s-and t-channel helicity conservation of pion induced nucleon diffraction dissociation at 3.9 GeV/c and the implications of a two-component model

A study of schannel and t-channel helicity conservation has been carried out on a prism plot separated sample of 3.9 GeV/cπ^±p → π (Nπ)_dd diffraction dissociation events. s-channel helicity conservation is found to be strongly violated while t-channel helicity conservation is found to be mildly violated. These results are similar to that found at 11.7 GeV/c. We explain these violations on the basis of a “two-component model” of which the first component is a single exchange amplitude. We postulate that this amplitude is the generalization of the pomeron exchange amplitude which may conserve s-channel helicity. The second component of the model is a double exchange mechanism which strongly violates s-channel helicity. The predictions of this model agree with the experimental data.     

Factorization in high energy hadron collisions

The concept of factorization is discussed for elastic diffraction scattering and diffraction dissociation of hadrons at high energy. In addition to the usual definition in terms of the t-channel, a natural definition of factorization in the s-channel is proposed and compared with the former. It is shown that s-channel factorization of all diffractive processes is consistent with the assumption that elastic scattering is identical to the shadow of the diffraction dissociation processes.     

Evaluation of a zero intercept dual model by rational functions

A ghost-free zero-intercept dual model constructed by Gervais and Neveu is found to be Regge-behaved but not st symmetric in the four-point function. If the s-channel is taken to be tachyon-free, a tachyon appears in the t-channel.     

On the structure function in the scaling law for partial-wave amplitudes

An expression is obtained for the structure function β(x) occuring in a scaling law for s-channel partial wave amplitudes which has been recently derived from t-channel unitarity at threshold.     

The asymptotic behaviour of a non-planar orientable dual two-loop amplitude

Both the s- and t-channel asymptotic behaviour of a non-planar orientable two-loop four-point amplitude are investigated. A factorized expression for the iterated pomeron singularity, contributing to the s-channel behaviour, has been obtained with an internal pomeron blob closely related to the off-shell “propagator” of Cremmer and Scherk. These results suggest an interpretation in terms of a renormalization scheme of the pomeron. For t-channel asymptotics Regge-cut behaviour arises. Remarks are also made for the corresponding six-point case. Direct expansions of all the relevant functions in terms of group parameters as well as a thorough study of Jacobi's transformation in the double parabolic limit are of crucial importance to prove these results.     

Scaling laws for inelastic partial-wave amplitudes and the high-energy behaviour of multiparticle production

t-channel unitarity equations are derived for n-particle overlap functions. Together with s-channel unitarity they lead to scaling laws for the inelastic s-channel partial-wave amplitudes $\text{?}{}_{\mathrm{l}}{}^{\mathrm{(n)}}\text{(s)}$ in the limits $\text{s → ∞, l → ∞ x = l (}\text{μ}\text{√s}\text{)}{}^3\text{=}\text{fixed}$. Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for $\text{l > L (s) = (α(4μ}{}^2\text{) ? 1) (}\text{s}\text{4μ}\text{)}\text{log}\text{(}\text{s}\text{s}{}_1\text{)}$ we obtain constant production cross sections σ⁽ⁿ⁾(s) at high energies s → ∞ up to s factors.     

Unitarizing high-energy scattering amplitudes in field theories I: QED

Using a procedure which incorporates the s-channel unitarity and t-channel unitarity at every step, we calculate the scattering amplitudes of QED in the high-energy limit. We find that all scattering amplitudes, elastic and inelastic, are summarized by a single eikonal formula which is explicitly unitary.     

Fixed angle dispersion relations and t-channel contribution in photo-pion production

We propose a method of evaluation of the contribution of t-channel singularities for the photon-pion production process on the basis of dispersion relations for invariant amplitudes in the s-plane at fixed angle (cos ? = ± 1). These dispersion relations are studied in the approximation scheme of retaining only the contributions from exchanges at low energy, viz., N, N^∗ (1237) in the s- and u-channels and π, ?, ω and A₁ in the t-channel. It is shown that the dispersion relations require more accurate evaluation in general than what the above approximation scheme can provide in order that the information obtained about the t-channel be reliable.     

Production properties of A1 in πp interactions at 5.45 GeV/c

The production of the peripheral 3π mass enhancement in the A₁ region is described. The differential cross section and its variation with 3π mass is studied and the spin density matrix elements are given for the t-channel and s-channel helicity frames. As observed in π⁻p interactions t channel but not s channel helicity is conserved. A Deck type double Regge trajectory exchange amplitude gives good fits to the experimental distributions. Its use is supported by the equality of ?_{0 0} for the A₁ and ?00 for the ? in the t-channel, as noted by Donohue.     

The cutting rules for the 4-reggeon amplitude

We derive the s-channel cutting rules for the four-pomeron amplitude in the context of a ø³ weak coupling model.     

Scale of corrections to the t-channel pole approximation in quasielastic pion knockout from a nucleon by high-energy electrons

An investigation of a dominant role of the simplest t-channel pole diagrams in pion electroproduction on nucleons for quasielastic-knockout kinematics at an electron energy of a few GeV is completed-namely, the competition between the t-channel pion and rho-meson pole amplitudes, on one hand, and the s-channel pole amplitude (tree diagram), on the other hand, is considered. When the virtual-photon mass is sufficiently large [Q ²>2(GeV/c)²], the last amplitude does not make significant contributions to relevant cross sections, either the longitudinal (dσ _L/dt) or the transverse (dσ _T/dt) one. At Q ²=0.7(GeV/c)², the term associated with the interference between the t-channel pion-pole amplitude and the s-channel pole amplitude is still noticeable in the longitudinal cross section. The vertex functions g _ρ NN(t) as obtained from the cross section for the quasielastic knockout of rho mesons and from the cross section for pion photoproduction are compared. Their disagreement must give impetus to a further development of the gauge-invariant theory of pion photoproduction.     

Two-body propagators with dynamic effective interactions in a many-fermion medium: I. General structure

Excitations of the many-body medium cause dynamic effective interactions between fermions. In actual calculations these interactions are almost always replaced by static approximations. In this paper a Green function approach is outlined which preserves the dynamic structure of the interactions. The central quantity is the four-vertex or two-fermion scattering amplitude Γ in the medium, which depends on three energy variables s, t, and u. Integral equations connect Γ to irreducible effective interactions in the three channels. With static interactions the s- and t-channels correspond to particle-particle and particle-hole configurations, respectively. Dynamic interactions mix these configurations. They also introduce poles in the crossed channels: the exchange of a phonon is a t-pole in the s-channel while pairons induce s-poles in the t-channel. Poles of the one-body propagator G(ω) and the two-body propagators K(s) and K(t) correspond to states of the A ± 1, A ± 2 and A-particle systems. The dynamic coupling between channels results in an intricate connection between various aspects of the many-fermion problem.     

The s-channel dual absorptive model as a consequence also of t-channel absorption

The dual absorptive model applied to t-channel predicts that Regge residues above threshold are I_n-functions which for t ? 0, for the leading trajectory, are simply J_n(R_o√−t). Thus s-channel absorptive models can be expressed entirely in terms of t-channel quantities. Implications to complex Regge poles is discussed.     

Higgs boson physics in the s-channel at μ+μ− colliders

Techniques and strategies for discovering and measuring the properties of Higgs bosons via s-channel production at a μ⁺μ⁻ collider, and the associated requirements for the machine and detector, are discussed in detail. The unique feature of s-channel production is that, with good energy resolution, the mass, total width and partial widths of a Higgs boson can be directly measured with remarkable accuracy in most cases. For the expected machine parameters and luminosity the standard model (SM) Higgs boson h_SM, with mass ≲ 2m_W, the light h⁰ of the minimal supersymmetric standard model (MSSM), and the heavier MSSM Higgs bosons (the CP-odd A⁰ and the CP-even H⁰) can all be studied in the s-channel, with the heavier states accessible up to the maximal √s over a large fraction of the MSSM parameter space. In addition, it may be possible to discover the A⁰ and H⁰ by running the collider at full energy and observing excess events in the bremsstrahlung tail at lower energy. The integrated luminosity, beam resolution and machine/detector features required to distinguish between the h_SM and h⁰ are delineated.     

A comparative study of ϱ0 photoproduced on d,n and p at 7.5 GeV

A 7.5 GeV linearly polarized photon beam was used to study ?⁰ production on d, n and p in the SLAC 82 inch bubble chamber. The production of ?⁰ is found to proceed mainly viat-channel natural parity exchange and to conserve s-channel c.m.s. helicity for small t. The I = 1 contribution to the γN → ?⁰t-channel amplitude is found to be small at 7.5 GeV.     

Spontaneous symmetry breaking in Reggeon field theory

We consider a Reggeon field theory when the bare or input Regge intercept α_O is greater than one. This corresponds to a negative mass squared term in conventional field theory and allows for a spontaneous symmetry break-down. A theory with Regge intercept at one emerges, restoring the Froissart bound by t-channel considerations alone. In our elementary example the resulting bare trajectory is nearly of the square root variety familiar from s-channel eikonalization of models which violate the Froissart bound.     

The scattering amplitude for four dual fermions

The amplitude for the scattering of four dual fermions is written down and evaluated in terms of three complicated functions. One of these is then expressed in terms of the other two. The s-channel spectrum is that of the Neveu-Schwarz model, but it is not possible at present to describe the t-channel spectrum. The spinor structure of the amplitude is also discussed.