How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

The QCD effective coupling constant in e+e− annihilation

The QCD effective coupling constant α_s(Q²) is determined by comparing the O(α_s)² jet-distributions with the high-energy e⁺e^? data from PETRA. We get α_s(Q² = 1225 GeV²) = 0.125 ± 0.01, which corresponds to $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}\text{= 110}{}^{\mathrm{+70}}{}_{\mathrm{?50}}\text{MeV}$ with five flavours.     

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.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

Investigation of rare non-strange decay modes of the f meson in Π+p interactions at 5GeVc

Rare decay modes of the f meson are studied in the final states Δ⁺⁺π⁺π^?π⁺π^?, Δ⁺⁺π⁺π^?MM and Δ⁺⁺π⁺π^?π⁺π^?MM. The ratio $\text{Γ (f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0\text{π}{}^0\text{)}\text{Γ(f → π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ is 0.23 ± 0.09 and Γ(f → 4 π) saturates the f inelasticity. A 2 s.d. upper limit of 0.09 is found for the branching ratio $\text{(f → ηη)}\text{(f → 2π)}$.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

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.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

The role of instantons in generation of mesonic mass spectrum

It is suggested that instantons play the leading role in the mixing of $\text{s}\text{s and}\text{u}\text{u}\text{+}\text{d}\text{d}$ quark states in mesonic nonets and in the explanation of the Okubo-Zweig-Iizuka (OZI) rule. The non-diagonal polarization operator Π^su = 〈0|T{j^s(x)j^u(y)}0〉 is considered where $\text{j}{}^{\mathrm{<mtext>s</mtext>}}\text{=}\text{s}\text{O}\text{s}$ and $\text{j}{}^{\mathrm{<mtext>u</mtext>}}\text{=}\text{u}\text{O}\text{u}$ are the currents of the s and u quarks. It is proved that in the dilute instanton gas approximation for quarks in the external instanton field Π^su = 0 for the vector and tensor currents and Π^su≠0 for the axial current. Hence, after saturating Π^su by the low-lying mesonic states, we obtain the qualitative explanation of the OZI rule. The Q² dependence of the non-diagonal polarization operator of the axial currents, Π^su(Q²), is calculated and compared with the η′ meson pole term. Taking account of terms ～m_q² allows one, using the experimentally known ηη′ mixing angle, to find the η′ meson coupling constant with the axial current F_η′ ≈ 150 MeV and to estimate the η′π mixing angle.     

Non-perturbative QCD effects at large momentum transfers

We calculate the simplest one-instanton correction to the perturbative QCD prediction for e⁺e^? annihilation to hadrons. At high centre-of-mass energies Q we find a contribution to the total cross section from a simple fermion loop of the form

$\text{δR}\text{R}\text{∝}\text{Q}{}^2\text{→∞}\text{Q}{}^{\mathrm{<mtext>?11?</mtext><mtext>Nf</mtext><mtext>3</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)</mtext><mtext>or</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)?1</mtext>}}$

where N_f is the number of quark flavours. The numerical value of this contribution is O(1) for Q ～ 1 to 2 GeV.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

Electromagnetic effects in the production of dimuons at large transverse momentum

The effects of single-photon corrections to the simple Drell-Yan mechanism $\text{(}\text{q}\text{q}\text{→ γ}{}^1\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{)}$ are studied for massive dimuons at large transverse momentum in the processes $\text{π}{}^{\mathrm{?}}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X and}\text{p}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X}$. It is found that single-photon emission by the muons constitutes an important correction to the effects of single-gluon emission by the quarks for very massive (M_μμ² ? m_μ²) muon pairs.Interference of the amplitude for photon emission from the muons with that for radiation from the quarks generates an asymmetry in the muon angular distribution. The forward-backward asymmetry is studied in detail as a function of pair mass and transverse momentum.     

An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

A class of solutions of Einstein-Maxwell equations

A metric defined by $\text{ds}{}^2\text{= [}\text{(p}{}^2\text{+ q}{}^2\text{)}\text{P}\text{] dp}{}^2\text{+ [}\text{P}\text{(p}{}^2\text{+ q}{}^2\text{)}\text{](dτ + q}{}^2\text{dσ)}{}^2\text{+ [}\text{(p}{}^2\text{+q}{}^2\text{)}\text{Q}\text{] dq}{}^2\text{? [}\text{Q}\text{(p}{}^2\text{+ q}{}^2\text{)}\text{](dτ ? p}{}^2\text{dσ)}{}^2$, with P = P(p), Q = Q(q), is studied; the first sections investigate its connections and curvature; the metric is of type D, with Einstein tensor of the electromagnetic algebraic type. Metrics with R = const are characterized by $\text{P}$ and $\text{Q}$ being polynomials of 4th order. In Section 5, by applying Rainich-Wheeler procedure, the electromagnetic field associated with the studied metric is constructed. Section 6 describes change-of-scale transformations of the derived solution of Einstein-Maxwell equations with λ; Sections 7 and 8 study geodesics and trajectories of charged test particles in the field of this solution; with H-J equation separable, the integration process reduces to quadratures. Section 9 gives a summary of basic results, Sections 10 and 11 investigate contractions of general solution with 6 continuous and 1 discrete parameter to the generalized NUT, anti-NUT and Bertotti-Robinson solutions. Section 12 specializes our general solution to the combined NUT and Kerr-Newman solution. Section 13 investigates a complex extension and the double Kerr-Schild form of our solution of Einstein-Maxwell equations with λ. Finally, Section 14 investigates the special-relativistic limit of the discussed solutions: a construction of a topology of flat space-time is proposed in such a manner, that in a sense it represents a “riemannian sheet” of the analytic structure of the electromagnetic field of the Kerr-Newman solution. Concluding remarks which indicate a further generalization of the present results, derived together with Demiañski, close this paper.     

Neutral K1(890) and ρ0 meson production in e+e− annihilation at ;s=29GeV

The production of neutral K¹(890) and ρ⁰ mesons was studied in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ using the High Resolution Spectrometer at PEP. Differential cross sections are presented as a function of the scaled energy variable z and compared to π⁰ and K⁰ production. The measured multiplicities are 0.84±0.08 ?⁰ mesons and $\text{0.57±0.09 K}{}^{10}\text{(890)}$ mesons per event for a meson momentum greater than 725 MeV/c. The ratios of vector meson to pseudoscalar meson production for (u,d), s and c quark are compared to predictions of the Lund model.     

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 $\text{δ(4μ}{}^2\text{) ?}\text{1}\text{2}$.