The two-body hadronic decays of B_c meson in the perturbative QCD approach:a short review

Along with the running of Large Hadron Collider(LHC)located at CERN in November 2009,a large number of data samples of Bc meson have been collected and some hadronic Bc decay modes have been measured by the LHC experiments.In view of the special and important roles of Bc meson decays playing in the heavy flavor sector,we here give a short review on the status of two body hadronic decays Bc!M1M2at both experimental and theoretical aspects.For the theoretical progresses,specifically,we will show lots of theoretical studies on two body hadronic Bcdecays involving pseudoscalar,vector,scalar,axial-vector,even tensor meson(s)in the final states by employing the perturbative QCD(pQCD)factorization approach.We will present a general analysis about the twobody hadronic decays of the heavy Bc meson and also provide some expectations for the future developments.

The semileptonic decays of B/B_s meson in the perturbative QCD approach:a short review

In this short review,we present the current status about the theoretical and experimental studies for some important semileptonic decays of B=Bsmesons.We firstly gave a brief introduction for the experimental measurements for B=Bs!Peltl;l ml;m mT decays,the BaBar’s ReDT and ReD T anomaly,the P05deviation for B0!K 0ltl decay.We then made a careful discussion about the evaluations for the relevant form factors in the light-cone QCD sum rule,the heavy quark effective theory,and the perturbative QCD factorization approach.By using the form factors calculated in the perturbative(pQCD)approach,we then calculate and show the pQCD predictions for the decay rates of many semileptonic decays of B=Bsmesons.We also made careful phenomenological analysis for these pQCD predictions and found,in general,the following points:(a)For all the considered B=Bssemileptonic decays,the next-to-leading order pQCD predictions for their decay rates agree well with the data and those from other different theoretical methods;(b)For ReDT and ReD T,the pQCD predictions agree very well with the data,the BaBar’s anomaly of ReDe TT are therefore explained successfully in the standard model by employing the pQCD approach;and(c)We defined several new ratios Rl;s Dand Rl;s Ds,they may be more sensitive to the QCD dynamics which controls the B=Bs!eDe T;De T sT transitions than the old ratios,we therefore strongly suggest LHCb and the forthcoming Super-B experiments to measure these new ratios.

Semileptonic decays B→D^(*) lυ in the perturbative QCD factorization approach

In this paper,we study the B→D^(*) l-l -ι semileptonic decays and calculate the branching ratios B(B→D^(*) l-l -ι) and the ratios R(D^(*)) and R_D^( l,s) by employing the perturbative QCD(pQCD)factorization approach.We find that(a)for R(D)and R(D*)ratios,the pQCD predictions are R(D)=0.430-0.026?0.021,R(D*)=0.301±0.013 and agree well with BaBar’s measurements of ReD e?T T;(b)for the newly defined R_D^1 and R_D^s ratios,the pQCD predictions are R_D^l=0.450-0.051+0.064 and R_D^s=0.642-0.070+0.081,which may be more sensitive to the QCD dynamics of the considered semileptonic decays than R(D^(*)) and should be tested by experimental measurements.

The B→D^(*)lv_l decays in the pQCD approach with the Lattice QCD input

In this decays B → D^（＊）l^-vl paper, we studied by using the the semileptonic ＂pQCD ＋ Lattice QCD＂ method. We made the extrapolation for the six relevant form factors by using the input values obtained from the pQCD factorization approach in the low q2 region of 0 ≤ q^2≤≤mt^2 and the lattice QCD input at the endpoint q^2 = q^2max· We then calculated the ratios R（D） and R（D^＊） of the branching ratios B（B→ D^（＊）l^-vl） and found numeri- cally that （1） the ＂pQCD ＋ Lattice QCD＂ predictions for the branching ratios B（B → D^（＊）l^-vl） agree well with the measured values within one standard deviation; and （2） the ＂pQCD ＋ Lattice QCD＂ predictions for the ratios R（D^（＊）） are R（D） =0.037-0.037^＋0.038 and R（D^＊） = 20269-03020^＋03021;they agree with the data within 2σ deviation, in other words, one can explain the ＂R（D（^＊）-puzzle＂ in the framework of the Standard Model.

Semileptonic decays B/Bs→(D^(?),D^(?)s)lνl in the PQCD approach with the lattice QCD input

We study the semileptonic B/Bs→(D^(?),D^(?)s)lνl decays in the framework of the Standard Model(SM),by employing the perturbative QCD(PQCD)factorization formalism combined with the lattice QCD input for the relevant transition form factors.We calculate the branching ratios B(B(s)→D^(?)(s)lνl)with l=(e,μ,τ),the ratios of the branching fractions R(D^(?))and R(D^(?)s),and the physical observables Pτ(D^(?)(s)),FL(D?(s))and AFB(τ).The“PQCD+Lattice”predictions for B(B→D^(?)lνl)and R(D^(?))agree with the available experimental measurements within errors.For the ratios R(Ds)and R(D^?s),the"PQCD+Lattice"predictions agree with the other predictions.For Pτ(D^?)and FL(D^?),our theoretical predictions agree with the measured values within errors.Our theoretical predictions of the semileptonic B/Bs decays considered could be tested in the near future by the LHCb and Belle II experiments.

Semileptonic decays B_c■(η_c, J/ψ)l■_l in the “PQCD+Lattice” approach

We study the semileptonic decaysBc-→(ηc,J/ψ)l-■lusing the PQCD factorization approach with the newly defined distribution amplitudes of the B c meson and a new kind of parametrization for extrapolating the form factors which takes into account the recent lattice QCD results.We find the following main results:(a)the PQCD predictions of the branching ratios of theBc→(ηc,J/ψ)l■decays are smaller by about 5%-16%when the lattice results are taken into account in the extrapolation of the relevant form factors;(b)the PQCD predictions of the ratio Rηc,RJ/ψand of the longitudinal polarization PτareRηc=0.34±0.01,RJ/ψ=0.28±0.01,Pτ(ηc)=0.37±0.01and Pτ(J/ψ)=-0.55±0.01;and(c)after including the lattice results,the theoretical predictions slightly change:Rηc=0.31±0.01,RJ/ψ=0.27±0.01,Pτ(ηc)=0.36±0.01andPτ(J/ψ)=-0.53±0.01.The theoretical predictions of RJ/ψagree with the measurements within the errors.The other predictions could be tested by the LHCb experiment in the near future.

The PQCD approach towards to next-to-leading order:A short review

In this short review we elaborate the significance of resummation in kτ factorization theorem,and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD(PQCD)approach.We also comment on the current sta-tus of the PQCD approach and highlight some key issues to develop it in the near future for more phenomenological applications.

S-wave resonance contributions to B(s)^0→ηc(2S)π^+π^-in the perturbative QCD factorization approach

By employing the perturbative QCD（PQCD） factorization approach, we study the quasi-two-body B（s）^0→ηc（2S）π^＋π^- decays, where the pion pair comes from the S-wave resonance f0（X）. The Breit-Wigner formula for the f0（500） and f0（1500） resonances and the Flatt′e model for the f0（980） resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes. As a comparison, Bugg＇s model is also used for the wide f0（500） in this work. For decay rates, we found the following PQCD predictions：（a）-B（Bs^0 →ηc（2S）f0（X）[π^＋π^-]s）= 2.67-1.08^＋1.78 ×10^-5 when the contributions from f0（980） and f0（1500） are all taken into account;（b）B（B0→η-c（2S）f0（500）[π^＋π^-]s） = 1.40（-0.56）（＋0.92） ×10^-6 in the Breit-Wigner model and 1.53（-0.61）^（＋0.97） ×10^-6 in Bugg＇s model.

Charmless two-body B meson decays in the perturbative QCD factorization approach

The perturbative quantum chromodynamics(PQCD)approach based on k_(T)factorization has resulted in great achievements in the QCD calculation of hadronic B decays.By regulating the endpoint divergence by the transverse momentum of quarks in the propagators,one can perform the perturbation calculation for various diagrams,including annihilation type diagrams.In this paper,we review the current status of the PQCD factorization calculation of two-body charmless B→PP,PV,VVU.decays up to next-to-leading order(NLO)QCD corrections.Two new power suppressed terms in the decaying amplitudes are also considered.Using universal input(non-perturbative)parameters,we collect the branching ratios and CP asymmetry parameters of all charmless two body B decays,which are calculated in the PQCD approach up to NLO.The results are compared with those of the QCD factorization approach,soft-collinear effective theory approach,and current experimental measurements.For most of the considered B meson decays,the PQCD results for branching ratios agree well with those of other approaches and experimental data.The PQCD predictions for the CP asymmetry parameters of many of the decay channels do not agree with those of other approaches but have better agreement with experimental data.The longstanding Kπpuzzle regarding the pattern of the direct CP asymmetries of penguin-dominated B→Kπdecays can be understood after the inclusion of NLO contributions in PQCD.The NLO corrections and power suppressed terms play an important role in color suppressed and pure annihilation type B decay modes.These rare decays are more sensitive to different types of corrections,providing an opportunity to examine the factorization approach with more precise experimental measurements.

Rescattering mechanism of weak decays of double-charm baryons

The doubly charmed baryon■cc++was recently observed by LHCb via the decay processes of■cc++→∧+cK^(-)π^(+)π^(+)and■c+π^(+).These discovery channels were successfully predicted in a framework in which the short-distance contributions are calculated under the factorization hypothesis and the long-distance contributions are estimated using the rescattering mechanism for the final-state-interaction effcts.In this paper,we illustrate the above framework in detail by systematic studies on the tw o-body baryonic decays Bcc→BcP involving the doubly charmed baryons Bcc=(■cc++,■cc++,Ωcc+),the singly charmed baryons Bc=(B3,B6)and the light pseudoscalar mesons P=(π,K,η1,8).

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)]ψKπby employing the perturbative QCD(PQCD)factorization approach,where the charmoniaψrepresents J/ψandψ(2S).The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude(DA)ΦKπP,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 FKπappearing 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)ψKπare accommodated by tuning hadronic parameters for the kaon-pion DAs.The PQCD predictions for B(s)ψ[K*(1410)K*(1680)]ψKπmodes from the same set of parameters can be tested by precise data obtained in the future from LHCb and BelleⅡexperiments.