Ratios Of Helicity Amplitudes Research Articles

Endpoint symmetries of helicity amplitudes

We investigate helicity amplitudes (HAs) of A→BC-type decays for arbitrary spin towards the kinematic endpoint. We show that HAs are proportional to product of Clebsch-Gordan coefficients (CGC) and the velocity to a non-negative power. The latter can be zero in which case the HA is non-vanishing at the endpoint. At the kinematic endpoint the explicit breaking of rotational symmetry, through the external momenta, is restored and the findings can be interpreted as a special case of the Wigner-Eckart theorem. Our findings are useful for i) checking theoretical computations and ii) the case where there is a sequence of decays, say B→B1B2 with the pair (B1B2) not interacting (significantly) with the C-particle. Angular observables, which are ratios of HAs, are given by ratios of CGC at the endpoint. We briefly discuss power corrections in the velocity to the leading order.

Overview of recent HERMES results

An overview of more recent and important results from the HERMES experiment is presented in this paper. HERMES collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This allows for a series of unique measurements of observables sensitive to the multidimensional structure of the nucleon. Amongst them are the semi-inclusive deep-inelastic scattering measurements of azimuthal modulations sensitive to the leading-twist transverse momentum distributions and the distributions sensitive to convolutions of the twist-2 and twist-3 distribution and fragmentation functions. They all provide information on the three-momentum-dependent quark distributions. Knowledge about the quark distribution as a function of longitudinal momentum and transverse position in impact-parameter space can be accessed, e.g., through exclusive vector–meson leptoproduction. Particularly, the measurement of spin-density-matrix elements on an unpolarized hydrogen target and the measurement of azimuthal modulations on transversely polarized hydrogen target for the ω–meson production are described in this paper. The results of the measurement of ratios of helicity amplitudes for the ρ0 –meson leptoproduction on transversely polarized hydrogen target are also presented.

Extraction of helicity amplitude ratios from exclusive ρ0-meson electroproduction on transversely polarized protons

Exclusive ρ0-meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV2 < Q2 < 7.0 GeV2, 3.0 GeV < W < 6.3 GeV, and −t′ < 0.4 GeV2. Using an unbinned maximum-likelihood method, 25 parameters are extracted. They determine the real and imaginary parts of the ratios of certain helicity amplitudes (describing ρ0-meson production by a virtual photon) and the dominant amplitude without the nucleon-helicity flip. The latter amplitude describes the production of a longitudinal ρ0 meson by a longitudinal virtual photon. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to . The ratios of nucleon-helicity-non-flip amplitudes to are found to be in good agreement with those from the previous HERMES analysis. A comparison of the extracted amplitude ratios with the Goloskokov-Kroll model shows the necessity to add pion exchange amplitudes with positive πρ form factor to the amplitudes based on generalized parton distributions to improve the HERMES data description.

Ratios of helicity amplitudes for exclusive rho ^0 electroproduction on transversely polarized protons

Exclusive rho ^0-meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV^2<Q^2< 7.0 GeV^2, 3.0 GeV <W< 6.3 GeV, and -t^prime < 0.4 GeV^2. Using an unbinned maximum-likelihood method, 25 parameters are extracted. These determine the real and imaginary parts of the ratios of several helicity amplitudes describing rho ^{0}-meson production by a virtual photon. The denominator of those ratios is the dominant amplitude, the nucleon-helicity-non-flip amplitude F_{0frac{1}{2}0frac{1}{2}}, which describes the production of a longitudinal rho ^{0}-meson by a longitudinal virtual photon. The ratios of nucleon-helicity-non-flip amplitudes are found to be in good agreement with those from the previous HERMES analysis. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to F_{0frac{1}{2}0frac{1}{2}}. Results obtained in a handbag approach based on generalized parton distributions taking into account the contribution from pion exchange are found to be in good agreement with these ratios. Within the model, the data favor a positive sign for the pi -rho transition form factor. By also exploiting the longitudinal beam polarization, a total of 71 rho ^0 spin-density matrix elements is determined from the extracted 25 parameters, in contrast to only 53 elements as directly determined in earlier analyses.

Ratios of helicity amplitudes for exclusiveρ0electroproduction on transversely polarized proton

Exclusive ρ 0 -meson electroproduction is studied by the HERMES experiment, using the 27.6 GeV longitudinally polarized electron/positron beam of HERA and a transversely polarized hydrogen target, in the kinematic region 1.0 GeV 2 Q 2 2 , 3.0 GeV t ′ 2 . Using an unbinned maximum-likelihood method, 25 parameters are extracted. They determine the real and imaginary parts of the ratios of certain helicity amplitudes describing ρ 0 -meson production by a virtual photon, where the denominator is the dominant amplitude . The latter is the nucleon-helicity-non-flip amplitude, which describes the production of a longitudinal ρ 0 meson by a longitudinal virtual photon. The transverse target polarization allows for the first time the extraction of ratios of a number of nucleon-helicity-flip amplitudes to . The ratios of nucleon-helicity-non-flip amplitudes are found to be in good agreement with those from the previous HERMES analysis.

Phenomenological study of helicity amplitudes of high energy exclusive leptoproduction of theρmeson

We apply a previously developed scheme to consistently include the twist-3 distribution amplitudes for transversely polarized rho meson in order to evaluate, in the framework of kT factorization, the helicity amplitudes for exclusive leptoproduction of a light vector meson, at leading order in alphaS. We compare our results with high energy experimental data for the ratios of helicity amplitudes T11/T00 and T01/T00 and get a good description of the data.

Helicity Amplitude Ratios in Exclusive Electroproduction of the ρ0 Meson at HERMES

Electroproduction of the ρ0 vector meson in the process γ* + N → V + N′ is studied with a 27.6 GeV longitudinally polarized electron/positron beam in the HERMES experiment. Kinematical dependences of real and imaginary parts of the ratio of the natural-parity-exchange helicity amplitudes T11/T00 (γ*T → ρT) and T01/T00 (γ*T → ρL) are extracted from the data. The same dependences are extracted for the unnatural-parity-exchange ratio |U11/T00.

Ratios of helicity amplitudes for exclusive ρ0 electroproduction

Exclusive ρ 0-meson electroproduction is studied in the HERMES experiment, using a 27.6 GeV longitudinally polarized electron/positron beam and unpolarized hydrogen and deuterium targets in the kinematic region 0.5 GeV2<Q 2<7.0 GeV2, 3.0 GeV <W<6.3 GeV, and −t′<0.4 GeV2. Real and imaginary parts of the ratios of the natural-parity-exchange helicity amplitudes T 11 ( $\gamma^{*}_{T} \rightarrow\rho_{T}$ ), T 01 ( $\gamma^{*}_{T} \rightarrow \rho_{L}$ ), T 10 ( $\gamma^{*}_{L} \rightarrow\rho_{T}$ ), and T 1−1 ( $\gamma^{*}_{-T} \rightarrow\rho_{T}$ ) to T 00 ( $\gamma^{*}_{L}\rightarrow\rho_{L}$ ) are extracted from the data. For the unnatural-parity-exchange amplitude U 11, the ratio |U 11/T 00| is obtained. The Q 2 and t′ dependences of these ratios are presented and compared with perturbative QCD predictions.

Partial wave analyses ofJ/ψ→γK+K−andγKS0KS0

Results are presented on $J/\psi $ radiative decays to $K^+K^-$ and $K^0_SK^0_S$ based on a sample of 58M $J/\psi$ events taken with the BES II detector. A partial wave analysis is carried out using the relativistic covariant tensor amplitude method in the 1-2 GeV mass range. There is conspicuous production due to the $f'_2(1525)$ and $f_0(1710)$. The latter peaks at a mass of $1740\pm 4^{+10}_{-25}$ MeV with a width of $166{^{+5}_{-8}}{^{+15}_{-10}}$ MeV. Spin 0 is strongly preferred over spin 2. For the $f'_2(1525)$, the helicity amplitude ratios are determined to be $x^2 = 1.00\pm0.28^{+1.06}_{-0.36}$ and $y^2 = 0.44\pm{0.08}^{+0.10}_{-0.56}$.

Factorization in color-favored B-meson decays to charm

Improved $B$ meson decay data have permitted more incisive tests of factorization predictions. A concurrent benefit is the ability to constrain the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$. Using a simultaneous fit to differential distributions $d \Gamma(\ob \to D^{*+} l^- \bar \nu_l)/ dq^2$ measured by the CLEO and LEP Collaborations, the rates for the color-favored decays $\ob \to D^{(*)+} (\pi^-,\rho^-,a_1^-)$, and the rate for $\ob \to D^+ l^- \bar \nu_l$, we find $|V_{cb}| = 0.0415 \pm 0.0022$. The slope of the universal Isgur-Wise form factor is described by a parameter found to be $\rs = 1.52 \pm 0.11$. Taking the $D_s$ meson decay constant from the world average of direct measurements, we predict satisfactorily the branching ratios for $\ob \to D^{(*)+} D_s^{(*)-}$. Ratios of helicity amplitudes for color-favored processes are also found to be in accord with predictions.

Extraction of theD13(1520)photon-decay couplings from pion- andη-photoproduction data

We compare results for the D13(1520) photon-decay amplitudes determined in analyses of eta- and pion-photoproduction data. The ratio of helicity amplitudes (A_3/2 / A_1/2), determined from eta-photoproduction data, is quite different from that determined in previous analyses of pion-photoproduction data. We consider how strongly the existing pion-photoproduction data constrain both this ratio and the individual photon-decay amplitudes.

Three-step two-body decay of J/ psi and the generalized moment analysis.

The three-step two-body decay process of {ital J}/{psi}, {ital J}/{psi}{r_arrow}{ital V}+{ital X}, {ital X}{r_arrow}{ital P}{sub 1}+{ital Y}, {ital Y}{r_arrow}{ital P}{sub 2}+{ital P}{sub 3} (where {ital V} and {ital P}{sub {ital i}} represent vector and pseudoscalar mesons, respectively) is discussed by using the generalized moment analysis method. The spin-parity of the boson resonance {ital X} and the ratios of helicity amplitudes of the process can be determined in terms of measuring the corresponding moments except for a very special case.