedure is validated with fully simulated MC events [34] and the result is consistent with null input asymmetry. We also consider other sources of systematic uncertainty. The dominant one in the measurement is the determination, the uncertainty of which is mainly due to the statistical uncertainties in the and samples. These are found to be 0.029% and 0.119%, respectively, from a simplified simulation study. A possible in the final state is estimated using [35]. A calculation with 95% upper and lower limits on mixing and violation parameters , , and strong phase difference and Cabibbo suppression factor from ref. [3], in the final state is estimated to be less than 0.005% and this is included as one of systematic uncertainties in the determination. As reported in our previous publication [29], the magnitude of for the reconstruction in decays is 0.051%, which is also added to the systematic uncertainty in the measurement. By adding the contributions in quadrature, the systematic uncertainty in the determination is estimated to be 0.133%. We estimate 0.008% and 0.021% systematic uncertainties due to the choice of the fitting method and that of the binning, respectively. Finally, we add the systematic uncertainty in the correction, which is 0.010% based on ref. [26]. The quadratic sum of the above uncertainties, 0.135%, is taken as the total systematic uncertainty.
6 Results
We find . This measurement supersedes our previous determination of [28]. In Table 1, we compare all the available measurements and give their weighted average.
According to Grossman and Nir [27], we can estimate the experimentally measured asymmetry induced by SM mixing, . The efficiency as a function of decay time in our detector is obtained from MC simulated events. The efficiency is then used in eq. (2.10) of ref. [27] to obtain the correction factor that takes into account, for , the dependence on the kaon decay time. The result is . By multiplying the correction factor and the asymmetry due to the neutral kaons [2], we find the experimentally measured to be .
Experiment | (%) |
---|---|
FOCUS [36] | |
CLEO [37] | |
Belle (this measurement) | |
New world average |
7 Conclusion
We report the most sensitive asymmetry measurement to date for the decay using a data sample corresponding to an integrated luminosity of 977 fb collected with the Belle detector. The asymmetry in the decay is measured to be . After subtracting the contribution due to mixing (), the asymmetry in the charm decay () is measured to be , which can be compared with direct violation in . For the latter the current averages of and asymmetry in favor a negative value [3]. Our result, on the other hand, does not show this tendency for decays, albeit with a significant statistical uncertainty. \acknowledgmentsWe thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, the National Institute of Informatics, and the PNNL/EMSL computing group for valuable computing and SINET4 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council and the Australian Department of Industry, Innovation, Science and Research; the National Natural Science Foundation of China under contract No. 10575109, 10775142, 10875115 and 10825524; the Ministry of Education, Youth and Sports of the Czech Republic under contract No. LA10033 and MSM0021620859; the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; the BK21 and WCU program of the Ministry Education Science and Technology, National Research Foundation of Korea Grant No. 2011-0029457, 2012-0008143, 2012R1A1A2008330, BRL program under NRF Grant No. KRF-2011-0020333, and GSDC of the Korea Institute of Science and Technology Information; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Education and Science of the Russian Federation and the Russian Federal Agency for Atomic Energy; the Slovenian Research Agency; the Swiss National Science Foundation; the National Science Council and the Ministry of Education of Taiwan; and the U.S. Department of Energy and the National Science Foundation. This work is supported by a Grant-in-Aid from MEXT for Science Research in a Priority Area (“New Development of Flavor Physics”), and from JSPS for Creative Scientific Research (“Evolution of Tau-lepton Physics”). B. R. Ko acknowledges support by NRF Grant No. 2012-0007319, and E. Won by NRF Grant No. 2010-0021174.
Footnotes
- Throughout this paper, the charge-conjugate decay modes are implied unless stated otherwise.
- In helicity suppression, a spinless meson decaying to a back-to-back quark-antiquark pair is suppressed by the conservation of angular momentum. In color suppression, the final state quarks are required to carry the correct color charge in order for the final state to be colorless.
- We define . Hence .
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