Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f ₀(980), a ₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η ₈ mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p ⁴) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m _s/ , in terms of the O(p ⁴) CHPT low-energy constant combinations 2L ^r ₈ - L ^r ₅ and 2L ^r ₆ - L ^r ₄. In this way, we give a range for the values of these low-energy counterterms and for 3L ₇ + L ^r ₈, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m _s/ = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.     

In-medium chiral perturbation theory

We report on how to tackle the problem of establishing a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources (Ann. Phys. 297, 27 (2002)). We have made use of the results of J.A. Oller (Phys. Rev. C 65, 025204 (2002)) where the generating functional for the in-medium chiral SU(2) x SU(2) Lagrangian has been derived. Within this approach we develop the so-called standard power counting rules for the calculation of in-medium pion properties if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Fe Chiral Lagrangians - 11.30.Rd Chiral symmetries - 21.65. + f Nuclear matter     

In-medium chiral perturbation theory

This talk will report about a systematical implementation of a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources[1]. Within the generating functional approach of Ref.[2] the so-called standard power counting rules for the calculation of in-medium pion properties are developed that apply if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We report about a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.     

Low-energy limit of chiral meson theory

Based on a phenomenologically successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons, all the coefficients of the chiral perturbation theory are predicted. There is no new adjustable parameter in these predictions. Up to O(m ² _q) the formulas of the masses of the pseudoscalar mesons are the same as the ones obtained by ChPT. Received: 31 August 2000 / Accepted: 16 March 2001     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

Topics in chiral perturbation theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.     

Review of chiral perturbation theory

A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.     

Topics in chiral perturbation theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.     

The pionium lifetime in generalized chiral perturbation theory

Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential–constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination (a₀⁰−a₀²) of the ππ S-wave scattering lengths with isospin I=0, 2.     

The pionic beta decay in chiral perturbation theory

Within the framework of chiral perturbation theory with virtual photons and leptons, we present an updated analysis of the pionic beta decay including all electromagnetic contributions of order e ² p ² . We discuss the extraction of the Cabibbo-Kobayashi-Maskawa matrix element |V _ud | from the experimental data. The method employed here is consistent with the analogous treatment of the decays and the determination of |V _us |. Received: 19 September 2002 / Published online: 24 January 2003     

Rho meson properties in the chiral theory framework

We study the mass, width and couplings of the lightest resonance multiplet with I (J ^PC ) = 1 (1^-) quantum numbers. Effective field theories based on chiral symmetry are employed in order to describe the form factor associated with the two pseudoscalar matrix element of the QCD vector current. The bare poles of the intermediate resonances are regularized through a Dyson-Schwinger-like summation. We explore the role of the resonance width in physical observables and make a coupled-channel analysis of the final-state interactions. This provides many interesting properties, like the pole mass MeV. At energies GeV, a second 1 (1^-) resonance multiplet is considered in order to describe the data in a more consistent way. From the phenomenologically extracted resonance couplings, we obtain the chiral coupling , at MeV, and show how the running with the scale μ affects the resonance parameters. A 1/N _C counting is adopted in this work and the consistency of the large-N_C expansion is tested. Finally, we make an estimation of the contribution from diagrams with resonances in crossed channels. Received: 23 August 2002 / Published online: 19 February 2003     

Massive states in chiral perturbation theory

It is shown that the chiral nonanalytic terms generated by ₃₃ resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself.