skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Relativistic, model-independent, multichannel 2 2 transition amplitudes in a finite volume

Abstract

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $$\rho$$-meson form factor, in which the unstable nature of the $$\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.

Authors:
 [1];  [2]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Johannes Gutenberg-Univ. Mainz, Mainz (Germany)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1262312
Alternate Identifier(s):
OSTI ID: 1262447
Report Number(s):
JLAB-THY-15-2140; DOE/OR/23177-3556; arXiv:1509.08507
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
AC05-06OR23177
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite volume

Citation Formats

Briceno, Raul A., and Hansen, Maxwell T. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume. United States: N. p., 2016. Web. doi:10.1103/PhysRevD.94.013008.
Briceno, Raul A., & Hansen, Maxwell T. Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume. United States. doi:10.1103/PhysRevD.94.013008.
Briceno, Raul A., and Hansen, Maxwell T. Wed . "Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume". United States. doi:10.1103/PhysRevD.94.013008. https://www.osti.gov/servlets/purl/1262312.
@article{osti_1262312,
title = {Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume},
author = {Briceno, Raul A. and Hansen, Maxwell T.},
abstractNote = {We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.},
doi = {10.1103/PhysRevD.94.013008},
journal = {Physical Review D},
number = 1,
volume = 94,
place = {United States},
year = {2016},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Scalar mesons in a finite volume
journal, January 2011

  • Bernard, V.; Lage, M.; Meißner, U. -G.
  • Journal of High Energy Physics, Vol. 2011, Issue 1
  • DOI: 10.1007/JHEP01(2011)019

Parity violation in proton-proton scattering at 13.6 MeV
journal, February 1991


Connecting physical resonant amplitudes and lattice QCD
journal, June 2016


On the Recovery and Resolution of Exponential Relaxation Rates from Experimental Data: A Singular-Value Analysis of the Laplace Transform Inversion in the Presence of Noise
journal, September 1982

  • Bertero, M.; Boccacci, P.; Pike, E. R.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 383, Issue 1784
  • DOI: 10.1098/rspa.1982.0117

Helicity operators for mesons in flight on the lattice
journal, January 2012


Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
journal, October 2014


Resonance parameters of the rho-meson from asymmetrical lattices
journal, January 2013


Measurement of parity-violating γ -ray asymmetry in the capture of polarized cold neutrons on protons
journal, January 2011


Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012


Hadronic parity violation
journal, July 2013


S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD
journal, August 2012


Search for parity violation in neutron-proton capture
journal, March 1977


Observation of 1.5% Parity-Nonconserving γ -Ray Asymmetry
journal, June 1971


Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013


Parity nonconservation in polarized-neutron transmission through La 139
journal, November 1991


Timelike pion form factor in lattice QCD
journal, March 2015


Nucleon-Nucleon Scattering from Fully Dynamical Lattice QCD
journal, July 2006


Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

  • Lellouch, Laurent; Lüscher, Martin
  • Communications in Mathematical Physics, Vol. 219, Issue 1
  • DOI: 10.1007/s002200100410

Measurement of Parity Nonconservation in pp Scattering at 45 MeV
journal, March 1980


Experimental Test of Parity Conservation in Beta Decay
journal, February 1957


Parity Violation in Proton-Proton Scattering at 221 MeV
journal, December 2001


Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995


Nucleon to Δ and Δ form factors in lattice QCD
conference, January 2012

  • Alexandrou, Constantia
  • THE 8TH INTERNATIONAL WORKSHOP ON THE PHYSICS OF EXCITED NUCLEONS: NSTAR 2011, AIP Conference Proceedings
  • DOI: 10.1063/1.3701190

Two-nucleon systems in a finite volume: Quantization conditions
journal, August 2013


Predicting positive parity B s mesons from lattice QCD
journal, November 2015


Relativistic, model-independent, three-particle quantization condition
journal, December 2014


Three particles in a finite volume
journal, May 2012


Precision measurement of parity nonconservation in proton-proton scattering at 45 MeV
journal, April 1987


Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013


Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD
journal, November 2015


Resonance parameters of the ρ meson from lattice QCD
journal, May 2011


Lattice QCD calculation of the ρ meson decay width
journal, November 2007


Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD
journal, June 2012


The anapole form factor of the deuteron
journal, April 2001


Toward the excited meson spectrum of dynamical QCD
journal, August 2010


Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014


Parity-violating polarization in np d γ with a pionless effective field theory
journal, May 2010


Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015


Multichannel 1 2 transition amplitudes in a finite volume
journal, February 2015


Multichannel 0 2 and 1 2 transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015


A new experimental study of the circular polarization of np capture γ-rays
journal, April 1984


Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry
journal, August 2013


Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

  • Lüscher, M.
  • Communications in Mathematical Physics, Vol. 105, Issue 2
  • DOI: 10.1007/BF01211097

Parity violation in proton-proton scattering at 221 MeV
journal, September 2003


Two particle states and the S -matrix elements in multi-channel scattering
journal, July 2005


Matrix elements of unstable states
journal, September 2012

  • Bernard, V.; Hoja, D.; Meißner, U. -G.
  • Journal of High Energy Physics, Vol. 2012, Issue 9
  • DOI: 10.1007/JHEP09(2012)023

D s mesons with D K and D * K scattering near threshold
journal, August 2014


Parity-Violating Asymmetry of the 501-keV Gamma Ray Emitted in the Decay of Hf 180 m
journal, November 1971


Two nucleon systems at m π 450 MeV from lattice QCD
journal, December 2015


Coupled channel analysis of the ρ meson decay in lattice QCD
journal, September 2011


A framework for the calculation of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>N</mml:mi><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math> transition form factors on the lattice
journal, September 2014


Resonances in Coupled π K η K Scattering from Quantum Chromodynamics
journal, October 2014


K π scattering and the K * decay width from lattice QCD
journal, September 2013


Finite volume corrections to the two-particle decay of states with nonzero momentum
journal, December 2005


Resonances in coupled π K , η K scattering from lattice QCD
journal, March 2015


Reanalysis of lattice QCD spectra leading to the D s0 ∗ (2317) and D s1 ∗ (2460)
journal, May 2015

  • Torres, A. Martínez; Oset, E.; Prelovsek, S.
  • Journal of High Energy Physics, Vol. 2015, Issue 5
  • DOI: 10.1007/JHEP05(2015)153

The theory of parity violation in few-nucleon systems
journal, September 2013


Erratum: Coupled channel analysis of the ρ meson decay in lattice QCD [Phys. Rev. D 84, 054503 (2011)]
journal, March 2014


Parity-violating neutron spin rotation in hydrogen and deuterium
journal, January 2012

  • Grießhammer, H. W.; Schindler, M. R.; Springer, R. P.
  • The European Physical Journal A, Vol. 48, Issue 1
  • DOI: 10.1140/epja/i2012-12007-8

Electroweak matrix elements in the two-nucleon sector from lattice QCD
journal, October 2004


Energy dependence of the ρ resonance in π π elastic scattering from lattice QCD
journal, February 2013


Parity in Nuclear Reactions
journal, August 1957


Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991


Parity violation in proton-proton scattering at 45 MeV
journal, November 1984


Excited meson radiative transitions from lattice QCD using variationally optimized operators
journal, June 2015


ρ meson decay in 2 + 1 flavor lattice QCD
journal, November 2011


K→ππ decays in a finite volume
journal, December 2001


Two parity-violating asymmetries from in pionless effective field theories
journal, November 2010


Resonant π + γ π + π 0 Amplitude from Quantum Chromodynamics
journal, December 2015


An effective-field-theory analysis of low-energy parity-violation in nucleon–nucleon scattering
journal, May 2009


Two-nucleon systems in a finite volume. II. S 1 3 D 1 3 coupled channels and the deuteron
journal, December 2013


Ab initio Calculation of the n p d γ Radiative Capture Process
journal, September 2015


Finite-volume effects for two-hadron states in moving frames
journal, October 2005


Possible Interference Phenomena between Parity Doublets
journal, November 1956


Δ ( 1232 ) Axial Charge and Form Factors from Lattice QCD
journal, September 2011


Finite-volume matrix elements in multiboson states
journal, April 2015


Upper bound on parity-violating neutron spin rotation in He 4
journal, February 2011


Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics
journal, December 2014


Lattice QCD calculation of nuclear parity violation
journal, February 2012