Electroweak radiative corrections to single top production

Fortran subroutines to calculate helicity amplitudes with massive spin-3/2 particles, such as massive gravitinos, which couple to the standard model and supersymmetric particles via the supercurrent, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external gravitinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the gauge invariance of the helicity amplitudes.     

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.     

On the Decay Analysis of Electroproduced Higher-Spin Hadrons

We study exclusive electroproduction of two hadrons where one or both of the hadrons is a higherspin resonance whose decay is analysed. Interesting electroproduction experiments of this type are discussed. A complete formal apparatus is given for the decay analysis of spin-J particles produced in this way with polarized or unpolarized electron beams and targets. The cases J = 1, 3/2, 2 and 5/2 are worked out in detail. A conventional helicity frame analysis in terms of s-channel helicity amplitudes is given. Also we rearrange the formalism for use in the Gottfried-Jackson frame with everything given in terms of t-channel helicity amplitudes. The t-channel formalism makes it possible to completely separate the contributions from longitudinal and transverse virtual photon t-channel helicity states when only the laboratory azimuthal angle between the lepton and hadron planes is variable.     

Standard model light-by-light scattering in SANC: Analytic and numeric evaluation

The implementation of the Standard Model process γγ → γγ through a fermion and boson loop into the framework of SANC system and additional precomputation modules used for calculation of massive box diagrams are described. The computation of this process takes into account nonzero mass of loop particles. The covariant and helicity amplitudes for this process, some particular cases of D ₀ and C ₀ Passarino-Veltman functions, and also numerical results of corresponding SANC module evaluation are presented. Whenever possible, the results are compared with those existing in the literature.     

The \gamma \gamma \to \gamma Z process at high energies and the search for virtual SUSY effects

We study the helicity amplitudes and the observables of the process at high energy. As in the case of the process studied before, the relevant diagrams in the standard model (SM) involve W, charged-quark, and lepton loops, while in SUSY we also have contributions from charginos and charged-sfermion or Higgs-loop diagrams. Above 250 GeV, the dominant SM amplitudes are themselves dominated by the W loop, and as for , they are helicity conserving and almost purely imaginary. We discuss the complementary information provided by for the identification of possible nonstandard effects. This process, together with , should provide very useful information on the nature of possible new physics particles, above the threshold of their direct production. Received: 26 April 1999 / Published online: 8 September 1999     

General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in $$\mathcal {}$$-cut representation

In this paper, we give the general expressions for a special series of tree amplitudes of the Yang–Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive helicity gluons. With special helicity choices, we use the spinor helicity formalism to express these n-point amplitudes in compact forms, and find a clever way to use the BCFW recursion relations to prove the results. Then these amplitudes are used to form the complete 1-loop all-plus integrand with any number of gluons, expressed in the \(\mathcal {Q}\)-cut representation.     

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.     

On the uniqueness of the smooth zero mass limit for invariant amplitudes

The behavior of the invariant amplitudes for processes involving massive vector mesons is investigated in the limit as the mass goes to zero. The constraints of gauge invariance impose a definite structure on the amplitudes at k² = 0, and the question of the uniqueness of this structure is examined. It is shown that if the limit is smooth, the consequent relations between the massive and massless helicity amplitudes are unique, provided only that any additional dynamical assumptions are made consistently. Some of the implications of this result are discussed, with particular reference to the unambiguous covariant formulation of vector meson dominance for scattering amplitudes.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

Diffractive vector mesons beyond the s-channel helicity conservation

We derive a full set, and determine the twist, of helicity amplitudes for diffractive production of light to heavy vector mesons in deep inelastic scattering. For large Q ² all helicity amplitudes but the double-flip are calculable in perturbative QCD and are proportional to the gluon structure function of the proton at a similar hardness scale. We find a substantial breaking of the s-channel helicity conservation, which must persist in real photoproduction also. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 667–673 (10 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Description of spin-dependent observables in elastic proton-deuteron scattering on the basis of a generalized diffraction model

Spin-dependent observables of elastic proton-deuteron (pd) scattering at intermediate energies are considered on the basis of calculations within a generalized diffraction model. The generalization in question takes into account all ten helicity proton-proton (pp) and proton-neutron (pn) amplitudes constructed on the basis of a present-day partial-wave analysis and precise deuteron wave functions derived from two alternative models of nucleon-nucleon (NN) forces. Explicit relations between the invariant amplitudes of pd scattering and input NN helicity amplitudes are found. Among other things, these relations make it possible to reconstruct unknown pn amplitudes at energies above 1 GeV on the basis of data on pd scattering. The predictions of the generalized diffraction model for differential cross sections and analyzing powers are compared with the latest experimental data. Surprisingly good agreement with experimental data over a broad interval of scattering angles is found both for differential cross sections and for vector and tensor analyzing powers.     

Regge Models and Dispersion Relations for Partial Waves

The asymptotic behaviour of partial wave amplitudes is calculated supposing various Regge models for the total scattering amplitude A(s, t, u). The high energy partial wave behaviour obtained is combined with the validity of partial wave dispersion relations. It is shown that consistency of these assumptions can only be achieved by demanding. 1) a definite asymptotic behaviour of the discontinuity of the left hand cut of partial wave amplitudes. 2) the validity of partial wave sum rules of similar kind as the well-known finite energy sum rules for the total amplitude. All steps of the derivation shall first be demonstrated for elastic scattering of identical scalar particles. Then within the helicity formalism the results are generalized for particles with arbitrary spin and different masses. Finally the question is studied whether the sum rules can be employed to determine unknown CDD-pole parameters in an N/D approach for the I = J = 1/2 state in πN scattering. It is shown that the sum rules of highest order are able to do that.     

New method for calculating helicity amplitudes of jet-like QED processes for high-energy colliders

As a continuation of our previous paper [Eur. Phys. J. C 23, 633 (2002)] we further develop our new method for calculating helicity amplitudes of jet-like QED processes described by tree diagrams, applying it to lepton pair production. This method consists in replacing spinor structures for real and weakly virtual intermediate leptons by simple transition vertices. New vertices are introduced for the pair production case, and previous bremsstrahlung vertices are generalized to include virtual photons inside the considered jet. We present a diagrammatic approach that allows us to write down in an efficient way the leading helicity amplitudes, at tree level. The obtained compact amplitudes are particularly suitable for numerical calculations in jet-like kinematics. Several examples with up to four particles in a jet are discussed in detail. Received: 31 March 2003, Published online: 18 June 2003     

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.     

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     

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     

HELAS and MadGraph with goldstinos

Fortran subroutines to calculate helicity amplitudes with goldstinos, which appear as the longitudinal modes of massive gravitinos in high energy processes, are added to the HELAS (HELicity Amplitude Subroutines) library. They are coded in such a way that arbitrary amplitudes with external goldstinos can be generated automatically by MadGraph, after slight modifications. All the codes have been tested carefully by making use of the goldstino equivalence theorem and the gauge invariance of the helicity amplitudes. Hadronic total cross sections for associated gravitino productions with a gluino and a squark are also presented.     

The \gamma \gamma \to Z Z process and the search for virtual SUSY effects at a \gamma \gamma Collider

We study the helicity amplitudes of the process in the Standard Model at high energy. These amplitudes receive contributions from the W and charged quark and lepton loops, analogous to those encountered in the cases studied before. But also receives contributions from the Higgs s-channel poles involving the effective Higgs- vertex. At energies , the amplitudes in all three processes are mainly helicity-conserving and almost purely imaginary; which renders them a very useful tool in searching for New Physics. As an example, a SUSY case is studied, and the signatures due to the virtual effects induced by a chargino-, charged slepton- or a lightest stop-loop in , are explored. These signatures, combined with the analogous ones in and , should help identifying the nature of possible New Physics particles. Received: 3 September 1999 / Published online: 3 February 2000     

Angular correlation for nuclear muon capture

Formulae for the capture rates, gamma-neutrino correlations, and angular distributions of recoil in muon capture processes J_i J_f by an unpolarized nucleus for J_i ≦ 3 and J_f ≦ 5/2, with and without change of parity of nuclear levels, are given explicitely in terms of the multipole amplitudes. Relation of helicity amplitudes for muonic atom decay to the multipole amplitudes and to amplitudes introduced by other authors is presented. The derivation is based on kinematics only, and the formulae are strictly valid for the muon capture by any nuclei. The formulae are convenient for model calculations of partial transitions with realistic nuclear and muon wave functions and for the phenomenological analysis of a weak interaction.     

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.