skip to main content


Title: Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections
A bstract We perform a dedicated study of the $$ q\overline{q} $$ q q ¯ -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and α s one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ 5 scheme and Kreimer’s anticommuting γ 5 scheme.  more » « less
Award ID(s):
1719863
NSF-PAR ID:
10231410
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2021
Issue:
5
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. A bstract It is well-known that on-shell maximally helicity-violating gluon scattering amplitudes in planar maximally supersymmetric Yang-Mills theory are dual to a bosonic Wilson loop on a null-polygonal contour. The light-like nature of the intervals is a reflection of the mass-shell condition for massless gluons involved in scattering. Presently, we introduce a Wilson loop prototype on a piece-wise curvilinear contour that can be interpreted in the T-dual language to correspond to nonvanishing gluon off-shellness. We analyze it first for four sites at one loop and demonstrate that it coincides with the four-gluon amplitude on the Coulomb branch. Encouraged by this fact, we move on to the two-loop order. To simplify our considerations, we only focus on the Sudakov asymptotics of the Wilson loop, when the off-shellness goes to zero. The latter serves as a regulator of short-distance divergences around the perimeter of the loop, i.e., divergences when gluons are integrated over a small vicinity of the Wilson loop cusps. It does not however regulate conventional ultraviolet divergences of interior closed loops. This unavoidably introduces a renormalization scale dependence and thus scheme dependence into the problem. With a choice of the scale setting and a finite renormalization, we observe exponentiation of the double logarithmic scaling of the Wilson loop with the accompanying exponent being given by the so-called hexagon anomalous dimension, which recently made its debut in the origin limit of six-leg gluon amplitudes. This is contrary to the expectation for the octagon anomalous dimension to rather emerge from our analysis suggesting that the current object encodes physics different from the Coulomb branch scattering amplitudes. 
    more » « less
  2. A bstract We compute the three-loop corrections to the helicity amplitudes for q $$ \overline{q} $$ q ¯ → Q $$ \overline{Q} $$ Q ¯ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours. 
    more » « less
  3. Abstract

    We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble$$\hbox {CLE}_{\kappa '}$$CLEκfor$$\kappa '$$κin (4, 8) that is drawn on an independent$$\gamma $$γ-LQG surface for$$\gamma ^2=16/\kappa '$$γ2=16/κ. The results are similar in flavor to the ones from our companion paper dealing with$$\hbox {CLE}_{\kappa }$$CLEκfor$$\kappa $$κin (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\hbox {CLE}_{\kappa '}$$CLEκin terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a$$\hbox {CLE}_{\kappa '}$$CLEκindependently into two colors with respective probabilitiespand$$1-p$$1-p. This description was complete up to one missing parameter$$\rho $$ρ. The results of the present paper about CLE on LQG allow us to determine its value in terms ofpand$$\kappa '$$κ. It shows in particular that$$\hbox {CLE}_{\kappa '}$$CLEκand$$\hbox {CLE}_{16/\kappa '}$$CLE16/κare related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {FK}_q$$FKqpercolation and theq-state Potts model (which makes sense even for non-integerqbetween 1 and 4) if and only if$$q=4\cos ^2(4\pi / \kappa ')$$q=4cos2(4π/κ). This provides further evidence for the long-standing belief that$$\hbox {CLE}_{\kappa '}$$CLEκand$$\hbox {CLE}_{16/\kappa '}$$CLE16/κrepresent the scaling limits of$$\hbox {FK}_q$$FKqpercolation and theq-Potts model whenqand$$\kappa '$$κare related in this way. Another consequence of the formula for$$\rho (p,\kappa ')$$ρ(p,κ)is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.

     
    more » « less
  4. null (Ed.)
    A bstract Systematic studies of charge-dependent two- and three-particle correlations in Pb-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 2.76 and 5.02 TeV used to probe the Chiral Magnetic Effect (CME) are presented. These measurements are performed for charged particles in the pseudorapidity ( η ) and transverse momentum ( p T ) ranges | η | < 0 . 8 and 0 . 2 < p T < 5 GeV/ c . A significant charge-dependent signal that becomes more pronounced for peripheral collisions is reported for the CME-sensitive correlators γ 1, 1  = 〈cos( φ α  +  φ β  − 2Ψ 2 )〉 and γ 1, − 3  = 〈cos( φ α  − 3 φ β  + 2Ψ 2 )〉. The results are used to estimate the contribution of background effects, associated with local charge conservation coupled to anisotropic flow modulations, to measurements of the CME. A blast-wave parametrisation that incorporates local charge conservation tuned to reproduce the centrality dependent background effects is not able to fully describe the measured γ 1 , 1 . Finally, the charge and centrality dependence of mixed-harmonics three-particle correlations, of the form γ 1, 2  = 〈cos( φ α  + 2 φ β  − 3Ψ 3 )〉, which are insensitive to the CME signal, verify again that background contributions dominate the measurement of γ 1 , 1 . 
    more » « less
  5. null (Ed.)
    The measures of information transfer which correspond to non-additive entropies have intensively been studied in previous decades. The majority of the work includes the ones belonging to the Sharma–Mittal entropy class, such as the Rényi, the Tsallis, the Landsberg–Vedral and the Gaussian entropies. All of the considerations follow the same approach, mimicking some of the various and mutually equivalent definitions of Shannon information measures, and the information transfer is quantified by an appropriately defined measure of mutual information, while the maximal information transfer is considered as a generalized channel capacity. However, all of the previous approaches fail to satisfy at least one of the ineluctable properties which a measure of (maximal) information transfer should satisfy, leading to counterintuitive conclusions and predicting nonphysical behavior even in the case of very simple communication channels. This paper fills the gap by proposing two parameter measures named the α-q-mutual information and the α-q-capacity. In addition to standard Shannon approaches, special cases of these measures include the α-mutual information and the α-capacity, which are well established in the information theory literature as measures of additive Rényi information transfer, while the cases of the Tsallis, the Landsberg–Vedral and the Gaussian entropies can also be accessed by special choices of the parameters α and q. It is shown that, unlike the previous definition, the α-q-mutual information and the α-q-capacity satisfy the set of properties, which are stated as axioms, by which they reduce to zero in the case of totally destructive channels and to the (maximal) input Sharma–Mittal entropy in the case of perfect transmission, which is consistent with the maximum likelihood detection error. In addition, they are non-negative and less than or equal to the input and the output Sharma–Mittal entropies, in general. Thus, unlike the previous approaches, the proposed (maximal) information transfer measures do not manifest nonphysical behaviors such as sub-capacitance or super-capacitance, which could qualify them as appropriate measures of the Sharma–Mittal information transfer. 
    more » « less