Effects of vacuum polarization and of proton polarizability in the Lamb shift of muonic hydrogen

The contributions to the Lamb shift in muonic hydrogen from hadronic vacuum polarization and from the correction associated with electron vacuum polarization and with the proton polarizability are calculated by using present-day experimental data on the cross section for e ⁺ e ⁻ annihilation into hadrons and on structure functions for deep-inelastic ep scattering. The numerical value of the total contribution to the (2P-2S) shift in muonic hydrogen is found to be 10.95 μeV. __________ Translated from Yadernaya Fizika, Vol. 64, No. 7, 2001, pp. 1358–1363. Original Russian Text Copyright ? 2001 by Martynenko, Faustov.     

A new unitarity bound on e+e− annihilation

Unitarity relates σ_h the electron-positron annihilation cross-section into hadrons and σ_μ the cross-section into muon pairs. This relation provides much more restrictive bounds on σ_h than the simple unitarity bound, for the case in which the hadronic channels dominate the total annihilation cross-section.     

Electron-positron annihilation above 2 GeV and the new particles

This paper reviews the experimental and phenomenological aspects of electron-positron annihilation into hadrons at center-of-mass energies above 2 GeV. The behavior of the total cross section for hadron production as a function of energy is described; and the important parameter R - the ratio of this cross section to the muon-pair production cross section - is discussed. Data on charged particle multiplicities, particle production ratios, and single particle inclusive distributions is also summarized. The paper than summarizes our knowledge of the newly discovered ψ particles; and examines the various theories as to their nature and their relation to conventional hadronic physics.     

Uncertainties in the hadronic contribution to the QED vacuum polarization

We describe an updated evaluation of the hadronic contribution to the QED vacuum polarization. It is obtained from a dispersion integral over the measured cross section ofe ⁺ e ^?→hadrons.     

Hadronic vacuum polarization correction in muonic atoms

The contribution of hadronic vacuum polarization to the energy levels of muonic atoms is reevaluated using an improved parametrization of the total cross section for e⁺ e^?→hadrons. The numerical results can be simply related to the correction due to muonic vacuum polarization.     

Search for narrow resonances in e+e− annihilation into hadrons at adone in the mass region 2.5–3.0 GeV/c2

The mass region 2.5 to 3.0 GeV/c² has been searched for evidence of ψ-like narrow resonance in e⁺e^? annihilation into hadrons. No evidence for new narrow resonances has been found with a sensitivity of about the 10% of the integrated cross section of the J/ψ (3100).     

Total cross section for hadron production bye + e − annihilation between 9.4 and 9.5 GeV

The total cross section fore ⁺ e ^? annihilation into hadrons for center of mass energies from 9.4 to 9.5 GeV has been measured with the nonmagnetic DESY-Heidelberg detector at DORIS. A value ofR=σ_had/σ_µµ=3.8±0.7 for the continuum region around the Υ (9.46) resonance has been determined. The ratioΓ _ee Γ _had/Γ _tot of electronic, hadronic and total widths has been reevaluated to be (1.00±0.23) keV for the Υ resonance and (0.37±0.16) keV for the Υ′. In addition, a search for directly produced pohotons from Υ decays of the type Υ→γ+gluon+gluon has been performed. The Υ decay into muon pairs has also been searched for.     

Evolution of parton densities beyond leading order: The non-singlet case

We develop a technique, based explicitly on the factorization properties of mass singularities, which allows one to calculate the evolution of parton densities beyond leading order. We present the results for the evolution of hadronic structure functions as well as for parton fragmentation functions into hadrons. Within our scheme the predictions for a particular process are obtained by convoluting a universal parton density with a “short-distance” cross section specific to the process. As an application, we calculate the QCD predictions for the Q² dependence of deep inelastic lepton-hadron scattering and of one-particle iclusive e⁺ e^? annihilation cross sections. Our results for electroproduction agree with those obtained with the operator product expansion technique. Physical quantities in scattering are related to the corresponding ones in annihilation by analytic continuation, whereas the Gribov-Lipatov relation is strongly violated.     

Scanning of the e + e − → π+π− cross section below 1 GeV at DAΦNE by radiative events

The tagged photon events for the measurement of the e ⁺ e ^? → π⁺π^? total cross section by the radiative return method at DAΦNE is discussed. The effects caused by the not exactly head-on collision of beams and by the QED radiative corrections are investigated. The essential part consists of the analysis of the event selection rules that ensure the rejection of the 3-pion hadronic state and take the main properties of the multiple purpose KLOE detector into account. The study of the non-head-on effect is performed in the Born approximation by integrating over the tagged photon angles, whereas the radiative corrections are calculated neglecting this effect. Together with the quasireal electron approach, this allows us to derive analytical formulas for the correction to the cross section of the initial-state radiative process. Some numerical calculations illustrate our analytical results.     

Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low-energy e ⁺ e ^? colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on τ decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and τ decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.     

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions

A new approach is proposed to the problem of the relationship between the e⁺e^? hadron annihilation cross section and the behaviour of the hadronic vacuum polarization tensor Π_μν(q) in the space-like region. By using this approach based on the principles of functional analysis, one can uniquely transform the information about the behaviour of Π_μν(q) at q² → ?∞, which is available in asymptotically free theories and in theories with anomalous dimensions, into constraints on the e⁺e^? total cross section.     

Results and techniques of multi-loop calculations

In this review some recent multi-loop results obtained in the framework of perturbative quantum chromodynamics (QCD) and quantum electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore, the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low-energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α_s⁴ and α_s³, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e⁺e⁻ annihilation. The knowledge of the complete mass dependence at order α_s² has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α² QED corrections to the μ decay. Its relevance for the determination of the Fermi constant G_F is discussed. Finally, the calculation of the three-loop relation between the $\text{MS}$ and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the appendix, where also explicit analytical results are listed.     

Photoproduction of πΔ(1236) from protons below 1.1 GeV

A model for the annihilation of electron-positron pairs into hadrons for q² = s > 4 GeV² and up to the highest measured energies is developed. The main ingredients are point-like couplings between three resonances and photons and the high level of opening thresholds that follows from an effective Lagrangian formalism. The model gives an almost constant annihilation cross section, soft pions everywhere and at all energies, high multiplicities and a large absolute cross section. The details of all exclusive channels are also predicted. Other consequences of this point of view concern the discovery of hitherto ignored couplings in low-energy photon initiated reactions. We argue that the energy regime explored by SPEAR is not the asymptopia and we discuss possible further constancy of the cross section in a range of s.     

Effects of neutral weak currents in inclusive e+e− annihilation

Inclusive e⁺e^? annihilation into n hadrons is studied in one-photon and one-neutral Z-meson exchange approximation for polarized e⁺e^? beams. The measurability of the hadronic structure functions and weak effects are discussed for arbitrary n.     

Weak Neutrino-Lepton Annihilation into Hadrons

An exploratory study of weak neutrino-lepton annihilation into hadrons, v̄_l + l → hadrons is presented. Simple cross-section estimates indicate processes of this type may be observable in a large bubble chamber. We discuss the information one could hope to obtain from such experiments. General formulas for amplitudes and cross sections are given for v̄_l + l → hadrons assuming a point-like V – A interaction. To establish tests of the V – A interaction, we recalculate the annihilation amplitudes assuming a point-like scalar-pseudoscalar or tensor-pseudotensor interaction. The extension to theories with intermediate vector bosons is sketched. We discuss the connection between v̄_l + l → hadrons and e⁺e⁻ → hadrons implied by the conserved vector current hypothesis. We note that in v̄_l + l → rH, K⋆(890), A₁, B creation (these reactions enjoy comparatively large cross sections) the leptonic as well as hadronic couplings of these J = 1 , I = 1/2 or 1 mesons could be determined. A related possibility is the direct creation of new heavy charged J = 1 mesons. The normal J = 1 resonance region could be explored with neutrino energies of the order 500–2000 GeV. For this, and for higher-energy work, a TeV proton accelerator is clearly necessary.     

First measurements of positronium total scattering cross sections

A new type of experiment has been devised in which ortho-positronium diffusion to the metal walls of a series of parallel-sided cells is studied by measuring the annihilation lifetimes. Experimental results are subjected to an analysis in which two parameters are varied to give a best fit, one of the two parameters being the scattering cross section. The method requires a number of systematic corrections which have still to be worked out. Preliminary cross section values for helium, argon and isobutane are 0.017 πa ₀ ² , 0.09 πa ₀ ² , and 0.54 πa ₀ ² , respectively.     

Scanning of hadra]on cross section at DAΦNE by analysis of the initial-state radiative events

The initial-state radiative events in electron-positron annihilation into hadrons at DAΦNE are considered. The corresponding cross section with the full first-order radiative corrections is calculated. The analytical calculations take into account the actual angular acceptance and energy cutoff of the DAΦNE photon detector. Zh. éksp. Teor. Fiz. 69, No. 11, 769–775 (10 June 1999)     

Momentum analysis of kaon and pion pairs produced from time-like photons at 1.6 GeV energy

We present results for the total cross section of e⁺e^? annihilation into two hadrons at 1.6 GeV: σ_ππ = σ_KK = (1.8 ± 1.1) × 10^-33 cm².From these values we obtain the time-like electromagnetic form factors these mesons: |F_π|² = 0.24 ± 0.14 and |F_K|² = 0.46 ± 0.26.     

Annihilation of slow antiprotons in flight and in traps

The antiproton-nucleus annihilation in two possible experimental situations (low energy in-flight annihilation and annihilation in a trap) is investigated taking into account the Coulomb interaction. For these two cases, the formulas giving the relation between the antiproton-nucleus scattering lengtha _cs and observables (annihilation cross section and antiprotons time-of-life in a trap) are obtained. These relations are proposed to determinea _cs.     

Characteristics of double-pomeron exchange

A detailed kinematic study is made of the cross section for double-pomeron exchange. We consider reactions of the type a + b → c + d + (h₁ + h₂ + …) where a → c and b → d are quasi-elastic transitions with limited momentum transfer and (h₁ + h₂ + …) is a centrally produced hadron cluster. The dependence of the cross section on the relative azimuthal angle φ between the final hadrons c and d provides an important test for double-pomeron exchange. We calculate this φ-dependence for all cases of interest, using a model in which pomeron exchange is represented by an effective current-current interaction. For limited momentum transfer, where the pomeron spin is nearly equal to one, this model is equivalent to Reggeized pomeron exchange. We give a complete formalism for the partial-wave analysis of the double-pomeron reaction ab → cd + h₁₂ which differs from the one given by Rushbrooke and Webber. Furthermore, we discuss the two-pomeron vertex, and the construction of detailed and realistic models for double-pomeron reactions.