Staggered Chiral Perturbation Theory

We discuss how to formulate a staggered chiral perturbation theory. This amounts to a generalization of the Lee-Sharpe Lagrangian to include more than one flavor (i.e. multiple staggered fields), which turns out to be nontrivial. One loop corrections to pion and kaon masses and decay constants are computed as examples in three cases: the quenched, partially quenched, and full (unquenched) case. The results for the one loop mass and decay constant corrections have already been presented in Ref. [1].Comment: talk presented by C. Aubin at Lattice2002(spectrum); 3 pages, 1 figur

On the absence of fifth-order contributions to the nucleon mass in heavy-baryon chiral perturbation theory

(New version with some expanded discussion; figures and minor typos corrected.) We have calculated the contribution proportional to the fifth power of the pion mass in the chiral expansion of the nucleon mass in two flavour HBCPT. Only one irreducible two-loop integral enters, and this vanishes. All other corrections in the heavy-baryon limit can be absorbed in the physical pion-nucleon coupling constant which enters in the third order term, and so there are no contributions at fifth order. Including finite nucleon mass corrections, the only contribution agrees with the expansion of the relativistic one-loop graph in powers of the ration of the pion and nucleon masses, and is only 0.3% of the third order term. This is an encouraging result for the convergence of two-flavour heavy-baryon chiral perturbation theory.Comment: 4 pages RevTex, 4 eps figure

Towards a lattice calculation of the coefficients of the QCD chiral Lagrangian

We discuss a general strategy to compute the coefficients of QCD chiral Lagrangian by using the lattice regularization of QCD with Wilson fermions. This procedure requires the introduction of an effective Lagrangian for lattice QCD as an intermediate step in the calculation. The continuum QCD chiral Lagrangian can be then obtained by expanding the lattice effective Lagrangian in increasing powers of the external momenta. A suitable renormalization procedure is required to account for the chiral symmetry breaking introduced by the Wilson term in the lattice action. In anticipation of a numerical simulation, the lattice effective Lagrangian is computed analytically and investigated in the strong coupling and large $N$ limitComment: Talk presented at LATTICE96(chirality in qcd) , 3 pages, no figures. Latex file with espcrc2 styl

Thermal Pions ns Isospin Chemical Potential Effects

The density corrections, in terms of the isospin chemical potential $\mu_I$, to the mass of the pions are investigated in the framework of the SU(2) low energy effective chiral invariant lagrangian. As a function of temperature and $\mu_I =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, the dependence for a non-vanishing chemical potential turns out to be much more dramatic. In particular, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the $\pi ^{\pm}$ should condensate when $\mu_{I} = \mp m_{\pi}$. This is not longer valid anymore at finite $T$. The mass of the $\pi_0$ acquires also a non trivial dependence on $\mu_I$ at finite $T$.Comment: 5 pages, 2 figures. To appear in the proceedings of the International High-Energy Physics Conference on Quantum Chromodynamics QCD02, Montpellier, 2-9 July (2002

Integrating out the heaviest quark in N--flavour ChPT

We extend a known method to integrate out the strange quark in three flavour chiral perturbation theory to the context of an arbitrary number of flavours. As an application, we present the explicit formulae to one--loop accuracy for the heavy quark mass dependency of the low energy constants after decreasing the number of flavours by one while integrating out the heaviest quark in N--flavour chiral perturbation theory.Comment: 18 pages, 1 figure. Text and references added. To appear in EPJ

Is the up-quark massless?

We report on determinations of the low-energy constants alpha5 and alpha8 in the effective chiral Lagrangian at O(p^4), using lattice simulations with N_f=2 flavours of dynamical quarks. Precise knowledge of these constants is required to test the hypothesis whether or not the up-quark is massless. Our results are obtained by studying the quark mass dependence of suitably defined ratios of pseudoscalar meson masses and matrix elements. Although comparisons with an earlier study in the quenched approximation reveal small qualitative differences in the quark mass behaviour, numerical estimates for alpha5 and alpha8 show only a weak dependence on the number of dynamical quark flavours. Our results disfavour the possibility of a massless up-quark, provided that the quark mass dependence in the physical three-flavour case is not fundamentally different from the two-flavour case studied here.Comment: references added, typos correcte

Strangeness in the Scalar Form Factor of the Nucleon

The scalar form factor of the nucleon and related physical quantities are investigated in the framework of the semibosonized SU(3) Nambu-Jona-Lasinio soliton model. We take into account the rotational $1/N_c$ corrections and linear $m_s$ corrections. The strangeness content of the nucleon in the scalar form factor is discussed in detail. In particular, it is found that the $m_s$ corrections play an essential role of reducing the $\langle N | \bar{s} s | N \rangle$ arising from the leading order and rotational $1/N_c$ contributions. We obtain the \sigma_{\pi N} (0)=40.80\;\mbox{MeV}, \Delta \sigma = \sigma_{\pi N} (2m^{2}_{\pi})-\sigma_{\pi N} (0) = 18.18\;\mbox{MeV} and \langle r^2\rangle^{S}_{N} = 1.50\;\mbox{fm}^2. The results are in a remarkable agreement with empirical data analyzed by Gasser, Leutwyler, and Sainio~\cite{gls}.Comment: 13 pages, RevTex is used. 3 figures as uufiles are include

Baryon Electromagnetic Properties in Partially Quenched Heavy Hadron Chiral Perturbation Theory

The electromagnetic properties of baryons containing a heavy quark are calculated at next-to-leading order in partially quenched heavy hadron chiral perturbation theory. Calculations are performed for three light flavors in the isospin limit and additionally for two light non-degenerate flavors. We use partially-quenched charge matrices that are easy to implement on the lattice. The results presented are necessary for the light quark mass extrapolation and zero-momentum extrapolation of lattice QCD and partially quenched lattice QCD calculations of heavy hadron electromagnetic properties. Additionally relations between the sextet electromagnetic form factors and transition form factors are derived.Comment: 29 pages, 3 figures, RevTex