S-wave contributions to ■→(D~0,■)π~+π~- in the perturbative QCD framework

■→(D~0,■)π+π-is induced by the b→c■s/b→u■s transitions,which can interfere if a CP-eigenstate DCP is formed.The interference contribution is sensitive to the CKM angle y.In this work,we study the S-wave π+π-contributions to the process in the perturbative QCD factorization.In the factorization framework,we adopt twomeson light-cone distribution amplitudes,whose normalization is parametrized by the S-wave time-like two-pion form factor with resonance contributions from f_0(500),f_0(980),f_0(1500),f_0(1790).We find that the branching ratio of ■→(D~0,■)(π~+π~-)S is of the order of 10~(-6),and that significant interference exists in ■→D_(CP)(π+π-)S.Future measurement could not only provide useful constraints on the CKM angle y,but would also be helpful for exploring the multi-body decay mechanism of heavy mesons.     

P-wave contributions to B_((s))→ψKπ decays in perturbative QCD approach

We study the quasi-two-body decays B_((s)) ψ[K~*(892) K~*(1410) K~*(1680)] ψKπ by employing the perturbative QCD(PQCD) factorization approach, where the charmonia ψ represents J/ψ and ψ(2S). The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude(DA) Φ_(Kπ)~P, which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor F_(Kπ) appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account,which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of B_((s)) ψK~*(892) ψKπ are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for B_((s)) ψ[K~*(1410) K~*(1680)] ψKπ modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle Ⅱ experiments.     

B→（J/ψ,η_c）K decays in the perturbative QCD approach

In this paper,we calculated the B →（J/ψ,ηc） K decays in the perturbative QCD（pQCD） factorization approach with the inclusion of the partial next-to-leading order（NLO） contributions. With the inclusion of the significant enhancement from the NLO vertex corrections,the NLO pQCD predictions for the branching ratios agree with the data within 2σ errors：Br（B0 → J/ψK0） = 5.2-＋32..58×10-4,Br（B＋ → J/ψK＋） = 5.6-＋32..79×10-4,Br（B0 →ηcK0） = 5.5-＋22..30 × 10-4,Br（B＋ →ηcK＋） = 5.9-＋22..51 × 10-4.     

Study of the process e~+e~- →π~+π~-π~0π~0 at energies s～(1/2)<1 GeV

In an experiment with the Spherical Neutral Detector at VEPP-2M collider the cross section of the process e+e-→π+π-π0π0 was measured.At energies s～(1/2)920 MeV this cross section was measured for the first time.The energy dependence of the cross section is well discribed by the vector dominance model with contributions from ρ,ρ,ρ mesons.The decay probability ρ→π+π-π0π0 was found to be Bρ =(1.60±0.74±0.18)×10-5.The upper limit for the decay ω→π+π-π0π0 was improved by two orders of magnitude compared to the previous measurements and is Bω 2×10-4 at 90% confidence level.     

Phenomenological studies on B~0 → [K~-π~+]_(S/V)[π~+π~-]_(V/S) → K~-π~+π~+π~- decay

Within the quasi-two-body decay model,we study the localized CP violation and branching fraction of the four-body decay B~0→[K~-π~+]_(s/V)[π~+π~-]_(V/)S→K-π~+π~-π~+ when the K~-π~+and π~-π~+ pair invariant masses are0.35 m(K~-π~+)2.04 GeV and 0 mπ~-π~+1.06 GeV,with the pairs being dominated by the K_0~*(700)~0,K~*(892)~0,K~*(1410)~0,K_0~*(1430) and K~*(1680)~0,and fo(500),ρ~0(770),ω(782) and fo(980) resonances,respectively.When dealing with the dynamical functions of these resonances,fo(500),ρ~0(770),fo(980) and K_0~*(1430) are modeled with the Bugg model,Gounaris-Sakurai function,Flatte formalism and LASS lineshape,respectively,while the others are described by the relativistic Breit-Wigner function.Adopting the end point divergence parameters ρA ∈[0,0.5] andΦ_A∈[0,2π],our predicted results are F_(CP)(B~0→K~-π~+π~+π~-)∈[-0.365,0.447] and B(B~0→K-π~+π~+π~-)∈[6.11,185.32] x 10~(-8),based on the hypothetical qq structures for the scalar mesons in the QCD factorization approach.Meanwhile,we calculate the CP violating asymmetries and branching fractions of the two-body decays B~0→SV(VS) and all the individual four-body decays B~0→SV(VS)→K~-π~+π~-π~+,respectively.Our theoretical results for the two-body decays B~0→K~*(892)~0 fo(980),B~0→K_0~*(1430)~0ω(782),B~0→K~*(892)~0 f~0(980),B~0→K_0~*(1430)~0ρ,and B~0→(1430)~0ω are consistent with the available experimental data,with the remaining predictions await testing in future high precision experiments.     

A test of CPT symmetry in K~0 vs ■~0 →π~+π~-π~0 decays

I show that the CP-violating asymmetry in K0 vs K0 →π+π-π0 decays differs from that in KL →π+π-,KL →π0π0 or the semileptonic KL transitions,if there exists CPT violation in K0-K0 mixing.A delicate measurement of this difference at a super flavor factory(e.g.,the φ factory) will provide us with a robust test of CPT symmetry in the neutral kaon system.     

Constraining the UT angle γ by CP violation parameters in B~0→π~+π~-

We calculate the tree and penguin amplitudes in the B~0→π~+π~-decay channel employing the perturbative QCD factorization approach. Using the amplitudes as input with the theoretical uncertainties sufficiently considered, we constrain the UT angle γ to 53°γ 70°, from the measurements of the CP violation parameters C_(π~+π~-) and S_(π~+π~-)in B~0→π~+π~-. The U-spin breaking effect between B~0→π~+π~-and B~0 s →K~+K~-is estimated to be around 30%.     

Study of the a_1(1260) resonance in the γp→π~+π~+π~-n reaction

Within an effective Lagrangian approach and resonance model, we study the γp→a_1(1260)~+n andγp→π~+π~+π~-n reactions via the π-exchange mechanism. For the γp→π~+π~+π~-n reaction, we perform a calculation of the differential and total cross-sections by considering the contributions of the a1(1260) intermediate resonance decaying into per and then into π~+π~+π~-. Besides,the non-resonance process is also considered. With a lower mass of a1(1260), the experimental data for the invariant π~+π~+π~-mass distributions can be fairly well reproduced. For theγp→a_1(1260)~+n reaction, with the model parameters, the total cross-section is of the order of 10 μb at the photon beam energy Eγ~2.5 GeV. It is expected that the model calculations in this work could be tested by future experiments.     

Pure annihilation type D→PP(V) decays in the perturbative QCD approach

The annihilation type diagrams are di cult to calculate in any kind of model or method. Encouraged by the successful calculation of pure annihilation type B decays in the perturbative QCD factorization approach, we calculate the pure annihilation type D→PP(V) decays in the perturbative QCD approach based on the k_T factorization. Although the expansion parameter 1/m_D is not very small, our leading order numerical results agree with the existing experimental data for most channels. We expect more accurate observation from experiments, which can help us learn about the dynamics of D meson weak decays.     

Short-distance CP-violating contributions to the KL→π0e+e− decay

New constributions to the K_L→π⁰e⁺e⁻ amplitude are presented. Short-distance penguin induced diagrams for the s→dγ¹ transition supplement the previously considered electromagnetic penguin. The new CP-violating amplitude corresponds to a new piece of the relevant anomalous dimension matrix. Strong interaction corrections to the new part of the effective hamiltonian are calculated in the leading logarithmic approximation. The role of subleading terms is also discussed.     

Pure annihilation decays of B_s~0→a_0~+a_0~- and B_d~0→K_0~(*+)K_0~(*-) in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays ofB _s~0→a_0~+a _0~-andB _d~0→K_0~(*+)K_0~(*-),where a_0[K_0~*]denotes the scalar a_0(980) and a_0(1450)[K_0~*(800)(ork)and K_0~*(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_0and K_0~*states.The numerical results show that the branching ratios of theB _d~0→K_0~(*+)K_0~(*-)decays are in the order of 10~(-6),while the decay rates of theB_s~0→a_0~+a _0~-modes are in the order of 10~(-5).In light of the measured modes with the same quark components in the pseudoscalar sector,namely,B _d~0→K~+K~-and B_s~0→p p~(+-),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱ experiments in the (near) future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudes φ~S and φ~T with inclusion of the Gegenbauer polynomials for the scalar a_0(1450) and K_0~*(1430)states in scenario2 contribute slightly to the branching ratios while significantly to the CP violations in the B_d~0→K_0~*(14 30)~+K_0*(14 30)~-and B_s~0→a_0(1450)~+a_0(1450)~-decays,which indicates that,compared to the asymptotic φ~Sand φ~T,these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels.These predictions await for the future confirmation experimentally,which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.     

B→K_0~*(1430)η~(') decays in the pQCD approach

Based on the assumption of two-quark structure of the scalar meson K*0(1430),we calculate the CP-averaged branching ratios for B→K0*(1430)η(') decays in the framework of the perturbative QCD(pQCD) approach here.We perform the evaluations in two scenarios for the scalar meson spectrum.We find that:(a) the pQCD predictions for Br(B→K*0(1430)η(')) which are about 10-5-10-6,basically agree with the data within large theoretical uncertainty;(b) the agreement between the pQCD predictions and the data in Scenario I is better than that in Scenario II,which can be tested by the forthcoming LHC experiments;(c) the annihilation contributions play an important role for these considered decays.     

B→K_0~*(1430)η~(') decays in the pQCD approach

Based on the assumption of two-quark structure of the scalar meson K*0(1430),we calculate the CP-averaged branching ratios for B→K0*(1430)η(') decays in the framework of the perturbative QCD(pQCD) approach here.We perform the evaluations in two scenarios for the scalar meson spectrum.We find that:(a) the pQCD predictions for Br(B→K*0(1430)η(')) which are about 10-5-10-6,basically agree with the data within large theoretical uncertainty;(b) the agreement between the pQCD predictions and the data in Scenario ...     

B→(J/ψ,ηc)K decays in the perturbative QCD approach

In this paper, we calculated the B→(J/ψ,ηc)K decays in the perturbative QCD (pQCD) factoriza-tion approach with the inclusion of the partial next-to-leading order (NLO) contributions. With the inclusion of the significant enhancement from the NLO vertex corrections, the NLO pQCD predictions for the branching ra-tios agree with the data within 2σ errors: Br(B0→J/ψK0)=5.2+3.5-2.8×10-4,Br(B+→J/ψK+)=5.6+3.7-2.9×10-4,Br(B0→ηcK0)=5.5+2.3-2.0×10-4,Br(B+→ηcK+)=5.9+2.5-2.1×10-4.     

B→f0(980)(π,η') decays in the PQCD approach

Based on the assumption of a two-quark structure of the scalar meson f0(980), we calculate the branching ratios and CP-violating asymmetries for the four B→f0(980)π and B→f0(980)η(') decays by employing the perturbative QCD (Pqcd) factorization approach. The leading order Pqcd predictions for branching ratios are, Br(B-→f0(980)π-)～2.5×10-6, Br(B0→f0(980)πo)～2.6×10-7, Br(B0→f0(980)η)～ 2.5×10-7 and Br(B0→f0(980)η')～6.7×10-7, which are consistent with both the QCD factorization predictions and the experimental upper limits.     

Analysis of B → a_1(1260)(b_1(1235))K decays in the perturbative QCD approach

Within the framework of the perturbative quantum chromodynamics(PQCD) approach, we study the charmless two-body decays B → a_1(1260)K*, b_1(1235)K*. Using the decay constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results.(a) Our predictions for the branching ratios are consistent with the QCD factorization(QCDF) results within errors, but much larger than the naive factorization approach calculation values.(b) We predict that the anomalous polarizations occurring in the decays B→φK*, ρK*also happen in B→a_1 K*decays, while they do not happen in B→b_1 K*decays. Here the contributions from the annihilation diagrams play an important role in explaining the larger transverse polarizations in the B→a_1 K*decays, while they are not sensitive to the polarizations for the B→b_1 K*decays.(c) Our predictions for the direct C P-asymmetries agree well with the QCDF results within errors. The decaysˉB~0→b_1_+K*-, B-→b_1~0K*-have larger direct C P-asymmetries, which could be measured by the present LHCb experiment and the forthcoming Super-B experiment.     

Search for the doubly heavy baryons Ω_(bc)~0 and Ξ_(bc)~0 decaying to Λ_c~+π~- and Ξ_c~+π~-

The first search for the doubly heavy Ω_(bc)~0 baryon and a search for the Ξ_(bc)~0 baryon are performed using pp collision data collected via the LHCb experiment from 2016 to 2018 at a centre-of-mass energy of 13 TeV,corresponding to an integrated luminosity of 5.2 fb~(-1).The baryons are reconstructed via their decays to ∧_c~+π~-andΞ_c~+π~-.No significant excess is found for invariant masses between 6700 and 7300 MeV/c2,in a rapidity range from2.0 to 4.5 and a transverse momentum range from 2 to 20 MeV/c.Upper limits are set on the ratio of the Ω_(bc)~0 andΞ_(bc)~0 production cross-section times the branching fraction to ∧_c~+π~-(Ξ_c~+π~-) relative to that of the ∧_b~0(Ξ_b~0) baryon,for different lifetime hypotheses,at 95% confidence level.The upper limits range from 0.5×10~(-4) to 2.5×10~(-4) for theΩ_(bc)~0→∧_c~+π~-(Ξ_(bc)~0→∧_c~+π~-) decay,and from 1.4×10~(-3) to 6.9×10~(-3) for the Ω_(bc)~0→Ξ_c~+π~-(Ξ_(bc)~0→Ξ_c~+π~-) decay,depending on the considered mass and lifetime of the Ω_(bc)~0(Ξ_(bc)~0) baryon.     

D~0-~0 mixing sensitivity estimation at Belle II in wrong-sign decays D~0→K~+π~-π~0 via time-dependent amplitude analysis

The sensitivity of the D~0-~0 mixing parameters x and y is estimated in the wrong-sign decay D~0→K~+π~-π~0 by time-dependent amplitude analysis. The resolution of the D~0 lifetime is essential in time-dependent Dalitz analyses. The Belle II detector, which aims to collect a total integrated luminosity of 50 ab~(-1) of data, has σ = 140 fs in Monte Carlo studies, a factor of two improvement over that of Belle and Ba Bar, so the produced Dalitz signal Monte Carlo samples are smeared with this resolution. Then a time-dependent Dalitz plot fitting is performed on these smeared samples, and the sensitivity of D~0-~0mixing parameters are σ_x = 0.057% and σ_y = 0.049%. These are about an order of magnitude improvement on current experimental results, without considering background effects.     

TheK S 0 →π0 l + l − andK L 0 →π0 l + l − decays in the standard model and the extended Nambu-Jona-Lasinio model

TheK _S ^{0 0} l ⁺ l ^– andK _L ^{0 0} l ⁺ l ^– decays are considered within the framework of the Standard model in the one-photon exchange approximation, i.e.K _S,L ^{0 0}+ *⁰ +l ⁺ l ^–. To evaluate the low-energy matrix elements of theK ⁰(¯K ⁰)⁰+ * transitions, the constituentquark-loop approximation, based on the extended Nambu-Jona-Lasino (NJL) model, is used. The obtained results are compared with other theoretical estimates and the experimental bounds.