Consistency of electron scattering data with a small proton radius

We determine the charge radius of the proton by analyzing the published low momentum transfer electron-proton scattering data from Mainz. We note that polynomial expansions of the form factor converge for momentum transfers squared below 4m(pi)(2), where m(pi) is the pion mass. Expansions with enough terms to fit the data, but few enough not to overfit, yield proton radii smaller than the CODATA or Mainz values and in accord with the muonic atom results. We also comment on analyses using a wider range of data, and overall obtain a proton radius R-E = 0.840(16) fm

Proton structure corrections to hyperfine splitting in muonic hydrogen

We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncertainty in the hyperfine splitting. Additionally, hyperfine splittings have an impact on the muonic hydrogen Lamb shift/proton radius measurement, however the correction we advocate has a small effect there.Comment: 6 pages, 3 figure

Establishing a metacognitive model for instrumental music assessment

Traditional instrumental music assessment models may often contain the inclusion of grades that are based upon non-musical criteria. This type of grading leads to difficulties in assessment validity, reliability and fairness, and do not lead to an increase in metacognitive abilities that develop students’ technique and musicianship. A metacognitive assessment model that is based upon assessments for, as, and of learning is needed as metacognitive musical learning potentially aids students in developing the skills necessary to become independent musicians who can identify and address challenges in their own performance. Through the use of feedback, reflection and goal setting, modeling and self-assessment, teacher instructed strategies, a consideration of students’ bio-ecology, and a consistent focus upon the constructs that need to be assessed, assessment tools have been designed to help develop student metacognition and foster greater independence, musicianship, and skill in instrumental music students

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting

We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.Comment: 9 pages, 1 figur

Semi-Inclusive Pi(0) Target and Beam-Target Asymmetries from 6 GeV Electron Scattering with CLAS

We present precision measurements of the target and beam-target spin asymmetries from neutral pion electroproduction in deep-inelastic scattering (DIS) using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. We scattered 6-GeV, longitudinally polarized electrons off longitudinally polarized protons in a cryogenic 14NH3 target, and extracted double and single target spin asymmetries for ep→e′ π0 X in multidimensional bins in four-momentum transfer (1.0 2 \u3c 3.2 GeV2), Bjorken -x (0.12 \u3c x \u3c 0.48), hadron energy fraction (0.4 \u3c z 0.7), tranverse pion meomentum (0 \u3c PT \u3c 1.0 GeV), and azimuthal angle ϕh between the lepton scattering and hadron production planes. We extracted asymmetries as a function of both x and PT, which provides access to transverse-momentum distributions of longitudinally polarized quarks. The double spin asymmetries depend weakly on PT. The sin 2ϕh moments are zero within uncertainties, which is consistent with the expected suppression of the Collins fragmentation function. The observed sin ϕh moments suggest that quark gluon correlations are significant at large x

Determination of the Proton Spin Structure Functions for 0.05 \u3c Q\u3csup\u3e2\u3c/sup\u3e \u3c5GEV\u3csup\u3e2\u3c/sup\u3e Using CLAS

We present the results of our final analysis of the full data set of gp1 Q2, the spin structure function of the proton, collected using CLAS at Jefferson Laboratory in 2000-2001. Polarized electrons with energies of 1.6, 2.5, 4.2, and 5.7 GeV were scattered from proton targets 15NH3 dynamically polarized along the beam direction) and detected with CLAS. From the measured double spin asymmetries, we extracted virtual photon asymmetries Ap1 and Ap2 and spin structure functions g p1 and gp2 over a wide kinematic range (0.05 GeV2 \u3c Q2 \u3c 5 GeV2 and 1.08 GeV\u3c W \u3c 3 GeV) and calculated moments of gp1. We compare our final results with various theoretical models and expectations, as well as with parametrizations of the world data. Our data, with their precision and dense kinematic coverage, are able to constrain fits of polarized parton distributions, test pQCD predictions for quark polarizations at large x, offer a better understanding of quark-hadron duality, and provide more precise values of higher twist matrix elements in the framework of the operator product expansion

Exclusive eta electroproduction at W \u3e 2 GeV with CLAS and transversity generalized parton distributions

The cross section of the exclusive eta electroproduction reaction ep -\u3e e\u27p\u27eta was measured at Jefferson Laboratorywith a 5.75 GeV electron beam and the CLAS detector. Differential cross sections d(4) sigma/dtdQ(2) dx(B)d phi(eta) and structure functions sigma(U) = sigma(T) + epsilon sigma(L), sigma(TT), and sigma(LT), as functions of t, were obtained over a wide range of Q(2) and x(B). The eta structure functions are compared with those previously measured for pi(0) at the same kinematics. At low t, both pi(0) and eta are described reasonably well by generalized parton distributions (GPDs) in which chiral-odd transversity GPDs are dominant. The pi(0) and eta data, when taken together, can facilitate the flavor decomposition of the transversity GPDs

Determination of the proton spin structure functions for 0.05 \u3c Q(2) \u3c 5GeV(2) using CLAS

We present the results of our final analysis of the full data set of g(1)(p) (Q(2)), the spin structure function of the proton, collected using CLAS at Jefferson Laboratory in 2000-2001. Polarized electrons with energies of 1.6, 2.5, 4.2, and 5.7 GeV were scattered from proton targets ((NH3)-N-15 dynamically polarized along the beam direction) and detected with CLAS. From the measured double spin asymmetries, we extracted virtual photon asymmetries A(1)(p) and A(2)(p) and spin structure functions g(1)(p) and g(2)(p) over a wide kinematic range (0.05 GeV2 \u3c Q(2) \u3c 5 GeV2 and 1.08 GeV\u3c W \u3c 3 GeV) and calculated moments of g(1)(p). We compare our final results with various theoretical models and expectations, as well as with parametrizations of the world data. Our data, with their precision and dense kinematic coverage, are able to constrain fits of polarized parton distributions, test pQCD predictions for quark polarizations at large x, offer a better understanding of quark-hadron duality, and provide more precise values of higher twist matrix elements in the framework of the operator product expansion