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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Galilean invariant resummation schemes of cosmological perturbations

Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Resummation of electroweak Sudakov logarithms for real radiation

Using the known resummation of virtual corrections together with knowledge of the leading-log structure of real radiation in a parton shower, we derive analytic expressions for the resummed real radiation after they have been integrated over all of phase space. Performing a numerical analysis for both the 13 TeV LHC and a 100 TeV pp collider, we show that resummation of the real corrections is at least as important as resummation of the virtual corrections, and that this resummation has a sizable effect for partonic center of mass energies exceeding √s=O(few TeV). For partonic center of mass energies √s≳10 TeV, which can be reached at a 100 TeV collider, resummation becomes an O(1) effect and needs to be included even for rough estimates of the cross-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

NNLL resummation of Sudakov shoulder logarithms in the heavy jet mass distribution

The heavy jet mass event shape has large perturbative logarithms near the leading order kinematic threshold at ρ = $\frac{1}{3}$. Catani and Webber named these logarithms Sudakov shoulders and resummed them at double-logarithmic level. A resummation to next-to-leading logarithmic level was achieved recently. Here, we extend the resummation using an effective field theory framework to next-to-next-to-leading logarithmic order and show how to combine it with the resummation of dijet logarithms. We also solve the open problem of an unphysical singularity in the resummed momentum space distribution, in a way similar to how it is resolved in the Drell-Yan q T spectrum: through a careful analysis of the kinematics and scale-setting in position space. The heavy jet mass Sudakov shoulder is the first observable that does not involve transverse momentum for which position space resummation is critical. These advances may lead to a more precise extraction of the strong coupling constant from e + e – data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Resummation of jet veto logarithms at N 3 LL a + NNLO for W + W ? production at the LHC

We compute the resummed on-shell W+W- production cross section under a jet veto at the LHC to partial N3LL order matched to the fixed-order NNLO result. Differential NNLO cross sections are obtained from an implementation of qT subtraction in Sherpa. The two-loop virtual corrections to the qq¯→W+W- amplitude, used in both fixed-order and resummation predictions, are extracted from the public code qqvvamp. We perform resummation using soft collinear effective theory, with approximate beam functions where only the logarithmic terms are included at two-loop. In addition to scale uncertainties from the hard matching scale and the factorization scale, rapidity scale variations are obtained within the analytic regulator approach. Our resummation results show a decrease in the jet veto cross section compared to NNLO fixed-order predictions, with reduced scale uncertainties compared to NNLL+NLO resummed predictions. We include the loop-induced gg contribution with jet veto resummation to NLL+LO. The prediction shows good agreement with recent LHC measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Subleading power resummation of rapidity logarithms: the energy-energy correlator in $ \mathcal{N} $ = 4 SYM

We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the “rapidity identity operators”, that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in \( \mathcal{N} \) = 4 super-Yang-Mills. These logarithms can also be extracted to \( \mathcal{O}\left({\alpha}_s^3\right) \) from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawson’s integral, with an argument related to the cusp anomalous dimension. We call this functional form “Dawson’s Sudakov”. Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the p T spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

First subleading power resummation for event shapes

We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables τ at subleading power in the τ « 1 expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call θ-jet and θ-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in αs, and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for H → gg in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to O(α$3\atop{s}$). Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the θ-soft and θ-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Momentum conservation and unitarity in parton showers and NLL resummation

We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms formulated in terms of color dipoles are analyzed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

$\mathrm{Z}$ero-jettiness resummation for top-quark pair production at the $\mathrm{LHC}$

We study the resummation of the 0-jettiness resolution variable $\mathcal{T}_o$ for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $\mathcal{T}_o$→ o limit. We then calculate the $\mathcal{O}(a_s)$ corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL', NNLL and Approximate NNLL' (NNLL$^{'}_{a}$). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the $t\bar{t}$+jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at NNLL$^{'}_{a}$+NLO accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Improved thermal resummation for multi-field potentials

The resummation of large thermal corrections to the effective potential is mandatory for the accurate prediction of phase transitions. We discuss the accuracy of different prescriptions to perform this resummation at the one- and two-loop level and point out conceptual issues that appear when using a high-temperature expansion at the two-loop level. Moreover, we show how a particular prescription called partial dressing, which does not rely on a high-temperature expansion, consistently avoids these issues. We introduce a novel technique to apply this resummation method to the case of multiple mixing fields. Our approach significantly extends the range of applicability of the partial dressing prescription, making it suitable for phenomenological studies of beyond the Standard Model extensions of the Higgs sector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

On the IR-resummation in the EFTofLSS

Here, we propose a simplification for the IR-resummation scheme of [1] and also include its next-to-leading order corrections coming from the tree-level three-point function of the long displacement field. First we show that the new simplified formula shares the same properties of the resummation of [2]. In Fourier space, the IR-resummed power spectrum has no residual wiggles and the two-loop calculation matches the non-linear power spectrum of the Dark Sky simulation at z = 0 up to k ≃ 0.34 h Mpc –1 within cosmic variance. Then, we find that the additional subleading terms (although parametrically infrared-enhanced) modify the leading-order IR-resummed correlation function only in a marginal way, implying that the IR-resummation scheme can robustly predict the shape of the BAO peak.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

An analytic implementation of the IR-resummation for the BAO peak

We develop an analytic method for implementing the IR-resummation of [1], which allows one to correctly and consistently describe the imprint of baryon acoustic oscillations (BAO) on statistical observables in large-scale structure. We show that the final IR-resummed correlation function can be computed analytically without relying on numerical integration, thus allowing for an efficient and accurate use of these predictions on real data in cosmological parameter fitting. In this work we focus on the one-loop correlation function and the BAO peak. We show that, compared with the standard numerical integration method of IR-resummation, the new method is accurate to better than 0.2%, and is quite easily improvable. We also give an approximate resummation scheme which is based on using the linear displacements of a fixed fiducial cosmology, which when combined with the method described above, is about six times faster than the standard numerical integration. Finally, we show that this analytic method is generalizable to higher loop computations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Bootstrapping rapidity anomalous dimensions for transverse-momentum resummation

Soft function relevant for transverse-momentum resummation for Drell-Yan or Higgs production at hadron colliders are computed through to three loops in the expansion of strong coupling, with the help of bootstrap technique and supersymmetric decomposition. The corresponding rapidity anomalous dimension is extracted. Furthermore, an intriguing relation between anomalous dimensions for transverse-momentum resummation and threshold resummation is found.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Systematic Extraction of Pion Parton Distributions Using Threshold Resummation and Applications to Pion TMDs

Following our recent Monte Carlo determination of the pion?s PDFs from Drell-Yan (DY) and leading neutron electroproduction data from the Jefferson Lab Angular Momentum (JAM) collaboration, we extend the analysis by including effects from threshold resummation. At higher orders in the strong coupling, ?S, soft gluon emissions cause large logarithmic corrections, which become important in the qq¯ channel of the DY partonic cross section near threshold. These corrections can be summed over all orders of ?S. However, different prescriptions exist for how the threshold resummation is implemented, for instance, using varying levels of approximation in the Minimal Prescription with cosine, expansion, and double Mellin methods. We present the Monte Carlo results of the first simultaneous fit of the valence, sea, and gluon distributions in the pion taking into account the ambiguities in the resummation calculations. The wide ranges of valence distributions at large x and the effective behavior of the valence distribution as x approaches 1 is discussed. While the PDFs are extracted through collinear factorization, we additionally present a dedicated study to the low and large lepton pair transverse momentum distributions (TMDs) in the same DY experimental data. By adjusting the nonperturbative TMD components, we analyze the degree of compatibility between data and theory across all regions of transverse momentum dependence. We attempt to match the description of the low transverse momentum region using Collins-Soper-Sterman (CSS) formalism and the large transverse momentum region, which is best described using collinear factorization.

Sato, Nobuo↗
DOE OSTI2025

Threshold resummation for double-deeply virtual Compton scattering

The threshold region for double-deeply virtual Compton scattering (DDVCS) is discussed. I derive a resummation formula for the (partonic) threshold logarithms in the flavor non-singlet case. The resummations can be done by using (re)factorization theorems for the coefficient functions near the partonic thresholds. As a byproduct, we obtain the leading term in the threshold limit of the two-loop coefficient function in double-deeply-virtual Compton scattering, which agrees with the recent result from explicit calculation, providing a highly non-trivial cross-check.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Effects of threshold resummation for large-x PDF in large momentum effective theory

Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum P z expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xP z , and the threshold soft function, associated with the spectator momentum (1 − x)P z . The renormalization group equation of the soft function enables the resummation of the threshold double logarithms α k ln 2k (1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)P z approaches Λ QCD , but remains valid when both xP z and (1 − x)P z are much larger than Λ QCD . Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.

factorization↗
DOE OSTI2017

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

Here, one can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3 /CFT 2 . In this paper we use the technique to perform calculations in the small 1/c ∝ GN expansion: (1) we prove the all-orders resummation of logarithmic factors ∝1/clog z in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c with fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3 , and (4) we derive the heavy-light vacuum blocks in theories with N = 1, 2 superconformal symmetry.

1/N expansion↗
DOE OSTI2019

Simple non-perturbative resummation schemes beyond mean-field: case study for scalar $\phi^4$ theory in 1+1 dimensions

I present a sequence of non-perturbative approximate solutions for scalar $\phi^4$ theory for arbitrary interaction strength, which contains, but allows to systematically improve on, the familiar mean-field approximation. This sequence of approximate solutions is apparently well-behaved and numerically simple to calculate since it only requires the evaluation of (nested) one-loop integrals. To test this resummation scheme, the case of $\phi^4$ theory in 1+1 dimensions is considered, finding approximate agreement with known results for the vacuum energy and mass gap up to the critical point. Because it can be generalized to other dimensions, fermionic fields and finite temperature, the resummation scheme could potentially become a useful tool for calculating non-perturbative properties approximately in certain quantum field theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗