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Arie Bodek

Publications and source records attributed to Arie Bodek.

At least 19 recordsLinked to original sources
arXiv2026

Summary of the Precision Measurements of the Electroweak Mixing Angle in the Region of the Z pole

This contribution presents an overview of an improved extraction of the effective leptonic weak mixing angle, $\sin^2\theta^\ell_{\mathrm{eff}}$, based on the published CMS measurement of the forward-backward asymmetry in Drell-Yan events at 13 TeV [1]. While the original CMS analysis [2] achieved a significant reduction in experimental uncertainties, its overall precision remains limited by residual uncertainties in the parton distribution functions (PDFs). This proceeding highlights the impact of incorporating complementary CMS measurements that probe different combinations of parton densities, thereby providing additional PDF constraints beyond those obtained from the asymmetry measurement alone. The improved analysis leads to a substantially reduced total uncertainty, yielding $\sin^2\theta^\ell_{\mathrm{eff}} = 0.23156\pm0.00024$. This result is consistent with the Standard Model prediction and represents the most precise single determination of this parameter to date.

hep-ex↗
arXiv2025

Precision Measurements of the Electroweak Mixing Angle in the Region of the Z pole

We review the current status and techniques used in precision measurements of the effective leptonic weak mixing angle $\sin^2\theta^\ell_{\rm eff}$ (a fundamental parameter of the Standard Model (SM)) in the region of the Z pole with emphasis on hadron colliders. We also build on these techniques to extract the most precise single measurement to date of $\sin^2\theta^\ell_{\rm eff}$ from a new analysis of the published forward-backward asymmetry ($A_{\rm FB}$) in Drell-Yan dielpton production in proton-proton collisions at a center of mass energy of 13 TeV measured by the CMS collaboration at the large hadron collider. The uncertainty in $\sin^2\theta^\ell_{\rm eff}$ published by CMS is dominated by uncertainties in Parton Distribution Functions (PDFs), which are reduced by PDF profiling using the dilepton mass dependence of $A_{\rm FB}$. Our new extraction of $\sin^2\theta^\ell_{\rm eff}$ from the CMS values of $A_{\rm FB}$ includes profiling with additional new CMS measurements of the $W$-boson decay lepton asymmetry, and W/Z cross section ratio at 13 TeV. We obtain the most precise single measurement of $\sin^2\theta^\ell_{\rm eff}$ to date of 0.23156$\pm$0.00024, which is in excellent agreement with the SM prediction of 0.23161$\pm$0.00004. We also discuss outlook for future measurements at the LHC including more precise measurements of $\sin^2\theta^\ell_{\rm eff}$, a measurement of $\sin^2\theta^\ell_{\rm eff}$ for b-quarks in the initial state, and a measurement of the running of $\sin^2\theta^{\overline{\rm MS}}(\mu)$ up to 3 TeV.

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arXiv2025

Parameterizations of Electron Scattering Form Factors for Elastic Scattering and Electro-Excitation of Nuclear States for $\rm ^{27}Al$ and $\rm ^{40}Ca$

We report on empirical parameterizations of longitudinal (${\cal R}_L$) and transverse (${\cal R}_T$) nuclear electromagnetic form factors for elastic scattering and the excitations of nuclear states in ${\rm ^{27}Al}$ and ${\rm ^{40}Ca}$. The parameterizations are needed for the calculations of radiative corrections in measurements of electron scattering cross sections on ${\rm ^{27}Al}$ and ${\rm ^{40}Ca}$ in the quasi-elastic, resonance and inelastic continuum regions, provide the contribution of nuclear excitations in investigations of the Coulomb Sum Rule, and test theoretical model predictions for excitation of nuclear states in electron and neutrino interactions on nuclear targets at low energies.

nucl-th↗
arXiv2024

Summary of Global Extraction of the $\rm^{12}C$ Nuclear Electromagnetic Response Functions and Comparisons to Nuclear Theory and Neutrino/Electron Monte Carlo Generators at Nufact24

We present a brief report (at the Nufact-2024 conference) summarizing a global extraction of the ${\rm ^{12}C}$ longitudinal (${\cal R}_L$) and transverse (${\cal R}_T$) nuclear electromagnetic response functions from an analysis of all available electron scattering data on carbon. Since the extracted response functions cover a large kinematic range they can be readily used for comparison to theoretical predictions as well as validation and tuning Monte Carlo (MC) generators for electron and neutrino scattering experiments. Comparisons to several theoretical approaches and MC generators are given in arXiv:2409.10637v1 [hep-ex]. We find that among all the theoretical models that were investigated, the ``Energy Dependent-Relativistic Mean Field'' (ED-RMF) approach provides the best description of both the Quasielastic (QE) and {\it nuclear excitation} response functions (leading to single nucleon final states) over all values of four-momentum transfer. he QE data are also well described by the "Short Time Approximation Quantum Monte Carlo" (STA-QMC) calculation which includes both single and two nucleon final states which presently is only valid for momentum transfer $0.3<{\bf q} < 0.65$ GeV and does not include nuclear excitations. An analytic extrapolation of STA-QMC to lower $\bf q$ has been implemented in the GENIE MC generator for $\rm^{4}He$ and a similar extrapolation for ${\rm ^{12}C}$ is under development. STA validity for ${\bf q} >$ 0.65 GeV requires the implementation of relativistic corrections. Both approaches have the added benefit that the calculations are also directly applicable to the same kinematic regions for neutrino scattering. In addition we also report on a universal fit to all electron scattering data that can be used in lieu of experimental data for validation of Monte Carlo generators (and is in the process of being implemented in GENIE).

hep-ex↗
arXiv2024

Global Extraction of the $\rm^{12}C$ Nuclear Electromagnetic Response Functions (${\cal R}_L$ and ${\cal R}_T$) and Comparisons to Nuclear Theory and Neutrino/Electron Monte Carlo Generators

We have performed a global extraction of the ${\rm ^{12}C}$ longitudinal (${\cal R}_L$) and transverse (${\cal R}_T$) nuclear electromagnetic response functions from an analysis of all available electron scattering data on carbon. The response functions are extracted for energy transfer $\nu$, spanning the nuclear excitation, quasielastic (QE), resonance and inelastic continuum over a large range of the square of the four-momentum transfer, $Q^2.$ In addition, we perform a universal fit to all ${\rm ^{12}C}$ electron scattering data which also provides parmeterizations of ${\cal R}_L$ and ${\cal R}_T$ over a larger kinematic range. Given the nuclear physics common to both electron and neutrino scattering from nuclei, extracted response functions from electron scattering spanning a large range of $Q^2$ and $\nu$ also provide a powerful tool for validation and tuning of neutrino Monte Carlo (MC) generators. In this paper we focus on the nuclear excitation, single nucleon (QE-1p1h) and two nucleon (2p2h) final state regions and compare the measurements to theoretical predictions including ``Energy Dependent-Relativistic Mean Field'' (ED-RMF), ``Green's Function Monte Carlo'' (GFMC), "Short Time Approximation Quantum Monte Carlo" (STA-QMC), an improved superscaling model (SuSAv2), "Correlated Fermi Gas" (CFG), as well as the \nuwro{}, and \achilles~ generators. Combining the ED-RMF-QE-1p1h predictions with the SuSAv2-MEC-2p2h predictions provides a good description of ${\cal R}_L$ and ${\cal R}_T$ for both single nucleon (from QE and nuclear excitations) and two nucleon final states over the entire kinematic range.

hep-ex↗
arXiv2022

Axial and Vector Structure Functions for Lepton-Nucleon Scattering, NuFact 2021 Update

We report on an update (2021) of a phenomenological model for inelastic neutrino- and electron-nucleon scattering cross sections using effective leading order parton distribution functions with a new scaling variable $ξ_w$. Non-perturbative effects are well described using the $ξ_w$ scaling variable in combination with multiplicative $K$ factors at low $Q^2$. The model describes all inelastic charged-lepton-nucleon scattering data (HERA/NMC/BCDMS/SLAC/JLab) ranging from very high $Q^2$ to very low $Q^2$ and down to the $Q^2=0$ photo-production region. The model has been developed to be used in analyses of neutrino oscillation experiments in the few GeV region. The 2021 update accounts for the difference between axial and vector structure functions which brings it into much better agreement with neutrino-nucleon total cross section measurements. The model has been developed primarily for hadronic final state masses $W$ above 1.8 GeV. However with additional parameters the model also describes the $average$ neutrino cross sections in the resonance region down to $W$=1.4 GeV.

hep-ph↗
arXiv2021

Pauli Blocking for a Relativistic Fermi Gas in Quasielastic Lepton Nucleus Scattering

The expressions for the overall effect of Pauli blocking in quasielastic (QE) lepton scattering from nuclear targets within the framework of the Relativistic Fermi Gas (RFG) given in several publications are incorrect. For example, the expressions published by Bell and Llewelyn Smith in 1972 are incorrect (probably a typographical error). The expressions for Pauli blocking presented in several subsequent publications including the paper of C.H. Llewelyn Smith in 1972 and the paper of Paschos and Yu in 2002 have the same error. Another example is a 1992 paper by Singh and Oset which has a different (probably also a typographical) error. Other papers such as the papers of Tsai in 1974 and Bosted and Mamyan in 2012 use the correct expressions. In this short preprint we review the geometrical derivation of the overall reduction of the QE cross sections due to Pauli blocking for electron and neutrino scattering for targets with equal numbers of neutrons and protons and for targets with unequal numbers of neutrons and protons and derive the correct expressions. However, we note that the effects of Pauli blocking within the framework of the RFG model are much larger than in other more realistic models of QE scattering such as $ψ^\prime$ superscaling or a spectral function approach.

nucl-th↗
arXiv2021

Inelastic Axial and Vector Structure Functions for Lepton-Nucleon Scattering 2021 Update

We report on an update (2021) of a phenomenological model for inelastic neutrino- and electron-nucleon scattering cross sections using effective leading order parton distribution functions with a new scaling variable $ξ_w$. Non-perturbative effects are well described using the $ξ_w$ scaling variable in combination with multiplicative $K$ factors at low $Q^2$. The model describes all inelastic charged-leptron-nucleon scattering data (HERA/NMC/BCDMS/SLAC/JLab) ranging from very high $Q^2$ to very low $Q^2$ and down to the $Q^2=0$ photo-production region. The model has been developed to be used in analysis of neutrino oscillation experiments in the few GeV region. The 2021 update accounts for the difference between axial and vector structure function which brings it into much better agreement with neutrino-nucleon total cross section measurements. The model has been developed primarily for hadronic final state masses $W$ above 1.8 GeV. However with additional parameters the model also describe the $average$ neutrino cross sections in the resonance region down to $W$=1.4 GeV.

hep-ph↗
arXiv2020

Nuclear Potential of Final State Nucleons and Nucleons Plus Pions in Lepton Nucleus Scattering

Within the impulse approximation, the modeling of the energy of final state leptons in electron and neutrino quasielastic and pion production processes on nuclear targets in the region of the $Δ$ resonance depends on several parameters. These parameters include the removal energy of the initial state nucleon from the nucleus $ε^{P,N}$, the potentials of electrons, nucleons and pions in the Coulomb field of the nucleus $|V_{eff}|$, and the kinetic energy dependent nuclear potential for final state nucleons ($U^{QE}_{opt}$) and "nucleon plus pion" final states in the region of the $Δ$ resonance which we refer to as $U^Δ_{opt}$. We extract these parameters from electron scattering data. Previous studies have shown that real part of the optical potential for a nucleon bound in $_{6}^{12}C$ at zero kinetic energy $U^{P,N}_{opt}(T=0)\approx$ 44 MeV is larger than that for the $Δ$(1232) resonance $U^Δ_{opt}(T=0)\approx$ 30 MeV. We find the reverse at higher kinetic energies. For example at T=100 MeV we find a nucleon potential $U^{P,N}_{opt}(T=100 MeV)$=20$\pm$5 MeV and $U^Δ_{opt}(T=100 MeV)$= 30$\pm$5 MeV. The two results are consistent for two reasons. First, theoretically the kinetic energy dependence of the $Δ$ potential is flatter than that of the nucleon. Secondly, in our analysis the extracted $U^Δ_{opt}$ values are the nuclear potential for {\it"nucleon plus pion"} final states in the region of the $Δ$ resonances and therefore includes contributions from both resonance and non resonance pion production processes. For Monte Carlo generators that only include the effects of Fermi motion and nuclear potentials, the relevant parameter is the effective nuclear potential for the "nucleon plus pion" final state.

nucl-th↗
arXiv2020

Comparison of optical potential for nucleons and $Δ$ resonances

Precise modeling of neutrino interactions on nuclear targets is essential for neutrino oscillations experiments. The modeling of the energy of final state particles in quasielastic (QE) scattering and resonance production on bound nucleons requires knowledge of both the removal energy of the initial state bound nucleon as well as the average Coulomb and nuclear optical potentials for final state leptons and hadrons. We extract the average values of the real part of the nuclear optical potential for final state nucleons ($U_{opt}^{QE}$) as a function of the nucleon kinetic energy from inclusive electron scattering data on nuclear targets ($\bf_{6}^{12}C$+$\bf_{8}^{16}O$, $\bf_{20}^{40}Ca$+$\bf_{18}^{40}Ar$, $\bf_{3}^{6}Li$, $\bf_{18}^{27}Al$, $\bf_{26}^{56}Fe$, $\bf_{82}^{208}Pb$) in the QE region and compare to calculations. We also extract values of the average of the real part of the nuclear optical potential for a $Δ(1232)$ resonance in the final state ($U^Δ_{opt}$) within the impulse approximation. We find that $U^Δ_{opt}$ is more negative than $U_{opt}^{QE}$ with $U^Δ_{opt}\approx$1.5~$U_{opt}^{QE}$ for $\bf_{6}^{12}C$.

hep-ph↗
arXiv2020

Measurement of the effective weak mixing angle $sin^2θ^{lept}_{eff}$ from the forward-backward asymmetry of Drell-Yan events at CMS

We report on a precision measurement of the effective weak mixing angle using the forward-backward asymmetry, $A_{FB}$, in Drell-Yan ($ee$ and $μμ$) events in pp collisions at $\sqrt{s}=8~\mathrm{TeV}$ at the CMS experiment at the Large Hadron Collider (LHC). The results are compared to other hadron collider measurements published by ATLAS, LHCb, CDF, D0 and Tevatron combination.

hep-ex↗
arXiv2019

Removal Energies and Final State Interaction in Lepton Nucleus Scattering

We investigate the binding energy parameters that should be used in modeling electron and neutrino scattering from nucleons bound in a nucleus within the framework of the impulse approximation. We discuss the relation between binding energy, missing energy, removal energy ($ε$), spectral functions and shell model energy levels and extract updated removal energy parameters from ee$^{\prime}$p spectral function data. We address the difference in parameters for scattering from bound protons and neutrons. We also use inclusive e-A data to extract an empirical parameter $U_{FSI}( (\vec q_3+\vec k)^2)$ to account for the interaction of final state nucleons (FSI) with the optical potential of the nucleus. Similarly we use $V_{eff}$ to account for the Coulomb potential of the nucleus. With three parameters $ε$, $U_{FSI}( (\vec q_3+\vec k)^2)$ and $V_{eff}$ we can describe the energy of final state electrons for all available electron QE scattering data. The use of the updated parameters in neutrino Monte Carlo generators reduces the systematic uncertainty in the combined removal energy (with FSI corrections) from $\pm$ 20 MeV to $\pm$ 5 MeV.

nucl-th↗
arXiv2018

Optical Potential and Removal Energies in Lepton Nucleus Scattering

We summarize some of the results presented in arXiv:1801.07975 [nucl-th]\cite{FSIpaper}(to be published in EPJC in 2018) on modeling electron and neutrino QE scattering on a variety of nuclei within the impulse approximation. We find that with three parameters we can describe the final state lepton energy for all of available electron QE data on Lithium, Carbon+Oxygen, Aluminum, Calcium+Argon, Iron and Lead+Gold. The first parameter, the removal energy $ε^{P,N}$ is extracted from exclusive ee$^{\prime}$p spectral function data. The second parameter $V_{eff}$, which accounts for the interaction of final state leptons and protons with the Coulomb potential of the nucleus, is available from published comparisons of inclusive QE electron and positron cross section. We extract the third parameter $U_{FSI}(\vec {q}_3^2)$, which accounts for the interaction of the final state nucleon with the optical potential of the spectator nucleus (FSI), by fitting all available inclusive QE cross sections on nuclear targets. Here $q_3$ is the three momentum transfer. With these three parameters we can model the energy of final state electrons and nucleons for all available electron QE scattering data. At present the uncertainty in the value of the removal energy parameters is a the largest source of systematic error in the extraction of the neutrino oscillation parameter $Δ{m}^2$. The use of the updated parameters in neutrino Monte Carlo generators reduces the systematic uncertainty in the combined removal energy (with FSI corrections) from $\pm$ 20 MeV to $\pm$ 5 MeV. In this short contribution we only summarize the results for Carbon+Oxygen and Calcium+Argon

hep-ph↗
arXiv2015

Precision Measurements of Electroweak Parameters with Z Bosons at the Tevatron

We report on the extraction of $\sin^2θ^{\rm lept}_{\rm eff}(M_Z)$ and an indirect measurement of the mass of the W boson from the forward-backward asymmetry of dilepton events in the $Z$ boson mass region at the Tevatron. The data samples of $e^+e^-$ and $μ^+μ^-$ events collected by the CDF detector correspond to the full 9.4 fb$^{-1}$ run II sample and yield an effective electroweak mixing angle $\sin^2θ^{\rm lept}_{\rm eff}(M_Z) = 0.23222 \pm 0.00046$. The corresponding result reported by the D0 collaboration with the full 9.4 fb$^{-1}$ $e^+e-$ sample is $\sin^2θ^{\rm lept}_{\rm eff}(M_Z) = 0.23146 \pm 0.00047$. The CDF collaboration also extracts the on-shell electroweak mixing angle $ \sin^2 θ_W = 0.22401 \pm 0.00044$ which corresponds to an indirect measurement of the W boson mass $M_W ({\rm indirect}) = 80.327 \pm 0.023 \;{\rm GeV}$. The quoted uncertainties include both statistical and systematic contributions.

hep-ex↗
arXiv2013

Axial and Vector Structure Functions for Electron- and Neutrino- Nucleon Scattering Cross Sections at all $Q^2$ using Effective Leading order Parton Distribution Functions

We construct a model for inelastic neutrino- and electron-nucleon scattering cross sections using effective leading order parton distribution functions with a new scaling variable $ξ_w$. Non-perturbative effects are well described using the $ξ_w$ scaling variable, in combination with multiplicative $K$ factors at low $Q^2$.Our model describes all inelastic charged lepton-nucleon scattering (including resonance) data (HERA/NMC/BCDMS/SLAC/JLab) ranging from very high $Q^2$ to very low $Q^2$ and down to the photo-production region. The model describes existing inelastic neutrino-nucleon scattering measurements, and has been developed to be used in analysis of neutrino oscillation experiments in the few GeV region.

hep-ph↗
arXiv2010

Update to the Bodek-Yang Unified Model for Electron- and Neutrino- Nucleon Scattering Cross Sections

We construct a model for inelastic neutrino- and electron-nucleon scattering cross sections using effective leading order parton distribution functions with a new scaling variable $ξ_w$. Non-perturbative effects are well described using the $ξ_w$ scaling variable, in combination with multiplicative $K$ factors at low $Q^2$. Our model describes all inelastic charged lepton-nucleon scattering (including resonance) data (HERA/NMC/BCDMS/SLAC/JLab) ranging from very high $Q^2$ to very low $Q^2$ and down to the photo-production region. The model describes existing inelastic neutrino-nucleon scattering measurements, and is currently used in analyses of neutrino oscillation experiments in the few GeV region.

hep-ph↗
arXiv2010

A simple event weighting technique for optimizing the measurement of the forward-backward asymmetry of Drell-Yan dilepton pairs at hadron colliders

We describe a simple technique for optimizing the extraction of the forward-backward asymmetry ($A_{fb}$) of Drell-Yan lepton pairs ($e^+e^-$,$ μ^+μ^-$) produced in $\bar{p}p$ and $pp$ collisions at hadron colliders. The method employs simple event weights which are functions of the rapidity and $cosθ$ decay angle of the lepton pair. It yields the best estimate of the acceptance corrected parton level ($\bar{q}q$) forward backward asymmetry as a function of final state dilepton mass ($M_{\ell\ell}$). Typically, when compared to the simple count method, the technique reduces the statistical errors by 20% for $\bar{p}p$, and 40% for $pp$ collisions, respectively. The technique can be used to search for new high mass and large width Z' bosons which may be best detected through the observation of deviations from the Standard Model expectation for the forward-backward asymmetry. In addition, we derive expressions for the QCD angular coefficients for Drell-Yan events.

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