Direct CP Violation Research Articles

A global likelihood for precision constraints and flavour anomalies

We present a global likelihood function in the space of dimension-six Wilson coefficients in the Standard Model Effective Field Theory. The likelihood includes contributions from flavour-changing neutral current B decays, lepton flavour universality tests in charged- and neutral-current B and K decays, meson-antimeson mixing observables in the K, B, and D systems, direct CP violation in Krightarrow pi pi , charged lepton flavour violating B, tau, and muon decays, electroweak precision tests on the Z and W poles, the anomalous magnetic moments of the electron, muon, and tau, and several other precision observables, 265 in total. The Wilson coefficients can be specified at any scale, with the one-loop running above and below the electroweak scale automatically taken care of. The implementation of the likelihood function is based on the open source tools flavio and wilson as well as the open Wilson coefficient exchange format (WCxf) and can be installed as a Python package. It can serve as a basis either for model-independent fits or for testing dynamical models, in particular models built to address the anomalies in B physics. We discuss a number of example applications, reproducing results from the EFT and model building literature.

Direct CP Violation from Isospin Symmetry Breaking Effects for the Decay Process B-s→P(V)π0 in PQCD

We investigate the direct CP violation for the decay process of B-s→P(V)π0 (P,V refer to the pseudoscalar meson and vector meson, resp.) via isospin symmetry breaking effects from the π0-η-η′ mixing mechanism in PQCD factorization approach. Isospin symmetry breaking arises from the electroweak interaction and the u-d quark mass difference by the strong interaction, which are known to be tiny. However, we find that isospin symmetry breaking at the leading order shifts the CP violation due to the new strong phases.

Master formula for ε′/ε beyond the Standard Model

We present for the first time a master formula for ε′/ε, the ratio probing direct CP violation in K→ππ decays, valid in any ultraviolet extension of the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM operators calculated recently in the Dual QCD approach and the ones of the SM operators from lattice QCD. We emphasize the large impact of several scalar and tensor BSM operators in the context of the emerging ε′/ε anomaly. We have implemented the results in the open source code flavio.

Charm Mixing and CP violation at LHCb

The LHCb experiment has collected the world’s largest sample of charmed hadrons. This sample is used to measure mixing and to search for direct and indirect CP violation, and its sensitivity is now approaching the Standard Model expectations. In this document, the most recent LHCb results on CP violation in charm sector and on charm mixing are reported.

ϵ′/ϵ from charged-Higgs-induced gluonic dipole operators

We study the effect of charged-Higgs-induced chromomagnetic operator, Q8G(−)≡s¯σμνTaγ5dGaμν, on the Kaon direct CP violation Re(ϵ′/ϵ). Using the matrix element 〈ππ|O8G(−)|K0〉 recently obtained by a large Nc dual QCD approach, we find that if the Kobayashi–Maskawa phase is the origin of CP violation, the charged-Higgs-induced gluon penguin dipole operator in the type-III two-Higgs-doublet model can explain the measured Re(ϵ′/ϵ) when the constraints from the relevant low energy flavor physics, such as ΔB(K)=2, B→Xsγ, Bs→μ+μ−, and Kaon indirect CP violation parameter ϵ, are included.

Exploring Brightarrow pi pi , pi K decays at the high-precision frontier

The Brightarrow pi pi ,pi K system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic Brightarrow pi pi parameters from data where new measurements of direct CP violation in B^0_drightarrow pi ^0pi ^0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the Brightarrow pi pi parameters can be converted into their Brightarrow pi K counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is B^0_drightarrow pi ^0 K_mathrm{S} as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of B^0_drightarrow pi ^0 K_mathrm{S}, which are the theoretically cleanest Brightarrow pi K probes. Interestingly, they show tensions with respect to the Standard Model. Should this Brightarrow pi K puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the Brightarrow pi K dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.

Direct CP violation in Cabibbo-favored charmed meson decays and \u03f5\u2032/\u03f5 in SU(2)L \xd7 SU(2)R \xd7 U(1)B\u2212L model

Since the standard model contribution is virtually absent, any observation of direct CP violation in the Cabibbo-favored charmed meson decays would be evidence of new physics. In this paper, we conduct a quantitative study on direct CP violation in D0 → K−π+, Ds+ → ηπ+ and Ds+ → η′π+ decays in the SU(2)L ×SU(2)R ×U(1)B−L gauge extension of the standard model. In the model, direct CP violation arises mainly from the interference between the decay amplitude coming from the SM left-left current operators and that from the right-right current operators induced by WR+ gauge boson exchange. Interestingly, the strong phase between the two amplitudes is evaluable, since it stems from difference in QCD corrections to the left-left and right-right current operators, which is a short-distance QCD effect given by sim left({alpha}_sleft({M}_{W_L}^2right)/4pi right) log left({M}_{W_R}^2/{M}_{W_L}^2right) . We assess the maximal direct CP violation in the above decays in the SU(2)L × SU(2)R × U(1)B−L model. Additionally, we present a correlation between direct CP violation in these modes and one in K → ππ decay parametrized by ϵ′, since WR+ gauge boson has a sizable impact on the latter.

Recent results on CP violation at B factories

We review recent results of the Beauty Factories BaBar and Belle on CP violation in the quark sector and constraints on the CKM unitarity triangle. We first present the recent measurement, using BaBar and Belle data, of cos(2β) = cos(2ϕ1) in B0 → D(∗)h0 with $D \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{-}$ decays, using a combined time-dependent Dalitz plot analysis. The BaBar Dalitz plot analysis of the $B^{+} \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{0}$ decay is also presented, and shows an evidence for direct CP violation in B+ → K∗(892)π0. A recently published BaBar measurement of the |V ub| CKM matrix element allows to contrain one side of the unitarity triangle. These analyses use the data sets of the BaBar and Belle experiments containing 471 × 106 and 772 × 106 $B\overline {B}$ pairs collected at the Υ(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively.

Re(\u03f5K\u2032/\u03f5K) and Kto pi nu overline{nu} in a two-Higgs doublet model

The Kaon direct CP violation Re(ϵK′/ϵK) below the experimental data of a 2σ in the standard model, which is calculated using the RBC-UKQCD lattice and a large Nc dual QCD, indicates the necessity of a new physics effect. In order to resolve the insufficient Re(ϵK′/ϵK), we study the charged-Higgs contributions in a generic two-Higgs-doublet model. If we assume that the origin of the CP-violation phase is uniquely from the Kobayashi-Maskawa (KM) phase when the constraints from the B- and K-meson mixings, B → Xsγ, and Kaon indirect CP violating parameter ϵK are simultaneously taken into account, it is found that the Kaon direct CP violation through the charged-Higgs effects can reach Re(ϵK′/ϵK)H ± ∼ 8 × 10− 4. Moreover, with the constrained values of the parameters, the branching ratios of the rare Kto pi nu overline{nu} decays can be BRleft({K}^{+}to {pi}^{+}nu overline{nu}right)sim 13 times 1{0}^{-11} and BRleft({K}_Lto {pi}^0nu overline{nu}right)sim 3.6times 1{0}^{-11} , where the results can be tested through the NA62 experiment at CERN and the KOTO experiment at J-PARC, respectively.

Updated Standard Model Prediction for ε′/ε

A recent lattice evaluation of ε′/ε, finding a 2.1 σ deviation from the experimental value, has revived the old debate about a possible ε′/ε anomaly. The unfounded claims of a too low Standard Model prediction are based on incorrect estimates that neglect the long-distance re-scattering of the final pions in K → 2π. In view of the current situation, we have recently updated the Standard Model calculation, including all known short- and long-distance contributions. Our result, Re(ε′/ε)=(15±7)⋅10−4 [H. Gisbert and A. Pich, “Direct CP violation in K0→ππ: Standard Model Status”, Rept. Prog. Phys. 81 (2018) no. 7, 076201 arXiv:1712.06147 [hep-ph].], is in complete agreement with the experimental measurement.

Recent QCD results from the NA48/2 experiment

The NA48/2 experiment collected data in 2003 and 2004 with the main purpose to study direct CP violation in charged kaons decaying in three pions. Thanks to the huge statistics collected, other studies are also possible. In this paper two recent results, in the framework of QCD studies, are reported: the measurement of the K± → π0e±ν Form Factors and the first observation of the rare decay K± → π±π0e+e−.

Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

In light of a discrepancy of the direct CP violation in K → ππ decays, ε′/εK , we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to ΔS = 2 observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of ε′/εK for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify mathrm{mathcal{B}}left(Kto pi nu overline{nu}right) , ℬ(KS → μ+μ−)eff and ΔACP(b → sγ). Such large effects could be measured in future experiments.

Study of the K_1(1270)-K_1(1400) mixing in the decays Brightarrow J/Psi K_1(1270), J/Psi K_1(1400)

We study the B meson decays Brightarrow J/Psi K_1(1270,1400) in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are predicted as Br(B^+rightarrow J/Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}times 10^{-3}, Br(B^+rightarrow J/Psi K_1(1400)^+)=6.47^{+2.50}_{-2.34}times 10^{-4}, and Br(B^0rightarrow J/Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})times 10^{-3} with the mixing angle theta _{K_1}=33^circ , which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that theta _{K_1}sim 33^circ is much more favored than 58^{circ }. Furthermore, we also give the predictions of the polarization fractions, the direct CP violations, the relative phase angles for the considered decays with the mixing angle theta _{K_1}=33^circ and 58^circ , respectively. The direct CP violations of the two charged decays B^+rightarrow J/Psi K_1(1270,1400)^+ are very small (10^{-4}sim 10^{-5}), because the weak phase is very tiny. In order to check the dependence of the results on the nonperturbative input parameters, we also calculate them by using the harmonic-oscillator type wave functions for the J/Psi meson. These results can be tested at the running LHCb and forthcoming Super-B experiments.

Updated determination of D0–D¯0 mixing and CP violation parameters with D0→K+π− decays

We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of $D^0\to K^+\pi^-$ to $D^0\to K^-\pi^+$ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of $5.0$ fb$^{-1}$ recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity (CP) symmetry, the mixing parameters are determined to be $x'^2=(3.9 \pm 2.7) \times10^{-5}$, $y'=(5.28 \pm 0.52) \times 10^{-3}$, and $R_D=(3.454 \pm 0.031)\times10^{-3}$. Without this assumption, the measurement is performed separately for $D^0$ and $\overline{D}{}^0$ mesons, yielding a direct CP-violating asymmetry $A_D =(-0.1\pm9.1)\times10^{-3}$, and magnitude of the ratio of mixing parameters $1.00< |q/p| <1.35$ at the $68.3\%$ confidence level. All results include statistical and systematic uncertainties and improve significantly upon previous single-measurement determinations. No evidence for CP violation in charm mixing is observed.

CP asymmetries in Strange Baryon Decays**Supported by National Science Foundation (PHY-1520966), National Natural Science Foundation of China (11335009, 11125525), Joint Large-Scale Scientific Facility Funds of the NSFC and CAS (U1532257), the National Key Basic Research Program of China (2015CB856700), Key Research Program of Frontier Sciences, CAS, (QYZDJ-SSW-SLH003), XWK’s work is also supported by MOST (Taiwan) (104-2112-M-001-022)

While indirect and direct CP violation (CPV) has been established in the decays of strange and beauty mesons, no CPV has yet been found for baryons. There are different paths to finding CP asymmetry in the decays of strange baryons; they are all highly non-trivial. The HyperCP Collaboration has probed CPV in the decays of single Ξ and Λ []. We discuss future lessons from collisions at BESIII/BEPCII: probing decays of pairs of strange baryons, namely Λ, Σ and Ξ. Realistic goals are to learn about non-perturbative QCD. One can hope to find CPV in the decays of strange baryons; one can also dream of finding the impact of New Dynamics. We point out that an important new era will start with the BESIII/BEPCII data accumulated by the end of 2018. This also supports new ideas to trigger at the LHCb collaboration.

Progress in the improved lattice calculation of direct CP-violation in the Standard Model

We discuss the ongoing effort by the RBC &amp; UKQCD collaborations to improve our lattice calculation of the measure of Standard Model direct CP violation, ∊’, with physical kinematics. We present our progress in decreasing the (dominant) statistical error and discuss other related activities aimed at reducing the systematic errors.

Mixing and CPV in Charm Hadrons at LHCb

LHCb continues to expand its world-leading sample of charmed hadrons collected during LHCs Run 1 (2010-2012) and Run 2 (2015-present). This sample is yielding some of the most stringent tests of the Standard Model understanding of charm physics. This includes precise measurements of the neutral D-meson mixing parameters and some of the most sensitive searches for direct and indirect CP violation in charm interactions.

Charm Physics: Another Route Towards New Physics

We summarize recent results for charm physics. These results span several categories: charm mixing, indirect (time-dependent) CP violation, direct (time-integrated) CP violation, T violation, semileptonic and leptonic decays, and decays of charm baryons.

Direct CP Violation in K→μ^{+}μ^{-}.

A rare decay K_{L}→μ^{+}μ^{-} has been measured precisely, while a rare decay K_{S}→μ^{+}μ^{-} will be observed by an upgrade of the LHCb experiment. Although both processes are almost CP-conserving decays, we point out that an interference contribution between K_{L} and K_{S} in the kaon beam emerges from a genuine direct CP violation. It is found that the interference contribution can change K_{S}→μ^{+}μ^{-} standard-model predictions at O(60%). We also stress that an unknown sign of A(K_{L}→γγ) can be determined by a measurement of the interference, which can much reduce a theoretical uncertainty of B(K_{L}→μ^{+}μ^{-}). We also investigate the interference in a new physics model, where the ε_{K}^{'}/ε_{K} tension is explained by an additional Z-penguin contribution.

CP violation induced by the double resonance for pure annihilation decay process in perturbative QCD

In a perturbative QCD approach we study the direct CP violation in the pure annihilation decay process of bar{B}^0_{s}rightarrow pi ^+pi ^-pi ^+pi ^- induced by the rho and omega double resonance effect. Generally, the CP violation is small in the pure annihilation type decay process. However, we find that the CP violation can be enhanced by double rho –omega interference when the invariant masses of the pi ^+pi ^- pairs are in the vicinity of the omega resonance. For the decay process of bar{B}^0_{s}rightarrow pi ^+pi ^-pi ^+pi ^-, the CP violation can reach A_{CP}(bar{B}^0_{s}rightarrow pi ^+pi ^-pi ^+pi ^-)=27.20^{+0.05+0.28+7.13}_{-0.15-0.31-6.11}%.