Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction pˉ → l ⁺ l ^- in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction pˉ → Bˉ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the pˉ → l ⁺ l ^- annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange.     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

Phase shift analysis of hyperon-nucleon elastic scattering using optimized polynomial expansion techniques

A relatively stable method of phase shift analysis of hyperon-nucleon scattering proposed by us is applied to Σ⁺ p and Λp scattering. The analytic cutt-planes of analyticity of the helicity amplitudes are mapped into the interior of unifocal ellipses. The helicity amplitudes are then expressed as accelerated convergent expansions in the mapped variable. A definite economy is observed in the number of free parameters for fixed energy phase shift analysis of Σ⁺ p and Λp scattering at 40 and 100 MeV and 100 MeV respectively. Twenty six more phase shifts and coupling parameters corresponding to higherJ values are also predicted.     

Spin density matrix elements in exclusive ρ0 electroproduction on?1H and 2H targets at 27.5?GeV beam?energy

Spin Density Matrix Elements (SDMEs) describing the angular distribution of exclusive ρ ⁰ electroproduction and decay are determined in the HERMES experiment with 27.6 GeV beam energy and unpolarized hydrogen and deuterium targets. Eight (fifteen) SDMEs that are related (unrelated) to the longitudinal polarization of the beam are extracted in the kinematic region 1<Q ²<7 GeV², 3.0<W<6.3 GeV, and −t<0.4 GeV². Within the given experimental uncertainties, a hierarchy of relative sizes of helicity amplitudes is observed. Kinematic dependences of all SDMEs on Q ² and t are presented, as well as the longitudinal-to-transverse ρ ⁰ electroproduction cross-section ratio as a function of Q ². A small but statistically significant deviation from the hypothesis of s-channel helicity conservation is observed. An indication is seen of a contribution of unnatural-parity-exchange amplitudes; these amplitudes are naturally generated with a quark-exchange mechanism.     

Electromagnetic properties of strange baryons in a relativistic quark model

We present some of our results for the electromagnetic properties of excited Σ hyperons, computed within the framework of the Bonn constituent-quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model are fitted against the best-known baryon masses. Accordingly, the results for the form factors and helicity amplitudes are genuine predictions. We compare with the scarce experimental data available and discuss the processes in which Σ ^*'s may play an important role.     

On πd elastic scattering using aligned deuteron targets

A theoretical study is made of the advantages to be gained in polarizing a deuteron target by applying an external electric quadrupole field with non-zero asymmetry parameter for carrying outd(π, π)d experiments, in order to determine empirically the helicity amplitudes A, B, C, D characterizing the scattering, without any phase ambiguities.     

Hadronic <Emphasis Type="Italic">B</Emphasis> decays in the MSSM with large tan <Emphasis Type="Italic">β</Emphasis>

We present an analysis of non-leptonic B decays in the minimally flavour-violating MSSM with large tan β. We relate the Wilson coefficients of the relevant hadronic scalar operators to leptonic observables, showing that the present limits on the B _s →μ ⁺ μ ⁻ and B ⁺→τ ⁺ ν _τ branching fractions exclude any visible effect in hadronic decays. We study the transverse helicity amplitudes of B→VV decays, which exhibit an enhanced sensitivity to the scalar operators, showing that even though an order one modification relative to the SM is not excluded in some of these amplitudes, they are too small to be detected at B factories. X.-Q. Li is a Alexander-von-Humboldt fellow.     

Zeros of the helicity amplitudes of Σ−-p and Λ-p elastic scattering

The forces of interaction as reflected in the cosθ plane analytic structures of the helicity amplitudes of Σ⁻-p and Λ-p scattering are optimally exploited using the conformal mapping technique of Cutkosky and coworkers. A suitable parametrization of these amplitudes in the mapped variable is then chosen so that it can see the zeros better. These zeros are then located by making a good fit to the differential scattering cross-section curves. The effect of these zeros upon the cross-sections is discussed. Values for the phase shifts and coupling parameters between channels of fixedJ values are also computed.     

Polarization in hyperon photo- and electro-production<Superscript>⋆</Superscript>

Multiple polarization observables must be measured to access the amplitude structure of pseudoscalar meson photoproduction off the proton. The hyperon-producing reactions are especially attractive to study, since the weak decays allow straightforward measurement of the induced and recoil polarization observables. In this paper we emphasize γ + p → K ⁺ + Λ , discussing recent measurements of C_x, C_z, and P for this reaction. An empirical constraint on the helicity amplitudes is obtained. A simplified model involving spin-flip and spin-non-flip amplitudes is presented. Finally, a semi-classical model of how the polarization may arise is presented.     

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins

In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH ^[u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH ^[u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.     

Associated production of light gravitinos in e+e? and e?γ collisions

Light gravitino productions in association with a neutralino (selectron) in e ⁺ e ⁻ (e ⁻ γ) collisions are restudied in a scenario that the lightest supersymmetric particle is a gravitino and the produced neutralino (selectron) promptly decays into a photon (electron) and a gravitino. We explicitly give the helicity amplitudes for the production processes by using the effective goldstino interaction Lagrangian, and present the cross sections with different collision energies and mass spectra. We also examine selection efficiencies by kinematical cuts and beam polarizations for the signal and background processes, and show that the energy and angular distributions of the photon (electron) can explore the mass of the t-channel exchange particle as well as the mass of the decaying particle at a future e ⁺ e ⁻ (e ⁻ γ) collider.     

Use of \Lambda_b polarimetry in top quark spin-correlation functions

Due to the absence of hadronization effects and the large mass, top quark decay will be uniquely sensitive to fundamental electroweak physics at the Tevatron, at the LHC, and at a future linear collider. A “complete measurement” of the four helicity amplitudes in decay is possible by the combined use of andW polarimetry in stage-two spin-correlation functions (S2SC). In this paper, the most general Lorentz-invariant decay density matrix is obtained for the decay sequence where and [or ], and likewise for . These density matrices are expressed in terms of b-polarimetry helicity parameters which enable a unique determination of the relative phases among the amplitudes. Thereby, S2SC distributions and single-sided b-W-interference distributions are expressed in terms of these parameters. The four b-polarimetry helicity parameters involving the amplitude are considered in detail. polarimetry signatures will not be suppressed in top quark analyses when final angles-and-energy variables are used for . Received: 26 January 2001 / Published online: 15 March 2001     

Photon splitting in an ultrastrong magnetic field

We analyze the splitting of a photon with energy ω below the e ⁺ e ⁻ pair-production threshold in an ultrastrong magnetic field. We use the amplitudes found by employing the operator diagrammatic technique. In a field considerably above the critical values the process amplitudes become independent of the field strength. A study of the polarization operator of a photon in an external field of arbitrary strength in the energy range considered in the present investigation shows that there is only one set of polarizations of the initial and final photons for which the splitting amplitude is nonzero. Zh. éksp. Teor. Fiz. 111, 52–62 (January 1997)     

Zeros of the helicity amplitudes of Σ+-p elastic scattering

Optimally exploiting the analytic structure of the helicity amplitudes of Σ⁺-p scattering we locate their zeros by making a fit to the differential cross-section curves at 40, 100 and 150 MeV energies. Minute changes in the positions of the zeros produced detectable noises in the fit. It was observed that quite reliable predictions for the phase shifts can also be obtained from this analysis.     

Effective-Lagrangian approach to γγ → WW I: Couplings and amplitudes

We consider the gauge-boson sector of a locally SU(2) × U(1) invariant effective Lagrangian with ten dimension-six operators added to the Lagrangian of the standard model. These operators induce anomalous three- and four-gauge-boson couplings and an anomalous γγH coupling. In the framework of this effective Lagrangian we calculate the helicity amplitudes and differential and total cross sections for the process γγ → WW at a photon collider. We give relations between different parts of the amplitudes that show which linear combinations of anomalous couplings are measurable in this reaction. The transformation properties of the differential cross section under CP are discussed. We find that three linear combinations of CP-conserving and of CP-violating couplings can be measured independently of the photon polarization in γγ → WW. M. Pospischil: now at CNRS UPR 2191, 1 Avenue de la Terrasse, 91198 Gif-sur-Yvette, France.     

s- and t-Channel transformation matrices for helicity and invariant amplitudes for γ + N → 1 + N

The Algebraic transformation matrices, valid for all s and t, connecting the s- and t-channel helicity amplitudes to a corresponding set of gauge invariant covariant amplitudes are presented for the photoproduction processes γ + N → 1^± + N.     

Measurement of helicity parameters in top quark decay

It is important to be able to quantitatively assay future measurements of competing observables consistent with the coupling predictions for decay, so plots of the values of these helicity parameters are given in terms of a “ + Additional Lorentz Structure”. Three phase-type ambiguities are shown to exist, but measurement of the sign of the large interference between the W longitudinal/transverse amplitudes will resolve two of them. The large effects in both and amplitudes from some couplings demonstrate that it is less model dependent to measure helicity parameters, instead of setting limits on some arbitrary subset of coupling constants. Received: 12 November 1998 / Published online: 27 April 1999     

Kl3γ+ decays revisited: Branching ratios and T-ODD momenta correlations

We calculate the branching ratios of the K ⁺ → π ⁰ l ⁺ ν _lγ (l = e, μ) decays, and the T-odd triple momenta correlations ξ = q · [p _l × p _π ]/M _K ³, due to the electromagnetic final-state interaction, in these processes. The contributions on the order of ω ⁻¹ and ω ⁰ to the corresponding amplitudes are treated exactly. For the branching ratios, the corrections on the order of ω are estimated and demonstrated to be small. We compare the results with those of other authors. In some cases our results differ considerably from the previous ones.     

Higgs Boson Decay into Two Gluons and a <Emphasis Type="Italic">Z</Emphasis> Boson

Results for the one-loop calculation of the decay width Γ(H→ggZ) in the standard model with Higgs boson masses in the range 115 GeV<m _H <2m _W are presented. We find that among all the helicity amplitudes contributing to the width only those for which the gluons have the same polarization and the Z is longitudinally polarized contribute in any significant way. The calculation includes all contributions from the second and third generations, and kinematic cuts to enhance the H→ggZ signal. Compared to the width of H→gg, we find Γ(H→ggZ)/Γ(H→gg)≲10⁻⁴.     

Proton polarization in the p(e,e′p)π0 reaction and the measurement of quadrupole components in the N to Δ transition

The recoil proton polarization in the π⁰ production off the proton with longitudinally polarized electron beam has been studied as a means to measure quadrupole components in the N to Δ transition. On top of the Δ resonance a high sensitivity to a possible Coulomb quadrupole excitation is found in parallel kinematics. The ratio of S ₁₊/M ₁₊ multipole amplitudes can be determined from the ratio of the two in-scattering-plane recoil proton polarization components. Avoiding the absolute measurement of the polarizations, such a ratio allows small experimental uncertainties. Furthermore, the electron helicity independent proton polarization component enables the characterization of resonant and non-resonant pieces. Received: 3 November 1997