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.     

Spin versus helicity: Processes involving transversity

We construct the spin formalism in order to deal naturally with processes involving transversity which are now of increasing popularity. The helicity formalism which is more appropriate for collision processes of definite helicity has been so far used to also manage processes with transversity, but at the price of computing numerous helicity amplitudes which generally involve unnecessary kinematical variables.     

Relativistic calculation of the two photon coupling of scalar and tensor mesons

The decay rates of scalar and tensor mesons into two photons are calculated in the Bethe-Salpeter bound state formalism. The suppression of the non-relativistic estimates due to relativistic kinematics is found to be substantial. Production crosssections in colliding beam experiments are estimated to be in the picobarn range. Also in the relativistic case the helicity 0 production cross-section of tensor mesons is found to be negligible.     

Angular Distributions and Generalized Moment Analysis for the Doubly Radiative Decay J/ψ→γγV

The doubly radiative decay process J/ψ→γ+X,X→γ+V,V→2P(or 3P) is discussed in this paper.For the intermediate state X with various spin-parity J^P,the corresponding helicity formalism of angular distribution formulas and the moments developed from the generalized moment analysis are presented.They are helpful for determining the spin of the intermediate state.     

On the partial-wave analysis of mesonic resonances decaying to multiparticle final states produced by polarized photons

Meson spectroscopy is going through a revival with the advent of high statistics experiments and new advances in the theoretical predictions. The Constituent Quark Model (CQM) is finally being expanded considering more basic principles of field theory and using discrete calculations of Quantum Chromodynamics (lattice QCD). These new calculations are approaching predictive power for the spectrum of hadronic resonances and decay modes. It will be the task of the new experiments to extract the meson spectrum from the data and compare with those predictions. The goal of this report is to describe one particular technique for extracting resonance information from multiparticle final states. The technique described here, partial wave analysis based on the helicity formalism, has been used at Brookhaven National Laboratory (BNL) using pion beams, and Jefferson Laboratory (JLab) using photon beams. In particular this report broadens this technique to include production experiments using linearly polarized real photons or quasi-real photons. This article is of a didactical nature. We describe the process of analysis, detailing assumptions and formalisms, and is directed towards people interested in starting partial wave analysis.     

Covariant Helicity Amplitude Analysis for J／ψ→γPP

Covariant helicity amplitude analysis for the process of J/ψ→γPP is discussed starting from the Smatrix elements of decay process,we deduce the formulae of helicity coupling amplitudes for two-body decay process,These formulae are used to analyze intermediate resonance states in the process of J/ψ decay to γππ,γKK,γηη′     

Formulation of few-body equations without partial waves

A formalism is developed whereby the two-body Lippmann-Schwinger equation may be solved in momentum space without partial-wave decomposition. The integral equation derived is two-dimensional and so is amenable to direct numerical solution. Because the technique uses the well-known helicity formalism, the matrices involved can be further reduced by taking advantage of symmetries common in nuclear and atomic systems (parity conservation, particle symmetry). An example is shown for nucleon-nucleon scattering, and the results are compared to those obtained from the usual partial-wave method.     

Study of (∧) decay parameter in J/ψ→∧(∧)decay

The helicity amplitudes fot J/ψ→∧(∧)and the relevant background decays are presented for measuring the A decay parameter α+((∧)→(p)π)in J/ψ→∧(∧).The Monte Carlo(MC)simulations based on the helicity amplitudes information are carried out.The likelihood fit method to determine the A decay parameter is presented.Based on the MC generated sample,the sensitivity of the measurement for α+has been estimated,which shows that the J/ψ→∧(∧) channel can be used to measure the A decay parameter α+((∧)→(p)π+)well.     

Comment on phase conventions in helicity formalism

Using the sequential decay process e<'+>e<'->→ J/ψ→ΛΛ, Λ→pπ<'->,Λ→pπ<'+> as an example, the procedure for deducing the full angular distribution is illustrated by adopting both the Jacob-Wick and Jackson conventions in the helicity formalism. To make sure that the final physical result is free of phase conventions, we point out that the coefficients that relate the angular momentum states in different coordinate systems of reference frames have to be taken into account properly in the procedure. The fact that those coefficients are constants suggests that the Jackson convention is favorable in dealing with the processes with sequential decays.     

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     

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.     

Partial-wave analysis of the reactions pp → ϱ0ϱ0, ωϱ0, ϱ0f,and ωf in the T(2200) region

The helicity formalism is used to derive expressions for the joint decay distributions for ?⁰?⁰, ω?⁰, ?⁰f and ωf states in terms of the joint density matrix elements. These expressions are used to extract the density matrix elements from the data of the Rutgers- Stevens-Albany collaboration in the T(2200) region. A partial-wave analysis is then performed in an attempt to determine the dominant partial-wave amplitudes. The results are discussed and comparisons are made to the extremely limited amount of data available at neighboring energies. Finally it is pointed out that the expressions derived for this analysis could be applied without modification to e^?e⁺ annihilations into these states.     

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.     

On the photon-drag effect of photocurrent of surface states of topological insulators

The photocurrent of surface states of topological insulator due to photon-drag effect is computed, being based on pure Dirac model of surface states. The scattering by disorder is taken into account to provide a relaxation mechanism for the photocurrent. The Keldysh–Schwinger formalism has been employed for the systematic calculation of photocurrent. The helicity dependent photocurrent of sizable magnitude transverse to the in-plane photon momentum is found, which is consistent with experimental data. Other helicity independent photocurrents with various polarization states are also calculated.     

Complete angular analysis of the decay cascadeB→D ** (→D *(→Dπ)+π+W(→lv)

We develop a general algorithm for describing angular decay distributions in cascade decay chains of arbitrary length. The general algorithm is used to study joint angular decay distributions for the cascade decayB→D ^**(→D ^*(→Dπ)+W(→lv) where theD ^** is a genericP-wave charm meson state. Lepton mass effects are fully incorporated. The joint angular decay distribution depend on 43 independently measurable decay parameters if the spin parity of theD ^** is 1⁺ and on 48 decay parameters if the spin parity of theD ^** is 2⁺. We give expressions for these decay parameters in terms of the helicity amplitudes of the two-body decay processes. An absolute prediction for all the parameters is presented in the framework of the heavy quark effective theory. A method for obtaining the helicity amplitudes from measured joint angular distributions is suggested.     

Relativistic nuclear corrections to the spin structure function of the deuteron in the light-cone variables

The relativistic deuteron has been considered in the light-cone formalism as a system of two strongly interacting nucleons (two-nucleon approximation). The technique for the calculation of the average helicity of the proton in the deuteron has been considered in the light-cone variables. A receipt has been pro-posed for the consistent calculation of relativistic nuclear corrections to the average helicity of the proton in the deuteron and to the spin structure function of the deuteron g ₁ ^D . Relativistic-correction-induced change in the Bjorken sum rule has been discussed.     

Helicity suppression mechanism of decay amplitudes in relativistic quark model

Structures of the matrix elements of two-and four-quark operators are investigated in connection with the argument of “helicity suppression” in the decay amplitudes. The analysis is made by expanding the quark operators in terms of the constituentquark modes in a relativistic way. It is shown that the naive consideration of helicity suppression can be applied to the case of two-quark operators. The situation is quite different in the case of four-quark operators; sometimes we find maximum value of the decay amplitude, which is suppressed according to the naive helicity suppression. It is made clear which aspects of the constituent-quark picture are essential to cause the difference between our results and those from the free quark picture. Remarks are given on nonleptonic decays ofK-andD-mesons.     

Helicity representation of the N-N bound-state problem

The two-nucleon bound-state problem described in the momentum space is presented in the helicity state formalism.     

Spin correlations in a pair of atoms induced by spontaneous emission of photons

An analysis is presented of the state that arises after photons have been spontaneously emitted by a pair of spatially separated excited two-level atoms with spin-1/2 ground and excited states. Selection of possible decay scenarios conditioned on the helicities of the photons (even on the helicity of the one emitted first) makes it possible to reveal ground-state spin-projection correlations between atoms. The correlations are due to quantum interference between alternative scenarios (the atom that has emitted a particular photon cannot be identified). The correlations obtained by the chosen selection method are classical.     

Canonical nonequilibrium ensembles and subdynamics

A method for constructing a canonical nonequilibrium ensemble for systems in which correlations decay exponentially has recently been proposed by Coveney and Penrose. In this paper, we show that the method is equivalent to the subdynamics formalism, developed by Prigogine and others, when the dimension of the subdynamic kinetic subspace is finite. The comparison between the two approaches helps to clarify the nature of the various operators used in the Brussels formalism. We discuss further the relationship between these two approaches, with particular reference to a simple discrete-time dynamical system, based on the baker's transformation, which we call the baker's urn.