Parity-violating M?ller scattering

The A4 collaboration at the MAMI accelerator at Mainz investigates the contribution of strange quarks to the form factors of the nucleon by measuring the parity violating asymmetry A _PV in the cross section of elastic scattering of longitudinally polarized electrons off hydrogen and deuterium. Recently, measurements at backward angles at a four momentum transfer of Q ²?=?0.22 GeV² were completed. Together with previous results at forward angles at the same momentum transfer, the strange electric and magnetic form factors $G_E^s$ and $G_M^s$ can be disentangled.     

Nucleon and {\Delta} Elastic and Transition Form Factors

We present a unified study of nucleon and \({\Delta}\) elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector \({\otimes}\) vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: \({G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}\) possesses a zero at Q ² = 9.5 GeV²; any change in the interaction which shifts a zero in the proton ratio to larger Q ² relocates a zero in \({G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}\) to smaller Q ²; there is likely a value of momentum transfer above which \({G_{E}^{n} > G_{E}^{p}}\) ; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the \({\Delta(1232)}\) -baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the \({\Delta(1232)}\) Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the \({N \to \Delta}\) transition, the momentum-dependence of the magnetic transition form factor, \({G_{M}^{*}}\) , matches that of \({G_{M}^{n}}\) once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.     

On the polarization of the final nucleon in NC elastic \nu _\mu (\bar \nu _\mu )-N scattering

New short baseline neutrino experiments open new possibilities of high precision study of different neutrino processes. We present here results of the calculation of the polarization of final nucleon in elastic NC $\nu _\mu (\bar \nu _\mu )$ -nucleon scattering. In a numerical analysis the sensitivity to the different choices of the axial and axial strange form factors is examined. Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. From measurement of the nucleon polarization in the NC elastic scattering a new additional information about the axial G _A (Q ²) and the strange axial G ^s _A (Q ²) form factors of the nucleon could be inferred.     

Extreme \alpha -clustering in the 18O nucleus

The structure of the ¹⁸O nucleus at excitation energies above the $ \alpha$ decay threshold was studied using ¹⁴C + $ \alpha$ resonance elastic scattering. A number of states with large $ \alpha$ reduced widths have been observed, indicating that the $ \alpha$ -cluster degree of freedom plays an important role in this N $ \ne$ Z nucleus. A 0⁺ state with an $ \alpha$ reduced width exceeding the single-particle limit was identified at an excitation energy of 9.9±0.3 MeV. We discuss evidence that states of this kind are common in light nuclei and give possible explanations of this feature.     

Quasi-elastic electroproduction of charged \rho -mesons on nucleons

The electroproduction of charged $ \rho$ -mesons on the nucleon at intermediate energy is discussed for quasi-elastic kinematics. It is shown that at these kinematics both the longitudinal $ \sigma_{{L}}^{}$ and transverse $ \sigma_{{T}}^{}$ cross-sections are dominated by the $ \rho$ -meson t -pole contribution, and thus the corresponding dσ _L(T)/dt data can give a valuable information on the $ \rho$ -meson component of the nucleon cloud. The differential cross-sections for the reaction p(e, e ^′ $ \rho^{+}_{}$ )n at Q ² = 2 , 3.5GeV^2 and at the invariant mass W = 3 and 4GeV are calculated on the basis of quasi-elastic knockout mechanism with form factors. Questions about the gauge invariance of the electroproduction amplitude are considered and it is noted an important difference between photo- and electroproduction amplitudes.     

Qweak, N → Δ, and physics beyond the standard model

The data-taking phase of the Qweak experiment ended in May of 2012 at the Thomas Jefferson National Accelerator Facility. Qweak aims to measure the weak charge of the proton, Q _W ^p , via parity-violating elastic electron-proton scattering. The expected value of Q _W ^p is fortuitously suppressed, which leads to an increased sensitivity to physics beyond the Standard Model.     

The energy dependence of the hard exclusive diffractive processes in pQCD as the function of momentum transfer

We predict the dependence on energy of photo (electro) production processes: γ(γ ^*)+p→V+X with large rapidity gap at small x and large momentum ?t transferred to V in pQCD. Here V is a heavy quarkonium (J/ψ,?) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer t, photon virtuality Q ² and/or quarkonium mass. In the kinematical region $Q_{0}^{2}\le -t\ll Q^{2}+M^{2}_{V}$ the nontrivial energy dependence of the cross section for the vector meson production due to the photon scattering off a parton follows within QCD from the summing of the double logarithmic terms. In the second regime $-t\ge Q^{2}+M^{2}_{V}$ within DGLAP approximation in all orders of perturbation theory the $q\bar{q}$ -parton elastic cross section is energy independent. We show that the correct account of the double logarithmic terms and of the gluon radiation including kinematical constraints removes the disagreement between pQCD calculations and recent HERA experimental data. The explicit formula for the dependence of the differential cross section $\frac{d^{2}\sigma}{dt\,dx_{J}}$ of these processes on $s_{\gamma^{*}N}$ is obtained. We show that perturbative Pomeron type behavior may reveal itself only at energies significantly larger than those available at HERA. In addition we evaluate the energy dependence of DVCS processes.     

On the physical meaning of Sachs form factors and on the violation of the dipole dependence of G E and G M on Q 2

The questions of how a dipole character of the dependence of the form factors G _E and G _M on the square of the momentum transfer to a proton, Q ², arise and why a violation of this dependence occurs, which was first observed in a JLab polarization experiment, are investigated. The answers to these questions could be obtained owing to the use of the simplest QCD concepts of the proton structure and the results obtained by calculating the matrix elements of the proton current in the case of non-spin-flip and spin-flip transitions for protons in the diagonal spin basis (DSB), where the Little Lorentz group common to the initial and final proton states is realized. In DSB, the form factors G _E and G _M are determined by the matrix elements J _p ^??,?? and J _p ^???,?? of the proton current in the cases of non-spin-flip and spin-flip transitions for protons. In an arbitrary reference frame, the relations between these matrix elements and the form factors are J _p ^??,?? ?? G _E and J _p ^???,?? $\sqrt \tau G_M$ , where ?? = Q ²/4m ², with m being the proton mass. In considering the problem in question at the quark level, use is made of the model where the proton consists of three pointlike quarks having identical masses and where the respective matrix element of the proton current is the product of three quark-current amplitudes having the form J _p ^??,?? ?? 1 and J _p ^???,?? ?? $\sqrt \tau$ . It is shown that the aforementioned dipole dependence arises if the proton spin flip is due to spin flip for only one of the three quarks. As to violations of this dependence, they are caused by the contributions to J _p ^??,?? from spin-flip transitions for two quarks or by the contribution to J _p ^???,?? from spin-flip transitions for all three quarks constituting the proton.     

Test of 600 and 750 MeV NN matrix on elastic scattering Glauber model calculations

The 600 and 750 MeV proton nucleus elastic scattering cross section and polarization calculations have been performed in the framework of the Glauber model to test the pp and pn scattering amplitudes deduced from a phase shift analysis by Bystricky, Lechanoine and Lehar. It is well known that up to now we do not possess a non-phenomenological NN scattering matrix at intermediate energies. However proton-nucleus scattering analyses are used to extract information about short range correlations¹), Δ resonance²) or pion condensation presences)... etc. Most scattering calculations made at these energies have been done with phenomenological NN amplitudes having a gaussian q-dependence $$A(q) = \frac{{k\sigma }}{{4\pi }}(\alpha + i) e^{ - \beta ^2 q^2 /2} $$ and $$C(q) = \frac{{k\sigma }}{{4\pi }}iq(\alpha + i) D_e - \beta ^2 q^2 /2$$ K andσ being respectively the projectile momentum and the total pN total cross section. The parameters α, β and D are badly known and are adjusted by fitting some specific reactions as p+⁴He elastic scattering⁴). Even when these amplitudes provide good fits to the data, our understanding of the dynamics of the scattering remains obscure.     

The Qweak: Precision Measurement of the Proton’s Weak Charge by Parity Violating Experiment

The Qweak experiment at the Thomas Jefferson National Accelerator Facility measures the parity violating asymmetry in longitudinally polarized electron scattering from the proton at very low momentum transfer, Q ² = 0.026 (GeV/c)², at an incident electron beam energy of 1.16 GeV. With this measurement and the earlier results of the parity violating elastic scattering experiments, the Qweak experiment determines the weak charge of the proton, ${Q^p_{\rm W}}$ , with a 4% combined statistical and systematic error. This measurement will be used to determine the weak mixing angle, ${\sin^2\theta_{\rm W}}$ , that is predicted by the Standard Model from the Z ⁰ pole down to lower energies. Qweak will determine ${\sin^2\theta_{\rm W}}$ to a 0.3% relative precision, providing a competitive measurement of the running of this quantity. Moreover, if there is a significant deviation of the weak mixing angle from the Standard Model prediction, then the Qweak experiment will give a glimpse of possible extensions of the Standard Model.     

Color-conductivity in nuclei and the EMC-effect

We advocate that gluons and quarks of sufficiently short wavelengths are delocalized in nuclei. This hypothesis leads us to structure functions measured in μ-nucleus scattering, which depend at fixedx only on the ratio of the resolving power 1/Q and the radius of the nucleusR _A, whereA denotes the mass number of the nucleus. Thus we suggest that the structure functionF ₂(x, Q ²,A) per nucleon of an isoscalar nucleusA scales essentially as \(F_2 (x,Q^2 ,A) = \tilde F_2 (x,R_A^2 \cdot Q^2 )\) with a universal function \(\tilde F_2\) . The ratio of the so obtained structure functions of iron to deuterium agrees rather well with the one measured recently by the European Muon Collaboration. This observation implies that nuclei are “color-insulators” at lowQ ², but “color conductors” at largeQ ².     

Spin-alignment and g-factor measurement of the I^{\pi} = 12+ isomer in 192Pb produced in the relativistic-energy fragmentation of a 238U beam

Reactions of a 16.8 MeV ⁶He beam with a ⁹Be target have been investigated using highly segmented detector setup covering a large solid angle. Data on elastic and quasi-free scattering, as well as two-neutron transfer, are reported. The results for elastic scattering are fairly well reproduced by a CDCC calculation, in agreement with the interpretation of a breakup effect already observed for the scattering of ⁶He on other light targets. Exotic quasi-free scattering of ⁶He on $ \alpha$ -cluster in ⁹Be is clearly observed. Inclusive and coincident events were used to extract information on the two-neutron transfer reaction ⁹Be(⁶He, $ \alpha$ )¹¹Be . Sequential decay of the ¹¹Be state at the excitation energy $\ensuremath E_x = 10.6$ MeV through different channels is discussed.     

Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .     

The isosinglet and isovector ππ scattering lengths

The ππ scattering lengthsa ₀ ⁰ ,a ₂ ⁰ anda ₁ ¹ are determined from πN elastic scattering data using interior dispersion relations. The importance of the Born-Term contribution, via unitarity, to the imaginary part of all amplitudes is discussed. Proper consideration of these contributions and the analytic properties of the amplitudes near threshold allows us to obtain from the recent πN partial wave analysis of Pietarinen the following scattering lengths $$\begin{gathered} \mu a_0^0 = 0.27 \pm 0.03,\mu ^3 a_1^1 = 0.032 \pm 0.005, \hfill \\ \mu ^5 a_2^0 = 0.002 \pm 0.001. \hfill \\ \end{gathered} $$      

Mixing of intermediate bosons with Q\bar Q bound states

We discuss the effects of a close degeneracy between theZ ⁰ and vectorQ \(\bar Q\) bound states; large mixing effects can appear modifying mainly theQ \(\bar Q\) states (widths and couplings) and leading to curious structures inside theZ peak.     

Invariant-mass distributions for the pp \rightarrow pp \eta reaction at Q = 10 MeV

Proton-proton and proton- $ \eta$ invariant-mass distributions and the total cross-section for the pp $ \rightarrow$ pp $ \eta$ reaction have been determined near the threshold at an excess energy of Q = 10 MeV. The experiment has been conducted using the COSY-11 detector setup and the cooler synchrotron COSY. The determined invariant-mass spectra reveal significant enhancements in the region of low proton-proton relative momenta, similarly as observed previously at higher excess energies of Q = 15.5 MeV and Q = 40 MeV.     

MC-Simulation of the Transverse Double Spin Asymmetry for RHIC

We give a leading order estimate of the hadronic transverse double spin asymmetry in the Drell-Yan process at RHIC using Sphinx tt,anew polarized version ofthe Monte Carlo Pythia 5.6. We also calculate the statistical error to next to leading order with Pythia 5.7. Both quantities are of the same order if one assumes that the transversity weighted parton distributions equal the helicity weighted ones at some low perturbative scale Q ₀ ² .     

Largep cT cross-section differences as tests of quark-gluon scattering

It is shown that certain cross-section differences, such as \(d\sigma (p\bar p \to CX) - d\sigma (p\bar p \to \bar CX)\) or \(d\sigma (pp \to CX) - d\sigma (pp \to \bar CX)\) provide a more direct and stringent test of the QCD partonic picture than do the individual cross-sections. In particular they are very sensitive to quark-gluon scattering and to the three-gluon vertex. They also provide a severe test of the evolution of the distribution functions into a new régime ofQ ². We carry out detailed numerical studies for π andK production, at ISR and collider energies. We find very good agreement with the recent ISR data onpp→π^± x. The cross-section differences for \(p\bar p\) collisions are predicted to be also large and measurable with significant accuracy.     

\mathfrak{Q}-, \mathfrak{P}-, and Weyl-ordering of Squeezing Operators: New Operator Identities and Applications

The basic operator ordering regarding to coordinate-momentum operator is discussed by virtue of the technique of integration within $\mathfrak{Q}$ -ordering (all Q are on the left of all P) and $\mathfrak{P}$ -ordering (all P are on the left of all Q). We derive new operator-ordering identities about $\mathfrak{Q}$ -ordering , $\mathfrak{P}$ -ordering and Weyl-ordering of both single-mode and two-mode squeezing operators. Its application in combinatorics is pointed out.     

Faddeev Treatment of the Quasi-Bound and Scattering States in the {\bar{K}NN - \pi\Sigma N} System: New Results

A chiral-motivated \({\bar{K}N - \pi\Sigma - \pi\Lambda}\) potential was constructed and used in Faddeev calculations of different characteristics of \({\bar{K}NN - \pi\Sigma N}\) system. First of all, binding energy and width of the K ^? pp quasi-bound state were newly obtained. The low-energy K ^? d scattering amplitudes, including scattering length, together with the 1s level shift and width of kaonic deuterium were calculated. Comparison with the results obtained with the phenomenological \({\bar{K}N - \pi\Sigma}\) potential demonstrates that the chiral-motivated potential gives more shallow K ^? pp state, while the characteristics of K ^? d system are less sensitive to the form of \({\bar{K}N}\) interaction.