Planar amplitudes in maximally supersymmetric Yang-Mills theory

The collinear factorization properties of two-loop scattering amplitudes in dimensionally regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the anti-de Sitter/conformal field theory correspondence that the form of the large-N(c) L-loop amplitudes should be simple enough to allow a resummation to all orders.     

Soft-gluon resummation for single-particle inclusive hadroproduction at high transverse momentum

We consider the cross section for one-particle inclusive production at high transverse momentum in hadronic collisions. We present the all-order resummation formula that controls the logarithmically-enhanced perturbative QCD contributions to the partonic cross section in the threshold region, at fixed rapidity of the observed parton (hadron). The explicit resummation up to next-to-leading logarithmic accuracy is supplemented with the computation of the general structure of the near-threshold contributions to the next-to-leading order cross section. This next-to-leading order computation allows us to extract the one-loop hard-virtual amplitude that enters into the resummation formula. This is a necessary ingredient to explicitly extend the soft-gluon resummation beyond the next-to-leading logarithmic accuracy. These results equally apply to both spin-unpolarized and spin-polarized scattering processes.     

Two-loop anomalous-dimension matrix for soft-gluon exchange

The resummation of soft-gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2-->n massless processes for the first time at two loops. Using color-generator notation, we show that it is proportional to the one-loop matrix. This result reproduces all pole terms in dimensional regularization of the explicit calculations of massless 2-->2 amplitudes in the literature, and it predicts all poles at next-to-next-to-leading order in any 2-->n process that has been computed at next-to-leading order. The proportionality of the one- and two-loop matrices makes possible the resummation in closed form of the next-to-next-to-leading logarithms and poles in dimensional regularization for the 2-->n processes.     

One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.     

小横动量半深度非弹性散射的量子色动力学因子化

论证了在小横动量区域内半深度非弹性散射量子色动力学因子化公式. 为完成因子化, 引进了依赖于横动量的部分子分布函数和碎裂函数, 并扣除了软胶子辐射. 在单圈图的情形下, 证明了因子化的成立, 同时论证了在微扰论的任意阶该因子化的正确性.     

On transverse-momentum dependent light-cone wave functions of light mesons

Transverse-momentum dependent (TMD) light-cone wave functions of a light meson are important ingredients in the TMD QCD factorization of exclusive processes. This factorization allows one conveniently resume Sudakov logarithms appearing in collinear factorization. The TMD light-cone wave functions are not simply related to the standard light-cone wave functions in collinear factorization by integrating them over the transverse momentum. We explore relations between TMD light-cone wave functions and those in the collinear factorization. Two factorized relations can be found. One is helpful for constructing models for TMD light-cone wave functions, and the other can be used for resummation. These relations will be useful to establish a link between two types of factorization.     

Next-to-next-to-leading-order logarithmic corrections at small transverse momentum in hadronic collisions

We study the region of small transverse momenta in q&qmacr;- and gg-initiated processes with no colored particle detected in the final state. We present the universal expression of the O(alpha(2)(s)) logarithmically enhanced contributions up to next-to-next-to-leading-order logarithmic accuracy. From there we extract the coefficients that allow the resummation of the large logarithmic contributions. We find that the coefficient known in the literature as B((2)) is process dependent, since it receives a hard contamination from the one-loop correction to the leading-order subprocess. We present the general result of B((2)) for both quark and gluon channels.     

The PQCD approach towards to next-to-leading order: A short review

In this short review we elaborate the significance of resummation in k_T factorization theorem, and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD (PQCD) approach. We also comment on the current status of the PQCD approach and highlight some key issues to develop it in the near future for more phenomenological applications.     

On-shell methods in perturbative QCD

We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.     

Comment on quarks and gluons at small x and the SDIS factorization scheme

I present some comments on the partonic interpretation of the HERA data on the proton structure function. The effects of the resummation of the leading and next-to-leading ln x-contributions are discussed. A new factorization scheme, in which these resummation effects are absorbed into a steep redefinition of the gluon density, is introduced and its (possible) interpretation and phenomenological relevance are suggested.     

One-loop corrections to the Drell–Yan process in SANC: the charged current case

Radiative corrections to the charged current Drell–Yan processes are revisited. Complete one-loop electroweak corrections are calculated within the automatic SANC system. Electroweak scheme dependence and the choice of the factorization scale are discussed. Comparisons with earlier calculations are presented. PACS 13.85.Qk, 12.15.Lk     

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we prove the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft–Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredients we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory. Received: 4 May 2001 / Published online: 6 July 2001     

Scale choice and collinear contributions to Mueller–Navelet jets at LHC energies

We investigate the stability under variation of the renormalization, factorization and energy scales entering the calculation of the cross section, at next-to-leading order in the BFKL formalism, for the production of Mueller–Navelet jets at the Large Hadron Collider, following the experimental cuts on the tagged jets. To find optimal values for the scales involved in this observable it is possible to look for regions of minimal sensitivity to their variation. We show that the scales found with this logic are more natural, in the sense of being more similar to the squared transverse momenta of the tagged jets, when the BFKL kernel is improved with a resummation of collinear contributions than when the treatment is at a purely next-to-leading order. We also discuss the good perturbative convergence of the ratios of azimuthal angle correlations, which are quite insensitive to collinear resummations and well described by the original BFKL framework.     

Soft-gluon resummation for pseudoscalar Higgs boson production at hadron colliders

We compute the threshold-resummed cross section for pseudo-scalar MSSM Higgs boson production by gluon fusion at hadron colliders. The calculation is performed at next-to-next-to leading logarithmic accuracy. We present results for both the LHC and Tevatron Run II. We analyze the factorization and renormalization scale dependence of the results, finding that after performing the resummation the corresponding cross section can be computed with an accuracy better than 10%.     

Factorization and hence reggeization in Yang-Mills theories

We show how to calculate high-energy gauge meson exchange reactions in general, spontaneously broken Yang-Mills theories. We exploit a class of non-covariant gauges in which the scattering amplitudes take on a factorized form in leading order in ln s. Such factorization can only be consistent with Lorentz invariance if the amplitudes have a power law, or Regge behaviour. We evaluate the trajectory functions by a one-loop calculation and verify that the gauge mesons lie on the trajectories.     

Invariant-mass distribution of top-quark pairs and top-quark mass determination

In this study, we investigate the invariant-mass distribution of top-quark pairs near the 2m_t threshold, which strongly influences the determination of the top-quark mass m_t. Higher-order non-relativistic corrections lead to large contributions, which are not included in the state-of-the-art theoretical predictions. A factorization formula is derived to resum such corrections to all orders in the strong-coupling, and necessary ingredients are calculated to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numerical results. The resummation effect significantly increases the differential cross-section in the threshold region and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of \begin{document}$m_t $\end{document} will lead to a value closer to the direct measurement result.     

Towards collinear evolution equations in electroweak theory

We investigate collinear factorization in electroweak radiative corrections to hard inclusive processes at the TeV scale. Because of the uncanceled double logs found previously, we find a factorization pattern which is qualitatively different from the analogous one in QCD. New types of splitting functions emerge which are needed to describe the initial beam charges and are dependent on an infrared cutoff provided by the symmetry breaking scale. We derive such splitting functions at the one-loop level for broken SU(2) gauge theory, and we also discuss the structure functions' evolution equations, under the assumption that isospin breaking terms are sufficiently subleading at higher orders.     

On next-to-eikonal corrections to threshold resummation for the Drell–Yan and DIS cross sections

We study corrections suppressed by one power of the soft gluon energy to the resummation of threshold logarithms for the Drell–Yan cross section and for Deep Inelastic structure functions. While no general factorization theorem is known for these next-to-eikonal (NE) corrections, it is conjectured that at least a subset will exponentiate, along with the logarithms arising at leading power. Here we develop some general tools to study NE logarithms, and we construct an ansatz for threshold resummation that includes various sources of NE corrections, implementing in this context the improved collinear evolution recently proposed by Dokshitzer, Marchesini and Salam (DMS). We compare our ansatz to existing exact results at two and three loops, finding evidence for the exponentiation of leading NE logarithms and confirming the predictivity of DMS evolution.     

Goldstone mode singularities and equation of state of an isotropic magnet

Static properties of an isotropic magnet are calculated in the whole critical region including the magnetization curve. The method proposed is a resummation of renormalized perturbation theory without use of recursion relations. This is possible because only special diagrams or subdiagrams show infrared divergencies at the magnetization curve due to Goldstone modes. The arguments given are heavily based on Ward identities. The resulting perturbation theory is well behaved in the total critical region and exhibits explicitely the form of the Goldstone mode singularities at the magnetization curve. The equation of state is calculated including two-loop contribution. Resulting effective exponents are then correct in order in the whole critical region. In various limits agreement with known results is found. A one-loop calculation of the correlation functions is also given.     

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects, while including none of the plasmon terms, which is the main reason for requiring improved resummation schemes. Received: 27 June 2002 / Revised version: 23 September 2002 / Published online: 31 January 2003