arXiv subjects

Rudi Rahn

Publications and source records attributed to Rudi Rahn.

17 recordsLinked to original sources

arXiv2026

NNLO soft functions for heavy-quark pair production at hadron colliders

We generalise the SoftSERVE framework for the automated computation of soft functions involving final-state heavy quarks in back-to-back kinematics up to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our algorithm employs suitable phase-space parameterisations for both massive and mixed massless-massive contributions, allowing for an efficient numerical evaluation. Focusing on SCET$_\mathrm{I}$ observables that satisfy non-Abelian exponentiation, we present explicit results for the 0-jettiness soft function in hadronic top-quark pair production in the form of two-dimensional grids. We describe the renormalisation procedure in detail and discuss the singular behaviour of the tripole colour correlations in the threshold limit.

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arXiv2026

Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC

We present a theoretical study of the azimuthal decorrelation $\delta\phi$ and transverse momentum imbalance $q_T$ in dijet production at the LHC, offering intriguing insights into the dynamics of quantum chromodynamics. We define the jet axes using the recoil-free winner-take-all (WTA) recombination scheme. For the azimuthal decorrelation $\delta\phi$, this axis choice eliminates non-global logarithms (NGLs) entirely. For the transverse momentum imbalance $q_T$, NGLs emerge specifically in the small jet radius limit ($R \ll 1$). In this regime, the WTA scheme simplifies the theoretical framework by restricting jet radius logarithms to the soft sector. We derive factorization formulae for both observables within soft-collinear effective theory. To address the small-$R$ NGLs in the $q_T$ distribution, we refactorize the soft function into global soft, collinear-soft, and ultra-collinear-soft modes. We perform the resummation of global large logarithms $\ln(\delta\phi)$ and $\ln(q_T/Q)$ up to next-to-next-to-leading logarithmic accuracy. For the $q_T$ distribution, this is combined with a leading-logarithmic resummation of the non-global $\ln R$ terms. We match our predictions to leading fixed-order $O(\alpha_s^3)$ calculations. We also numerically investigate the structure of the first subleading power corrections. Comparisons with PYTHIA8 simulations demonstrate that the observables we consider are robust against non-perturbative multi-parton interactions and hadronization effects.

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arXiv2024

$q_T$-slicing with multiple jets

Modern collider phenomenology requires unprecedented precision for the theoretical predictions, for which slicing techniques provide an essential tool at next-to-next-to-leading order (NNLO) in the strong coupling. The most popular slicing variable is based on the transverse momentum $q_T$ of a color-singlet final state, but its generalization to final states with jets is known to be very difficult. Here we propose two generalizations of $q_T$ that can be used for jet processes, providing proof of concept with an NLO slicing for $pp \to 2$ jets. We present factorization formulae that enable our approach to NNLO, calculate the NNLO collinear-soft function and demonstrate slicing at this order for $e^+e^- \to 2$ jets. One of these generalizations of $q_T$ only applies to planar Born processes, such as $pp \to 2$ jets, but offers a dramatic simplification of the soft function. We also discuss how our approach can directly be extended to obtain predictions for the fragmentation of hadrons. This presents a promising path for high-precision QCD calculations with multi-jet final states.

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arXiv2023

The NNLO soft function for N-jettiness in hadronic collisions

We compute the N-jettiness soft function in hadronic collisions to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an extension of the SoftSERVE framework to soft functions that involve an arbitrary number of lightlike Wilson lines. We present numerical results for 1-jettiness and 2-jettiness, and illustrate that our formalism carries over to a generic number of jets by calculating a few benchmark points for 3-jettiness. We also perform a detailed analytic study of the asymptotic behaviour of the soft-function coefficients at the edges of phase space, when one of the jets becomes collinear to another jet or beam direction, and comment on previous calculations of the N-jettiness soft function.

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arXiv2023

N$^3$LL resummation of one-jettiness for $Z$-boson plus jet production at hadron colliders

We present the resummation of one-jettiness for the colour-singlet plus jet production process $p p \to ( \gamma^*/Z \to \ell^+ \ell^-) + {\text{jet}}$ at hadron colliders up to the fourth logarithmic order (N$^3$LL). This is the first resummation at this order for processes involving three coloured partons at the Born level. We match our resummation formula to the corresponding fixed-order predictions, extending the validity of our results to regions of the phase space where further hard emissions are present. This result paves the way for the construction of next-to-next-to-leading order simulations for colour-singlet plus jet production matched to parton showers in the GENEVA framework.

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arXiv2023

Discrete symmetries and Efficient Counting of Operators

We present DECO ("Discrete and Efficient Counting of Operators"), an implementation of the Hilbert Series to enumerate subleading operator bases for SMEFT-like EFTs with symmetry groups as typically found in flavour and BSM physics. DECO can accommodate EFTs with arbitrary numbers and combinations of the SM gauge groups, as well as the discrete groups S4, A4, and Zn, and U(1) groups with residual global charge (and these groups' most important representations). The program is highly modular and can easily be extended to additional groups and/or representations. We demonstrate the design cases for DECO by using it to cross-check subleading operator bases of EFTs in the literature, which allows us to identify a missing operator in a widely used model for the neutrino masses and discuss said operator's impact.

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arXiv2023

Towards Double Parton Distributions from First Principles using Large Momentum Effective Theory

In double parton scattering (DPS), two partonic collisions take place between one pair of colliding hadrons. The effect of DPS can be significant for precision measurements due to the additional radiation from secondary partonic collisions, and especially for specific processes such as same-sign WW production. Its effect is usually included through Monte Carlo parton showers. In a factorization approach to DPS, the initial state is described by double parton distributions (DPDs). These are currently poorly constrained by experiment, but provide a view on interesting correlations between partons in the hadron. Here we show that the Large Momentum Effective Theory approach can be applied to DPDs. Specifically, we present a general matching relation between DPDs and lattice-calculable quasi-DPDs for general flavor, spin and color structures. We furthermore calculate the one-loop matching coefficients for the quark-quark DPDs, verifying that the infrared logarithms and divergences cancel in the matching. While we restrict to the flavor-non-singlet case, we do take color and spin correlations into account. Interestingly, quasi-DPDs combines nontrivial features from both the collinear and transverse momentum dependent quasi-parton distribution functions. This represents a first step in extending the quasi-PDF approach to DPDs, opening up a new way to constrain these distributions using lattice QCD.

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arXiv2022

Recoil-free azimuthal angle for precision boson-jet correlation

The azimuthal decorrelation between a vector boson and a jet is an essential hard probe in high energy proton-proton and heavy-ion collisions. We overcome intrinsic limitations of previous studies by using a recoil-free axis, achieving unprecedented next-to-next-to-leading logarithmic accuracy with small nonperturbative corrections. This choice of axis also makes the observable robust in the presence of a large background. Furthermore, the azimuthal angle distribution is minimally changed when determined using only charged particle tracks, which offer superior angular resolution for precise measurements. Our effective field theory includes full jet dynamics, and we find contributions from linearly-polarized gluon transverse momentum distributions in the initial and final state.

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arXiv2022

Precision boson-jet azimuthal decorrelation at hadron colliders

The azimuthal angular decorrelation of a vector boson and jet is sensitive to QCD radiation, and can be used to probe the quark-gluon plasma in heavy-ion collisions. By using a recoil-free jet definition, the sensitivity to contamination from soft radiation on the measurement is reduced, and the complication of non-global logarithms is eliminated from our theoretical calculation. Specifically we will consider the $p_T^n$ recombination scheme, as well as the $n\to \infty$ limit, known as the winner-take-all scheme. These jet definitions also significantly simplify the calculation for a track-based measurement, which is preferred due to its superior angular resolution. We present a detailed discussion of the factorization in Soft-Collinear Effective Theory, revealing why the transverse momentum $\vec q_T$ is more complicated than the azimuthal angle. We show that potential glauber contributions do not spoil our factorization formalism, at least up to and including order $\alpha_s^3$. The resummation is carried out using the renormalization group, and all necessary ingredients are collected or calculated. We conclude with a detailed phenomenological study, finding an enhanced matching correction for high jet $p_T$ due to the electroweak collinear enhancement of a boson emission off di-jets. We also compare with the Pythia event generator, finding that our observable is very robust to hadronization and the underlying event.

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arXiv2020

..., 83106786, 114382724, 1509048322, 2343463290, 27410087742, ... Efficient Hilbert Series for Effective Theories

We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in the Standard Model Effective Theory (SMEFT) can be obtained in a minute on a single CPU core. While our implementation focusses on SMEFT, we allow for a flexible user input of the light degrees of freedom. Furthermore, gravity, as well as additional U(1) global or gauge symmetries can be included.

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arXiv2020

Generic dijet soft functions at two-loop order: uncorrelated emissions

We extend our algorithm for automating the calculation of two-loop dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, i.e. to those that require an independent calculation of the uncorrelated-emission contribution. As the singularity structure of uncorrelated double emissions differs substantially from the one for correlated emissions, we introduce a novel phase-space parametrisation that isolates the corresponding divergences. The resulting integrals are implemented in SoftSERVE 1.0, which we release alongside of this work, and which we supplement by a regulator that is consistent with the rapidity renormalisation group framework. Using our automated setup, we confirm existing results for various jet-veto observables and provide a novel prediction for the soft-drop jet-grooming algorithm.

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arXiv2019

Generic dijet soft functions at two-loop order: correlated emissions

We present a systematic algorithm for the perturbative computation of soft functions that are defined in terms of two light-like Wilson lines. Our method is based on a universal parametrisation of the phase-space integrals, which we use to isolate the singularities in Laplace space. The observable-dependent integrations can then be performed numerically, and they are implemented in the new, publicly available package SoftSERVE that we use to derive all of our numerical results. Our algorithm applies to both SCET-1 and SCET-2 soft functions, and in the current version it can be used to compute two out of three NNLO colour structures associated with the so-called correlated-emission contribution. We confirm existing two-loop results for about a dozen $e^+e^-$ and hadron-collider soft functions, and we obtain new predictions for the C-parameter as well as thrust-axis and broadening-axis angularities.

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arXiv2019

Two-loop anomalous dimensions of generic dijet soft functions

We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+ e- event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly exponent. We confirm existing two-loop results for about a dozen dijet soft functions and obtain new predictions for the angularity event shape and the soft-drop jet-grooming algorithm.

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arXiv2018

Automated Calculation of ${\pmb N}$-jet Soft Functions

We present a systematic framework for the calculation of soft functions that are defined in terms of $N\geq2$ light-like Wilson lines. The formalism represents an extension of a method that we developed earlier for the calculation of dijet soft functions to the general $N$-jet case. We discuss the technical aspects of this generalisation, focussing on SCET-1 soft functions that obey the non-Abelian exponentiation theorem in this contribution. As a first application of our method, we consider the $N$-jettiness observable and present numerical results for the $1$-jettiness and $2$-jettiness hadron-collider soft functions to next-to-next-to-leading order in the perturbative expansion.

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arXiv2018

Automated Calculation of Dijet Soft Functions in the Presence of Jet Clustering Effects

We extend our framework for the automated calculation of dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, like jet-veto or grooming soft functions that are sensitive to clustering effects of the jet algorithm. Although the matrix element for uncorrelated double emissions has a simpler structure than the one for correlated emissions, we argue that its singularity structure poses more stringent constraints on the required phase-space parametrisation. Our algorithm applies to both SCET-1 and SCET-2 soft functions and it is implemented in the novel program SoftSERVE. We present results for various jet-veto observables and obtain new predictions for the soft-drop jet-grooming algorithm.

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arXiv2017

Non-global and rapidity logarithms in narrow jet broadening

We derive an all-order factorization theorem for the narrow jet broadening event shape, a measure of the transverse momentum in jet events. This is a non-global observable which receives logarithmically enhanced contributions associated with the large rapidity difference between soft and collinear radiation and which is also sensitive to soft recoil effects. Our work is the first factorization analysis of an observable of this type and we show that with regard to the non-global nature, the rapidity logarithms do not constitute an essential complication since they can be tied to the jet function, which is the same as for global observables. As a consequence, the leading non-global logarithms in narrow jet broadening are encoded in the same overall factor relevant for the hemisphere soft function and light jet mass.

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arXiv2015

Automated Calculation of Dijet Soft Functions in Soft-Collinear Effective Theory

We present a systematic framework for the calculation of dijet soft functions, which are defined as a matrix element of two light-like Wilson lines that is weighted by a generic measurement function. Based on a universal parametrisation of the phase-space integrals, we isolate the singular terms in Laplace space and evaluate the observable-dependent integrations numerically. We discuss the implementation of our algorithm into the public program SecDec, and present results for various SCET-1 soft functions to two-loop order. In particular, we obtain new predictions for the C-parameter and the angularity variables. Finally, we discuss ongoing extensions and the future outlook of the project.

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