Pseudoscalar Spectrum Research Articles

SU(3) breaking and the pseudo-scalar spectrum in multi-taste QCD

Using the Sigma model to explore the lowest order pseudo-scalar spectrum with SU(3) breaking, this talk considers an additional exact “taste” symmetry to mimic species doubling. Rooting replicas of a valid approach such as Wilson fermions reproduces the desired physical spectrum. In contrast, extra symmetries of the rooted staggered approach leave spurious states and a flavor dependent taste multiplicity.

Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality

In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of $U(3)$ chiral perturbation theory with explicit tree level exchanges of resonances. The meson-meson scattering calculation from Guo and Oller [Phys. Rev. D 84, 034005 (2011)] is extended as well. The spectral functions of the nonet scalar-scalar ($SS$) and pseudoscalar-pseudoscalar ($PP$) correlators are constructed by using the corresponding form factors. After fitting the unknown parameters to the scattering data, we discuss the resonance content of the resulting scattering amplitudes. We also study spectral-function sum rules in the $SS\ensuremath{-}SS$, $PP\ensuremath{-}PP$, and $SS\ensuremath{-}PP$ sectors as well as semilocal duality from scattering. The former relate the scalar and pseudoscalar spectra between themselves while the latter mainly connects the scalar spectrum with the vector one. Finally we investigate these items as a function of ${N}_{C}$ for ${N}_{C}>3$. All these results pose strong constraints on the scalar dynamics and spectroscopy that are discussed. They are successfully fulfilled by our meson-meson scattering amplitudes and spectral functions.

Study of the Nambu-Jona-Lasinio model on the lattice.

We present our full analysis of the two flavor Nambu--Jona-Lasinio model with SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) chiral symmetry on the four-dimensional hypercubic lattice with naive and Wilson fermions. We find that this model is an excellent toy field theory to investigate issues related to lattice QCD. We use the large-N approximation to leading order in 1/N to obtain nonperturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the 1/N corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading-order large-N calculations. We obtain results regarding the approach to the continuum chiral limit, the effects of the zero momentum fermionic modes on finite lattices, and the scalar and pseudoscalar spectrum.

The Nambu-Jona-Lasinio model of QCD on the lattice

In an effort to obtain insights on the behavior of an interacting theory of fermions on the lattice that posseesses the QCD chiral symmetry, the two flavor Nambu-Jona-Lasinio model with SU (2) × SU (2) chiral symmetry is studied on the four-dimensional hypercubic lattice using large N techniques and numerical simulations. Naive and Wilson fermions are considered and transparent results are obtained regarding the following: the approach to the zero quark and zero pion mass limits, the size of the 1/ N corrections, the effects of the zero momentum fermionic modes on finite lattices, and the scalar and pseudoscalar spectrum. Some interesting observations are made by viewing the model as the low energy approximation to QCD, as well as an embedding theory of the Higgs sector.

Results from a study of the Nambu-Jona-Lasinio model on the lattice

The main results of our analysis of the two flavor Nambu-Jona-Lasinio model with SU(2) × SU(2) chiral symmetry on the four-dimensional hypercubic lattice with naive and Wilson fermions are presented. Large N techniques and numerical simulations are used to study various properties of the model. The scalar and pseudoscalar spectrum, the approach to the continuum and chiral limits, the size of the 1/ N corrections, and the effects of the zero momentum fermionic modes on finite lattices are studied. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector.

Corrections to the extraction of light quark mass ratios from pseudoscalar meson splittings

We argue that terms in the effective chiral lagrangian of O( αm s and O( M 3), where M is the quark mass matrix, significantly increase the uncertainties in the extraction of light quark mass ratios from the pseudoscalar spectrum. In particular, within the range of magnitudes expected for the coefficients accompanying such terms, the observed spectrum can be compatible with an up to down quark mass ratio between ∼0.05 and 0.78 without necessitating unreasonably large contributions of second (and third) order in the quark masses, even when the constraints of ηη′ mixing are taken into account.

Parton recombination model including resonance production

Possible effects of resonance production on the meson inclusive distribution in the fragmentation region are investigated in the framework of the parton recombination model. From a detailed study of the data on vector-meson production, a reliable ratio of the vector-to-pseudoscalar rates is determined. The authors examine the influence of the decay of the vector mesons on the pseudoscalar spectrum and find the effect to be no more than 25% for x>0.5. The normalisation of the nonstrange antiquark distributions are still higher than those in a quiescent proton.