Two-particle elastic scattering in a finite volume including QED

Beane, Silas R.; Savage, Martin J.

doi:10.1103/physrevd.90.074511

Cited by 35 publications

(112 citation statements)

References 65 publications

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“…For example, as is demonstrated in Ref. [50], the power-law corrections to the mass of charged particles modify the kinematics of 2 → 2 scattering processes, requiring keeping track of this change in subsequent calculations. Starting out with the incoming and outgoing hadrons that are already close to their infinite-volume mass simplifies the formalism that extracts scattering amplitudes from energy spectra.…”

Section: Infrared Improvement Of the Qed L Theorymentioning

confidence: 98%

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

et al. 2019

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First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-1 2 particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called QED L . By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to QED L . Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of QED L , a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.

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Section: Infrared Improvement Of the Qed L Theorymentioning

confidence: 98%

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

et al. 2019

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“…Eventually, the inclusion of electromagnetism will shift the single and two-nucleon spectra and will introduce Coulomb repulsion between the final-state protons, requiring extensions of the formalism developed in Refs. [59][60][61] to extract the physical matrix elements.…”

Section: Finite-volume Effectsmentioning

confidence: 99%

Double- β decay matrix elements from lattice quantum chromodynamics

et al. 2017

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A lattice quantum chromodynamics (LQCD) calculation of the nuclear matrix element relevant to the nn → ppeeν e ν e transition is described in detail, expanding on the results presented in Ref.[1]. This matrix element, which involves two insertions of the weak axial current, is an important input for phenomenological determinations of double-β decay rates of nuclei. From this exploratory study, performed using unphysical values of the quark masses, the long-distance deuteron-pole contribution to the matrix element is separated from shorter-distance hadronic contributions. This polarizability, which is only accessible in double-weak processes, cannot be constrained from single-β decay of nuclei, and is found to be smaller than the long-distance contributions in this calculation, but non-negligible. In this work, technical aspects of the LQCD calculations, and of the relevant formalism in the pionless effective field theory, are described. Further calculations of the isotensor axial polarizability, in particular near and at the physical values of the light-quark masses, are required for precise determinations of both two-neutrino and neutrinoless double-β decay rates in heavy nuclei.

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“…The bound-state relation connects the finite-volume correction to the asymptotic properties of the two-particle wave function, whereas the elastic scattering result relates the volume dependence of discrete energy levels to physical scattering parameters. This work has since been extended in several directions, including non-zero angular momenta [4][5][6], moving frames [7][8][9][10][11], generalized boundary conditions [12][13][14][15][16], particles with intrinsic spin [17], and perturbative Coulomb corrections [18]. 1 With improved numerical techniques and computational resources enabling the calculation of systems with an increasing number of constituents, understanding the volume dependence of more complex systems is of timely relevance.…”

Section: Introductionmentioning

confidence: 99%

Volume dependence of N-body bound states

König

Lee

2018

Physics Letters B

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We derive the finite-volume correction to the binding energy of an N -particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

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Two-particle elastic scattering in a finite volume including QED

Cited by 35 publications

References 65 publications

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

Double- β decay matrix elements from lattice quantum chromodynamics

Volume dependence of N-body bound states

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