Invariant Amplitudes Research Articles

Pion-nucleon partial-wave analysis with fixed-t dispersion relation constraints.

We have performed a set of partial-wave analyses of the pion-nucleon elastic scattering data to 2 GeV employing rigorous constraints from simultaneous forward and fixed-t dispersion relations. Constraints were generated from the forward ${\mathit{C}}^{\ifmmode\pm\else\textpm\fi{}}$ amplitudes and the invariant amplitudes A and B at fixed t in the range 0 to -0.3 ${\mathrm{GeV}}^{2}$. Solutions were generated for a range of pion-nucleon coupling constants (${\mathit{g}}^{2}$/4\ensuremath{\pi}) and isoscalar scattering lengths (${\mathit{a}}^{(+)}$). A chi-squared map for these (${\mathit{g}}^{2}$/4\ensuremath{\pi},${\mathit{a}}^{(+)}$) solutions exhibits a clear minimum near ${\mathit{g}}^{2}$/4\ensuremath{\pi}=13.75 (${\mathit{f}}^{2}$/4\ensuremath{\pi}=0.076) for both the fits to the data and the dispersion relations. While favoring a particular ${\mathit{g}}^{2}$/4\ensuremath{\pi}, this work shows that it is possible to obtain good, stable fits for nearby values, but at the cost of increased chi squared. Consequently, this approach provides a criterion for defining the preferred value and uncertainty of ${\mathit{g}}^{2}$/4\ensuremath{\pi} from pion-nucleon scattering data. On this basis, we conclude that ${\mathit{g}}^{2}$/4\ensuremath{\pi}=13.75\ifmmode\pm\else\textpm\fi{}0.15 (${\mathit{f}}^{2}$/4\ensuremath{\pi}=0.076\ifmmode\pm\else\textpm\fi{}0.001).

Helicity amplitudes for matter-coupled gravity

The great simplicity attained by the Weyl-van der Waerden spinor technique in the evaluation of helicity invariant amplitudes is shown to apply in the cumbersome calculations within the framework of linearized gravitation. Once the graviton couplings to spin-0, 1/2, 1, and 3/2 particles are given, we exhibit the reach of this method by evaluating, as an example, the helicity amplitudes for the process electron + positron → photon + graviton in a very straightforward way.

Power corrections to QCD sum rules for Compton scattering

We extend previous work on sum rules for the invariant amplitudes of pion Compton scattering by deriving a complete lowest-order perturbative spectral functin — and its leading non-perturbative power corrections — for a specific combination of the two helicities ( H 1 + H 2) of this process. Using some properties of a modified version of the Borel transform, we develop a method of calculation of the gluonic corrections which can be easily extended to other similar reactions, such as proton Compton scattering. A preliminary comparison of the new sum rule with the pion form factor sum rule is made.

QCD sum rule and perturbative QCD approaches to pion Compton scattering

We compare two approaches to the description of pion Compton scattering at moderate momentum transfer, one being based on local duality QCD sum rules for the invariant amplitudes of the process, which have been derived recently, and the other on the modified factorization formula with Sudakov effects included. We find that perturbative QCD predictions are dominant over those from QCD sum rules only for the scattering angle greater than 40°.

Do [formula omitted]p annihilations at rest choose the Eightfold way?

Dynamical selection rules observed in p p annihilation at rest are linked to relations between SU(3) invariant amplitudes. The ϱπ puzzle, the K K suppression in P wave, and the unexplained production rates of πa 2 (1320) are shown to be manifestions of one SU(3) amplitude ratio. The dynamical selection rules observed in the production of strange mesons lead to symmetries in SU(3) amplitudes. We conjecture that these symmetries reflect the underlying quark-gluon dynamic. It is shown that the contribution of annihilation diagrams to important annihilation channels like ϱ 0 π 0 or ηω is small or vanishes. Hence rearrangement must play an important role. The use of SU(3) relations in the context of N N interactions has been critized since the small rate for strangeness production seems to imply very large SU(3) breaking effects. The weakness of this argument is pointed out.

Covariant trace formalism for heavy mesons-wave top-wave transitions

Heavy meson,s- top-wave, weakb→c transitions are studied in the context of the heavy quark effective theory using covariant meson wave functions. We use the trace formalism to evaluate the weak transitions. As expected from heavy quark symmetry, the eight transitions betweens- andp-wave states are described in terms of only two universal form factors which are given in terms of explicit wave function overlap integrals. We present our results in terms of both invariant and helicity amplitudes. Using our helicity amplitude expressions we discuss rate formulae, helicity structure functions and joint angular decay distributions in the decays $$\bar B \to D^{**} ( \to (D,D^* ) + \pi ) + W^ - ( \to l^ - \bar v_l )$$ . The heavy quark symmetry predictions for the one pion transitionsD **→(D,D *)+π are similarly worked out by using trace techniques.

THE POLARIZED PHOTON STRUCTURE FUNCTION $g_1^\gamma $ AS A PROBE OF CHIRAL SYMMETRY REALIZATIONS

The first moment of the polarized photon structure function [Formula: see text] is determined by the anomalous three-current axial-vector-vector (AVV) correlation function. Its dependence on the off-shell momentum κ2 of the target photon is a direct probe of the way chiral symmetry is realized in the AVV function. A careful account is given of the effect of different realizations of chiral symmetry on the AVV correlation function with special emphasis on the delicate chiral limit, where the occurrence of singularities in the invariant amplitudes makes the relation with the first moment of [Formula: see text] more subtle. The behavior of [Formula: see text] as κ2 is increased through the thresholds associated with the different quarks and leptons is described.

Microscopic approach to pion-nucleus dynamics.

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum-space first-order optical potential combined with microscopic estimates of second-order corrections. The calculation of the first-order potential includes (1) full Fermi-averaging integration including the \ensuremath{\Delta} propagation and the intrinsic nonlocalities in the \ensuremath{\pi}-N amplitude, (2) covariant kinematics, (3) invariant amplitudes, and (4) a finite-range off-shell pion-nucleon model which contains the nucleon-pole term. The \ensuremath{\Delta} nucleus interaction is included via the mean spectral-energy approximation. This approach produces a convergent perturbation theory in which the Pauli corrections (treated as a second-order term) cancel remarkably against the pion true-absorption terms. Parameter-free results, including the \ensuremath{\Delta}-nucleus shell-model potential, Pauli corrections, pion true absorption, and short-range correlations, are presented.

Meson-nucleus dynamics

A diagrammatic perturbation theory for the interaction of a pion with a finite nucleus is developed. The theory allows us to identify the various pieces of the physics which are believed to be important and to put into a unifying language the understanding which is emerging from apparently diverse studies. The theory proposed here is arranged so that it maintains the use of the nearly free pion-nucleon T-matrix and contemporary nuclear structure work which utilizes a nucleon-nucleon Bethe-Goldstone g-matrix. Within this framework, we calculate in momentum space and without approximation the first-order optical potential. This potential includes: (1) an exact performance of the Fermi-averaging integral (delta propagation), (2) covariant kinematics including the recoil of the nuclear target, (3) the use of invariant amplitudes and invariant normalizations and phase space factors, (4) the inclusion of the delta-nucleus interaction through a mean-spectral approximation, and (5) a realistic off-shell extrapolation of the pion-nucleon amplitude. The elastic scattering cross sections predicted by this potential are remarkably close to the data. The higher-order effects are classified and their inter-relationships discussed. Three of the higher-order corrections, Pauli effects, pion true-absorption, and short range correlation effects, are calculated and the success of the first-order potential is found to be validated by a large cancellation between the Pauli and true-absorption corrections. A detailed discussion of and comparison to alternate approaches to investigating pion-nucleus dynamics is provided.

One-loop improved Born approximation for e +e − → W +W −

The one-loop-corrected helicity amplitudes and the cross section for e +e − → W +W − are represented in terms of invariant amplitudes related to corrections to Born-level gauge couplings as well as magnetic dipole, electric quadrupole, anapole, t-channel-exchange and contact interactions. Neglecting all but the (three) ultraviolet and infrared sensitive corrections to the gauge couplings yields an improved Born approximation which is sufficiently accurate for most practical purposes.

DIMENSIONAL REGULARIZATION IN THE 1/N EXPANSION

Two classes of renormalizable 1/N expandable two-dimensional models are analyzed to O(1/N) and the asymptotic behavior of the renormalized two-point functions is nonperturbatively evaluated. These results are taken as a benchmark to study the applicability of dimensional regularization and perturbative minimal subtraction renormalization to the context of the 1/N expansion. Perturbation theory is applied to O(1/N) diagrams to all orders in the weak coupling constant and, after resummation, the same finite renormalization group invariant asymptotic amplitudes are obtained. As a byproduct, the O(1/N) contributions to renormalization group Z functions in the minimal subtraction scheme are extracted and the critical index η is evaluated and compared to previous nonperturbative results, finding complete agreement. The appendix is devoted to the extension of these results to a supersymmetric version of the models.

Form factors and gauge invariance in pion photoproduction.

We consider the effect of strong-vertex form factors on the gauge invariance of Born diagrams for the pion photoproduction reaction. The minimal-substitution prescription of Ohta for the electromagnetic current operator in pion photoproduction yields the same result as the simplest Born approach for one particular invariant amplitude. This is incompatible with recipes that multiply the Born amplitude by an overall form factor.

K+-nucleus scattering and the nucleon in the nuclear medium.

The ${\mathit{K}}^{+}$-nucleus interaction is investigated in the context of a covariant, momentum-space optical potential that incorporates covariant kinematics, relativistic normalizations, and phase-space factors, a covariant treatment of the recoil of the target nucleus, utilizes invariant amplitudes which are free of kinematic singularities, and allows an exact performance of the Fermi integration over the momentum of the struck nucleon. Elastic differential cross sections for ${\mathit{K}}^{+}$ scattering from $^{12}\mathrm{C}$ and $^{40}\mathrm{Ca}$ and total cross sections for ${\mathit{K}}^{+}$ scattering from $^{12}\mathrm{C}$ are calculated. An enhanced, in-medium, two-body interaction is indicated as the data is consistent with an approximate 30% enhancement of the theoretical calculations.

Differential equations for the energy of a single particle in a helicoidal wiggler with invariant guiding field and travelling plasma wave (non-self-consistent Raman regime)

We are interested in the orbital motion of a single particle in a helically wound wiggler, in the presence of a constant longitudinal guiding magnetic field B g and also of an electrical longitudinally travelling plasma wave field E z of invariant amplitude and phase. This could be a model for a free electron Raman laser, at least for the end of the wiggler, with coherent longitudinal plasma wave owing to neglected transverse electromagnetic travelling waves. Near the axis of the wiggler Bessel functions of the wiggler fields have been drastically neglected [P. Diament, Phys. Rev. A23 (1981) 2537]. In this case and using a rotating frame with a fixed origin but following the helicoidal field, we have been able to deduce a nonalgebraic time-dependent constant of the motion which generalizes the axial invariant of Freund-Drobot and Davidson-Uhm [H.P. Freund and A.T. Drobot, Phys. Fluids 25 (1982) 736]. Further we have deduced a third-order nonlinear differential equation (NLDE) for the energy. This equation can be reduced to a nonlinear second-order one, owing to an integrating factor. Actually, this second-order NLDE may be much more easily directly deduced. Finally we have studied this NLDE from a mathematical point of view, first for the preliminary case E z − E 0 = constant, then for the case E z = E 0 cos Φ = E 0 cos( Kz − ωt + φ 0). However, due to the lack of space, the results of this mathematical study will be published elsewhere [J. Valat, submitted].

Anomalies in non-polynomial closed string field theory

The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.

Relativistic off-shell analysis of elastic scattering of 200 MeV protons by 40Ca.

Off-shell effects due to momentum dependence of the optical potential are calculated for the relativistic approach to 200 MeV proton elastic scattering by $^{40}\mathrm{Ca}$. Optical potentials are based on the optimally factorized impulse approximation using complete sets of invariant amplitudes based on the Utrecht meson-exchange model for the NN interaction.

Doorway-resonance model for pion-nucleon D- and F-wave scattering

A model for the resonant pion-nucleon D- and F-waves is developed which assumes that the pion-plus-nucleon couples to a resonance and that the resonance can serve as a doorway to the inelastic channels. With the use of simple form factors, the model is capable of reproducing the pion-nucleon phase shifts up to an energy of T π = 1.4 GeV if the coupling of the elastic channel to the inelastic channels is taken from data as input into the model. A value for the mass of the resonance that would result in the absence of the coupling to decay channels is extracted from the data utilizing the model. This is the mass that is most easily modeled by bag models. For the non-resonant D- and F-wave channels a separable potential model is used. This model, like the resonance model, is developed utilizing the invariant amplitude which is free of kinematic singularities and uses invariant norms and phase spaces. The model is also applied to the S-wave channels. A relation between the resonance model and the Chew-Low model is discovered and used to derive an extended Chew-Low model which is applied to the P 13, P 31, and P 33 channels. Implications of the model for understanding the range of the pion-nucleon interaction and the dynamic structure of the interaction are presented.

Direct reconstruction of pp elastic scattering amplitudes from experimental data between 0.83 and 2.7 GeV

The direct reconstruction of the elastic scattering amplitudes at eleven energies between 0.83 and 2.7 GeV is described. Complete sets of spin dependent observables used for this reconstruction were measured in the nucleon-nucleon experimental program at Saturne II. The invariant amplitudes a, b, c, d and e were deduced using the least square method fit to the experimental data. A search for solutions starting from random initial values was performed to determine different possible sets of amplitudes. The absolute values show a similar angular dependence at all energies and for all solutions. The dependence of phases show discrete ambiguities especially at the higher energies. One of the solutions at 2.1 GeV suggests a behaviour which could be related to a dibaryon resonance of mass 2.73 GeV with the half-width at the half-maximum less than 50 MeV.

Radiative corrections to helicity amplitudes forW-pair production ine + e?-annihilation

Radiative corrections toW pair production ine+ e−-annihilation are investigated. In an earlier work we discussed only the weak corrections to this process. Here we present the complete calculation including QED corrections. Full agreement with other authors is achieved. We use the helicity formalism for the projection of theS-matrix into invariant amplitudes and study the dependence of cross sections on the Higgs and top masses. Effects due to the choice of the renormalization scheme are considered.

Flavor selection rules and two-body decays of charmed mesons into pseudoscalar plus vector mesons

We analyse the measured branching ratios for the Cabibbo-allowed decays of charmed mesons into pseudoscalar plus vector mesons in terms of the flavor SU (3) selection rules of the standard model plus nonet symmetry. Our fit to the invariant amplitudes for the 6 ∗ and 15 interactions indicates that the effective hamiltonian involves comparable admixtures of the two SU (3) representations. The branching ratio for D s→ φπ + is foound to be 2.5% and that for D 0→ K 0∗η is close to its upper limit of 2.9%; the branching ratios for the K ∗+ K 0 and ϱ + η decay modes of the D s are predicted to be 4.3% and 5.8% respectively.