arXiv subjects

Zhengwen Liu

Publications and source records attributed to Zhengwen Liu.

At least 19 recordsLinked to original sources

arXiv2026

Nonlocal-in-time tail effects in gravitational scattering to fifth Post-Minkowskian and tenth self-force orders

Using the worldline effective field theory formalism, we derive the nonlocal-in-time conservative contributions arising from tail effects in gravitational scattering to fifth Post-Minkowskian (5PM) and tenth self-force (10SF) orders. The result features multiple polylogarithms of up to weight three. This challenging computation relies on state-of-the-art integration techniques, including a novel integration-by-parts algorithm: the Sparse Integral Reducer (SpideR). We find perfect agreement in the overlap with all existing literature through sixth post-Newtonian order. The results presented here provide a key ingredient for isolating the local-in-time component of the conservative two-body dynamics of binary inspirals at 5PM order.

hep-th↗

arXiv2026

Conservative binary dynamics to third post-Minkowskian order beyond General Relativity

We present the conservative dynamics of compact binaries to third order in the post-Minkowskian approximation in a theory that extends general relativity by a massless scalar field coupled to the Gauss-Bonnet invariant. We employ the effective field theory approach to construct the effective action of binary systems by integrating out the metric and scalar degrees of freedom that mediate the gravitational interactions between the two bodies. We derive analytical expressions for the scattering impulse and the deflection angle to third order in the post-Minkowskian expansion. Our results are found to be in agreement, in the overlapping regimes, with state-of-the-art calculations in the post-Newtonian/post-Minkowskian theory.

gr-qc↗

arXiv2025

Exiting National Anti-Poverty Campaign, Social Support, and Improved Mental Health

We study the psychological and social impacts of exiting a national anti-poverty campaign, leveraging China's phase-out of its national poverty assistance as a natural experiment. Using a regression discontinuity design, we find that exiting the national campaign improves mental wellbeing. These improvements are accompanied by stronger social and family ties -- such as greater perceived support and communication, while income and material conditions remain largely unchanged. Our findings offer insights into the design of policy exits and underscore the importance of incorporating measures that sustain community- and family-based support systems when implementing or ending assistance programs.

econ.GN↗

arXiv2025

Local-in-Time Conservative Binary Dynamics at Fifth Post-Minkowskian and First Self-Force Orders

We report the local-in-time conservative dynamics of nonspinning binary systems at fifth Post-Minkowskian (5PM) and first self-force (1SF) orders. This follows from an explicit calculation of the 5PM/1SF nonlocal-in-time tail-type contribution to the deflection angle via worldline effective field theory techniques. Proceeding as in [2403.04853], we subtract the nonlocal tail terms from the result in [2403.07781] and reconstruct a local-in-time Hamiltonian in isotropic gauge -- valid for generic orbits. For completeness, we reinstate the nonlocal terms relevant for elliptic-like motion up to 6PN/1SF in a small-eccentricity expansion. Via the connection between the (source) energy flux in [2210.05541] and tail effects, we also derive the SF-exact logarithmic-dependent part of the full 5PM bound Hamiltonian. Our results provide the most accurate description to date of the dynamics of bound compact objects within the framework of relativistic scattering computations.

hep-th↗

arXiv2024

Tree-level soft emission for two pairs of quarks

We compute the tree-level current for the emission of two soft quark-antiquark pairs in a hard scattering. We also compute the square of this current and discuss the resulting color correlations, featuring dipole correlations and three-parton correlations. This object is essential for analyzing the infrared singularities at next-to-next-to-next-to-next-to-leading-order (N4LO) predictions in perturbative QCD.

hep-ph↗

arXiv2024

Local-in-time Conservative Binary Dynamics at Fourth Post-Minkowskian Order

Leveraging scattering information to describe binary systems in generic orbits requires identifying local- and nonlocal-in-time tail effects. We report here the derivation of the universal (non-spinning) local-in-time conservative dynamics at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$. This is achieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [2112.11296,2210.05541]. Unlike the total result, the integration problem involves two scales, velocity and mass ratio, and features multiple polylogarithms, complete elliptic and iterated elliptic integrals, notably in the mass ratio. We reconstruct the local radial action, center-of-mass momentum and Hamiltonian, as well as the exact logarithmic-dependent part(s), all valid for generic orbits. We incorporate the remaining nonlocal terms for elliptic-like motion to sixth Post-Newtonian order. The combined Hamiltonian is in perfect agreement in the overlap with the Post-Newtonian state of the art. The results presented here provide the most accurate description of gravitationally-bound binaries harnessing scattering data to date, readily applicable to waveform modelling.

hep-th↗

arXiv2023

Machine Learning Post-Minkowskian Integrals

We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine learning approach improves the convergence of the Monte Carlo algorithm for high-precision evaluation of multi-dimensional integrals compared to traditional algorithms. In particular, we use a neural network to improve the importance sampling. For a set of representative integrals appearing in the computation of the conservative dynamics for a compact binary system in General Relativity, we perform a quantitative comparison between the Monte Carlo integrators VEGAS and i-flow, an integrator based on neural network sampling.

hep-th↗

arXiv2023

Bootstrapping the relativistic two-body problem

We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop" integration problem via the methodology of differential equations and expansion by regions. This allows us to "bootstrap" the two-body relativistic dynamics in the Post-Minkowskian (PM) expansion from boundary data evaluated in the near-static (soft) limit. We illustrate the procedure with the derivation of the total spacetime impulse in the scattering of non-spinning bodies to 4PM (three-loop) order, i.e. ${\cal O}(G^4)$, including conservative and dissipative effects.

hep-th↗

arXiv2022

Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order

We obtain the total impulse in the scattering of non-spinning binaries in general relativity at fourth Post-Minkowskian order, i.e. ${\cal O}(G^4)$, including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multi-loop" integration techniques from collider physics. The complete results are in agreement with various partial calculations in the Post-Newtonian/Minkowskian expansion.

hep-th↗

arXiv2022

Tree-level soft emission of a quark pair in association with a gluon

We compute the tree-level current for the emission of a soft quark-antiquark pair in association with a gluon. This soft current is the last missing ingredient to understand the infrared singularities that can arise in next-to-next-to-next-to-leading-order (N$^3$LO) computations in QCD. Its square allows us to understand for the first time the colour correlations induced by the soft emission of a quark pair and a gluon. We find that there are three types of correlations: Besides dipole-type correlations that have already appeared in soft limits of tree-level amplitudes, we uncover for the first time also a three-parton correlation involving a totally symmetric structure constant. We also study the behaviour of collinear splitting amplitudes in the triple-soft limit, and we derive the corresponding factorisation formula.

hep-ph↗

arXiv2022

Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to ${\cal O}(G^2)$, which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

hep-th↗

arXiv2022

Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach

We present the contribution from potential interactions to the dynamics of non-spinning binaries to fourth Post-Minkowskian (4PM) order. This is achieved by computing the scattering angle to ${\cal O}(G^4)$ using the effective field theory approach and deriving the bound radial action through analytic continuation. We reconstruct the Hamiltonian and center-of-mass momentum in an isotropic gauge. The (three-loop) integrals involved in our calculation are computed via differential equations, including a sector yielding elliptic integrals. Using the universal link between potential and tail terms, we also report: 1) The instantaneous energy flux at ${\cal O}(G^3)$; 2) The contribution to the 4PM unbound/bound radial action(s) depending on logarithms of the binding energy; 3) The (scheme-independent) logarithmic contribution to the 4PM non-local tail Hamiltonian for circular orbits. Our results in the potential region are in agreement with the recent derivation from scattering amplitudes. We also find perfect agreement in the overlap with the state-of-the-art in Post-Newtonian theory.

hep-th↗

arXiv2022

Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion

We compute the conservative dynamics of non-spinning binaries at fourth Post-Minkowskian order in the large-eccentricity limit, including both potential and radiation-reaction tail effects. This is achieved by obtaining the scattering angle in the worldline effective field theory approach and deriving the bound radial action via analytic continuation. The associated integrals are bootstrapped to all orders in velocities through differential equations, with boundary conditions in the potential and radiation regions. The large angular momentum expansion captures all the local-in-time effects as well as the trademark logarithmic corrections for generic bound orbits. Agreement is found in the overlap with the state-of-the-art in Post-Newtonian theory.

hep-th↗

arXiv2021

Infrared photons and asymptotic symmetries

S-matrix elements exhibit universal factorization when multiple infrared photons are emitted in scattering processes. We explicitly show that the leading soft factorization of tree-level amplitudes with the emission of any number of soft photons can be interpreted as the Ward identity of the asymptotic symmetry of gauge theory.

hep-th↗

arXiv2021

The old conformal bootstrap revisited

The "old" conformal bootstrap was originally formulated by Migdal and Polyakov (MP) as a method for calculating conformal dimensions self-consistently. In this work we revisit the MP bootstrap and apply efficient multi-loop Feynman integral techniques in order to solve the corresponding equations. We obtain solutions at first order in the skeleton expansion for finite coupling and for integer values of the spacetime dimension. We focus in particular on the $ϕ^3$ theory in seven dimensions and the $O(N)$ vector models in three dimensions.

hep-th↗

arXiv2020

Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach

We derive the conservative dynamics of non-spinning binaries to third Post-Minkowskian order, using the Effective Field Theory (EFT) approach introduced in [2006.01184] together with the Boundary-to-Bound dictionary developed in [1910.03008, 1911.09130]. The main ingredient is the scattering angle, which we compute to ${\cal O}(G^3)$ via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with Post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern et al. [1901.04424, 1908.01493].

hep-th↗

arXiv2020

Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order

Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the recent derivation of its quadrupolar part using the classical limit of scattering amplitudes.

hep-th↗

arXiv2019

Bootstrapping solutions of scattering equations

The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations based on the numerical algebraic geometry. The cornerstone of our method is the concept of the physical homotopy between different points in the kinematic space, which naturally induces a homotopy of the scattering equations. As a result, the solutions of the scattering equations with different points in the kinematic space can be tracked from each other. Finally, with the help of soft limits, all solutions can be bootstrapped from the known solution for the four-particle scattering.

hep-th↗