Deep-inelastic scattering, in the laboratory and on the lattice, is most instructive for understanding how the nucleon is built from quarks and gluons. The long-term goal is to compute the associated ...structure functions from first principles. So far this has been limited to model calculations. In this Letter we propose a new method to compute the structure functions directly from the virtual, all-encompassing Compton amplitude, utilizing the operator product expansion. This overcomes issues of renormalization and operator mixing, which so far have hindered lattice calculations of power corrections and higher moments.
The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, ...the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, Q2. By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta 3 ≲ Q2 ≲ 7 GeV2. This allows for the Q2 dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.
Accessing hadronic form factors at large momentum transfers has traditionally presented a challenge for lattice QCD simulations. Here, we demonstrate how a novel implementation of the ...Feynman-Hellmann method can be employed to calculate hadronic form factors in lattice QCD at momenta much higher than previously accessible. Our simulations are performed on a single set of gauge configurations with three flavors of degenerate mass quarks corresponding to mπ≈470 MeV. We are able to determine the electromagnetic form factors of the pion and nucleon up to approximately 6 GeV2, with results for the ratio of the electric and magnetic form factors of the proton at our simulated quark mass agreeing well with experimental results.
A
bstract
In this paper we present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED, concentrating particularly on violations of isospin symmetry. We calculate ...the
π
+
-
π
0
splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in 1. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the
u
and
d
quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashen’s theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as
M
S
¯
, in which Dashen’s theorem for neutral mesons is violated.
Systems with the quantum numbers of up to 12 charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and ...quantum electrodynamics (QCD + QED) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A nonrelativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charged hadrons and found to accurately reproduce the lattice QCD + QED results. QED effects on charged multihadron systems beyond Coulomb photon exchange are determined by comparing the two- and three-body interaction parameters extracted from the lattice QCD + QED results for charged and neutral multihadron systems.
We compute the electric dipole moment d(n) of the neutron from a fully dynamical simulation of lattice QCD with 2+1 flavors of clover fermions and nonvanishing θ term. The latter is rotated into a ...pseudoscalar density in the fermionic action using the axial anomaly. To make the action real, the vacuum angle θ is taken to be purely imaginary. The physical value of dd(n) is obtained by analytic continuation. We find d(n)=-3.9(2)(9)×10(-16) θ e cm, which, when combined with the experimental limit on d(n), leads to the upper bound |θ|≲7.4×10(-11).
Mixing in the Σ0–Λ0 system is a direct consequence of broken isospin symmetry and is a measure of both isospin-symmetry breaking as well as general SU(3)-flavor symmetry breaking. In this work we ...present a new scheme for calculating the extent of Σ0–Λ0 mixing using simulations in lattice QCD+QED and perform several extrapolations that compare well with various past determinations. Our scheme allows us to easily contrast the QCD-only mixing case with the full QCD+QED mixing.
By considering a flavor expansion about the SU(3) flavor symmetric point, we investigate how flavor blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference ...between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavor symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line-disconnected terms in the three-point correlation functions is also given. As we consider Wilson cloverlike fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavor-conserving matrix elements of the vector first-class form factors.
The SU(3) beta function is computed from Wilson loops to 20th order numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically ...to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.
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