NLO perturbativity bounds on quartic couplings in renormalizable theories withϕ4-like scalar sectors

Abstract

The apparent breakdown of unitarity in low order perturbation theory is often is used to place bounds on the parameters of a theory. In this work we give an algorithm for approximately computing the next-to-leading order (NLO) perturbativity bounds on the quartic couplings of a renormalizable theory whose scalar sector is φ 4 -like. By this we mean theories where either there are no cubic scalar interactions, or the cubic couplings are related to the quartic couplings through spontaneous symmetry breaking. The quantity that tests where perturbation theory breaks down itself can be written as a perturbative series, and having the NLO terms allows one to test how well the series converges. We also present a simple example to illustrate the effect of considering these bounds at different orders in perturbation theory. For example, there is a noticeable difference in the viable parameter when the square of the NLO piece is included versus when it is not.

HEPfit: a code for the combination of indirect and direct constraints on high energy physics models

“…4.4 are very useful to restrict the NP parameter space. In this case approximate expressions for the NLO perturbative unitarity conditions were obtained following the method described in [138]. These expressions are valid in the large center-of-mass limit and therefore they are only considered above a certain energy scale, default value of which is set to 750 GeV.…”

Constraints on coloured scalars from global fits

“…This condition is usually expressed in terms of the partial wave amplitudes a j . Using their LO (a (0) j ) and NLO (a (1) j ) expressions [25], perturbative unitarity can be imposed at LO, NLO and at the so-called NLO+ approximation [42] that includes the square of the NLO correction and therefore contains some, but not all, NNLO terms [25]:…”

How heavy can dark matter be? Constraining colourful unitarity with SARAH

“…Unitarity of scattering amplitudes has long been used to constrain the masses and couplings of thermal relic dark matter (DM) particles [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. More generally, it is applied to constrain new physics Beyond the Standard Model such as Z couplings [5,13,[16][17][18], and most often (and relevant for this work) scalar couplings [10][11][12]14,15,[44][45][46][47][48][49] (including some one-loop calculations [44,[50][51][52]). Unitarity famously limits the maximum possible crosssection for dark-matter annihilation, and thus gives an upperbound on the mass of DM particles.…”