We develop a general expression for weighted cross sections in leptonic annihilation to hadrons based on time-ordered perturbation theory (TOPT). The analytic behavior of the resulting integrals over spatial momenta can be analyzed in the language of Landau equations and infrared (IR) power counting. For any infrared-safe weight, the cancellation of infrared divergences is implemented locally at the integrand level, and in principle can be evaluated numerically in four dimensions. We go on to show that it is possible to eliminate unphysical singularities that appear in time-ordered perturbation theory for arbitrary amplitudes. This is done by reorganizing TOPT into an equivalent form that combines classes of time orderings into a “partially time-ordered perturbation theory”. Applying the formalism to leptonic annihilation, we show how to derive diagrammatic expressions with only physical unitarity cuts.
- Award ID(s):
- 1914731
- PAR ID:
- 10280969
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2021
- Issue:
- 3
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
A<sc>bstract</sc> -
Abstract In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter.more » « less
-
more » « less
Experimental demonstrations of modified chemical structure and reactivity under strong light–matter coupling have spurred theoretical and computational efforts to uncover underlying mechanisms. Ab initio cavity quantum electrodynamics (QED) combines quantum chemistry with cavity QED to investigate these phenomena in detail. Unitary transformations of ab initio cavity QED Hamiltonians have been used to make them more computationally tractable. We analyze one such transformation, the coherent state transformation, using perturbation theory. Applying perturbation theory up to third order for ground state energies and potential energy surfaces of several molecular systems under electronic strong coupling, we show that the coherent state transformation yields better agreement with exact ground state energies. We examine one specific case using perturbation theory up to ninth order and find that coherent state transformation performs better up to fifth order but converges more slowly to the exact ground state energy at higher orders. In addition, we apply perturbation theory up to second order for cavity mode states under bilinear coupling, elucidating how the coherent state transformation accelerates the convergence of the photonic subspace toward the complete basis limit and renders molecular ion energies origin invariant. These findings contribute valuable insights into computational advantages of the coherent state transformation in the context of ab initio cavity quantum electrodynamics methods.
-
We introduce the notions of static regular of type (I) and type (II) and show that they are sufficient conditions for local well-posedness of solving asymptotically flat, static vacuum metrics with prescribed Bartnik boundary data. We then show that hypersurfaces in a very general open and dense family of hypersurfaces are static regular of type (II). As applications, we confirm Bartnik’s static vacuum extension conjecture for a large class of Bartnik boundary data, including those that can be far from Euclidean and have large ADM masses, and give many new examples of static vacuum metrics with intriguing geometry.more » « less
-
A bstract A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory and $$ \mathcal{N} $$ N = 8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP03(2021)080
