Positive moments for scattering amplitudes

By B. Bellazzini, Joan Elias Mir'o, R. Rattazzi, M. Riembau, F. Riva. Physical Review D, 2020

167 citations recorded by the source corpus.

We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/49350eac017871195ad21f449bed9824941a3de8

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Citations in the corpus

New positivity bounds from full crossing symmetry (2020, background): “rix has found interesting applications in the weak gravity conjecture [61] and string theory amplitudes [62,63]. The optimal positivity of the sderivative amplitudes has been recently sought after in [56] with arc dispersion relations and positive moments, conrming the results of [60] and obtaining ”
The EFT-hedron (2020, background): “In particular, new positivity constraints involving scale dependent “arc moments" were introduced in [8], are intimately related to the geometry of the gap discussed in subsection 7.”
Extremal effective field theories (2020, result): “ries appear smooth except for two kinks at ( 10:19;0:5) and (3;0:5). the convex hull of the parabola connecting (0;0) to (3;1 2 ). (This is qualitatively similar to what is found in the forward limit [5, 7].) The Spin-J2 region is more complicated { while it also displays a parabolic underbelly near”