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Register a new userMatching effective chiral Lagrangians with dimensional and lattice regularization
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We compute the free energy in the presence of a chemical potential coupled to a conserved charge in effective O($n$) scalar field theory (without explicit symmetry breaking terms) to NNL order for asymmetric volumes in general $d$--dimensions, using dimensional (DR) and lattice regularizations. This yields relations between the 4-derivative couplings appearing in the effective actions for the two regularizations, which in turn allows us to translate results, e.g. the mass gap in a finite periodic box in $d=3+1$ dimensions, from one regularization to the other. Consistency is found with a new direct computation of the mass gap using DR. For the case $n=4, d=4$ the model is the low-energy effective theory of QCD with $N_{rm f}=2$ massless quarks. The results can thus be used to obtain estimates of low energy constants in the effective chiral Lagrangian from measurements of the low energy observables, including the low lying spectrum of $N_{rm f}=2$ QCD in the $delta$--regime using lattice simulations, as proposed by Peter Hasenfratz, or from the susceptibility corresponding to the chemical potential used.
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We investigate two-point correlation functions of left-handed currents computed in quenched lattice QCD with the Neuberger-Dirac operator. We consider two lattice spacings a~0.09,0.12 fm and two different lattice extents L~ 1.5, 2.0 fm; quark masses span both the p- and the epsilon-regimes. We compare the results with the predictions of quenched chiral perturbation theory, with the purpose of testing to what extent the effective theory reproduces quenched QCD at low energy. In the p-regime we test volume and quark mass dependence of the pseudoscalar decay constant and mass; in the epsilon-regime, we investigate volume and topology dependence of the correlators. While the leading order behaviour predicted by the effective theory is very well reproduced by the lattice data in the range of parameters that we explored, our numerical data are not precise enough to test next-to-leading order effects.
This work discusses reliability, possible obstacles and the future perspective of chiral extrapolation of lattice results. In the first part, chiral perturbation theory fits to lattice calculations of the nucleon mass are thoroughly explored in terms of statistical uncertainty and convergence. Lattice volume dependence is exploited as a source of additional fit constraints. In discussing consistency with pion-nucleon scattering, the role of the Delta(1232) excitation is clarified. In the second part of the work, pion and kaon mass lattice data are analyzed using three-flavor chiral perturbation theory. SU(3)-SU(2) matching conditions permit to examine deviations from the Gell-Mann, Oakes, Renner relation. Introductory chapters provide a quick start guide to manifestly covariant baryon chiral perturbation theory, basic understanding of lattice QCD and a self-contained explanation of the relevant statistical methods.
In simulations with dynamical quarks it has been established that the ground state rho in the infrared is a strong mixture of the two chiral representations (0,1)+(1,0) and (1/2,1/2)_b. Its angular momentum content is approximately the 3S1 partial wave which is consistent with the quark model. Effective chiral restoration in an excited rho-meson would require that in the infrared this meson couples predominantly to one of the two representations. The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the non-perturbatively determined excited state at different resolution scales. We present results for the first excited state of the rho-meson using simulations with n_f=2 dynamical quarks. We point out, that in the infrared a leading contribution to rho= rho(1450) comes from (1/2,1/2)_b, in contrast to the rho. Its approximate chiral partner would be a h_1(1380) state. The rho wave function contains a significant contribution of the 3D1 wave which is not consistent with the quark model prediction.
We use the chiral effective field theory to study the lattice finite-volume energy levels from the meson-meson scattering. The hadron resonance properties and the scattering amplitudes at physical masses are determined from the lattice energy levels calculated at unphysically large pion masses. The results from the $pieta, Kbar{K}$ and $pieta$ coupled-channel scattering and the $a_0(980)$ resonance are explicitly given as a concrete example.
We review heavy quark flavor and spin symmetries, their exploitation in heavy meson effective theories and the flavored couplings of charmed and light mesons in the definition of their effective Lagrangians. We point out how nonperturbative continuum QCD approaches based on Dyson-Schwinger and Bethe-Salpeter equations can be used to calculate strong and leptonic decays of open-charm mesons and heavy quarkonia. The strong decay $D^*to Dpi$ serves as a benchmark, as it is the only physical open-charm observable that can be related to the effective Lagrangians couplings. Nonetheless, a quantitative comparison of $D^*Dpi$, $rho DD$, $rho D^*D$ and $rho D^* D^*$ couplings for a range of off-shell momenta of the $rho$-meson invalidates SU(4)$_F$ symmetry relations between these couplings. Thus, besides the breaking of flavor symmetry by mass terms in the Lagrangians, the flavor-symmetry breaching in couplings and their dependence on the $rho$-meson virtuality cannot be ignored. We also take the opportunity to present new results for the effective $J/psi DD$ and $J/psi D^*D$ couplings. We conclude this contribution with a discussion on how the description of pseudoscalar and vector $D$, $D_s$, $B$ and $B_s$ meson properties can be drastically improved with a modest modification of the flavor-dependence in the Bethe-Salpeter equation.
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