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

In this paper, 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 $$N_f=2+1+1$$ 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 excited-state systematics with the new method and obtain a value of $$g_A = 1.213(26)$$ with a quark-mass-dependent renormalization coefficient.
Authors:
 [1] ;  [2] ;  [2] ;  [3] ;  [4]
  1. Univ. of Glasgow, Glasgow (United Kingdom); The College of William and Mary, Williamsburg, VA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. The College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  4. 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):
JLAB-THY-17-2419; DOE/OR/23177-4075; arXiv:1612.06963
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:
AC05-06OR23177; AC02-05CH11231; FG02-04ER41302; SC0015376; KB0301052; NQCDAWL
Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2470-0010
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) (SC-26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
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