Mass Singularities Research Articles

Electromagnetic electron-positron pair production in heavy-ion collisions with impact parameter zero.

We present a calculation of the second-order process of electron-positron pair creation by the electromagnetic fields of two relativistic heavy ions for impact parameter b zero. Total probabilities as well as differential ones are presented. A comparison with the results of the double equivalent-photon approximation (DEPA) shows explicitly the inapplicability of this approximation in the case of total probabilities. We discuss the creation of pairs with large invariant mass. The DEPA results are too high, which can be traced back to the mass singularity of the photon cross section at very small angles, giving a discrepancy, whereas the agreement between our result and DEPA is good for larger angles.

Cancellation of mass singularities in thermal reaction rates.

Thermal amplitudes exhibit mass singularities when particle(s) with vanishing mass is (are) involved. We show that such singularities do not appear in the perturbation expansions of the thermal reaction rates, provided the theory in consideration does not bring about such mass singularities in zero-temperature reaction rates. The latter is supposed to be the case for physically sensible quantities in a wide class of theories, including QED and QCD (Kinoshita-Lee-Nauenberg theorem).

Charge Mass Singularity in Two-Dimensional Hubbard Model

Two-dimensional Hubbard model with both nearest- and next-nearest-neighbor transfers is studied. A singularity in the charge susceptibility at the Mott transition point δ→0 is observed, leading to the anomaly of the charge mass m c * in the form m c * ∝|δ| -1 , where δ is the doping concentration. The singularity is similar to that in the case without the next-nearest-neighbor transfer. This indicates that the singularity in the charge mass is a universal nature of this model, irrespective of its band structure.

High-energy factorization in QCD and minimal subtraction scheme

The relationship between high-energy factorization and the factorization theorem of mass singularities is fully established by performing a complete resummed calculation in dimensional regularization. This result is achieved by deriving and solving a new evolution equation for the gluon-gluon forward scattering amplitude at high energy in n space-time dimensions. This equation reduces to the Balitskii-Fadin-Kuraev-Lipatov equation in the limiting case of four dimensions.

Coherent-state parametrization of the QCD long-distance dynamics

A parametrization of long-distance effects in perturbative QCD is proposed based on the concept of coherent-state scattering, that follows from the asymptotic properties of the S-matrix in massless theories. The resulting perturbation theory is free of mass singularities and independent of mass regulators. As an application, the flavour-singlet axial anomaly is perturbatively calculated and proven non-zero and mass-regulator independent.

Gauge-fixing dependence of gluon and quark-damping rates in hot quantum chromodynamics

The recently observed gauge-fixing dependence in covariant gauges of the damping rates of the quantum chromodynamics (QCD) gluonic and fermionic excitations at high temperatures and long wavelengths is reviewed. The analysis is based on the method by Braaten and Pisarski for resumming hard thermal loops using the Ward identities satisfied by the effective propagators and vertex functions. A proposed resolution of the gauge problem by regularizing the mass singularities is also discussed.

Partons and the EMC spin effect

We focus on the parton model and the role of the axial anomaly in polarised deep inelastic scattering. We show that the axial anomaly is relevant to each of the higher moments of the spin dependent structure functiong 1 (x) and not just the first moment. This result implies that the factorisation of mass singularities is not sufficient to define the parton model in spin dependent QCD. (It is certainly a necessary condition.) We also need to consider the locality of the photon parton interaction. The anomaly is observed over allx in the EMCg 1 (x) data.

GLUONIC CONTRIBUTIONS TO SPIN-DEPENDENT WEAK STRUCTURE FUNCTIONS: METHOD OF FACTORIZATION

We compute the gluonic contributions to the spin-dependent weak structure functions [Formula: see text](i=1, 3, 4), using the factorization theorem in the minimal subtraction scheme, [Formula: see text]. We have considered the most general case where the quark flavor masses are distinguished and the gluons are off mass shell. The gluonic contribution to the first moment of [Formula: see text] is found to vanish and [Formula: see text] do not receive leading order gluonic contribution. These results are shown to be free of mass singularities.

The two-loop three-point functions. General massive cases

We present a calculation of the two-loop three-point scalar functions for the two overlapping topologies. These are the master functions for the ladder and the crossed ladder graphs. We also present a method for the extraction of possible (on-shell) mass singularities.

Logarithmic pion-mass singularities in the radiative corrections to tau --> pi nu tau.

We study the logarithmic pion-mass singularities in the radiative corrections, to order {alpha}, to the decay {tau}{r arrow}{pi}{nu}{sub {tau}}. We show that such contributions are independent of strong-interaction effects. We verify that the total decay rate is in agreement with the Kinoshita-Lee-Nauenberg theorem on the cancellation of mass singularities.

Production rate of hard thermal photons and screening of quark mass singularity

The emission of hard real photons from a quark-gluon plasma at high temperatures is studied. At lowest order the QCD processes for quark-antiquark annihilation\((q\bar q \to \gamma g)\) and for Compton scattering (qg→γq) lead to logarithmically divergent thermal production rates for massless quarks. By applying recently developed resummation methods of finite temperature perturbation theory we show that effects due to Landau damping on the exchanged quark provide finite rates. Comparisons with previous estimates and phenomenological implications are discussed.

Calculation of the quark damping rate in hot QCD.

We present a complete calculation of the quark damping rate at zero momentum, to leading order in the QCD coupling constant g at a nonzero temperature T. All terms of leading order in g are included by the resummation of an infinite subset of higher-loop diagrams. At zero momentum the damping rates for the quark and the plasmino (a collective mode with opposite chirality and/or helicity) are equal: for three flavors of massless quarks, the result is \ensuremath{\gamma}\ensuremath{\simeq}0.151${\mathit{g}}^{2}$T. We also examine the recent controversy over the gauge dependence of the quark damping rate, and show how it is resolved when dimensional regularization is used as an infrared regulator of mass singularities.

Production of gamma gamma pairs in a hot quark-gluon plasma and shielding of the quark mass singularity.

We study the thermal production of large-invariant-mass photon pairs emitted from a quark-gluon plasma at high temperature. To lowest order in perturbation theory the cross section for the annihilation process $q\overline{q}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ is known to lead to logarithmically divergent thermal production rates for massless quarks. We apply recently developed resummation methods of finite-temperature perturbation theory and show how screening effects on quarks in the plasma provide finite thermal rates for $\ensuremath{\gamma}\ensuremath{\gamma}$ pairs. We compare these results with previous estimates of $\ensuremath{\gamma}\ensuremath{\gamma}$ production rates. Finally, for the phenomenology of heavy-ion collisions we present the screened $\ensuremath{\gamma}\ensuremath{\gamma}$ emission spectra by taking into account the space-time history of these collisions.

Physical consequences of mass singularities

We argue that the perturbation expansion of massless field theories are uniquely and unambiguously defined for properly formed observables. In so doing, we generalize the Kinoshita-Lee-Nauenberg theorem to show that there are no observable “mass-shell anomalies”. Paradoxically, in realistic circumstances, massive electrons give rise to non-intuitive, enhanced effects, for example, an unexpected background to the search for right-handed charged currents at HERA.

One-Loop QCD Corrections to the Inclusive Production Cross-Section for Heavy Quarks inp Collisions at High Transverse Energies

We calculate one-loop QCD corrections to the production cross-section for heavy quarks in protonantiproton collisions. We are interested in the behaviour of the cross-section at high transverse energies. At high PT the quark mass should become an irrelevant parameter. Therefore we work in the framework of massless QCD and absorb all mass singularities in a redefinition of the parton densities and fragmentation functions. Numerical results of the cross-section at √S = 0.63, 1.8 and 10 TeV are presented and the dependence of these results on the factorization scheme is examined.

ONE-LOOP RADIATIVE CORRECTIONS TO A HEAVY TOP DECAY IN THE STANDARD MODEL

We study one-loop radiative corrections to the top-quark decay: t→bW. For a heavy top (i.e. mt≳100 GeV ), simple analytic formulas are derived. For the inclusive process, t→bW+X due to QCD, cancellations of infrared and mass singularities are shown explicitly. The final result agrees with an earlier calculation in the literature, and is an 8% reduction in the partial width for αs=0.1. Also, leading terms of the electroweak corrections are shown to be proportional to an enhancement factor [Formula: see text]. Their effect is about 1-3%. We also study the angular distributions of the leptons from the subsequent exclusive (or semi-inclusive) W decay. An asymmetry parameter which measures the polarizations of the W is introduced. We find that it is sensitive to the QCD corrections especially in the vicinity of [Formula: see text].

A comment on form factor mass singularities in flavor-changing neutral currents

Flavor-changing effective verticesq l q h V 0, whereV 0 represents a neutral gauge boson (γ,Z 0,g), involving a heavy external quark, are discussed within the standard model at one-loop level and second-order approximation in external momenta and masses: the logarithmic singular terms in the form factors at vanishing mass of the internal quark in the loop have to be replaced by pieces coming from next order in external momenta. Implications in theb→d+X penguin transitions are commented.

Smooth massless limit of QED

Massless QED is studied by introducing different regularization schemes for the resulting mass singularities. It is demonstrated, for the one-loop corrections to electron scattering off an external potential, that cancellation of regulator-dependent finite parts within a Lee and Nauenberg (LN) set renders the observable process unique, thus establishing existence of its smooth massless limit.

Finite-temperature radiative corrections to early universe neutron-proton ratio: Cancellation of infrared and mass singularities

Finite-temperature radiative corrections to the weak neutron-proton decay rates are examined in the framework of real-time field theory. It is shown that infrared and collinear (electron mass) singularities cancel at O(α) when the total neutron ↔ proton conversion rates are computed. As a consequence, their perturbative expansion is valid at this order and may be used in helium abundance estimates.

Smooth mass corrections to massless theories

We analyze the transition from massive to massless theories in cases in which mass singularities are present. In massless theories these singularities are absorbed into densities or fragmentation functions. We define a subtraction procedure for massive theories which is a canonical generalization of the “minimal subtraction” in massless theories. We use this procedure to calculate smooth mass corrections to the structure functionsF 2 andG 1 of deep inelastic scattering. In particular we show how, in our scheme, heavy quarks affect the spin of the proton.