Matching of resummation with fixed order NNLO for event shapes

2008 ◽  
Author(s):  
Gionata Luisoni ◽  
Thomas Gehrmann ◽  
Hasko Stenzel
Keyword(s):  
Fixed Order ◽  
Event Shapes

scholarly journals Massive event-shape distributions at N2LL

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Alejandro Bris ◽  
Vicent Mateu ◽  
Moritz Preisser
Keyword(s):  
Cross Sections ◽  
Numerical Study ◽  
Renormalization Group Equation ◽  
Effective Theory ◽  
Event Shape ◽  
Group Equation ◽  
Soft Collinear Effective Theory ◽  
Fixed Order ◽  
Collinear Limit ◽  
Event Shapes

Abstract In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2LL + $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s precision. Our results can be used for thrust, heavy jet mass and C-parameter distributions in any massive scheme, and are easily generalized to angularities and other event shapes. We show that the so-called E- and P-schemes coincide in the collinear limit, and compute the missing pieces to achieve this level of accuracy: the P-scheme massive jet function in Soft-Collinear Effective Theory (SCET) and boosted Heavy Quark Effective Theory (bHQET). The resummed expression is subsequently matched into fixed-order QCD to extend its validity towards the tail and far- tail of the distribution. The computation of the jet function cannot be cast as the dis- continuity of a forward-scattering matrix element, and involves phase space integrals in d = 4 − 2ε dimensions. We show how to analytically solve the renormalization group equation for the P-scheme SCET jet function, which is significantly more complicated than its 2-jettiness counterpart, and derive rapidly-convergent expansions in various kinematic regimes. Finally, we perform a numerical study to pin down when mass effects become more relevant.

The relative cycle in Hungarian declaratives

2018 ◽  
Author(s):  
Julia Bacskai-Atkari
Keyword(s):  
Word Order ◽  
Relative Position ◽  
Left Periphery ◽  
Word Order Variation ◽  
Order Variation ◽  
Fixed Order ◽  
Embedded Clauses ◽  
Head Positions

This chapter examines word order variation and change in the high CP-domain of Hungarian embedded clauses containing the finite subordinating C head hogy ‘that’. It is argued that the complementizer hogy developed from an operator of the same morphophonological form, meaning ‘how’, and that its grammaticalization path develops in two steps. In addition to the change from an operator, located in a specifier, into a C head (specifier-to-head reanalysis), the fully grammaticalized complementizer hogy also changed its relative position on the CP-periphery, ultimately occupying the higher of two C head positions (upward reanalysis). Other complementizers that could co-occur with hogy in Old Hungarian eventually underwent similar reanalysis processes. Hence the possibility of accommodating two separate C heads in the left periphery was lost and variation in the relative position of complementizers was replaced by a fixed order.

QCD at Fixed Order: Processes

2018 ◽  
Author(s):  
John Campbell ◽  
Joey Huston ◽  
Frank Krauss
Keyword(s):  
Hadron Collider ◽  
Detailed Comparison ◽  
Theoretical Description ◽  
Higgs Bosons ◽  
Final States ◽  
Collider Physics ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Fixed Order ◽  
The Subject

At the core of any theoretical description of hadron collider physics is a fixed-order perturbative treatment of a hard scattering process. This chapter is devoted to a survey of fixed-order predictions for a wide range of Standard Model processes. These range from high cross-section processes such as jet production to much more elusive reactions, such as the production of Higgs bosons. Process by process, these sections illustrate how the techniques developed in Chapter 3 are applied to more complex final states and provide a summary of the fixed-order state-of-the-art. In each case, key theoretical predictions and ideas are identified that will be the subject of a detailed comparison with data in Chapters 8 and 9.

scholarly journals Soft-drop grooming for hadronic event shapes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Jeremy Baron ◽  
Daniel Reichelt ◽  
Steffen Schumann ◽  
Niklas Schwanemann ◽  
Vincent Theeuwes
Keyword(s):  
Event Generator ◽  
Experimental Measurements ◽  
Event Shape ◽  
Matrix Elements ◽  
Underlying Event ◽  
Hadronic Event ◽  
Wide Range ◽  
Event Shapes ◽  
The Impact ◽  
Perturbative Corrections

Abstract Soft-drop grooming of hadron-collision final states has the potential to significantly reduce the impact of non-perturbative corrections, and in particular the underlying-event contribution. This eventually will enable a more direct comparison of accurate perturbative predictions with experimental measurements. In this study we consider soft-drop groomed dijet event shapes. We derive general results needed to perform the resummation of suitable event-shape variables to next-to-leading logarithmic (NLL) accuracy matched to exact next-to-leading order (NLO) QCD matrix elements. We compile predictions for the transverse-thrust shape accurate to NLO + NLL′ using the implementation of the Caesar formalism in the Sherpa event generator framework. We complement this by state-of-the-art parton- and hadron-level predictions based on NLO QCD matrix elements matched with parton showers. We explore the potential to mitigate non-perturbative corrections for particle-level and track-based measurements of transverse thrust by considering a wide range of soft-drop parameters. We find that soft-drop grooming indeed is very efficient in removing the underlying event. This motivates future experimental measurements to be compared to precise QCD predictions and employed to constrain non-perturbative models in Monte-Carlo simulations.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Counting subgroups of fixed order in finite abelian groups

2021 ◽  
Vol 24 (1) ◽  
pp. 263-276
Author(s):  
Fikreab Solomon Admasu ◽  
Amit Sehgal
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Fixed Order

scholarly journals Toward massless and massive event shapes in the large-β0 limit

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
N. G. Gracia ◽  
V. Mateu
Keyword(s):  
Top Quark ◽  
Matrix Elements ◽  
Position Space ◽  
Positive Real ◽  
Full Agreement ◽  
Anomalous Dimensions ◽  
Fixed Order ◽  
Principal Value ◽  
Contour Deformation ◽  
Perturbative Corrections

Abstract We present results for SCET and bHQET matching coefficients and jet functions in the large-β0 limit. Our computations exactly predict all terms of the form $$ {\alpha}_s^{n+1}{n}_f^n $$ α s n + 1 n f n for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to $$ \mathcal{O}\left({\alpha}_s^4\right) $$ O α s 4 . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of αs using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor Hm that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

Sign in / Sign up

Export Citation Format

Share Document