Direct CP Violation Research Articles

The decays B → Ψ(2S)π(K),ηc(2S)π(K) in the pQCD approach beyond the leading-order

Two body B meson decays involving the radially excited meson ψ(2S)/ηc(2S) in the final states are studied by using the perturbative QCD (pQCD) approach. We find that: (a) The branching ratios for the decays involving a K meson are predicted as Br(B+→ψ(2S)K+)=(5.37−2.22+1.85)×10−4, Br(B0→ψ(2S)K0)=(4.98−2.06+1.71)×10−4, Br(B+→ηc(2S)K+)=(3.54−3.09+3.18)×10−4, which are consistent with the present data when the next-to-leading-order (NLO) effects are included. Here the NLO effects are from the vertex corrections and the NLO Wilson coefficients. The large errors in the decay B+→ηc(2S)K+ are mainly induced by using the decay constant fηc(2S)=0.243−0.111+0.079 GeV with large uncertainties. (b) While there seems to be some room left for other higher order corrections or the non-perturbative long distance contributions in the decays involving a π meson, Br(B+→ψ(2S)π+)=(1.17−0.50+0.42)×10−5, Br(B0→ψ(2S)π0)=0.54−0.23+0.20×10−5, which are smaller than the present data. The results for other decays can be tested via running LHCb and forthcoming Super-B experiments. (c) There is no obvious evidence of the direct CP violation being seen in the decays B→ψ(2S)π(K),ηc(2S)π(K) in the present experiments, which is supported by our calculations. If a few percent value is confirmed in the future, this would definitely indicate the existence of new physics.

CP Violation in b- and c-hadron decays at LHCb

Testing the Standard Model of particle physics by precision measurements of CP violating observables in the decays of b and c hadrons has been one of the design goals of the LHCb experiment. World-leading measurements have been performed of the semileptonic asymmetry, , and of the mixing-induced CP-violating phase ϕs in the system. The CKM angle γ is still the least known angle of the Unitarity Triangle, and the only one easily accessible using tree-level decays. A recent combination of LHCb measurements in various B → DK decay modes has yielded the most precise determination of γ from a single experiment to date. The LHCb experiment is collecting unprecedented samples of beauty baryons, allowing for the first time to study CP violating observables in their decays. A recent analysis provided the first evidence for CP violation in the beauty baryon sector. Finally, LHCb has the largest samples of charmed hadron decays collected by any experiment to date. These samples yield some of the world’s most sensitive searches for direct and indirect CP violation in the charm sector.

On model-independent searches for direct CP violation in multi-body decays

Techniques for performing model-independent searches for direct violation in three and four-body decays are discussed. Comments on the performance and the optimisation of a binned approach and an unbinned approach, known as the energy test, are made. The use of the energy test in the presence of background is also studied. The selection and treatment of the coordinates used to describe the phase-space of the decay are discussed. The conventional model-independent techniques, which test for P-even violation, are modified to create a new approach for testing for P-odd violation. An implementation of the energy test using graphical processing units is described.

Revisiting kaon physics in general Z scenario

New physics contributions to the Z penguin are revisited in the light of the recently-reported discrepancy of the direct CP violation in K→ππ. Interference effects between the standard model and new physics contributions to ΔS=2 observables are taken into account. Although the effects are overlooked in the literature, they make experimental bounds significantly severer. It is shown that the new physics contributions must be tuned to enhance B(KL→π0νν¯), if the discrepancy of the direct CP violation is explained with satisfying the experimental constraints. The branching ratio can be as large as 6×10−10 when the contributions are tuned at the 10% level.

An ϵ′ improvement from right-handed currents

Recent lattice QCD calculations of direct CP violation in $K_L \to \pi \pi$ decays indicate tension with the experimental results. Assuming this tension to be real, we investigate a possible beyond-the-Standard Model explanation via right-handed charged currents. By using chiral perturbation theory in combination with lattice QCD results, we accurately calculate the modification of $\epsilon'/\epsilon$ induced by right-handed charged currents and extract values of the couplings that are necessary to explain the discrepancy, pointing to a scale around $10^2$ TeV. We find that couplings of this size are not in conflict with constraints from other precision experiments, but next-generation hadronic electric dipole moment searches (such as neutron and ${}^{225}$Ra) can falsify this scenario. We work out in detail a direct link, based on chiral perturbation theory, between CP violation in the kaon sector and electric dipole moments induced by right-handed currents which can be used in future analyses of left-right symmetric models.

Supersymmetry and Kaon physics

Kaon physics has played an essential role in testing the Standard Model and in searching for new physics with measurements of CP violation and rare decays. Current progress of lattice calculations enables us to predict kaon observables accurately, especially for the direct CP violation, ε′/ε, and there is a discrepancy from the experimental data at the 2.9 σ level. On the experimental side, the rare kaon decays and are ongoing to be measured at the SM accuracy by KOTO at J-PARC and NA62 at CERN. These kaon observables are good probes for new physics. We study supersymmetric effects; the chargino and gluino contributions to Z penguin, in kaon observables.

Towards NNLO accuracy for ε′/ε

The quantity ε′/ε measures direct CP violation in Kaon decays. Recent SM predictions show a 2.9σ tension with data, with the theoretical uncertainty dominating. As rapid progress on the lattice is bringing nonperturbative long-distance effects under control, a more precise knowledge of short-distance contributions is needed. We describe the first NNLO results for ε′/ε and discuss future prospects, as well as issues of scheme dependence and the separation of perturbative and nonperturbative effects. Finally we also comment on the solution of the renormalisation-group evolution in one of the talks at this conference and present the correct solution.

Direct CP violation in charmless three-body decays of B mesons

Direct CP violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $\langle M_1M_2|\bar q_1 q_2|0\rangle$. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances and the matrix element of scalar density. In order to accommodate the branching fraction and CP asymmetries observed in $B^-\to K^-\pi^+\pi^-$, the matrix element $\langle K\pi|\bar sq|0\rangle$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional CP asymmetries and find that nonresonant CP violation is usually much larger than the resonant one and that the interference effect is generally quite significant. If nonresonant contributions are turned off in the $K^+K^-K^-$ mode, the predicted CP asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^-\to \pi^-\pi^+\pi^-$, we find that ${\cal A}_{C\!P}(\rho^0\pi^-)$ should be positive in order to account for CP asymmetries observed in this decay. However, all theories predict a large and negative CP violation in $B^-\to \rho^0\pi^-$. Measurements of CP-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of violation in some (large) invariant mass regions to test our model.

Higher order effects in ϵ'/ϵ

The quantity ϵ'/ϵ measures direct CP violation in Kaon decays. Recent analysis of this ratio resulted in a 2.9 sigma discrepancy between the Standard Model predictions and the experimental data. Our ability to observe or constrain New Physics depends on the accuracy of determining the SM “background”, hence a precise evaluation of ϵ'/ϵ is particularly important. We discuss the Standard Model prediction and the relevant matching calculations at NNLO for this observable.

Search for direct CP violation in baryonic b-hadron decays

We first review direct CP violation in the three-body baryonic [Formula: see text] decays of [Formula: see text] with [Formula: see text] and [Formula: see text]. We then present our recent results of the direct CP violating asymmetries in the two-body [Formula: see text] decays of [Formula: see text] as well as the three-body [Formula: see text]. In particular, we emphasize that the large direct CP violating asymmetries in [Formula: see text] and [Formula: see text] are both around 20%, which are accessible to the b-hadron experiments.

Effect of [formula omitted] mixing and CP violation in the measurement of γ with B± → D(⁎)0K(⁎)± decays

The datasets that the LHCb and Belle II experiments are expected to collect in the coming years will allow a 1-degree precision measurement of the angle γ(ϕ3) of the unitarity triangle using B±→D(⁎)0K(⁎)± decays. To reach this goal a number of subleading effects must be taken into account, including D−D‾ mixing, possible direct CP violation in D decays and CP violation in the neutral kaon system. We discuss these effects and quantify their magnitude in the main analysis methods.

ϕ1 Measurements at Belle

We present the recent measurements of the B0→η′K0 and the B→ωK decay modes based on the full data set of 772×106BB‾ pairs collected by the Belle detector at the KEKB e+e− collider. In the B0→η′K0 mode, we obtain the CP-violating parametersAη′K0=+0.03±0.05 (stat)±0.04 (syst),Sη′K0=+0.68±0.07 (stat)±0.03 (syst).This is the world's most precise result on the η′K0CP parameters. In B→ωK decays, we measure the branching fractionsBB0→ωK0=(4.5±0.4 (stat)±0.3 (syst))×10−6,BB−→ωK−=(6.8±0.4 (stat)±0.4 (syst))×10−6,which are their current most precise results. We measure the first evidence of CP violation in the B0→ωKS0 decay mode, obtaining the CP-violating parametersAωKS0=−0.36±0.19 (stat)±0.05(syst),SωKS0=+0.91±0.32 (stat)±0.05 (syst).In the B−→ωK− mode, we measure the direct CP-violation parameterAωK−=−0.03±0.04 (stat)±0.01 (syst),which is its most precise measurement to date.

Study on the ϒ(1S)→BcDs decay

The branching ratio and direct CP asymmetry of the ϒ(1S)→BcDs weak decay are estimated with the perturbative QCD approach firstly. It is found that (1) the direct CP-violating asymmetry is close to zero, (2) the branching ratio Br(ϒ(1S)→BcDs)≳10−10 might be measurable at the future experiments.

Heavy flavor at the Tevatron

The CDF and D0 experiments at the Tevatron proton-antiproton collider have pioneered and established the role of hadron collisions in exploring flavor physics through a broad program that continues to offer competitive results. I report on latest results in the flavor sector obtained using the whole CDF and D0 data sets corresponding to ∼ 10 fb−1 of integrated luminosity; including B-mesons spectroscopy and production asymmetries, flavor specific decay bottom-strange mesons lifetime. I also present measurements of direct and indirect CP violation in bottom and charm meson decays.

Localized direct CP violation in $$B^\pm \rightarrow \rho ^0 (\omega )\pi ^\pm \rightarrow \pi ^+ \pi ^-\pi ^\pm $$ B ± → ρ 0 ( ω ) π ± → π + π - π ±

We study the localized direct CP violation in the hadronic decays $B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow\pi^+ \pi^-\pi^\pm$, including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between $\rho^0$ and $\omega$. We calculate the localized integrated direct CP violation when the low invariant mass of $\pi^+\pi^-$ [$m(\pi^+\pi^-)_{low}$] is near $\rho^0(770)$. For five models of form factors investigated, we find that the localized integrated direct CP violation varies from -0.0170 to -0.0860 in the ranges of parameters in our model when $0.750<m(\pi^+\pi^-)_{low}<0.800$\,GeV. This result, especially the sign, agrees with the experimental data and is independent of form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV are positive and negative, respectively. We find that $\rho$-$\omega$ mixing makes the localized integrated CP asymmetry move towards the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also model independent. We also calculate the localized integrated direct CP violating asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV and find that they agree with the experimental data in some models of form factors.

Theoretical analysis of direct CP violation and differential decay width in $$D^\pm \rightarrow \pi ^\pm \pi ^+\pi ^-$$ D ± → π ± π + π - in phase space around the resonances $$\rho ^0(770)$$ ρ 0 ( 770 ) and $$f_0(500)$$ f 0 ( 500 )

We perform a theoretical study on direct $CP$ violation in $D^\pm\to \pi^\pm \pi^+\pi^-$ in phase space around the intermediate states $\rho^0(770)$ and $f_0(500)$. The possible interference between the amplitudes corresponding to the two resonances is taken into account, and the relative strong phase of the two amplitudes is treated as a free parameter. Our analysis shows that by properly chosen the strong phase, both the $CP$ violation strength and differential decay width accommodate to the experimental results.

Subtleties in the BABAR measurement of time-reversal violation

A first measurement of time-reversal (T) asymmetries that are not also CP asymmetries has been recently achieved by the BABAR collaboration. In this talk, which follows the work done in Ref. [1], I discuss the subtleties of this measurement in the presence of direct CP violation, CPT violation, wrong strangeness decays and wrong sign semi-leptonic decays. In particular, I explain why, in order to identify the measured asymmetries with time-reversal violation, one needs to assume (i) the absence of wrong strangeness decays or of CPT violation in strangeness changing decays, and (ii) the absence of wrong sign decays.

Dark Z implication for flavor physics

Dark Z/dark photon (Z ′) is one candidate of dark force carrier, which helps to interpret the properties of dark matter (DM). Other than conventional studies of DM including direct detection, indirect detection and collider simulation, in this work we take flavor physics as a complementary approach to investigate the features of dark matter. We give an exact calculation of the new type of penguin diagram induced by Z ′ which further modifies the well-known X, Y, Z functions in penguin-box expansion. The measurement of rare decays B → K (*) μ + μ − and B s → μ + μ − at LHC, together with direct CP violation ε ′ /ε in K → ππ as well as K L → μ + μ −, are used to determine the parameter space. The size of coupling constant, however, is found to be $$ \mathcal{O}(1) $$ which is much weaker than the known constraints.

Refined applications of the collapse of the wave function

In a two-part system the "collapse of the wavefunction" of one part can put the other part in a state which would be difficult or impossible to achieve otherwise, in particular one sensitive to small effects in the `collapse' interaction. We present some applications to the very symmeteric and experimentally accessible situations of the decays $\phi(1020)\to K^oK^o$, $\psi(3770)\to D^oD^o$, or $\Upsilon(4s)\to B^oB^o$, involving the internal state of the two-state $K^o$, $D^o$ or $B^o$ mesons. The "collapse of the wavefunction" occasioned by a decay of one member of the pair (`away side') fixes the state vector of that side's two-state system. Bose-Einstein statistics then determines the state of the recoiling meson (`near side'), whose evolution can then be followed further. In particular the statistics requirement dictates that the `away side' and `near side' internal states must be orthogonal at the time of the "collapse". Thus a CP violation in the `away side', decay implies a complementary CP impurity on the `near side', which can be detected in the further evolution. The CP violaion so manifested is necessarily direct CP violation, since neither the mass matrix nor time evolution was involved in the "collapse". A parametrization of the direct CP violation is given and various manifestations are presented. Certain rates or combination of rates are identified which are nonzero only if there is direct CP violation. The very explicit and detailed use made of "collapse of the wavefunction" makes the procedure interesting with respect to the fundamentals of quantum mechanics. We note an experimental consistency test for our treatment of the "collapse of the wavefunction", which can be carried out by a certain measurement of partial decay rates.

Scalar leptoquarks and the rareBmeson decays

We study some rare decays of $B$ meson involving the quark level transition $b \to q l^+l^- (q=d,s)$ in the scalar leptoquark model. We constrain the leptoquark parameter space using the recently measured branching ratios of $B_{s,d} \to \mu^+ \mu^-$ processes. Using such parameters, we obtain the branching ratios, direct CP violation parameters and isospin asymmetries in $B \to K \mu^+ \mu^-$ and $B \to \pi \mu^+ \mu^-$ processes. We also obtain the branching ratios for some lepton flavour violating decays $B \to l_i^+ l_j^-$. We find that the various anomalies associated with the isospin asymmetries of $B \to K \mu^+ \mu^-$ process can be explained in the scalar leptoquark model.