Lowest-order Cross Section Research Articles

One-loop corrections for e +e − annihilation into μ+μ− in the Weinberg model

Analytical experessions for the e +e − → μ + μ − cross section including all the one-loop radiative corrections in the context of the Weinberg model are presented. The systematic calculation of one-loop diagrams has been carried out using a recently proposed scheme. Numerical results are shown in a region from 40–200 GeV c.m. energy and different values of the scattering angle; they indicate that the percentage corrections are mainly due to soft photons. The only departure from QED-like correction can be seen in a region where the lowest-order cross section is lowered by weak-e.m. interference. In that region hard photon contributions are relatively prominent and perhaps within experimental possibilities.

A leading log derivation of the Sterman-Weinberg jets

Per turba t ive quantum ehromodynamics (QCD) has emerged as the leading candidate for a theory of strong interactions at (( short-distances >>. I t predicts scale-breakings which is identical to the violation of Bjorken scaling in lepton-hadron reactions derived using the operator product expansion (~). Furthermore, the universal i ty of the scalingbreaking for all hard-scat ter ing processes (~.7) provides the theoret ical justification for the applicat ion of the par ton model in reactions like dilepton production in hadronic collisions (s) and hadronie processes at large PT (9.10). The partonic structure of leading log QCD calculations is demonstrated in the work of ALTAR]~LLI and PAnISl (1~). In a specific gauge, the diagrams contr ibut ing lead ing logs are generalized ladders with emit ted QCD quanta eollinear to ini t ia l or final QCD quanta (4-~). This shows tha t for a hard-scat ter ing process (e.g. quark-current), the cross-section is given as a convolut ion of the lowest-order cross-section with a resealed par ton dis t r ibut ion q(x, Q2), where Q2 is a typical large invar iant of the process. The rescaled par ton dis tr ibut ion is determined via the Altarel l i -Paris i functions, which give the probabi l i ty to find within a QCD par ton another collincar parton.

Study of the photodetachment ofC−andF−by many-body perturbation theory

Photodetachment cross sections of ${\mathrm{C}}^{\ensuremath{-}}$ and ${\mathrm{F}}^{\ensuremath{-}}$ are calculated by means of the many-body perturbation theory with multiple basis sets. The ${V}^{N\ensuremath{-}1}$ basis set is defined to include the intrachannel interaction. The ${V}^{N\ensuremath{-}2}$ basis set is introduced to describe the correlation in the Hartree-Fock ground states of negative ions. The lowest-order cross sections agree very well with experiment. The first-order corrections are calculated in the case of ${\mathrm{F}}^{\ensuremath{-}}$, and a large cancellation is found between the initial-state correlation and the final-state interchannel interactions. The importance of the use of the energy relations in the lower-order calculations is pointed out.

Neutrino-pair production by photons

The neutrino-pair production process\(\gamma + \gamma \to \nu + \bar \nu \) is considered. Using an intermediate-boson theory, the cross-section for νe,\(\bar \nu _e \) and for ν μ ,\(\bar \nu _\mu \) production is evaluated to lowest order by dispersion relation techniques. The result is found to be essentially the same whether one uses the Haller, Landovitz and Goldberg intermediate-boson theory or the Lee and Yang intermediate-boson theory. The lowest-order nonvanishing matrix element is of the order ω3, and hence the lowest-order cross-section is of the order ω6. For electron-type neutrinos and a boson mass of 2 GeV, one obtains σ =(4.8)(10−46)(ω/Mp)6 cm2 whereMp is the proton mass. The corresponding black-body neutrino luminosity isL =(2.4)(10−7) · (T/109)13 erg/cm3s. For muon-type neutrinos, both of the above formulas are reduced by a factor of ten.