Static properties of hadrons such as their radii and other moments of the electric and magnetic distributions can only be extracted using theoretical methods and not directly measured from experiments. As a result, discrepancies between the extracted values from different precision measurements can exist. The proton charge radius, $r_p$, which is either extracted from electron proton elastic scattering data or from hydrogen atom spectroscopy seems to be no exception. The value $r_p = 0.84087(39)$ fm extracted from muonic hydrogen spectroscopy is about 4% smaller than that obtained from electron proton scattering or standard hydrogen spectroscopy. The resolution of this so called proton radius puzzle has been attempted in many different ways over the past six years. The present article reviews these attempts with a focus on the methods of extracting the radius.
The precise determination of the proton radius from recent elastic scattering electron-proton data is discussed. The necessary precision on the elastic cross section to discriminate among the values coming from atomic spectroscopy is scrutinized in terms of the relevant quantity, i.e., the derivative of the form factor. It is shown that such precision is two orders of magnitude higher than the precision on the cross section, that is the measured observable. Different fits on the available data and of their discrete derivative, with analytical constraints are shown. The systematic error associa…
We performed the first simultaneous extraction of the six leading-order proton polarizabilities. We reached this milestone thanks to both new high-quality experimental data and an innovative bootstrap-base fitting method. These new results provide a self-consistent and fundamental benchmark for all future theoretical and experimental polarizability estimates.
We present the first extraction of the transversity distribution in the framework of collinear factorization based on the global analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets and in proton-proton collisions with one transversely polarized proton. The extraction relies on the knowledge of di-hadron fragmentation functions, which are taken from the analysis of electron-positron annihilation data. For the first time, the chiral-odd transversity is extracted from a global analysis similar to what is usually done for the chiral-even spin-averaged a…
In a series of recent publications, different authors produce a wide range of electron radii when reanalyzing electron proton scattering data. In the light of the proton radius puzzle, this is a most unfortunate situation. However, we find flaws in most analyses that result in radii around 0.84 fm. In this paper, we explain our reasoning and try to illustrate the most common pitfalls.
The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently PRad, a new electron-proton scattering experiment at Jefferson Lab, reported a proton charge radius of $0.831\pm 0.007_\textnormal{statistical}\pm 0.012_\textnormal{systematic}$. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using $z$-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50\% larger c…
Forward-backward multiplicity correlations have been studied in electron-positron, proton-proton and more recently in lead-lead collisions. For the proton-proton case, comparison of experimental results to different models reveals an incomplete understanding of the physical phenomenon associated with these correlations. In this work, we present a study of forward-backward multiplicity correlations in proton-proton collisions using the PYTHIA event generator, at LHC energies. A detailed analysis is presented with and without weak decays, splitting data samples into soft and hard QCD processes, …
Up to now, all charge radius measurements of the proton and deuteron assumed uniform spheroidal charge distribution. We investigate the nuclear deformation effects on these charge radius measurements by assuming a uniform prolate charge distribution for the proton and deuteron. We solve the energy levels of the corresponding muonic and electric atoms with such deformed nucleus and present how the purely quadruple deformation of proton and deuteron affects their Lamb shifts. The numerical results suggest that the deformation of proton and deuteron leads to that the charge radius extracted from …
The weak charge of the proton determines its coupling to the $Z^0$ boson. The distribution of weak charge is found to be dramatically different from the distribution of electric charge. The proton's weak radius $R_W= 1.545\pm 0.017$ fm is 80\% larger than its charge radius $R_{ch}\approx 0.84$ fm because of a very large pion cloud contribution. This large weak radius can be measured with parity violating electron scattering and may provide insight into the structure of the proton, various radiative corrections, and possible strange quark contributions.
The proton charge-radius determinations from the electromagnetic form-factor measurements in electron-proton scattering require an extrapolation to zero momentum transfer ($Q^2=0$) which is prone to model-dependent assumptions. We show that the data at finite momentum transfer can be used to establish a rigorous lower bound on the proton charge radius. Using the available $ep$ data at low $Q^2$, we obtain $R_E > 0.850(1)$ fm as the lower bound on the proton radius. This reaffirms the discrepancy between the $ep$ and muonic-hydrogen values, while bypassing the model-dependent assumptions that g…
We reanalyze electron-proton scattering data in the momentum transfer region $Q^2 < 1\ GeV^2$, which were used to determine proton electric radius, with main focus on the Mainz experiment (Bernauer et al., 2010). We examine dependence of fit results and $χ^2$ on the cut-off in $Q^2$ and degree of fitting polynomial, using pseudo-data and compare it with the case of real experimental data. We find that under some assumptions, the data could be consistent with the radius, obtained from muonic hydrogen.
Nucleons (protons and neutrons) are the building blocks of atomic nuclei, and are responsible for more than 99\% of the visible matter in the universe. Despite decades of efforts in studying its internal structure, there are still a number of puzzles surrounding the proton such as its spin, and charge radius. Accurate knowledge about the proton charge radius is not only essential for understanding how quantum chromodynamics (QCD) works in the non-perturbative region, but also important for bound state quantum electrodynamics (QED) calculations of atomic energy levels. It also has an impact on …
The discrepancy between the measured Lamb shift in muonic hydrogen and expectations from electron-proton scattering and regular hydrogen spectroscopy has become known as the proton radius puzzle, whose most "mundane" resolution requires a $> 5 σ$ shift in the value of the fundamental Rydberg constant. I briefly review the status of spectroscopic and scattering measurements, recent theoretical developments, and implications for fundamental physics.
Anti-protonic hydrogen and helium atoms are analyzed. Level shifts and width are expressed in terms of $\bar{p}$-nucleon sub-threshold scattering lengths and volumes. Experimental data are compared to results obtained from the 2009 version of the Paris $N\bar{N}$ interaction potential. Comparison with 1999 version is also made. Effects of $N\bar{N}$ quasi-bound states are discussed. Atomic 2P hyperfine structure is calculated for antiprotonic deuterium and the significance of new measurements is indicated.
In this paper, we apply the Maximum Entropy Method to estimate the proton radius and determine the valence quark distributions in the proton at extremely low resolution scale Q$^{2}_{0}$. Using the simplest functional form of the valence quark distribution and standard deviations of quark distribution functions in the estimation of the proton radius, we obtain a quadratic polynomial for the relationship between the proton radius and the momentum fraction of other non-perturbative components in the proton. The proton radii are approximately equal to the muonic hydrogen experimental result $r_p$…
We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).
We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from …
Extracting the proton charge radius from electron scattering data requires determining the slope of the charge form factor at $Q^2$ of zero. But as experimental data never reach that limit, numerous methods for making the extraction have been proposed, though often the functions are determined after seeing the data which can lead to confirmation bias. To find functional forms that will allow for a robust extraction of the input radius for a wide variety of functional forms in order to have confidence in the extraction from upcoming low $Q^2$ experimental data such as the Jefferson Lab PRad exp…
We present an analysis of the proton mass radius by studying the $t$-dependence of the differential cross sections of the vector meson photoproductions near the thresholds. At low energy, the photoproduction of a quarkonium off the proton is connected to the scalar gravitational form factor of the proton, which is sensitive to the proton mass distribution from the QCD trace anomaly. Under an assumption of the scalar form factor of dipole form, the proton mass radius is extracted via the near-threshold photoproduction data of J/$ψ$, $ϕ$ and $ω$ vector mesons. The average value of the proton mas…
I summarize the dispersion-theoretical analysis of the nucleon electromagnetic form factors. Special emphasis is given on the extraction of the proton charge radius and its relatives, the proton magnetic radius as well as the neutron magnetic radius. Some recent work on the hyperfine splitting in leptonic hydrogen and on radiative corrections to muon-proton scattering is also discussed. Some views on future studies are given.
The status of the proton radius puzzle (as of the date of the Confer- ence) is reviewed. The most likely potential theoretical and experimental explanations are discussed. Either the electronic hydrogen experiments were not sufficiently accurate to measure the proton radius, the two- photon exchange effect was not properly accounted for, or there is some kind of new physics. I expect that upcoming experiments will resolve this issue within the next year or so.Ta
We present the first attempt to extract the scalar dipole dynamical polarizabilities from proton real Compton scattering data below pion-production threshold. The theoretical framework combines dispersion relations technique, low-energy expansion and multipole decomposition of the scattering amplitudes. The results are obtained with statistical tools that have never been applied so far to Compton scattering data and are crucial to overcome problems inherent to the analysis of the available data set.
The mass radius is a fundamental property of the proton that so far has not been determined from experiment. Here we show that the mass radius of the proton can be rigorously defined through the formfactor of the trace of the energy-momentum tensor (EMT) of QCD in the weak gravitational field approximation, as appropriate for this problem. We then demonstrate that the scale anomaly of QCD enables the extraction of the formfactor of the trace of the EMT from the data on threshold photoproduction of $J/ψ$ and $Υ$ quarkonia, and use the recent GlueX Collaboration data to extract the r.m.s. mass r…
In 2010 the proton charge radius was extracted for the first time from muonic hydrogen, a bound state of a muon and a proton. The value obtained was five standard deviations away from the regular hydrogen extraction. Taken at face value, this might be an indication of a new force in nature coupling to muons, but not to electrons. It also forces us to reexamine our understanding of the structure of the proton. Here I describe an ongoing theoretical research effort that seeks to address this "proton radius puzzle". In particular, I will present the development of new effective field theoretical …
A puzzling discrepancy exists between the values of the proton charge radius obtained using different experimental techniques: elastic electron-proton scattering and spectroscopy of electronic and muonic hydrogen. The proton radius is defined through the slope of the electric form factor, $G_E(Q^2)$, at zero four-momentum transfer, which is inaccessible in scattering experiments. We propose a novel method for extracting the proton radius from scattering data over a broad $Q^2$ range rather than attempting to directly determine the slope of $G_E$ at $Q^2 = 0$. This method relates the radius of …
The modification of quark- and gluon-initiated jets in the quark-gluon plasma produced in heavy-ion collisions is a long-standing question that has not yet received a definitive answer from experiments. In particular, the size of the modifications in the quark-gluon plasma differs between theoretical models. Therefore a fully data-driven technique is crucial for an unbiased extraction of the quark and gluon jet spectra and substructure. Corroborating past results, I demonstrate the capability of a fully data-driven technique called topic modeling in separating quark and gluon contributions to …
Systematic differences exist between values of the proton's electric form factors in the low-$Q^2$ region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at $Q^{2} \rightarrow 0$. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dis…
This note is motivated by preparations of a new $ep$ elastic scattering experiment in the low transfer momentum region to be carried out in the 720 MeV electron beam of the Mainz Microtron MAMI. This experiment will use an innovative method allowing for detection of recoil protons in coincidence with the scattered electrons. The goal is to measure the $ep$ differential cross sections in the $Q^2$ range from 0.001 GeV$^2$ to 0.04 GeV$^2$ and to determine the proton charge radius with sub-percent precision.
