Unpolarized Differential Cross Section Research Articles

Polarization phenomena in the reaction e++e−→N+N¯+π0 in the framework of the nonresonant mechanism

The dependence of the nucleon polarization in the reaction ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}N+\overline{N}+{\ensuremath{\pi}}^{0}$ over different invariant variables is derived for the nonresonant mechanism. The nucleon polarization is expressed in terms of six invariant complex amplitudes, assuming the conservation of the hadron electromagnetic currents and the P invariance of the hadron electromagnetic interaction. An inclusive experimental setup when the proton (or the antiproton) and the pion are detected in coincidence is considered. Numerical estimations are performed for the so-called normal polarization in the energy range from threshold up to $s=16\text{ }\text{ }{\mathrm{GeV}}^{2}$, using selected parametrizations of the nucleon electromagnetic form factors in frame of a formalism derived in a previous work for the calculation of the unpolarized differential cross section.

Inclusive and semi-inclusive production of spin- 3/2 hadrons in e+e− annihilation

We investigate the inclusive and semi-inclusive productions of spin-3/2 hadrons, such as $\Omega$, in unpolarized $e^+ e^-$ annihilation. The general differential cross sections are expressed in terms of structure functions in accordance to the polarization of the hadron and the azimuthal modulations. We derive a complete definition of quark transverse momentum dependent (TMD) fragmentation functions (FFs) to spin-3/2 hadrons for the first time from the decomposition of the quark-quark correlation matrix at leading twist, 14 of which are newly defined corresponding to rank-3 tensor polarized hadron. The collinear FFs are obtained from the $k_T$-integrated correlation matrix, and only two TMD FFs with rank-3 tensor polarization have nonvanishing collinear counterparts. Then we perform a leading order calculation of the unpolarized differential cross sections. In the single-hadron inclusive production, only two structure functions are found nonzero and none of the rank-3 tensor polarized FFs contributes. For the nearly back-to-back two-hadron production, half of the 48 structure functions are found nonzero even if the spin of the second hadron is not analyzed, and ten of the rank-3 tensor polarized TMD FFs contribute. Therefore, one can study the rank-3 tensor polarized FFs via the production of a spin-3/2 hadron and an unpolarized hadron in unpolarized $e^+ e^-$ collision experiments. These newly defined FFs can be further applied in semi-inclusive deep inelastic scattering processes for the study of nucleon structures.

Two-photon-exchange effects in ep→enπ+ and their corrections to separated cross sections σL,T,LT,TT at small −t

In this work, the two-photon-exchange (TPE) effects in $ep\rightarrow en\pi^+$ at small $-t$ are discussed within a hadronic model. Under the pion dominance approximation the TPE contribution to the amplitude can be described by a scalar function in the limit $m_e\rightarrow 0$. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated when only the elastic intermediate state is considered. We find that the TPE corrections to the unpolarized differential cross section are about from $-4\%$ to $-20\%$ at $Q^2=1$--$ 1.6$ GeV$^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$. We find that the TPE corrections (at $Q^2=1$--$1.6$ GeV$^2$) to $\sigma_{\textrm{L}}$ are about from $-10\%$ to $-30\%$, to $\sigma_{\textrm{T}}$ are about $20\%$, and to $\sigma_{\textrm{LT,TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $ep\rightarrow en\pi^+$ at small $-t$ are important to extract the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$ and the electromagnetic magnetic form factor of $\pi^+$ in the experimental analysis.

Coherent π0-Photoproduction on the Deuteron near Threshold and the Role of D-Wave Component of the Deuteron Wave Function

Near-threshold coherent photoproduction of π0-meson on the deuteron is investigated. Numerical results for the unpolarized differential and total cross sections, the linear photon Σ-asymmetry, the vector T11 and tensor T2M (M = 0, 1, 2) deuteron spin asymmetries, and the spin asymmetry $$\tilde{T}_{20}$$ of the total cross section are presented. The role of D-wave component of the deuteron wave function on these physical observables is studied. The calculations are based on the impulse approximation in which we use the realistic and high-precision Bonn NN potential (full model) for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary γN → πN amplitude that describes well the threshold region. We have found that the D-wave component has a negligible effect on the unpolarized cross sections and the vector deuteron T11-asymmetry at photon lab-energies close to threshold. On the contrary, we have obtained a significant role of the D-wave part of the deuteron wave function on the Σ, T2M, and $$\tilde{T}_{20}$$ spin asymmetries. The results for the unpolarized differential cross section are compared to the experimental data from TAPS and a satisfactory agreement within the uncertainties has been obtained at forward pion angles. At backward pion angles, our results underestimate the experimental data and a disagreement has been found.

Near-threshold incoherent pion photoproduction on the deuteron with final-state interaction effects

Incoherent pion photoproduction on the deuteron γd→πNN is investigated in the energy region Eγthr≤Eγ≤ 160 MeV. The model applied contains the amplitudes of the impulse approximation as well as the NN and πN rescattering in the final state. For the elementary γN→πN amplitude, the unitary isobar MAID-2007 model is used. This model is parameterized in terms of invariant amplitudes and allows one to give a more reliable description of the threshold region. The half-off-shell NN and πN scattering amplitudes are obtained from separable representations of realistic NN and πN interactions, respectively. For the first time, numerical results for the linear photon asymmetry Σ, vector T11 and tensor T2M (M=0,1,2) deuteron spin asymmetries for the reactions γd→π−pp, γd→π+nn, and γd→π0np are presented. In addition, results for the unpolarized differential and total cross sections are given. We found that the influence of NN rescattering is moderate in both charged-and neutral-pion production channels, whereas πN rescattering is almost negligible in the charged-pion production channels which is not the case in neutral-pion production since a noticeable contribution is obtained. The calculated results for unpolarized differential and total cross sections are compared with the available experimental data and other theoretical models, and a satisfactory agreement is obtained.

General analysis of polarization effects in coherent pseudoscalar photo- and electroproduction of mesons on the deuteron

General expressions for the unpolarized differential cross section and for various polarization observables in the coherent pseudoscalar meson photo- and electroproduction on the deuteron target have been obtained in one-photon-exchange approximation. The spin structure of the matrix element is explicitly derived in terms of structure functions. The correspondence with the helicity amplitudes is given. The polarization effects have been investigated for the case of a longitudinally polarized electron beam and vector or tensor polarized deuteron target. The polarization (vector or tensor) of the scattered deuteron for the case of unpolarized or a longitudinally polarized electron beam is also considered. In the case of the photoproduction reaction, we consider linearly, circularly or elliptically polarized photon beam. Numerical estimations have been done for the unpolarized differential cross section and for some polarization observables.

Polarimetry for a storage-ring electric-dipole-moment measurement

These proceedings summarize the progress which has been made within the Jülich Electric Dipole Moment Investigations (JEDI) Collaboration on deuteron beam polarimetry for a storage-ring electric-dipole-moment (EDM) measurement. The design of a dedicated EDM polarimeter requires a precise database for optimization purposes. To address this need, a measurement of a deuteron-carbon scattering database has been performed with the forward part of the WASA-at-COSY detector. Preliminary results for vector analyzing powers and unpolarized differential cross sections for different deuteron beam energies are presented.

Measurement of the proton scalar polarizabilities at MAMI

The electric (αE1) and magnetic (βM1) scalar polarizabilities describe the response of the nucleon to an applied electric or magnetic field. They are not only fundamental properties related to the internal structure and dynamics of the nucleon, but they are important also in other areas of physics, such as atomic structure. The values of αE1 and βM1 quoted by the Particle Data Group were determined using data on the unpolarized differential cross-section of the Compton scattering $\gamma p \to \gamma p$. The measurement of the beam asymmetry Σ3, provides an alternative approach to the extraction of the scalar polarizabilities, with different sensitivity and systematics compared to the unpolarized crosssection. This asymmetry was measured recently for the first time below the pion photoproduction threshold by the A2 Collaboration with the Crystal Ball/TAPS experiment at MAMI (Mainz, Germany). A new high precision measurement of both a unpolarized cross-section and beam asymmetry Σ3a is ongoing at MAMI and the polarizabilities αE1 and βM1 will be extracted with unprecedented precision.

Sivers effect in inelastic J/ψ photoproduction in ep↑ collision in color octet model

The prediction of single-spin asymmetry in inelastic photoproduction of $J/\psi$ in $ep^\uparrow$ collision is presented. At next-to-leading order, the dominating process is photon-gluon fusion, $\gamma+g\rightarrow J/\psi+g$ for the production of $J/\psi$ in $e+p^\uparrow\rightarrow J/\psi+X$, which directly probes the gluon Sivers function. Using the non-relativistic QCD based color octet model, the color octet states $\leftidx{^{3}}{S}{_1}^{(8)}$, $\leftidx{^{1}}{S}{_0}^{(8)}$ and $\leftidx{^{3}}{P}{_{J(0,1,2)}}^{(8)}$ contribution to $J/\psi$ production is calculated. Sizable asymmetry is estimated as a function of transverse momentum $P_T$ and energy fraction $z$ of $J/\psi$ in the range $0<P_T\leq 1$ GeV and $0.3<z\leq 0.9$. The unpolarized differential cross section of inelastic $J/\psi$ photoproduction is found to be in good agreement with H1 and ZEUS data.

A Perturbative QCD Approach to varvec{pi ^{-}~p rightarrow D^{-}~{varLambda }_{c}^{+}}

We employ the generalized parton picture to analyze the reaction pi ^{-}~p rightarrow D^{-}~{varLambda }_{c}^{+}. Thereby it is assumed that the process amplitude factorizes into one for the perturbatively calculable subprocess bar{u} urightarrow bar{c} c and hadronic matrix elements that can be parameterized in terms of generalized parton distributions for the pi ^-rightarrow D^- and prightarrow {varLambda }_c^+ transitions, respectively. Representing these parton distributions in terms of valence-quark light-cone wave functions for pi , D, p and {varLambda }_c allows us to make numerical predictions for unpolarized differential and integrated cross sections as well as spin observables. In the kinematical region where this approach is supposed to work, i.e. sgtrsim 20 GeV^2 and in the forward hemisphere, the resulting cross sections are of the order of nb. This is a finding that could be of interest in view of plans to measure pi ^{-}~p rightarrow D^{-}~{varLambda }_{c}^{+}, e.g., at J-PARC or COMPASS.

Influence of the Choice of NN Potential Model on γd → π0d Observables near η-Threshold

Influence of the choice of the NN potential model governing the deuteron wave function on the observables for coherent π0-photoproduction on the deuteron near η-threshold is investigated by using a three-body model for the intermediate ηNN system with separable two-body interactions. Results for unpolarized differential cross section and polarization observables are predicted. It is revealed that the choice of the NN potential model has a visible effect on the differential cross section and most of the polarization observables, especially in the photon energy range of 600–800 MeV and extreme backward pion angles. We find that the deviation among results obtained by using different deuteron wave functions is quite large. The use of the CD-Bonn NN potential for deuteron wave function doubles the differential cross section in this kinematic region. Compared with the experimental data from CLAS collaboration for differential cross section, sizeable discrepancies are found.

New fit to the reactionγp→K+Σ0

The reaction $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{0}$ has been investigated using a tree-level effective Lagrangian model similar to that employed previously by the author to study the electromagnetic production of $\mathrm{\ensuremath{\Lambda}}$'s from protons. In addition to the Born terms, the model incorporates a number of baryon resonances with spins up to $\frac{5}{2}$ and the two kaon resonances, ${K}^{\ensuremath{\star}}(892)$ and $K1(1270)$. Momentum- and energy-dependent widths for the nucleon and $\mathrm{\ensuremath{\Delta}}$ resonances are included by means of a dynamical model that makes use of empirical on-shell branching ratios. The model parameters, consisting of products of the coupling strengths at the electromagnetic and strong interaction vertices in the resonance contributions, are fit to a large pool of photoproduction data from the CLAS and GRAAL Collaborations. Results are presented for the unpolarized differential cross section, the photon beam asymmetry $\mathrm{\ensuremath{\Sigma}}$, the hyperon recoil asymmetry $P$, and the double-polarization observables ${C}_{x}$ and ${C}_{z}$ in a variety of kinematical situations and compared with the data.

π−p→D−Λc+within the generalized parton picture

We investigate the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ within the generalized parton picture. The process is described by a handbag-type mechanism with the charm-quark mass acting as the hard scale. As in the case of preceding work on $\overline{p}p\ensuremath{\rightarrow}{\overline{\mathrm{\ensuremath{\Lambda}}}}_{c}^{\ensuremath{-}}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ we assume that the process amplitude factorizes into one for the perturbatively calculable partonic subprocess $\overline{u}u\ensuremath{\rightarrow}\overline{c}c$ and hadronic matrix elements that can be parametrized in terms of generalized parton distributions. Modeling the generalized parton distributions by overlaps of (valence-quark) light-cone wave functions for the hadrons involved, we obtain numerical results for unpolarized differential and integrated cross sections as well as spin observables. Our approach works well above the production threshold ($s\ensuremath{\gtrsim}20\text{ }\text{ }{\mathrm{GeV}}^{2}$) in the forward hemisphere and predicts unpolarized cross sections of the order of nb, a finding that could be of interest in view of plans to measure ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{D}^{\ensuremath{-}}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$ at J-PARC.

Polarization observables in lepton-deuteron elastic scattering including the lepton mass

Expressions for the unpolarized differential cross section and for various polarization observables in the lepton-deuteron elastic scattering, $\ell+D\to \ell+D$, $\ell=e$, $\mu$, $\tau$, have been obtained in one-photon-exchange approximation, taking into account the lepton mass. Polarization effects have been investigated for the case of a polarized lepton beam and polarized deuteron target which can have vector or tensor polarization. Numerical estimations of the lepton mass effects have been done for the unpolarized differential cross section and for some polarization observables and applied to the case of low energy muon deuteron elastic scattering.

The complete-experiment problem of photoproduction of pseudoscalar mesons in a truncated partial-wave analysis

The complete experiment problem in the truncated partial wave analysis of pseudoscalar meson photoproduction with suppressed t-channel exchanges is investigated. The focus is set to ambiguities of the group S observables with the unpolarized differential cross section, $\sigma_0$, and the three single-spin observables, $\Sigma$, $T$ and $P$. For this purpose, the approach and formalism already worked out by Omelaenko in 1981 is revisited in this work. A numerical study using multipoles of the PWA solution MAID2007 shows how only one additional double polarization observable can resolve all ambiguities. Therefore, the possibility emerges to perform a complete experiment with only five observables.

Two-photon exchange in theℓ+p→ℓ+pprocess with a massive lepton

Stimulated by the proton size puzzle and the proposal of $\ensuremath{\mu}p$ scattering at the Paul Scherrer Institute (PSI), we study the two-photon exchange corrections to the massive-lepton--proton scattering. The leptonic helicity broken caused by lepton mass introduces new form factors. We estimate the two-photon exchange corrections to these form factors as well as to the unpolarized differential cross sections.

Electromagnetic production of kaons from protons, and baryon electromagnetic form factors

The reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ and $ep\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{K}^{+}\ensuremath{\Lambda}$ have been investigated in a tree-level effective Lagrangian model that incorporates most of the well-established baryon resonances with spins up to $\frac{5}{2}$, four less well-established nucleon resonances with larger mass, and the ${K}^{\ensuremath{\star}}(892)$ and $K1(1270)$ resonances in the $t$ channel. The off-shell structure of the electromagnetic vertices in electroproduction is incorporated by the addition of electromagnetic form factors. To achieve a good fit to the electroproduction data, it was found necessary to treat the ground-state hyperon form factors as adjustable parameters rather than simply equating them with the neutron form factors as was done in past studies. Photoproduction data consisting of unpolarized differential cross sections from the CLAS Collaboration, hyperon polarization asymmetries from CLAS, GRAAL, and SAPHIR, photon beam asymmetries from GRAAL and LEPS, and double polarization observables from CLAS were fit over the c.m. energy range from threshold up to 2.3 GeV. Electroproduction data for the virtual photoproduction structure functions ${\ensuremath{\sigma}}_{U}$, ${\ensuremath{\sigma}}_{T}$, ${\ensuremath{\sigma}}_{L}$, ${\ensuremath{\sigma}}_{TT}$, and ${\ensuremath{\sigma}}_{LT}$ from the CLAS collaboration were fit over the $\ensuremath{\Sigma}K$ c.m. energy range from threshold up to 2.3 Gev and for several values of ${q}^{2}$, the square of the virtual photon 4-momentum. For each intermediate resonance included, the fitted parameters in the photoproduction fit consist of the products of the coupling strengths at the electromagnetic and strong interaction vertices. In the electroproduction fit, there were, in addition, two form-factor parameters for each intermediate baryon in the $s$ and $u$ channels and one form factor parameter for each kaon resonance in the $t$ channel. Results are presented for the fitted photoproduction and electroproduction observables and compared with the data for several sets of kinematical variables.

Role of the tensor exchange potential in nucleon-nucleus scattering

We give a microscopic derivation of the spin-spin components of the optical potential for elastic scattering of a nucleon from a target with nonzero spin. A realistic nucleon-nucleon interaction containing direct and exchange terms is used to generate a folded nucleon-nucleus potential whose spin-spin components are treated in distorted-wave Born approximation. We show how folding leads to spin-spin tensor interactions with higher order couplings in the projectile and target spin that have not been explicitly considered before. We place particular emphasis on the polarization transfer coefficient DNN for 200-MeV protons elastically scattered from 10 B, which is rigorously unity in the absence of any spin-spin interactions and for which experimental data exist. We find that deviations of DNN from unity are particularly sensitive to spin-spin exchange terms arising from the nucleon-nucleon tensor interaction and the nuclear wave functions describing the target one-body density matrix. Unpolarized differential cross sections and vector analyzing powers are found to be very insensitive to these terms. DOI: 10.1103/PhysRevC.84.041601

Hadron production from μ–Deuteron scattering at [formula omitted] at COMPASS

Hadrons proceeding from quasi-real photo-production are one of the many probes accesible at the Common Muon Proton Apparatus for Structure and Spectroscopy (COMPASS) at CERN. These hadrons provide information on the scattering between photon and partons through γ-gluon(g) direct channels as well as q-g resolved processes. Comparisons of unpolarized differential cross section measurements to next-to-leading order (NLO) pQCD calculations are essential to develop our understanding of proton-proton and lepton-nucleon scattering at varying center of mass energies. These measurements are important to asses the applicability of NLO pQCD in interpreting polarized processes. In this talk we will present the unidentified charged separated hadron cross-sections measured by the COMPASS experiment at center of mass energy of √ s = 17 GeV ,l owQ 2 (Q 2 1.0 GeV/c.)

Hard quasi-real photo-production of charged hadrons at COMPASS energies

The Common Muon Proton Apparatus for Structure and Spectroscopy (COMPASS) at CERN with its use of beams of naturally polarized muons scattered of a polarized deuteron target, provides an environment of hard scattering between quasi-real photons and partons. Hard hadron quasi-real photo-production with polarized initial states is sensitive to the polarized gluon distribution ΔG through γ-gluon(g) direct channels as well as q-g resolved processes. Comparisons of unpolarized differential cross section measurements to next-to-leading order (NLO) pQCD calculations are essential to develop our understanding of proton-proton and lepton-nucleon scattering at varying center of mass energies. These measurements are important to asses the applicability of NLO pQCD in interpreting polarized processes. In this talk we will discuss unidentified charged separated hadron production at low Q2 (Q2 < 0.1 GeV2/c2) and high transverse momenta (pT > l.0GeV/c). < p2T > spectra of charged hadrons at Q2 > 1 GeV2/c2 will also be discussed.