Dispersive and chiral symmetry constraints on the light meson form factors

The form factors of the light pseudoscalar mesons are investigated in a dispersive formalism based on hadronic unitarity, analyticity and the OPE expansion of the QCD Green functions. We propose generalizations of the original mathematical techniques, suitable for including additional low energy information provided by experiment or Chiral Perturbation Theory (CHPT). The simultaneous treatment of the electroweak form factors of the and K mesons allows us to test the consistency with QCD of a low energy CHPT theorem. By applying the formalism to the pion electromagnetic form factor, we derive quite strong constraints on the higher Taylor coefficients at zero momentum, using information about the phase and the modulus of the form factor along a part of the unitarity cut. Received: 16 July 1999 / Published online: 6 March 2000     

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.     

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 .     

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.     

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.     

New constraints on the pion EM form factor using $ \Pi^{{ \prime}}_{}$(- Q2)

We study the constraints arising on the expansion parameters c and d of the pion electromagnetic form factor from the inclusion of pure spacelike data and the phase of timelike data along with one spacelike datum, using as input the first derivative of the QCD polarization amplitude (- Q ²) . These constraints when combined with other analyses, provide a valuable check on a determination of c due to Guo et al. and on our previous work where pionic contribution to the (g - 2) of the muon was used as the input. This work further illustrates the power of analyticity techniques in form factor analysis.     

General laws of hadron scattering at very high energies

We review the general properties of particle scattering at extremely high energy and fixed momentum transfer, concentrating on features which can be derived from analyticity, crossing symmetry, unitarity and other general principles. The progress since 1973 is reported; it is pointed out that the rigorous approach yields fairly tight high-energy correlations between the phase and the modulus of the crossing-even as well as the crossing-odd forward scattering amplitude, without assuming any particular model of the interaction mechanism. The approach becomes particularly predictive when the formalism is supplemented by the phenomenological assumption that the total cross section rises unboundedly at high energies. Relation of the results to existing hadron-hadron scattering data and to future experiments is discussed.     

Exact form factors in integrable quantum field theories: the sine-Gordon model

We provide detailed arguments on how to derive properties of generalized form factors, originally proposed by one of the authors (M.K.) and Weisz twenty years ago, solely based on the assumption of ‘maximal analyticity” and the validity of the LSZ reduction formalism. These properties constitute consistency equations which allow the explicit evaluation of the n-particle form factors once the scattering matrix is known. The equations give rise to a matrix Riemann-Hilbert problem. Exploiting the “off-shell” Bethe ansatz we propose a general formula for form factors for an odd number of particles. For the sine-Gordon model alias the massive Thirring model we exemplify the general solution for several operators. In particular we calculate the three-particle form factor of the soliton field, carry out a consistency check against the Thirring model perturbation theory and thus confirm the general formalism.     

Relativistic analysis of four-body final states

The constraints of unitarity and analyticity on four-body final states are studied. It is shown that unitarity alone forces the amplitudes to be coherent and have singular behaviour. The implementation of unitarity with total energy analyticity yields a set of relativistic linear integral equations for the four-body amplitude. This is the minimal set consistent with quantum mechanics and also is the full dynamical set of equations with two-body separable interactions. These equations will provide important ingredients for the phenomenological analysis of four-body final states using the isobar model.     

Some analyticity properties arising from asymptotic completeness in quantum field theory

It is well-known that two-particle unitarity of the S-Matrix in quantum field theory implies (modulo regularity assumptions) second sheet analyticity for the 2-body scattering amplitude. Here this is first used to prove off-mass-shell analyticity for the 4 point function in a complex neighborhood of any real mass-shell point under the 3-particle threshold. Then this is applied to the study of the 5 and 6-point functions near the real mass-shell of 2→3 and 3→3 processes below the 4-particle threshold: the results are those suggested by perturbation theory apart from the 3-particle cut and away from some submanifolds. The advantage of this method, which could presumably be extended to the exploitation ofn-particle unitarity, is that the regularity assumptions only refer to the physical scattering amplitudes.     

The spectrum of theP-wave baryons and hadronic loops

In current QCD inspired analyses of the hadron spectrum nonperturbative quark loops are generally neglected. We study the validity of this assumption by estimating mass splittings and mixings induced by hadronic mass renormalization to the (70,1^?) baryon multiplet. All intermediate states in the loop composed of a ground state meson (0^?+, 1^??) and a ground state baryon (1/2⁺, 3/2⁺) are included. We use a³ P ₀ type model for the partial decay widths and spectral functions. Using unitarity and analyticity one finds a definite prediction for the masses and mixings, in good agreement with experiment, even when the perturbative one-gluon exchange is completely ignored. Our result thus allows for a smaller one-gluon exchange overall contribution, which would resolve the difficulty of the apparent smallness of the observed spin-orbit coupling. In particular if one adds the (nonperturbative) unitarity corrections to the one-gluon exchange contribution the gluon coupling constant can be reduced by a factor of 3 giving a reasonable value α_s≈0.3.     

The pomeron and the f: An identity crisis

We show that the seemingly independent and plausible properties of pomeron-f identity, asymptotic planarity and standard analyticity and unitarity constraints on trajectories are not compatible. This has strong implications for current realizations of the topological expansion.     

Sigma-->gammagamma width from nucleon electromagnetic polarizabilities

The lightest QCD resonance, the sigma, has been recently fixed in the pipi scattering amplitude. The nature of this state remains nowadays one of the most intriguing and difficult issues in particle physics. Its coupling to photons is crucial for discriminating its structure. We propose a new method that fixes this coupling using only available precise experimental data on the proton electromagnetic polarizabilities together with analyticity and unitarity. By taking into account the uncertainties in the analysis and in the parameter values, our result is Gamma{pole}(sigma-->gammagamma)=1.2+/-0.4 keV.     

关于π-N低能大P波散射的一个注记

从解析性、阈行为和么正性的考虑出发,可以给出π-N散射的(3,3)分波振幅的一个近似表示式,其中只含耦合常数和共振能级两个参量。此表示式在从阈值直到入射π介子实验室动能E_π≈350MeV范围内都同实验很好地符合。与Chew-Low结果相比较,它给出的q³/ω ctgδ₃₃随ω的变化不是一直线,而是一向下弯曲的曲线,这种对Chew-Low理论的改进,正是实验所要求的。分析表明,Chew-Low展开在解析性方面存在着缺点,此项缺点在现今的处理中已经得到改正。     

Resonance estimates of \mathcal{O}(p^6) low-energy constants and QCD short-distance constraints

Starting from the study of the low-energy and high-energy behaviors of the QCD three-point functions , and , several low-energy constants of the chiral Lagrangian are evaluated within the framework of the lowest meson dominance (LMD) approximation to the large- limit of QCD. In certain cases, values that differ substantially from estimates based on a resonance Lagrangian are obtained. It is pointed out that the differences arise through the fact that QCD short-distance constraints are in general not correctly taken into account in the approaches using resonance Lagrangians. We discuss the implications of our results for the counterterm contributions to the vector form factor of the pion and to the decay , and for the pion–photon–photon transition form factor. Received: 4 June 2001 / Published online: 31 August 2001     

Resonant elastic scattering of protons from analog and compound states

In this note we give a general derivation of the amplitude for elastic scattering in the presence of one analog state and many compound (T-lower) states. We derive the form of the amplitude in a rather general scattering formalism, using unitarity and invariance under time reversal.     

Unitary amplitudes with cut-plane analyticity from given scattering data

We continue the study of constructing the scattering amplitude for scalar particles from elastic scattering data at a given energy. Here we require the scattering amplitude, f (z), to be analytic in a suitably cut z-plane; (z is the cosine of the scattering angle). We find that, in the elastic domain, the unitarity constraint is satisfied by a continuum of amplitudes, all corresponding to the same elastic scattering data. This continuum ambiguity in determination of f (z), which was noted earlier in formulations based on a smaller domain on analyticity, is associated with lack of knowledge of the contribution to unitarity from inelastic channels. We discuss the problem of incorporating smooth energy dependence in the determination of the scattering amplitude over some range of energy, and show that, under certain restrictions on the scattering data, there is a continuum of amplitudes having smooth energy dependence.