One-loop Anomalous Dimensions Research Articles

Decoding stringy near-supersymmetric black holes

Building on the recent discovery of the first candidate black hole operator in the \mathcal{N}=4𝒩=4 super-Yang-Mills, we explore the near-supersymmetric aspects of the theory that capture lightly excited, highly stringy black holes. We extend the superspace formalism describing the classically supersymmetric (1/16-BPS) sector of \mathcal{N}=4𝒩=4 super-Yang-Mills and compute a large number of one-loop anomalous dimensions. Despite being in the highly stringy regime, we find hints of a gap in the spectrum, similar to that found by a gravitational path integral. We also determine the actual expression of the first candidate black hole operator at weak gauge coupling, going beyond the cohomological construction.

Anomalous Dimensions from the N=4 Supersymmetric Yang-Mills Hexagon.

We consider the correlator ⟨LKK[over ˜]⟩ of the Lagrange operator of N=4 super Yang-Mills theory and two conjugate two-excitation operators in an su(2) sector. We recover the planar one-loop anomalous dimension of the renormalized operators from this hexagon computation.

Revisiting renormalization group equations of the SMEFT dimension-seven operators

In this work, we revisit the renormalization group equations (RGEs) of dimension-seven (dim-7) operators in the Standard Model effective field theory (SMEFT) resulting from mixing among dim-7 operators themselves by means of the background field method. Adopting a recently proposed physical basis for dim-7 operators, we achieve the explicit RGEs of all non-redundant dim-7 operators in the SMEFT for the first time. Together with those originating from the dim-5 and dim-6 operators, these results constitute the complete RGEs of dim-7 operators, and hence can be exploited to study full RG-running effects on some lepton- or baryon-number-violating processes involving dim-7 operators in the SMEFT, such as neutrino masses, neutrinoless double beta decay, meson and nucleon decays. We perform an analysis of the structure and perturbative power counting of the obtained one-loop anomalous dimension matrix, which is consistent with a non-renormalization theorem and the naive dimension analysis. Additionally, a partial check on some results is carried out by means of different tools and quantum field gauges.

Factorization and resummation for sequential recombination jet cross sections

We extend the class of factorization theorems for non-global observables from fixed angular constraints to cross sections defined in terms of sequential jet clustering. The associated hard and soft functions depend not only on the directions of the hard partons, but also on their energy fractions. We derive the one-loop anomalous dimension of the hard functions that drives the leading-logarithmic resummation. The anomalous dimension imposes energy ordering, which simplifies the clustering sequence. We perform resummations for gap-between-jet observables defined with different jet algorithms and explain the effects of the clustering on the importance of secondary emissions and on the effective gap size.

Anomalous dimensions in hypercubic theories

We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures are then used to compute the anomalous dimensions of scalar operators with up to four fields and arbitrary representations to six-loop order. Moreover, we determine one-loop anomalous dimensions for a large number of low-lying operators in the spectrum which include more powers of the fundamental field and/or insertions of derivatives. As an aside we show how projectors used in the conformal bootstrap can be conveniently reused in computations of anomalous dimensions. The results of our study are of use to the conformal bootstrap. They also illuminate features of conformal perturbation theory and the large n expansion. Our results may be of interest for various crossover phenomena in statistical field theory. In total, we compute the scaling dimension of more than 300 operators, of which 16 are computed to six-loops. Our analysis is exhaustive with respect to group theory up to rank 4 for any number of flavours n, and also exhaustive with respect to which representations exist for n ⩽ 4.

Renormalisation group effects on SMEFT interpretations of LHC data

We explore the impact of Renormalisation Group (RG) effects in the Standard Model Effective Field Theory (SMEFT) interpretations of LHC measurements. We implement the RG running and mixing for the Wilson coefficients as obtained from the one-loop anomalous dimension matrix in the SMEFT into a Monte Carlo generator. This allows to consistently predict and combine in global fits collider observables characterised by different scales. As a showcase, we examine the impact of RG running in the strong coupling on the SMEFT predictions for tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} production cross sections and differential distributions as well as on the bounds on the Wilson coefficients that can be obtained from current LHC data.

Integrable Wilson loops in ABJM: a Y-system computation of the cusp anomalous dimension

We study the integrability properties of Wilson loops in the \U0001d4a9 = 6 three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matrices that govern the interaction of spin-chain excitations with the boundary, including their dressing factors, and we check them against weak- and strong-coupling results. Furthermore, we propose a Y -system of equations for the cusped Wilson line of ABJM, and we use it to reproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-size correction. Finally, we write a set of BTBA equations consistent with the Y -system proposal.

Matching generalised transverse-momentum-dependent distributions onto generalised parton distributions at one loop

The operator definition of generalised transverse momentum-dependent (GTMD) distributions is exploited to compute for the first time the full set of one-loop corrections to the off-forward matching functions. These functions allow one to obtain GTMDs in the perturbative regime in terms of generalised parton distributions (GPDs). In the unpolarised case, non-perturbative corrections can be incorporated using recent determinations of transverse-momentum-dependent (TMD) distributions. Evolution effects for GTMDs closely follow those for TMDs and can thus be easily accounted for up to next-to-next-to-leading logarithmic accuracy. As a by-product, the relevant one-loop anomalous dimensions are derived, confirming previous results. As a practical application, numerical results for a specific kind of GTMD are presented, highlighting some salient features.

Gluonic evanescent operators: classification and one-loop renormalization

Evanescent operators are a special class of operators that vanish classically in four-dimensional spacetime, while in general dimensions they are non-zero and are expected to have non-trivial physical effects at the quantum loop level in dimensional regularization. In this paper we initiate the study of evanescent operators in pure Yang-Mills theory. We develop a systematic method for classifying and constructing the d-dimensional Lorentz invariant evanescent operators, which start to appear at mass dimension ten. We also compute one-loop form factors for the dimension-ten operators via the d-dimensional unitarity method and obtain their one-loop anomalous dimensions. These operators are necessary ingredients in the study of high dimensional operators in effective field theories involving a Yang-Mills sector.

Light-cone distribution amplitudes of heavy mesons with QED effects

We discuss the QED-generalized leading-twist light-cone distribution amplitudes of heavy mesons, that appear in QCD QED factorization theorems for exclusive two-body B decays. In the presence of electrically charged particles, these functions should be more appropriately regarded as soft functions for heavy-meson decays into two back-to-back particles. In this paper, we derive the one-loop anomalous dimension of these soft functions and study their behaviour under renormalization-scale evolution, obtaining an exact solution in Laplace space. In addition, we provide numerical solutions for the soft functions and analytical solutions to all orders in the strong and to first order in the electromagnetic coupling. For the inverse (and inverse-logarithmic) moments, we obtain an all-order solution in both couplings. We further provide numerical estimates for QED corrections to the inverse moments.

Radiative quark jet function with an external gluon

Factorization theorems in soft-collinear effective theory at subleading order in power counting involve “radiative jet functions”, defined in terms of matrix elements of hard-collinear fields with a soft momentum emitted from inside the jet. Of particular importance are the radiative quark jet functions with an external photon or gluon, which arise e.g. in the factorization theorems for the Higgs-boson amplitudes h → γγ, h → gg and gg → h induced by light-quark loops. While the photon case has been studied extensively in previous work, we present here a detailed study of the radiative jet function with an external gluon. We calculate this jet function at one- and two-loop order, derive its one-loop anomalous dimension and study its renormalization-group evolution.

Applications of dispersive sum rules: $ε$-expansion and holography

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in d=4-\epsilond=4−ϵ dimensions. We re-derive many of the known results to order \epsilon^4ϵ4 and we make new predictions. No assumption of analyticity down to spin 00 was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

Anomalous dimensions from Yukawa couplings in SMNEFT: four-fermion operators

The Standard Model Neutrino Effective Field Theory (SMNEFT) is the Standard Model Effective Field Theory (SMEFT) augmented with right-handed neutrinos. Building on our previous work, arXiv:2010.12109, we calculate the Yukawa coupling contributions to the one-loop anomalous dimension matrix for the 11 dimension-six four-fermion SMNEFT operators. We also present the new contributions to the anomalous dimension matrix for the 14 four-fermion SMEFT operators that mix with the SMNEFT operators through the Yukawa couplings of the right-handed neutrinos.

Bounds on multiscalar CFTs in the \u03b5 expansion

We study fixed points with N scalar fields in 4 − ε dimensions to leading order in ε using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling λijkl that describes such CFTs. In particular, we show that λiijj and {lambda}_{ijkl}^2 are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in ε, there are no bosonic QED fixed points with N < 183 flavors.

Anomalous dimensions of effective theories from partial waves

On-shell amplitude methods have proven to be extremely efficient for calculating anomalous dimensions. We further elaborate on these methods to show that, by the use of an angular momentum decomposition, the one-loop anomalous dimensions can be reduced to essentially a sum of products of partial waves. We apply this to the SM EFT, and show how certain classes of anomalous dimensions have their origin in the same partial-wave coefficients. We also use our result to obtain a generic formula for the one-loop anomalous dimensions of nonlinear sigma models at any order in the energy expansion, and apply our method to gravity, where it proves to be very advantageous even in the presence of IR divergencies.

Anomalous dimensions from gauge couplings in SMEFT with right-handed neutrinos

Standard Model Neutrino Effective Field Theory (SMNEFT) is an effective theory with Standard Model (SM) gauge-invariant operators constructed only from SM and right-handed neutrino fields. For the full set of dimension-six SMNEFT operators, we present the gauge coupling terms of the one-loop anomalous dimension matrix for renormalization group evolution (RGE) of the Wilson coefficients between a new physics scale and the electroweak scale. We find that the SMNEFT operators can be divided into five subsets which are closed under RGE. Our results apply for both Dirac and Majorana neutrinos. We also discuss the operator mixing pattern numerically and comment on some interesting phenomenological implications.

Structure of two-loop SMEFT anomalous dimensions via on-shell methods

We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott.

One-loop non-planar anomalous dimensions in super Yang-Mills theory

We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

Scalar and tensor neutrino interactions

We constrain general Dirac neutrino interactions based on the Standard Model Effective Field Theory framework extended with right-handed neutrinos N (SMNEFT) using deep inelastic and coherent elastic neutrino scattering, nuclear beta decay, and meson decay data, and high energy electron-proton and proton-proton collider data. We compute the one-loop anomalous dimensions of the low-energy effective field theory (LEFT) below the electroweak scale and of SMNEFT above the electroweak scale. The tree-level matching between LEFT and SMNEFT is performed at the electroweak scale. Currently, the most stringent limits on scalar and tensor interactions arise from pseudoscalar meson decays and the LHC measurements at the per mille level. In the future, the upcoming High-Luminosity LHC (HL-LHC) has the potential to reach the 10−4 level and LHeC can play an important role under certain theoretical assumptions.

One-loop matching in the SMEFT extended with a sterile neutrino

We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos (νSMEFT). Our aim is twofold. First, to contextualise new collider signatures in models with sterile neutrinos so far studied only using the bottom-up approach. And second and more important, to provide a thorough example of one-loop matching in the diagrammatic approach, of which other matching techniques and automatic tools can benefit for cross-checks. As byproducts of this work, we provide for the first time: (i) a complete off-shell basis for the νSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy effective field theory (νLEFT) and the tree-level matching onto the νSMEFT; (iii) partial one-loop anomalous dimensions in the νLEFT. This way, our work comprises a new step forward towards the systematisation of one-loop computations in effective field theories, especially if the SM neutrinos are Dirac.