Loops In QCD Research Articles

Heavy-quark production in gluon fusion at two loops in QCD

We present the two-loop virtual QCD corrections to the production of heavy quarks in gluon fusion. The results are exact in the limit when all kinematical invariants are large compared to the mass of the heavy quark up to terms suppressed by powers of the heavy-quark mass. Our derivation uses a simple relation between massless and massive QCD scattering amplitudes as well as a direct calculation of the massive amplitude at two loops. The results presented here together with those obtained previously for quark–quark scattering form important parts of the next-to-next-to-leading order QCD corrections to heavy-quark production in hadron–hadron collisions.

Heavy-quark production in massless quark scattering at two loops in QCD

We present the two-loop virtual QCD corrections to the production of heavy quarks in the quark–anti-quark annihilation channel in the limit when all kinematical invariants are large compared to the mass of the heavy quark. Our result is exact up to terms suppressed by powers of the heavy-quark mass. The derivation is based on a simple relation between massless and massive scattering amplitudes in gauge theories proposed recently by two of the authors as well as a direct calculation of the massive amplitude at two loops. The results presented here form an important part of the next-to-next-to-leading order QCD contributions to heavy-quark production in hadron–hadron collisions.

Can the pomeron be derived from a Euclidean–Minkowskian duality?

After a brief review, in the first part, of some relevant analyticity and crossing-symmetry properties of the correlation functions of two Wilson loops in QCD, when going from Euclidean to Minkowskian theory, in the second part we shall see how these properties can be related to the still unsolved problem of the asymptotic s-dependence of the hadron–hadron total cross sections. In particular, we critically discuss the question if (and how) a pomeron-like behaviour can be derived from this Euclidean–Minkowskian duality.

Dimension-2 condensates and Polyakov Chiral Quark Models

We address a possible relation between the expectation value of the Polyakov loop in pure gluodynamics and full QCD based on Polyakov Chiral Quark Models where constituent quarks and the Polyakov loop are coupled in a minimal way. To this end we use a center symmetry breaking Gaussian model for the Polyakov loop distribution which accurately reproduces gluodynamics data above the phase transition in terms of dimension 2 gluon condensate. The role played by the quantum and local nature of the Polyakov loop is emphasized.

On the probabilistic interpretation of the evolution equations with pomeron loops in QCD

We study some structural aspects of the evolution equations with pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.

An alternate smearing method for Wilson loops in lattice QCD

A gauge field link smearing method developed for calculations with staggered fermions, namely the use of unitarized fat7 links, is applied to mesonic and baryonic Wilson loop calculations. This method is found to be very effective for reducing statistical fluctuations for large Wilson loops. Examination of chromo-electric field distributions shows that self-interactions of the static sources are reduced when unitarized fat7 smearing is used but long-distance inter-quark effects are unchanged.

Weak isospin violations in charged and neutral Higgs couplings from supersymmetric loop corrections

Supersymmetric QCD and supersymmetric electroweak loop corrections to the violations of weak isospin to Yukawa couplings are investigated. Specifically it involves an analysis of the supersymmetric loop corrections to the Higgs couplings to the third generation quarks and leptons. Here we analyze the SUSY loop corrections to the charged Higgs couplings which are then compared with the supersymmetric loop corrections to the neutral Higgs couplings previously computed. It is found that the weak isospin violations can be quite significant, i.e, as much as 40-50% or more of the total loop correction to the Yukawa coupling. The effects of CP phases are also studied and it is found that these effects can either enhance or suppress the weak isospin violations. We also investigate the weak isospin violation effects on the branching ratio $BR(H^-\to\bar t b)/ BR(H^-\to \bar\nu_{\tau}\tau^-)$ and show that the effects are sensitive to CP phases. Thus an accurate measurement of this branching ratio along with the branching ratio of the neutral Higgs boson decays can provide a measure of weak isospin violation along with providing a clue to the presence of supersymmetry.

Heavy Quark Free Energies and the Renormalized Polyakov Loop in Full QCD

We study the renormalized free energy of a heavy quark anti-quark pair in the different colour channels in full QCD at finite temperature. Similarities and differences to the quenched case are discussed and the temperature dependence as well as their short distance behavior are analyzed. The asymptotic large distance behavior of the free energy is used to define the non-perturbatively renormalized Polyakov loop which is well behaved in the continuum limit.

Erratum: Supersymmetric QCD and supersymmetric electroweak loop corrections tob,t,andτmasses including the effects ofCPphases [Phys. Rev. D67, 095003 (2003)

We compute supersymmetric QCD and supersymmetric electroweak corrections to the b and t quark masses and to the $\tau$ lepton mass in the presence of CP phases valid for all $\tan\beta$. The analysis includes one loop diagrams arising from the exchange of gluinos, charginos and neutralinos. We find that the CP effects can change both the magnitude as well as the sign of the supersymmetric loop correction. In the region of parameter space studied we found that the numerical size of the correction to the b quark mass can be as large as 30 percent and to the $\tau$ lepton mass as much as 5 percent. For the top quark mass the correction is typically less than a percent. These corrections are of importance in unified models since $b-\tau$ and $b-t-\tau$ unification is strongly affected by the size of these corrections. More generally these results will be of importance in analyses of quark-lepton textures with the inclusion of CP phases. Further, the analysis presented here is relevant in a variety of low energy phenomena where supersymmetric QCD and supersymmetric electroweak corrections on b mass enter prominently in B physics, e.g., in processes such as $B^0_{s,d}\to l^+\l^-$.

Supersymmetric QCD and supersymmetric electroweak loop corrections tob,t,andτmasses including the effects ofCPphases

We compute supersymmetric QCD and supersymmetric electroweak corrections to the b and t quark masses and to the $\ensuremath{\tau}$ lepton mass in the presence of CP phases valid for all $\mathrm{tan}\ensuremath{\beta}.$ The analysis includes one loop diagrams arising from the exchange of gluinos, charginos and neutralinos. We find that the CP effects can change both the magnitude as well as the sign of the supersymmetric loop correction. In the region of parameter space studied we found that the numerical size of the correction to the b quark mass can be as large as 30 % and to the $\ensuremath{\tau}$ lepton mass as much as 5%. For the top quark mass the correction is typically less than a percent. These corrections are of importance in unified models since $b\ensuremath{-}\ensuremath{\tau}$ and $b\ensuremath{-}t\ensuremath{-}\ensuremath{\tau}$ unification is strongly affected by the size of these corrections. More generally these results will be of importance in analyses of quark-lepton textures with the inclusion of CP phases. Further, the analysis presented here is relevant in a variety of low energy phenomena where supersymmetric QCD and supersymmetric electroweak corrections on the b mass enter prominently in B physics, e.g., in processes such as ${B}_{s,d}^{0}\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}.$

Effective potential for Polyakov loops in lattice QCD

Toward the derivation of an effective theory for Polyakov loops in lattice QCD, we examine Polyakov loop correlation functions using the multi-level algorithm which was recently developed by Luscher and Weisz.

Dimensionally regulated one-loop box scalar integrals with massless internal lines

Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating one$-$loop $(N\ge 5)-$point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic variables and presented in a simple and compact form.

Top quark decay into a light gluino and top squark

We have calculated the decay width of the process t-->(g) over tilde (t) over tilde(1) including one loop QCD corrections. We found that the decay width of this process could be comparable with that of the standard channel t-->bW*, and, its QCD correction could enhance the widths over 30% in a very large mass range of the light top squark.

Renormalization group effects in the processH→γγ

The partial Higgs boson width $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{H}\ensuremath{\gamma}\ensuremath{\gamma})$ is important at the CERN LHC for Higgs boson masses in the MSSM mass window up to 140 GeV as a relatively background free signal of a fundamental scalar. At the photon-photon mode at the NLC it would be the Higgs boson production mechanism. Two loop QCD corrections exist for the fermionic contribution and in the case of the bottom loop large non-Sudakov double logarithms can be resummed to all orders and contribute up to 12% compared to the t quark. In more complicated Higgs sectors, such as in the MSSM, large $\mathrm{tan}\ensuremath{\beta}$ enhancements of bottom type Yukawa couplings can potentially dominate even the whole partial width. A main uncertainty in all existing calculations is the scale of the strong coupling as it is only renormalized at the three loop level. In this paper we include the exact two loop running coupling to all orders into the bottom contribution. We find that the effective scale is close to ${\ensuremath{\alpha}}_{s}{(10m}_{b}^{2}).$

Reconsidering Composite Higgs Loop Effects in the Top Mode Standard Model

Composite Higgs loop effects in the top mode standard model are discussed by using the Miransky-Tanabashi-Yamawaki (MTY) approach based on the Schwinger-Dyson equation. The top mass is obtained as 179 GeV for the Planck scale cutoff (\Lambda \simeq 10^{19} GeV). This result is different from that of the Bardeen-Hill-Lindner (BHL) approach based on the renormalization group equation (RGE), with QCD plus Higgs loop effects included (m_t \simeq 205 GeV). Detailed comparison of the MTY approach with the BHL approach is made. We derive ``RGE'' from the Pagels-Stokar formula by considering the infrared mass as the ``renormalization point''. Then, it is found that the MTY approach including the composite Higgs loop effects is only partially equivalent to the BHL approach with QCD plus Higgs loop effects. The difference essentially results from the treatment of the composite Higgs propagator, or more precisely, of Z_H^{-1}. Our results can be summarized as m_t (Ours) \simeq 1/\sqrt{2} m_t (MTY), in contrast to m_t (BHL) \simeq \sqrt{2/3} m_t (MTY), where m_t (MTY) \simeq 250 GeV is the original MTY prediction without Higgs loop effects.

Asymptotic Padé approximant predictions: Up to five loops in QCD and SQCD

We use Asymptotic Pade Approximants (APAP's) to predict the four- and five-loop \beta-functions in QCD and N=1 supersymmetric QCD (SQCD), as well as the quark mass anomalous dimensions in Abelian and non-Abelian gauge theories. We show how the accuracy of our previous \beta-function predictions at the four-loop level may be further improved by using estimators weighted over negative numbers of flavours (WAPAP's). The accuracy of the improved four-loop results encourages confidence in the new five-loop \beta-function predictions that we present. However, the WAPAP approach does not provide improved results for the anomalous mass dimension, or for Abelian theories.

Polyakov loops and fermionic zero-modes in QCD 2 on the torus

A direct derivation of the free energy and expectation values of Polyakov loops in QCD 2 via path integral methods is given. The chosen gauge fixing has no Gribov copies and has a natural extension to four dimensions. The Faddeev-Popov determinant and the integration over the space component of the gauge field cancel exactly. It only remains an integration over the zero components of the gauge field in the Cartan sub-algebra. This way the Polyakov-loop operators become Vertex operators in a simple quantum mechanical model. The number of fermionic zero-modes is related to the winding numbers of Ao in this gauge.

Unitarity constraints on the B and B* form factors from QCD analyticity and heavy quark spin symmetry.

A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $\sigma(e^+e^- \rightarrow \Upsilon)$ are used as input. We obtain bounds on the charge radius of the elastic form factor of the $B$ meson, which considerably improve previous results derived in the same framework.

Final state QCD corrections to off-shell single top production in hadron collsions

In this paper, I study final state QCD radiative corrections to off-shell single top production via decaying W at hadron collider energies. The tree level Breit-Wigner distribution of the produced top invariant mass is distorted by final state QCD radiation, while the peak position remains unchanged. The exact one loop QCD calculation and the narrow width approximation agree in predicting the cross section, the hadronic transverse energy distribution and the bottom-lepton invariant mass distribution.

Massive loop amplitudes from unitarity

We show, for previously uncalculated examples containing a uniform mass in the loop, that it is possible to obtain complete massive one-loop gauge theory amplitudes solely from unitarity and known ultraviolet or infrared mass singularities. In particular, we calculate four-gluon scattering via massive quark loops in QCD. The contribution of a heavy quark to five-gluon scattering with identical helicities is also presented.