What do we learn from the ρ-π puzzle

The experimental observation indicates that the branching ratio of ψ→ρπ is very small while the ρ-π channel is a main one in J/ψ decays.To understand the puzzle,various interpretations have been proposed.Meanwhile according to the hadronic helicity selection rule,this decay mode should be suppressed.Numerical calculations are needed to determine how it is suppressed.We calculate the branching ratios of J/ψ→ρπ and ππ in the framework of QCD.The results show that the branching ratios are proportional to [(Mu+md)/(mJ/ψ)]2 for the ρπ mode and [(Mu-md)/(mJ/ψ)]2 for the ππ mode which is isospin violated.The theoretical prediction of the ratio of J/ψ→ρπ is smaller than data,but not too small to invoke a completely new mechanism.Thus the puzzle is still standing even though we learn much knowledge towards the puzzle and this will help to finally interpret the puzzle and then gain a deeper insight to the heavy quarkonia.     

Further insights into the “ρπ puzzle”

Based on a systematic investigation of J/ψ(ψ) → VP,where V and P stand for light vector and pseudoscalar mesons,we identify the role played by the electromagnetic(EM) transitions and intermediate meson loop transitions,which are essential ingredients for understanding the J/ψ and ψ couplings to VP.We show that on the one hand,the EM transitions have relatively larger interferences in ψ→ρπ and K*K+c.c.as explicitly shown by vector meson dominance(VMD).On the other hand,the strong decay of ψ receives relatively larger destructive interferences from the intermediate meson loop transitions.By identifying these mechanisms in an overall study of J/ψ(ψ)→VP,we provide a coherent understanding of the so-called "ρπ puzzle".     

Study of the production of Λ_b~0 band ~0 hadrons in pp collisions and first measurement of the Λ_b~0→J/ψpK~- branching fraction

The product of the A_b~0(B~0) differential production cross-section and the branching fraction of the decay A_b~0→J/ψpK~-(B~0→J/ψK~*(892)~0) is measured as a function of the beauty hadron transverse momentum,p_T,and rapidity,y.The kinematic region of the measurements is p_T 20 GeV/c and 2.0y4.5.The measurements use a data sample corresponding to an integrated luminosity of 3fb~(-1) collected by the LHCb detector in pp collisions at centre-of-mass energies s~(1/2)=7 TeV in 2011 and s~(1/2)= 8TeV in 2012.Based on previous LHCb results of the fragmentation fraction ratio,f_∧_b~0/f_d,the branching fraction of the decay ∧_b~0→J/ψpK~- is measured to be B(∧_b~0→J/ψpK~-)=(3.17±0.04±0.07±0.34_(-0.28)~(+0.45)×10~(-4)where the first uncertainty is statistical,the second is systematic,the third is due to the uncertainty on the branching fraction of the decay B~0→J/ψK~*(892)~0,and the fourth is due to the knowledge of f_∧_b~0/f_d.The sum of the asymmetries in the production and decay between A_b and A_b~0 is also measured as a function of p_T and y.The previously published branching fraction of A_b~0→J/φpπ~-,relative to that of A_b~0→J/ψpK~-,is updated.The branching fractions of∧_b~0→P_c~+(→J/ψp)K~- are determined.     

Charmonium results from BES

Using ～ 14 × 10^6 ψ（2S） and ～ 58 × 10^ J/ ψ data collected at BES Ⅱ/BEPC, the branching fraction of ψ（2S）→Ω-Ω^＋ is measured with about 5a statistical significance. The A electric dipole and ∧ decay parameter are studied using the decay J/ψ →∧∧→ ppπ^＋π^-. Using （106±3）× 10^6 ψ（2S） decays collected at BESⅢ/BEPC Ⅱ, we have obtained some interesting physics results. The branching fractions of XcJ→π^0π^0, ηη are measured with precision improved. The mass and width of he（l^1P1） state, together with the branching fractions of Br（ψ（2S） →π^0hc） and Br（hc →γηc） are the first measurements. Surprisingly, the decays of Xc1→φφ, ωω, and ωφ are firstly observed in BESⅢ data.     

Further insights into the ＂ρπ puzzle＂

Based on a systematic investigation of J/ψ（ψ＇）→VP, where V and P stand for light vector and pseudoscalar mesons, we identify the role played by the electromagnetic （EM） transitions and intermediate meson loop transitions, which are essential ingredients for understanding the J/ψ and ψ＇ couplings to VP. We show that on the one hand, the EM transitions have relatively larger interferences in ψ＇→ρπ and K^＊^-K ＋c.c. as explicitly shown by vector meson dominance （VMD）. On the other hand, the strong decay of ψ＇ receives relatively larger destructive interferences from the intermediate meson loop transitions. By identifying these mechanisms in an overall study of J/ψ（ψ＇） → VP, we provide a coherent understanding of the so-called ＂ρπ puzzle＂.     

Study of pure annihilation decays Bd,s→DOD-O

Within the heavy quark limit and the hierarchy approximation Λqcd << Md << Mb,we analyze the B→DOD-O and Bs→ DOD-O decays,which occur purely via annihilation type diagrams.As a rough estimate,we calculate their branching ratios and CP asymmetries in the perturbative QCD (PQCD) approach.The branching ratio of B→ DOD-O is about 3.8×10-5 that is just below the latest experimental upper limit.The branching ratio of Bs→ DOD-O is about 6.8 × 10-4,which could be measured in LHC-b.From the calculation,it is found that this branching ratio is not sensitive to the weak phase angle γ.In these two decay modes,there exist CP asymmetries because of the interference between weak and strong interaction.However,these asymmetries are too small to be measured easily.     

Study of pure annihilation decays B_(d,s)→D~0~0

Within the heavy quark limit and the hierarchy approximation λQCD mD mB, we analyze the B → D00 and Bs → D00 decays, which occur purely via annihilation type diagrams. As a rough estimate, we calculate their branching ratios and CP asymmetries in the perturbative QCD (PQCD) approach. The branching ratio of B → D00 is about 3.8×10-5 that is just below the latest experimental upper limit. The branching ratio of Bs → D00 is about 6.8×10-4, which could be measured in LHC-b. From the calculation, it is found that this branching ratio is not sensitive to the weak phase angle γ. In these two decay modes, there exist CP asymmetries because of the interference between weak and strong interaction. However, these asymmetries are too small to be measured easily.     

B_u→ψM decays and S-D wave mixing effects

The B_u →ψM decays are studied with the perturbative QCD approach, where the psion ψ = ψ(2S),ψ(3770), ψ(4040) and ψ(4160), and the light meson M = π, K, ρ and K*. The factorizable and non-factorizable contributions, and the S-D wave mixing effects on the psions, are considered in the calculation. With appropriate inputs, the branching ratios for the B_u →ψK decays are generally coincident with the experimental data within errors. However, due to the large theoretical and experimental errors, it is impossible for the moment to give a severe constraint on the S-D wave mixing angles.     

Cabibbo-Suppressed Non-leptonic Decays of ∧c and Final State Interaction

With the diquark structure of ∧c, we investigate the branching ratio of ∧c→nπ^ and pπ^0. The results show that without considering the finM state interaction (FSI), the branching ratio of ∧c→pπ^0 is only of order 10^-6 whereas this ratio could reach 10^-4 and is at the same order as ∧c→nπ^ if taking into account the FSI effects. Concrete values depend on phenomenologicM parameters adopted in the calculations. These branching ratios can be measured in the experiments to come.     

Study ao（980）-f0（980） mixing in charmonium decays

In this proceeding, we propose to directly measure the a0^0（980）-f0 （980） mixing in J/ψ→φf0（980）→φa0^0（980） and Xc1→π^0a0^0（980） →π^0f0（980） with the upgraded Beijing Electron Positron Collider（BEPCII） with BESIII detector. We show that a narrow peak of about 8 MeV will be produced by the a0^0（980）-f0（980） mixing, and the predominant feature makes it standing out from the background contributions. The predicted branching ratios for these two reactions are both expected to be about O（10^-6）, which is unambiguously accessible with 10^9 J/ψ and 3 × 10^8 Xc1 at BESⅢ.     

Study of ππ final state interactions in ψ（2S） →π^＋π^-J/ψ

The π^＋π^ transition of heavy quarkonia in decay ψ（2S） →π^＋π^-J/ψ is studied. With the BESII data on the decay ψ（2S） →π^＋π^-J/ψ, we update the values of coupling constants （gi） and chromopolarizability （αψ（2s）J/ψ） in this process.     

Partial Wave Analysis of J/ψ Decays into ρρπ

The possible place to search for exotic states in J/ψ hadronic decays is in J/ψ→ρρπ. Because of the symmetry of identical particle and the symmetry of isospin, the physical analysis on this channel is quite complicated. In this paper, the method to use the partial wave analysis based on covariant helicity amplitude analysis to study the invariant mass spectrum of ρπ and to find the evidence of exotic states in ρπ spectrum is discussed. The decay amplitude for the decay sequence J/ψ→ρX, X →ρπ is given first. Then we discuss how to realize the identical particle symmetry and the isospin symmetry in the decay amplitude, which is the key point in the analysis of this channel. Then the total decay amplitude of this channel including all decay components is given. After that, how to identify the exotic states in the ρπ spectrum is discussed. What is discussed in this paper is the theoretical basis on experimentally searching for exotic states at BEPC/BES.     

Role of Electromagnetic Dipole Operator in the Electroweak Penguin Dominated Vector Meson Decays of B Meson

The pure annihilation type decays Dd^0→Фγand Bs→ργ receive only colour suppressed penguin contributions with a very small branching ratio in the standard model. When we include the previously neglected electromagnetic dipole operator, the branching ratios can be enhanced to R（^-Bd^0→Фγ）≈ 1×10^-11 and R（^-Bs→ργ）～（6 - 16） ×10^-10, which are one order magnitude larger than previous study using the QCD factorization approach. The new effect can also give a large contribution, of order 10^-9, to transverse polarization of B→Фρ and B →ωФ, which is comparable to the longitudinal part. These effects can be detected in the LHCb experiment and the super-B factories.     

Search for ψ(4S) → ηJ/ψ in B~±→ ηJ/ψK~± and e~+e~-→ ηJ/ψ processes

We search for the ψ(4S) state in the B~±→ηJ/ψK~± and e~+e~-→ηJ/ψ processes based on the Belle measurements with the assumed mass M =(4230±8) MeV/c~2 and width Γ =(38±12) MeV. No significant signal is observed in the ηJ/ψ mass spectra. The 90% confidence level upper limit on the product branching fraction B(B~±→ψ(4S)K~±)B(ψ(4S)→ηJ/ψ) 6.8×10~(-6) is obtained in the B~±→ηJ/ψK~± decays. By assuming the partial width of ψ(4S)→e~+e~-to be 0.63 ke V, a branching fraction limitB(ψ(4S)→ηJ/ψ) 1.3% is obtained at the 90%confidence level in e~+e~-→ηJ/ψ, which is consistent with the theoretical prediction.     

Partial Wave Analysis of J/ψ Decays into ρρπ

The possible place to search for exotic states in J/ψ hadronic decays is in J/ψ→ρρπ. Because of the symmetry of identical particle and the symmetry of isospin, the physical analysis on this channel is quite complicated. In this paper, the method to use the partial wave analysis based on covariant helicity amplitude analysis to study the invariant mass spectrum of ρπ and to find the evidence of exotic states in ρπ spectrum is discussed. The decay amplitude for the decay sequence J/ψ→ρX, X →ρπ is given first. Then we discuss how to realize the identical particle symmetry and the isospin symmetry in the decay amplitude, which is the key point in the analysis of this channel. Then the total decay amplitude of this channel including all decay components is given. After that, how to identify the exotic states in the ρπ spectrum is discussed. What is discussed in this paper is the theoretical basis on experimentally searching for exotic states at BEPC/BES.     

Supersymmetric contributions to B_s → K~-π~＋ decay

Recently,the CDF Collaboration has measured the branching fraction and time-integrated direct CP asymmetry of Bs → K-π＋ decay.The branching ratio is lower than the previous predictions based on QCD factorization.The experimental results favor a large CP asymmetry in Bs → K-π＋ decay while the standard model prediction is very small.We compute the supersymmetry contributions to Bs → K-π＋ decay using the mass insertion method,and find that the LR and RL mass insertions could suppress this branching ratio and increase this direct CP asymmetry well in line with the experimental data.     

Cabibbo-Suppressed Non-leptonic Decays of Ac and Final State Interaction

With the diquark structure of Ac, we investigate the branching ratio of Ac → nr and pro. The results show that without considering the final state interaction (FSI), the branching ratio of Ac → pπ0 is only of order 10-6 whereas this ratio could reach 10-4 and is at the same order as Ac → nr if taking into account the FSI effects. Concrete values depend on phenomenological parameters adopted in the calculations. These branching ratios can be measured in the experiments to come.     

Partial Wave Analysis of J/ψ Decays into ρρπ

The possible place to search for exotic states in J/ψ hadronic decays is in J/ψ →ρρπ. Because of the symmetry of identical particle and the symmetry of isospin, the physical analysis on this channel is quite complicated. In this paper, the method to use the partial wave analysis based on covariant helicity amplitude analysis to study the invariant mass spectrum of ρρπ and to find the evidence of exotic states in ρρπ spectrum is discussed. The decay amplitude for the decay sequence J/ψ→ρX, X →ρπ is given first. Then we discuss how to realize the identical particle symmetry and the isospin symmetry in the decay amplitude, which is the key point in the analysis of this channel. Then the total decay amplitude of this channel including all decay components is given. After that, how to identify the exotic states in the ρρπ spectrum is discussed. What is discussed in this paper is the theoretical basis on experimentally searching for exotic states at BEPC/BES.     

Charmonium results from BES

Using ～14×106ψ(2S) and ～58×106J/ψ data collected at BESⅡ/BEPC,the branching fraction of ψ(2S) →Ω+Ωˉ+ is measured with about 5σ statistical significance.The Λ electric dipole and Λ decay parameter are studied using the decay J/ψ→ΛΛ→ ppˉπ+π-.Using(106±3)×106 ψ(2S) decays collected at BESⅢ/BEPCⅡ,we have obtained some interesting physics results.The branching fractions of χcJ →π0π0,ηη are measured with precision improved.The mass and width of hc(11P1) state,together with the branching fractions of Br(ψ(2S) →π0hc) and Br(hc →γηc) are the first measurements.Surprisingly,the decays of χc1 →φφ,ωω,and ωφ are firstly observed in BESⅢ data.     

ρ-ω mixing in J/ψ→VP decays

The study of ρ-ω mixing has mainly focused on vector meson decays with isospin I = 1, namely theρ(ω)→π+π- process. In this paper, we present a study of ρ-ω mixing in ρ(ω)→π+π-π0(I = 0) using a flavor parameterization model for the J/ψ→VP process. By fitting a theoretical framework to PDG data, we obtain the SU(3)-breaking effect parameters sV = 0.03±0.12, sP = 0.17±0.17 and the ρ-ω mixing polarization operatorΠρω =(0.006±0.011) GeV2. New values are found for the branching ratios when the mixing effect is incorporated:Br(J/ψ→ωπ0)=(3.64±0.37)×10-4, Br(J/ψ→ωη)=(1.48±0.17)×10-3, Br(J/ψ→ωη)=(1.55±0.56)×10-4, these are different from the corresponding PDG2012 values by 19%, 15% and 15%, respectively.