Self-healing of unitarity in effective field theories and the onset of new physics

Abstract

In effective field theories it is common to identify the onset of new physics with the violation of tree-level unitarity. However, we show that this is parametrically incorrect in the case of chiral perturbation theory, and is probably theoretically incorrect in general. In the chiral theory, we explore perturbative unitarity violation as a function of the number of colors and the number of flavors, holding the scale of the"new physics" (i.e. QCD) fixed. This demonstrates that the onset of new physics is parametrically uncorrelated with tree-unitarity violation. When the latter scale is lower than that of new physics, the effective theory must heal its unitarity violation itself, which is expected because the field theory satisfies the requirements of unitarity. In the chiral theory, the self-healing results in a resonant structure with scalar quantum numbers. In the electroweak variant of this argument, the structure must have the properties of the Higgs and must couple proportional to the mass in both gauge boson and fermion scattering. A similar example can be seen in the case of general relativity coupled to multiple matter fields, where iteration of the vacuum polarization diagram restores unitarity. We present arguments that suggest the correct identification should be connected to the onset of inelasticity rather than unitarity violation. We describe how the onset of inelasticity can occur in the effective theory, although it does not appear possible to predict the onset reliably.

The horizon of the lightest black hole

“…This resummation was first considered when studying the perturbative unitarity of the effective action (1.1) [6][7][8][9][10][11][12].…”

“…This correction is calculated [6] in the large N limit, where N = N s + 3N f + 12N V (N s , N f , and N V are, respectively, the number of real scalar fields, fermions and spin 1 fields in the model), while keeping N G N small. One uses dimensional analysis to regulate the integrals and absorb the divergent parts of the diagrams into the coefficients of R 2 and R μν R μν .…”

Multiple Higgs and vector boson production beyond the Standard Model

“…In this article we study the inelastic production of longitudinally polarised W and Z bosons (denoted collectively by V L ) and Higgs bosons in the context of an effective Lagrangian. We estimate the energy scale at which these processes become relevant, which signals the onset of new physics, as recently discussed in [4]. In particular, we will be interested in the sensitivity to non-SM Higgs couplings in the growth of the cross section for these processes.…”

The lightest of black holes

“…Recently, there has been a renewed interest in the gravitational scattering of fields and the question of whether perturbative unitarity could be violated below the Planck scale [10][11][12][13][14][15][16]18,19]. By studying the two to two elastic gravitational scattering of fields, it has been argued that perturbative unitarity is violated at an energy scale E ∼M P / √ N [10], where N is loosely speaking the number of fields in the model andM P the reduced Planck mass.…”