Complete Set Of Polarization Observables Research Articles

New graphical criterion for the selection of complete sets of polarization observables and its application to single-meson photoproduction as well as electroproduction

This paper combines the graph-theoretical ideas behind Moravcsik's theorem with a completely analytic derivation of discrete phase ambiguities, recently published by Nakayama. The result is a new graphical procedure for the derivation of certain types of complete sets of observables for an amplitude-extraction problem with $N$ helicity amplitudes. The procedure is applied to pseudoscalar meson photoproduction ($N=4$ amplitudes) and electroproduction ($N=6$ amplitudes), yielding complete sets with minimal length of $2N$ observables. For the case of electroproduction, this is the first time an extensive list of minimal complete sets is published. Furthermore, the generalization of the proposed procedure to processes with a larger number of amplitudes, i.e., $N>6$ amplitudes, is sketched. The generalized procedure is outlined for the next more complicated example of two-meson photoproduction ($N=8$ amplitudes).

Moravcsik's theorem on complete sets of polarization observables reexamined

We revisit Moravcsik's theorem on the unique extraction of amplitudes from polarization observables, which has been originally published in 1985. The proof is (re-) written in a more formal and detailed way and the theorem is corrected for the special case of an odd number of amplitudes (this case was treated incorrectly in the original publication). Moravcsik's theorem, in the modified form, can be applied in principle to the extraction of an arbitrary number of $N$ helicity amplitudes. The uniqueness theorem is then applied to hadronic reactions involving particles with spin. The most basic example is Pion-Nucleon scattering ($N=2$), the first non-trivial example is pseudoscalar meson photoproduction ($N=4$) and the most technically involved case treated here is given by pseudoscalar meson electroproduction ($N=6$). The application of Moravcsik's theorem to electroproduction yields new results, which for the first time provide insights into the structure and content of complete sets for this particular process. The uniqueness-statements for the various reactions are compared and an attempt is made to recognize general patterns, which emerge under the application of the theorem.

Global analysis of charmless B decays into two vector mesons in soft-collinear effective theory

Under the framework of soft-collinear effective theory, we analyze the charmless $B\to VV$ decays in a global way at leading power in $1/m_b$ and leading order in $\alpha_s$ with $V$ denoting a light vector meson. In the flavor SU(3) symmetry, decay amplitudes for the 28 decay modes are expressed in terms of 8 nonperturbative parameters. With 35 experimental results, we fit these 8 nonperturbative parameters. Annihilation contributions are neglected due to power suppression in the $m_b\to \infty$ limit, so we include in the fit the nonperturbative charm penguins, which will play an important role in understanding the direct CP asymmetries. Charming penguins are also responsible for the large transverse polarizations of penguin-dominated and color-suppressed decays. With the best fitted parameters, we calculate all possible physical observables of 28 decay modes, including branching fractions, direct CP asymmetries, and the complete set of polarization observables. Most of our results are compatible with the present experimental data when available, while the others can be examined on the ongoing LHCb experiment and the forthcoming Belle-II experiment. Moreover, the agreements and differences with results in QCD factorization and perturbative QCD approach are also discussed. A few observables are suggested to discriminate these different approaches.

Branching ratios, CP asymmetries and polarizations of Brightarrow psi (2S) V decays

We analyze the non-leptonic decays B/B_srightarrow psi (2S) V with V=(rho , omega , K^{*}, phi ) by employing the perturbative QCD (pQCD) factorization approach. Here the branching ratios, the CP asymmetries and the complete set of polarization observables are investigated systematically. Besides the traditional contributions from the factorizable and non-factorizable diagrams at the leading order, the next-to-leading order (NLO) vertex corrections could also provide considerable contributions. The pQCD predictions for the branching ratios of the B_{(s)}rightarrow psi (2S)K^{*}, psi (2S)phi decays are consistent with the measured values within errors. As for Brightarrow psi (2S) rho , psi (2S) omega decays, the branching ratios can reach the order of 10^{-5} and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct CP asymmetries of the considered decays are very small. Thus the observation of any large direct CP asymmetry for these decays will be a signal for new physics. The mixing-induced CP asymmetries in the neutral modes are very close to sin 2beta _{(s)}, which suggests that these channels can give a cross-check on the measurement of the Cabbibo–Kobayashi–Maskawa (CKM) angle beta and beta _s. We find that the longitudinal polarization fractions f_0 are suppressed to sim 50% due to the large non-factorizable contributions. The magnitudes and phases of the two transverse amplitudes mathcal {A}_{parallel } and mathcal {A}_{perp } are roughly equal, which is an indication for the approximate light-quark helicity conservation in these decays. The overall polarization observables of Brightarrow psi (2S) K^{*0} and B_srightarrow psi (2S) phi channels are also in good agreement with the experimental measurements as reported by LHCb and BaBar. Other results can also be tested by the LHCb and Belle-II experiments.

Complete Experiments in Meson Photoproduction

The problem of the Complete Experiment for photoproduction of pseudoscalar mesons is treated. First the issue is reviewed briefly in the context of full production spin amplitudes as well as a truncated partial wave analysis (TPWA). Complete sets of polarization observables are given for both cases. Then, a numerical procedure for single energy TPWA fits is presented and first results are shown.

Exploring the structure of the proton through polarization observables inlp→jetX

We present results for a complete set of polarization observables for jet production in lepton proton collision, where the final state lepton is not observed. The calculations are carried out in collinear factorization at the level of Born diagrams. For all the observables we also provide numerical estimates for typical kinematics of a potential future Electron Ion Collider. On the basis of this numerical study, the prospects for the transverse single target spin asymmetry are particularly promising. This observable is given by a certain quark-gluon correlation function, which has a direct relation to the transverse momentum dependent Sivers parton distribution.

Polarization transfer measurements forC12(p→,n→)N12(g.s.,1+)at 296 MeV and nuclear correlation effects

Differential cross sections and complete sets of polarization observables are presented for the Gamow-Teller {sup 12}C(p-vector,n-vector){sup 12}N(g.s.,1{sup +}) reaction at a bombarding energy of 296 MeV with momentum transfers q of 0.1 to 2.2 fm{sup -1}. The polarization transfer observables are used to deduce the spin-longitudinal cross section, ID{sub q}, and spin-transverse cross sections, ID{sub p} and ID{sub n}. The data are compared with calculations based on the distorted-wave impulse approximation (DWIA) using shell-model wave functions. Significant differences between the experimental and theoretical results are observed for all three spin-dependent ID{sub i} at momentum transfers of q > or approx. 0.5 fm{sup -1}, suggesting the existence of nuclear correlations beyond the shell model. We also performed DWIA calculations employing random-phase approximation (RPA) response functions and found that the observed discrepancy is partly resolved by the pionic and {rho}-mesonic correlation effects.

SPIN DEGREES AND POLARIZATION OBSERVABLES IN ELECTROMAGNETIC REACTIONS

After a brief introduction into the general importance of polarization observables for the analysis of a reaction, the basic density matrix formalism for the description of polarization phenomena is outlined and illustrated by explicit examples for spin one-half and one. Then various electromagnetic processes like photoreactions and electron scattering are discussed in some detail. Finally, the question of how to determine a complete set of polarization observables providing the maximum information on a reaction is considered.

Study of nuclear correlation effects via [formula omitted] at 296 MeV

We report measurements of the cross section and a complete set of polarization observables for the Gamow–Teller C12(p→,n→)N12(g.s.,1+) reaction at a bombarding energy of 296 MeV. The data are compared with distorted wave impulse approximation calculations employing transition form factors normalized to reproduce the observed beta-decay ft value. The cross section is significantly under-predicted by the calculations at momentum transfers q≳0.5 fm−1. The discrepancy is partly resolved by considering the non-locality of the nuclear mean field. However, the calculations still under-predict the cross section at large momentum transfers of q≃1.6 fm−1. We also performed calculations employing random phase approximation response functions and found that the observed enhancement can be attributed in part to pionic correlations in nuclei.

Isovector effective NN interaction in Si28(p→,n→)P28(6−) at 198 MeV

Abstract We report measurements of the cross section and a complete set of polarization observables for the Si 28 ( p → , n → ) P 28 ( 6 − ) reaction at a bombarding energy of 198 MeV. The data are compared with distorted wave impulse approximation calculations employing response functions normalized to inelastic electron scattering. The spin-longitudinal polarized cross section I D q is slightly over-predicted by the calculations, while the normal spin-transverse polarized cross section I D n is significantly under-predicted. The calculated in-plane spin-transverse I D p and spin-scalar I D 0 polarized cross sections agree well with the experimental data. These results are consistent with those for Si 28 ( p → , p → ′ ) Si 28 ( 6 − , T = 1 ) scattering at the same energy, and thus it is concluded that isospin-mixing effects are not responsible for the discrepancy between theory and experiment in the ( p → , p → ′ ) case. Energy half-off-shell effects as medium effects on the effective nucleon–nucleon interaction are also investigated and found to be too small to be responsible for the discrepancy.

Pionic enhancement in quasielastic(p⃗,n⃗)reactions at345MeV

Differential cross sections and a complete set of polarization observables have been measured for quasielastic $(\stackrel{P\vec}{p},\stackrel{P\vec}{n})$ reactions on $^{12}\mathrm{C}$ and $^{40}\mathrm{Ca}$ at a bombarding energy of $345\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The laboratory momentum transfers are ${q}_{\text{lab}}\ensuremath{\simeq}1.2$, 1.7, and $2.0\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$ for $^{12}\mathrm{C}$ and ${q}_{\text{lab}}\ensuremath{\simeq}1.7\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$ for $^{40}\mathrm{Ca}$. In these momentum transfer regions, the isovector spin-longitudinal interaction is attractive where the one-pion exchange is dominant. The spin-longitudinal and spin-transverse polarized cross sections, $I{D}_{q}$ and $I{D}_{p}$, are deduced. The theoretically expected enhancement in the spin-longitudinal mode is observed at ${q}_{\text{lab}}\ensuremath{\simeq}1.7$ and $2.0\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$. The observed $I{D}_{q}$ is consistent with the pionic enhanced $I{D}_{q}$ evaluated in distorted wave impulse approximation (DWIA) calculations employing random phase approximation (RPA) response functions. The enhanced $I{D}_{q}$ implies the existence of a precursor to pion condensation in nuclei. On the other hand, the theoretically predicted quenching in the spin-transverse mode is not observed. The observed $I{D}_{p}$ is not quenched, but rather enhanced relative to that predicted via the $\mathrm{DWIA}+\mathrm{RPA}$ calculations. Two-step contributions are responsible in part for the enhancement of $I{D}_{p}$.

Polarization transfer and spin response functions of theH2(p⃗,n⃗)reaction at345MeV

Differential cross sections and a complete set of polarization observables have been measured in the quasielastic $^{2}\mathrm{H}(p,n)$ reaction at a bombarding energy of $345\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and laboratory scattering angles of $16\ifmmode^\circ\else\textdegree\fi{}$, $22\ifmmode^\circ\else\textdegree\fi{}$, and $27\ifmmode^\circ\else\textdegree\fi{}$. The data are compared with plane-wave impulse approximation calculations employing an optimal factorization approximation. The agreement between the experimental and theoretical results validates these approximations in the present momentum- and energy-transfer regions. The experimental spin-longitudinal and spin-transverse response functions, ${R}_{L}$ and ${R}_{T}$, respectively, are deduced from the data. The obtained ${R}_{T}$ is consistent with that obtained from the quasielastic electron scattering. The theoretical calculations with the Reid soft core potential give good descriptions for ${R}_{L}$ and ${R}_{T}$, whereas the latter is slightly underestimated around the quasielastic peak.

Polarization transfer measurements for the13C(p→,n→)13Nreaction at 197 MeV and empirical isovector spin-longitudinal response for the(1/2)g.s.−→(1/2)1+transition

We present differential cross sections and complete sets of polarization-transfer coefficients, ${D}_{\mathrm{ij}},$ obtained in the ${}^{13}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n}{)}^{13}\mathrm{N}$ reaction studied at 197 MeV incident proton energy and laboratory angles between $0\ifmmode^\circ\else\textdegree\fi{}$ and $33\ifmmode^\circ\else\textdegree\fi{}.$ These complete sets of polarization observables are used to obtain spin-longitudinal and spin-transverse components for transitions to the ground state, to the first, and to the unresolved second and third excited states in ${}^{13}\mathrm{N}$ at 2.36 MeV and $(3.50+3.55) \mathrm{MeV},$ respectively. The results are used to obtain the two $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}$ contributions for the ground and first excited state transitions and are compared with corresponding distorted-wave impulse approximation (DWIA) calculations. In particular, empirical angular distribution values for the unique spin-longitudinal $\ensuremath{\Delta}{J=0}^{\ensuremath{-}}$ transition to the first excited state in ${}^{13}\mathrm{N}$ are obtained and compared with DWIA calculations.

DeuteronPwave in elastic backward proton-deuteron scattering

The elastic backward proton-deuteron scattering is analyzed within a fully covariant approach based on the invariant expansion of the reaction amplitude. The method of calculation of any observables for any reaction mechanism is developed. The cross section and spin observables, like tensor analyzing power and polarization transfer coefficient etc., are investigated in explicit form within framework of the impulse approximation using different kinds of the relativistic deuteron wave function (DWF) with P-wave components. Our results of numerical calculation for complete set of polarization observables are compared with the experimental data and other calculations performed within both the non-relativistic and relativistic approaches. An experimental verification of the reaction mechanism is suggested by constructing some combinations of different observables.

Zero degree polarization transfer measurements for the13C(p→,n→)13Nreaction at 197 MeV and empirical Gamow-Teller strength distribution

In this paper, we present differential cross sections and complete sets of polarization transfer coefficients, ${D}_{\mathrm{ij}},$ obtained in the ${}^{13}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n}{)}^{13}\mathrm{N}$ reaction studied at zero degree and at 197 MeV incident proton energy. The complete set of polarization observables is used to obtain the Fermi and Gamow-Teller (GT) cross section contributions in the ground state transition, which are then used to deduce GT transition strengths. The sum of the GT strength up to 20 MeV of excitation is compared with shell model calculations. In the region between 20 to 46 MeV of excitation, the differential cross section has been separated in spin and nonspin components.

Complete Sets of Polarization Observables in Electromagnetic Deuteron Breakup

For deuteron photo- and electrodisintegration the selection of complete sets of polarization observables is discussed in detail by applying a recently developed new criterion for the check of completeness of a chosen set of observables. The question of ambiguities and their resolution by considering additional observables is discussed for a numerical example, for which the role of experimental uncertainties is also investigated. Furthermore, by inversion of the expressions of the observables as hermitean forms in the $t$-matrix elements a bilinear term of the form $t_{j'}^*t_j$ can be given as a complex linear form in the observables from which an explicit solution for $t_j$ in terms of observables can be obtained. These can also be used to select sets of observables for the explicit representation of the $t$-matrix.

Elastic proton-deuteron backward scattering: Relativistic effects and polarization observables

The elastic proton-deuteron backward reaction is analyzed within a covariant approach based on the Bethe-Salpeter equation with realistic meson-exchange interaction. Lorentz boost and other relativistic effects in the cross section and spin correlation observables, such as tensor analyzing power and polarization transfer, etc., are investigated in explicit form. Results of numerical calculations for a complete set of polarization observables are presented.

Relations between polarization observables and complete sets for deuteron photodisintegration

The polarization observables for deuteron photodisintegration are given as Hermitean forms of theT-matrix elementsti. By inversion we are able to express a given productti*tj in terms of polarization observables. This allows (i) to derive linear relations between observables for unpolarized, circularly and linearly polarized photons, (ii) to construct explicitly complete sets of polarization observables, and (iii) to derive quadratic relations between observables.