Study of the conformal hyperscaling relation through the Schwinger-Dyson equation

Abstract

We study corrections to the conformal hyperscaling relation in the conformal window of the large Nf QCD by using the ladder Schwinger-Dyson (SD) equation as a concrete dynamical model. From the analytical expression of the solution of the ladder SD equation, we identify the form of the leading mass correction to the hyperscaling relation. We find that the anomalous dimension, when identified through the hyperscaling relation neglecting these corrections, yields a value substantially lower than the one at the fixed point γ_m^* for large mass region. We further study finite-volume effects on the hyperscaling relation, based on the ladder SD equation in a finite space-time with the periodic boundary condition. We find that the finite-volume corrections on the hyperscaling relation are negligible compared with the mass correction. The anomalous dimension, when identified through the finite-size hyperscaling relation neglecting the mass corrections as is often done in the lattice analyses, yields almost the same value as that in the case of the infinite space-time neglecting the mass correction, i.e., a substantially lower value than γ_m^* for large mass. We also apply the finite-volume SD equation to the chiral-symmetry-breaking phase and find that when the theory is close to the critical point such that the dynamically generated mass is much smaller than the explicit breaking mass, the finite-size hyperscaling relation is still operative. We also suggest a concrete form of the modification of the finite-size hyperscaling relation by including the mass correction, which may be useful to analyze the lattice data.

17 pages, 9 figures

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• Lattice Simulations and Infrared Conformality
• Scaling relations for the entire spectrum in mass-deformed conformal gauge theories
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• Technicolor models with coupled systems of Schwinger-Dyson equations
• Perturbative corrections to technicolor
• Anomalous mass dimension of multi-flavor QCD
• Many flavor QCD as exploration of the walking behavior with the approximate IR fixed point
• Anomalous mass dimensions and Schwinger-Dyson equations boundary condition
• Many flavor QCD with N_f=12 and 16
• Fermion mass splitting in the technicolor coupled scenario
• Low energy spectra in many flavor QCD with Nf=12 and 16
• A Note on the Analytic Structure of Celestial Amplitudes
• Composite scalar boson mass dependence on the constituent mass anomalous dimension
• Exploring walking behavior in SU(3) gauge theory with 4 and 8 HISQ quarks
• The mass splitting in an 331-TC coupled Scenario