Search

Phenomenological amplitudes obtained in partial-wave analyses (PWA) of single-pion photoproduction are used to evaluate the contribution of this process to the Gerasimov-Drell-Hearn (GDH), Baldin and Gell-Mann-Goldberger-Thirring (GGT) sum rules, by integrating up to 2 GeV in photon energy. Our study confirms that the single-pion contribution to all these sum rules converges even before the highest considered photon energy, but the levels of saturation are very different in the three cases. Single-pion production almost saturates the GDH sum rule for the proton, while a large fraction is missing in the neutron case. The Baldin integrals for the proton and the neutron are both saturated to about four fifths of the predicted total strength. For the GGT sum rule, the wide variability in predictions precludes any definitive statement., Comment: 12 pages, 7 figure, 3 tables; discussion refined, references added, Minor fixes to the authorship list found during production; acknowledgement added; final version accepted by Phys Rev C

We report measurements of the exclusive neutral pion electroproduction cross section off protons at large values of $x_B$ (0.36, 0.48 and 0.60) and $Q^2$ (3.1 to 8.4 GeV$^2$) obtained from Jefferson Lab Hall A experiment E12-06-014. The corresponding structure functions $d\sigma_L/dt+\epsilon d\sigma_T/dt$, $d\sigma_{TT}/dt$, $d\sigma_{LT}/dt$ and $d\sigma_{LT'}/dt$ are extracted as a function of the proton momentum transfer $t-t_{min}$. The results suggest the amplitude for transversely polarized virtual photons continues to dominate the cross-section throughout this kinematic range. The data are well described by calculations based on transversity Generalized Parton Distributions coupled to a helicity flip Distribution Amplitude of the pion, thus providing a unique way to probe the structure of the nucleon.

Understanding the nucleon spin structure in the regime where the strong interaction becomes truly strong poses a challenge to both experiment and theory. At energy scales below the nucleon mass of about 1 GeV, the intense interaction among the quarks and gluons inside the nucleon makes them highly correlated. Their coherent behaviour causes the emergence of effective degrees of freedom, requiring the application of non-perturbative techniques, such as chiral effective field theory. Here, we present measurements of the neutron's generalized spin-polarizabilities that quantify the neutron's spin precession under electromagnetic fields at very low energy-momentum transfer squared down to 0.035 GeV$^2$. In this regime, chiral effective field theory calculations are expected to be applicable. Our data, however, show a strong discrepancy with these predictions, presenting a challenge to the current description of the neutron's spin properties., V1: initial version submitted to Nature Physics. V2: Published version. 16 pages, 7 figures. Additional material: 4 data tables (18 pages) V3: Typo corrected in author list. Paper content unchanged

The E12-14-012 experiment, performed in Jefferson Lab Hall A, has collected exclusive electron-scattering data (e,e$^\prime$p) in parallel kinematics using natural argon and natural titanium targets. Here, we report the first results of the analysis of the data set corresponding to beam energy of 2,222 MeV, electron scattering angle 21.5 deg, and proton emission angle -50 deg. The differential cross sections, measured with $\sim$4% uncertainty, have been studied as a function of missing energy and missing momentum, and compared to the results of Monte Carlo simulations, obtained from a model based on the Distorted Wave Impulse Approximation.

Positron beams, both polarized and unpolarized, are identified as essential ingredients for the experimental programs at the next generation of lepton accelerators. In the context of the hadronic physics program at Jefferson Lab (JLab), positron beams are complementary, even essential, tools for a precise understanding of the electromagnetic structure of nucleons and nuclei, in both the elastic and deep-inelastic regimes. For instance, elastic scattering of polarized and unpolarized electrons and positrons from the nucleon enables a model independent determination of its electromagnetic form factors. Also, the deeply-virtual scattering of polarized and unpolarized electrons and positrons allows unambiguous separation of the different contributions to the cross section of the lepto-production of photons and of lepton-pairs, enabling an accurate determination of the nucleons and nuclei generalized parton distributions, and providing an access to the gravitational form factors. Furthermore, positron beams offer the possibility of alternative tests of the Standard Model of particle physics through the search of a dark photon, the precise measurement of electroweak couplings, and the investigation of charged lepton flavor violation. This document discusses the perspectives of an experimental program with high duty-cycle positron beams at JLab., Comment: 18 pages, 7 figures This version superseeds the previous version which scientific content was decomposed into several more elaborated articles. All of these articles will be collected in the EPJ A Topical Issue about "Positron beam and physics at Jefferson Lab (e+@Jlab)"

Measuring the spin structure of protons and neutrons tests our understanding of how they arise from quarks and gluons, the fundamental building blocks of nuclear matter. At long distances the coupling constant of the strong interaction becomes large, requiring non-perturbative methods to calculate quantum chromodynamics processes, such as lattice gauge theory or effective field theories. Here we report proton spin structure measurements from scattering a polarized electron beam off polarized protons. The spin-dependent cross-sections were measured at large distances, corresponding to the region of low momentum transfer squared between 0.012 and 1.0 GeV$^2$. This kinematic range provides unique tests of chiral effective field theory predictions. Our results show that a complete description of the nucleon spin remains elusive, and call for further theoretical works, e.g. in lattice quantum chromodynamics. Finally, our data extrapolated to the photon point agree with the Gerasimov-Drell-Hearn sum rule, a fundamental prediction of quantum field theory that relates the anomalous magnetic moment of the proton to its integrated spin-dependent cross-sections., Published version. 10 pages, 5 figures. 20 pages of supplementary material (data tables and a figure)

We propose to use the High Momentum Spectrometer of Hall C combined with the Neutral Particle Spectrometer (NPS) to perform high precision measurements of the Deeply Virtual Compton Scattering (DVCS) cross section using a beam of positrons. The combination of measurements with oppositely charged incident beams is the only unambiguous way to disentangle the contribution of the DVCS $$^2$$ term in the photon electroproduction cross section from its interference with the Bethe-Heitler amplitude. This provides a stronger way to constrain the Generalized Parton Distributions of the nucleon. A wide range of kinematics accessible with an 11 GeV beam off an unpolarized proton target will be covered. The $$Q^2-$$ dependence of each contribution will be measured independently.

In the original PDF online version of this article, the references 22–26 were missing.These are the missing references.

The spin-structure functions $g_1$ and $g_2$, and the spin-dependent partial cross-section $\sigma_\mathrm{TT}$ have been extracted from the polarized cross-sections differences, $\Delta \sigma_{\parallel}\hspace{-0.06cm}\left(\nu,Q^{2}\right)$ and $\Delta \sigma_{\perp}\hspace{-0.06cm}\left(\nu,Q^{2}\right)$ measured for the $\vec{^\textrm{3}\textrm{He}}(\vec{\textrm{e}},\textrm{e}')\textrm{X}$ reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons with energies from 1.147 to 4.404 GeV were scattered at angles of 6$^{\circ}$ and 9$^{\circ}$ from a longitudinally or transversely polarized $^{3}$He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments $\overline{\Gamma_1}\hspace{-0.06cm}\left(Q^{2}\right)$, $\Gamma_2\hspace{-0.06cm}\left(Q^{2}\right)$ and $I_{\mathrm{TT}}\hspace{-0.06cm}\left(Q^{2}\right)$ are evaluated with high precision for the neutron in the $Q^2$ range from 0.035 to 0.24~GeV$^{2}$. The comparison of the data and the chiral effective field theory predictions reveals the importance of proper treatment of the $\Delta$ degree of freedom for spin observables., Comment: 7 pages, 5 figures, 3 tables. Version published in Phys. Lett. B

We report the first measurement of the (e,e^{'}p) three-body breakup reaction cross sections in helium-3 (^{3}He) and tritium (^{3}H) at large momentum transfer [⟨Q^{2}⟩≈1.9 (GeV/c)^{2}] and x_{B}>1 kinematics, where the cross section should be sensitive to quasielastic (QE) scattering from single nucleons. The data cover missing momenta 40≤p_{miss}≤500 MeV/c that, in the QE limit with no rescattering, equals the initial momentum of the probed nucleon. The measured cross sections are compared with state-of-the-art ab initio calculations. Overall good agreement, within ±20%, is observed between data and calculations for the full p_{miss} range for ^{3}H and for 100≤p_{miss}≤350 MeV/c for ^{3}He. Including the effects of rescattering of the outgoing nucleon improves agreement with the data at p_{miss}>250 MeV/c and suggests contributions from charge-exchange (SCX) rescattering. The isoscalar sum of ^{3}He plus ^{3}H, which is largely insensitive to SCX, is described by calculations to within the accuracy of the data over the entire p_{miss} range. This validates current models of the ground state of the three-nucleon system up to very high initial nucleon momenta of 500 MeV/c.

We report the measurements of the transverse ($P'x$) and longitudinal ($P'z$) components of the polarization transfer to a bound proton in carbon via the quasi-free $^{12}{\rm C}(\vec e,e'\vec p)$ reaction, over a wide range of missing momenta. We determine these polarization-transfers separately for protons knocked out from the $s$- and $p$-shells. The electron-beam polarization was measured to determine the individual components with systematic uncertainties which allow a detailed comparison with theoretical calculations.

Background: Generalized polarizabilities (GPs) are important observables to describe the nucleon structure, and measurements of these observables are still scarce. Purpose: This paper presents details of a virtual Compton scattering (VCS) experiment, performed at the A1 setup at the Mainz Microtron by studying the $e p \to e p \gamma$ reaction. The article focuses on selected aspects of the analysis. Method: The experiment extracted the $P_{LL} -P_{TT} / \epsilon$ and $P_{LT}$ structure functions, as well as the electric and magnetic GPs of the proton, at three new values of the four-momentum transfer squared $Q^2$: 0.10, 0.20 and 0.45 GeV$^2$. Results: We emphasize the importance of the calibration of experimental parameters. The behavior of the measured $e p \to e p \gamma$ cross section is presented and compared to the theory. A detailed investigation of the polarizability fits reveals part of their complexity, in connection with the higher-order terms of the low-energy expansion. Conclusions: The presented aspects are elements which contribute to minimize the systematic uncertainties and improve the precision of the physics results., Comment: 16 pages, 15 figures, Version 4, regular article to appear in Phys.Rev.C, more final version of some figures

Measurements of elastic electron scattering data within the past decade have highlighted two-photon exchange contributions as a necessary ingredient in theoretical calculations to precisely evaluate hydrogen elastic scattering cross sections. This correction can modify the cross section at the few percent level. In contrast, dispersive effects can cause significantly larger changes from the Born approximation. The purpose of this experiment is to extract the carbon-12 elastic cross section around the first diffraction minimum, where the Born term contributions to the cross section are small to maximize the sensitivity to dispersive effects. The analysis uses the LEDEX data from the high resolution Jefferson Lab Hall A spectrometers to extract the cross sections near the first diffraction minimum of $$^{12}$$ C at beam energies of 362 MeV and 685 MeV. The results are in very good agreement with previous world data, although with less precision. The average deviation from a static nuclear charge distribution expected from linear and quadratic fits indicate a 30.6% contribution of dispersive effects to the cross section at 1 GeV. The magnitude of the dispersive effects near the first diffraction minimum of $$^{12}$$ C has been confirmed to be large with a strong energy dependence and could account for a large fraction of the magnitude for the observed quenching of the longitudinal nuclear response. These effects could also be important for nuclei radii extracted from parity-violating asymmetries measured near a diffraction minimum.

Short Range Correlations (SRCs) have been identified as being responsible for the high momentum tail of the nucleon momentum distribution, n(k). Hard, short-range interactions of nucleon pairs generate the high momentum tail and imprint a universal character on n(k) for all nuclei at large momentum. Triple coincidence experiments have shown a strong dominance of np pairs, but these measurements involve large final state interactions. This paper presents the results from Jefferson Lab experiment E08014 which measured inclusive electron scattering cross-section from Ca isotopes. By comparing the inclusive cross section from 48Ca to 40Ca in a kinematic region dominated by SRCs we provide a new way to study the isospin structure of SRCs., Comment: 7 pages, 3 figures

In the K1.8 beam-line at Hadron Experimental Facility of J-PARC, a new magnetic spectrometer S-2S is being installed. S-2S was designed to achieve a high momentum resolution of Δp/p = 6 × 10−4 in FWHM. Several strangeness-physics programs which require the high resolution will be realized by S-2S. The present article introduces J-PARC E70 (missing-mass spectroscopy of Ξ12Be) and E94 (missing-mass spectroscopy of Λ7Li, Λ10B, and Λ12C) experiments.

We report the first measurement of the $(e,e'p)$ reaction cross-section ratios for Helium-3 ($^3$He), Tritium ($^3$H), and Deuterium ($d$). The measurement covered a missing momentum range of $40 \le p_{miss} \le 550$ MeV$/c$, at large momentum transfer ($\langle Q^2 \rangle \approx 1.9$ (GeV$/c$)$^2$) and $x_B>1$, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with plane-wave impulse approximation (PWIA) calculations using realistic spectral functions and momentum distributions. The measured and PWIA-calculated cross-section ratios for $^3$He$/d$ and $^3$H$/d$ extend to just above the typical nucleon Fermi-momentum ($k_F \approx 250$ MeV$/c$) and differ from each other by $\sim 20\%$, while for $^3$He/$^3$H they agree within the measurement accuracy of about 3\%. At momenta above $k_F$, the measured $^3$He/$^3$H ratios differ from the calculation by $20\% - 50\%$. Final state interaction (FSI) calculations using the generalized Eikonal Approximation indicate that FSI should change the $^3$He/$^3$H cross-section ratio for this measurement by less than 5\%. If these calculations are correct, then the differences at large missing momenta between the $^3$He/$^3$H experimental and calculated ratios could be due to the underlying $NN$ interaction, and thus could provide new constraints on the previously loosely-constrained short-distance parts of the $NN$ interaction., 8 pages, 3 figures (4 panels)

The E12-14-012 experiment performed at Jefferson Lab Hall A has collected inclusive electron-scattering data for different targets at the kinematics corresponding to beam energy 2.222 GeV and scattering angle 15.54 deg. Here we present a comprehensive analysis of the collected data and compare the double-differential cross sections for inclusive scattering of electrons, extracted using solid targets (aluminum, carbon, and titanium) and a closed argon-gas cell. The data extend over broad range of energy transfer, where quasielastic interaction, Delta-resonance excitation, and inelastic scattering yield contributions to the cross section. The double-differential cross sections are reported with high precision (~3%) for all targets over the covered kinematic range., 11 pages, 10 figures

The success of the ambitious programs of both long- and short-baseline neutrino-oscillation experiments employing liquid-argon time-projection chambers will greatly rely on the precision with which the weak response of the argon nucleus can be estimated. In the E12-14-012 experiment at Jefferson Lab Hall A, we studied the properties of the argon nucleus by scattering a high-quality electron beam off a high-pressure gaseous argon target. Here, we present the measured Ar40(e,e′) double differential cross section at incident electron energy E=2.222 GeV and scattering angle θ=15.54∘. The data cover a broad range of energy transfers, where quasielastic scattering and delta production are the dominant reaction mechanisms. The result for argon is compared to our previously reported cross sections for titanium and carbon, obtained in the same kinematical setup.

We investigate the formation of resonances in the P33 partial wave with the emphasis on possible emergence of dynamically generated quasi-bound states as a consequence of a strong $p$-wave pion attractive interaction in this partial wave, as well as their possible interaction with the genuine quark excited states. By using the Laurent-Pietarinen expansion we follow the evolution of the $S$-matrix poles in the complex energy plane as a function of the interaction strength. Already without introducing a genuine quark resonant state, two physically interesting resonances emerge with pole masses around 1200 MeV and 1400 MeV, with the dominant $\pi N$ and $\pi\Delta$ component, respectively. The added genuine resonant state in the $(1s)^3$ quark configuration mixes with the lower dynamically generated resonance forming the physical $\Delta(1232)$ resonance, and pushes the second dynamical resonance to around 1500 MeV, which allows it to be identified with the $\Delta(1600)$ resonance. Adding a second resonant state with one quark promoted to the $2s$ orbit generates another pole whose evolution remains well separated from the lower two poles. We calculate the helicity amplitudes at the pole and suggest that their $Q^2$ dependence could be a decisive test to discriminate between different models of the $\Delta(1600)$ resonance., Comment: 10 pages, 10 figures, to be published in Phys. Rev. C

A systematic study on the Λ ground state binding energy of hyperhydrogen H Λ 4 measured at the Mainz Microtron MAMI is presented. The energy was deduced from the spectroscopy of mono-energetic pions from the two-body decays of hyperfragments, which were produced and stopped in a 9Be target. First data, taken in the year 2012 with a high resolution magnetic spectrometer, demonstrated an almost one order of magnitude higher precision than emulsion data, while being limited by systematic uncertainties. In 2014 an extended measurement campaign was performed with improved control over systematic effects, increasing the yield of hypernuclei and confirming the observation with two independent spectrometers and two targets of different thicknesses. The analysis of these data is in agreement with the previously published value for the H Λ 4 binding energy as well as with a consistent re-analysis of the 2012 data. When compared to the He Λ 4 binding energy from emulsion data, a large charge symmetry breaking effect in the A = 4 hypernuclear system is confirmed.

International audience; We report on new p(e,e′p)π∘p(e,e′p)π∘ measurements at the Δ+(1232)Δ+(1232) resonance at the low momentum transfer region, where the mesonic cloud dynamics is predicted to be dominant and rapidly changing, offering a test bed for chiral effective field theory calculations. The new data explore the Q2Q2 dependence of the resonant quadrupole amplitudes and for the first time indicate that the Electric and the Coulomb quadrupole amplitudes converge as Q2→0Q2→0. The measurements of the Coulomb quadrupole amplitude have been extended to the lowest momentum transfer ever reached, and suggest that more than half of its magnitude is attributed to the mesonic cloud in this region. The new data disagree with predictions of constituent quark models and are in reasonable agreement with dynamical calculations that include pion cloud effects, chiral effective field theory and lattice calculations. The measurements indicate that improvement is required to the theoretical calculations and provide valuable input that will allow their refinements.

To probe CP violation in the leptonic sector using GeV energy neutrino beams in current and future experiments using argon detectors, precise models of the complex underlying neutrino and antineutrino interactions are needed. The E12-14-012 experiment at Jefferson Lab Hall A was designed to perform a combined analysis of inclusive and exclusive electron scatterings on both argon ($N = 22$) and titanium ($Z = 22$) nuclei using GeV energy electron beams. The measurement on titanium nucleus provides essential information to understand the neutrino scattering on argon, large contribution to which comes from scattering off neutrons. Here we report the first experimental study of electron-titanium scattering as double differential cross section at beam energy $E=2.222$ GeV and electron scattering angle $\theta = 15.541$ deg, measured over a broad range of energy transfer, spanning the kinematical regions in which quasielastic scattering and delta production are the dominant reaction mechanisms. The data provide valuable new information needed to develop accurate theoretical models of the electromagnetic and weak cross sections of these complex nuclei in the kinematic regime of interest to neutrino experiments.

Subsequent to the release of our original paper, we discovered in the context of preparing our technical supplement [1] for journal publication that a typographical error had existed in the text file that the analysis program used to construct the beam polarization "database" for both the original analysis, published in Ref. [2], and our final analysis. The electron-beam polarization P e and the analyzing power A y cancel exactly in the ratio R , which is proportional to the ratio P t / P l of the transferred polarization components. On the other hand, the extraction of the relative e dependence of P l / P Born l relies on knowledge of the beam polarization. As such, data taking was interrupted roughly every two days during the GEp - 2 ? experiment to perform invasive measurements of the beam polarization using the Hall C Moller polarimeter [3]. The run range affected by the typographical error was entirely contained within the data collected at Q 2 = 2.5 GeV 2 with a beam energy of E e = 3.680 GeV during January 2008. The data from this configuration were combined with the data collected at E e = 3.548 GeV due to the nearly complete overlap of these two settings in terms of Q 2 and e acceptance. It is worth remarking that this typographical error went unnoticed for so long because it only affected a small fraction of the data (less than half of the combined data for ? e ? = 0.790 ) and the difference between the actually assigned beam polarization and the polarization that should have been assigned was comparable in magnitude to the point-to-point systematic uncertainty of the measurement itself. As such, its effect did not show up in various diagnostic plots and statistical tests, such as the time stability of the extracted P l / P Born l ratio. The data for both E e = 3.548 and E e = 3.680 GeV were reprocessed using the corrected beam polarizations to determine the effect of the typographical error on the combined physics results at ? e ? = 0.790 . Because the value of P e cancels in the ratio R , changes in the assumed beam polarization can only affect the results for R via statistical fluctuations due to changes in the relative weighting of different run ranges in the unbinned maximum-likelihood estimators for R . These effects are negligible on the scale of both the statistical and the systematic uncertainties of the data. More noticeable changes are expected in the ratio P l / P Born l since the extracted value of P l is inversely proportional to the assumed value of P e . Table I shows the effect of the corrected beam polarization database on the polarization transfer observables for the combined data for the ? e ? = 0.790 setting, the only measurement affected by the typographical error. The analyzing power did not need to be recalibrated since it was determined using the ? e ? = 0.153 data, which were not affected by the typographical error. As expected, the change in the ratio R is negligible. The value of P Born l , which is computed event by event from the global fit described in the Appendix of the original paper and does not depend on P e , is also unchanged. The magnitudes of P t , P l , and P l / P Born l are reduced by a common multiplicative factor, reflecting the fact that the beam polarization had been underestimated for the run range affected by the typographical error. The most important result of the corrected analysis is that the ratio P l / P Born l has decreased by 0.0024 from 1.0167 to 1.0143, a change comparable in magnitude to the statistical uncertainty but small compared to the total and point-to-point systematic uncertainties. The P l / P Born l result for the original publication [2] would be reduced by the same multiplicative factor as the final result. The physics conclusions of both publications are not materially changed by this correction. (Table Presented). (Figure Presented).

Finite-difference methods for one-dimensional partial differential equations are introduced by first identifying the classes of equations upon which suitable discretizations are constructed. It is shown how parabolic equations and the corresponding boundary conditions are discretized such that a desired local order of error is achieved and that the discretization is consistent and yields a stable and convergent solution scheme. Convergence criteria are established for a variety of explicit and implicit difference schemes. Energy estimates and theorems on maxima are given as auxiliary tools that allow us to ascertain that the solutions are physically meaningful. Difference schemes for hyperbolic equations are introduced from the standpoint of the Courant–Friedrich–Lewy criterion, dispersion and dissipation. Various techniques for non-linear equations and equations of mixed type are given, including high-resolution schemes for equations that can be expressed in terms of conservation laws. The Problems include the (parabolic) diffusion and (hyperbolic) advection equation, Burgers equation, the shock-tube problem, Korteweg–de Vries equation, and the non-stationary linear and cubic Schrodinger equations.

We present new data probing short-range correlations (SRCs) in nuclei through the measurement of electron scattering off high-momentum nucleons in nuclei. The inclusive 4He/3He cross section ratio is observed to be both x and Q2 independent for 1.5 < x < 2, confirming the dominance of two- nucleon (2N) short-range correlations (SRCs). For x > 2, our data do not support a previous claim of three-nucleon (3N) correlation dominance. While contributions beyond those from stationary 2N- SRCs are observed, our data show that isolating 3N-SRCs is more complicated than for 2N-SRCs., 6 pages, 2 figures, new experimental results from JLab E08-014

The ability to reliably solve initial-value problems for ordinary differential equations is essential in order to understand the evolution of dynamical systems. In this chapter we deal with methods of advancing the given initial state of a system to later times, explaining clearly the role of stiffness, local discretization and round-off errors, and introducing the crucial concepts of consistency, convergence, and stability of difference schemes by which the differential equations are approximated. Single-step explicit and implicit methods are treated at length; automatic step-size control, embedding, and dense output are presented. Explicit and implicit multi-step (Adams, predictor–corrector, and backward differentiation) methods are analyzed from the viewpoint of stability and long-term integration. Runge–Kutta–Nystrom methods are introduced as a special means to solve conservative second-order equations. Geometric and Lie series integrators are discussed as most viable options for high-precision integration requiring the preservation of certain invariants. The Examples and Problems include the Lorentz system, synchronization of globally coupled oscillators, chaotic scattering in two dimensions, problems in chemical kinetics, and a variety of astrophysical problems involving planets, stars and galaxies.

The discrete Fourier transformation is one of the most important tools in the analysis of functions and signals, but its detailed numerical aspects are often disregarded or neglected. Fourier and sampling theorems, Parseval’s equality, and power spectral densities are introduced, and the concepts of signal uncertainty, aliasing, and leakage are discussed, along with the caveats due to different notations and nomenclatures. Transformations with orthogonal polynomials (Legendre and Chebyshev) are described, and their relation to quadrature formulas is explained. The numerical computation of the Laplace transformation and its inverse is introduced in the context of differential equations for transfer functions of physical systems. The continuous and discrete Hilbert transformations are discussed next, introducing the concept of the analytic signal, and their relation to the Kramers–Kronig dispersion relations is given. The last Section deals with the continuous wavelet transform. The Examples and Problems include the multiplication of polynomials by FFT, the Fourier analysis of realistic acoustic signals and the Doppler effect, and the analysis of brain potentials by the Hilbert transform.

The representation of spatial derivatives is at the heart of spectral methods for partial differential equations, so the three main kinds (Fourier, Chebyshev and Legendre) are analyzed at the outset, together with efficient means to compute them. Galerkin methods involving all three classes of basis functions are discussed for both stationary (Helmholtz equation) and non-stationary (advection equation) problems. Tau methods are also applicable to both types of problems and are presented next. Due to their straightforward implementation of boundary conditions, they offer an exciting alternative to Galerkin approaches. Separate Sections are devoted to collocation methods and efficient means to solve non-linear equations in the spectral framework. Useful hints for time integration and dealing with semi-infinite and infinite definition domains are given. The Examples and Problems include the Galerkin method for the advection, diffusion and Poisson equations (Poiseuille flow), the tau method for the Poisson equation, the diffusion equation in collocation approaches, and the Burgers equation.

When we evaluate the expression \({{\varvec{f}}} = A{{\varvec{u}}}\), where \({{\varvec{u}}}\) and \({{\varvec{f}}}\) are vectors and A is a matrix, we solve a direct or forward problem. Given A we can precisely calculate \({{\varvec{f}}}\) for any \({{\varvec{u}}}\). The only danger we may anticipate in a computer is the one of over- or underflow, or perhaps loss of precision. Solving a backward or inverse problem is a step in the opposite direction: we either wish to reconstruct \({{\varvec{u}}}\) from \({{\varvec{f}}}\), knowing A — this is the so-called inverse reconstruction problem — or learn something about A from given \({{\varvec{u}}}\) and \({{\varvec{f}}}\), which is known as the inverse identification problem because we are identifying the parameters of the underlying “model” — the presumed linear mapping embodied by the matrix A. In either case trouble is brewing: A may not be invertible, and even if it were, it may be ill-conditioned. The difficulties could be compounded by the data \({{\varvec{f}}}\) being noisy, or A depending on \({{\varvec{u}}}\), introducing nonlinearity.

Author(s): Puckett, AJR; Brash, EJ; Jones, MK; Luo, W; Meziane, M; Pentchev, L; Perdrisat, CF; Punjabi, V; Wesselmann, FR; Afanasev, A; Ahmidouch, A; Albayrak, I; Aniol, KA; Arrington, J; Asaturyan, A; Baghdasaryan, H; Benmokhtar, F; Bertozzi, W; Bimbot, L; Bosted, P; Boeglin, W; Butuceanu, C; Carter, P; Chernenko, S; Christy, ME; Commisso, M; Cornejo, JC; Covrig, S; Danagoulian, S; Daniel, A; Davidenko, A; Day, D; Dhamija, S; Dutta, D; Ent, R; Frullani, S; Fenker, H; Frlez, E; Garibaldi, F; Gaskell, D; Gilad, S; Gilman, R; Goncharenko, Y; Hafidi, K; Hamilton, D; Higinbotham, DW; Hinton, W; Horn, T; Hu, B; Huang, J; Huber, GM; Jensen, E; Keppel, C; Khandaker, M; King, P; Kirillov, D; Kohl, M; Kravtsov, V; Kumbartzki, G; Li, Y; Mamyan, V; Margaziotis, DJ; Marsh, A; Matulenko, Y; Maxwell, J; Mbianda, G; Meekins, D; Melnik, Y; Miller, J; Mkrtchyan, A; Mkrtchyan, H; Moffit, B; Moreno, O; Mulholland, J; Narayan, A; Nedev, S; Nuruzzaman; Piasetzky, E; Pierce, W; Piskunov, NM; Prok, Y; Ransome, RD; Razin, DS; Reimer, P; Reinhold, J | Abstract: Background: Interest in the behavior of nucleon electromagnetic form factors at large momentum transfers has steadily increased since the discovery, using polarization observables, of the rapid decrease of the ratio GEp/GMp of the proton's electric and magnetic form factors for momentum transfers Q21 GeV2, in strong disagreement with previous extractions of this ratio using the traditional Rosenbluth separation technique. Purpose: The GEp-III and GEp-2γ experiments were carried out in Jefferson Laboratory's (JLab's) Hall C from 2007 to 2008, to extend the knowledge of GEp/GMp to the highest practically achievable Q2 given the maximum beam energy of 6 GeV and to search for effects beyond the Born approximation in polarization transfer observables of elastic ∫ - p scattering. This article provides an expanded description of the common experimental apparatus and data analysis procedures, and reports the results of a final reanalysis of the data from both experiments, including the previously unpublished results of the full-acceptance dataset of the GEp-2γ experiment. Methods: Polarization transfer observables in elastic ∫ - p→∫ - scattering were measured at central Q2 values of 2.5, 5.2, 6.8, and 8.54 GeV2. At Q2=2.5GeV2, data were obtained for central values of the virtual photon polarization parameter ϵ of 0.149, 0.632, and 0.783. The Hall C High Momentum Spectrometer detected and measured the polarization of protons recoiling elastically from collisions of JLab's polarized electron beam with a liquid hydrogen target. A large-acceptance electromagnetic calorimeter detected the elastically scattered electrons in coincidence to suppress inelastic backgrounds. Results: The final GEp-III data are largely unchanged relative to the originally published results. The statistical uncertainties of the final GEp-2γ data are significantly reduced at ϵ=0.632 and 0.783 relative to the original publication. Conclusions: The final GEp-III results show that the decrease with Q2 of GEp/GMp continues to Q2=8.5GeV2, but at a slowing rate relative to the approximately linear decrease observed in earlier Hall A measurements. At Q2=8.5GeV2, GEp/GMp remains positive but is consistent with zero. At Q2=2.5GeV2, GEp/GMp derived from the polarization component ratio R-Pt/P shows no statistically significant ϵ dependence, as expected in the Born approximation. On the other hand, the ratio P""/P""Born of the longitudinal polarization transfer component to its Born value shows an enhancement of roughly 1.7% at ϵ=0.783 relative to ϵ=0.149, with ≈2.2σ significance based on the total uncertainty, implying a similar effect in the transverse component Pt that cancels in the ratio R.

We report the measurement of the beam-vector and tensor asymmetries A_{ed}^{V} and A_{d}^{T} in quasielastic (e[over →],e^{'}p) electrodisintegration of the deuteron at the MIT-Bates Linear Accelerator Center up to missing momentum of 500 MeV/c. Data were collected simultaneously over a momentum transfer range 0.1

Beam helicity asymmetries in the $\overrightarrow{e}p \rightarrow e' K^{+} \Lambda $ reaction have been measured at unprecedentedly low four-momentum transfers $\langle Q^{2} \rangle = 0.05$ (GeV/c)2. At the Mainz Microtron (MAMI), the experiment was performed with a longitudinally polarized beam and an out-of-plane detection of the scattered electron. This experiment probed the associated helicity-dependent structure function ${\rm d} \sigma_{LT'}/{\rm d} \Omega_K^{c.m.}$ , which is sensitive to the details of resonances of the proton. The results were compared to models for kaon electroproduction using effective Lagrangians. The MAMI data is not supporting the Kaon-Maid isobar model, which uses strong longitudinal couplings of the virtual photon to nucleon resonances and predicts a strong peaking of the structure function at forward angles and low $Q^{2}$ . The data is also in disagreement with a Regge-plus-resonance model that predicts the incorrect sign of the structure function. The combination of the MAMI results wih data taken at higher four-momentum transfers measured at Jefferson Lab indicates a smooth transition in $Q^{2}$ without significant changes of the interference pattern in the electroproduction process.

We report the first longitudinal-transverse separation of the deeply virtual exclusive π^{0} electroproduction cross section off the neutron and coherent deuteron. The corresponding four structure functions dσ_{L}/dt, dσ_{T}/dt, dσ_{LT}/dt, and dσ_{TT}/dt are extracted as a function of the momentum transfer to the recoil system at Q^{2}=1.75 GeV^{2} and x_{B}=0.36. The ed→edπ^{0} cross sections are found compatible with the small values expected from theoretical models. The en→enπ^{0} cross sections show a dominance from the response to transversely polarized photons, and are in good agreement with calculations based on the transversity generalized parton distributions of the nucleon. By combining these results with previous measurements of π^{0} electroproduction off the proton, we present a flavor decomposition of the u and d quark contributions to the cross section.

$[Background]$ Measurements of the neutron charge form factor, $G^n_E$, are challenging due to the fact that the neutron has no net charge. In addition, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting $G^n_E$ with different targets and techniques provides an important test of our handling of these effects. $[Purpose]$ The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of $1~(\rm{GeV/c})^2$. This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly. $[Method]$ The inclusive quasi-elastic reaction $^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ was measured at Jefferson Lab. The neutron electric form factor, $G_E^n$, was extracted at $Q^2 = 0.98~(\rm{GeV/c})^2$ from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This $Q^2$ is high enough that the sensitivity to $G_E^n$ is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production. $[Results]$ The neutron electric form factor, $G_E^n$, was determined to be $0.0414\pm0.0077\;{(stat)}\pm0.0022\;{(syst)}$; providing the first high precision inclusive extraction of the neutron's charge form factor. $[Conclusions]$ The use of the inclusive quasi-elastic $^3\overrightarrow{\rm{He}}(\overrightarrow{e},e')$ with a four-momentum transfer near $1~(\rm{GeV/c})^2$ has been used to provide a unique measurement of $G^n_E$. This new result provides a systematically independent validation of the exclusive extraction technique results., 7 pages, 2 figures, 2 tables

The unpolarized semi-inclusive deep-inelastic scattering (SIDIS) differential cross sections in He3(e,e′π±)X have been measured for the first time in Jefferson Lab experiment E06-010 with a 5.9GeVe− beam on a He3 gas target. The experiment focuses on the valence quark region, covering a kinematic range 0.12

The Jožef Stefan Institute (Institut “Jožef Stefan”) was founded by the Slovenian Academy of Sciences and Arts in 1949 as the Physics Institute for Nuclear Research. In 1952 it was renamed in honor of the Slovenian physicist Jožef Stefan (1835–1893)

Symmetry permeates nature and is fundamental to all laws of physics. One example is parity (mirror) symmetry, which implies that flipping left and right does not change the laws of physics. Laws for electromagnetism, gravity and the subatomic strong force respect parity symmetry, but the subatomic weak force does not. Historically, parity violation in electron scattering has been important in establishing (and now testing) the standard model of particle physics. One particular set of quantities accessible through measurements of parity-violating electron scattering are the effective weak couplings C2q, sensitive to the quarks' chirality preference when participating in the weak force, which have been measured directly only once in the past 40 years. Here we report a measurement of the parity-violating asymmetry in electron-quark scattering, which yields a determination of 2C2u - C2d (where u and d denote up and down quarks, respectively) with a precision increased by a factor of five relative to the earlier result. These results provide evidence with greater than 95 per cent confidence that the C2q couplings are non-zero, as predicted by the electroweak theory. They lead to constraints on new parity-violating interactions beyond the standard model, particularly those due to quark chirality. Whereas contemporary particle physics research is focused on high-energy colliders such as the Large Hadron Collider, our results provide specific chirality information on electroweak theory that is difficult to obtain at high energies. Our measurement is relatively free of ambiguity in its interpretation, and opens the door to even more precise measurements in the future.

In a recent set of measurements at Jefferson Laboratory, we have studied the missing-momentum dependence of beam-target asymmetries in exclusive \({\overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm p}){\rm pn}, \overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm p}){\rm d} }\), and \({\overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm d}){\rm p}}\) channels at a previously unattainable level of precision and unreached range in missing momenta. We have also measured single-spin asymmetries in the processes \({\overrightarrow{^3{{\rm He}}}({\vec{{\rm e}}},{\rm e}')}\) and \({\overrightarrow{^3{{\rm He}}}({{\rm \vec{e}}},{\rm e}'{\rm n})}\), where the nuclei were polarized vertically. Preliminary results are presented.

At the Mainz Microtron MAMI exploratory experiments on the spectroscopy of mesonic weak decays (MWD) of electroproduced Λ-hypernuclei were performed. A unique setup was realized to use the broad momentum-band kaon spectrometer Kaos at zero degree angle with respect to the high-intensity electron beam direction to tag strangeness producing processes. A sample of order 103 MWD from a beryllium target was collected by the coincidence technique with the high-resolution multi-spectrometer facility of the A1 Collaboration. It is conjectured that this sample contains monochromatic two-body decays from stopped hyperfragment decays as well as a wide momentum distribution of quasi-free produced Λ- and Σ-hyperon decays and three-body decays from hyperfragments. Stopped hyperfragments will be identified as monochromatic peaks in the π − momentum spectrum from which their masses can be extracted with a precision of 50 keV/c 2.

The Mainz Microtron MAMI provides a continuous-wave unpolarized or spin-polarized electron beam with energies up to 1.6 GeV and high degrees of polarization. Electro-production of strange mesons is performed in the multi-spectrometer facility with the Kaos spectrometer for kaon detection and a high-resolution spectrometer for electron detection in plane or out of plane. Differential cross section measurements of exclusive p ( e , e ′ K + ) Λ , Σ 0 reactions at low four-momentum transfers in the nucleonʼs third resonance region have been done, followed by a measurement of the beam helicity asymmetry for p ( e → , e ′ K + ) Λ . These studies are important for the understanding of the effective coupling of photons to the hadrons and their resonances and electromagnetic form factors entering different effective Lagrangian models for photo- and electro-production of strangeness. The polarized structure function, extracted from the beam helicity asymmetry, shows an especially high sensitivity to model parameters.

Delivering precisely the desired dose distribution to the patient during radiotherapy is of crucial importance for treatment success and monitoring the actual distributed dose opens the possibility to correct for deposition inaccuracies and thus achieve better conformance to the treatment plan. Positron emission tomography has already been successfully used to measure the residual radioactivity from (γ, n) reactions in the patient after the treatment with hadron therapy or high-energy gamma-ray radiotherapy (above ∼20 MV) [1], [2]. When trying to use a similar approach for gamma-rays of lower energies (most commonly 6 to 18 MV) the only source of positrons is prompt pair production in the beam, calling for measurements while the linac is operating and saturating the detector. The problems with saturation were alleviated to a formidable extent by using advanced digital processing techniques to measure energies of incident particles at rates beyond 10 Mcps per each scintillation crystal. The approach suggested by [3] builds on the discovery that there is a strong correlation between the delivered dose and the density of pair production. Our research confirmed the findings, but only as long as homogeneous objects were involved. In an inhomogeneous object, the annihilation density was no longer proportional to the dose, but rather to the density of deposited energy. This means that the intimate knowledge of the material density is required for proper reconstruction of the dose field image from the PET measurement. Additionally, one gets 2–4 mm thick regions at material boundaries where the charge particle equilibrium gets broken and the correlation no longer holds. This is, in principle, possible to account for based on ct data that is always available in such cases, but definitely calls for further work.

We report on the results of the E06-014 experiment performed at Jefferson Lab in Hall A, where a precision measurement of the twist-3 matrix element d_2 of the neutron (d^n_2) was conducted. The quantity dn_2 represents the average color Lorentz force a struck quark experiences in a deep inelastic electron scattering event off a neutron due to its interaction with the hadronizing remnants. This color force was determined from a linear combination of the third moments of the ^3He spin structure functions, g_1 and g_2, after nuclear corrections had been applied to these moments. The structure functions were obtained from a measurement of the unpolarized cross section and of double-spin asymmetries in the scattering of a longitudinally polarized electron beam from a transversely and a longitudinally polarized ^3He target. The measurement kinematics included two average Q^2 bins of 3.2 GeV^2 and 4.3 GeV^2, and Bjorken-x 0.25≤ x ≤0.90 covering the deep inelastic and resonance regions. We have found that d^n_2 is small and negative for ⟨Q^2⟩=3.2 GeV^2, and even smaller for ⟨Q^2⟩=4.3 GeV^2, consistent with the results of a lattice QCD calculation. The twist-4 matrix element f^n_2 was extracted by combining our measured d^n_2 with the world data on the first moment in x of g^n_1, Γ^n_1. We found f^n_2 to be roughly an order of magnitude larger than dn2. Utilizing the extracted d^n_2 and f^n_2 data, we separated the Lorentz color force into its electric and magnetic components, F^(y,n)_E and F^(y,n)_B, and found them to be equal and opposite in magnitude, in agreement with the predictions from an instanton model but not with those from QCD sum rules. Furthermore, using the measured double-spin asymmetries, we have extracted the virtual photon-nucleon asymmetry on the neutron A^n_1, the structure function ratio g^n_1/F^n_1, and the quark ratios (Δu+Δu)/(u+u) and (Δd+Δd)/(d+d). These results were found to be consistent with deep-inelastic scattering world data and with the prediction of the constituent quark model but at odds with the perturbative quantum chromodynamics predictions at large x.

We present deeply virtual $\pi^0$ electroproduction cross-section measurements at $x_B$=0.36 and three different $Q^2$--values ranging from 1.5 to 2 GeV$^2$, obtained from experiment E07-007 that ran in the Hall A at Jefferson Lab. The Rosenbluth technique was used to separate the longitudinal and transverse responses. Results demonstrate that the cross section is dominated by its transverse component, and thus is far from the asymptotic limit predicted by perturbative Quantum Chromodynamics. An indication of a non-zero longitudinal contribution is provided by the interference term $\sigma_{LT}$ also measured. Results are compared with several models based on the leading twist approach of Generalized Parton Distributions (GPDs). In particular, a fair agreement is obtained with models where the scattering amplitude is described by a convolution of chiral-odd (transversity) GPDs of the nucleon with the twist-3 pion distribution amplitude. Therefore, neutral pion electroproduction may offer the exciting possibility of accessing transversity GPDs through experiment., Comment: Submitted to Physical Review Letters

The Monte–Carlo method is introduced as a generic tool for the solution of mathematical physics models by means of computer simulation. These problems range from simple one-dimensional integration to sophisticated multi-dimensional models involving elaborate geometries and complex system states. A historical introduction and an exposition of the basic idea are followed by a basic treatment of numerical integration and discussing methods of variance reduction like importance sampling and use of quasi-random sequences. Markov-chain Monte Carlo is presented as a powerful method to generate random numbers according to arbitrary, even extremely complicated distributions. A specific implementation in the form of the Metropolis–Hastings algorithm is offered.