The origin of the proton radius puzzle

The European Physical Journal A - This review represents a detailed and comprehensive discussion of the Thermal Field Theory (TFT) concepts and key results in Yukawa-type theories. We start with a...     

The Lamb shift in muonic hydrogen and the proton radius puzzle

The recent measurement of the Lamb shift in muonic hydrogen resulted in a tenfold improved value of the rms charge radius of the proton. The value is, however, 7 standard deviations discrepant from the world average of this quantitiy which is obtained from elastic electron-proton scattering and precision spectroscopy of hydrogen and deuterium. New input from both theory and experiment is needed to resolve this so-called “proton radius puzzle”.     

Precision laser spectroscopy and the proton radius puzzle

The problem of the discrepancy between the proton radius values obtained via spectroscopy of ordinary and muonic hydrogen is discussed. It is shown that there is a flaw in the standard theory of quantum electrodynamics that could produce such a discrepancy.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.     

QED confronts the radius of the proton

Recent results on muonic hydrogen (Pohl et al., 2010) [1] and the ones compiled by CODATA on ordinary hydrogen and ep-scattering (Mohr et al., 2008) [2] are 5σ away from each other. Two reasons justify a further look at this subject: (1) One of the approximations used in Pohl et al. (2010) [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by ∼3 of the standard deviations of Pohl et al. (2010) [1], in the “right” direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius “runs”, much as the QCD coupling “constant” does. (2) The result of Pohl et al. (2010) [1] requires a choice of the “third Zemach moment”. Its published independent determination is based on an analysis with a p  -value – the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis – of 3.92×¹⁰⁻¹²$3.92\times {10}^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of “tension” between muonic- and ordinary-hydrogen results, currently at most  ∼4σ$\sim 4\sigma$. There is no tension between the results of Pohl et al. (2010) [1] and the proton radius determined with help of the analyticity of its form-factors.     

The RMS charge radius of the proton and Zemach moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al. De Rújula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.     

Shares of sea and valence quarks in the proton spin puzzle

The first moments of the polarized valence parton distribution functions truncated to the wide Bjorken x region 0.004 < x < 0.7 are directly (without any fitting procedure) extracted in NLO QCD from the combined COMPASS and HERMES semi-inclusive deep inelastic scattering data. Applying the proposed original procedure to these results, we estimate the contributions of light sea quarks to the proton spin, which occur just zero within the errors.     

鞘场加速机理中质子束的特性与其初始尺寸的关系

为了研究激光鞘场中质子层的尺寸对质子束特性的影响,本文应用中国工程物理研究院 激光聚变研究中心的二维Particle-In-Cell (2D-PIC)数值模拟程序Flips2D进行了相关数值模拟研究. 研究了质子束总能量随时间的变化,得出了加速持续过程与激光脉冲持续时间的关系; 研究了质子层的宽度对加速后质子束发散角和能谱的影响;研究了质子层的厚与加速后质子束 发散角和能谱的关系;得出了质子层的初始尺寸对加速后质子特性的影响规律.     

Probing the flavor-specific scalar mediator for the muon(g-2)deviation,the proton radius puzzle and the light dark matter production

Flavor-specific scalar bosons exist in various Standard Model extensions and couple to a single generation of fermions via a global flavor symmetry breaking mechanism. Given this strategy, we propose a Me V flavor-specific scalar model in dimension-5 operator series, which explains the muon g-2 anomaly and proton radius puzzle by coupling with the muon and down-quark at the same time. The framework is consistent with the null result of high-intensity searches. Specifically, the supernova constraints for muon couplings become weakened by including the contribution of down-quark interaction. The parameter space for explaining muon g-2 discrepancy is available when 10% energy deposition is required in the energy explosion process in the supernova,but this is ruled out by the 1% energy deposition requirement. We also investigate the searches for mediator and dark matter and the resulting constraints on viable parameter space such as nuclear physics constraints, direct detection for light boosted dark matter, and possible CMB constraints. When compared with conventional dark matter production, light dark matter production has two additional modifications: bound state formation and early kinetic equilibrium decoupling. We are now looking into the implications of these effects on the relic density of light dark matter.     

Proton-electron elastic scattering and the proton charge radius

It is suggested that proton elastic scattering on atomic electrons allows a precise measurement of the proton charge radius. The main advantage is that inverse kinematics allows one to access with a huge cross section very small values of transferred momenta, up to four orders of magnitude smaller than the ones presently achieved.     

Estimating proton radius and proportion of other non-perturbative components in the proton by the maximum entropy method

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_0~2.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 = 0.841 fm and the CODATA analysis r_p = 0.877fm when the other non-perturbative components account for 17.5% and 22.3% respectively.We propose "ghost matter" to explain the difference in other non-perturbative components(4.8%) that the electron can detect.     

The effects of density-dependence and exchange on the equivalent sharp radius of the real proton optical potential

The real part of the proton optical potential is calculated using the folding model with Green's strongly density-dependent nucleon-nucleon interaction. The results for a range of nuclei give, approximately, for the equivalent sharp radius for proton optical potential $\text{R}{}_{\mathrm{<mtext>v</mtext>}}\text{= 1.13 A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{+0.55}$ with exchange. The additive constant is interpreted as the range of the hard core of the nucleon-nucleon interaction.     

New parity-violating muonic forces and the proton charge radius

The recent discrepancy between proton charge radius measurements extracted from electron-proton versus muon-proton systems is suggestive of a new force that differentiates between lepton species. We identify a class of models with gauged right-handed muon number, which contains new vector and scalar force carriers at the ～100 MeV scale or lighter, that is consistent with observations. Such forces would lead to an enhancement by several orders-of-magnitude of the parity-violating asymmetries in the scattering of low-energy muons on nuclei. The relatively large size of such asymmetries, O(10(-4)), opens up the possibility for new tests of parity violation in neutral currents with existing low-energy muon beams.     

Resolution of the pion puzzle: The QCD string in Nambu-Goldstone mesons

Pions and kaons have a double nature: the chiral dynamics of Nambu-Goldstone bosons together with the usual string dynamics common to all mesons. To uncover the interplay of both dynamics, the effective chiral Lagrangian is derived from the QCD Lagrangian using the field correlator method, and the pion self-energy (mass) operator is written explicitly. The latter contains an infinite number of poles, but is normalized to zero at zero momentum because of spontaneous chiral symmetry breaking. As a result, one obtains the Gell-Mann-Oakes-Renner relation for the ground-state pion and (slightly shifted by chiral dynamics) the usual spectrum of radially excited pions starting with π(1300).