Soft Matrix Elements Research Articles

Infrared Singularities of Multileg QCD Amplitudes with a Massive Parton at Three Loops

We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations involving a massive parton are studied in detail. The analytical expression of tripole correlations between one massive and two massless partons is obtained at three loops for the first time. We regularize the infrared divergences in the soft matrix element in a novel approach, where no extra scale dependence is involved, and the calculation can be performed in momentum space. Our results are essential to improve the theoretical predictions of single top and top quark pair productions at hadron colliders.

Transverse momentum dependent distributions in dijet and heavy hadron pair production at EIC

We discuss the measurement of gluon transverse momentum distribution (TMD) in dijet and heavy hadron pair (HHP) production in semi-inclusive deep inelastic scattering. The factorization of these processes in position space shows the appearance of a specific new soft factor matrix element on top of angular and complex valued anomalous dimensions. We show in detail how these features can be treated consistently and we discuss a scale prescription for the evolution kernel of the dijet soft function. As a result we obtain phenomenological predictions for unpolarized and angular modulated cross-sections for the electron-ion collider (EIC) using current available information on unpolarized TMD.

Applications of the Nambu\u2013Jona-Lasinio model to the partonic structure of the pion

We present a brief review of results of chiral quark models for soft matrix elements in the pion state, appearing in high-energy processes as well as accessible in present and future lattice studies. A particular attention is paid to the recently explored double parton distribution functions of the pion.

Towards quasi-transverse momentum dependent PDFs computable on the lattice

Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the light-cone. Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasi-TMDPDFs with finite-length spacelike Wilson lines that are amenable to such calculations. We define an infrared consistency test to determine which quasi-TMDPDF definitions are related to the TMDPDF, by carrying out a one-loop study of infrared logarithms of transverse position bT ∼ ΛQCD−1, which must agree between them. This agreement is a necessary condition for the two quantities to be related by perturbative matching. TMDPDFs necessarily involve combining a hadron matrix element, which nominally depends on a single light-cone direction, with soft matrix elements that necessarily depend on two light-cone directions. We show at one loop that the simplest definitions of the quasi hadron matrix element, the quasi soft matrix element, and the resulting quasi-TMDPDF all fail the infrared consistency test. Ratios of impact parameter quasi-TMDPDFs still provide nontrivial information about the TMD-PDFs, and are more robust since the soft matrix elements cancel. We show at one loop that such quasi ratios can be matched to ratios of the corresponding TMDPDFs. We also introduce a modified “bent” quasi soft matrix element which yields a quasi-TMDPDF that passes the consistency test with the TMDPDF at one loop, and discuss potential issues at higher orders.

The two-loop soft function for heavy quark pair production at future linear colliders

We report on the calculation of the threshold soft function for heavy quark pair production in e+ e- annihilation at two-loop order. Our main result is a generalization of the familiar Drell-Yan threshold soft function to the case of non-zero primary quark mass. We set up a framework based on the method of differential equations which allows for the straightforward calculation of the bare soft function to arbitrarily high orders in the dimensional regularization parameter. Remarkably, we find that we can obtain the bare two-loop Drell-Yan soft function from the heavy quark soft function to the order in epsilon required for a two-loop calculation by making simple replacements. We expect that our results will be of use, both as an important input for precision physics calculations at linear colliders and, more formally, as a first step towards a better understanding of the connection between vacuum matrix elements of massive soft Wilson lines and vacuum matrix elements of massless soft Wilson lines.

Enhanced Nonperturbative Effects through the Collinear Anomaly

We show that nonperturbative effects are logarithmically enhanced for transverse-momentum-dependent observables such as qT spectra of electroweak bosons in hadronic collisions and jet broadening at e+ e- colliders. This enhancement arises from the collinear anomaly, a mechanism characteristic for transverse observables, which induces logarithmic dependence on the hard scale in the product of the soft and collinear matrix elements. Our analysis is based on an operator product expansion and provides, for the first time, a systematic, model-independent way to study nonperturbative effects for this class of observables. For the case of jet broadening, we relate the leading correction to the nonperturbative shift of the thrust distribution.

Production of heavy meson pairs in pp̄ collisions within a double handbag approach

We study the pair-production of heavy mesons in proton-antiproton annihilations within a perturbative QCD-motivated framework. In particular we investigate pp̄ → D0 within a double handbag approach, where a hard subprocess factorizes from soft hadronic matrix elements. The soft matrix elements can be parametrized by transition distribution amplitudes, which are off-diagonal in flavor space. The transition distribution amplitudes are modelled as overlaps of light-cone wave functions. We obtain rather robust model results for pp̄ → D0 cross sections, which are expected to be measured at the future detector at GSI-FAIR.

ON RAPIDITY DIVERGENCES IN THE SOFT AND COLLINEAR LIMITS OF QCD

We consider the definition of a transverse-momentum-dependent parton distribution function (TMDPDF) and its evolution properties given a factorization theorem of Drell-Yan lepton pair production with a non-vanishing transverse momentum. We discuss rapidity divergences that exist in both limits of QCD: the soft and collinear. We argue that only when a specific combination of the soft and collinear matrix elements is formed, rapidity divergences cancel. We also argue that the soft matrix element, calculated in perturbation theory, contains only rapidity divergences and there is no genuine long-distance infra-red divergences.

QCD description of charmonium plus light meson production in [formula omitted] annihilation

The associated production of a J/ψ and a π meson in antiproton–nucleon annihilation is studied in the framework of QCD collinear factorization. In this approach, a hard subprocess responsible for the production of the heavy quark–antiquark pair factorizes from soft hadronic matrix elements, such as the antiproton (nucleon) distribution amplitude and the nucleon-to-pion (antiproton-to-pion) transition distribution amplitude. This reaction mechanism should dominate the forward and backward kinematical regions, where the cross sections are expected to be measurable in the set-up of the P̄ANDA experiment at the GSI-FAIR facility.

Self-organizing maps algorithm for parton distribution functions extraction

We describe a new method to extract parton distribution functions from hard scattering processes based on Self-Organizing Maps. The extension to a larger, and more complex class of soft matrix elements, including generalized parton distributions is also discussed.

Factorization of heavy-to-light baryonic transitions in SCET

In the framework of the soft-collinear effective theory, we demonstrate that the leading-power heavy-to-light baryonic form factors at large recoil obey the heavy quark and large energy symmetries. Symmetry breaking effects are suppressed by Λ/mb or Λ/E, where Λ is the hadronic scale, mb is the b quark mass and E∼mb is the energy of light baryon in the final state. At leading order, the leading power baryonic form factor ξΛ,p(E), in which two hard-collinear gluons are exchanged in the baryon constituents, can factorize into the soft and collinear matrix elements convoluted with a hard-kernel of order αs2. Including the energy release dependence, we derive the scaling law ξΛ,p(E)∼Λ2/E2. We also find that this form factor ξΛ(E) is numerically smaller than the form factor governed by soft processes, although the latter is formally power-suppressed.

Use of dispersion relations in hard exclusive processes and the partonic interpretation of deeply virtual Compton scattering

Recently dispersion relations have been applied to hard exclusive processes such as deeply virtual Compton scattering, and a holographic principle was proposed that maps out the generalized parton distributions entering the soft matrix elements for the processes from their values on a given kinematical ridge. We examine possible pitfalls associated with the implicit, direct identification in this approach of the physical hadronic states with colored partons, and suggest an improved treatment of this assumption.

Analysis of the decay B0 → χc1π0 with light-cone QCD sum rules

In this article, we calculate the contribution from the nonfactorizable soft hadronic matrix element to the decay B0 → χc1π0 with the light-cone quantum chromo-dynamic (QCD) sum rules. The numerical results show that its contribution is rather large and should not be neglected. The total amplitudes lead to a branching fraction which is in agreement with the experimental data marginally.

Application of Probablistic Neural Network for the Development of Wear Mechanism Map for Glass Fiber Reinforced Plastics

Glass fiber reinforced plastic composite materials are finding increased applications due to their excellent properties. Fiber reinforced plastic (FRP) composite materials comprise soft matrix and fiber elements. This article presents the tribological aspects of glass fiber reinforced plastic composites. The wear test is carried out for FRP in a pin-on-roller wear tester. The wear rate obtained from different sliding speeds and normal pressure are plotted as a contour map. The scanning electron microscopy images are taken to study the deformations that occurred in the wear zone. The regions of different wear mechanisms are identified using scanning electron microscopy. The regions of wear mechanisms are classified using probabilistic neural networks and superimposed over wear rate contours. The wear mechanisms observed using scanning electron microscopy, along with wear rate data, are used for the construction of wear mechanism maps.

Generalized distribution amplitudes at theZpole

We investigate the exclusive two-pion production at the Z-pole through the process e{sup +}e{sup -}{yields}Z{yields}{pi}{pi}{gamma}. In the kinematical region where the invariant mass of the two pions is much smaller than the mass of the Z boson, the process can be factorized into the convolution of a hard coefficient and a soft matrix element, the generalized distribution amplitude of two pions. We calculate the differential cross-section of charged pion pair production and neutral pion pair production and find the former to be much larger than the latter. We show that combining the measurements of charged pion pair production and neutral pion pair production at the Z-pole provides a convenient approach to access the C-odd part of the 2{pi} distribution amplitudes.

Nonfactorizable soft contributions in theB→ηcK,xc0Kdecays with the light-cone sum rule approach

In this article, we calculate the nonfactorizable soft contributions in the $B\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}K,{\ensuremath{\chi}}_{c0}K$ decays with the light-cone QCD sum rules approach. Our results show that the nonfactorizable corrections from the soft-gluon exchanges in the decay $B\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}K$ are of $(15\ensuremath{-}30)%$ and should be taken into account. As for the decay $B\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c0}K$, the factorizable contributions are zero and the nonfactorizable contributions from the soft hadronic matrix elements are too small to accommodate the experimental data.

Factorization of heavy-to-light form factors in soft-collinear effective theory

Heavy-to-light transition form factors at large recoil energy of the light meson have been conjectured to obey a factorization formula, where the set of form factors is reduced to a smaller number of universal form factors up to hard-scattering corrections. In this paper we extend our previous investigation of heavy-to-light currents in soft-collinear effective theory to final states with invariant mass Λ 2 as is appropriate to exclusive B meson decays. The effective theory contains soft modes and two collinear modes with virtualities of order m b Λ (“hard-collinear”) and Λ 2. Integrating out the hard-collinear modes results in the hard spectator-scattering contributions to exclusive B decays. We discuss the representation of heavy-to-light currents in the effective theory after integrating out the hard-collinear scale, and show that the previously conjectured factorization formula is valid to all orders in perturbation theory. The naive factorization of matrix elements in the effective theory into collinear and soft matrix elements may be invalidated by divergences in convolution integrals. In the factorization proof we circumvent the explicit regularization of endpoint divergences by a definition of the universal form factors that includes hard-collinear, collinear and soft effects.

Probing the nucleon at large momentum transfer

The central role of soft nucleon matrix elements in reactions of high energy electrons or real photons with nucleons is emphasized. These soft matrix elements are described in terms of skewed parton distributions. Their connections to ordinary parton distributions, form factors, Compton scattering and hard meson electroproduction is discussed.