# Observation of and search for violation in radiative charm decays

###### Abstract

We report the first observation of the radiative charm decay and the first search for violation in decays , , and , using a data sample of collected with the Belle detector at the KEKB asymmetric-energy collider. The branching fraction is measured to be , where the first uncertainty is statistical and the second is systematic. The obtained asymmetries, , , and , are consistent with no violation. We also present an improved measurement of the branching fractions and .

###### pacs:

11.30.Er, 13.20.Fc, 13.25.Ft^{†}

^{†}preprint: Belle Preprint 2016-11 KEK Preprint 2016-24

The Belle Collaboration

Within the Standard Model (SM), charge-parity () violation in weak decays of hadrons arises due to a single irreducible phase in the Cabibbo-Kobayashi-Maskawa matrix Kobayashi and Maskawa (1973) and is expected to be very small for charmed hadrons: up to a few Bigi et al. (2011); Isidori et al. (2012); Brod et al. (2012). Observation of violation above the SM expectation would be an indication of new physics. This phenomenon in the charm sector has been extensively probed in the past decade in many different decays Amhis et al. (2014), reaching a sensitivity below 0.1% in some cases Aaij et al. (2016). The search for violation in radiative charm decays is complementary to the searches that have been exclusively performed in hadronic or leptonic decays. Theoretical calculations Isidori and Kamenik (2012); Lyon and Zwicky (2012) show that, in SM extensions with chromomagnetic dipole operators, sizable asymmetries can be expected in and decays. No experimental results exist to date regarding violation in any of the radiative decays.

Radiative charm decays are dominated by long-range non-perturbative processes that can enhance the branching fractions up to , whereas short-range interactions are predicted to yield rates at the level of Burdman et al. (1995); Fajfer (2015). Measurements of branching fractions of these decays can therefore be used to test the QCD-based calculations of long-distance dynamics. The radiative decay was first observed by Belle Tajima et al. (2004) and later measured with increased precision by BABAR Aubert et al. (2008). In the same study, BABAR made the observation of . As for , CLEO II has set an upper limit on its branching fraction at Asner et al. (1998).

In this Letter, we present the first observation of , improved branching fraction measurements of and , as well as the first search for violation in all three decays. Inclusion of charge-conjugate modes is implied unless noted otherwise. The measurements are based on of data collected at or near the resonances () with the Belle detector Abashian et al. (2002); Brodzicka et al. (2012), operating at the KEKB asymmetric-energy collider Kurokawa and Kikutani (2003); Abe et al. (2013). The detector components relevant for our study are: a tracking system comprising a silicon vertex detector and a 50-layer central drift chamber (CDC), a particle identification (PID) system that consists of a barrel-like arrangement of time-of-flight scintillation counters (TOF) and an array of aerogel threshold Cherenkov counters (ACC), and a CsI(Tl) crystal-based electromagnetic calorimeter (ECL). All are located inside a superconducting solenoid coil that provides a 1.5 T magnetic field.

We use Monte Carlo (MC) events, generated using EVTGEN Lange (2001), JETSET Sjostrand (1994) and PHOTOS Golonka and Was (2006), followed with a GEANT3 Brun et al. (1987) based detector simulation, representing six times the data luminosity, to devise selection criteria and investigate possible sources of background. The selection optimization is performed by maximizing , where () is the number of signal (background) events in a signal window of the reconstructed invariant mass . The branching fraction of is set to in simulations in accordance with Ref. Isidori and Kamenik (2012), while the branching fractions of the other two decay modes are set to their world-average values Olive et al. (2014).

We reconstruct mesons by combining a , , or a with a photon. The vector resonances are formed from (), (), and () combinations. Charged particles are reconstructed in the tracking system. A likelihood ratio for a given track to be a kaon or pion is obtained by utilizing specific ionization in the CDC, light yield from the ACC, and information from the TOF. Photons are detected with the ECL and required to have energies of at least 540 MeV. To suppress events with two daughter photons from a decay forming a merged cluster, we restrict the ratio of the energy deposited in a array of ECL crystals () and that in the enclosing array () to be above 0.94. About 63% of merged clusters are rejected by this requirement. We retain candidate , , or resonances if their invariant masses are within or of their nominal masses Olive et al. (2014), respectively. The mesons are required to originate from in order to identify the flavor and to suppress the combinatorial background. The associated track must satisfy the aforementioned pion-hypothesis requirement. The daughters are refitted to a common vertex, and the resulting and the slow pion candidate from decay are constrained to originate from a common point within the interaction point region. Confidence levels exceeding are required for both fits. To suppress combinatorial background, we restrict the energy released in the decay, , where is the nominal mass, to lie in a window around the nominal value Olive et al. (2014). To further reduce the combinatorial background contribution, we require the momentum of the in the center-of-mass system [] to exceed , , and in the , , and modes, respectively.

We measure the branching fractions and asymmetries of aforementioned radiative decays relative to well-measured hadronic decays to , , and for the , , and mode, respectively. The signal branching fraction is

(1) |

where is the extracted yield, the reconstruction efficiency, and the branching fraction for the corresponding mode. The raw asymmetry in decays of mesons to a specific final state ,

(2) |

depends not only on the asymmetry, , but also on the contributions from the forward-backward production asymmetry () Berends et al. (1973); Brown et al. (1973); Cashmore et al. (1986) and the asymmetry due to different reconstruction efficiencies for positively and negatively charged particles (): . Here, we have used a linear approximation assuming all terms to be small. The last two terms can be eliminated using the same normalization mode as used in the branching fraction measurements:

(3) |

where is the nominal value of asymmetry of the normalization mode Amhis et al. (2014).

The dominant background arises from decays, with the subsequently decaying to a pair of photons, e.g., . If one of the daughter photons is missed in the reconstruction, the final state mimics the signal decay. Such events are suppressed with a dedicated veto in the form of a neural network Feindt and Kerzel (2006) constructed from two mass-veto variables, described below. The signal photon is paired for the first (second) time with all other photons in the event having an energy greater than 30 (75) MeV. The pair in each set whose diphoton invariant mass lies closest to is fed to the network. The final criterion on the veto variable rejects about of background while retaining of signal. With this method, we reject 13% more background at the same signal efficiency as compared to the veto used in previous Belle analyses Koppenburg et al. (2004). A similar veto is considered for background from , but is found to be ineffective due to the larger mass, which shifts the background further away from the signal peak.

We extract the signal yield and asymmetry via a simultaneous unbinned extended maximum likelihood fit of and samples to the invariant mass of the candidates and the cosine of the helicity angle . The latter is the angle between the momenta of the and the , , or in the rest frame of the , , or , respectively. By angular momentum conservation, the signal distribution depicts a dependence; no background contribution is expected to exhibit a similar shape. For the and modes, we restrict the helicity angle range to to suppress backgrounds that peak at the edges of the distribution. For the mode, where the background levels are lower overall, the entire range is used. The candidate mass is restricted to for all three signal channels.

The invariant mass distribution of signal events is modeled with a Crystal-Ball probability density function Skwarnicki (1986) (PDF) for the and modes, and with the sum of a Crystal-Ball and two Gaussians for the mode. To take into account possible differences between MC and data, a free offset and scale factor are implemented for the mean and width of the PDF, respectively. The obtained values are applied to the other two modes.

The - and -type background distributions are described with a pure Crystal-Ball or the sum of either a Crystal-Ball or logarithmic Gaussian Ikeda et al. (2000) and up to two additional Gaussians. For the mode, the -type backgrounds are , and with the kaon being misidentified as pion. For the mode, the only -type background is the decay . For the mode, the - and -type backgrounds are the decays nonresonant , and nonresonant . In all three signal modes, the ‘other-’ background comprises all other decays wherein the is reconstructed from the majority of daughter particles. In the () mode, there are two additional small backgrounds: with the photon being emitted as final state radiation (FSR), and with the photon arising from the radiative decay of the charged meson. As there are no missing particles, these decays exhibit the same distribution as the signal decays. We jointly denote them as irreducible background. Their yields are fixed to MC expectations and the known branching fractions Olive et al. (2014). The remaining combinatorial background is parametrized in with an exponential function in the mode and a second-order Chebyshev polynomial in the and modes. All parameters describing the combinatorial background are allowed to vary in the fit. Possible correlations among the fit variables are negligible, except for the and backgrounds in the mode that are accomodated with an additional Gaussian in the mass PDF whose relative contribution is a function of .

The PDF shape for the -type background, obtained from MC samples, is calibrated using the forbidden decay , which yields mostly background from and . The same PID criteria as for signal decays are applied, along with the and requirements as determined for the mode. The candidates in a window around the nominal mass are accepted. To calibrate the distribution, the simulated shape is smeared with a Gaussian function of width and an offset .

The signal distribution is parametrized as for all three modes. For the and () categories, the shape is close to and described with a second- ( and mode) or third-order ( mode) Chebyshev polynomial. In the mode, a linear term in is added with a free coefficient to take into account possible interference between resonant and nonresonant amplitudes. For other background categories, the distributions are modeled using suitable PDFs based on MC predictions.

Apart from normalizations, the asymmetries of signal and background modes are left free in the fit. All PDF shapes are fixed to MC values, unless previously stated otherwise.

In the mode, the yields (and ) of certain backgrounds that contain a small number of events (one or two orders of magnitude less than signal) are fixed: , and the ‘other-’ background. The same is done for backgrounds with a photon from FSR or radiative decay in the and modes. All fixed yields are scaled by the ratio between reconstructed signal events in data and simulation of the normalization modes. We impose an additional constraint in the mode by assigning two common variables to - and -type backgrounds, respectively. Since all are Cabibbo-favored decays, is expected to be zero, while other asymmetries contributing to are the same for decays with the same final-state particles.

Fig. 1 shows the signal-enhanced projections of the combined sample in the region for all three signal modes, as well as the signal-enhanced projection in the region for the mode sup (). The obtained signal yields and raw asymmetries are listed in Table 1, along with reconstruction efficiencies. The background raw asymmetries are consistent with zero.

Efficiency [%] | Yield | ||
---|---|---|---|

The analysis of the normalization modes relies on the previous analysis by Belle Staric et al. (2008). The same selection criteria as for signal modes for PID, vertex fit, and are applied. The signal yield is extracted by subtracting the background in a signal window of , where the background is estimated from a symmetrical upper and lower sideband. The signal window and sidebands for the mode are and (20-35) around the nominal value Olive et al. (2014), respectively. For the mode, the signal window is and sidebands are (31-45) , whereas for the mode, the signal window is and sidebands are (28.8-45.0) . The obtained signal yields and raw asymmetries are also listed in Table 1.

The systematic uncertainties are listed in Table 2. All uncertainties are simultaneously estimated for and , unless stated otherwise. There are two main sources: those due to the selection criteria and those arising from the signal extraction method, both for signal and normalization modes. Some of the uncertainties from the first group cancel if they are common to the signal and respective normalization mode, such as those related to PID, vertex fit, and the requirement on . A 2.2% uncertainty is ascribed to photon reconstruction efficiency Nisar et al. (2016). Due to the presence of the photon in the signal modes, the resolution of the distribution is worse than in the normalization modes. Thus, the related uncertainties cannot be assumed to cancel completely. We separately estimate the uncertainty due to the requirement using the control channel . For both MC and data, the efficiency is estimated by calculating the ratio of the signal yield, extracted with and without the requirement on . Then, the double ratio is calculated to assess the possible difference between simulation and data. We obtain . We do not correct the efficiency by the central value; instead, we assign a systematic uncertainty of 1.16%.

The double-ratio method is also used to estimate the uncertainty due to the -veto requirement on the control channel . The veto is calculated by pairing the first daughter photon (the more energetic one) of the with all others, but for the second daughter. The ratio of so-discarded events is calculated for MC and data, with all other selection criteria applied. The obtained double ratio is . The error directly translates to the systematic uncertainty of the efficiency.

The systematic uncertainties due to the and requirements are estimated on the mode by repeating the fit without any constraint on the variable in question. The systematic error is the difference between the central value of the ratio from this fit and that of the nominal fit. The obtained uncertainties are 0.23% for and 1.15% for .

The systematic uncertainties due to the requirement on the mass of the vector meson are estimated using the mass distribution, modeled with a relativistic Breit-Wigner function. In the signal window, we compare the integrals of the nominal function and the same modified by the uncertainties on the central value and width. The obtained uncertainties are 0.2% for the mode, 0.1% for the mode, and 1.7% for the mode. All uncertainties described above are summed in quadrature and the final value is listed as ‘Efficiency’ in Table 2. They affect only the branching fraction, as they cancel in Eq. 2.

For the fit procedure, a systematic uncertainty must be ascribed to every parameter that is determined and fixed to MC values but might differ in data. The fit procedure is repeated with each parameter varied by its uncertainty on the positive and negative sides. The larger deviation from the nominal branching fraction or value is taken as the double-sided systematic error and these are summed in quadrature for all parameters. An uncertainty is assigned to the calibration offset and width of the -type backgrounds. For the and modes, the uncertainty is calculated for the width scale factor (and offset) of the signal PDF and -type background varied simultaneously. All these quadratically summed uncertainties are listed as ‘Fit parametrization’ in Table 2.

The values of the fixed yields of some backgrounds in the and mode are varied according to the uncertainties of the respective branching fractions Olive et al. (2014). For the category with the FSR photon, a 20% variation is used Benayoun et al. (1999). As the branching fractions contributing to the ‘other-’ background in the mode are unknown, we apply the largest variation from among other categories. The quadratically summed uncertainty is listed as ‘Background normalization’ in Table 2.

For the normalization modes, the procedure is repeated with shifted sidebands, starting from from the nominal value. The statistical error from sideband subtraction is taken into account. Since possible differences in the signal shape between simulation and data could also affect the signal yield, a similar procedure as for the calibration of the background is performed. A systematic uncertainty is assigned for the case when the MC shape is smeared by a Gaussian of width . All uncertainties arising from normalization modes are summed in quadrature and listed as ‘Normalization mode’ in Table 2.

Finally, an uncertainty is assigned by varying the nominal values of the branching fractions and of the normalization modes and vector meson sub-decay modes by their respective uncertainties.

()/ [%] | [] | |||||
---|---|---|---|---|---|---|

Efficiency | 2.8 | 3.3 | 2.8 | – | – | – |

Fit parametrization | 1.0 | 2.8 | 2.3 | 0.1 | 0.4 | 5.3 |

Background normalization | – | 0.3 | 0.6 | – | 0.2 | 0.5 |

Normalization mode | 0.0 | 0.0 | 0.1 | 0.5 | 0.0 | 0.3 |

External and | 2.0 | 1.0 | 1.8 | 1.2 | 0.0 | 1.5 |

Total | 3.6 | 4.5 | 4.1 | 1.3 | 0.4 | 5.5 |

We have conducted a measurement of the branching fraction and in three radiative charm decays , , and using the full dataset recorded by the Belle experiment. We report the first observation of with a significance of 5.5, including systematic uncertainties. The significance is calculated as , where is the likelihood value with the signal yield fixed to zero and is that of the nominal fit. The systematic uncertainties are included by convolving the statistical likelihood function with a Gaussian of width equal to the systematic uncertainty that affects the signal yield. The measured ratios of branching fractions to their normalization modes are , and for , , and , respectively. The first uncertainty is statistical and the second systematic. Using world-average values for the normalization modes Olive et al. (2014), we obtain

For the mode, the obtained value is considerably larger than theoretical expectations Khodjamirian et al. (1995); Fajfer et al. (1999). The result of the mode is improved compared to the previous determinations by Belle and BABAR, and is consistent with the world average value Olive et al. (2014). Our branching fraction of the mode is 3.3 above the BABAR measurement Aubert et al. (2008). Both and results agree with the latest theoretical calculations Fajfer (2015).

We also report the first measurement of in these decays. The values, obtained from Eq. 3:

are consistent with no violation. Since the uncertainty is statistically dominated, the sensitivity can be greatly enhanced at the upcoming Belle II experiment Abe et al. (2010).

###### Acknowledgements.

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 (Australia); FWF (Austria); NSFC and CCEPP (China); MSMT (Czechia); CZF, DFG, EXC153, and VS (Germany); DST (India); INFN (Italy); MOE, MSIP, NRF, BK21Plus, WCU and RSRI (Korea); MNiSW and NCN (Poland); MES and RFAAE (Russia); ARRS (Slovenia); IKERBASQUE and UPV/EHU (Spain); SNSF (Switzerland); MOE and MOST (Taiwan); and DOE and NSF (USA).## References

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