Preshin Moodley | Searcharxiv

arXiv2024

A Quantum Field Theory for the interaction of pions and rhos

We extend the Kroll-Lee-Zumino model in its particle content to include the charged rho vector mesons and the neutral pion meson. This entailed using the larger SU(2) gauge group. The masses for the vector mesons were generated via spontaneous symmetry breaking using the Higgs mechanism. The Lagrangian was then quantized and gauge fixed using the generalized class of $R_ξ$ gauges. Tree scattering lengths were calculated for pion-pion scattering and the values for the $a^0_0$ and $a^2_0$ scattering lengths are found to be comparable with experiment. The one particle irreducible diagrams that contribute to the one loop corrections to the tree scattering lengths are renormalized.

hep-ph↗

arXiv2024

Chiral Corrections to the Gell-Mann-Oakes-Renner Relation from QCD Sum Rules

We calculate the next-to-leading order corrections to the $SU(2)\otimes SU(2)$ and $SU(3)\otimes SU(3)$ Gell-Mann-Oakes-Renner relations. We use a pseudoscalar correlator calculated from Perturbative QCD up to five loops and use the QCD Finite Energy Sum Rules with integration kernels tuned to suppress the importance of the hadronic resonances. This leads to a substantial reduction in the systematic uncertainties from the experimentally unknown resonance spectral function. We use the method of Fixed Order and Fixed Renormalization Scale Perturbation Theory to compute the integrals. We calculate these corrections to be $δ_π= 0.060 \pm 0.014$ and $δ_K =0.64 \pm 0.24$. As a result of these new values, we predict the value of the light quark condensate $\left\langle {0|\bar qq|0} \right\rangle = - \left( {266 \pm 5{\text{ MeV}}} \right)^3$ and the Chiral Perturbation Theory low energy constant $H_2^r = - \left( {4.9 \pm 1.8} \right) \times 10^{ - 3}$. Results from this work have been published as: J. Bordes, C.A. Dominguez, P. Moodley, J. Pe$\widetilde{\text{n}}$arrocha and K. Schilcher, J. High Ener. Phys. 05 (2010) 064.

hep-ph↗