Gross-Llewellyn Smith sum rule from lattice QCD

Abstract

We compute the Gross-Llewellyn Smith sum rule, i.e. the lowest odd moment of the parity-violating structure function, $F_3$, of the nucleon from a lattice QCD calculation of the Compton amplitude. Our calculations are performed on $48^3\times 96$ lattices at the $SU(3)$ symmetric point for two lattice spacings. We extract the moments for several values of the current momenta in the range $0.5\lesssim Q^2\lesssim 10{\mathrm{GeV}}^2$, covering both the nonperturbative and perturbative regimes. We compare our moments to the Gross-Llewellyn Smith sum rule and discuss the implications for higher-twist effects, a determination of ${\alpha }_s(Q^2)$ from a hadronic quantity complementing the phenomenological and other lattice approaches, and electroweak box contributions crucial for Cabibbo-Kobayashi-Maskawa matrix unitarity studies.

16 pages, 12 figures

References in corpus (42)

• The Chroma Software System for Lattice QCD
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• The QCD Running Coupling
• Reduced hadronic uncertainty in the determination of $V_{ud}$
• Improved Calculation of Electroweak Radiative Corrections and the Value of V_ud
• Superallowed 0+ --> 0+ nuclear beta decays: 2014 critical survey, with precise results for Vud and CKM unitarity
• Nucleon structure functions from lattice operator product expansion
• Review of two-photon exchange in electron scattering
• Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• Flavour blindness and patterns of flavour symmetry breaking in lattice simulations of up, down and strange quarks
• Low Energy Measurements of the Weak Mixing Angle
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• Tuning the strange quark mass in lattice simulations
• Standard Model $\mathcal{O}(\alpha )$ renormalization of $g_A$ and its impact on new physics searches
• Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element
• First-principles calculation of electroweak box diagrams from lattice QCD
• Precise determination of the strong coupling constant in Nf=2+1 lattice QCD with the Schrödinger functional scheme
• Non-perturbative improvement of stout-smeared three flavour clover fermions
• QCD Running Couplings and Effective Charges
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited
• Determination of the QCD coupling from the static energy and the free energy
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• Disconnected contributions to the spin of the nucleon
• New formulation of gamma-Z box corrections to the weak charge of the proton
• Charged multi-hadron systems in lattice QCD+QED
• Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions
• Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem
• Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays
• An update on the BQCD Hybrid Monte Carlo program
• Generalised parton distributions from the off-forward Compton amplitude in lattice QCD
• Toward a First-Principles Calculation of Electroweak Box Diagrams
• Running coupling constant from position-space current-current correlation functions in three-flavor lattice QCD
• Strong coupling constant from moments of quarkonium correlators revisited
• Superallowed nuclear beta decays and precision tests of the Standard Model
• Determination of ${\alpha }_s(m_Z)$ by the non-perturbative decoupling method
• Nucleon in a periodic magnetic field
• Constraining beyond the Standard Model nucleon isovector charges
• Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD
• Additional Corrections to the Gross-Llewellyn Smith Sum Rule
• Feynman--Hellmann approach to transition matrix elements and quasi-degenerate energy states
• Higher Twists

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