Threshold resummation of new partonic channels at next-to-leading power

Collider observables involving heavy particles are subject to large logarithmic terms near threshold, which must be summed to all orders in perturbation theory to obtain sensible results. Relatively recently, this resummation has been extended to next-to-leading power in the threshold variable, using a variety of approaches. In this paper, we consider partonic channels that turn on only at next-to-leading power, and show that it is possible to resum leading logarithms using well-established diagrammatic techniques in Quantum Chromodynamics. We first consider deep inelastic scattering, where we reproduce the results of a recent study using an effective theory approach. Next, we consider the quark-gluon channel in both Drell-Yan and Higgs boson production, showing that an explicit all-order form for the leading logarithmic partonic cross section can be obtained. Our results agree with previous conjectures based on fixed-order results.

Threshold resummation of transverse momentum distributions beyond next-to-leading log

We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.

Next-to-leading-logarithm threshold resummation for exclusive B meson decays

We extend the threshold resummation of the large logarithms $$\ln x$$ ln x which appear in factorization formulas for exclusive B meson decays, x being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $$x\sim 0$$ x ∼ 0 stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $$B\rightarrow K\pi $$ B → K π decays under the NLL resummation in the perturbative QCD approach, and find that it induces up to 20% variation of the direct CP asymmetries in various modes relative to the LL results. Our method to avoid the Landau singularity in the inverse Mellin transformation causes at most 10% theoretical uncertainty.

Fragmentation function of g → $$ Q\overline{Q} $$(3$$ {S}_1^{\left[8\right]} $$) in soft gluon factorization and threshold resummation

We study the fragmentation function of the gluon to color-octet 3S1 heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet 3S1 soft gluon distribution (SGD). The short distance hard part is calculated to the next-to-leading order in αs and all orders in velocity expansion. By deriving and solving the renormalization group equation of the SGD, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.

On Threshold Resummation S-Factor for a System of Two Relativistic Spinor Particles with Arbitrary Masses

We present a new threshold resummation S-factor obtained for a composite system of two relativistic spin 1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential. The analysis is performed in the framework of a relativistic quasipotential approach in the Hamiltonian formulation of the quantum field theory in the relativistic configuration representation. The pseudoscalar, vector, and pseudovector systems are considered. The difference in the behavior of the S-factor for these cases is discussed. A connection between the new and the previously obtained S-factors for spinless particles of arbitrary masses and relativistic spinor particles of equal masses is established.

Phenomenology of combined resummation for Higgs and Drell-Yan

We study the phenomenological impact of a recently suggested formalism for the combination of threshold and a so-called threshold-improved transverse momentum resummation, by using it to improve the fixed-order results. This formalism allows for a systematic improvement of the transverse momentum resummation that is valid in the entire range of pT by the inclusion of the threshold contribution. We use the Borel method as a suitable prescription for defining the inverse Mellin and Fourier transforms in the context of combined resummed expression. The study is applied to two QCD processes, namely the Higgs boson produced via gluon fusion and Z boson production via the Drell-Yan mechanism. We compare our results to the standard transverse momentum resummation, as well as to the fixed-order results. We find that the threshold-improved transverse momentum resummation leads to faster perturbative convergence at small pT while the inclusion of threshold resummation improves the agreement with fixed-order calculations at medium and large pT. These effects are more pronounced in the case of Higgs which is known to have slower perturbative convergence.

Kaon and pion parton distributions

Beginning with results for the leading-twist two-particle distribution amplitudes of $$\pi $$ π - and K-mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all $$\pi $$ π and K distribution functions (DFs), including glue and sea. The large-x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at $$\zeta _5=5.2\,$$ ζ 5 = 5.2 GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: $$\langle x_{\mathrm{valence}} \rangle ^\pi = 0.41(4)$$ ⟨ x valence ⟩ π = 0.41 ( 4 ) , $$\langle x_{\mathrm{glue}} \rangle ^\pi = 0.45(2)$$ ⟨ x glue ⟩ π = 0.45 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^\pi = 0.14(2)$$ ⟨ x sea ⟩ π = 0.14 ( 2 ) ; and $$\langle x_{\mathrm{valence}} \rangle ^K = 0.42(3)$$ ⟨ x valence ⟩ K = 0.42 ( 3 ) , $$\langle x_{\mathrm{glue}} \rangle ^K = 0.44(2)$$ ⟨ x glue ⟩ K = 0.44 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^K = 0.14(2)$$ ⟨ x sea ⟩ K = 0.14 ( 2 ) . The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all $$\pi $$ π and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.

Soft Anomalous Dimensions and Resummation in QCD

I discuss and review soft anomalous dimensions in QCD that describe soft-gluon threshold resummation for a wide range of hard-scattering processes. The factorization properties of the cross section in moment space and renormalization-group evolution are implemented to derive a general form for differential resummed cross sections. Detailed expressions are given for the soft anomalous dimensions at one, two, and three loops, including some new results, for a large number of partonic processes involving top quarks, electroweak bosons, Higgs bosons, and other particles in the standard model and beyond.