On-shell Quark Research Articles

Accessing the nucleon transverse structure in inclusive deep inelastic scattering

We revisit the standard analysis of inclusive Deep Inelastic Scattering off nucleons taking into account the fact that on-shell quarks cannot be present in the final state, but they rather decay into hadrons – a process that can be described in terms of suitable “jet” correlators. As a consequence, a spin-flip term associated with the invariant mass of the produced hadrons is generated nonperturbatively and couples to the target's transversity distribution function. In inclusive cross sections, this provides an hitherto neglected and large contribution to the twist-3 part of the g2 structure function, that can explain the discrepancy between recent calculations and fits of this quantity. It also provides an extension of the Burkhardt–Cottingham sum rule, providing new information on the transversity function, as well as an extension of the Efremov–Teryaev–Leader sum rule, suggesting a novel way to measure the tensor charge of the proton.

Non-thermal photon production in the quark–gluon plasma

We have implemented leading order photon production processes in nonequilibrium partonic transport simulations. These include Compton scattering, quark-antiquark annihilation and bremsstrahlung. We use BAMPS (Boltzmann Approach To Multi-Parton Scatterings), a numerical code which solves the 3+1d ultrarelativistic Boltzmann equation for massless on-shell quarks and gluons with Monte-Carlo methods. It allows us to study photon production microscopically, including strong nonequilibrium effects. BAMPS is applicable for the whole evolution of the quark-gluon plasma (QGP) in RHIC and LHC heavy-ion collisions, where the photon production is influenced by the chemical and thermal non-equilibrium state in the early phase. Highly energetic quark- and gluon jets will convert into or radiate photons, effects we include by default. We show results for photon spectra from the QGP and investigate its role for the elliptic flow of photons. The yield is smaller than results from other groups, the reason is the slow quark chemical equilibration. Photons induced by jet-like particles show very different momentum anisotropies compared to a hydrodynamically flowing medium.

Secondary lepton distributions as a probe of the top-Higgs coupling at the LHC

Abstract The differential distributions in rapidity and angles of the secondary lepton in the associated production of the top quark pair and higgs boson in proton-proton collisions at the LHC are quite sensitive to the top-higgs coupling. However, the effects of anomalous couplings of the most general $ t\overline{t}h $ interaction with operators of dimension-six that are clearly visible in the signal of the associated production of the top quark pair and higgs boson are to large extent obscured by the background sub-processes with the same final state. This means that analyses of such effects, in addition to higher order corrections that are usually calculated for the on-shell top quarks and higgs boson, should include their decays and possibly complete off resonance background contributions to the corresponding exclusive reactions.

DEAD CONE DUE TO PARTON VIRTUALITY

A general expression for the dead cone of gluons radiated by virtual partons has been derived. The conventional dead cone for massive on-shell quarks and the dead cone for the virtual partons have been obtained by using different limits of the general expression. Radiative suppression due to the virtuality of initial parton jets in heavy-ion collisions has been discussed. It is observed that the suppression caused by the high virtuality is overwhelmingly large as compared to that on account of conventional dead cone of heavy quarks.

A systematic study of direct photon production in heavy ion collisions

A theoretical derivation of photon bremsstrahlung, induced by the interactions of an energetic quark in a hot and dense quark–gluon plasma, is given in the framework of the reaction operator approach. For the physically relevant case of hard jet production, followed by few in-medium interactions, we find that the Landau–Pomeranchuk–Migdal suppression of the bremsstrahlung photon intensity is much stronger than in the previously discussed limit of on-shell quarks and a large number of soft scatterings. This result is incorporated in the first systematic study of direct photon production in minimum bias d+Cu and d+Au and central Cu+Cu and Au+Au heavy ion collisions at the Relativistic Heavy Ion Collider at center of mass energies s=62.4 GeV and 200 GeV. We find that the contribution of the photons created via final-state interactions is limited to 35% for 2 GeV<pT<5 GeV and at high transverse momenta the modification of the direct photon cross section is dominated by initial-state cold nuclear matter effects.

Third-order QCD results on form factors and coefficient functions

We summarize recent higher-order QCD results based, directly or indirectly, on the Mellin-space computation of the next-to-next-to-leading-order splitting functions governing the evolution of hadronic parton distributions. Specifically, we briefly present third-order results for the coefficient functions in inclusive deep-inelastic scattering (including the structure function F_3 not published so far), the on-shell quark and gluon form factors, and the total cross section for Higgs production at hadron colliders.

A perturbative determination of mass dependent [formula omitted] improvement coefficients in a relativistic heavy quark action

We present the results for a perturbative determination of mass dependent improvement coefficients ν, r s , c E and c B in a relativistic heavy quark action, which we have designed to control m Q a errors by extending the on-shell O ( a ) improvement program to the case of m Q ≫ Λ QCD , where m Q is the heavy quark mass. The parameters ν and r s are determined from the quark propagator and c E and c B are from the on-shell quark–quark scattering amplitude. We show that all the parameters, together with the quark wave function and the mass renormalization factors, are determined free from infrared divergences once their tree level values are properly tuned. Results of these parameters are shown as a function of m Q a for various improved gauge actions.

Four-momentum boosted fermion fields

A formulation of the fermion action is discussed which includes an explicit four momentum boost on the field prior to discretisation. This is used to shift the zero of lattice momentum to lie near one of the on-shell quark poles. The positive pole is selected if we wish to describe a valence quark, and negative pole for a valence antiquark. Like NRQCD, the typical lattice momenta involved in hadronic correlation functions can be kept small: of order O(αΛQCD), rather than O(amQ) even when describing heavy quarks. If we expand around the particle pole, the anti-particle correlator will be poorly described for large amQ. However, in that case the anti-particle will be far off shell and will only affect unphysical, renormalization factors. The formulation produces the correct continuum limit, and preliminary results have been obtained (for an unimproved action) of both the one-loop self energy and a non-perturbative correlation function.

Perturbative QCD with quark and gluon condensates

The quark 〈 ψψ〉 and gluon 〈 F μν F μν 〉 vacuum expectation values are non-vanishing at low orders in α s when the perturbative ground state includes quark and gluon pairs. This offers possibilities of studying the effects of a non-trivial vacuum using formally exact perturbative methods. The QCD Feynman rules are modified only for the free, on-shell quark and gluon propagators at zero four-momentum. Gauge and lorentz invariance is maintained, while chiral symmetry is spontaneously broken by the ground state.

Dressed gluon exponentiation

Perturbative and non-perturbative aspects of differential cross-sections close to a kinematic threshold are studied applying “dressed gluon exponentiation” (DGE). The factorization property of soft and collinear gluon radiation is demonstrated using the light-cone axial gauge: it is shown that the singular part of the squared matrix element for the emission of an off-shell gluon off a nearly on-shell quark is universal. We derive a generalized splitting function that describes the emission probability and show how Sudakov logs emerge from the phase-space boundary where the gluon transverse momentum vanishes. Both soft and collinear logs associated with a single dressed gluon are computed through a single integral over the running-coupling to any logarithmic accuracy. The result then serves as the kernel for exponentiation. The divergence of the perturbative series in the exponent indicates specific non-perturbative corrections. We identify two classes of observables according to whether the radiation is from an initial-state quark, as in the Drell–Yan process, or a final-state quark, forming a jet with a constrained invariant mass, as in fragmentation functions, event-shape variables and deep inelastic structure functions.

Power counting and β function in NRQCD

A computation of the NRQCD $\beta$ function both in the Lorentz gauge family and in the Coulomb gauge to one loop order endorses a velocity power counting scheme for dimensionally regularised NRQCD. In addition to the ultrasoft scale represented by bremsstrahlung gluons and the potential scale with Coulomb gluons and on-shell quarks, a soft r\'egime is identified in which energies and momenta are of order $Mv$, gluons are on shell and the quark propagator becomes static. The instantaneous gluon propagator has a non-zero vacuum polarisation only because of contributions from this r\'egime, irrespective of the gauge chosen. Rules are derived which allow one to read up from a given graph whether it is zero because of the homogene{\ia}ty of dimensional regularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order $Mv^2$ decouple from the theory.

Perturbative renormalization factors of bilinear operators for massive Wilson quarks on the lattice

Renormalization factors for local vector and axial vector currents for the Wilson quark action are perturbatively calculated to one loop order including finite quark masses from the ratio of the on-shell quark matrix elements in the Feynman gauge defined on the lattice and in the continuum. For large quark masses of order unity in lattice units, we find that finite quark mass effects are quite large: one-loop coefficients of the renormalization factors differ by 100% compared to those in the massless limit.

Electroweak calculations in the presence of nonperturbative quark self-energies.

Electroweak three- and four-point functions with two external quark legs are evaluated in the presence of arbitrarily momentum-dependent quark self-energy contributions of nonperturbative origin, such as those arising from QCD vacuum condensates. Gauge-parameter independence of $O({e}^{2})$ on-mass-shell quark two-point functions is recovered in the presence of such self-energies, provided electroweak three- and four-point functions retain consistency with the Ward identities arising from the Becchi-Rouet-Stora-Tyutin symmetries of the electroweak Lagrangian. These identities necessarily lead to departures from purely perturbative electroweak Feynman rules; four-point functions that to lowest order are entirely one-particle reducible in perturbative electroweak theory are seen to acquire one-particle-irreducible components of comparable magnitude in the presence of contributions to quark self-energies external to electroweak theory. Such additional contributions to three- and four-point functions, required for the gauge-parameter independence of on-shell quark two-point functions, do not contribute to Landau-gauge amplitudes. In the chiral limit, such self-energy contributions are also shown to induce gauge-parameter-independent Yukawa couplings to on-shell quarks. In the limit of a vanishing Higgs-field momentum, this Yukawa coupling is at most of order $\frac{{\ensuremath{\Sigma}}^{3}}{{M}_{Z}^{2}}$, where $\ensuremath{\Sigma}$ is the scale of the nonperturbative dynamical quark mass.

Flavor-changing neutral currents with heavy quarks.

The flavor-changing amplitudes $\ensuremath{\gamma}{q}_{i}{q}_{j}$ and $g{q}_{i}{q}_{j}$ are computed without approximations. The results for on-shell quarks and for the gluon and photon vertices are compared with the ones derived using the usual approximation of neglecting the external quark masses. For the $b\ensuremath{\rightarrow}sg(\ensuremath{\gamma})$ transitions this approximation is shown to be very good. The discrepancy with another calculation is discussed and the situation is clarified.

Dimensionally regularized two-loop on-shell quark form factor

Analytic results are presented for the dimensionally regularized two-loop Feynman diagrams which contribute to the electromagnetic form factor of an on-shell quark in massless quantum chromodynamics.

Flavor-changing electromagnetic transitions

We compute the ${q}_{i}{q}_{j}\ensuremath{\gamma}$ transition amplitude for off-shell and on-shell quarks with flavors $i\ensuremath{\ne}j$, in the standard weak-interaction model. The results we present are valid for all quark and photon momenta and for all external and internal quark masses. We discuss the Feynman rules and Ward-Takahashi identities in the 't Hooft---Feynman gauge. Our results can be applied to a variety of phenomena such as the electric dipole moment of the neutron, the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}t\overline{c}$, and flavor-changing transitions with either gluon or photon emission.

Evidence for Longitudinal Photon Polarization in Muon-Pair Production by Pions

Data on $\ensuremath{\mu}$-pair production by pions are examined as a function of $x$ and ${P}_{T}$ for longitudinal photon polarization. Evidence in the form of a ${{sin}^{2}\ensuremath{\theta}}^{*}$ term in the helicity angular distribution is observed for $x$ near 1. This is conclusive evidence that production in this region is not predominantly through on-shell quark annihilation. The result is consistent with a calculation based on quantum chromodynamics.

Angular distribution of dileptons in high-energy hadron collisions

We give the general form of the angular distribution of lepton pairs produced in hadron collisions, where each dilepton is assumed to come from the decay of a virtual photon. The Drell-Yan model extended to include parton transverse momentum (with on-shell quarks) is then used to calculate the three coefficients in the distribution.