Nucleon electromagnetic form factors in two-flavor QCD

Abstract

We present results for the nucleon electromagnetic form factors, including the momentum transfer dependence and derived quantities (charge radii and magnetic moment). The analysis is performed using O(a) improved Wilson fermions in N f = 2 QCD measured on the CLS ensembles. Particular focus is placed on a systematic evaluation of the influence of excited states in three-point correlation functions, which lead to a biased evaluation, if not accounted for correctly. We argue that the use of summed operator insertions and fit ansätze including excited states allow us to suppress and control this effect. We employ a novel method to perform joint chiral and continuum extrapolations, by fitting the form factors directly to the expressions of covariant baryonic chiral effective field theory. The final results for the charge radii and magnetic moment from our lattice calculations include, for the first time, a full error budget. We find that our estimates are compatible with experimental results within their overall uncertainties.

Baryons as relativistic three-quark bound states

“…Whereas the early quenched calculations are summarized in the review articles [442,450], nowadays essentially all calculations are performed using dynamical fermions. Studies of electromagnetic nucleon form factors are available from various collaborations for N f = 2 [451][452][453][454][455], N f = 2 + 1 [397,[456][457][458][459][460][461][462] and N f = 2 + 1 + 1 flavours [463,464], including calculations nearly at the physical pion mass [397] which agree reasonably well with the experimental data. However, they are so far restricted to moderately low Q 2 and still carry sizeable statistical errors; for example, the necessary precision for an unambiguous determination of the proton's charge radius is not yet within reach.…”

“…For example, the three-point correlator in (4.8) singles out the ground state matrix element for asymptotically large Euclidean time separations, but in practice one has to deal with the admixture from excited states whose magnitude is encoded in the overlaps r λ . Several methods have been developed to address the problem such as the summation method or employing two-state fits; see [397,455,464] for details. For form factors involving unstable particles such as the ∆ or the Roper resonance, disentangling the physical from the scattering states becomes an additional obstacle.…”

Towards extracting the timelike pion form factor on CLS twoflavour ensembles

“…For this study, we use a Clover action on three different CLS 2-flavor lattices with β = 5.3 and c sw = 1.90952 which corresponds to a lattice spacing of a = 0.0658(7)(7) fm [16] and pion masses ranging from 437 MeV to 265 MeV [17], listed in Table 1. Table 1.…”

Nucleon structure from 2+1 flavor lattice QCD near the physical point

“…The hopping parameters for the light sea quarks {κ ud , κ s } = {0.126117, 0.124812} are chosen to be near the physical point. We calculate iso-vector nucleon form factors in the vector, axial-vector and pseudo-scalar channels with a large spatial volume of (8.1 fm) 3 and a simulated pion mass reaching down to m π = 145 MeV in 2+1 flavor QCD. A brief summary of our simulation parameters are tabulated in Table 1.…”