We study bounds arising from the analyticity and unitarity of scattering amplitudes in the context of effective field theories with massless particles. We provide an approach that only uses dispersion relations away from the forward limit. This is suitable to derive constraints in the presence of gravity, in a way that is robust with respect to radiative corrections. Our method not only allows us to avoid the Coulomb pole, but also the singularities associated with calculable loop effects, which would otherwise diverge.

Switzerland

Carl Beadle

United States

Giulia Isabella

Davide Perrone

Sara Ricossa

Francesco Riva

Italy

Francesco Serra

Non-forward UV/IR relations

We explore the impact of loop effects on positivity in effective field theories emerging in the infrared from unitary and causal microscopic dynamics. Focusing on massless particles coupled to gravity, we address the treatment of forward-limit divergences from loop discontinuities and establish necessary conditions for maintaining computational control in perturbation theory. While loop effects remain small, ensuring consistency in our approach leads to a significant impact on bounds, even at tree level.

The EFT bootstrap at finite $\textit{M}$

In this paper, we explore positivity bounds for the effective field theory (EFT) of a single weakly coupled massive vector field. The presence of both mass and spin makes the crossing properties of the amplitudes vastly complicated — we address this by parametrizing the amplitudes as products of a polarization matrix and a vector of appropriately chosen functions with simpler crossing properties. The resulting framework involves sum rules and null constraints that allows us to constrain any combination of low-energy observables, such as EFT amplitudes. By varying the value of the vector mass over the cutoff scale, some of our bounds asymptote to the bounds obtained in the context of photons and massless scalars. This work paves the way for future applications to e.g. non-abelian massive vectors, glueballs and theories with spin larger than one.

Francesco Bertucci

France

Johan Henriksson

Canada

Brian McPeak

Alessandro Vichi

Positivity bounds on massive vectors

We derive new positivity bounds at finite momentum transfer, assuming a large separation between the mass <math><mi>m</mi></math> of the lightest particle in the effective theory and the mass gap <math><mi>M</mi></math> to new heavy states. Massive gravity parametrically violates these bounds unless the cutoff is within 1 order of magnitude of the graviton mass <math><mi>M</mi><mo>≲</mo><mi>O</mi><mo>(</mo><mn>10</mn><mo>)</mo><mi>m</mi></math>. Nongravitational effective theories of massive spin-2 particles are similarly bounded.

Brando Bellazzini

Sergio Ricossa

Massive gravity is not positive

The simple analytic structure of meson scattering amplitudes in the large-N  c  limit, combined with positivity of the spectral density, provides precise predictions on low-energy observables. Building upon previous studies, we explore the allowed regions of chiral Lagrangian parameters and meson couplings to pions. We reveal a structure of kinks at all orders in the chiral expansion and develop analytical tools to show that kinks always correspond to amplitudes with a single light pole. We build (scalar- and vector-less) deformations of the Lovelace-Shapiro and Coon UV-complete amplitudes, and show that they lie close to the boundaries. Moreover, constraints from crossing-symmetry imply that meson couplings to pions become smaller as their spin increases, providing an explanation for the success of Vector Meson Dominance and holographic QCD. We study how these conclusions depend on assumptions about the high-energy behavior of amplitudes. Finally, we emphasize the complementarity between our results and Lattice computations in the exploration of large-N  c  QCD.

Spain

Clara Fernandez

CERN

Alex Pomarol

Francesco Sciotti

Cornering large-N  c  QCD with positivity bounds

We present a nonperturbative recipe for directly computing the S-matrix in strongly-coupled QFTs. The method makes use of spectral data obtained in a Hamiltonian framework and can be applied to a wide range of theories, including potentially QCD. We demonstrate the utility of this prescription in the specific example of the 2+1d O(N) model at large N, using energy eigenstates computed with Hamiltonian truncation to reproduce the full 2 → 2 scattering amplitude for arbitrary (complex) center-of-mass energy.

Brian Henning

Japan

Hitoshi Murayama

Jedidiah Thompson

Ireland

Matthew Walters

Towards a nonperturbative construction of the S-matrix

We show how calculable IR loop effects impact positivity bounds in effective field theories with causal and unitary UV completions. We identify infrared singularities that appear in dispersion relations at <math><mrow><mo>|</mo><mi>t</mi><mo>|</mo><mo>≲</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in <math><mi>s</mi></math> even for large negative <math><mi>t</mi></math>, i.e., <math><mo>|</mo><mi>t</mi><mo>|</mo><mo>≫</mo><msup><mi>m</mi><mn>2</mn></msup></math>, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally, we show that the singularity do not affect the bounds based on smearing in the impact parameter.

Marc Riembau

IR side of positivity bounds

We find the complete set of conditions satisfied by the forward <math><mrow><mn>2</mn><mo>→</mo><mn>2</mn></mrow></math> scattering amplitude in unitary 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 a 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 energy and couplings, where the latter has to satisfy two-sided bounds. We also extend our results to the case of small but finite <math><mi>t</mi></math>. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than <math><msup><mi>E</mi><mn>6</mn></msup></math> cannot be UV completed.

Joan Elias Miró

Riccardo Rattazzi

Positive moments for scattering amplitudes

We study $$W^+W^-$$ <math><mrow><msup><mi>W</mi><mo>+</mo></msup><msup><mi>W</mi><mo>-</mo></msup></mrow></math>  and Zh final sstates at future linear $$e^+e^-$$ <math><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>-</mo></msup></mrow></math>  colliders; designing analyses specific to the various final state polarizations allows us to target specific beyond the Standard Model (BSM) effects, parametrized in the form of dimension-6 operators. We find that CLIC can access effects roughly an order of magnitude smaller than HL-LHC or ILC, and two orders of magnitude smaller than LEP. These results are interpreted in the context of well-motivated BSM scenarios–at weak and strong coupling–where we expect correlated effects in Drell–Yann processes. The latter turn out to have better discovery potential, although the diboson processes provide additional discriminating power, potentially furnishing a way to measure the spin and coupling of BSM states.

Davide Lombardo

Improved BSM sensitivity in diboson processes at linear colliders

The measurement of Higgs couplings constitutes an important part of present standard model precision tests at colliders. We show that modifications of Higgs couplings induce energy-growing effects in specific amplitudes involving longitudinally polarized vector bosons, and we initiate a novel program to study these effects off shell and at high energy, rather than on the Higgs resonance. Our analysis suggests that these channels are complementary and competitive with familiar on-shell measurements; moreover, they offer endless opportunities for refinement and improvements.

Measuring Higgs Couplings without Higgs Bosons