Pion-nucleon vertex function and the one-pion exchange potential

We calculate the πNN vertex function from field theory and dispersion relations. It contains no adjustable parameters, the only input being S- and P- waves for $\text{ππ →}\text{N}\text{N}$. Our vertex function, having an effective cut-off mass of 5μ and an rms radius of 0.52 fm, compares well with previous experimental determinations. We find negligible effects from the 3π dressing of the π propagator. The corrected OPEP is significantly different from the uncorrected OPEP for r < 1.5 fm. The inclusion of the corrected OPEP in meson exchange potentials will improve agreement with phenomenology.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.     

The ϱ and A2 exchange amplitudes in meson-baryon scattering for ϱlab between 2.5 and 200 GeV/c

We present a parametrization of the ? and A₂ exchange amplitudes which fits all the available data on the reactions $\text{π}{}^{\mathrm{?}}\text{p}\text{→ π}{}^0\text{n}\text{, π}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^0\text{n}\text{,}\text{and K}{}^{\mathrm{+}}\text{n}\text{→}\text{K}{}^0\text{p}$ in the momentum range from 2.5 to 200 GeV/c and for momentum transfers up to t = ?2.0 (GeV/c)².     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

Dibaryon signals in the excitation functions of polarized πd scattering

Quantitative estimates of the role of the dibaryon resonances ¹D₂, ³F₃ and ¹G₄ in the πd channel are made. Exc functions for vector and tensor polarisations for πd → π$\text{d}$ are calculated for T^π < 650 MeV by admixing dibaryon resonances of conservative strength to the impulse approximation background. The reliability of the background amplitudes for θ ? 70° is checked by comparing with results from a Faddeev calculation.     

Scale and conformal covariance in quantum electrodynamics

The paper consists of two independent parts. First, we review the situationin scale invariant massless QED from an axiomatic standpoint. Assuming that the τ-functions (or, equivalently, the Euclidean Schwinger functions) transform covariantly under dilatations, we deduce that the current j_τ(x) has zero n-point Wightman functions, but nonvanishing τ-functions. Assuming in addition conformal invariance of the current-field vertex function, we write down a bootstrap equation similar to the one derived in [7] from the point of view of pertubation theory. Next we consider a non-Lagrangian, conformal invariant model of interacting antisymmetric tensor field F_μv (of scale dimension d) and Dirac field ψ (of dimension d'. The model involves two conserved currents (an “electric” and a “magnetic” one) and two effective coupling constants. We demonstrate that it is free of ultravioletdivergences in the range of dimensions $\text{2 < d < 3,}\text{3}\text{2}\text{< d′ <}\text{5}\text{2}$.     

pp interactions at 303 GeVc: Analysis of diffraction excitation in the reaction pp → pX

The properties of the diffractively excited system observed at low missing mass in the inclusive pp → pX reaction at $\text{303}\text{GeV}\text{c}$ are presented. For diffraction excitation with |x| > 0.9, the cross section, σ_D=(5.6±0.8) mb, the mean charged multiplicity depends on the mass of the diffractive system approximately at 〈n_c〉 ≈ 0.6M_x + 2, and the slope of the momentum transfer distribution with |t| < 0.5 GeV² is 7.5±0.8 GeV^?2.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

Peripheral pn production and decay angular distributions in the reaction π−p → (pn)p at 12 GeV/c incident momentum

The reaction $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}$, where p_s is a slow proton, was measured at 12 GeV/c incident momentum with the CERN-OMEGA spectrometer. Both antiproton and proton were identified uniquely by electronics information. We obtained 1844 events with four-momentum Transfer squared in the range 0.13 ? |t| ? 0.33 GeV² and with invariant masses $\text{M(}\text{p}\text{n}\text{)}$ up to 2.5 GeV. The corresponding cross section in this t range is determined to be σ = 4 ± 0.4 μb. Extrapolating the differential cross section over the whole t range assuming dσ/dt ≈ exp(5.3t) we estimate a cross section of σ = 9.3 ± 2.0 μb. Comparison with data on $\text{π}{}^{\mathrm{?}}\text{p}\text{→ (}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ (where n_s is a slow neutron) in the same t range shows that the $\text{(}\text{p}\text{n}\text{)}\text{p}{}_{\mathrm{s}}\text{and}\text{(}\text{p}\text{p}\text{)}\text{n}{}_{\mathrm{s}}$ cross sections have approximately the same magnitude.     

Polarization measurement of the pp → nn charge exchange at 8 Gev/c

The $\text{p}\text{p}\text{→}\text{n}\text{n}$ polarization has been measured at 8 GeV/c and for ?t values ranging from 0 up to 0.8 (GeV/c)². A small and negative polarization has been found.     

A study of the reaction pp → π− π+ at 10 GeV/c

The reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}$ has been studied at 10.1 GeV/c in the ?t interval from 0.15 to 1.5 (GeV/c)². A line-reversal comparison with backward elastic scattering π⁺p → pπ⁺ shows good agreement for ?t > 0.3 (GeV/c)².     

Rise of proton proton total cross section and inclusive spectra

The origin of the rise of p-p total cross section (σ_t(pp)) is investigated by making use of the inclusive sum rule. The contribution to the rise of σ_t(pp) from the development of sharp peak near the kinematical boundary in the process p+p→p+ “anything” is almost completely canceled out by the decrease of the cross section in other x-region between s=45 (GeV/c)² and s=2820 (GeV/c)². Then the net contribution to the rise of σ_t(pp) from the process p+p→p+ “anything” is very likely to be zero. The true origin of the rise of σ_t(pp) is found to be the increase of inclusive cross sections at x ? 0 between PS and ISR energies. The contribution from the process p+p→π+ “anything” at x ? 0 to the rise of σ_t(pp) is estimated to be 3.2 mb, that from the process p+p→K + “anything”, 0.71 mb and that from the process p+p→$\text{p}$ “anything”, 0.62 mb. According to our conclusion we expect that all total cross sections will rise with energy at high energy.     

The A-dependence of J/ψ-particle inclusive distributions

The differential cross sections $\text{d}\text{σ}\text{d}\text{x}$ and $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2$ of inclusive J/ψ production by 43 GeV/c π^? off Be, Cu and W nuclei have been measured. Fitting $\text{d}\text{σ}\text{d}\text{p}{}_{\mathrm{t}}{}^2\text{～ A}{}^{\mathrm{\alpha }}\text{(p}{}_{\mathrm{t}}{}^2\text{)}$ we observed the increase of α with p_t².     

Differential cross sections for the charge exchange process π+p → π0 (π+p) at 8, 16 and 23 GeV/c

The differential cross section $\text{d}\text{σ}\text{d}\text{t′}$ for the charge-exchange process π⁺p → π⁰ (π⁺p) at 8, 16 and 23 GeV/c is presented for several regions of the π⁺p effective mass. It is found that the dip at t′ ≈ 0.6 (GeV/c)² which is observed in the Δ(1236) mass band becomes a less pronounced structure in the higher mass regions. However, while the slope of the $\text{d}\text{σ}\text{d}\text{t′}$ distributions in the near-forward direction decreases strongly with increasing π⁺p mass, there is no evidence that the observed structure moves to higher values of t′ as the π⁺p mass increases. These results are consistent with a Regge-exchange picture where the position of the dip is determined by the exchanged trajectory, but are inconsistent with a simple geometrical picture.     

Study of K−p→K1(890)n at 13 GeV

The results of a wire chamber spectrometer experiment studying $\text{K}$¹ (890) production in the reaction K^?p→ K^?π⁺n at 13 GeV are presented. Strong forward structure is observed for |t|< m²_π in the s-channel density matrix elements and differential cross section. These features are similar to those observed in π^?p→?⁰n data and are characteristics of π exchange. In contrast in the intermediate, |t| ～ 0.2 GeV², and large momentum transfer regions $\text{K}$¹ (890) production is demonstrated by the natural parity ??A₂ exchange contribution.     

The charge exchange pp → nn at 5.0 and 7.76 GeV/c near the forward direction

The differential cross section for the charge exchange $\text{p}\text{p}\text{→}\text{n}\text{n}$ has been measured with high statistics at 7.76 GeV/c and at 5.0 GeV/c. The 7.76 GeV/c data show a very narrow [Δt ? 0.01 (GeV/c)²] forward peak superposed on a slow exponential fall-off.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

Interpretations of the differential cross-sections for pp → π−π+

The differential cross-sections for $\text{p}$p → π^?π⁺ in the momentum range 0.8 to 2.4 GeV/c (centre-of-mass energy 2.02 to 2.57 GeV) are analysed in terms of the possible existence of s-channel resonances. The systematics of the dip structures and the s-dependence of dσ/dt are presented.     

The nature of three-pion enhancements in the minimal K-matrix model

The square of the magnitude of the inverse Fredholm determinant associated with the minimal K-matrix integral equations describing three-pion to three-pion scattering was calculated as a function of three-pion mass ¢M from threshold to 1900 MeV for the 0 ≦ I ≦ 2, 0 ≦ J ≦ 2 channels of the three-pion system. The input for these equations consisted of the on-shell π-π t-matrices t₀⁰, t₀², t₁¹, and t₀² obtained from phenomenological phase-shift analyses. For the minimal K-matrix model, the only structure in the natural parity states is an enhancement of kinematical origin at 1284 MeV in the ω-channel. Spurious enhancements appear in all the unnatural parity states considered at roughly 1150 MeV corresponding to the ρπ → ρπ Peierls singularity. In the I = 1 unnatural parity channels, broad enhancements at $\text{1450}\text{MeV}\text{≦ ¢M ≦ 1675}\text{MeV}$ occur. These correspond to the ρπ → fπ fit generalized Peierls singularity.