arXiv subjects

Chia-Hsien Shen

Publications and source records attributed to Chia-Hsien Shen.

At least 19 recordsLinked to original sources

arXiv2026

Positivity in the Renormalization of Effective Field Theory

We show that the direction of renormalization in effective field theory is constrained by fundamental principles in the infrared$\unicode{x2014}$unitarity, analyticity, and Lorentz invariance. Our theorem, in the spirit of the $a$-theorem in conformal field theory, determines the sign of the one-loop running of couplings in the forward limit, when one inserts two operators whose mass dimensions are identical and even. The theorem holds for a broad class of effective field theories with arbitrary ultraviolet completions. The constraint directly applies to linear positivity bounds derived using tree-level amplitudes in the infrared, providing a criterion for whether renormalization effects can preserve the positivity bounds, or lead to their apparent violation. We discuss the phenomenological implications of our theorem in chiral perturbation theory and the Standard Model Effective Field Theory, where our theorem is particularly constraining for the running at dimension eight. We provide several examples and show various extensions and applications even at dimension six.

hep-ph↗

arXiv2026

Gravitational Sommerfeld Effects: Formalism, Renormalization, and Perturbation to $O(G^{10})$

In the effective field theory (EFT) description of binary inspirals, the radiated gravitational waveform receives universal corrections from the curved background, the so-called ``tail effects'', that resum into the so-called ``Sommerfeld factor''. We develop a systematic framework for computing this gravitational Sommerfeld factor for scalar perturbations with the presence of tidal effects on the system. Using the worldline EFT, we recast the diagrammatic resummation as a solution to the $d$-dimensional wave equation with a localized source, and derive a closed-form expression for the Sommerfeld factor in terms of the EFT connection matrix. We prove that the phase of the Sommerfeld factor is exactly the same as elastic Compton scattering phase shift when there is no tidal dissipation. By combining the renormalization techniques in EFT with the Mano--Suzuki--Takasugi method in black hole perturbation theory, we analytically solve the Sommerfeld factor for both the magnitude and phase to $O(G^{10})$ for the $\ell = 0, 1, 2$ partial waves. We further establish a new renormalization group equation for the radiative multipole moments, whose exact solution yields an improved resummation of the waveform beyond the universal tail logarithms. These high-precision data and exact relations pave the way for future waveform resummation.

hep-th↗

arXiv2025

Renormalizing Two-Fermion Operators in the SMEFT via Supergeometry

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.

hep-ph↗

arXiv2025

Bound-Unbound Universality and the All-Order Semi-Classical Wave Function in Schwarzschild

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 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 $G$.

gr-qc↗

arXiv2023

Positivity from Cosmological Correlators

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 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.

hep-th↗

arXiv2023

Anharmonic effects in nuclear recoils from sub-GeV dark matter

Direct detection experiments are looking for nuclear recoils from scattering of sub-GeV dark matter (DM) in crystals, and have thresholds as low as ~ 10 eV or DM masses of ~ 100 MeV. 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 ~ 1-10 MeV, 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 O(MeV). 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 ~ 10 MeV.

hep-ph↗

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.

hep-th↗

arXiv2023

Fermion Geometry and the Renormalization of the Standard Model Effective Field Theory

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.

hep-ph↗

arXiv2023

Inflationary Adler Conditions

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 sub-horizon (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 (non-relativistic) 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.

hep-th↗

arXiv2022

Radiated Angular Momentum and Dissipative Effects in Classical Scattering

We present a new formula for the angular momentum $J^{μν}$ carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum $P^μ$, completes the set of radiated Poincare charges due to scattering. We parametrize $P^μ$ and $J^{μν}$ by non-perturbative form factors and derive exact relations using the Poincare algebra. There is a contribution to $J^{μν}$ 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 $J^{μν}$ due to the scattering of two spinless particles to third order in Newton's constant $G$, 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 $\mathcal{O}(G^3)$. Our new results have several nontrivial implications for binary scattering at $\mathcal{O}(G^4)$. We give a procedure to bootstrap an effective radiation reaction force from the loss of Poincare charges due to scattering.

hep-th↗

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.

hep-th↗

arXiv2020

Hidden Conformal Invariance of Scalar Effective Field Theories

We argue that conformal invariance is a common thread linking several scalar effective field theories that appear in the double copy and scattering equations. For a derivatively coupled scalar with a quartic ${\cal O}(p^4)$ vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension $D=0$. For the case of a quartic ${\cal O}(p^6)$ vertex, classical conformal invariance constrains the theory to be the special Galileon in $D=-2$ dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.

hep-th↗

arXiv2020

Leading Nonlinear Tidal Effects and Scattering Amplitudes

We present the two-body Hamiltonian and associated eikonal phase, to leading post-Minkowskian order, for infinitely many tidal deformations described by operators with arbitrary powers of the curvature tensor. Scattering amplitudes in momentum and position space provide systematic complementary approaches. For the tidal operators quadratic in curvature, which describe the linear response to an external gravitational field, we work out the leading post-Minkowskian contributions using a basis of operators with arbitrary numbers of derivatives which are in one-to-one correspondence with the worldline multipole operators. Explicit examples are used to show that the same techniques apply to both bodies interacting tidally with a spinning particle, for which we find the leading contributions from quadratic in curvature tidal operators with an arbitrary number of derivatives, and to effective field theory extensions of general relativity. We also note that the leading post-Minkowskian order contributions from higher-dimension operators manifest double-copy relations. Finally, we comment on the structure of higher-order corrections.

hep-th↗

arXiv2020

Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory

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 spin1-spin2 terms of a two-body effective Hamiltonian through O(G^2) 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.

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.

hep-th↗

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.

hep-th↗

arXiv2018

Gravitational Radiation from Color-Kinematics Duality

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to next-to-leading order in couplings. The radiation is sourced by the scattering of two relativistic massive scalar sources with the dynamical effect taken into account, corresponding to the post-Minkowskian regime in gravity. We show how to arrange the Yang-Mills radiation such that the duality between colors and kinematics is manifest, including the three-term Jacobi identity. The search for duality-satisfying expressions exploits an auxiliary bi-adjoint scalar theory as a guide for locality. The double copy is obtained by replacing the color factors in Yang-Mills with kinematic counterparts, following Bern-Carrasco-Johansson construction in S- matrix. On the gravity side, the radiation is directly computed at the third post-Minkowskian order with massive sources. We find perfect agreement between observables in dilaton gravity and the Yang-Mills double copy. This non-trivially generalizes the leading-order rules by Goldberger and Ridgway. For the first time, the kinematic Jacobi identity appears beyond field-theory S-matrix, suggesting that the color-kinematics duality holds more generally. Our results offer a path for simplifying analytical calculations in post-Minkowskian regime.

hep-th↗