Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

Based on the diquark model, we assume that the light scalar mesons are q^2q^-2 states rather than qq^-. The chiral effective Lagrangian for the light scalar meson is constructed, and the mass relations are obtained： the isotriplet （a0） and the isosinglet （f0） are the heaviest and are degenerate, the isodoublets （κ） are heavier and the other isosinglet （σ） is the lightest; and 2Mκ^2 = Mα0^2＋ Mσ^2. Using experimental value for a0 and σ mass, we obtain Mκ=794 MeV, which is consistent with the experimental value. Then taking Г（a0^0 →ηπ^0） = 90 MeV and Г（f0→π^0π^0） = 20 MeV, we get the width of σ is： Г（σ0→π^＋π^-）= 150 MeV.

KLOE results on scalar and pseudoscalar mesons

The data collected by the KLOE Collaboration at the Frascati φ-factory DAФNE from 2001 to 2006 have been used for extensive studies in meson spectroscopy. The decays of the scalar mesons a0（980） and f0（980） into two pseudoscalar mesons have been exploited to measure the relevant parameters of those resonances. The radiative decays φ →ηγ and η＇γ have been used for the determination of the pseudoscalar mixing angle and to search for a possible gluonium content in the η＇. The dynamics of the η → 3π decay has been studied and the Dalitz Plot parameters have been measured. The large amount of η mesons produced allowed also to study interesting rare η decays.

Dynamical study of light scalar mesons below 1GeV in a flux-tube model

The light scalar mesons below 1GeV configured as tetraquark systems are studied in the framework of the flux-tube model. Comparative studies indicate that a multi-body confinement,instead of the additive two-body confinement, should be used in a multiquark system.The σ and κ mesons could be well accommodated in the diquark-antidiquark tetraquark picture, and could be colour-confinement resonances. The a0（980） and fo（980） mesons are not described as KK molecular states and ns diquark-antidiquark states.However, the mass of the first radial excited state of the diquark-antidiquark state, nn is 1019 MeV,is close to the experimental data of the fo （980）.

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states ao（980）, f0（980）,k, within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the ＂fall apart＂ mechanism.

Scalar mesons and glueballs in D_p-D_q hard-wall models

We investigate the light scalar mesons and glueballs in the Dp-Dq hard-wall models, including D3-Dq, D4-Dq, and D6-Dq systems. It is found that only in the D4-D6 and D4-Ds hard-wall models are the predicted masses of the clq scalar meson fo scalar glueball consistent with their experimental or lattice results. This indicates that D4-D6 and D4-Ds hard-wall models are the favorite candidates of the realistic holographic QCD model.

Chiral Lagrangian Treatment of 0^＋＋ Mesons and 0^＋＋ Glueballs

Within the framework of a nonlinear chiral Lagrangian the mass spectra and the decay properties of 0^＋＋ states below 2 GeV are studied. Assuming that f0（980）, a0（980）, K0（1430）, and f0（1500） comprise an SU（3） nonet, we make a detailed prediction about the static properties of the 0^＋＋ mesons. The substructure analysis of these states in terms of two- and four-quark components as well as a glueball component is carried out. We also consider the interaction Lagrangian and provide a preliminary study of the strong and radiative decays of the 0＋＋ mesons. The scalar glueball masses and partial widths are also presented. In view of the fact that few data of 0＋＋ mesons are clearly given in the present PDG （Particle Data Group） list and that the four-quark content of mesons is a hot issue both experimentally and theoretically, the predicted results of the paper may be helpful for upcoming experimental and theoretical studies of these mesons.

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.

B→a_0(1450)ρ(ω) Decays in Perturbative QCD Approach

In the two-quark model supposition for the meson ao（1450）, which can be viewed as either the first excited state （scenario I） or the lowest lying state （scenario II）, the branching ratios and the direct CP-violating asymmetries for decays B→a0（1450）ρ（ω） are studied by employing the perturbative QCD factorization approach. We find the following results： （a） For the decays B- B→a0（1450）ρ- andB→a0^＋（1450）ρ^-, their branching ratios have large difference between two scenarios. Although their branching ratios are larger than other considered decay modes, their direct CP-violating asymmetries in both scenarios are small. （b） For the decays B-→a0^-（1450）ρ0 and B0→ a0（1450）ρ＋, a0^0（1450）ρ0, a00 （1450）w, their branching ratios are dose to each other between two scenarios, respectively. （c） Comparing with the decays a0^0（1450）ρ0,π0ρ0 π0π0, the decay B-→a0^-（1450）ρ0 receives a larger branching ratio in each scenario, which is sensitive to the variation of the Cabibbo-Kobayashi-Maskawa angle α.

Nature of light scalars through photon-photon collisions

The surprising thing is that arising almost 50 years ago from the linear sigma model （LSM） with spontaneously broken chiral symmetry, the light scalar meson problem has become central in the nonperturbative quantum chromodynamics （QCD） for it has been made clear that LSM could be the low energy realization of QCD. First we review briefly signs of four-quark nature of light scalars. Then we show that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq mesons that are produced via two-quark transitions γγ→qq. Thus we get new evidence of the four-quark nature of these states.

Scalar meson spectroscopy with a fine lattice

With sufficiently light u and d quarks the isovector （a0） and isosinglet （f0） scalar meson propagators are dominated at large distances by two-meson states. In the staggered fermion formulation of lattice QCD, taste-symmetry breaking causes a proliferation of multihadron states that complicates the analysis of these channels. Of special interest is the bubble contribution, which makes a considerable contribution to these channels. Using numerical simulation we have measured the correlators for both a0 and f0 channels in the ＂Asqtad＂ improved staggered fermion formulation in a MILC fine （a = 0.09 fm） lattice ensemble. We analyze those correlators using rooted staggered chiral perturbation theory （rSxPT） and achieve chiral couplings that are well consistent with previous determinations.

Bubble contributions to scalar correlators with mixed actions

Within mixed-action chiral perturbation theory （MAxPT）, Sasa＇s derivation of the bubble contribution to scalar a0 meson is extended to those of scalar K and o- mesons. We revealed that the K bubble has two double poles and the （~ bubble contains a quadratic-in-t2 growth factor stemming from the multiplication of two double poles for a general mass tuning of valence quarks and sea quarks. The corresponding preliminary analytical expressions in MAxPT with 2＋1 chiral valence quarks and 2＋1 staggered sea quarks will be helpful for lattice studies of scalar mesons.

I=1/2 low-lying mesons in lattice QCD

Using a conventional constituent-quark model, I = 1/2 scalar K, vector K＊（892）, and axial vector K1 mesons are studied in the asqtad-improved staggered fermion with wall-source and point-sink interpolators. The mass ratio of mK/mz＊（892） is numerically confirmed to apparently vary with quark mass, and the experimental ordering mK.（892） 〉 mK holds elegantly when the light u/d quark masses are sufficiently small, while the valence strange quark mass is fixed to its physical value. We also get reasonable signals for the K1 meson suggested by the SCALAR Collaboration from lattice QCD. The computations are conducted with the MILC Nf=3 flavor gauge configurations at three lattice spacings： a≈0.15, 0.12, and 0.09 fm.

Multiquark states and the mixing of scalar meson

In order to describe Kaon-Nucleon scattering data, the mixing of scalar meson σ0 and σs must be introduced in the chiral SU（3） quark model. Inspired by this, now the mixing of scalar meson is further considered to study some interesting dibaryons in the chiral SU（3） quark model. The results show that the mixing of scalar meson has different effects on these dibaryons.

A Study of Effects from a_(0)(980)Meson to Asymmetric Matter Based on a Parity Doublet Model

In the present work,we study the effect of the isovector scalar meson a_(0)(980)(also calledδ)to the asymmetric matter properties by constructing a parity doublet model with including the a_(0)(980)meson based on the approximate chiral U(2)_(L)×U(2)_(R)symmetry.The effect of a_(0)(980)to the properties of symmetric matter such as symmetry energy S(n_(B)),symmetry incompressibility K_(sym),symmetry skewness Q_(sym)is investigated.We find that,a_(0)(980)meson has significant effect to these nuclear matter properties especially when the chiral invariant mass of nucleon m_(0)is small.We also study the effect of the a_(0)(980)meson to the neutron star(NS)properties and find that it increase the radius of NSs,especially those having intermediate mass.Finally,we further constrain the value of the chiral invariant mass of the nucleon to 640 MeV≲m_(0)≲860 MeV for L_(0)=57:7MeV by comparing with the recent accepted value of K_(sym)and neutron star(NS)observational data.

Pure annihilation decays of B^(s)_(0)→a^(+)_(0)a^(−)_(0)and B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0)in the PQCD approac

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays of B^(s)_(0)→a^(+)_(0)a^(−)_(0)and B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0),where a_(0)[K^(∗)_(0)]denotes the scalar a_(0)(980)and a_(0)(1450)[K^(∗)_(0)(800)(orκ)and K^(∗)_(0)(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_(0)and K^(∗)_(0)states.The numerical results show that the branching ratios of the B^(0)_(d)→K^(∗+)_(0)K^(∗−)_(0)decays are in the order of 10^(−6),while the decay rates of the B^(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^(0)_(d)→K^(+)k_(-)and B^(0)_(s)→π^(+)π_(−),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱexperiments in the(near)future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudesφ^(S)andφ^(T)with inclusion of the Gegenbauer polynomials for the scalar a_(0)(1450)and K^(∗)_(0)(1430)states in scenario 2 contribute slightly to the branching ratios while significantly to the CP violations in the B^(0)_(d)→K^(∗)_(0)(1430)+K^(∗)_(0)(1430)−and B^(0)_(s)→a_(0)(1450)+a_(0)(1450)−decays,which indicates that,compared to the asymptoticφ^(S)andφ^(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.

Production representation of partial wave scattering amplitudes and the fo（600） particle

The establishlnent of production representation of partial wave scattering alnplitudes is reviewed in the context of quantum field theory. Its relation to the production representation, or Ning Hu representation in quantum mechanical scattering theory is pointed out. One of the most important application of the production representation is the physics of the fo（600） and K（700） scalar hadron resonances, on which we also give a brief review. It is emphasized that all evidences accunmlated so far are consistent with the picture that the fo（600） meson is the chiral partner of the Nambu Goldstone bosons in a linear realization of chiral symmetry.

B→f_0(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（Bˉ^0 → f0（980） π^0） ～ 2.6×10^-7,Br（Bˉ^0 → f0（980） η） ～ 2.5×10^-7 and Br（Bˉ^0 → f0（980） η ） ～ 6.7×10^-7,which are consistent with both the QCD factorization predictions and the experimental upper limits.

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

Based on the assumption of two-quark structure of the scalar meson K0^＊（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→K0^＊（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_s → f_0 (980) Transition Form Factors Within the k_T Factorization Approach

In the paper, we apply the kT factorization approach to deal with the B8 → fofo（980） transition form factors in the large recoil regions, i.e. the small q2 regions. For the purpose, we adopt the B-meson wave-functions ЖB, ЖB and that include the three-Fock states contributions to do our discussion. Although the scalar meson fo（980） is widely perceived as the 4-quark bound state （scenario 2）, but the distribution amplitudes of 4-quark states are still unknown to us, so we adopt 2-quark model （scenario 1） for scalar meson fo（980） in our discussion. By varying the B-meson wave-function parameters within their reasonable regions, we obtain Fo（0） = F＋（0） = 0.20 ± 0.02, FT（O） = 0.24 4± 0.02. Our present results for these form factors are consistent with the light-cone sum rule results obtained in the literature.

Searching for a_(0)(980)-meson parton distribution function

In this paper,we calculate the scalar a_(0)(980)-meson leading-twist wave function by using the light-cone harmonic oscillator model(LCHO),where the model parameters are determined by fitting theξ-moments■of its light-cone distribution amplitudes.Then,the a_(0)(980)-meson leading-twist light-cone distribution amplitudes with three different scalesζ=(1.0,2.0,5.2)Ge V are given.After constructing the relationship between the a_(0)(980)-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wave function,we exhibit the■(x,ζ)and■(x,ζ)with different scales.Furthermore,we also calculate the Mellin moments of the a_(0)(980)-meson’s valence quark distribution function■with n=(1,2,3),i.e.■=0.027,■=0.018 and■=0.013.Finally,the scale evolution for the ratio of the Mellin moments x■are presented.