Direct CP Violation Research Articles

Su(3) symmetry analysis in charmed baryon two body decays with penguin diagram contribution

An increasing number of experimental measurements from the BESIII, Belle, and Belle-II collaborations encourage investigations into charmed baryon two-body decay processes. By including contributions from the penguin diagrams that are ignored in previous studies, we perform a global analysis with SU(3) flavor symmetry. Assuming all form factors are real, we achieve a remarkable minimal χ2/d.o.f=0.788\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^{2}/d.o.f = 0.788$$\\end{document} and find that the contribution of the amplitude proportional to Vcb∗Vub\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{cb}^*V_{ub}$$\\end{document} is of the order ∼0.01\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 0.01$$\\end{document}, comparable with the contribution of the tree-level diagram. Additionally, by using the KPW theorem to reduce the number of amplitudes from 13 to 7 in the leading contribution, it becomes possible to consider the complex form factor case for the leading IRA amplitude in the global analysis. However, the analysis of complex form factors significantly conflicts with the experimental data Br(Ξc0→Ξ-π+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Br(\\Xi _c^0\\rightarrow \\Xi ^-\\pi ^+)$$\\end{document}, and by excluding this data, χ2/d.o.f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^2/d.o.f$$\\end{document} is reduced from 5.95 to 1.19. Although the analysis of complex form factors shows a significant central value of the penguin diagram contribution, the large errors from the corresponding form factors make it a challenge to precisely determine its true contribution. Consequently, the direct CP violation in decay processes is predicted to be approximately zero. With more data in future experiments, the penguin diagram contribution with the amplitude proportional to Vcb∗Vub\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{cb}^*V_{ub}$$\\end{document} will be precisely determined, allowing for a more accurate prediction of CP violation. Our analysis necessitates further theoretical investigations and experimental measurements in the future.

New graph-neural-network flavor tagger for Belle II and measurement of sin 2ϕ1 in B0→J/ψKS0 decays

We present GFlaT, a new algorithm that uses a graph-neural-network to determine the flavor of neutral B mesons produced in ϒ(4S) decays. It improves previous algorithms by using the information from all charged final-state particles and the relations between them. We evaluate its performance using B decays to flavor-specific hadronic final states reconstructed in a 362 fb−1 sample of electron-positron collisions collected at the ϒ(4S) resonance with the Belle II detector at the SuperKEKB collider. We achieve an effective tagging efficiency of (37.40±0.43±0.36%), where the first uncertainty is statistical and the second systematic, which is 18% better than the previous Belle II algorithm. Demonstrating the algorithm, we use B0→J/ψKS0 decays to measure the mixing-induced and direct CP violation parameters, S=(0.724±0.035±0.009) and C=(−0.035±0.026±0.029). Published by the American Physical Society 2024

Estimated of CP violation in B^0 meson decays into D^{*+} and D^- mesons

The decay B^0rightarrow D^{*+}D^- is favorable mode for studying CP violation in the interference between mixing and decay for B^0 and bar{B}^0 mesons. The latest analysis of the CP parameters has been performed by the LHCb Collaboration values of S_{D^*D}=-,0.861pm 0.077pm 0.019, C_{D^*D}=-,0.059pm 0.092pm 0.020, triangle S_{D^*D}=0.019pm 0.075pm 0.012, triangle C_{D^*D}=-,0.031pm 0.092pm 0.016, and mathcal {A}_{D^*D}^{CP}=0.008pm 0.014pm 0.006pm 0.003. We have been estimated the parameters S_{D^*D} and C_{D^*D} of the B^0rightarrow D^{*+}D^- decay as -,0.709pm 0.024 and -,0.051pm 0.004. In the following, we have obtained the values of triangle S_{D^*D}=0.054pm 0.003 and triangle C_{D^*D}=0.020pm 0.001 and direct CP violation of 0.008pm 0.001. Also, we have calculated the branching ratio of B^0rightarrow D^{*+}D^- decay. The values obtained in this work are comparable with the corresponding experimental values.

Measurement of the Time-Integrated CP Asymmetry in D^{0}→K^{-}K^{+} Decays.

The time-integrated CP asymmetry in the Cabibbo-suppressed decay D^{0}→K^{-}K^{+} is measured using proton-proton collision data, corresponding to an integrated luminosity of 5.7 fb^{-1} collected at a center-of-mass energy of 13TeV with the LHCb detector. The D^{0} mesons are required to originate from promptly produced D^{*+}→D^{0}π^{+} decays, and the charge of the companion pion is used to determine the flavor of the charm meson at production. The time-integrated CP asymmetry is measured to be A_{CP}(K^{-}K^{+})=[6.8±5.4±1.6]×10^{-4} where the first uncertainty is statistical and the second systematic. The direct CP asymmetries in D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays, a_{K^{-}K^{+}}^{d} and a_{π^{-}π^{+}}^{d}, are derived by combining A_{CP}(K^{-}K^{+}) with the time-integrated CP asymmetry difference, ΔA_{CP}=A_{CP}(K^{-}K^{+})-A_{CP}(π^{-}π^{+}), and other inputs, giving a_{K^{-}K^{+}}^{d}=(7.7±5.7)×10^{-4},a_{π^{-}π^{+}}^{d}=(23.2±6.1)×10^{-4},with a correlation coefficient corresponding to ρ=0.88. The compatibility of these results with CP symmetry is 1.4 and 3.8 standard deviations for D^{0}→K^{-}K^{+} and D^{0}→π^{-}π^{+} decays, respectively. This is the first evidence for direct CP violation in a specific D^{0} decay.

Search for CP violation in {D}_{(s)}^{+} → K−K+K+ decays

A search for direct CP violation in the Cabibbo-suppressed decay {D}_s^{+} → K−K+K+ and in the doubly Cabibbo-suppressed decay D+ → K−K+K+ is reported. The analysis is performed with data collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 5.6 fb−1. The search is conducted by comparing the {D}_{(s)}^{+} and {D}_{(s)}^{-} Dalitz-plot distributions through a model-independent binned technique, based on fits to the K−K+K+ invariant-mass distributions, with a total of 0.97 (1.27) million {D}_s^{+} (D+) signal candidates. The results are given as p-values for the hypothesis of CP conservation and are found to be 13.3% for the {D}_s^{+} → K−K+K+ decay and 31.6% for the D+→ K−K+K+ decay. No evidence for CP violation is observed in these decays.

Fingerprinting CP-violating New Physics with B → Kμ+μ−

The B → Kℓ+ℓ− system is particularly interesting to explore physics beyond the Standard Model. Such effects could provide new sources of CP violation, thereby giving rise to Wilson coefficients which could not only be real, as assumed in most analyses, but also be complex. We propose a new strategy to extract the complex C9μ, C10μ from the data, utilising the complementarity of direct CP violation in B+ → K+μ+μ− and mixing-induced CP violation arising — in addition to direct CP violation — in {B}_d^0to {K}_S{mu}^{+}{mu}^{-} , as well as the differential rate in appropriate q2 bins. The long-distance effects, which play a key role to generate the direct CP asymmetries, cannot be reliably calculated due to their non-perturbative nature. In order to describe them, we apply a model by the LHCb Collaboration employing experimental data. Assuming specific scenarios, we demonstrate the fingerprinting of CP-violating New Physics and the distinction between ambiguities in the model of the long-distance contributions. Finally, New Physics could couple differently to muons and electrons, as probed through the lepton flavour universality ratio RK. We discuss these effects in the presence of CP violation and present a new way to measure the direct CP asymmetries of the B → Ke+e− channels.

Angular analysis of the low K+K− invariant mass enhancement in B+→K+K−π+ decays

We study the decay B+→K+K−π+ and investigate the angular distribution of K+K− pairs with invariant mass below 1.1 GeV/c2. This region exhibits both a strong enhancement in signal and very large direct CP violation. We construct a coherent sum model for the angular distribution of the S- and P-wave, and report the ratio of their amplitudes, the relative phase and the forward-backward asymmetry. We also report absolute differential branching fractions and direct CP asymmetry for the decay in bins of MK+K− and the differential branching fractions in bins of MK+π−. The results are based on a data sample that contains 772×106 BB¯ pairs collected at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e− collider. The result favors the presence of S- and D-waves in low MK+K− region to the detriment of a P-wave.1 MoreReceived 24 June 2022Accepted 3 February 2023DOI:https://doi.org/10.1103/PhysRevD.107.032013Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBranching fractionHadronic decaysParticle decaysRare decaysPhysical SystemsMesonsPropertiesCP violationParticles & Fields

Direct CP violation in K → ππ decay on the lattice with periodic boundary conditions

Following our recent publication on direct CP violation and the ΔI = 1/2 rule in K → ππ decay, which was made with G-parity boundary conditions, we revisit this problem with a conventional lattice setup employing periodic boundary conditions and two lattice spacings to check our previous result and to improve the precision. We show that the physical amplitude, which corresponds to an excited state in this case, can be obtained reliably with the Generalized Eigenvalue Problem (GEVP) method. Not only are periodic boundary conditions cheaper and allow the use of existing ensembles to take the continuum limit, but they provide a straightforward path to introduce electromagnetism and strong isospin symmetry breaking, which will be needed in the near future. In this article we show our preliminary results and discuss the prospect of the high-precision calculation of K → ππ decay with periodic boundary conditions.

Kaon processes in general 2HDM

We discuss new physics (NP) contributions to kaon mixing parameter εK , direct CP violation parameter ε′/ε of K → ππ, and rare decays , and KL,S → μ+μ− in the context of general two Higgs doublet model. We focus on contributions of top quark related exotic couplings, and show that simultaneous presence of flavor conserving and flavor violating interactions can lead to large NP effects in kaon sector, while being consistent with the stringent constraints from B physics observables such as mixing, Bs → μ+μ−, and b → sγ. We stress on the importance of correlations between εK , and Bs → μ + μ − that can be exploited to distinguish the parameter space corresponding to a light (sub-TeV) or heavy (TeV) scale charged Higgs boson.

Strange processes in general two Higgs doublet model

In the general two Higgs doublet model (g2HDM) that has extra Yukawa couplings, we analyze their New Physics (NP) contributions to kaon mixing parameter εK, direct CP violation parameter ε′/ε, and rare {K}^{+}to {pi}^{+}nu overline{nu} , {K}_Lto {pi}^0nu overline{nu} , and KL,S→ μ+μ− decays. We study correlations between these observables, and call special attention to a unique complementarity of kaon mixing and rare Kto pi nu overline{nu} decays in probing the exotic Higgs mass spectrum of g2HDM. The importance of kaon physics in probing NP vis-à-vis B physics is stressed. One unexpected feature we uncover is the special sensitivity of {K}^{+}to {pi}^{+}nu overline{nu} to TeV scale charged Higgs boson.

Insights into the nature of X(3872) through B meson decays* *Supported by the National Natural Science Foundation of China (11347030) and the Program of Science and Technology Innovation Talents in Universities of Henan Province (14HASTIT037)

We study the decays in the perturbative QCD (PQCD) approach, involving the puzzling resonance , where P represents a light pseudoscalar meson (K or π). Assuming to be a charmonium state, we obtain the following results. (a) The branching ratios of the and decays are consistent with the results predicted by the covariant light-front approach within errors; however, they are larger than those given by the generalized factorization approach. (b) The branching ratio of the decay is predicted as , which is smaller than the previous PQCD calculation result but still slightly larger than the upper limits set by Belle and BaBar. Hence, we suggest that the decays should be precisely measured by the LHCb and Belle II experiments to help probe the inner structure of . (c) Compared with the decays, the decays have significantly smaller branching ratios, which drop to values as low as . (d) The direct CP violations of these considered decays are small () because the penguin contributions are loop suppressed compared to the tree contributions. The mixing-induced CP violation of the decay is highly consistent with the current world average value %. Experimentally testing the results for the branching ratios and CP violations, including the implicit and isospin symmetries of these decays, helps probe the nature of .

Direct CP violation of three body decay processes from the resonance effect* *Supported by National Natural Science Foundation of China (11605041)

The physical state of mesons can be mixed using the unitary matrix. The decay processes and originate from isospin symmetry breaking. The , , and interferences lead to a resonance contribution to produce strong phases. violation is considered from isospin symmetry breaking due to the new strong phase of the first order. violation can be enhanced greatly for the decay process when the invariant masses of pairs are in the area around the resonance range and resonance range in perturbative QCD. We also discuss the possibility of searching for the predicted violation at the LHC.

Direct CP violation and the ΔI= 1/2 rule inK→ππdecay in the Standard Model

We discuss the RBC & UKQCD collaborations’ recent [1] lattice calculation of ϵ′, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4× the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the ΔI= 1/2 rule, and present our plans for future calculations.

Lattice determination of I=0 and 2 ππ scattering phase shifts with a physical pion mass

Phase shifts for $s$-wave $\pi\pi$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to\pi\pi$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $\pi\pi$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $\pi\pi$ interpolating operators including a scalar bilinear "$\sigma$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

A Review of CP Violation Measurements in Charm at LHCb

The LHCb experiment has been able to collect the largest sample ever produced of charm-hadron decays, performing a number of measurements of observables related to CP violation in the charm sector. In this document, the most recent results from LHCb on the search of direct CP violation in D0→Ks0Ks0, D(s)+→h+π0 and D(s)+→h+η decays are summarised, in addition to the most precise measurement of time-dependent CP asymmetry in D0→h+h− decays and the first observation of mass difference between neutral charm-meson eigenstates.

Recent results on branching fraction and CP asymmetry in B → ϕϕK decays

We present precise measurements of the branching fraction and CP-violation asymmetry in the B meson system, specifically in the charmless decays B → ϕϕK, ϕ → K+K−. This study is based on the full ϒ(4S) data set of 772×106BB‾ pairs collected by the Belle detector at KEKB asymmetric energy e+e− collider. These decays are mediated by the b → s flavor-changing neutral current (FCNC) transition, which could exhibit large CP violations due to interference of potential new-physics amplitudes appearing in the quantum loop with the b → c tree-level transition of B → ηcK, ηc → ϕϕ. Therefore, an observation of direct CP violation in B → ϕϕK decays would be a clear sign of physics beyond the standard model. In addition to being an NP probe, the decay is sensitive to possible production of glue-ball candidate that later decays as ξ → ϕϕ. Our results obtained with nine times larger statistics and refined analysis techniques significantly improve upon, and supersede, the Belle's earlier result with due consideration of the nonresonant K+K− contribution underneath the ϕ resonance.

In BLMSSM * *Supported by National Natural Science Foundation of China (11805140, 11347185, 11905002), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2017113), Natural Science Foundation of Shanxi Province (201801D221021, 201801D221031), Natural Science Foundation of Hebei Province (A2020201002), the China Scholarship Council (201906935031)

Applying the effective Lagrangian method, we study the flavor changing neutral current process within the minimal supersymmetric extension of the Standard Model, where baryon and lepton numbers are local gauge symmetries. Constraints on the parameters are investigated numerically with the experimental data for the branching ratio of . Additionally, we present the corrections to direct CP-violation in and time-dependent CP-asymmetry in . With appropriate assumptions on the parameters, we find the direct CP-violation is very small, while one-loop contributions to can be significant.

The \(\varepsilon '/\varepsilon \)-story: 1976–2021

The ratio $\epsilon'/\epsilon$ measures the size of the direct CP violation in $K_L\to\pi\pi$ decays $(\epsilon^\prime)$ relative to the indirect one described by $\epsilon$ and is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years. Due to the smallness of $\epsilon'/\epsilon$ its measurement required heroic efforts in the 1980s and the 1990s on both sides of the Atlantic with final results presented by NA48 and KTeV collaborations 20 years ago. Unfortunately, even 45 years after the first calculation of $\epsilon'/\epsilon$ we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics contributions to this ratio. This is due to significant non-perturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. While the significant control over the short distance perturbative effects has been achieved already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to $\epsilon'/\epsilon$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $\epsilon'/\epsilon$ is very significant. My own work on $\epsilon'/\epsilon$ started in 1983 and involved both perturbative and non-perturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of $\epsilon'/\epsilon$ including several historical remarks not known to everybody. The present status of the $\Delta I=1/2$ rule is also summarized. This story is dedicated to Jean-Marc Gerard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.

Bd,s0→f1f1 decays with f1(1285)−f1(1420) mixing in the perturbative QCD approach

We investigate the $B_{d,s}^0 \to f_1 f_1$ decays in the framework of perturbative QCD(PQCD) approach with a referenced value $\phi_{f_1} \sim 24^\circ$. Here, $f_1$ denotes the axial-vector mesons $f_1(1285)$ and $f_1(1420)$ with mixing angle $\phi_{f_1}$ in the quark-flavor basis. The observables such as branching ratios, direct CP violations, and polarization fractions of the $B_s^0 \to f_1 f_1$ decays are predicted for the first time. We find that: (i) the almost pure penguin modes $B_s^0 \to f_1 f_1$ have large branching ratios in the order of $10^{-6} \sim 10^{-5}$ due to the Cabibbo-Kobayashi-Maskawa enhancement and generally constructive interferences between the amplitudes of $B_s^0 \to f_n f_s$ and $B_s^0 \to f_s f_s$ with $f_n$ and $f_s$ being the quark-flavor states of $f_1$ mesons; (ii) The observables receive important contributions from the weak annihilation diagrams in the PQCD approach. In particular, without the annihilation contributions, the $B_s^0 \to f_1(1420) f_1(1420)$ branching ratio will decrease about 81% and its longitudinal polarization fraction will reduce around 43%. And (iii) the dependence of the $B_{d,s}^0 \to f_1 f_1$ decay rates on $\phi_{f_1}$ exhibits some interesting line shapes, whose confirmations would be helpful to constrain the determination of $\phi_{f_1}$ inversely. All the PQCD predictions await for the (near) future examinations at Large Hadron Collider beauty and/or Belle-II experiments to further understand the properties of the axial-vector mesons and the perturbative dynamics released from the considered decay modes.

Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model

We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to\pi\pi$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to\pi\pi$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi\pi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$\Delta I = 1/2$ rule" enhancement.