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Title: Nucleon structure functions with domain wall fermions

Abstract

We present a quenched lattice QCD calculation of the first few moments of the polarized and unpolarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing a{sup -1}{approx_equal}1.3 GeV, physical volume V{approx_equal}(2.4 fm){sup 3}, and light quark masses down to about 1/4 the strange quark mass (m{sub {pi}}{approx_equal}400 MeV). Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of the flavor nonsinglet momentum fraction to the helicity distribution, <x>{sub u-d}/<x>{sub {delta}}{sub u-{delta}{sub d}}, which is in very good agreement with experiment. We discuss the implications of this result. Next, we show that the chiral symmetry of domain wall fermions is useful in eliminating mixing of power divergent lower dimensional operators with twist-3 operators. Finally, we compute the isovector tensor charge at renormalization scale {mu}=2 GeV in the MS scheme, <1>{sub {delta}}{sub u-{delta}}{sub d}=1.192(30), where the error is the statistical error only.

Authors:
 [1];  [2];  [3];  [4];  [5];  [3]
  1. CTP/LNS, Room 6-304, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139-4307 (United States)
  2. RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973 (United States)
  3. (United States)
  4. Institute for Particle and Nuclear Studies, KEK, Tsukuba, Ibaraki, 305-0801 (Japan)
  5. (SOKENDAI), Tsukuba, Ibaraki 305-0801 (Japan)
Publication Date:
OSTI Identifier:
20783005
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.73.094503; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; D QUARKS; DISTRIBUTION; FLAVOR MODEL; GEV RANGE; HELICITY; ISOVECTORS; LATTICE FIELD THEORY; MEV RANGE; NUCLEONS; QUANTUM CHROMODYNAMICS; RENORMALIZATION; REST MASS; S QUARKS; STRUCTURE FUNCTIONS; U QUARKS; WALLS

Citation Formats

Orginos, K., Blum, T., Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, Ohta, S., Graduate University for Advanced Studies, and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973. Nucleon structure functions with domain wall fermions. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.73.094503.
Orginos, K., Blum, T., Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, Ohta, S., Graduate University for Advanced Studies, & RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973. Nucleon structure functions with domain wall fermions. United States. doi:10.1103/PHYSREVD.73.094503.
Orginos, K., Blum, T., Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, Ohta, S., Graduate University for Advanced Studies, and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973. Mon . "Nucleon structure functions with domain wall fermions". United States. doi:10.1103/PHYSREVD.73.094503.
@article{osti_20783005,
title = {Nucleon structure functions with domain wall fermions},
author = {Orginos, K. and Blum, T. and Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046 and Ohta, S. and Graduate University for Advanced Studies and RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973},
abstractNote = {We present a quenched lattice QCD calculation of the first few moments of the polarized and unpolarized structure functions of the nucleon. Our calculations are done using domain wall fermions and the DBW2 gauge action with inverse lattice spacing a{sup -1}{approx_equal}1.3 GeV, physical volume V{approx_equal}(2.4 fm){sup 3}, and light quark masses down to about 1/4 the strange quark mass (m{sub {pi}}{approx_equal}400 MeV). Values of the individual moments are found to be significantly larger than experiment, as in past lattice calculations, but interestingly the chiral symmetry of domain wall fermions allows for a precise determination of the ratio of the flavor nonsinglet momentum fraction to the helicity distribution, <x>{sub u-d}/<x>{sub {delta}}{sub u-{delta}{sub d}}, which is in very good agreement with experiment. We discuss the implications of this result. Next, we show that the chiral symmetry of domain wall fermions is useful in eliminating mixing of power divergent lower dimensional operators with twist-3 operators. Finally, we compute the isovector tensor charge at renormalization scale {mu}=2 GeV in the MS scheme, <1>{sub {delta}}{sub u-{delta}}{sub d}=1.192(30), where the error is the statistical error only.},
doi = {10.1103/PHYSREVD.73.094503},
journal = {Physical Review. D, Particles Fields},
number = 9,
volume = 73,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2006},
month = {Mon May 01 00:00:00 EDT 2006}
}
  • We report on numerical lattice QCD calculations of some of the low moments of the nucleon structure functions. The calculations are carried out with gauge configurations generated by the RBC and UKQCD Collaborations with (2+1)-flavors of dynamical domain-wall fermions and the Iwasaki gauge action ({beta} = 2.13). The inverse lattice spacing is a{sup -1} = 1.73 GeV, and two spatial volumes of (2.7 fm){sup 3} and (1.8 fm){sup 3} are used. The up and down quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV, while the strange mass is about 12% heavier than the physicalmore » one. The structure function moments we present include the fully nonperturbatively renormalized isovector quark momentum fraction x{sub u-d}, the helicity fraction x{sub {Delta}u-{Delta}d}, and transversity 1{sub {delta}u-{delta}d}, as well as an unrenormalized twist-3 coefficient d{sub 1}. The ratio of the momentum to helicity fractions, x{sub u-d}/x{sub {Delta}u-{Delta}d}, does not show dependence on the light quark mass and agrees well with the value obtained from experiment. Their respective absolute values, fully renormalized, show interesting trends toward their respective experimental values at the lightest quark mass. A prediction for the transversity, 0.7 < 1{sub {delta}u-{delta}d} < 1.1, in the MS{sup -} scheme at 2 GeV is obtained. The twist-3 coefficient, d{sub 1}, though yet to be renormalized, supports the perturbative Wandzura-Wilczek relation.« less
  • We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Non-perturbative renormalization of the relevant quark currents is performed where necessary. The inverse lattice spacing,more » $$a^{-1}$$, is about 1.7 GeV. We use degenerate up and down dynamical quark masses around 1, 3/4 and 1/2 the strange quark mass. The physical volume of the lattice is about $$(1.9{fm})^3$$. The ratio of the isovector vector to axial charges, $$g_A/g_V$$, trends a bit lower than the experimental value as the quark mass is reduced toward the physical point. We calculate the momentum-transfer dependences of the isovector vector, axial, induced tensor and induced pseudoscalar form factors. The Goldberger-Treiman relation holds at low momentum transfer and yields a pion-nuc« less
  • We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.
  • We present a numerical lattice quantum chromodynamics calculation of isovector form factors and the first few moments of the isovector structure functions of the nucleon. The calculation employs two degenerate dynamical flavors of domain-wall fermions, resulting in good control of chiral symmetry breaking. Nonperturbative renormalization of the relevant quark currents is performed where necessary. The DBW2 gauge action is used to further improve the chiral behavior while maintaining a reasonable physical lattice volume. The inverse lattice spacing, a{sup -1}, is approximately 1.7 GeV. Degenerate up and down dynamical quark masses of approximately 1, 3/4 and 1/2 times the strange quarkmore » mass are used. The physical volume of the lattice is about (1.9 fm){sup 3}. The ratio of the isovector vector to axial charges, g{sub A}/g{sub V}, tends to a lower value than the experimental value as the quark mass is reduced toward the physical point. Momentum-transfer dependences of the isovector vector, axial, induced-tensor and induced-pseudoscalar form factors are calculated. The Goldberger-Treiman relation holds at low momentum transfer and yields an estimation of the pion-nucleon coupling, g{sub {pi}}{sub NN}=15.5(1.4), where the quoted error is only statistical. We find that the flavor nonsinglet quark momentum fraction <x>{sub u-d} and quark helicity fraction <x>{sub {delta}}{sub u-{delta}}{sub d} overshoot their experimental values after linear chiral extrapolation. We discuss possible systematic errors for this discrepancy. An estimate for transversity, <1>{sub {delta}}{sub u-{delta}}{sub d}=0.93(6) in MS at 2 GeV, is obtained and a twist-3 polarized moment, d{sub 1}, appears small, suggesting that the Wandzura-Wilczek relation holds approximately. We discuss in detail the systematic errors in the calculation, with particular attention paid to finite volume, excited-state contamination, and chiral extrapolations.« less