Spinning S-matrix bootstrap in 4d

Abstract

We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

Bootstrapping 2d ϕ4 theory with Hamiltonian truncation data

“…Rather, in practical terms it appears that the origin of this close agreement is that even at strong coupling, the stress tensor form factor at s ≤ 0 and the spectral density at 4m 2 < s < 16m 2 , which we compute in LCT, is very similar to that of sinh-Gordon/staircase model. 17 Although 2-to-2 elastic scattering appears to be very similar in φ 4 theory and the sinh-Gordon model, we do not expect it to be similar at large s and it certainly cannot be similar for 2-to-2 + n since particle production exactly vanishes in sinh-Gordon. The S-matrix bootstrap with both two-and four-particle external states would therefore be particularly illuminating in this case since it would uncover more of the qualitative difference between the two models.…”

“…One could instead try to obtain the finite volume spectrum from lattice Monte Carlo rather than from truncation methods. 17 We also compute the stress tensor spectral density at s > 16m 2 , and here we do see a significant deviation between φ 4 and sinh-Gordon. However, the S-matrix bootstrap result for the elastic scattering amplitude does not seem to be very sensitive to the detailed behavior of the spectral density in this regime.…”

“…In this paper we will refer to it as the numerical S-matrix bootstrap. The S-matrix bootstrap gained further attention in recent years, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The recent work [23,24] made a concrete proposal for how to extended the S-matrix bootstrap to accommodate form factors and spectral densities.…”

Two-point functions and bootstrap applications in quantum field theories

“…It was first introduced in [49]. 15 It is a universal quantity in any number of dimensions. In unitary theories C T > 0.…”

“…The numerical S-matrix bootstrap program was recently revived in [1][2][3] and received further attention in [4][5][6][7][8][9][10][11][12][13][14][15]. This program allows to numerically construct scattering amplitudes which obey crossing and unitarity at all energies.…”