Quark Form Factor Research Articles

The infrared regularization dependence of the asymptotic behavior of the Sudakov form factor in QCD

We report the results of an explicit calculation of the leading contributions including O(α s 2) corrections to the asymptotic behavior of the quark form factor in QCD in the limit of large virtual mass of the photon. In contrast to previous investigations, we regularize infrared singularities by keeping either one (on/off), or both quarks (off) off shell, or both quarks on shell (on) and employing dimensional regularization in addition. Up to the investigated order, our final result is represented by the beginning of an exponential series, no matter which regularization prescription is chosen. We give a representation which comprises the three limits of the form factor in a uniform manner.

On the Quark and Lepton form factors

It is shown that if subquarks have no subcolour, the Quark (Lepton) form factors will have a nodal structure.

A measurement of σtot(e +e − → hadrons) for cm energies between 12.0 and 36.7 GeV

The ration R = σ(e +e − → hadrons) σ μμ was measured between 12.0 and 36.7 GeV c.m. energy W with a precision of typically ± 5.2%. R is found to be constant with an average R = 4.01 ± 0.03 (stat) ± (syst.) for W ⩾ 14 GeV. Quarks are found to be point-like, the mass parameter describing a possible quark form-factor being larger than 186 GeV. Fits including QCD corrections and a weak neutral-current contribution are presented.

Summing soft emission in QCD

We analyze multiple soft gluon emission in QCD. Leading and next-to-leading contributions to the effective quark form factor are resummed in impact parameter space at two-loop level. The cross section for e +e − → a + b + X is also given.

Asymptotic behavior of the Sudakov form factor in quantum chromodynamics

In this paper we give an algorithm to compute the asymptotic behavior of the on-shell quark form factor in the limit of large momentum transfer (Sudakov form factor) in Abelian and non-Abelian gauge theories. We ignore terms which are suppressed by a power of momentum transfer, but keep all nonleading logarithms of the momentum transfer and all powers of the coupling constant.

Asymptotic dynamics of QCD, coherent states, and the quark form factor

The method of asymptotic dynamics for large times developed by Kulish and Fadde'ev for QED is applied to QCD. We study the solution and calculate the on shell quark form factor in leading logarithmic order.

Logarithmic approximations, quark form factors, and quantum chromodynamics

The structure of perturbative quantum chromodynamics in kinematic regimes characterized by two large but different mass scales is investigated. The double-leading-logarithm approximation is reviewed, and the roles of the various elements of this approximation are emphasized. In particular, the question of whether a suppression of cross sections in the limit of small angles and large ratios of kinematic variables is predicted by the theory is treated at various levels of approximation. Improved analysis suggests that no suppression is predicted. It is argued, however, that a definitive answer can only arise from an exact analysis.

The quark form factor in quantum chromodynamics

It is shown how leading logarithmic predictions of certain quark form factor effects in QCD, such as the suppression of the Drell-Yan process at small transverse momenta and of the collinear energy-energy correlation in e +e − annihilation, are invalidated by non-leading logarithms corresponding to the vectorial cancellation of gluon transverse momenta. Simple improved expressions incorporating this phenomenon are presented.

Quark form factors and leading double logarithms in quantum chromodynamics

Perturbative quantum chromodynamic corrections involving the emission of gluons that are both soft and collinear are discussed for both hadronic production of lepton pairs and e/sup +/e/sup -/ annihilation. The result is an exponential, double logarithmic quark form factor. The differences between previous analyses are clarified, and the possible experimental observation of the form factor is discussed and illustrated. 9 figures, 1 table.

A treatment of hard processes sensitive to the infrared structure of QCD

We propose a modified jet evolution equation which resums large corrections to the usual leading logarithmic approximation when phase-space constraints expose the singular infrared structure of QCD. The modification, which consists simply of a rescaling of the argument of the running coupling constant, is based on perturbative arguments verified at the fourth-order level. Processes analyzed by this method include the quark (Sudakov) form factor, the large moments of structure and fragmentation functions, the asymptotic behaviour of multiplicities and the clustering of final quanta in colourless systems which occupy finite regions of (momentum and position) phase space.

On exponentiation of the singlet quark form factor in the leading-logarithm approximation

The leading-logarithm approximation of the singlet quark form factor is studied. In arbitrary order of perturbation theory the leading asymptotics of graphs involving no more than one three-gluon vertex is calculated. Cancellation of terms proportional to the Casimir operator CA is shown.

Exact Second Order Calculation of the Quark Form Factors in QCD

Exact Second Order Calculation of the Quark Form Factors in QCD

The on-shell QCD quark form factor and its determination from two-particle correlations in e +e − annihilation

Opposite side correlations in hadron jets produced in e +e − annihilation provide a possibility to measure directly the on-shell QCD quark form factor. Comparing recent PLUTO data with the leading log prediction yields 0.54 ± 0.1 GeV for the QCD parameter Λ.

Next-to-leading logarithms in the high-energy asymptotics of the quark form factor and the jet cross section

The logarithms ∼ α s n ln 2 n ( Q 2/ μ 2) and ∼ α s n ln 2 n−1 ( Q 2/ μ 2) in the asymptotics of the quark form factor in the Sudakov region Q 2 = | q 2|>| p 2| = | p′ 2| = μ 2 are summed. We get the simple result S(Q 2, μ 23) = exp − α s(μ 2 2φ C F 1n 2 Q 2 μ 2 + 3α s(μ 2)C F 4φ 1n Q 2 μ 2 The same expression S( Q 2, M 2) describes the jet cross section in the e + e −→ q q process where the jet is defined as a set of particles whose total invariant mass does not exceed M 2. The QCD predictions are compared with the experimental data available and the jets observed are shown to be much broader than QCD predicts.

Hard semi-inclusive processes in QCD

We present formulae resulting from a complete perturbative analysis of differential cross sections of (i) massive lepton pair production in hadron collisions, (ii) leptoproduction of a particle from the current fragmentation region, (iii) production of two particles from opposite jets in e +e − annihilation into hadrons. A new effective double logarithmic quark form factor is derived, which manifests itself in these processes. Experimental investigation of two-particle angle correlations in e +e − annihilation provides a possibility to measure directly this form factor and thus to make a nice test of QCD.

Instantons - how significant numerically at short distances?

It is attempted to calculate the instanton effects in the hadronic cross section of e +e − annihilation, the magnetic form factor of quark, and the potential of heavy quark-antiquark by expanding the quark-instanton interaction in the dilute gas limit.

Renormalization group and infrared behaviour in theories with coupled massless fields

The renormalization-group method is applied to investigate the infrared singularities in gauge theories with Abelian or non-Abelian symmetry, involving both massive and massless fermions. In the Abelian gauge model the infrared structures of massive and massless fermion propagators and of a massive fermion form factor are found. In the non-Abelian gauge model (quantum chromodynamics) the infrared behaviour of a massless gluon propagator and a massive quark form factor is considered in the logarithmic approximation.

Non-leading contributions to the asymptotic behavior of the quark form factor

We have explicitly calculated, to fourth-order in perturbation theory, the first non-leading contributions to the quark ( p, m)-quark ( p, m)-color-singlet current ( q = p′ − p) form factor in the region − q 2 ⪢ p 2 ≈ p′ 2 ⪢ m 2. These contributions, together with the leading ones, combine into the simple form F 1 = exp{ B 1 [ p; p′; g( k 2/ M 2; g M )]} where B 1 [ p; p′; g( k 2/ M 2; g M )] is the lowest-order contribution calculated replacing the renormalized coupling g M by the invariant running charge g( k 2/ M 2; g M ) = g M + β 0 g M 3 log k 2/ M 2 + O( g M 5), β 0 being the one-loop β-function coefficient and k the internal gluon momentum. This result, if true to all order and for all non-leading terms, implies that the asymptotic behavior of the form factor cannot be determined unless both the short-distance and long-distance behavior of g( k 2) are known.

Calculations of the infrared behavior of quantum chromodynamics: The color-singlet quark form factor in the near-mass-shell regime

Calculations of the infrared behavior of quantum chromodynamics: The color-singlet quark form factor in the near-mass-shell regime

Summing infrared singularities in non-abelian gauge theories: The behavior of the exclusive color-singlet quark form factor

The near-mass-shell behavior of the exclusive color-singlet quark form factor is calculated up to the two-loops. In the Landau gauge the result can be expressed as the second order expansion of exp [ B( p, p′; g 2 ( k 2))], where B( p, p′; g 2( k 2)) is the lowest order contribution evaluated with a gluon propagator of the form (−i/( k 2 − i ε)) ( g μν − ( k μ k ν / k 2) × g 2( k 2) being the long-distance invariant charge. This result is valid to all orders, in an order by order near-mass-shell leading logirithm approximation.