On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements
In this paper, the FeynmanHellmann theorem can be derived from the long Euclideantime 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 twopoint correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavorchanging, 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 groundstate matrix elements and the fact that all excited states and contact terms are Euclideantime dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradientflowed domainwall valence quarks on the $$N_f=2+1+1$$ 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 excitedstate systematics with the new method and obtain a value of $$g_A = 1.213(26)$$ with a quarkmassdependent renormalization coefficient.
 Authors:

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 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)
 Publication Date:
 Report Number(s):
 JLABTHY172419; DOE/OR/231774075; arXiv:1612.06963
Journal ID: ISSN 24700010; PRVDAQ
 Grant/Contract Number:
 AC0506OR23177; AC0205CH11231; FG0204ER41302; SC0015376; KB0301052; NQCDAWL
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1371542
 Alternate Identifier(s):
 OSTI ID: 1369486; OSTI ID: 1379899
Bouchard, Chris, Chang, Chia Cheng, Kurth, Thorsten, Orginos, Kostas, and WalkerLoud, Andre. On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements. United States: N. p.,
Web. doi:10.1103/PhysRevD.96.014504.
Bouchard, Chris, Chang, Chia Cheng, Kurth, Thorsten, Orginos, Kostas, & WalkerLoud, Andre. On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements. United States. doi:10.1103/PhysRevD.96.014504.
Bouchard, Chris, Chang, Chia Cheng, Kurth, Thorsten, Orginos, Kostas, and WalkerLoud, Andre. 2017.
"On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements". United States.
doi:10.1103/PhysRevD.96.014504. https://www.osti.gov/servlets/purl/1371542.
@article{osti_1371542,
title = {On the FeynmanHellmann theorem in quantum field theory and the calculation of matrix elements},
author = {Bouchard, Chris and Chang, Chia Cheng and Kurth, Thorsten and Orginos, Kostas and WalkerLoud, Andre},
abstractNote = {In this paper, the FeynmanHellmann theorem can be derived from the long Euclideantime 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 twopoint correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavorchanging, 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 groundstate matrix elements and the fact that all excited states and contact terms are Euclideantime dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradientflowed domainwall valence quarks on the $N_f=2+1+1$ 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 excitedstate systematics with the new method and obtain a value of $g_A = 1.213(26)$ with a quarkmassdependent renormalization coefficient.},
doi = {10.1103/PhysRevD.96.014504},
journal = {Physical Review D},
number = 1,
volume = 96,
place = {United States},
year = {2017},
month = {7}
}