arXiv subjects

A. M. Bernstein

Publications and source records attributed to A. M. Bernstein.

At least 19 recordsLinked to original sources

arXiv2015

The pi0, eta, eta' -> gamma gamma*(Q^2) Decay Rates and Radii

The low $Q^2$ slopes of the the transition form factors provide a unique method to measure the sizes of the neutral pseudo-scalar mesons, since they do not have electromagnetic form factors. From the slope one obtains the "axial transition RMS radius" $ R_{PS,A} = \sqrt{ }$ for each PS meson. The present status of theory and experiment for these quantities are presented. A comparison of the $ R_{PS,A}$ is presented along with the electromagnetic and scalar radii of the $π^{\pm}$ mesons and the proton. We observe the striking similarity of the values of axial transition radii of all of the pseudoscalar mesons to each other and to the charge radius of the $π^{\pm}$. In the $Q^2$ = 0 limit the transition form factor is a measure of the pseudo-scalar meson radiative width (lifetime) and is a possible fourth (unexploited) method to perform such a measurement. The $π^{0} \rightarrow γγ$ decay rate is a test of QCD at the confinement scale. There is a firm QCD prediction with a theoretical uncertainty of $\simeq $ 1 \% which calls for an experimental test at the same level of accuracy. There are three methods that have been utilized to perform this measurement and the present status of the experimental tests are outlined. The current accuracy is significantly less than the theoretical uncertainty. The efforts to improve this are briefly summarized.

nucl-ex↗

arXiv2015

A precision measurement of the $p$($e,e^\prime p\,$)$π^0$ reaction at threshold

New results are reported from a measurement of $π^0$ electroproduction near threshold using the $p(e,e^{\prime} p)π^0$ reaction. The experiment was designed to determine precisely the energy dependence of $s-$ and $p-$wave electromagnetic multipoles as a stringent test of the predictions of Chiral Perturbation Theory (ChPT). The data were taken with an electron beam energy of 1192 MeV using a two-spectrometer setup in Hall A at Jefferson Lab. For the first time, complete coverage of the $ϕ^*_π$ and $θ^*_π$ angles in the $p π^0$ center-of-mass was obtained for invariant energies above threshold from 0.5 MeV up to 15 MeV. The 4-momentum transfer $Q^2$ coverage ranges from 0.05 to 0.155 (GeV/c)$^2$ in fine steps. A simple phenomenological analysis of our data shows strong disagreement with $p-$wave predictions from ChPT for $Q^2>0.07$ (GeV/c)$^2$, while the $s-$wave predictions are in reasonable agreement.

nucl-ex↗

arXiv2013

Accurate Test of Chiral Dynamics in the \boldmath$\vecγ p \rightarrow π^0p$ Reaction

A precision measurement of the differential cross sections $dσ/dΩ$ and the linearly polarized photon asymmetry $Σ\equiv (dσ_\perp - dσ_\parallel) \slash (dσ_\perp + dσ_\parallel)$ for the $\vecγ p \rightarrow π^0p$ reaction in the near-threshold region has been performed with a tagged photon beam and almost $4π$ detector at the Mainz Microtron. The Glasgow-Mainz photon tagging facility along with the Crystal Ball/TAPS multi-photon detector system and a cryogenic liquid hydrogen target were used. These data allowed for a precise determination of the energy dependence of the real parts of the $S$- and all three $P$-wave amplitudes for the first time and provide the most stringent test to date of the predictions of Chiral Perturbation Theory and its energy region of agreement with experiment.

nucl-ex↗

arXiv2013

Symmetry Tests in Photo-Pion Production

Small angle electron scattering with intense electron beams opens up the possibility of performing almost real photon induced reactions with thin, polarized hydrogen and few body targets, allowing for the detection of low energy charged particles.This promises to be much more effective than conventional photon tagging techniques. For photo-pion reactions some fundamental new possibilities include: tests of charge symmetry in the N-N system by measurement of the neutron-neutron scattering length $a_{nn}$ in the $γD \rightarrow π^{+} nn$ reaction; tests of isospin breaking due to the mass difference of the up and down quarks; measurements with polarized targets are sensitive to $π$N phase shifts and will test the validity of the Fermi-Watson (final state interaction) theorem. All of these experiments will test the accuracy and energy region of validity of chiral effective theories.

nucl-ex↗

arXiv2013

Neutral Pion Lifetime Measurements and the QCD Chiral Anomaly

A fundamental property of QCD is the presence of the chiral anomaly, which is the primary component of the $π^0\rightarrowγγ$ decay amplitude. Based on this anomaly and its small ($\simeq$ 4.5%) chiral correction, a firm prediction of the $π^0$ lifetime can be used as a test of QCD at confinement scale energies. The interesting experimental and theoretical histories of the $π^0$ meson are reviewed, from discovery to the present era. Experimental results are in agreement with the theoretical prediction, within the current ($\simeq$ 3%) experimental error; however, they are not yet sufficiently precise to test the chiral corrected result, which is a firm QCD prediction and is known to $\simeq$ 1% uncertainty. At this level there exist experimental inconsistencies, which require attention. Possible future work to improve the present precision is suggested.

hep-ph↗

arXiv2013

Measurements of the γ* p --> Δ(1232) reaction at low Q2

We report new p$(\vec{e},e^\prime p)π^\circ$ measurements in the $Δ^{+}(1232)$ resonance at the low momentum transfer region utilizing the magnetic spectrometers of the A1 Collaboration at MAMI. The mesonic cloud dynamics are predicted to be dominant and appreciably changing in this region while the momentum transfer is sufficiently low to be able to test chiral effective calculations. The results disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations with pion cloud effects, chiral effective field theory and lattice calculations. The reported measurements suggest that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements.

nucl-ex↗

arXiv2013

Upper Energy Limit of Heavy Baryon Chiral Perturbation Theory in Neutral Pion Photoproduction

With the availability of the new neutral pion photoproduction from the proton data from the A2 and CB-TAPS Collaborations at Mainz it is mandatory to revisit Heavy Baryon Chiral Perturbation Theory (HBChPT) and address the extraction of the partial waves as well as other issues such as the value of the low-energy constants, the energy range where the calculation provides a good agreement with the data and the impact of unitarity. We find that, within the current experimental status, HBChPT with the fitted LECs gives a good agreement with the existing neutral pion photoproduction data up to $\sim$170 MeV and that imposing unitarity does not improve this picture. Above this energy the data call for further improvement in the theory such as the explicit inclusion of the Δ(1232). We also find that data and multipoles can be well described up to $\sim$185 MeV with Taylor expansions in the partial waves up to first order in pion energy.

nucl-th↗

arXiv2013

Pions: Experimental Tests of Chiral Symmetry Breaking

Based on the spontaneous breaking of chiral symmetry, chiral perturbation theory (ChPT) is believed to approximate confinement scale QCD. Dedicated and increasingly accurate experiments and improving lattice calculations are confirming this belief, and we are entering a new era in which we can test confinement scale QCD in some well chosen reactions. This is demonstrated with an overview of low energy experimental tests of ChPT predictions of $ππ$ scattering, pion properties, $π$N scattering and electromagnetic pion production. These predictions have been shown to be consistent with QCD in the meson sector by increasingly accurate lattice calculations. At present there is good agreement between experiment and ChPT calculations, including the $ππ$ and $π$N s wave scattering lengths and the $π^{0}$ lifetime. Recent, accurate pionic atom data are in agreement with chiral calculations once isospin breaking effects due to the mass difference of the up and down quarks are taken into account, as was required to extract the $ππ$ scattering lengths. In addition to tests of the theory, comparisons between $ππ$ and $π$N interactions based on general chiral principles are discussed. Lattice calculations are now providing results for the fundamental, long and inconclusively studied, $π$N $σ$ term and the contribution of the strange quark to the mass of the proton. Increasingly accurate experiments in electromagnetic pion production experiments from the proton which test ChPT calculations (and their energy region of validity) are presented. These experiments are also beginning to measure the final state $π$N interaction. This paper is based on the concluding remarks made at the Chiral Dynamics Workshop CD12 held at Jefferson Lab in Aug. 2012.

hep-ex↗

arXiv2011

Consistent threshold pi0 electro-production at Q^2=0.05, 0.10, and 0.15 GeV^2/c^2

New, accurate data are presented on the near threshold p(e,e'p)pi^0 reaction in the range of four-momentum transfers between Q^2=0.05 and 0.15GeV^2/c^2. The data were taken with the spectrometer setup of the A1 Collaboration at the Mainz Microtron MAMI. The complete center of mass solid angle was covered up to a center of mass energy of 4MeV above threshold. These results supersede the previous analysis based on three separate experiments, and are compared with calculations in Heavy Baryon Chiral Perturbation Theory and with phenomenological models.

nucl-ex↗

arXiv2011

Neutral Pion Production in the Threshold Region

We give an overview of the physics motivation and evolution of the neutral pion photoproduction measurements in the threshold region conducted in the A2 collaboration at MAMI. The latest two experiments have been performed with the almost 4-pi Crystal Ball detector. The first was with a linearly polarized photon beam and unpolarized liquid-hydrogen target. The data analysis is now complete and the linearly polarized beam asymmetry along with differential cross sections provide the most stringent test to date of the predictions of Chiral Perturbation Theory and its energy region of convergence. More recently a measurement was performed using both circularly polarized photons and a transversely polarized butanol frozen-spin target, with the goal of extracting both the target and beam-target asymmetries. From these we intend to extract pi-N scattering sensitive information for the first time in photo-pion reactions. This will be used to test isospin conservation and further test dynamics of chiral symmetry breaking in QCD as calculated at low energies by Chiral Perturbation Theory.

nucl-ex↗

arXiv2010

A New Measurement of the $π^0$ Radiative Decay Width

High precision measurements of the differential cross sections for $π^0$ photoproduction at forward angles for two nuclei, $^{12}$C and $^{208}$Pb, have been performed for incident photon energies of 4.9 - 5.5 GeV to extract the ${π^0 \to γγ}$ decay width. The experiment was done at Jefferson Lab using the Hall B photon tagger and a high-resolution multichannel calorimeter. The ${π^0 \to γγ}$ decay width was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value for the decay width is $Γ{(π^0 \to γγ)} = 7.82 \pm 0.14 ~({\rm stat.}) \pm 0.17 ~({\rm syst.}) ~{\rm eV}$. With the 2.8% total uncertainty, this result is a factor of 2.5 more precise than the current PDG average of this fundamental quantity and it is consistent with current theoretical predictions.

nucl-ex↗

arXiv2009

Unexpected impact of D waves in low-energy neutral pion photoproduction from the proton and the extraction of multipoles

Contributions of $D$ waves to physical observables for neutral pion photoproduction from the proton in the near-threshold region are studied and means to isolate them are proposed. Various approaches to describe the multipoles are employed --a phenomenological one, a unitary one, and heavy baryon chiral perturbation theory. The results of these approaches are compared and found to yield essentially the same answers. $D$ waves are seen to enter together with $S$ waves in a way that any means which attempt to obtain the $E_{0+}$ multipole accurately must rely on knowledge of $D$ waves and that consequently the latter cannot be dismissed in analyses of low-energy pion photoproduction. It is shown that $D$ waves have a significant impact on double-polarization observables that can be measured. This importance of $D$ waves is due to the soft nature of the $S$ wave and is a direct consequence of chiral symmetry and the Nambu--Goldstone nature of the pion. $F$-wave contributions are shown to be negligible in the near-threshold region.

nucl-th↗

arXiv2009

Low-Energy D-Wave Effects in Neutral Pion Photoproduction

The contribution of D waves to physical observables for neutral pion photoproduction in the near threshold region is studied. Heavy Baryon Chiral Perturbation Theory to one loop, and up to ${\cal O}(q^4)$, is used to account for the S and P waves, while D waves are added in an almost model-independent way using standard Born terms and vector mesons. It is found that the inclusion of D waves is necessary to extract the $E_{0+}$ multipole reliably from present and forthcoming data and to assess the low-energy constants of Chiral Perturbation Theory. Arguments are presented demonstrating that F-wave contributions are negligible in the near-threshold region.

nucl-th↗

arXiv2008

Virtual Compton Scattering measurements in the $γ^* N\to Δ$ transition

We report on new H$(e,e^\prime p)γ$ measurements in the $Δ(1232)$ resonance at $Q^2=0.06$ (GeV/c) carried out simultaneously with H$(e,e^\prime p)π^0$. It is the lowest $Q^2$ for which the virtual Compton scattering (VCS) reaction has been studied in the first resonance region. The VCS measured cross sections are well described by dispersion-relation calculations in which the multipole amplitudes derived from H$(e,e^\prime p)π^0$ data are used as input, thus confirming the compatibility of the results. The derived resonant magnetic dipole amplitude $M^{3/2}_{1+} = (40.60 \pm 0.70_{stat+sys})(10^{-3}/m_{π^+})$ at $W=$ 1232 MeV is in excellent agreement with the value extracted from H$(e,e^\prime p)π^0$ measurements.

nucl-ex↗

arXiv2007

Opening Remarks at Chiral Dynamics 2006:Experimental Tests of Chiral Symmetry Breaking

A physical introduction to the basics of chiral dynamics is presented. Emphasis is placed on experimental tests which have generally demonstrated a strong confirmation of the predictions of chiral perturbation theory, a low energy effective field theory of QCD. Special attention is paid to a few cases where discrepancies exist, requiring further work. Some desirable future tests are also recommended.

hep-ph↗

arXiv2007

Energy Dependence of the Delta Resonance: Chiral Dynamics in Action

There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presented

hep-ph↗

arXiv2007

Ovrview: The Shape of Hadrons

In this article we address the physical basis of the deviation of hadron shapes from spherical symmetry (non-spherical amplitudes) with focus on the nucleon and $Δ$. An overview of both the experimental methods and results and the current theoretical understanding of the issue is presented. At the present time the most quantitative method is the $γ^{*} p \to Δ$ reaction for which significant non-spherical electric (E2) and Coulomb quadrupole (C2) amplitudes have been observed with good precision as a function of Q^{2} from the photon point through 6 GeV^{2}. Quark model calculations for these quadrupole amplitudes are at least an order of magnitude too small and even have the wrong sign. Lattice QCD, chiral effective field theory, and dynamic model calculations which include the effects of the pion-cloud are in approximate agreement with experiment. This is expected due to the spontaneous breaking of chiral symmetry in QCD and the resulting, long range (low Q^{2}) effects of the pion-cloud. Other observables such as nucleon form factors and virtual Compton scattering experiments indicate that the pion-cloud is playing a significant role in nucleon structure. Semi-inclusive deep inelastic scattering experiments with transverse polarized beam and target also show the effect of non-zero quark angular momentum.

hep-ph↗

arXiv2007

Separated cross sections in π^0 electroproduction at threshold at Q^2 = 0.05 GeV^2/c^2

The differential cross sections σ_0=σ_T+εσ_L, σ_{LT}, and σ_{TT} of π^0 electroproduction from the proton were measured from threshold up to an additional center of mass energy of 40 MeV, at a value of the photon four-momentum transfer of Q^2= 0.05 GeV^2/c^2 and a center of mass angle of θ=90^\circ. By an additional out-of-plane measurement with polarized electrons σ_{LT'} was determined. This showed for the first time the cusp effect above the π^+ threshold in the imaginary part of the s-wave. The predictions of Heavy Baryon Chiral Perturbation Theory are in disagreement with these data. On the other hand, the data are somewhat better predicted by the MAID phenomenological model and are in good agreement with the dynamical model DMT.

nucl-ex↗