Simplified Bethe-Salpeter equation for positronium

The Bethe-Salpeter equation for a fermion-antifermion system, coupled by photons, is considered in the Feynman gauge. The kernel is that resulting from exchange of a single photon. The usual reduction of the sixteen B-S spinor amplitudes in terms of tensors leads to 16 coupled integro-differential equations. By straightforward application of charge conjugation-, parity-, and Lorentz-invariance, the system of coupled equations is reduced to ones involving no more than eight and as few as three scalar structure functions for the various parity, charge conjugation, and total angular momentum states. The results hold for arbitrary coupling strength. As a check of the equations obtained, a perturbation theory is carried out for the Coulomb interaction. It leads to effective potentials in agreement with those obtained previously to order mα⁴ for positronium.     

Intensity detection of picosecond ruby laser pulses by two photon absorption

The peak intensity of single picosecond light pulses from a mode locked ruby laser and its second harmonic is detected by two photon transmission measurements. The two photon absorption coefficients α⁽²⁾ of the applied crystals CdS and KI are measured (α⁽²⁾_CdS (14400 cm^-1) = 19 cm/GW, α⁽²⁾_KI (28 800 cm^-1) = 8 cm/GW) and calibration curves are presented.     

On the connection between the vacuum polarization potential in muonic atoms andg-2 of the muon

A simple connection, between the vacuum polarization potential used in muonic atoms and the muon anomaly arising from the second-order vertex graph with electron vacuum polarization insertions, is established. In particular, the leading log-term and the orderm _e/m _μ term are essentially the same in the two cases. We make use of this connection to determine the vacuum polarization potential in order α³(Zα).     

Quasi-confinement in theSU(3)-gluon plasma

We investigate a phenomenological equation of state for the gluon plasma, which differs from the ideal gluon gas equation of state in three aspects: (a) it is assumed that gluons withlow momentum are subject to confining interactions anddo not contribute to the energy spectrum of free gluons; (b)only gluons withhigh momentum are considered as an ideal gas with perturbative corrections of orderO(α_s); (c) a non-perturbative vacuum pressure is included. We show that feature (a) allows for a reasonable perturbative treatment of the interaction between gluons with high momentum. The equation of state reproduces lattice data for the thermodynamical functions of theSU(3) pure gauge theory above the deconfinement transition temperatureT _c. This result suggests that a possible way to describe the gluon plasma is in terms of perturbatively interacting gluons and non-perturbative “glueball” states.     

The Three-Boson System at Next-to-Next-to-Leading Order

We discuss effective field-theory treatments of the problem of three particles interacting via short-range forces (range R ≪ a ₂, with a ₂ the two-body scattering length). We show that forming a once-subtracted scattering equation yields a scattering amplitude whose low-momentum part is renormalization-group invariant up to corrections of O(R ³/a ₂ ³). Since corrections of O(R/a ₂) and O(R ²/a ₂ ²) can be straightforwardly included in the integral equation’s kernel, a unique solution for 1 + 2 scattering phase shifts and three-body bound-state energies can be obtained up to this accuracy. We use our equation to calculate the correlation between the binding energies of Helium-4 trimers and the atom-dimer scattering length. Our results are in excellent agreement with recent three-dimensional Faddeev calculations that used phenomenological inter-atomic potentials.     

Study of the Morin Transition in Pseudocubic α-Fe2O3 Particles

We have studied the Morin transition in nanostructured pseudocubic α-Fe₂O₃ particles of about 1.8 μm side. The preparation was carefully chosen to obtain a system with a very narrow crystallite size distribution and particles of homogeneous morphology. Two samples were studied: one without thermal treatment (α-Fe₂O₃(ap)) and another annealed at 673 K in air for 12 h (α-Fe₂O₃(an)). Both were characterized by XRD, SEM, TGA and Mössbauer spectroscopy. The results indicate that the Morin transition is suppressed for α-Fe₂O₃(ap), however, α-Fe₂O₃(an) has a T _M ≈ 230 K and the transition is completed over a very narrow temperature range. These results are discussed in connection with the crystallite size, the cell parameters, and the presence of OH^? groups (hydrohematite) or incorporated water (protohematite).     

A Gribov equation for the photon Green’s function

We present a derivation of the Gribov equation for the gluon/photon Green’s function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Trln?D(q), which we interpret as the gauge-boson ‘self-loop’. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, α _S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov’s light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a ∝ Q ² behavior for space-like Q ²=?q ². This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.     

Why are perturbative corrections to highP T hadron production in photon-photon collisions very small?

TheO(α _s ) corrections to the single hadron inclusive cross-section at high transverse momentum has recently ben found to be very small. This is in sharp contrast to similar corrections to Drell-Yan cross-sections where the first perturbative terms can more than double the size of naive parton model predictions. In this paper we present an intuitive explanation of these results. By considering gauge symmetries of various sets of Feynman diagrams, we have obtained well defined relationships between photon-photon ande ⁺ e ^? annihilation cross-sections. These have been used to study dominant sectors of the phase-space for the two processes, resulting in a simple interpretation of the perturbative results. A by-product is a much simplified algorithm which has enabled us to extend our previous no-tag calculation to the case of single-tag events. In particular, by keeping one of the incomming photons off-shell by an arbitrary amount, we have exposed photon mass dependence of the cross-section right down to the region of deep inelastic scattering on a photon target.     

QCD Jets at HERA II.O(α s 2 ) four-jet cross-sections

We present exact expressions for theO(α _s ² ) tree graph four-jet cross-sections in neutral current and charged current deep inelasticep scattering initiated by quarks, antiquarks and gluons including lepton polarization effects. Using helicity amplitudes the partonic cross-sections are given in concise form including all colour, flavour and statistical factors. We explicate the electroweak coupling dependence and state how the partonic cross-sections are folded with the respective parton densities to obtain theep jet cross-sections toO(α _s ² ). We present some numerical results for the neutral current one-photon exchange case. We elaborate on the cut dependence of the jet rates and present differential distributions in some basic kinematical variables.     

The Breit equation as a zeroth-order approximation for calculation of the bound-state energy

An equation whose kernel is determined by the one-photon exchange between interacting particles is analyzed in the framework of the Bethe-Salpeter formalism. This equation is considered as a zeroth-order approximation in the calculation of the corrections to the energy levels. This is the Breit equation that takes into account additional small terms (with respect to the parameter (Zα)²). A procedure that employs the Brillouin-Wigner perturbation theory and makes it possible to sequentially take into account the corrections to the energy levels is considered.     

Higher order QCD corrections to the photoproduction of a direct photon at HERA

The contribution of resolved photons to the photoproduction cross section of direct photons is reexamined. Higher order,O(α ² α _s), QCD corrections to this contribution are calculated and turn out to be important at HERA energies. The observation of direct photons in the medium-p _⊥ range (p _⊥～5 GeV/c) should provide the opportunity to measure the gluon content of the photon.     

Radiative corrections to positronium decay

In this work a method for calculating radiative corrections to positronium decay is presented that is direct, and allows for a systematic extension applicable to the calculation of corrections beyond the first [o(α)] correction. An expression for the decay amplitude in terms of the Bethe-Salpeter wavefunction is employed. The Bethe-Salpeter wavefunction is evaluated perturbatively in a scheme having a lowest-order bound state equation that is exactly soluble. The decay amplitude is evaluated in Coulomb gauge, without the introduction of a photon mass. One-loop renormalization in Coulomb gauge is shown to be consistent. Using this method the known analytic result for the o(α) correction to the parapositronium decay rate is obtained. The same method is applied to orthopositronium, and the existing theoretical discrepancy in the value of the o(α) correction to the decay rate is resolved. This o(α) correction is obtained with an error which corresponds to an uncertainty in the total rate much smaller than α²Γ_LO (where Γ_LO is the lowest-order rate). Also, the o(α) correction to the differential decay rate is computed for the first time.     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Two-loop QCD corrections to top quark width

We present O(α_s²) corrections to the decay t → bW in the limit of a very large top quark mass, m_t ⪢ m_W. We find that the O(α_s²) effects decrease the top quark decay width Γ_t by about 2%: Γ_t = Γ₀ (1 − 0.8α_t (m_t) − 1.7α_s²). The complete corrections are smaller by about 24% than their estimate based on the BLM effects O(α_s²). We explain how to compute a new type of diagrams which contribute to Γ(t → bW) at the O(α_s²) level.     

SUSY-QCD corrections to scalar quark pair production in e+e− annihilation

We calculate the supersymmetric O(α_s) QCD corrections to the cross section e⁺e⁻ → q̃_iq̃_j (i, j = 1,2) within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left-right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies, even for a gluino mass of a few hundred GeV.     

Remarks on optimized predictions for the Drell-Yan process

We discuss the optimization of the Drell-Yan pair production cross section calculated atO(α _s ) and compare it with theO(α _s ² ) results of van Neerven et al. It is shown that the optimized predictions do agree analytically with the latter calculation near the phase space boundary. They also provide a good numerical approximation wherever the stability equations have a solution.     

Theoretical studies of energy-energy correlation ine + e− annihilation

We calculate theO(α _s ² ) correction to the energy-energy corelation cross section ine ⁺ e^? annihilation using different resolution criteria in the limit of vanishing resolution cuts. We compare this in the back-to-back angular region with results of the logarithm approximation (LA) and deduce higher order corrections (beyondO(α _s ² )) from the LA formula. The final results are compared with recent TASSO data.     

Quantum electrodynamic corrections to the 23S1 → 11S0 + one photon transition rate in helium and helium-like lons

The order (Zα)⁵, α(Zα)⁴, and α(Zα)⁴ log(Zα) energy denominator and recoil corrections to the leading order (Zα)⁴ decay amplitude for the 2³S₁ → 1¹S₀ + one photon transition are considered. It is found that order α(Zα)⁴ terms arise in the individual diagrams but exactly cancel upon summation. In view of the results of this and other recent theoretical work it is concluded that the rates predicted by pure quantum electrodynamics are known to considerable precision. The recent discrepancy between theory and experiment in the decay rate for several helium-like ions appears to have been resolved by placing the detector farther downstream from the foil where the metastable states are produced. At present, all the experimental values are in good agreement with the theory.     

Three photon virtual annihilation contributions to positronium hyperfine structure

Three photon virtual annihilation contributions to the positronium hyperfine interval are calculated to order α⁶m(α⁴R_∞). The result is obtained in analytic form and leads to the small value of -0.91 MHz for the contribution to the ground state energy difference from this source.     

CompleteO(α) corrections to polarized Compton scattering

General expressions for Compton scattering and itsO(α) real and virtual corrections are given for electron and photon beams with arbitrary polarization. The expressions obtained are suitable for use in Monte Carlo simulations of Compton polarimeters planned for polarizede ⁺ e ^? colliders. The basis for the calculation is the spinor techniques recently applied to photon and gluon bremsstrahlung. The practical application of these techniques for massive fermions is discussed.