Generalized elastic positivity bounds on interacting massive spin-2 theories

Abstract

We use generalized elastic positivity bounds to constrain the parameter space of multi-field spin-2 effective field theories. These generalized bounds involve inelastic scattering amplitudes between particles with different masses, which contain kinematic singularities even in the t = 0 limit. We apply these bounds to the pseudo-linear spin-2 theory, the cycle spin-2 theory and the line spin-2 theory respectively. For the pseudo-linear theory, we exclude the remaining operators that are unconstrained by the usual elastic positivity bounds, thus excluding all the leading (or highest cutoff) interacting operators in the theory. For the cycle and line theory, our approach also provides new bounds on the Wilson coefficients previously unconstrained, bounding the parameter space in both theories to be a finite region (i.e., every Wilson coefficient being constrained from both sides). To help visualize these finite regions, we sample various cross sections of them and estimate the total volumes.

QED positivity bounds

“…These original forward limit scalar bounds have been extended to general spins [4,5] away from the forward limit [5,6]. These bounds have proven fruitful in placing constraints on interacting spin-2 fields [7][8][9][10][11][12][13][14], restricting beyond standard model interactions [15][16][17][18][19][20][21][22][23][24], and providing a new light on properties of string amplitudes [25,26]. Most recently it has been recognized that by using more information from crossing symmetry and the partial wave expansion it is possible to put upper and lower bounds on Wilson coefficients [27][28][29][30][31] in certain cases ruling out classes of theories from having a standard UV completion such as weakly broken Galileon theories [27,28].…”

Natural selection rules: new positivity bounds for massive spinning particles

“…Other particle physics applications include chiral perturbation theory [1][2][3] and its gauged siblings [30,31]. Positivity bounds have also been recently applied to a variety of EFTs relevant for cosmology, including the study of corrections to general relativity [32][33][34][35]; the effective theories describing massive gravity [36][37][38][39][40][41][42][43] and higherspin states [44][45][46]; various scalar field theories [47][48][49][50][51]; Einstein-Maxwell theory and the Weak Gravity Conjecture [52][53][54][55][56][57]; and paired with observational constraints [58,59]. Any improvement in the constraining power of positivity bounds can therefore impact a wide range of areas throughout theoretical physics.…”

Triple crossing positivity bounds for multi-field theories

“…Note that finding the upper bounds here is different from obtaining the v 2 convex cone from the lower bounds. In the case of the lower bounds, one can define a dual cone, and, to extract the optimal bounds for superposed state |u , one can restrict u i to be real numbers without any loss of generality [35]. For EFTs with a small number of modes such as bi-scalar theory, the superposed lower bounds is equivalent to the optimal v 2 convex cone.…”