# Evidence for CP Violation in the Decay $D^+\rightarrow K^0_Sπ^+$

## Abstract

We observe evidence for violation in the decay using a data sample with an integrated luminosity of 977 fb collected by the Belle detector at the KEKB asymmetric-energy collider. The asymmetry in the decay is measured to be , which is 3.2 standard deviations away from zero, and is consistent with the expected violation due to the neutral kaon in the final state.

###### pacs:

11.30.Er, 13.25.Ft, 14.40.LbThe Belle Collaboration

In the standard model (SM), violation of the combined charge-conjugation and parity symmetries arises from a nonvanishing irreducible phase in the Cabibbo-Kobayashi-Maskawa flavor-mixing matrix (1). In the SM, violation in the charm sector is expected to be very small, or below (2). Since the discovery of the (3) and the subsequent discovery of open charm particles (4), violation in charmed particle decays has been searched for extensively and only recently became experimentally accessible. To date, after the FOCUS (5), CLEO (6), Belle (7), and BaBar (8) measurements, the world average of the asymmetry in the decay (9) is , which is the first evidence of violation in charmed particles. However, it should be noted that the observed asymmetry is consistent with that expected due to the neutral kaon in the final state and is not ascribed to the charm sector. Recently, LHCb reported , where is the asymmetry difference between and decays (10). This is the first evidence of non-zero in charmed particle decays from a single experiment.

In this Letter we report the first evidence for violation in charmed meson decays from a single experiment and in a single decay mode, , where decays to . The asymmetry in the decay, , is defined as

(1) | |||||

where is the partial decay width, and and (11) denote asymmetries in the charm decay () and in mixing in the SM (13); (12), respectively. The observed final state is a coherent sum of amplitudes for and decays where the former is Cabibbo-favored (CF) and the latter is doubly Cabibbo-suppressed (DCS). In the absence of direct violation in CF and DCS decays (as expected within the SM), the asymmetry in decay within the SM is , which is measured to be % (14) from semileptonic decays (15). On the other hand, if processes beyond the SM contain additional weak phases other than the one in the Kobayashi-Maskawa ansatz (1), interference between CF and DCS decays could generate an direct asymmetry in the decay (13). Thus, observation of inconsistent with in decay would be strong evidence for processes involving new physics (13); (16).

We determine by measuring the asymmetry in the signal yield

(2) |

where is the number of reconstructed decays. The asymmetry in Eq. (2) includes the forward-backward asymmetry () due to - interference and higher order QED effects in (17), and the detection efficiency asymmetry between and () as well as . In addition, Ref. (18) calculated another source denoted due to the differences in interactions of and mesons with the material of the detector. (The existence of this effect was pointed out in Ref. (7).) Since we reconstruct the with combinations, the detection asymmetry cancels out for . The asymmetry of Eq. (2) can be written as

(3) | |||||

by neglecting the terms involving the product of asymmetries. In Eq. (3), is independent of all kinematic variables other than decay time due to the in the final state (19), is an odd function of the cosine of the polar angle of the momentum in the center-of-mass system (CMS), depends on the transverse momentum and the polar angle of the in the laboratory frame (lab), and is a function of the momentum of the in the lab. To correct for in Eq. (3), we use and decays, and assume the same for and mesons. Since these are CF decays for which the direct asymmetry is expected to be negligible, in analogy to Eq. (3), and include , , and . Thus with the additional term in , one can measure by subtracting from . We obtain according to Ref. (18). Using shown in Eq. (4), which is after the and corrections,

(4) |

we extract and using

(5a) | |||||

(5b) | |||||

Note that extracting in Eq. (4) is crucial in Belle due to the asymmetric detector acceptance in .

The data used in this analysis were recorded at the resonances or near the resonance with the Belle detector (20) at the asymmetric-energy collider KEKB (21). The data sample corresponds to an integrated luminosity of 977 fb.

We apply the same charged track selection criteria that were used in Ref. (22) without requiring associated hits in the silicon vertex detector (23). We use the standard Belle charged kaon and pion identification (22). We form candidates from pairs, fitted to a common vertex and requiring the invariant mass of the pair to be within GeV/, regardless of whether the candidate satisfies the standard requirements (22). (We refer to the candidates not satisfying the standard criteria as “loose ”.) The and candidates are combined to form a candidate by fitting them to a common vertex and the candidate is fitted to the interaction point to give the production vertex. To remove combinatorial background as well as mesons, which are produced in possibly violating meson decays, we require the meson momentum calculated in the CMS () to be greater than 2.5 and 3.0 GeV/ for the data taken at the and resonances, respectively. For the data taken below , which is free of mesons, we apply the requirement 2.0 GeV/. In addition to the selections described above, we further optimize the signal sensitivity with four variables: the of the decay and production vertex fits ( and ), the transverse momentum of the (), and the angle between the momentum vector, as reconstructed from the daughters, and the vector joining the production and decay vertices () (24). An optimization is performed by maximizing with the four variables varied simultaneously (25), 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, 0.50 GeV/, 160), (100, 10, 0.45 GeV/, 170), and (100, 10, 0.40 GeV/, no requirement) for the data taken below the , at the , and at the , respectively. The candidates with the loose requirement are further optimized with two additional variables which are the of the fit of pions from the decay and the pion from the meson decay to a single vertex (), and the angle between the momentum vector, as reconstructed from the 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 4 for all data. The inclusion of candidates with the loose requirement improves the statistical sensitivity by approximately 5%. After the final selections described above, there remains a background with a broad peaking structure in the invariant mass signal region, due to misidentification of charged kaons from decays. The background is found to be negligible from simulation (26). Figure 1 shows the distributions of and together with the results of the fits described below.

The signals are parameterized as a sum of a Gaussian and a bifurcated Gaussian distribution with a common mean. The combinatorial background is parameterized with the form , where and are free parameters. The shapes and normalizations of the misidentification backgrounds are obtained with taking the asymmetry in into account as described in Refs. (22); (7). Both the shapes and the normalizations of the misidentification backgrounds are fixed in the fit. 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 total signal yield, the common parameters in the simultaneous fit are the widths of the Gaussian and the bifurcated Gaussian and the ratio of their amplitudes. The asymmetry and the sum of the and yields from the fit are and (17382), respectively, where the errors are statistical.

To obtain we first extract from a simultaneous fit with the same parameterizations for the signal except for the misidentification background. The values of are evaluated in 44444 bins of the five-dimensional (5D) phase space (, , , , ). Each candidate is then weighted with a factor of in the corresponding bin of the 5D phase space, where the phase space of the with lower in decay is used. After this weighting, the asymmetry in decay sample becomes , where refers to the with higher in the decay. The detector asymmetry, , is measured from simultaneous fits to the weighted distributions in 1010 bins of the 2D phase space (, ) with the same parameterization used in decays. Figure 2 shows the measured in bins of and together with for comparison. The average of over phase space is , where the error is statistical.

Based on a recent study of the (18), we obtain the asymmetry in bins of momentum in the lab. For the present analysis, is approximately 0.1% after integrating over the phase space of the two-body decay (18).

The data samples shown in Fig. 1 are divided into 101016 bins of the 3D phase space (, , ). Each candidate is then weighted with a factor of in the 3D phase space. The weighted distributions in bins of are fitted simultaneously to obtain the corrected asymmetry. We fit the linear component in to determine while the component is uniform in . Figure 3 shows and as a function of . From a weighted average over the bins, we obtain , where the error is statistical. Without the correction as in previous publications (5); (6); (7); (8), the value of is .

The method is validated with fully simulated Monte Carlo events (26) and the result is consistent with no 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 0.040% and 0.048%, respectively, from a simplified simulation study. A possible in the final state is estimated with the relation, (27). Using the 95% upper and lower limits on mixing and violation parameters (28), in the final state is estimated to be less than 0.014% and this is included as one of systematic uncertainties in the determination. By adding the contributions in quadrature, the systematic uncertainty in the determination is estimated to be 0.064%. We estimate 0.003% and 0.008% 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 0.016% based on Ref. (18). The quadratic sum of the above uncertainties, 0.067%, is taken as the total systematic uncertainty.

We find . This measurement supersedes our previous determination of (7). In Table 1, we compare all the available measurements and give the new world average.

Experiment | (%) |
---|---|

FOCUS (5) | 1.61.50.9 |

CLEO (6) | 1.30.70.3 |

BaBar (8) | 0.440.130.10 |

Belle (this measurement) | 0.3630.0940.067 |

New world average | 0.410.09 |

According to Grossman and Nir (19), we can estimate the experimentally measured asymmetry induced by SM mixing, , assuming negligible DCS decay in the final state . By multiplying by the correction factor due to the acceptance effects as a function of decay time in our detector, we find the the measured asymmetry due to the neutral kaons to be .

In summary, we report evidence for violation in 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 , which represents the first evidence for violation in charmed meson decays from a single experiment and a single decay mode. After subtracting the contribution due to mixing (), the asymmetry due to the change of charm () is consistent with zero, . The measurement in the decay is the most precise measurement of in charm decays to date and can be used to place stringent constraints on new physics models in the charm sector (13); (16).

We thank the KEKB group for excellent operation of the accelerator; the KEK cryogenics group for efficient solenoid operations; and the KEK computer group, the NII, and PNNL/EMSL for valuable computing and SINET4 network support. We acknowledge support from MEXT, JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR (Australia); NSFC (China); MSMT (Czechia); DST (India); INFN (Italy); MEST, NRF, GSDC of KISTI, and WCU (Korea); MNiSW (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE and NSF (USA). B. R. Ko acknowledges support by a Korea University Grant, NRF Grant No. 2011-0025750, and E. Won by NRF Grant No. 2011-0030865.

### References

- M. Kobayashi and T. Maskawa, Prog. Theor. Phys., 49, 652 (1973).
- F. Buccella et al., Phys. Rev. D 51, 3478 (1995); Y. Grossman, A. L. Kagan, and Y. Nir, Phys. Rev. D 75, 036008 (2007).
- J. J. Aubert et al., Phys. Rev. Lett. 33, 1404 (1974); J. E. Augustin et al., Phys. Rev. Lett. 33, 1406 (1974).
- G. Goldhaber et al., Phys. Rev. Lett. 37, 255 (1976); I. Peruzzi et al., Phys. Rev. Lett. 37, 569 (1976).
- J. M. Link et al. (FOCUS Collaboration), Phys. Rev. Lett. 88, 041602 (2002).
- H. Mendez et al. (CLEO Collaboration), Phys. Rev. D 81, 052103 (2010).
- B. R. Ko et al. (Belle Collaboration), Phys. Rev. Lett. 104, 181602 (2010).
- P. del Amo Sanchez et al. (BaBar Collaboration), Phys. Rev. D 83, 071103 (2011).
- Throughout this Letter the charge-conjugate decay modes are implied unless stated otherwise.
- R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 108, 111602 (2012).
- We use since is dominated by .
- Ya. I. Azimov and A. A. Iogansen, Sov. J. Nucl. Phys. 33, 205 (1981); Z.-Z. Xing, Phys. Lett. B 353, 313 (1995); 363, 266 (1995).
- I. I. Bigi and H. Yamamoto, Phys. Lett. B 349, 363 (1995).
- where is the symbol for the asymmetry used in Ref. (15).
- K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).
- H. J. Lipkin and Z.-Z. Xing, Phys. Lett. B 450, 405 (1999); G. D’Ambrosio and D.-N. Gao, Phys. Lett. B 513, 123 (2001).
- F. A. Berends, K. J. F. Gaemers, and R. Gastmans, Nucl. Phys. B 63, 381 (1973); R. W. Brown, K. O. Mikaelian, V. K. Cung, and E. A. Paschos, Phys. Lett. B 43, 403 (1973); R. J. Cashmore, C. M. Hawkes, B. W. Lynn, and R. G. Stuart, Z. Phys. C 30, 125 (1986).
- B. R. Ko, E. Won, B. Golob, and P. Pakhlov, Phys. Rev. D 84, 111501(R) (2011).
- Y. Grossman and Y. Nir, JHEP 2012, 2 (2012).
- A. Abashian et al. (Belle Collaboration), Nucl. Instr. and Meth. A 479, 117 (2002).
- S. Kurokawa and E. Kikutani, Nucl. Instr. and Meth. A 499, 1 (2003), and other papers included in this volume.
- E. Won et al. (Belle Collaboration), Phys. Rev. D 80, 111101(R) (2009).
- Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instr. and Meth. A 560, 1 (2006); Y. Ushiroda (Belle SVD2 Group), Nucl. Instr. and Meth. A 511, 6 (2003).
- B. R. Ko et al. (Belle Collaboration), Phys. Rev. Lett. 102, 221802 (2009).
- E. Won et al. (Belle Collaboration), Phys. Rev. Lett. 107, 221801 (2011).
- D. J. Lange, Nucl. Instrum. Meth. Phys. Res., Sect. A 462, 152 (2001); R. Brun et al. GEANT 3.21, CERN Report DD/EE/84-1, 1984.
- A. A. Petrov, Phys. Rev. D 69, 111901(R) (2004).
- D. Asner et al. (Heavy Flavor Averaging Group), arXiv:1010.1589v3␣[hep-ex] and online update at http://www.slac.stanford.edu/xorg/hfag/.