We extend the geometric framework of field-space covariance for loop computations, thereby unifying the treatment of scalars, fermions, and gauge bosons in effective field theories. This allows us to derive a manifestly covariant formula for one-loop UV divergences that includes contributions from mixed boson-fermion graphs. The result is expressed in terms of geometric invariants of the field-space supermanifold. As a demonstration of this formula, we compute the renormalization group equations for two-fermion operators at the dimension-eight level in the Standard Model Effective Field Theory.

United States

Benoît Assi

Switzerland

Andreas Helset

Julie Pagès

Taiwan

Chia-Hsien Shen

Renormalizing two-fermion operators in the SMEFT via supergeometry

We present a systematic method for analytically computing time-dependent observables for a relativistic probe particle in Coulomb and Schwarzschild backgrounds. The method generates expressions valid both in the bound and unbound regimes, namely $\textit{bound-unbound universal}$ expressions. To demonstrate our method we compute the time-dependent radius and azimuthal angle for relativistic motion in a Coulomb background (relativistic Keplerian motion), as well as the electromagnetic field radiated by a relativistic Keplerian source. All of our calculations exhibit bound-unbound universality. Finally, we present an exact expression for the semi-classical wave function in Schwarzschild. The latter is crucial in applying our method to any time-dependent observable for probe-limit motion in Schwarzschild, to any desired order in velocity and the gravitational constant $\textit{G}$.

Israel

Majed Khalaf

Ofri Telem

Bound-unbound universality and the all-order semi-classical wave function in Schwarzschild

Direct detection experiments are looking for nuclear recoils from scattering of sub-GeV dark matter (DM) in crystals, and have thresholds as low as <math><mrow><mo>∼</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> or DM masses of <math><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Future experiments are aiming for even lower thresholds. At such low energies, the free nuclear recoil prescription breaks down, and the relevant final states are phonons in the crystal. Scattering rates into single as well as multiple phonons have already been computed for a harmonic crystal. However, crystals typically exhibit some anharmonicity, which can significantly impact scattering rates in certain kinematic regimes. In this work, we estimate the impact of anharmonic effects on scattering rates for DM in the mass range <math><mo>∼</mo><mn>1</mn><mi>–</mi><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, where the details of multiphonon production are most important. Using a simple model of a nucleus in a bound potential, we find that anharmonicity can modify the scattering rates by up to two orders of magnitude for DM masses of <math><mi>O</mi><mo>(</mo><mi>MeV</mi><mo>)</mo></math>. However, such effects are primarily present at high energies where the rates are suppressed, and thus only relevant for very large DM cross sections. We show that anharmonic effects are negligible for masses larger than <math><mo>∼</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

Tongyan Lin

Mukul Sholapurkar

Ethan Villarama

Anharmonic effects in nuclear recoils from sub-GeV dark matter

Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of particular oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.

Daniel Green

Yiwen Huang

Netherlands

Daniel Baumann

Positivity from Cosmological Correlators

The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.

Aneesh Manohar

Fermion geometry and the renormalization of the Standard Model Effective Field Theory

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a pointlike particle carrying a scalar charge <math><mi>Q</mi></math> off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full <math><mi>O</mi><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> scalar-field self-force term (but ignoring the gravitational self-force), and we 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 <math><mi>O</mi><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math>. 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.

United Kingdom

Leor Barack

Zvi Bern

Enrico Herrmann

Germany

Oliver Long

Julio Parra-Martinez

Radu Roiban

Michael S. Ruf

Mikhail P. Solon

Fei Teng

Mao Zeng

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

We derive a new soft theorem that corresponds to the spontaneous breaking of Lorentz boosts. This is motivated by the dynamics of inflation in the subhorizon (flat-space) limit, where spacetime becomes flat but Lorentz boosts are still broken. In this limit, the scattering amplitudes become sensible observables. We relate the soft emission of a Goldstone boson to the (nonrelativistic) Lorentz boost of the hard scattering amplitudes. This is the on-shell avatar of the spontaneous breaking of Lorentz boosts, analogous to the Adler zero of pions in the chiral symmetry breaking. We comment on several applications to inflation, including the demonstration that Dirac-Born-Infeld inflation is the unique theory that has an emergent Lorentz invariance when the boosts are spontaneously broken.

Inflationary Adler conditions

We present a new formula for the angular momentum <math><msup><mi>J</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum <math><msup><mi>P</mi><mi>μ</mi></msup></math>, completes the set of radiated Poincaré charges due to scattering. We parametrize <math><mrow><msup><mrow><mi>P</mi></mrow><mrow><mi>μ</mi></mrow></msup></mrow></math> and <math><msup><mi>J</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> by nonperturbative form factors and derive exact relations using the Poincaré algebra. There is a contribution to <math><msup><mi>J</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> due to static (zero-frequency) modes, which can be derived from Weinberg’s soft theorem. Using tools from scattering amplitudes and effective field theory, we calculate the radiated <math><msup><mi>J</mi><mrow><mi>μ</mi><mi>ν</mi></mrow></msup></math> due to the scattering of two spinless particles to third order in Newton’s constant <math><mi>G</mi></math>, but to all orders in velocity. Our form-factor analysis elucidates a novel relation found by Bini, Damour, and Geralico between energy and angular momentum loss at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math>. Our new results have several nontrivial implications for binary scattering at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>4</mn></msup><mo>)</mo></math>. We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincaré charges due to scattering.

Aneesh V. Manohar

Alexander K. Ridgway

Radiated Angular Momentum and Dissipative Effects in Classical Scattering

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>4</mn></msup><mo>)</mo></math> 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 2. 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.

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>4</mn></msup><mo>)</mo></math>

We describe a systematic framework for finding the conservative potential of compact binary systems with spin based on scattering amplitudes of particles of arbitrary spin and effective field theory. An arbitrary-spin formalism is generally required in the classical limit. By matching the tree and one-loop amplitudes of four spinning particles with those of a suitably chosen effective field theory, we obtain the <math><mrow><mrow><msub><mrow><mi>spin</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mtext>−</mtext><mrow><msub><mrow><mi>spin</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mrow></math> terms of a two-body effective Hamiltonian through <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>2</mn></msup><mo>)</mo></math> and valid to all orders in velocity. Solving Hamilton’s equations yields the impulse and spin changes of the individual bodies. We write them in a surprisingly compact form as appropriate derivatives of the eikonal phase obtained from the amplitude. It seems likely this structure persists to higher orders. We also point out various double-copy relations for general spin.

Andres Luna

Spinning black hole binary dynamics, scattering amplitudes, and effective field theory