Two--loop integrals in chiral perturbation theory

We consider chiral perturbation theory in the meson sector at order $E^6$. In the terminology of the external field technique, the two--loop graphs so generated are of the sunset type. We discuss the evaluation of several of these in the case where the masses of the particles running in the loops are equal. In particular, we present integral representations that are suitable for the evaluation of diagrams in kinematical regions where branch points and cuts are present.Comment: 28 pages, LaTeX, 5 figures embedded with epsf.st

Updated analysis of meson-nucleon sigma terms in the perturbative chiral quark model

We present an updated analysis of meson-baryon sigma terms in the perturbative chiral quark model, which is based on effective chiral Lagrangian. The new feature concerns the inclusion of excited states in the quark propagator. Its influence on meson loops is shown to lead in particular for the pion-nucleon sigma term to an enhancement relevant for the current evaluation of this quantity. We also determine various flavor combinations of the scalar nucleon form factors and their respective low-momentum transfer limits.Comment: 26 pages, 10 figures, to be published in Phys Rev

Renormalization of relativistic baryon chiral perturbation theory and power counting

We discuss a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. The method involves finite subtractions of dimensionally regularized diagrams beyond the standard $\bar{\rm MS}$ scheme of chiral perturbation theory to remove contributions violating the power counting. This is achieved by a suitable renormalization of the parameters of the most general effective Lagrangian. In addition to simplicity our method has the benefit that it can be easily applied to multiloop diagrams. As an application we discuss the mass and the scalar form factor of the nucleon and compare the results with the expressions of the infrared regularization of Becher and Leutwyler.Comment: 20 pages, RevTex, 1 figure, published version is shortene

Precision Pion-Proton Elastic Differential Cross Sections at Energies Spanning the Delta Resonance

A precision measurement of absolute pi+p and pi-p elastic differential cross sections at incident pion laboratory kinetic energies from T_pi= 141.15 to 267.3 MeV is described. Data were obtained detecting the scattered pion and recoil proton in coincidence at 12 laboratory pion angles from 55 to 155 degrees for pi+p, and six angles from 60 to 155 degrees for pi-p. Single arm measurements were also obtained for pi+p energies up to 218.1 MeV, with the scattered pi+ detected at six angles from 20 to 70 degrees. A flat-walled, super-cooled liquid hydrogen target as well as solid CH2 targets were used. The data are characterized by small uncertainties, ~1-2% statistical and ~1-1.5% normalization. The reliability of the cross section results was ensured by carrying out the measurements under a variety of experimental conditions to identify and quantify the sources of instrumental uncertainty. Our lowest and highest energy data are consistent with overlapping results from TRIUMF and LAMPF. In general, the Virginia Polytechnic Institute SM95 partial wave analysis solution describes our data well, but the older Karlsruhe-Helsinki PWA solution KH80 does not.Comment: 39 pages, 22 figures (some with quality reduced to satisfy ArXiv requirements. Contact M.M. Pavan for originals). Submitted to Physical Review

Baryon masses and nucleon sigma terms in manifestly Lorentz-invariant baryon chiral perturbation theory

We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.Comment: 18 pages, 3 figures, accepted for publication in J. Phys.

In-medium meson properties and field transformations

Since the existing calculations of the effective meson mass in nuclear medium involve approximations, it is important to examine whether they satisfy the general requirement of the equivalence theorem that the physical observables should be independent of the choice of field variables. We study here consequences of nucleon field transformations. As an illustrative case we consider the in-medium effective pion mass calculated for the s-wave pion-nucleon interaction in the linear density approximation. We demonstrate that it is necessary to include the Born term explicitly in order that the effective pion mass should obey the equivalence theorem.Comment: 10 pages, using RevTeX4. More detailed discussion, references added. To be published in Phys. Rev.

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature's fundamental parameters. A hadron's sigma-term is a measure of this dependence. The connection between a hadron's sigma-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit sigma_pi = m_pi/2. This truncation also provides a decent estimate of sigma_rho because the two dominant self-energy corrections to the rho-meson's mass largely cancel in their contribution to sigma_rho. The truncation is less accurate for the omega, however, because there is little to compete with an omega->rho+pi self-energy contribution that magnifies the value of sigma_omega by ~25%. A Poincare' covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Delta, and thereby sigma_N and sigma_Delta. This "quark-core" piece is augmented by the "pion cloud" contribution, which is positive. The analysis yields sigma_N~60MeV and sigma_Delta~50MeV.Comment: 22 pages, reference list expande

Recent Developments in Chiral Perturbation Theory

I review recent developments in chiral perturbation theory (CHPT) which is the effective field theory of the standard model below the chiral symmetry breaking scale. The effective chiral Lagrangian formulated in terms of the pseudoscalar Goldstone bosons ($\pi, \, K, \, \eta$) is briefly discussed. It is shown how one can gain insight into the ratios of the light quark masses and to what extent these statements are model--independent. A few selected topics concerning the dynamics and interactions of the Goldstone bosons are considered. These are $\pi \pi$ and $\pi K$ scattering, some non--leptonic kaon decays and the problem of strong pionic final state interactions. CHPT also allows to make precise statements about the temperature dependence of QCD Green functions and the finite size effects related to the propagation of the (almost) massless pseudoscalar mesons. A central topic is the inclusion of matter fields, baryon CHPT. The relativistic and the heavy fermion formulation of coupling the baryons to the Goldstone fields are discussed. As applications, photo--nucleon processes, the $\pi N$ $\Sigma$--term and non--leptonic hyperon decays are presented. Implications of the spontaneously broken chiral symmetry on the nuclear forces and meson exchange currents are also described. Finally, the use of effective field theory methods in the strongly coupled Higgs sector and in the calculation of oblique electroweak corrections is touched upon.Comment: TeX, 110 pages, 15 figures available upon request, BUTP-93/0

Colliders and Cosmology

Dark matter in variations of constrained minimal supersymmetric standard models will be discussed. Particular attention will be given to the comparison between accelerator and direct detection constraints.Comment: Submitted for the SUSY07 proceedings, 15 pages, LaTex, 26 eps figure