Patterns of $C$- and $CP$-violation in hadronic $η$ and $η'$ three-body decays
Hakan Akdag, Tobias Isken, Bastian Kubis
备注：
43 pages, 9 figures, 5 tables; v2: discussion extended, version published in JHEP; v3: incorporates an erratum that fixes the phases of the C-violating norms by hermiticity and time reversal
We construct hadronic amplitudes for the three-body decays $η^{(\prime)}\toπ^+π^-π^0$ and $η'\toηπ^+π^-$ in a non-perturbative fashion, allowing for $C$- and $CP$-violating asymmetries in the $π^+π^-$ distributions. These amplitudes are consistent with the constraints of analyticity and unitarity. We find that the currently most accurate Dalitz-plot distributions taken by the KLOE-2 and BESIII collaborations confine the patterns of these asymmetries to a relative per mille level. Our dispersive representation allows us to extract the individual coupling strengths of the $C$- and $CP$-violating contributions arising from effective isoscalar and isotensor operators in $η^{(\prime)}\toπ^+π^-π^0$ and an effective isovector operator in $η'\toηπ^+π^-$, while the strongly different sensitivities to these operators can be understood from chiral power counting arguments.
Final-state rescattering effects on the hadronic B decays and their impact on direct CP violation are examined. The phenomenology of the polarization anomaly in $B\toϕK^*$ decays is discussed.
Weak interactions between quarks give rise to hadronic parity violation which can be observed in nuclear and few-nucleon systems. We study the QCD renormalization of the isotensor component of parity violation at next-to-leading order accuracy. The renormalization group is employed to evolve the interaction down to hadronic scales. As the results are renormalization scheme dependent, we compare various schemes, including 't Hooft-Veltman dimensional regularization, and several regularization independent-momentum subtraction schemes.
We compute contributions to the parity-violating (PV) inelastic electron-deuteron scattering asymmetry arising from hadronic PV. While hadronic PV effects can be relatively important in PV threshold electro- disintegration, we find that they are highly suppressed at quasielastic kinematics. The interpretation of the PV quasielastic asymmetry is, thus, largely unaffected by hadronic PV.
An effective field theory program to analyze and interpret hadronic parity violation in two-, three-, and few-nucleon systems is described. Observables can be parameterized in terms of five low-energy constants, which have to be determined from experimental input. Results for parity-violating observables in the two- and three-nucleon sectors are presented, including a discussion of the relevance of parity-violating three-nucleon interactions.
CP violating interactions are required to realize the matter abundance of our Universe. It is however known that the standard model of particle physics does not contain sufficient CP violation. The electric dipole moment (EDM) of atomic systems is a very sensitive experimental probe of CP violation beyond the standard model, and it is very actively studied in experiments. The atomic EDM has a significant sensitivity to hadronic CP violation, but its quantification has for long been obstructed by the nonperturbative physics of quantum chromodynamics. Quite recently, the contribution of the Wein…
Using a recent reformulation of the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT), we show how predictions for parity-violating observables in low-energy light hadronic systems can be understood in an analytic fashion. It is hoped that such an analytic approach may encourage additional experimental work as well as add to the understanding of such parity-violation phenomena, which is all too often obscured by its description in terms of numerical results obtained from complex two-body potential codes.
We discuss the quantitative impact of duality violations on the determination of the strong coupling constant from hadronic tau decays, based on a preliminary analysis of OPAL data.
These proceedings review direct CP violation in hadronic B decays. The experimental results include those related to the measurement of the unitarity triangle angle gamma using B->D(*)K(*) decays and measurements of charmless hadronic B decays. The results reported have been made by the BABAR, Belle and LHCb collaborations. Theoretical calculations related to these decays are also summarised. The importance of inputs from the charm sector in determining gamma from B->D(*)K(*) decays is discussed. In addition, the future prospects for these measurements will be reviewed.
The nucleon sigma term of the isoscalar and isovector quark chromo-magnetic dipole moments are essential inputs for the determination of the CP-odd pion-nucleon couplings induced by quark chromo-electric dipole moments. We demonstrate that the former can be mapped to the third moment of the nucleon twist-three chiral-odd distribution functions $e^q(x)$ which are in principle measurable in semi-inclusive deep inelastic scattering processes. We perform a survey on existing model calculations as well as experimental data on $e^u(x)+e^d(x)$ and derive a predicted range for the isoscalar chromo-mag…
Within the Standard Model Effective Field Theory framework, with operators up to dimension 6, we perform a model-independent analysis of the lepton-flavour-violating processes involving tau leptons. Namely, we study hadronic tau decays and $\ell$--$τ$ conversion in nuclei, with $\ell = e,μ$. Based on available experimental limits, we establish constraints on the Wilson coefficients of the operators contributing to these processes. Our work paves the way to extract the related information from Belle II and foreseen future experiments.
The CP violating Weinberg operator (or the gluon chromo-electric dipole moment) is generated in many candidates of new physics beyond the standard model, and it contributes to observables such as the electric dipole moments (EDM) of the neutron, nuclei and atoms. In this proceedings contribution, we review the present understanding of the Weinberg operator as well as the result of the estimation of its effect to the EDM of $^3$He nucleus through the contact CP-odd nuclear force.
There are different approaches for the hadronic B decay calculations, recently. In this paper, we upgrade three of them, namely factorization, QCD factorization and the perturbative QCD approach based on $k_T$ factorization, by using new parameters and full wave functions. Although they get similar results for many of the branching ratios, the direct CP asymmetries predicted by them are different, which can be tested by recent experimental measurements of B factories.
We discuss the scalar meson mixing scenario and present an OZI rule violation mechanism for understanding the scalar productions in charmoium hadronic decays. We stress that the OZI violation could play a key role in disentangling the structure of the scalars: $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$.
We motivate lattice QCD studies of the parity-violating pion-nucleon coupling constant and extend flavor-conserving hadronic parity-violation from QCD to partially-quenched QCD. The parity-violating pion-nucleon coupling and the anapole form factor (and moment) of the proton are computed to one-loop order in the partially-quenched chiral expansion. For the parity-violating pion-nucleon interaction, we include the contributions from total derivative operators necessary to match the kinematics that will be used in lattice simulations.
Within the Standard Model Effective Field Theory framework, with operators up to dimension 6, we perform a model-independent analysis of the lepton-flavour-violating processes involving tau leptons. Namely, we study hadronic tau decays and $\ell$-$τ$ conversion in nuclei ($\ell=e,μ$). Based on available experimental limits, we establish constraints on the Wilson coefficients of the operators contributing to these processes. The related information from Belle II and foreseen future experiments can be easily incorporated into the resulting framework.
Studies of the strangeness changing hadronic weak interaction have produced a number of puzzles that have so far evaded a complete explanation within the Standard Model. Their origin may lie either in dynamics peculiar to weak interactions involving strange quarks or in more general aspects of the interplay between strong and weak interactions. In principle, studies of the strangeness conserving hadronic weak interaction using parity violating hadronic and nuclear observables provide a complementary window on this question. However, progress in this direction has been hampered by the lack of a…
We review recent results on hadronic B meson decays including rare as well as non-suppressed decays. The main emphasis is on those channels relevant to measurement of CP violation in the coming B factories. After briefly describing flavor-tagged charm counting, we cover B -> DK(*), B -> charmless 2-body decays, inclusive eta' production, and final-state-interaction phases in B -> Psi K* and B -> D* rho.
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bou…
We study hadronic and leptonic flavor physics in a SUSY SO(10) model proposed by Chang, Masiero, and Murayama, which links b -> s transitions to the observed large atmospheric neutrino mixing angle. We find large effects in B_s-B_s-bar mixing and BR(tau -> mu gamma) and comment on B_d -> phi K_S.
Three different methods, using $B_d\to J/ψK_S$, $J/ψK_S π^0$, $B_d\to K^-π^+, π^+π^-$ and $B_u\to K^- π^0, \bar K^0 π^-, π^-π^0$, to extract hadronic model independent information about new physics are discussed in this talk.
The flavor-conserving non-leptonic weak interaction can be studied experimentally through the observation of parity violation in nuclear and few-body systems. At hadronic scales, matrix elements of parity-violating four-quark operators ultimately give rise to the parity violating couplings between hadrons, and such matrix elements can be calculated non-perturbatively using lattice QCD. In this work, we investigate the running of isovector parity-violating operators from the weak scale down to hadronic scales using the renormalization group. We work at next-to-leading order in the QCD coupling,…
I present two disparate examples of isospin violation in hadronic B-decays. In the first, the presence of ρ^0-ωmixing in the decay B^\mp\toρ^\mpρ^0(ω)\toρ^\mpπ^+ π^- permits the extraction of sgn(\sin α), where αis the usual angle of the unitarity triangle, with minimal hadronic uncertainty. In the second, the presence of π^0-η,η' mixing can obscure the extraction of \sin 2αfrom an isospin analysis in B\toππdecays.
We study the rare decays $B_s^0\to D^\pm π^\mp$ and $\bar B_s^0\to D^\mp π^\pm$, which can occur only via annihilation type $W$ exchange diagrams in the standard model. The time-dependent decay rates of the four channels can provide four CP parameters, which are experimentally measurable. We show that the CKM angle $ϕ_3=γ$ can be determined from these parameters without any theoretical model dependence. These channels can be measured in future LHCb experiments to provide a clean way for $γ$ measurement.
In this talk I discuss three different methods, using B_d to J/psi K_S, J/psi K_s pi^o, B_d to K^- pi^+, pi^+ pi^- and B_u to K^- pi^0, bar K^0 pi^- pi^- pi^0, to extract hadronic model independent information about new physics.
We discuss a preliminary study of the impact of duality violations on extractions from tau decay data of the D=6 VEVs which determine chiral limit Standard Model K-->pi pi matrix elements of the electroweak penguin operators.
We present here the computation of electrical and thermal conductivity by solving the Boltzmann transport equation in relaxation time approximation. We use the $q$-generalized Boltzmann distribution function to incorporate the effects of non-extensivity. The behaviour of these quantities with changing temperature and baryochemical potential has been studied as the system slowly moves towards thermodynamic equilibrium. We have estimated the Lorenz number at NICA, FAIR and the top RHIC energies and studied as a function of temperature, baryochemical potential and the non-extensive parameter, $q$…
In the study of CP violation within and beyond the Standard Model of particle physics, pure hadronic B decays are the key players. Improving the determination of the CKM angle $γ$ is one of the important tasks in this endeavour. Besides, the full description of pure hadronic decays due to their strong interaction dynamics remains one of the challenges. In this summary, we discuss the recent results and progress on $γ$ determinations and direct CP violation in pure hadronic B decays as presented at CKM 2018.
We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging ($ΔS=0$) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the $W$ to the ${\cal O}(2\,\rm GeV)$ energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators …
Hadronic parity violation: successes, challenges, and future prospects
University of Kentucky（肯塔基大学）；University of Toronto（多伦多大学）；TRIUMF（特里厄姆夫国家粒子加速器中心）；Indiana University（印第安纳大学）；IU Center for Spacetime Symmetries（印第安纳大学时空对称性中心）
By choosing two typical input parameter points in the minimal supergravity (mSUGRA) model and using the QCD factorization (QCDF) approach, we studied the supersymmetric effects to the CP violation of the two-body charmless hadronic $B$ meson decays. We found that though the SUSY contributions can give large corrections to the CP asymmetries for some decay channels, they could not be distinguished experimentally from the SM values because of the large theoretical errors dominated by calculating the annihilation contributions in the QCDF approach.
There are some indications from recent determinations of the strong coupling constant alpha_s and the gluon condensate that the Operator Product Expansion may not be accurate enough to describe non-perturbative effects in hadronic tau decays. This breakdown of the Operator Product Expansion is usually referred to as being due to ``Duality Violations.'' With the help of a physically motivated model, we investigate these duality violations. Based on this model, we argue how they may introduce a non-negligible systematic error in the current analysis, which employs finite-energy sum rules with pi…
The fourth generation can give the correct trend of S_{phi K^0}, S_{pi^0 K^0} < sin2phi_1/beta, as indicated by data, and the effect, being largely leading order, is robust against hadronic uncertainties. The effect on S_{eta' K^0}, however, is diluted away by hadronic effects, and S_{eta' K^0} \simeq sin2phi_1/beta is expected. The near maximal arg[V^*_{t's}V_{t'b}] \lesssim 90^\circ that is needed could resolve the unequal direct CP violation seen in B -> K^+ pi^- and K^+ pi^0 modes, and is consistent with b ->s l^+l^- and B_s mixing constraints.
Axions and other pseudoscalar fields comprise an interesting class of ultralight dark matter candidates, that may independently play a role in solving the strong $CP$ problem. In the presence of $CP$-violating sources, these pseudoscalar fields can develop a coherent non-derivative coupling to nucleons, $\bar g_{aNN}$, thus mediating `mass-mass' and `mass-spin' forces in matter that can be probed experimentally. We revisit the non-perturbative generation of these $CP$-odd axion forces, and refine estimates of $\bar g_{aNN}$ generated by the EDMs and color EDMs of quarks. We also revisit the St…
The history and phenomenology of hadronic parity nonconservation (PNC) is reviewed. We discuss the current status of the experimental tests and theory. We describe a re-analysis of the asymmetry for polarized proton-proton scattering that, when combined with other experimental constraints and with a recent lattice QCD calculation of the weak pion-nucleon coupling, reveals a much more consistent pattern of PNC couplings. In particular, isoscalar coupling strengths are similar to but somewhat larger than the "best value" estimate of Donoghue, Desplanques, and Holstein, while both lattice QCD and…
Evidence is presented for the necessity of including duality violations in a consistent description of spectral function moments employed in the precision determination of $α_s$ from $τ$ decay. A physically motivated ansatz for duality violations in the spectral functions enables us to perform fits to spectral moments employing both pinched and unpinched weights. We describe our analysis strategy and provide some preliminary findings. Final numerical results await completion of an ongoing re-determination of the ALEPH covariance matrices incorporating correlations due to the unfolding procedur…
A way of circumventing the gauge and infrared problems with effective Wilson coefficients is shown. Implications of experimentally measured charmless $B$ decays are discussed.
We investigate the correlations between the scalar meson configurations and Okuba-Zweig-Iizuka (OZI) rule violations in the hadronic decays of heavy quarkonia, e.g. $J/ψ$ and $Υ$, into isoscalar vector meson ($ϕ$ and $ω$) and scalar mesons ($f_0(1710)$, $f_0(1500)$, and $f_0(1370)$). It shows that the dramatic change of the values of the branching ratio fraction of $ϕf_0/ωf_0$ from low (e.g. in $J/ψ$ decays) to high energies (e.g. in $Υ$ decays) will not only test the glueball-$Q\bar{Q}$ mixings, but also provide important information about the mysterious OZI-rule violations within the scalars…
Motivated by the recent observation of CP violation in the charm sector by LHCb, we study direct CP asymmetries in the standard model (SM) for the singly Cabibbo-suppressed two-body hadronic decays of charmed mesons using the topological-diagram approach. In this approach, the magnitude and the phase of topological weak annihilation amplitudes which arise mainly from final-state rescattering can be extracted from the data. Consequently, direct CP asymmetry $a_{dir}^{\rm (tree)}$ at tree level can be reliably estimated. In general, it lies in the range $10^{-4}<a_{dir}^{\rm (tree)}<10^{-3}$. Sh…
In the framework of precision experiments, the search for electric dipole moments and the precise determination of magnetic dipole moments (g-2) have since long been of prime interest. Hadronic decays offer the best accuracy, since only the kinematic information carried by a single neutrino per decay is lost. Thus, they reveal more easily precious information on the helicity of the initial tau lepton. However, in contrast to one- or two-body hadronic final states, the description of hadronic multi-body final states depends on the model for the hadronic current. In this work, we determine how t…
The extraction of CKM-matrix-element information from hadronic B-decays generally suffers from discrete ambiguities, hampering the diagnosis of physics beyond the Standard Model. We show that a measurement of the rate asymmetry, which is CP-violating, in $B^{\pm}\toρ^{\pm}ρ^0(ω)\toρ^{\pm}π^+π^-$, where the invariant mass of the $π^+π^-$ pair is in the vicinity of the $ω$ resonance, can remove the mod($π$) uncertainty in $α\equiv arg [-V_{td} V_{tb}^\ast/(V_{ud}V_{ub}^\ast)]$ present in standard analyses.
Orbital angular momentum is crucial for the description of several process at large momentum transfer in the impulse approximation in perturbative QCD. We review the mechanism of independent scattering which makes violation of the helicity conservation rule possible at leading order - and without any need to flip a quark helicity - in exclusive hadron-hadron reactions. We argue that helicity flip form factors, which violate the factorization assumptions of conventional approaches and are classified as ``higher-twist," are nevertheless calculable to leading order in perturbative QCD when inform…
Using the next-to-leading order low energy effective Hamiltonian, the CP asymmetries for the $B_{c}$ meson decays into meson pair are calculated in the spectator approximation. We do not compute the hadronic matrix elements directly, instead, we use the amplitude ratios to estimate the CP asymmetries. This is quite,different from the previous works in the literature. The values of the momentum squared carried by the virtual particles in timelike penguin dirgrams are also carefully discussed. From our calculated results, the best decay modes to observe CP violation in $B_{c}$ decays would be $B…
Some rare hadronic decays of B mesons, such as B->pi K, are sensitive to isospin-violating contributions from physics beyond the Standard Model. Although commonly referred to as electroweak penguins, such contributions can often arise through tree-level exchanges of heavy particles, or through strong-interaction loop diagrams. The Wilson coefficients of the corresponding electroweak penguin operators are calculated in a large class of New Physics models, and in many cases are found not to be suppressed with respect to the QCD penguin coefficients. Several tests for these effects using observab…
We examine CP violation in the Delta S=0 decays tau -> omega pi nu_tau and tau -> a_1 pi nu_tau and the Delta S=1 decay tau -> K pi pi nu_tau. We assume that the new physics is a charged Higgs. We show that sizeable CP-violating effects are possible in tau -> a_1 pi nu_tau (polarization-dependent rate asymmetry) and tau -> omega pi nu_ tau (triple-product asymmetry). The Delta S=1 decay tau -> K pi pi nu_tau can proceed via several resonances. We construct two modified rate asymmetries and a triple product asymmetry for this decay and discuss the potential sensitivities of these asymmetries.
If any violation of Lorentz symmetry exists in the hadron sector, its ultimate origins must lie at the quark level. We continue the analysis of how the theories at these two levels are connected, using chiral perturbation theory. Considering a two-flavor quark theory, with dimension-4 operators that break Lorentz symmetry, we derive a low-energy theory of pions and nucleons that is invariant under local chiral transformations and includes the coupling to external fields. The pure meson and baryon sectors, as well as the couplings between them and the couplings to external electromagnetic and w…
The SM predictions for CP violating effects in D meson systems are highly suppressed at the per mill level. Therefore, any experimental evidence for a sizable CP violation in D0-D0bar mixing would unambiguously point towards a New Physics (NP) signal. Within supersymmetric scenarios, the popular alignment models can naturally account for large, non-standard effects in D0-D0bar mixing. We demonstrate that, within alignment models, detectable CP violating effects in D0-D0bar mixing would unambiguously imply a lower bound for the electric dipole moment (EDM) of hadronic systems, like the neutron …
We discuss why, in the determination of $α_s(m_τ^2)$ from hadronic $τ$ decays, two important assumptions made in most of previous analyses, namely the neglect of higher-dimension condensates and of Duality Violations (DVs), have introduced uncontrolled systematic errors into this determination. Although the use of pinched weights is usually offered as a justification of these assumptions, we explain why it is not possible to simultaneously suppress these two contributions; particularly since the Operator Product Expansion is expected to be an asymptotic, rather than a convergent expansion. The…
A short review of our recent work on amplitude parametrizations of three-body hadronic weak $B$ and $D$ decays is presented. The final states are here composed of three light mesons, namely the various charge $πππ$, $Kππ$ and $KK\bar K$ states. These parametrizations are derived from previous calculations based on a quasi-two-body factorization approach where the two-body hadronic final state interactions are fully taken into account in terms of unitary $S$- and $P$-wave $ππ$, $πK$ and $K \bar K$ form factors. They are an alternative to the isobar-model description and can be useful in the int…
Probing the three-body force in hadronic systems with specific charge parity
Beihang University（北京航空航天大学）；Lanzhou University（兰州大学）；École Centrale de Pékin/School of General Engineering, Beihang University（北京航空航天大学中法工程师学院/通用工程学院）；Peng Huanwu Collaborative Center for Research and Education, Beihang University（北京航空航天大学彭桓武研究中心）；Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University（北京航空航天大学先进核材料物理北京市重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We consider CP-violating effects in tau -> 3 pi nu_ tau and 4 pi nu_ tau (Delta S = 0), and tau -> K pi pi nu_tau (Delta S = 1), assuming that the usual Standard Model amplitudes for these processes interfere with analogous amplitudes mediated by a charged Higgs boson. In the Delta S = 0 case we focus specifically on the intermediate resonant processes tau -> V pi nu_tau (with V=omega, rho, and a_1), and consider three CP-odd observables -- the partial rate asymmetry, a polarization-dependent asymmetry and a triple-product asymmetry. In the Delta S = 1 case we examine the partial rate asymmetr…
Experiments searching for the electric dipole moment (EDM) of the electron $d_e$ utilise atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to $d_e$. If the source of $CP$ violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce $CP$-odd semileptonic interactions, parametrised by the Wilson coefficient $C_{SP}$, and provide the dominant source of EDMs in paramagnetic systems instead of $d_e$. We evaluate the $C_{SP}$ coefficients …
The parity-violating nucleon-nucleon (NN) potential is considered up to next-to-next-to leading order in heavy-baryon chiral perturbation theory. We include one-pion exchange at leading order and the two-pion exchange and two-nucleon contact terms at next-to-next-to-leading order. The effects of intermediate (two-pion exchange) and short-range (two-nucleon contact) terms are probed by calculating the photon asymmetry $A_γ$ in $\vec{n} p \to d γ$ employing Siegert's theorem and an accurate phenomenological potential for the parity-conserving NN interaction. We explore in detail the uncertaintie…
Using the spectral functions measured in $τ$ decays, we investigate the actual numerical impact of duality violations on the extraction of the strong coupling. These effects are tiny in the standard $α_s(m_τ^2)$ determinations from integrated distributions of the hadronic spectrum with pinched weights, or from the total $τ$ hadronic width. The pinched-weight factors suppress very efficiently the violations of duality, making their numerical effects negligible in comparison with the larger perturbative uncertainties. However, combined fits of $α_s$ and duality-violation parameters, performed wi…
It has been pointed out recently that current low-energy constraints still allow for sizable flavor-changing decay rates of the 125 GeV boson into leptons, h -> tau ell (ell= e, mu). In this work we discuss the role of hadronic tau-lepton decays in probing lepton flavor violating couplings in the Higgs sector. At low energy, the effective Higgs coupling to gluons induced by heavy quarks contributes to hadronic tau decays, establishing a direct connection with the relevant process at the LHC, pp (gg)-> h -> tau ell. Semileptonic transitions like tau -> ell pi pi are sensitive to flavor-changing…
