Conformal scaling and the size of $m$-hadrons

Abstract

The scaling laws in an infrared conformal (IR) theory are dictated by the critical exponents of relevant operators. We have investigated these scaling laws at leading order in two previous papers. In this work we investigate further consequences of the scaling laws, trying to identify potential signatures that could be studied by lattice simulations. From the first derivative of the form factor we derive the behaviour of the mean charge radius of the hadronic states in the theory. We obtain $⟨r_H^2⟩\sim m^{-2/(1+{\gamma }_m^{\ast })}$ which is consistent with $⟨r_H^2⟩\sim 1/M_H^2$. The mean charge radius can be used as an alternative observable to assess the size of the physical states, and hence finite size effects, in numerical simulations. Furthermore, we discuss the behaviour of specific field correlators in coordinate space for the case of conformal, scale-invariant, and confining theories making use of selection rules in scaling dimensions and spin. We compute the scaling corrections to correlations functions by linearizing the renormalization group equations. We find that these correction are potentially large close to the edge of the conformal window. As an application we compute the scaling correction to the formula $M_H\sim m^{1/(1+{\gamma }_m^{\ast })}$ directly through its associated correlator as well as through the trace anomaly. The two computations are shown to be equivalent through a generalisation of the Feynman-Hellmann theorem for the fermion mass, and the gauge coupling.

26pp, 3 figures, version nearly identical to PRD version (added appendix B finite size effects)

References in corpus (7)

• Light composite scalar in twelve-flavor QCD on the lattice
• Scaling relations for the entire spectrum in mass-deformed conformal gauge theories
• Unparticle & Higgs as Composites
• Conformal Dynamics for TeV Physics and Cosmology
• Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours
• Approaching Conformality with Ten Flavors
• Renormalization group, trace anomaly and Feynman-Hellmann theorem

Cited by in corpus (12)

• Lattice tests of beyond Standard Model dynamics
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Finite size scaling of conformal theories in the presence of a near-marginal operator
• Crawling technicolor
• Large volumes and spectroscopy of walking theories
• Dilaton and Massive Hadrons in a Conformal Phase
• Global Structure of Conformal Theories in the SU(3) Gauge Theory
• Anomalous dimensions on the lattice
• Renormalization group, trace anomaly and Feynman-Hellmann theorem
• Gluon condensates from the Hamiltonian formalism
• Mass-induced confinement near the sill of the conformal window
• Soft pion scattering in infrared-conformal gauge-fermion theories