On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

Bouchard, Chris; Chang, Chia Cheng; Kurth, Thorsten; Orginos, Kostas; Walker-Loud, Andre

doi:10.1103/PhysRevD.96.014504

Title: On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

Journal Article · Wed Jul 12 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.014504· OSTI ID:1371542

Bouchard, Chris ^[1]; Chang, Chia Cheng ^[2]; Kurth, Thorsten ^[2]; Orginos, Kostas ^[3]; Walker-Loud, Andre ^[4]

Univ. of Glasgow, Glasgow (United Kingdom); The College of William and Mary, Williamsburg, VA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
The College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); The College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

© 2017 American Physical Society. The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the Nf=2+1+1 MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of gA=1.213(26) with a quark-mass-dependent renormalization coefficient.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-06OR23177; AC02-05CH11231; FG02-04ER41302; SC0015376; KB0301052; NQCDAWL

OSTI ID:: 1371542

Alternate ID(s):: OSTI ID: 1369486; OSTI ID: 1379899

Report Number(s):: JLAB-THY-17-2419; DOE/OR/23177-4075; arXiv:1612.06963; PRVDAQ

Journal Information:: Physical Review D, Vol. 96, Issue 1; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 40 works

Citation information provided by
Web of Science

References (46)

Scalar densities and baryon mass differences in lattice QCD with Wilson fermions Maiani, L.; Martinelli, G.; Paciello, M. L. Nuclear Physics B, Vol. 293 https://doi.org/10.1016/0550-3213(87)90078-2	journal	January 1987
On the extraction of zero momentum form factors on the lattice de Divitiis, G. M.; Petronzio, R.; Tantalo, N. Physics Letters B, Vol. 718, Issue 2 https://doi.org/10.1016/j.physletb.2012.10.035	journal	December 2012
Effective Field Theory for Heavy Weakly Interacting Massive Particles Scattering with Nucleons Hill, Richard J.; Solon, Mikhail P. Physical Review Letters, Vol. 112, Issue 21 https://doi.org/10.1103/PhysRevLett.112.211602	journal	May 2014
Modification of electromagnetic structure functions for the $γ Z$ -box diagram Rislow, Benjamin C.; Carlson, Carl E. Physical Review D, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevD.88.013018	journal	July 2013
Light baryon masses with dynamical twisted mass fermions Alexandrou, C.; Baron, R.; Blossier, B. Physical Review D, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevD.78.014509	journal	July 2008
Scalar strange content of the nucleon from lattice QCD Junnarkar, P. M.; Walker-Loud, A. Physical Review D, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevD.87.114510	journal	June 2013
Constrained curve fitting Lepage, G. P.; Clark, B.; Davies, C. T. H. Nuclear Physics B - Proceedings Supplements, Vol. 106-107 https://doi.org/10.1016/S0920-5632(01)01638-3	journal	March 2002
Octet baryon masses and sigma terms from an SU(3) chiral extrapolation Young, R. D.; Thomas, A. W. Physical Review D, Vol. 81, Issue 1 https://doi.org/10.1103/PhysRevD.81.014503	journal	January 2010
On the computation of hadron-to-hadron transition matrix elements in lattice QCD Bulava, John; Donnellan, Michael; Sommer, Rainer Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)140	journal	January 2012
Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry Ohki, H.; Fukaya, H.; Hashimoto, S. Physical Review D, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevD.78.054502	journal	September 2008
Clebsch-Gordan construction of lattice interpolated fields for excited baryons Basak, Subhasish; Edwards, Robert; Fleming, George T. Physical Review D, Vol. 72, Issue 7 https://doi.org/10.1103/PhysRevD.72.074501	journal	October 2005
Lattice QCD ensembles with four flavors of highly improved staggered quarks Bazavov, A.; Bernard, C.; Komijani, J. Physical Review D, Vol. 87, Issue 5 https://doi.org/10.1103/PhysRevD.87.054505	journal	March 2013
Intrinsic strangeness and charm of the nucleon using improved staggered fermions Freeman, W.; Toussaint, D. Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.054503	journal	September 2013
Solving lattice QCD systems of equations using mixed precision solvers on GPUs Clark, M. A.; Babich, R.; Barros, K. Computer Physics Communications, Vol. 181, Issue 9 https://doi.org/10.1016/j.cpc.2010.05.002	journal	September 2010
Light hadron spectroscopy using domain wall valence quarks on an asqtad sea Walker-Loud, A.; Lin, H. -W.; Richards, D. G. Physical Review D, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevD.79.054502	journal	March 2009
Forces in Molecules Feynman, R. P. Physical Review, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRev.56.340	journal	August 1939
Disconnected contributions to the spin of the nucleon Chambers, A. J.; Horsley, R.; Nakamura, Y. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114517	journal	December 2015
First evaluation of in lattice QCD in the quenched approximation Fucito, F.; Parisi, G.; Petrarca, S. Physics Letters B, Vol. 115, Issue 2 https://doi.org/10.1016/0370-2693(82)90816-4	journal	August 1982
Axial, scalar, and tensor charges of the nucleon from $2 + 1 + 1$ -flavor Lattice QCD Bhattacharya, Tanmoy; Cirigliano, Vincenzo; Cohen, Saul D. Physical Review D, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevD.94.054508	journal	September 2016
Electromagnetic and spin polarizabilities in lattice QCD Detmold, W.; Tiburzi, B. C.; Walker-Loud, A. Physical Review D, Vol. 73, Issue 11 https://doi.org/10.1103/PhysRevD.73.114505	journal	June 2006
Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory Ren, X. -L.; Geng, L. S.; Camalich, J. Martin Journal of High Energy Physics, Vol. 2012, Issue 12 https://doi.org/10.1007/JHEP12(2012)073	journal	December 2012
Sigma term and strangeness content of octet baryons Dürr, S.; Fodor, Z.; Hemmert, T. Physical Review D, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevD.85.014509	journal	January 2012
Neutron electric polarizability from unquenched lattice QCD using the background field approach Engelhardt, M. Physical Review D, Vol. 76, Issue 11 https://doi.org/10.1103/PhysRevD.76.114502	journal	December 2007
Erratum: Sigma term and strangeness content of octet baryons [Phys. Rev. D 85 , 014509 (2012)] Dürr, S.; Fodor, Z.; Hemmert, T. Physical Review D, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevD.93.039905	journal	February 2016
Lattice Quantum-Chromodynamics Calculation of Some Baryon Magnetic Moments Bernard, Claude; Draper, Terrence; Olynyk, Kirk Physical Review Letters, Vol. 49, Issue 15 https://doi.org/10.1103/PhysRevLett.49.1076	journal	October 1982
Feynman-Hellmann approach to the spin structure of hadrons Chambers, A. J.; Horsley, R.; Nakamura, Y. Physical Review D, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevD.90.014510	journal	July 2014
Lattice Computation of the Nucleon Scalar Quark Contents at the Physical Point Durr, S.; Fodor, Z.; Hoelbling, C. Physical Review Letters, Vol. 116, Issue 17 https://doi.org/10.1103/PhysRevLett.116.172001	journal	April 2016
$B_{(s)}^{0}$ -mixing matrix elements from lattice QCD for the Standard Model and beyond Bazavov, A.; Bernard, C.; Bouchard, C. M. Physical Review D, Vol. 93, Issue 11 https://doi.org/10.1103/PhysRevD.93.113016	journal	June 2016
Nucleon mass, sigma term, and lattice QCD Procura, Massimiliano; Hemmert, Thomas R.; Weise, Wolfram Physical Review D, Vol. 69, Issue 3 https://doi.org/10.1103/PhysRevD.69.034505	journal	February 2004
Precision lattice QCD computation of the $B^{⁎} B π$ coupling Bernardoni, Fabio; Bulava, John; Donnellan, Michael Physics Letters B, Vol. 740 https://doi.org/10.1016/j.physletb.2014.11.051	journal	January 2015
A stochastic method for computing hadronic matrix elements Alexandrou, Constantia; Constantinou, Martha; Dinter, Simon The European Physical Journal C, Vol. 74, Issue 1 https://doi.org/10.1140/epjc/s10052-013-2692-3	journal	January 2014
The proton and neutron magnetic moments in lattice QCD Martinelli, G.; Parisi, G.; Petronzio, R. Physics Letters B, Vol. 116, Issue 6 https://doi.org/10.1016/0370-2693(82)90162-9	journal	October 1982
Extracting electric polarizabilities from lattice QCD Detmold, W.; Tiburzi, B. C.; Walker-Loud, A. Physical Review D, Vol. 79, Issue 9 https://doi.org/10.1103/PhysRevD.79.094505	journal	May 2009
Group-theoretical construction of extended baryon operators in lattice QCD Basak, S.; Edwards, R. G.; Fleming, G. T. Physical Review D, Vol. 72, Issue 9 https://doi.org/10.1103/PhysRevD.72.094506	journal	November 2005
Sigma terms from an SU(3) chiral extrapolation Shanahan, P. E.; Thomas, A. W.; Young, R. D. Physical Review D, Vol. 87, Issue 7 https://doi.org/10.1103/PhysRevD.87.074503	journal	April 2013
Extracting nucleon magnetic moments and electric polarizabilities from lattice QCD in background electric fields Detmold, W.; Tiburzi, B. C.; Walker-Loud, A. Physical Review D, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevD.81.054502	journal	March 2010
Two-photon exchange correction to $2 S - 2 P$ splitting in muonic ${}^{3}{He}$ ions Carlson, Carl E.; Gorchtein, Mikhail; Vanderhaeghen, Marc Physical Review A, Vol. 95, Issue 1 https://doi.org/10.1103/PhysRevA.95.012506	journal	January 2017
Highly improved staggered quarks on the lattice with applications to charm physics Follana, E.; Mason, Q.; Davies, C. Physical Review D, Vol. 75, Issue 5 https://doi.org/10.1103/PhysRevD.75.054502	journal	March 2007
Nucleon mass and sigma term from lattice QCD with two light fermion flavors Bali, G. S.; Bruns, P. C.; Collins, S. Nuclear Physics B, Vol. 866, Issue 1 https://doi.org/10.1016/j.nuclphysb.2012.08.009	journal	January 2013
Isovector charges of the nucleon from $2 + 1$ -flavor QCD with clover fermions Yoon, Boram; Jang, Yong-Chull; Gupta, Rajan Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074508	journal	April 2017
First Determination of the Weak Charge of the Proton Androic, D.; Armstrong, D. S.; Asaturyan, A. Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.141803	journal	October 2013
Hyperon sigma terms for $2 + 1$ quark flavors Horsley, R.; Nakamura, Y.; Perlt, H. Physical Review D, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevD.85.034506	journal	February 2012
Nucleon strange quark content from $N_{f} = 2 + 1$ lattice QCD with exact chiral symmetry Ohki, H.; Takeda, K.; Aoki, S. Physical Review D, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevD.87.034509	journal	February 2013
Strangeness in the baryon ground states Semke, A.; Lutz, M. F. M. Physics Letters B, Vol. 717, Issue 1-3 https://doi.org/10.1016/j.physletb.2012.09.008	journal	October 2012
Nucleon mass: From lattice QCD to the chiral limit Procura, M.; Musch, B. U.; Wollenweber, T. Physical Review D, Vol. 73, Issue 11 https://doi.org/10.1103/PhysRevD.73.114510	journal	June 2006
The Chroma Software System for Lattice QCD Edwards, Robert G.; Joó, Bálint Nuclear Physics B - Proceedings Supplements, Vol. 140 https://doi.org/10.1016/j.nuclphysbps.2004.11.254	journal	March 2005

Cited By (11)

A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics Chang, C. C.; Nicholson, A. N.; Rinaldi, E. Nature, Vol. 558, Issue 7708 https://doi.org/10.1038/s41586-018-0161-8	journal	May 2018
Nucleon axial radius and muonic hydrogen—a new analysis and review Hill, Richard J.; Kammel, Peter; Marciano, William J. Reports on Progress in Physics, Vol. 81, Issue 9 https://doi.org/10.1088/1361-6633/aac190	journal	July 2018
FLAG Review 2019 Aoki, S.; Aoki, Y.; Becirevic, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-00055	text	January 2019
FLAG Review 2019: Flavour Lattice Averaging Group (FLAG) Aoki, S.; Aoki, Y.; Bečirević, D. The European Physical Journal C, Vol. 80, Issue 2 https://doi.org/10.1140/epjc/s10052-019-7354-7	journal	February 2020
Electromagnetic form factors at large momenta from lattice QCD Chambers, A. J.; Dragos, J.; Horsley, R. Universität Regensburg https://doi.org/10.5283/epub.39455	text	January 2017
FLAG Review 2019 Aoki, S.; Aoki, Y.; Bečirević, D. Springer https://doi.org/10.7892/boris.141201	text	January 2020
Electromagnetic form factors at large momenta from lattice QCD Chambers, A. J.; Dragos, J.; Horsley, R. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-01385	text	January 2017
FLAG Review 2019 Aoki, S.; Aoki, Y.; Becirevic, D. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-04064	text	January 2020
Iso-vector axial form factors of the nucleon in two-flavour lattice QCD Capitani, Stefano; Della Morte, Michele; Djukanovic, Dalibor arXiv https://doi.org/10.48550/arxiv.1705.06186	text	January 2017
Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review Hill, Richard J.; Kammel, Peter; Marciano, William J. arXiv https://doi.org/10.48550/arxiv.1708.08462	text	January 2017
A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics Chang, Chia Cheng; Nicholson, Amy; Rinaldi, Enrico arXiv https://doi.org/10.48550/arxiv.1805.12130	text	January 2018

Similar Records

Hellmann--Feynman theorem for approximate wave functions and its application to nonadiabatic coupling matrix elements with the aid of a coupled Hartree--Fock method

Journal Article · Thu May 15 00:00:00 EDT 1980 · J. Chem. Phys.; (United States) · OSTI ID:1371542

Habitz, P; Votava, C

Reliability of the Hellmann—Feynman Theorem for Approximate Charge Densities

Journal Article · Mon Jan 01 00:00:00 EST 1962 · Journal of Chemical Physics · OSTI ID:1371542

Salem, L.; Wilson, E. Bright

Hellmann-Feynman theorem and the definition of forces in quantum time-dependent and transport problems

Journal Article · Thu Jun 15 00:00:00 EDT 2000 · Physical Review. B, Condensed Matter and Materials Physics · OSTI ID:1371542

Di Ventra, Massimiliano; Pantelides, Sokrates T

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Title: On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

Citation Formats

References (46)

Cited By (11)

Similar Records

Related Subjects