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Register a new userA new method for the beta function in the chiral symmetry broken phase
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We describe a new method to determine non-perturbatively the beta function of a gauge theory using lattice simulations in the p-regime of the theory. This complements alternative measurements of the beta function working directly at zero fermion mass and bridges the gap between the weak coupling perturbative regime and the strong coupling regime relevant to the mass spectrum of the theory. We apply this method to ${mathrm {SU(3)} }$ gauge theory with two fermion flavors in the 2-index symmetric (sextet) representation. We find that the beta function is small but non-zero at the renormalized coupling value $g^2 = 6.7$, consistent with our previous independent investigation using simulations directly at zero fermion mass. The model continues to be a very interesting explicit realization of the near-conformal composite Higgs paradigm which could be relevant for Beyond Standard Model phenomenology.
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Recently, via calculation of spatial correlators of $J=0,1$ isovector operators using a chirally symmetric Dirac operator within $N_F=2$ QCD, it has been found that QCD at temperatures $T_c - 3 T_c$ is approximately $SU(2)_{CS}$ and $SU(4)$ symmetric. The latter symmetry suggests that the physical degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color singlet objects without chromomagnetic effects. This regime of QCD has been referred to as a Stringy Fluid. Here we calculate correlators for propagation in time direction at a temperature slightly above $T_c$ and find the same approximate symmetries. This means that the meson spectral function is chiral-spin and $SU(4)$ symmetric.
We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in $|V_{us}|$ and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincare generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstones theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann-Oakes-Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model.
We define a finite size renormalization scheme for $phi^4$ theory which in the thermodynamic limit reduces to the standard scheme used in the broken phase. We use it to re-investigate the question of triviality for the four dimensional infinite bare coupling (Ising) limit. The relevant observables all rely on two-point functions and are very suitable for a precise estimation with the worm algorithm. This contribution updates an earlier publication by analysing a much larger dataset.
The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has been the subject of significant interest for many years, including several investigations using lattice QCD. The majority of lattice studies have not observed a low-lying excited state energy level in the region of the Roper resonance. However, it has been claimed that chiral symmetry could play an important role in our understanding of this resonance. The purpose of this study is to systematically examine the role of chiral symmetry in the low-lying nucleon spectrum by directly comparing the clover and overlap fermion actions. To ensure any differences in results are attributable to the choice of fermion action, simulations are performed on the same set of gauge field configurations at matched pion masses. Correlation matrix techniques are employed to determine the excitation energy of the first positive-parity excited state for each action. The clover and overlap actions show a remarkable level of agreement. We do not find any evidence that fermion action chiral symmetry plays a significant role in understanding the Roper resonance on the lattice.
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