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Precision Measurements of the Neutron Magnetic Form Factor to High Momentum Transfer using Durand’s Method

Protons and neutrons, collectively known as nucleons, along with electrons, constitute the fundamental building blocks of the visible universe. Understanding their internal structure is crucial for addressing key scientific questions about our origin and existence. Elastic electron-nucleon scattering provides insights into the spatial distributions of charge and current within nucleons through their electromagnetic form factors. Accurate knowledge of these form factors over a broad range of Q2, the squared four-momentum transfer in the scattering process, reveals details about the nucleon's internal structure. However, high-Q2 data of the nucleon electromagnetic form factor is scarce due to the challenges associated with such measurements. This thesis reports preliminary results from high-precision measurements of the neutron magnetic form factor (GMn) to unprecedented Q2 using Durand's method, also known as the "ratio" method. Systematic errors are greatly reduced by ext

Datta, Provakar↗

Precision Measurements of the Neutron Magnetic Form Factor to High Momentum Transfer using Durand's Method

Protons and neutrons, collectively known as nucleons, along with electrons, constitute the funda- mental building blocks of the visible universe. Understanding their internal structure is crucial for addressing key scientific questions about our origin and existence. Elastic electron-nucleon scatter- ing provides insights into the spatial distributions of charge and current within nucleons through their electromagnetic form factors. Accurate knowledge of these form factors over a broad range of Q2, the squared four-momentum transfer in the scattering process, reveals details about the nucleon’s internal structure. However, high-Q2 data of the nucleon electromagnetic form factor is scarce due to the challenges associated with such measurements. This thesis reports preliminary results from high-precision measurements of the neutron magnetic form factor (Gn M ) to unprecedented Q2 using Durand’s method, also known as the “ratio” method. Systematic errors are greatly reduced by extracting Gn M from the ratio of neutron-coincident (D(e, e'n)) to proton-coincident (D(e, e'p)) quasi-elastic electron scattering from deuteron. The scattered electrons were detected in the BigBite spectrometer, which features multiple Gas Elec- tron Multiplier (GEM) layers with large active area for high-precision tracking at very high rates. Simultaneous nucleon detection was performed by the Super BigBite spectrometer, which utilizes a dipole magnet with large solid angle acceptance at forward angles and a novel hadron calorimeter with very high and comparable detection efficiencies for both protons and neutrons. This setup could handle very high luminosity, making high-Q2 measurements feasible. Data were collected at five Q2 points: 3, 4.5, 7.4, 9.9, and 13.6 (GeV/c)2. Preliminary results are reported for all, with the lowest two Q2 points in good agreement with existing world data, while the higher points significantly extend the Q2 range in which Gn M is known accurately. The precision of the highest Q2 point is expected to remain unmatched for years to come.

Datta, Provakar↗

Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs

We present a determination of the neutral current weak axial charge $G$ $^{Z}_{A}$(0) = –0.654(3) stat (5) sys using the strange quark axial charge $G$ $^{s}_{A}$(0) calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q 2 ≲ 0.71 GeV 2 to determine the neutral current weak axial form factor $G$ $^{Z}_{A}$(Q 2 ) in the range of 0 ≲ Q 2 ≤ 1 GeV 2 . This yields a phenomenological value of $G$ $^{Z}_{A}$(0) = –0.687(89)stat(40)sys. The value of $G$ $^{Z}_{A}$(0) constrained by the lattice QCD calculation of $G$ $^{s}_{A}$(0), when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $G$ $^{Z}_{A}$(Q 2 ) for Q 2 > 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q 2 = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G$ $^{Z}_{A}$(Q 2 ) obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Compilation and analysis of charge asymmetry measurements from electron and positron scattering on nucleon and nuclei

World data on the lepton-charge asymmetry in the elastic and inelastic lepton scattering off the proton and nuclei are compiled and discussed. After reviewing the published results, we compare the elastic data to a model calculation of the two-photon-exchange mechanism. We show that the existing data do not provide any evidence for enhancement of the two-photon contribution. At confidence level 95% the data allow to exclude the two-photon exchange as an explanation for the difference between Rosenbluth and polarization transfer measurements of proton electromagnetic form factors.

74 ATOMIC AND MOLECULAR PHYSICS↗

An experimental program with high duty-cycle polarized and unpolarized positron beams at Jefferson Lab

Positron beams, both polarized and unpolarized, are identified as important ingredients for the experimental programs at the next generation of lepton accelerators. In the context of the hadronic physics program at Jefferson Lab (JLab), positron beams are complementary, even essential, tools for a precise understanding of the electromagnetic structure of nucleons and nuclei, in both the elastic and deep-inelastic regimes. For instance, elastic scattering of polarized and unpolarized electrons and positrons from the nucleon enables a model independent determination of its electromagnetic form factors. Also, the deeply-virtual scattering of polarized and unpolarized electrons and positrons allows unambiguous separation of the different contributions to the cross section of the lepto-production of photons and of lepton-pairs, enabling an accurate determination of the nucleons and nuclei generalized parton distributions, and providing an access to the gravitational form factors of the energy-momentum tensor. Furthermore, positron beams offer the possibility of alternative tests of the Standard Model of particle physics through the search of a dark photon, the precise measurement of electroweak couplings, and the investigation of charged lepton flavor violation. This document discusses the perspectives of an experimental program with high duty-cycle positron beams at JLab.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Implementation of general background electromagnetic fields on a periodic hypercubic lattice

Nonuniform background electromagnetic fields, once implemented in lattice quantum chromodynamics calculations of hadronic systems, provide a means to constrain a large class of electromagnetic properties of hadrons and nuclei, from their higher electromagnetic moments and charge radii to their electromagnetic form factors. In this work, we show how nonuniform fields can be constructed on a periodic hypercubic lattice under certain conditions and determine the precise form of the background Uð1Þ gauge links that must be imposed on the quantum chromodynamics gauge-field configurations to maintain periodicity. Once supplemented by a set of quantization conditions on the background-field parameters, this construction guarantees that no nonuniformity occurs in the hadronic correlation functions across the boundary of the lattice. Lastly, the special cases of uniform electric and magnetic fields, a nonuniform electric field that varies linearly in one spatial coordinate (relevant to the determination of quadruple moment and charge radii), nonuniform electric and magnetic fields with given temporal and spatial dependences (relevant to the determination of nucleon spin polarizabilities) and plane-wave electromagnetic fields (relevant to the determination of electromagnetic form factors) are discussed explicitly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonperturbative aspects of the electromagnetic pion form factor at high energies

The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor.

Form factors↗

Nucleon-to-Roper electromagnetic transition form factors at large Q 2

High-precision nucleon-resonance electroproduction data on a large kinematic domain of energy and momentum transfer have proven crucial in revealing novel features of strong interactions within the Standard Model and unfolding structural details of baryon excited states. Thus, in anticipation of new data reaching to unprecedented photon virtuality, we employ a quark-diquark approximation to the three-valence-quark bound-state problem to compute γ*p → R + and γ*n → R 0 transition form factors on Q 2 /m 2 N ϵ[0,12], where m N is the nucleon mass. Having simultaneously analyzed both charged and neutral channels, we also provide a quark-flavor separation of the transition form factors. Furthermore, the results should be useful in planning new-generation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probing Novel Properties of Nucleons and Nuclei via Parity Violating Electron Scattering

This thesis reports on two experiments conducted by the HAPPEx (Hall A Proton Parity Experiment) collaboration at the Thomas Jefferson National Accelerator Facility. For both, the weak neutral current interaction (WNC, mediated by the Z 0 boson) is used to probe novel properties of hadronic targets. The WNC interaction amplitude is extracted by measuring the parity-violating asymmetry in the elastic scattering of longitudinally polarized electrons o unpolarized target hadrons. HAPPEx-III, conducted in the Fall of 2009, used a liquid hydrogen target at a momentum transfer of Q 2 = 0.62 GeV 2 . The measured asymmetry was used to set new constraints on the contribution of strange quark form factors (G s E,M ) to the nucleon electromagnetic form factors. A value of A PV = -23.803±} 0.778 (stat)± 0.359 (syst) ppm resulted in G s E + 0.517G s M = 0.003± 0.010 (stat)± 0.004 (syst)± 0.009 (FF). PREx, conducted in the Spring of 2010, used a polarized electron beam on a 208Pb target at a momentum transfer of Q 2 = 0.009 GeV 2 . This parity-violating asymmetry can be used to obtain a clean measurement of the root-mean-square radius of the neutrons in the 208 Pb nucleus. The Z 0 boson couples mainly to neutrons; the neutron weak charge is much larger than that of the proton. The value of this asymmetry is at the sub-ppm level and has a projected experimental fractional precision of 3%. We will describe the accelerator setup used to set controls on helicity-correlated beam asymmetries and the analysis methods for finding the raw asymmetry for HAPPEx-III. We will also discuss in some detail the preparations to meet the experimental challenges associated with measuring such a small asymmetry with the degree of precision required for PREx.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The proton form factor ratio results from Jefferson Lab

The ratio of the proton form factors, GE p/GMp, has been measured extensively, from Q2 of 0.5 GeV2 to 8.5 GeV2, at the Jefferson Laboratory, using the polarization transfer method. This ratio is extracted directly from the measured ratio of the transverse and longitudinal polarization components of the recoiling proton in elastic electron-proton scattering. The polarization transfer results are of unprecedented high precision and accuracy, due in large part to the small systematic uncertainties associated with the experimental technique. There is an approved experiment at JLab, GEP(5), to continue the ratio measurements to 12 GeV2. A dedicated experimental setup, the Super Bigbite Spectrometer (SBS), will be built for this purpose. It will be equipped with a focal plane polarimeter to measure the polarization of the recoil protons. The scattered electrons will be detected in an electromagnetic calorimeter. In this presentation, I will review the status of the proton elastic electromagnetic form factors and discuss a number of theoretical approaches to describe nucleon form factors.

43 PARTICLE ACCELERATORS↗

Measurement of the Neutron Magnetic Form Factor at Large Momentum Transfer Using the Super-Bigbite Apparatus in Jefferson Lab Hall-A

The nucleon elastic electromagnetic form factors help us study the electromagnetic structure of the nucleon, benchmark theoretical models, and improve our understanding of non-perturbative quantum chromodynamics and confinement. The Nobel Prize-winning electron-nucleon scattering experiments by Robert Hofstadter and collaborators in the 1950s at Stanford High Energy Physics Lab were the first nucleon form factor measurements performed using leptonic probes. The Super Bigbite Spectrometer (SBS) program at Hall-A of Jefferson Lab represents the latest efforts to measure nucleon form factors. This ambitious program aims to significantly extend the current data set in terms of square momentum transfer (Q2) with high precision. The advent of novel detector technologies, like Gas Electron Multipliers (GEM), which provide excellent position resolution (< 100 ?m) while withstanding high background particle rates (several hundred MHz/cm2) over a large active area, has paved the way for open-geometry, moderate solid angle spectrometers, which are central to all form factor experiments in the SBS program. The first experimental run group in SBS ran successfully between September 2021 and February 2022, collecting data for the measurement of the magnetic form factor of the neutron Gn M at five squared momentum-transfer values: 3.0, 4.5, 7.5, 9.8, and 13.5 (GeV /c)2. This extends the existing high-precision data for Gn M by about a factor of four. The ratio technique was used, which involved the simultaneous measurement of exclusive quasielastic scattering of D(e,e?n)p and D(e,e?p)n from a deuterium target. Pre-preliminary results for D(e,e?n)p and D(e,e?p)n quasi-elastic ratio, and the neutron magnetic form factor Gn M , for Q2 points 3.0, 9.8, and 13.5 (GeV /c)2 are presented.

Mudiyanselage, Anuruddha Rathnayake↗

Accessing the gravitational form factors of the nucleon and nuclei through a massive graviton

In contrast to the electromagnetic form factors of the nucleon and nuclei that have been extensively studied in electron scattering, there is no known way to directly measure the gravitational form factors (GFFs), the off-forward hadronic matrix element of the QCD energy-momentum tensor. I suggest exploring the possibility to access the GFFs of the proton and nuclei in conjunction with massive graviton searches at future TeV-scale lepton-ion colliders. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Precision Limit on the Strange Vector Form Factors of the Proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q 2 = 0.624 GeV 2 and beam energy E b = 3.48 GeV to be A PV = -23.80 ± 0.78 (stat) ± 0.36 (syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G E s + 0.517 G M s = 0.003 ± 0.010 (stat) ± 0.004 (syst) ± 0.009 (ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nuclear Structure Effects in the Hyperfine Structure of Muonic Lithium, Beryllium, and Boron

Nuclear structure corrections to hyperfine splitting of energy levels in muonic lithium, beryllium, and boron ions are calculated. Account is taken of the contributions from the two-photon exchange amplitudes, including the vacuum polarization effect, and from the one-photon amplitude, which provide corrections to the nuclear structure and recoil of order α{sup 5} and α{sup 6}. Numerical results for different parametrizations of electromagnetic form factors are compared.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗