arXiv subjects

Kelian Häring

Publications and source records attributed to Kelian Häring.

8 recordsLinked to original sources

arXiv2026

Walking Sudakov: From Cusp to Octagon

We study the Sudakov form factor and the four-point scattering amplitude on the Coulomb branch of planar $\mathcal{N}=4$ SYM as functions of the Coulomb-branch parameters and kinematic invariants. This setup provides a controlled probe of the interpolation between on- and off-shell regimes of infrared-sensitive quantities in gauge theories. We identify a novel scaling limit in which both observables exhibit double-logarithmic behavior governed by a walking anomalous dimension. As the mass scales are varied, this walking anomalous dimension interpolates between the cusp anomalous dimension of the on-shell regime and the octagon anomalous dimension of the off-shell regime. Based on the explicit two-loop result and the expected all-order structure, we propose an all-loop form for the walking anomalous dimension both for the form factor and for the four-point scattering amplitude. These all-loop expressions depend on new, presently unknown functions of the 't Hooft coupling.

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arXiv2025

From Partons to Strings: Scattering on the Coulomb Branch of $\mathcal{N}=4$ SYM

We study scattering on the Coulomb branch of planar ${\mathcal{N}}=4$ SYM at finite 't Hooft coupling. This setup defines a family of classical open-string S-matrices that smoothly interpolates between perturbative parton scattering at weak coupling and flat-space string scattering at strong coupling. We focus on the four-point amplitude, which exhibits a remarkably rich structure: nonlinear Regge trajectories, dual conformal invariance, an intricate spectrum of bound states with an accumulation point, and a two-particle cut. Dual conformal invariance relates the spectrum of Regge trajectories to the energy spectrum of the Maldacena-Wilson cusp Hamiltonian. This connection allows us to use integrability to compute the leading and subleading Regge trajectories at finite coupling, which we then input in the bootstrap analysis. At strong coupling, we use the worldsheet bootstrap to construct the first $AdS$-curvature correction to the Veneziano amplitude. We apply dispersion relations and S-matrix bootstrap techniques to derive bounds on Wilson coefficients, couplings to bound states, and the overall shape of the amplitude. We find that the $\mathcal{N}=4$ amplitude saturates the bootstrap bounds at weak coupling and nearly saturates them at strong coupling. At intermediate coupling, the amplitude traces a nontrivial path through the allowed space of observables. To characterize this path, we combine the weak- and strong-coupling information about the amplitude to construct a finite-coupling model for Wilson coefficients using a Padé approximation. The resulting model satisfies bootstrap constraints and yields sharp predictions for the finite-coupling behavior of the amplitude. We provide evidence that complete monotonicity of the scattering amplitude, previously observed perturbatively, persists at finite coupling.

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arXiv2024

From data to the analytic S-matrix: A Bootstrap fit of the pion scattering amplitude

We propose a novel strategy to fit experimental data using a UV complete amplitude ansatz satisfying the constraints of Analyticity, Crossing, and Unitarity. We focus on $ππ$ scattering combining both experimental and lattice data. The fit strategy requires using S-matrix Bootstrap methods and non-convex Particle Swarm Optimization techniques. Using this procedure, we numerically construct a full-fledged scattering amplitude that fits the data and contains the known QCD spectrum that couples to $ππ$ states below $1.4$ GeV. The amplitude constructed agrees below the two-particle threshold with the two-loop $χ$PT prediction. Moreover, we correctly predict the $D_2$ phase shift, the appearance of a spin three state, and the behavior of the high-energy total cross-section. Finally, we find a genuine tetraquark resonance around 2 GeV, which we argue might be detected by looking into the decays of B mesons.

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arXiv2024

What is the graviton pole made of?

We explore the physical mechanisms responsible for generating the graviton pole in twice-subtracted dispersion relations, both in flat space and in AdS. To characterize these mechanisms, we analyze the energy scale at which the graviton pole is generated in scattering experiments at various impact parameters. At large impact parameters, we identify the eikonal model of high-energy gravitational scattering as a universal mechanism that generates the graviton pole in dispersion relations. At smaller impact parameters, the graviton pole can arise from stringy higher-spin resonances. The length scale at which the graviton pole generation scale departs from its semiclassical eikonal value indicates the breakdown of gravitational EFT. In flat space, we derive a Tauberian theorem for the graviton pole, which must be satisfied by any UV completion of gravity that admits twice-subtracted dispersion relations. In AdS, free or non-holographic CFTs offer an alternative mechanism to generate the graviton pole. More broadly, we find that the existing picture of high-energy gravitational scattering, including phenomena such as black hole formation and various stringy effects, is compatible with the twice-subtracted dispersion relations.

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arXiv2023

The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness

We explore the space of meromorphic amplitudes with extra constraints coming from the shape of the leading Regge trajectory. This information comes in two guises: it bounds the maximal spin of exchanged particles of a given mass; it leads to sum rules obeyed by the discontinuity of the amplitude, which express the softness of scattering at high energies. We assume that the leading Regge trajectory is linear, and we derive bounds on the low-energy Wilson coefficients using the dual and primal approaches. For the graviton-graviton scattering in four dimensions, the maximal spin constraint leads to slightly more stringent bounds than those that follow from general constraints of analyticity, crossing, and unitarity. The exponential softness at high energies is manifest in our primal approach and is not used in our implementation of the dual approach. Nevertheless, we observe the agreement between the bounds obtained from both. We conclude that high-energy superpolynomial softness does not leave an obvious imprint on the low-energy observables. We exhibit a unitary three-parameter deformation of the Veneziano amplitude for the open string case. It has a novel, exponentially soft behavior at high energies and fixed angles. We generalize the previous analysis of this regime and present a stringy version of the lower bound on high-energy, fixed-angle scattering by Cerulus and Martin.

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arXiv2023

Bounds on scattering of neutral Goldstones

We study the space of $2\to 2$ scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT) for such particles. We reconstruct the analytic, crossing-symmetric, and unitary amplitudes saturating our bounds, and we study their physical content. We uncover non-perturbative Regge trajectories by continuing our numerical amplitudes to complex spins. We then explore the consequence of additional constraints arising when we impose the knowledge about the EFT up to the cut-off scale. In the process, we improve on some aspects of the numerical $S$-matrix bootstrap technology for massless particles.

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arXiv2022

Bounds on photon scattering

We study 2-to-2 scattering amplitudes of massless spin one particles in $d=4$ space-time dimensions, like real world photons. We define a set of non-perturbative observables (Wilson coefficients) which describe these amplitudes at low energies. We use full non-linear unitarity to construct various novel numerical bounds on these observables. For completeness, we also rederive some bounds using positivity only. We discover and explain why some of these Wilson coefficients cannot be bounded.

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arXiv2022

Gravitational Regge bounds

We review the basic assumptions and spell out the detailed arguments that lead to the bound on the Regge growth of gravitational scattering amplitudes. The minimal extra ingredient compared to the gapped case - in addition to unitarity, analyticity, subexponentiality, and crossing - is the assumption that scattering at large impact parameters is controlled by known semi-classical physics. We bound the Regge growth of amplitudes both with the fixed transferred momentum and smeared over it. Our basic conclusion is that gravitational scattering amplitudes admit dispersion relations with two subtractions. For a sub-class of smeared amplitudes, black hole formation reduces the number of subtractions to one. Finally, using dispersion relations with two subtractions we derive bounds on the local growth of relativistic scattering amplitudes. Schematically, the local bound states that the amplitude cannot grow faster than $s^2$.

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