Soft pion scattering in infrared-conformal gauge-fermion theories

Abstract

We consider the problem of soft scattering for the analogue of pion states in gauge-fermion theories which approach a conformal fixed point in the infrared limit. Introducing a fermion mass into such a theory will explicitly break both scale invariance and chiral symmetry, leading to confinement and a spectrum of bound states. We argue that in such a theory, the pion scattering length diverges in the limit of zero fermion mass, in sharp contrast to QCD-like theories where the chiral Lagrangian predicts a vanishing scattering length. We demonstrate this effect both with a simple dimensional argument, and in a generalized linear sigma model which we argue can be used to describe the interactions of light scalar and pseudoscalar bound states in the soft limit of a mass-deformed infrared-conformal theory. As a result, lattice calculations of pion scattering lengths could be a sensitive probe for infrared scale invariance in gauge-fermion theories.

arXiv comment11 pages, 1 figure. v2: updated to journal version

References in corpus (39)

• The Composite Nambu-Goldstone Higgs
• Fermionic UV completions of Composite Higgs models
• Hyperscaling relations in mass-deformed conformal gauge theories
• Lattice tests of beyond Standard Model dynamics
• Twelve massless flavors and three colors below the conformal window
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• Low-energy effective action for pions and a dilatonic meson
• Lattice Simulations and Infrared Conformality
• Pion-pion scattering and the K->3pi decay amplitudes
• Dilaton Chiral Perturbation Theory - Determining Mass and Decay Constant of Technidilaton on the Lattice
• Light composite scalar in twelve-flavor QCD on the lattice
• Dilaton EFT Framework For Lattice Data
• Lattice study of conformality in twelve-flavor QCD
• Technicolor and other QCD-like theories at next-to-next-to-leading order
• Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions
• The large-mass regime of the dilaton-pion low-energy effective theory
• Extending Chiral Perturbation Theory with an Isosinglet Scalar
• Scaling relations for the entire spectrum in mass-deformed conformal gauge theories
• Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions
• The infrared regime of SU(2) with one adjoint Dirac flavour
• Analysis of a Dilaton EFT for Lattice Data
• Composite Higgs model at a conformal fixed point
• Improved Lattice Spectroscopy of Minimal Walking Technicolor
• Meson-meson Scattering in QCD-like Theories
• Finite size scaling of conformal theories in the presence of a near-marginal operator
• Dynamics in the Conformal Window in QCD like Theories
• Effective pion mass term and the trace anomaly
• Large volumes and spectroscopy of walking theories
• Finite size scaling in minimal walking technicolor
• Near-conformal dynamics in a chirally broken system
• The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
• Conformal scaling and the size of $m$-hadrons
• Linear Sigma EFT for Nearly Conformal Gauge Theories
• Goldstone Boson Scattering with a Light Composite Scalar
• A linear sigma model for multiflavor gauge theories
• Low energy properties of SU(2) gauge theory with N_f = 3/2 flavours of adjoint fermions
• A novel approach to the study of conformality in the SU(3) theory with multiple flavors
• QCD inequalities for hadron interactions
• Mass splittings in a linear sigma model for multiflavor gauge theories