Goldstone Boson Scattering with a Light Composite Scalar

Appelquist, T.; Brower, R. C.; Cushman, K. K.; Fleming, G. T.; Gasbarro, A.; Hasenfratz, A.; Ingoldby, J.; Jin, X. Y.; Kiskis, J.; Neil, E. T.; Osborn, J. C.; Rebbi, C.; Rinaldi, E.; Schaich, D.; Vranas, P.; Weinberg, E.; Witzel, O.

doi:10.48550/arxiv.2106.13534

Cited by 1 publication

(4 citation statements)

References 55 publications

(94 reference statements)

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“…An important caveat is that for theories which are confining but just below the edge of the conformal window, the low-energy regime may be described by an effective theory such as a linear sigma model [42,44,45] or a dilaton EFT [30,[46][47][48][49][50][51][52]. In the latter case especially, it has been pointed out that the spectrum in the large-mass regime can show the same power-law scaling with m as expected for an MDCT [52], and recent results [29] found that a ππ is constant at leading order in m in this regime.…”

Section: Discussionmentioning

confidence: 93%

“…As an example, we consider the recent lattice results from [29] for I = 2 π-π scattering in a near-conformal theory, SU(3) with N f = 8 fermions in the fundamental representation. In Fig.…”

Section: B Pion Scatteringmentioning

confidence: 99%

“…We emphasize that this is an empirical argument valid only for this specific theory; in general, the leading mass scaling in the dilaton EFT scenario likely depends on the value of the mass anomalous dimension γ and on the form of the dilaton potential. 3) gauge theory with N f = 8 fermions in the fundamental representation, from [29]. We have re-plotted results for the combination Mπaππ against the fermion mass in lattice units am, where a is the lattice spacing.…”

Section: B Pion Scatteringmentioning

confidence: 99%

“…FIG.1. Lattice data for the I = 2 pion scattering length in SU(3) gauge theory with N f = 8 fermions in the fundamental representation, from[29]. We have re-plotted results for the combination Mπaππ against the fermion mass in lattice units am, where a is the lattice spacing.…”

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Soft pion scattering in infrared-conformal gauge-fermion theories

Hackett,

Neil

2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 93%

Section: B Pion Scatteringmentioning

confidence: 99%

Section: B Pion Scatteringmentioning

confidence: 99%

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confidence: 99%

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Soft pion scattering in infrared-conformal gauge-fermion theories

Hackett,

Neil

2021

Preprint

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Goldstone Boson Scattering with a Light Composite Scalar

Cited by 1 publication

References 55 publications

Soft pion scattering in infrared-conformal gauge-fermion theories

Soft pion scattering in infrared-conformal gauge-fermion theories

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