Selection rules for the S-Matrix bootstrap

Abstract

We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

Quantum field theory and the Bieberbach conjecture

“…The green points are for the pion lake [22]. The blue and red points are for the upper and lower river boundaries [23,24] while the black points are for the line of minimum averaged total cross section S-matrices [24].…”

“…Some additional phenomenological inputs like ρ-meson mass or certain theoretical constraints like S/D wave scattering length inequalities are used. For more details, the reader is referred to [22][23][24]. The allowed S-matrices are displayed as regions on the Adler-zeros (s 0 , s 2 ) plane.…”

“…As such this particular S-matrix is of interest to us. In the main text, we have considered a plethora of S-matrices like the lake in [22], the upper and lower boundaries of the river in [23] as well as the more interesting line of minimization (where the total scattering cross-section is minimized for a given s 0 ) in [24]. The amplitude for pion scattering from S-matrix bootstrap with…”

Dual EFT bootstrap: QCD flux tubes

“…Recent progress on the S-matrix bootstrap programme [24][25][26][27][28][29][30][31] has triggered a revision of the space of feasible EFTs, with applications to the EFT of: the QCD string [32], pions [33][34][35] and supergravity [36]. At this point a small digression is in order.…”

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

“…For the 3 + 1 dimensional case considered here, besides the previously mentioned references, the most relevant ones are [16,17] where the S-matrix bootstrap is applied to pion dynamics as originally envisioned [1,2]. Various other ideas have been discussed in the context of the S-matrix bootstrap and similar methods applied to gapped theories [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”