Strange Quark Magnetic Moment of the Nucleon at the Physical Point

Abstract

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of 0.051 GeV 2 < ∼ Q 2 < ∼ 1.31 GeV 2 . The finite lattice spacing and finite volume corrections are included in a global fit with 24 valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment G s M (0) = −0.064(14)(09) µN . The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius r 2 s E = −0.0043(16)(14) fm 2 .The determination of the strange (s) quark contribution to nucleon electromagnetic (EM) form factors is of immense importance since this is a pure sea quark effect. A nonzero value of the strange Sachs electric form factor (FF) G s E at any Q 2 = 0 would mean that the spatial distributions of s ands quarks are not the same in the nucleon. Since the extraction of the vector strange matrix elements N |sγ µ s|N was proposed in Refs. [1-3] via parity-violating e − N scattering for which the dominant contribution arises from interference between photon (γ) and weak boson (Z) exchanges by the following relation assuming isospin symmetry:a considerable number of experimental efforts by the SAMPLE, HAPPEX, G0, and A4 [4-15] Collaborations have been going on for the past two decades. The world data constrains that G s M (0) contributes less than 6% and r 2 s E contributes less than 5% to the magnetic moment and the mean-square charge radius of the proton respectively [16]. However, all these experimental results are limited by rather sizable error bars. Three different global analyses give G s M (Q 2 = 0.1 (GeV/c) 2 ) consistent with zero within uncertainties and differ in sign in their central values [17][18][19].Despite tremendous theoretical efforts, e.g. [20][21][22][23], a detailed convincing understanding about the sign and magnitude of strange EM FFs is still lacking. A detailed review of these theoretical efforts can be found in [24].Since the direct calculation of the s-quark loop in the (8) µ N and, for the first time, a nonzero signal for G s E (Q 2 ) which gave r 2 s E = −0.0067(25) fm 2 . However, one still has to perform the calculation at the physical pion mass and on several lattices to consider volume and finite cutoff corrections and over all beat down the noise to obtain a convincing result which will substantially sharpen our picture of strange quark contributions to the nucleon's EM structure.Conventionally, we omit the unit nucleon magneton µ N for G s M in the rest of the lette...

Light-quark contributions to the magnetic form factor of the Λ(1405)

“…As the loop is correlated with the quarks carrying the quantum numbers of the state only via gluon exchange, resolving a nontrivial signal requires high statistics and innovative methods. While there has been recent success in isolating the relevant disconnected-loop contributions in ground-state baryon matrix elements [3,4], challenges in isolating baryon excitations in lattice QCD [10,40,[45][46][47][48][49][50][51][52][53][54][55][56][57] render the resolution of disconnected contributions elusive.Here, we draw on partially-quenched chiral effective field theory [44,[58][59][60][61][62][63][64][65][66] to understand the relative weight of these disconnected contributions to the form factors in QCD. With this insight, one can test quantitatively whether the light-quark contribution to the magnetic form factor of the Λ(1405), calculated in lattice QCD, is consistent with a molecular KN description of the internal structure.…”

“…While lattice QCD simulation methods are increasingly able to probe the chiral regime of ground state observables with unprecedented accuracy [1][2][3][4], the resolution of excited-baryon form factors is still at a very early stage [5][6][7][8][9][10].…”

“…As the loop is correlated with the quarks carrying the quantum numbers of the state only via gluon exchange, resolving a nontrivial signal requires high statistics and innovative methods. While there has been recent success in isolating the relevant disconnected-loop contributions in ground-state baryon matrix elements [3,4], challenges in isolating baryon excitations in lattice QCD [10,40,[45][46][47][48][49][50][51][52][53][54][55][56][57] render the resolution of disconnected contributions elusive.…”

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

“…To shrink uncertainties from chiral extrapolations in calculations at unphysical light quark masses, the RBC-UKQCD Collaborations have generated configurations at the physical pion mass on 48 3 × 96 lattices [5]. On this gauge ensemble labeled as 48I, the χQCD Collaboration is studying the ρ resonance [6], nucleon magnetic moment [7,8], and decay constants of pseudoscalar and vector mesons [9]. To link hadronic matrix elements computed on the lattice to the continuum world, we need the RCs for the corresponding operators.…”

Disconnected loop subtraction methods in lattice QCD

“…In this work we concentrate on lattice operators which respond well to unpartitioned noise [1]: scalar and vector operators. Most physical amplitudes in QCD are affected by such loop effects; some examples include nucleon electromagnetic form factors [2,3], the strangeness and charm contents of the nucleon [4,5,6], the determination of the mass of flavor singlet mesons [7], multiquarks and scattering states [8], hadronic scattering lengths and structure functions [9,10], and electron or muon hadronic g − 2 loop contributions [11,12]. To tackle such difficult lattice problems one projects out operator expectation values using unbiased noise stochastic estimates [13,14,15].…”