Using dispersion theory with an improved description of the two-pion continuum based on the precise Roy-Steiner analysis of pion-nucleon scattering, we analyze recent data from electron-proton scattering. This allows for a high-precision determination of the electric and magnetic radius of the proton, $r_E = (0.838^{+0.005}_{-0.004}{}^{+0.004}_{-0.003})\,$fm and $r_M = (0.847\pm{0.004}\pm{0.004})\,$fm, where the first error refers to the fitting procedure using bootstrap and the data while the second one refers to the systematic uncertainty related to the underlying spectral functions.
We report on the first determination of the shear forces quarks inside the proton from experimental data on deeply virtual Compton scattering. The maximum shear force of approximately 40 MeV/fm occurs near 0.6 fm from the proton center, indicating where confinement forces may be strongest. On the macroscopic scale of the earth surface, this force corresponds to the weight of a mass of about 650 kg. The shear forces in the proton reverse direction at r = 0.45 fm from the center.
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 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…
We show that in previous analyses of electron-proton scattering, the uncertainties in the statistical procedure to extract the proton charge radius are underestimated. Using a fit function based on a conformal mapping, we can describe the scattering data with high precision and extract a radius value in agreement with the one obtained from muonic hydrogen.
Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyse proton magnetic form factor data obtained via electron+proton scattering on $Q^2 \in [0.027,0.55]\,$GeV$^2$ with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we find $r_M = 0.817(27)\,$fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are…
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…
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 …
We present a novel method for extracting the proton radius from elastic electron-proton ($ep$) scattering data. The approach is based on interpolation via continued fractions augmented by statistical sampling and avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto $Q^2\simeq 0$. Applying the method to extant modern $e p$ data sets, we find that all results are mutually consistent and, combining them, arrive at $r_p=0.847(8)\,$fm. This result compares favourably with values obtained from contemporary measurements of the Lamb shift…
We present an overview of the GW SAID group effort to analyze on new pion photoproduction on both proton- and neutron-targets. The main database contribution came from the recent CLAS and MAMI unpolarized and polarized measurements. The differential cross section for the processes gamma n --> pi- p was extracted from new measurements accounting for Fermi motion effects in the impulse approximation (IA) as well as NN and piN effects beyond the IA. The EM coupling results are compared to other recent studies.
The "proton radius puzzle" remains unsolved since it was established in 2010. This paper summarizes the current state and gives an overview over upcoming experiments.
Using differential cross-section data of inclusive $W$ and $Z/γ^\ast$ boson production and of their production in association with jets, and differential cross-section data of top-quark pair production in the lepton + jets and dilepton channels in proton$-$proton collisions at the CERN Large Hadron Collider at center-of-mass energies of $\sqrt{s}=7$ and 8 TeV, together with deep inelastic scattering data from electron$-$proton collisions at the HERA collider, several determinations of parton distribution functions of the proton have been performed by the ATLAS experiment. The results are prese…
In light of the proton radius puzzle, the discrepancy between measurements of the proton charge radius from muonic hydrogen and those from electronic hydrogen and electron-proton scattering measurements, we reexamine the charge radius extractions from electron scattering measurements. We provide a recommended value for the proton RMS charge radius, $r_E = 0.879 \pm 0.011$ fm, based on a global examination of elastic e-p scattering data. The uncertainties include contributions to account for tension between different data sets and inconsistencies between radii using different extraction procedu…
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.
It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. Very small values of transferred momenta (up to four order of magnitude smaller than the ones presently available) can be reached with high probability.
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 evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell-Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the in…
We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $Δ$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$Δ$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination o…
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 …
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 extract the proton magnetic radius from the high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-$Q^2$ form factors. It allows us to use data up to $Q^2\sim$ 0.5 GeV$^2$ for constraining the radii and overcomes the difficulties of empirical fits and $Q^2 \rightarrow 0$ extrapolation. We obtain a magnetic radius $r_M^p$ = 0.850 $\pm$0.001 (fit 68%) $\pm$0.010 (theory full range) fm, significantly different from earlier results ob…
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 electric and magnetic bag radiuses of the proton can be determined by MIT bag model based on electric and magnetic form factors of the proton. Also we determined electric and magnetic root mean squared radiuses of the proton, using of bag radius and compared with other results suggests a suitable compatibility.
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
The extremely precise extraction of the proton radius by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron-proton scattering. This is the proton radius puzzle. The origins of the puzzle and the reasons for believing it to be very significant are explained. Various possible solutions of the puzzle are identified, and future work needed to resolve the puzzle is discussed.
A potential explanation [U.~D.~Jentschura, Phys.\ Rev.\ A {\bf 88}, 062514 (2013)] of the proton radius puzzle originating from the non-perturbative lepton-pair content of the proton is studied. Well-defined quantities that depend on this lepton-pair content are evaluated. Each is found to be of the order of $10({α\over π})^2$, so that we find such a lepton-pair content exists in the proton. However, we argue that this relatively large result and general features of loop diagrams rule out the possibility of lepton-pair content as an explanation of the proton radius puzzle. In addition, the con…
We analyze the recent electron-proton scattering data from Mainz using a dispersive framework that respects the constraints from analyticity and unitarity on the nucleon structure. We also perform a continued fraction analysis of these data. We find a small electric proton charge radius, r_E^p = 0.84_{-0.01}^{+0.01} fm, consistent with the recent determination from muonic hydrogen measurements and earlier dispersive analyses. We also extract the proton magnetic radius, r_M^p = 0.86_{-0.03}^{+0.02} fm, consistent with earlier determinations based on dispersion relations.
We perform a new analysis of electron-proton scattering data to determine the proton electric and magnetic radii, enforcing model-independent constraints from form factor analyticity. A wide-ranging study of possible systematic effects is performed. An improved analysis is developed that rebins data taken at identical kinematic settings, and avoids a scaling assumption of systematic errors with statistical errors. Employing standard models for radiative corrections, our improved analysis of the 2010 Mainz A1 Collaboration data yields a proton electric radius $r_E = 0.895(20)$ fm and magnetic r…
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.
We argue that the proton charge radius conundrum can be resolved by weakening the assumption of perturbative formulation of quantum electrodynamics within the proton
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 $4m_π^2$, where $m_π$ 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.
We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $ππ$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric rad…
Using the available cross section and polarization data for elastic electron-proton scattering, we provide an extraction of the two-photon exchange amplitudes at a common value of four-momentum transfer, around Q^2 = 2.5 GeV^2. This analysis also predicts the e^+ p / e^- p elastic scattering cross section ratio, which will be measured by forthcoming experiments.
By using the convolution formula derived within the framework of relativistic quantum mechanics, we have examined the Fermi Motion effects on the ratios R_{pd/pp}= sigma^{pd}/(2 sigma^{pp}) between the proton-proton (p-p) and proton-deuteron (p-d) Drell-Yan cross sections. We have found that in the small x_2 < 0.3 region, the Fermi Motion effect is less than 1% and our results for the ratios R_{pd/pp} = sigma^{pd}/(2 sigma^{pp}) agree well with the data at 800 GeV. In the large Bjorken x_2 > about 0.4 region, the p-d Drell-Yan cross sections can be influenced strongly by the Fermi motion effec…
Background: There is significant current interest in knowing the value of the proton radius and also its proper definition. Purpose: Combine the disparate literatures of hydrogen spectroscopy and diverse modern parton distributions to show that the quantity $r_p^2\equiv -6 G_E'(0)$ is the relativistically proper definition that originates from the separate bodies of work. Methods: Use perturbation theory, light-front dynamics and elementary techniques to find relativistically correct definitions of the proton radius and charge density. Results: It is found that the very same proton radius is a…
Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue equations with the effective Coulomb potential that exhibits a tiny sensitivity to the characteristic momentum-scale of the bound system. The scale dependence is shown to be relevant to the theoretical interpretation of precisely measured lepton-proton bound-state energy levels in terms of a 4 percent difference between the proton radii in muon-proton and elect…
We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite $Q^2$ with the derivative at $Q^2 = 0$. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to u…
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.
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…
Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary hydrogen and deuterium, from relative measurements of the cross section of the elastic electron-proton scattering at MAMI and from evaluation of the world data on absolute measurements of e-p cross sections). Here, we question the accuracy of the determination of the proton charge radius by means of spectroscopy of ordinary hydrogen and deuterium and demonstra…
We present fits to determine Parton Distribution Functions using a diverse set of measurements from the ATLAS experiment at the LHC, including inclusive $W$ and $Z$ boson production, $t\bar{t}$ production, $W$+jets and $Z$+jets production, inclusive jet production and direct photon production. These ATLAS measurements are used in combination with deep-inelastic scattering data from the electron-proton collider HERA. Particular attention is paid to the correlation of systematic uncertainties within and between the various ATLAS data sets and to the impact of model, theoretical and parameterisat…
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 electro…
We apply a "color" tripole ansatz for describing the $D$-term of the proton. By fitting the experimental data of the vector meson J/$ψ$ and $ϕ$ photoproductions near the thresholds, we firstly obtained the gluonic $D$-term of the proton. $D_g(0)$ is estimated to be $-2.16\pm0.42$ for J/$ψ$ and $-1.31\pm0.48$ for $ϕ$, and the mechanical root mean square radius of proton is estimated to be $0.61\pm0.29$ fm for $ϕ$ and $0.42\pm0.11$ fm for J/$ψ$.
Recently the muonic hydrogen lamb shift has been measured with unprecedented accuracy, allowing for a precise determination of the proton radius. This determination is 5 sigma away from the previous CODATA value obtained from (mainly) the hydrogen lamb shift and the electron-proton scattering. Within an effective field theory formalism, I will define the proton radius and briefly review some aspects of the theoretical prediction for the muonic hydrogen lamb shift, studying both the pure QED-like computation and the hadronic effects.
The recent values of the proton charge radius obtained by means of muonic-hydrogen laser spectroscopy are about $4\%$ different from the electron scattering data. It has been suggested that the proton radius is actually measured in different frames and that, starting from a non relativistic quark model calculation, the Lorentz transformation of the form factors accounts properly for the discepancy. We shall show that the relation between the charge radii measured in different frames can be determined on very general grounds by taking into account the Lorentz transformation of the charge densit…
Proton charge radius is calculated from the electromagnetic form factor of proton parameterized by the dispersion relation. The calculated charge radius is a little larger than that obtained by the Lamb shift of the $μ$ mesic atom. As the result is sensitive to the experimental data of proton electric form factor at small momentum transfer, more accurate data are required to draw conclusion if the result of the nucleon form factor is different or not from that obtained Pohl et al.
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.
