Massive event-shape distributions at N 2 LL
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Springer
Received: June Revised: August Accepted: August Published: September
19, 11, 24, 21,
2020 2020 2020 2020
Massive event-shape distributions at N2LL
a
Departamento de F´ısica Te´ orica, Universidad Aut´ onoma de Madrid, Cantoblanco, 28049 Madrid, Spain b Instituto de F´ısica Te´ orica UAM-CSIC, E-28049 Madrid, Spain c Departamento de F´ısica Fundamental e IUFFyM, Universidad de Salamanca, E-37008 Salamanca, Spain d Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Wien, Austria
E-mail: [email protected], [email protected], [email protected] Abstract: In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at O(αs ) in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2 LL + O(αs ) 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 fartail of the distribution. The computation of the jet function cannot be cast as the discontinuity 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. Keywords: Jets, NLO Computations ArXiv ePrint: 2006.06383
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)132
JHEP09(2020)132
Alejandro Bris,a,b Vicent Mateub,c and Moritz Preisserd
Contents 1
2 Dijet kinematics
3
3 Massive schemes 3.1 Mass sensitivity 3.2 Massive schemes in the collinear limit
4 6 6
4 Factorization theorems 4.1 SCET 4.2 bHQET
9 9 13
5 SCET jet function computation 5.1 Virtual radiation 5.2 Real radiation 5.2.1 P-scheme thrust 5.2.2 Jettiness 5.3 Final result for the jet function
14 17 18 19 23 24
6 Fixed-order prediction in SCET
26
7 bHQET jet function computation 7.1 Thrust 7.2 Jettiness
28 30 30
8 RG 8.1 8.2 8.3
31 34 35 36
evolution of the SCET jet function Expansion around s = 0 Expansion around s = m2 Expansion around s = ∞
9 Kinematic, mass and hadronization power corrections
39
10 Numerical analysis
41
11 Conclusions
47
A Sector decomposition
49
P for s > m2 B Alternative analytic expression of Ind
50
–i–
JHEP09(2020)132
1 Introduction
1
Introduction
1
The
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