arXiv subjects

Mikhail P. Solon

Publications and source records attributed to Mikhail P. Solon.

At least 19 recordsLinked to original sources

arXiv2026

Universal Closed Form for Dynamical Love Numbers of Black Holes

Black hole static Love numbers vanish, but their dynamical counterparts do not. We present the scheme-independent dynamical response $\bar{F}_{\ell,s}$ of a Schwarzschild black hole in closed form, to all orders, and for every spin $s$ and multipole $\ell$. The result is $\bar{F}_{\ell,s}/4\pi R_S^{2\ell+1}=\Phi_{\ell,s}(\bar{y})-\tfrac12\eta\,\Phi_{\ell,s}'(\bar{y})$ with $\bar{y}=-\tfrac12\eta^2\tau$ and $\eta=i\omega R_S$. Here $\Phi_{\ell,s}$ is simply the leading-log solution to the renormalization group equation, but lifting the running logarithm to $\tau=\log(R_S/R)-2\sum_{k\ge2}\zeta_k\,\eta^{k-1}$ resums it to all orders. This tower of Riemann zeta values is the Newtonian phase in disguise: it originates from the same far-zone $\Gamma(1-\eta)$ that governs long-range scattering, and is universal across multipole and spin. Our result exhibits a factorization pinned to three ingredients: the hard matching coefficient at the horizon, the anomalous dimension in the near zone, and the dressed log in the far zone. Using shell effective field theory, we independently verify our formula for scalar, electromagnetic, and gravitational perturbations, reaching $\mathcal O(G^{15})$.

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arXiv2024

The hierarchical three-body problem at $\mathcal{O} (G^2)$

Employing techniques from scattering amplitudes and effective field theory, we model the dynamics of hierarchical triples, which are three-body systems composed of two bodies separated by a distance $r$ and a third body a distance $\rho$ away, with $r \ll \rho$. We apply the method of regions to systematically expand in the small ratio $r/\rho$ and illustrate this approach for evaluating Fourier transform integrals, which have been the bottleneck for deriving complete results in position space. In the limit where the distant third body is much heavier than the other two, we derive new analytic results in position space for the three-body conservative potential at $\mathcal{O}(G^2)$ and at leading and next-to-leading order in $r/\rho$. We also derive new results for arbitrary masses in the rest frame of the distant particle. Our results are exact in velocity, and can be used in analyses involving both bound and unbound hierarchical triples in astrophysical systems.

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arXiv2024

Gravitational Self Force from Scattering Amplitudes in Curved Space

We employ scattering amplitudes in curved space to model the dynamics of a light probe particle with mass $m$ orbiting in the background spacetime induced by a heavy gravitational source with mass $M$. Observables are organized as an expansion in $m/M$ to all orders in $G$ -- the gravitational self-force expansion. An essential component of our analysis is the backreaction of the heavy source which we capture by including the associated light degrees of freedom. As illustration we consider a Schwarzschild background and verify geodesic motion as well as the first-order self-force correction to two-body scattering through ${\cal O}(G^3)$. Amplitudes in curved space offer several advantages, and further developments along these lines may advance the computation of gravitational-wave signals for extreme-mass-ratio inspirals.

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arXiv2023

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge $Q$ off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full $O(Q^2)$ scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through $O(Q^2 G^3)$. At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones.

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arXiv2022

Snowmass White Paper: Gravitational Waves and Scattering Amplitudes

We review recent progress and future prospects for harnessing powerful tools from theoretical high-energy physics, such as scattering amplitudes and effective field theory, to develop a precise and systematically improvable framework for calculating gravitational-wave signals from binary systems composed of black holes and/or neutron stars. This effort aims to provide state-of-the-art predictions that will enable high-precision measurements at future gravitational-wave detectors. In turn, applying the tools of quantum field theory in this new arena will uncover theoretical structures that can transform our understanding of basic phenomena and lead to new tools that will further the cycle of innovation. While still in a nascent stage, this research direction has already derived new analytic results in general relativity, and promises to advance the development of highly accurate waveform models for ever more sensitive detectors.

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arXiv2022

Snowmass White Paper: Effective Field Theories for Dark Matter Phenomenology

The quest to discover the nature of dark matter continues to drive many of the experimental and observational frontiers in particle physics, astronomy, and cosmology. While there are no definitive signatures to date, there exists a rich ecosystem of experiments searching for signals for a broad class of dark matter models, at different epochs of cosmic history, and through a variety of processes with different characteristic energy scales. Given the multitude of candidates and search strategies, effective field theory has been an important tool for parametrizing the possible interactions between dark matter and Standard Model probes, for quantifying and improving model-independent uncertainties, and for robust estimation of detection rates in the presence of large perturbative corrections. This white paper summarizes a wide range of effective field theory applications for connecting dark matter theories to experiments.

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arXiv2021

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e. $O(G^4)$ and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight two. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

hep-th↗

arXiv2021

Scattering Amplitudes and Conservative Binary Dynamics at ${\cal O}(G^4)$

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order, ${\cal O}(G^4)$. As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at ${\cal O}(G^3)$ via its relation to the tail effect.

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arXiv2020

Mining the Geodesic Equation for Scattering Data

The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the presence of perturbatively small effects such as tidal distortion and higher derivative corrections to general relativity. We derive an algebraic map between the perturbed geodesic equation and the leading PM scattering amplitude at arbitrary mass ratio. As examples, we compute formulas for amplitudes and isotropic gauge Hamiltonians for certain infinite classes of tidal operators such as electric or magnetic Weyl to any power, and for higher derivative corrections to gravitationally interacting bodies with or without electric charge. Finally, we present a general method for calculating closed-form expressions for amplitudes and isotropic gauge Hamiltonians in the test-particle limit at all orders in the PM expansion.

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arXiv2020

Tidal Effects in the Post-Minkowskian Expansion

Tools from scattering amplitudes and effective field theory have recently been repurposed to derive state-of-the-art results for the black hole binary inspiral in the post-Minkowskian expansion. In the present work we extend this approach to include the tidal effects of mass and current quadrupoles on the conservative dynamics of non-spinning neutron star mergers. We compute the leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles. Our expressions are gauge invariant and, in the extreme mass ratio limit, consistent with the dynamics of a tidally deformed test body in a Schwarzschild background. Furthermore, they agree completely with existing results at leading post-Minkowskian and second post-Newtonian orders.

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arXiv2020

Classical Gravitational Scattering at ${\cal O}(G^3)$ from Feynman Diagrams

We perform a Feynman diagram calculation of the two-loop scattering amplitude for gravitationally interacting massive particles in the classical limit. Conveniently, we are able to sidestep the most taxing diagrams by exploiting the test-particle limit in which the system is fully characterized by a particle propagating in a Schwarzschild spacetime. We assume a general choice of graviton field basis and gauge fixing that contains as a subset the well-known deDonder gauge and its various cousins. As a highly nontrivial consistency check, all gauge parameters evaporate from the final answer. Moreover, our result exactly matches that of Bern et al., here verified up to sixth post-Newtonian order while also reproducing the same unique velocity resummation at third post-Minkowksian order.

hep-th↗

arXiv2020

Black Hole Binary Dynamics from the Double Copy and Effective Theory

We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.

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arXiv2019

Resummed Photon Spectra for WIMP Annihilation

We construct an effective field theory (EFT) description of the hard photon spectrum for heavy WIMP annihilation. This facilitates precision predictions relevant for line searches, and allows the incorporation of non-trivial energy resolution effects. Our framework combines techniques from non-relativistic EFTs and soft-collinear effective theory (SCET), as well as its multi-scale extensions that have been recently introduced for studying jet substructure. We find a number of interesting features, including the simultaneous presence of SCET$_{\text{I}}$ and SCET$_{\text{II}}$ modes, as well as collinear-soft modes at the electroweak scale. We derive a factorization formula that enables both the resummation of the leading large Sudakov double logarithms that appear in the perturbative spectrum, and the inclusion of Sommerfeld enhancement effects. Consistency of this factorization is demonstrated to leading logarithmic order through explicit calculation. Our final result contains both the exclusive and the inclusive limits, thereby providing a unifying description of these two previously-considered approximations. We estimate the impact on experimental sensitivity, focusing for concreteness on an SU(2)$_{W}$ triplet fermion dark matter - the pure wino - where the strongest constraints are due to a search for gamma-ray lines from the Galactic Center. We find numerically significant corrections compared to previous results, thereby highlighting the importance of accounting for the photon spectrum when interpreting data from current and future indirect detection experiments.

hep-ph↗

arXiv2019

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

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arXiv2019

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order

We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order.

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arXiv2018

Power Corrections to the Universal Heavy WIMP-Nucleon Cross Section

WIMP-nucleon scattering is analyzed at order $1/M$ in Heavy WIMP Effective Theory. The $1/M$ power corrections, where $M\gg m_W$ is the WIMP mass, distinguish between different underlying UV models with the same universal limit and their impact on direct detection rates can be enhanced relative to naive expectations due to generic amplitude-level cancellations at leading order. The necessary one- and two-loop matching calculations onto the low-energy effective theory for WIMP interactions with Standard Model quarks and gluons are performed for the case of an electroweak SU(2) triplet WIMP, considering both the cases of elementary fermions and composite scalars. The low-velocity WIMP-nucleon scattering cross section is evaluated and compared with current experimental limits and projected future sensitivities. Our results provide the most robust prediction for electroweak triplet Majorana fermion dark matter direct detection rates; for this case, a cancellation between two sources of power corrections yields a small total $1/M$ correction, and a total cross section close to the universal limit for $M \gtrsim {\rm few} \times 100\,{\rm GeV}$. For the SU(2) composite scalar, the $1/M$ corrections introduce dependence on underlying strong dynamics. Using a leading chiral logarithm evaluation, the total $1/M$ correction has a larger magnitude and uncertainty than in the fermionic case, with a sign that further suppresses the total cross section. These examples provide definite targets for future direct detection experiments and motivate large scale detectors capable of probing to the neutrino floor in the TeV mass regime.

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arXiv2017

Loop-Induced Stochastic Bias at Small Wavevectors

Primordial non-Gaussianities enhanced at small wavevectors can induce a power spectrum of the galaxy overdensity that differs greatly from that of the matter overdensity at large length scales. In previous work, it was shown that "squeezed" three-point and "collapsed" four-point functions of the curvature perturbation $ζ$ can generate these non-Gaussianities and give rise to so-called scale-dependent and stochastic bias in the galaxy overdensity power spectrum. We explore a third way to generate non-Gaussianities enhanced at small wavevectors: the infrared behavior of quantum loop contributions to the four-point correlations of $ζ$. We show that these loop effects lead to stochastic bias, which can be observable in the context of quasi-single field inflation.

astro-ph.CO↗

arXiv2017

Fermionic Glauber Operators and Quark Reggeization

We derive, in the framework of soft-collinear effective field theory (SCET), a Lagrangian describing the $t$-channel exchange of Glauber quarks in the Regge limit. The Glauber quarks are not dynamical, but are incorporated through non-local fermionic potential operators. These operators are power suppressed in $|t|/s$ relative to those describing Glauber gluon exchange, but give the first non-vanishing contributions in the Regge limit to processes such as $q\bar q \to gg$ and $q\bar q \to γγ$. They therefore represent an interesting subset of power corrections to study. The structure of the operators, which describe certain soft and collinear emissions to all orders through Wilson lines, is derived from the symmetries of the effective theory combined with constraints from power and mass dimension counting, as well as through explicit matching calculations. Lightcone singularities in the fermionic potentials are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the Reggeization of the quark at the amplitude level and the BFKL equation at the cross section level. We verify this at one-loop, deriving the Regge trajectory of the quark in the $3$ color channel, as well as the leading logarithmic BFKL equation. Results in the $\bar 6$ and $15$ color channels are obtained by the simultaneous exchange of a Glauber quark and a Glauber gluon. SCET with quark and gluon Glauber operators therefore provides a framework to systematically study the structure of QCD amplitudes in the Regge limit, and derive constraints on higher order amplitudes.

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