Theory of unitarity bounds and low-energy form factors

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K_l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.     

核物理中的手征微扰论

手征微扰论是基于量子色动力学的低能有效理论 ,已成为核物理和低能粒子物理研究的有力方法 .简单介绍了手征微扰论的基本概念、方法和应用 ,特别是近年来重子手征微扰论的形式发展和一些应用中的前沿问题. Chiral Perturbation Theory (CHPT), as a low-energy effective field theory based on QCD, is a powerful tool in the investigation of the nuclear and particle physics. We present an introduction to the basic idea, the method and the application of CHPT, and emphasize the recent development in the formalism and the application of baryon CHPT.     

Implications of unitarity and analyticity for the Dπ form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D → πlν. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(α _s ²) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low-energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the Dπ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.     

Exploring light-cone sum rules for pion and kaon form factors

We analyze the higher-twist effects and the SU(3)-flavor symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in an earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the weak transition form factors are predicted with accuracy. Received: 30 June 2002 / Published online: 7 October 2002 RID="a"     

Beyond the quark model of hadrons from lattice QCD

Lattice QCD can give direct information on OZI-violating contributions to mesons. Here we explore the contributions that split flavour singlet and non-singlet meson masses. I discuss in detail the spectrum and decays for scalar mesons (i.e. including glueball effects). I also review the status of hybrid mesons and their decays.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Gc Lattice QCD calculations - 12.39.Mk Glueball and nonstandard multi-quark/gluon states     

The Weak Form Factor in Heavy to Light Mesons

The weak form factor in heavy to light mesons is discussed. We have analyzed two different approaches: Bauer-Stech-Wirbel approach and the perturbative QCD approach. It is pointed out that the nonperturbative contribution dominates the weak form factor in heavy to light mesons.     

The contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen

In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into π,η mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.     

Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses

The meson spectrum of QCD is studied in the framework of nonperturbative QCD as a function of varying quark masses m _q . It is shown that the total spectrum consists of two branches: 1) the standard one, which may be called the flux-tube spectrum, depending approximately linearly on m _q , and 2) the chiral symmetry breaking (CSB) spectrum for pseudoscalar (PS) flavor nonsinglet mesons with mass dependence √m _q . The formalism for PS mesons is derived from the QCD Lagrangian with m _q corrections, and a unified form of the PS propagator was derived. It is shown that the CSB branch of PS mesons joins to the flux-tube branch at around m _q = 200 MeV. All these results are in close correspondence with recent numerical data on large lattices.     

Stringent constraints on the scalar K$ \pi$ form factor from analyticity,unitarity and low-energy theorems

We investigate the scalar K p \pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t = 0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher-order ChPT corrections at the second Callan-Treiman point.     

Semileptonic decays of charmed mesons in the effective action of QCD

Within the framework of phenomenological Lagrangians we construct the effective action of QCD relevant for the study of semileptonic decays of charmed mesons. Hence we evaluate the form factors of at leading order in the 1/N _C expansion and, by demanding their QCD-ruled asymptotic behavior, we constrain the couplings of the Lagrangian. The features of the model-independent parameterization of form factors are provided, and their relevance for the analysis of experimental data are pointed out. Received: 28 October 2002 / Published online: 24 January 2003     

Finite temperature effect in infrared-improved AdS/QCD model with back reaction of bulk vacuum

Based on an IR-improved soft-wall AdS/QCD model for mesons,which provides a consistent prediction for the mass spectra of resonance scalar,pseudoscalar,vector and axial-vector mesons,we investigate its finite temperature effect.By analyzing the spectral function of mesons and fitting it with a Breit-Wigner form,we perform an analysis for the critical temperature of mesons.The back-reaction effects of bulk vacuum are considered and the thermal mass spectral function of resonance mesons is calculated based on the back-reaction improved action.A reasonable melting temperature is found to be T_c≈150 ± 7 MeV.which is consistent with the recent results from lattice QCD simulations.     

Perturbative QCD analysis of B to π and B to ρ transitions

We calculate the form factors and of and V, , and of transition matrix elements by using the factorization formalism of perturbative QCD in the region . In the limit of , , and , the results show that and are of monopole type, V, and of dipole type, and of a combination of monopole and dipole types with dipole type dominating. Received: 20 April 1998 / Published online: 5 October 1998     

Unitarity and the BFKL pomeron

High energy onium-onium scattering is calculated as a function of impact parameter in the one- and two-pomeron exchange approximation. Difficulties with using the multiple scattering series to unitarize single pomeron exchange at high energy are noted. An operator formalism which sums all numbers of pomeron exchange is given. A toy model which has a similar operator structure at high energy as QCD is presented and the S-matrix is evaluated. Estimates of the energies and impact parameters at which blackness occurs in onium-onium scattering are given. It is emphasized that the problem of unitarity in high energy onium-onium scattering can be solved in a purely perturbative context, with a non-running coupling if the onium is heavy enough.     

Semileptonic Decays of Heavy Mesons to Light Pseudoscalar Mesons in the BS Formalism

The decay processes from heavy to light pseudoscalar mesons such as π, K, η,η' are studied in a relativistic constituent quark model based on the BS formalism. It is emphasized that the negative energy projector operators's contributions in the BS wavefunctions for light pseudoscalar mesons have to be considered. By taking into account these contributions, the previously encountered difficulties in calculating the decay constants and form factors are found to be removed. A11 the form factors for transitions such as D→π, D→K, D_s→K, D_s→η, D_s→η', B→π, B_s→K are estimated and the branching ratios for these semileptonic decays are calculated. The results of our calculations are consistent with experimental values.     

Improved bounds for the slope and curvature of form factors

We derive a theoretically allwed domain for the slope and curvature of the physical form factor appearing in the decay . Using heavy-quark symmetry, we relate this function to a particular form factor free of ground-state B_c poles below the threshold for BD production, for which almost model-independent constraints are derived from QCD using unitarity and analyticity. Our results are of interest for the extraction of |V_cb| from the recoil spectrum in exclusive semileptonic B decays. Making conservative estimates of the theoretical uncertainties, we find (up to 1/m_Q corrections) and . We also derive the corresponding bounds for the form factor in the decay .     

Measurement of diffractive photoproduction of vector mesons at large momentum transfer at HERA

Elastic and proton–dissociative photoproduction of , and vector mesons (, , respectively) have been measured in interactions at HERA up to GeV, where t is the four-momentum transfer squared at the photon–vector–meson vertex. The analysis is based on a data sample in which photoproduction reactions were tagged by detection of the scattered positron in a special-purpose calorimeter. This limits the photon virtuality, , to values less than 0.01 GeV, and selects a average center-of-mass energy of = 94 GeV. Results for the differential cross sections, , for , and mesons are presented and compared to the results of recent QCD calculations. Results are also presented for the t-dependence of the pion-pair invariant-mass distribution in the mass region and of the spin-density matrix elements determined from the decay-angle distributions. The Pomeron trajectory has been derived from measurements of the W dependence of the elastic differential cross sections for both and mesons. Received: 16 October 1999 / Revised version: 17 January 2000 / Published online: 6 April 2000     

Ds0DK vertex in QCD sum rules

We calculate the form factors and the coupling constant in the D_s0DK vertex in the framework of QCD sum rules. We evaluate the three point correlation functions of the vertex considering both D and K mesons off-shell. The form factors obtained are very different but give the same coupling constant.     

Constraints on the K_{l_3} form factors from analyticity and unitarity

The K?? form factors are investigated at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using as input the values of the form factors at t?=?0, and at the Callan?CTreiman point in the scalar case, stringent constraints are obtained on the slope and curvature parameters of the Taylor expansion at the origin.