Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.     

Perturbative QCD corrections in Drell-Yan processes

The influence of lowest-order QCD corrections on the Drell-Yan cross section $\text{Q}{}^4\text{(}\text{dσ}\text{dQ}{}^2\text{)(τ, Q}{}^2\text{)}$ is determined and compared with the asymptotic freedom (AF) corrections. The perturbative calculation exhibits the AF-characteristics of a (strongly) rising Q²-dependence for √τ?0.1 (qg-scattering) and falling for √τ?0.2 (qq?-annihilation). Qualitative agreement between the two calculation methods in the entire √τ-range is obtained with α_s = 0.3.     

Finite-size scaling of critical cumulants near the ferromagnetic phase boundary

We employ the recently proposed scaling theory for first-order transitions to derive a detailed prediction for the large-argument behaviour of the critical-point scaling function of the reduced fourth order cumulant $\text{g}{}_{\mathrm{L}}\text{≡}\text{<s}{}^4\text{>}\text{<s}{}^2\text{>}{}^2\text{?3}$ correct up to a term exponentially small in L/ξ(T).     

Experimental analysis of pp interactions between 0 and 1.2 GeV/c: Evidence for a pp → 5π effect near 1950 MeV/c2

An experimental analysis of $\text{p}\text{p}$ interactions between the $\text{p}$p threshold (√s = 1878 MeV) and √s = 2 100 MeV leads to clear evidence for an s-channel effect in the reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{at}\text{1949 ± 10}\text{MeV}\text{/c}{}^2\text{(Γ ? 80}\text{MeV}\text{/c}{}^2\text{)}$. A comparison is made with the backward elastic scattering and charge-exchange behaviour. An interpretation in terms of an object strongly coupled to mesonic decay modes, with small or middle-sized elasticity (x ? 0.135_?0.06^+0.13) is given. No significant narrow structure is observed in the backward elastic scattering between 1.9 and 2 GeV. The experimental resolution of √s in this case is 2 MeV.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Calculation of the γγ → ϱ0ϱ0 cross section at high energies

The processes with the cross sections not decreasing with energy become important at high energies. The simplest processes of this kind are γγ → V_i⁰V_j⁰ where V⁰ = ?⁰, ω, ?, ….. We calculate their cross sections in the high-energy small angle region s ? |t| ? μ². The cross section γγ → ?⁰?⁰ at high energies (s ? 10 GeV²) exceeds those of γγ → ππ, ?⁺?^? considerably. At $\text{s ? 10}{}^4\text{GeV}{}^2$ (this is the characteristic energy for the VLEPP and SLC colliders) and $\text{|t| ? 2}\text{GeV}{}^2$, the ratio $\text{(}\text{d}\text{σ/}\text{d}\text{t)(γγ → ?}{}^0\text{?}{}^0\text{)/(}\text{d}\text{σ/}\text{d}\text{t)(γγ → μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{) ? 70}$.     

Nuclear incompressibility: From finite nuclei to nuclear matter

The recent increase of experimental data concerning the giant monopole resonance energy E_M gives information on the incompressibility modulus of nuclear matter, provided one can extrapolate the incompressibility of a nucleus K_A, defined by $\text{E}{}_{\mathrm{<mtext>M</mtext>}}\text{=[}\text{h}\text{?}{}^2\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{/m〈r}{}^2\text{〉]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, to the infinite medium. We discuss the theoretical interpretation of the coefficients of an $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ expansion of K_A by studying the asymptotic behaviour of two RPA sum rules (corresponding to the scaling and the constrained model), evaluated using self-consistent Thomas-Fermi calculations. We show that the scaling model is the most suitable one as it leads to a rapidly converging $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ expansion of the corresponding incompressibility K_A^s, whereas this is not the case with the constrained model. Some semi-empirical relations between the coefficients of the expansion of K_A^s are established, which reduce to one the number of free parameters in a best-fit analysis of the experimental data. This reduction is essential due to the still limited number and accuracy of experimental data. We then show the compatibility of the data given by the various experimental groups with this parametrization and obtain a value of K_n.m. = 220 ± 20 MeV, in good agreement with more microscopic analyses.     

Plasma dynamics in GaAs under strong picosecond surface excitation

We have investigated the time-resolved luminescence of GaAs in air at room temperature, under strong picosecond surface excitation. The energy density was in the range 4–40 $\text{mJ}\text{cm}{}^2$ and the excitation wavelength λ_ex ? 0.53 μ. The peak temperature reached by the generated electron-hole plasma at the end of the excitation pulse amounts to T_M ? 720 K at an energy density of about 10 $\text{mJ}\text{cm}{}^2$. Further increase of the power induces surface damage on the sample. The plasma relaxes its kinetic energy at a slow rate of the order of 10¹⁰$\text{eV}\text{s}$, supporting our previous calculations which concluded that electron-phonon interactions are strongly screened by intravalley free-carrier collisions at high plasma density, so that the plasma cooling slows down.     

Has asymptotic freedom something to do with charmonium

We analyse the effects of logarithmic corrections due to asymptotic freedom in the potential describing short-range forces in charmonium. This allows us to show that due to the size of the effective quark-gluon coupling ($\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(M}{}_{\mathrm{J/\Psi }}{}^2\text{) ? 0.4}$), the wave function extensions are much larger than the region of space where asymptotic freedom really has predictive power. The resulting ambiguities in the spin-dependent medium-range forces are explored. Also, such a value of α_s makes perturbative calculations of widths unreliable. We point out that the situation is not significantly improved for quark masses of 5 GeV. Indeed, below 20 GeV, short-range forces play a marginal role as compared to confinement forces.     

Inclusive production of K̄1(890) and K̄1(1420) in K̄−p interactions at 10 and 16 GeV/c

The inclusive production of K?¹(890) and K?¹(1420) is studied in K?^?p interactions at 10 and 16 GeV/c. At 10 GeV/c an enhancement in the ($\text{K}\text{?}{}^0\text{π}{}^{\mathrm{?}}$) mass distribution is found at 1.74 GeV, but no clear signal is seen at 16 GeV/c. The fraction of $\text{K}{}^0\text{'}\text{s}$ coming from decay of the $\text{K}{}^1\text{(890)}\text{or}\text{K}{}^1\text{(1420)}$ is large, being (50 ± 6)% and (45 ± 5)% at 10 and 16 GeV/c, respectively. The inclusive cross sections for K^1?(890) and $\text{K}{}^{10}\text{(890)}$ production are almost constant with energy from 8 to 32 GeV/c with values of 3.5 and 3.3 mb, respectively. The $\text{K}{}^1\text{(890)}$ production cross section is studied as a function of transverse and longitudinal variables and found to derive mainly from fragmentation of the incident K^? meson. The spectra of $\text{K}{}^0\text{'}\text{s}$ resulting from the decay of $\text{K}{}^1\text{(890)}$ are studied.     

QCD effects in νN scattering above the threshold of W-boson production

The QCD effects are shown to result at $\text{s}\text{m}{}_{\mathrm{<mtext>w</mtext>}}{}^2\text{? 1}$ in a considerable increase of the νN cross section and modification of $\text{d}\text{σ}\text{d}\text{y}$ in comparison with scaling. At $\text{s}\text{m}{}_{\mathrm{<mtext>w</mtext>}}{}^2\text{≈ 3 × 10}{}^3$ the QCD cross section is twice that of scaling. At $\text{s}\text{m}{}_{\mathrm{<mtext>w</mtext>}}{}^2\text{? 1}$ the QCD structure functions of the nucleon acquire effective scaling behaviour.     

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.     

The Pomeron and the scaling law for partial wave amplitudes

From the scaling law for the s-channel partial wave amplitudes, which guarantees simultaneously t-channel unitarity at threshold t = 4μ² and s-channel unitarity, we derive: (i) The intercept α(0) of the Pomeron is always one, if α(4μ²) > 1. (ii) The total and the elastic cross sections are bounded from below for s → ∞.

where α(4μ²) and δ(4μ²) are the position and the type of te Pomeron singularity (J ? α(4μ²))^{?1?δ(4μ2) at t = 4μ2}. (iii) The type of the Pomeron singularity δ(4μ²) is restricted: either $\text{δ(4μ}{}^2\text{) ?}\text{1}\text{2}$ or $\text{δ(4μ}{}^2\text{) ?}\text{1}\text{2}$.     

Paзлoжeниe пo 1Z для чapтpи-фoкoвcкoй и кoppeляциoннoй энepгии, peлятивиcтcкич пoпpaвoк, дипoльнoгo мaтpичнoгo элeмeнтa

Energies and dipole matrix elements have been calculated for He, Li, Be, B, C, N, O, F, and Ne-like ions (configurations 1s²2sⁿ¹2pⁿ²?1s²2s^n1?12pⁿ²⁺¹). The Hartree-Fock energy, the correlation energy, and relativistic corrections were taken into account. Relativistic corrections were obtained by computing the entire quantity H_B. Numerical results are presented for energies of the terms in the form

$\text{E=E}{}_0\text{Z}{}^2\text{+ ΔE}{}_1\text{Z + ΔE}{}_2\text{+}\text{1}\text{Z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{Z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{Z}{}^3\text{)}$

, and for the fine structure of the terms in the form

$\text{〈1s}{}^2\text{2s}{}^{\mathrm{n1}}\text{2p}{}^{\mathrm{n2}}\text{LSJ|H}{}_{\mathrm{Б}}\text{|1s}{}^2\text{2s}{}^{\mathrm{n1\prime }}\text{2p}{}^{\mathrm{n2\prime }}\text{L′S′J〉=(?1)}{}^{\mathrm{L+S\prime +J}}\text{LSJ}\text{S′L′1}\text{×}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{[E}{}^{\mathrm{(0)}}\text{(Z ? B)+}\text{E}{}_{\mathrm{c0}}\text{]+(?1)}{}^{\mathrm{L\; +\; S\prime \; +\; J}}\text{LSJ}\text{S′L′2}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{E}{}_{\mathrm{cc}}$

. Dipole matrix elements are required for calculation of oscillator strengths or transition probabilities. For the dipole matrix elements, two terms of the expansion in $\text{1}\text{Z}$ have been obtained. Numerical results are presented in the form P(a, a′) = (a/Z)[1 + (τ/Z)].     

Energy dependence of topological cross-sections at nal energies

We calculate the normalized cross-sections $\text{σ}{}^1\text{= σ ·}\text{FLUX/LIPS}$ using recent data on topological cross-sections. We confirm the power law behaviour $\text{σ}{}^1\text{= AP}{}^{\mathrm{?n}}{}_{\mathrm{<mtext>lab</mtext>}}$ for energies up to 400 GeV. The exponent n appears to satisfy, approxima tely, the relation n ≈ m ?2 for multiplicities m up to 20.     

Heavy quarkonia and asymptotic freedom

We use semiclassical methods to discuss the scaling behaviour of quarkonium level splittings up to $\text{M(}\text{Q}\text{Q}\text{) = 200}\text{GeV}$. Special emphasis is laid on the effects of asymptotic freedom which are found to be essential for $\text{M(}\text{Q}\text{Q}\text{) ? 30}\text{GeV}$. The bound t$\text{t}$ system will almost look like the ? system except that $\text{R = ΔM (}{}^3\text{P}{}_2\text{?}{}^3\text{P}{}_1\text{)/ΔM(}{}^3\text{P}{}_1\text{?}{}^3\text{P}{}_0\text{)}$ is larger than 0.8. In the ? system R will already be close to 0.8.     

Radiative production of gravitinos and photinos in e+e− annihilation

We evaluate cross sections for the two processes e⁺e^? → γ-photino-antiphotino, e⁺e^? → γ-gravitino-antiphotino. In the local limit approximation they are proportional to $\text{α}{}^3\text{s}\text{m}{}^4$ (spin-0 electron) and $\text{G}{}_{\mathrm{Newton}}\text{α}{}^2\text{s}\text{m}{}^2$ (gravitino), respectively. I If spin-0 electrons have masses between 16 and $\text{40}\text{GeV}\text{c}{}^2$, the γ-photino-antiphotino production cross section would be of the order of 0.4 to 0.1 pb at $\text{s}\text{= 40}\text{GeV}$, with the cuts indicated in the text. Detecting this process is within the range of possibilities at PETRA. If no such signal is found the existence of light photinos coupled to spin-0 electrons lighter than $\text{≈40}\text{GeV}\text{c}{}^2$, or to gravitinos lighter than $\text{≈10}{}^{\mathrm{?6}}\text{eV}\text{c}{}^2$, would be excluded.     

A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.