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Higher-Point Positivity

High Energy Physics - Theory 2018-12-11 v2 High Energy Physics - Phenomenology

Abstract

We consider the extension of techniques for bounding higher-dimension operators in quantum effective field theories to higher-point operators. Working in the context of theories polynomial in X=(ϕ)2X=(\partial \phi)^2, we examine how the techniques of bounding such operators based on causality, analyticity of scattering amplitudes, and unitarity of the spectral representation are all modified for operators beyond (ϕ)4(\partial \phi)^4. Under weak-coupling assumptions that we clarify, we show using all three methods that in theories in which the coefficient λn\lambda_n of the XnX^n term for some nn is larger than the other terms in units of the cutoff, λn\lambda_n must be positive (respectively, negative) for nn even (odd), in mostly-plus metric signature. Along the way, we present a first-principles derivation of the propagator numerator for all massive higher-spin bosons in arbitrary dimension. We remark on subtleties and challenges of bounding P(X)P(X) theories in greater generality. Finally, we examine the connections among energy conditions, causality, stability, and the involution condition on the Legendre transform relating the Lagrangian and Hamiltonian.

Keywords

Cite

@article{arxiv.1804.03153,
  title  = {Higher-Point Positivity},
  author = {Venkatesa Chandrasekaran and Grant N. Remmen and Arvin Shahbazi-Moghaddam},
  journal= {arXiv preprint arXiv:1804.03153},
  year   = {2018}
}

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25 pages