POWER CORRECTIONS FROM MILAN TO LHC Gavin P . Salam, CERN Giuseppe - PowerPoint PPT Presentation

POWER CORRECTIONS FROM MILAN TO LHC Gavin P . Salam, CERN Giuseppe Marchesini Memorial Meeting 
 GGI, Florence, 19 May 2017 1

NUCLEAR A PIVOTAL ARTICLE PHYSICS B ELSEVIER Nuclear Physics B 469 (1996) 93-142 set out systematics of power corrections for almost any Dispersive approach to power-behaved QCD observable --k contributions in QCD hard processes “Wise Dispersive Method” 
 Yu.L. Dokshitzer a,1, G. Marchesini b B.R. Webber c a Theory Division, CERN, CIt-121! Geneva 23, Switzerland b Dipartimento di Fisica, Universit~ di Milano, and INFN, Sezione di Milano, haly c Cavendish Laboratory, University of Cambridge, UK Received 25 January 1996; accepted 18 March 1996 Abstract with process-dependent powers and coe ffi cients. We analyse a wide variety of We consider power-behaved contributions to hard processes in QCD arising from non-pertur- quark-dominated processes and observables, and show how the power contri- bative effects at low scales which can be described by introducing the notion of an infrared- butions are specified in lowest order by the behaviour of one-loop Feynman finite effective coupling. Our method is based on a dispersive treatment which embodies running coupling effects in all orders. The resulting power behaviour is consistent with expectations based diagrams containing a gluon of small virtual mass. We discuss both collinear on the operator product expansion, but our approach is more widely applicable. The dispersively generated power contributions to different observables are given by (log-)moment integrals of safe observables (such as the e + e − total cross section and τ hadronic width, a universal low-scale effective coupling, with process-dependent powers and coefficients. We DIS sum rules, e + e − event shape variables and the Drell-Yan K -factor) and analyze a wide variety of quark-dominated processes and observables, and show bow the power contributions are specified in lowest order by the behavioar of one-loop Feynman diagrams collinear divergent quantities (such as DIS structure functions, e + e − fragmen- containing a gluon of small virtual mass. We discuss both collinearosafe observables (such as the e+e - total cross section and z hadronic width, DIS sum rules, e+e - event shape variables and tation functions and the Drell-Yan cross section). the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e+e - fragmentation functions and the Drell-Yan cross section). 2 1. Introduction Power-behaved contributions to hard collision observables are by now widely rec- ognized both as a serious difficulty in improving the precision of tests of perturbative * Research supported in part by the UK Particle Physics and Astronomy Research Council and by the EC Programme "Human Capital and Mobility", Network "Physics at High Energy Colliders", contract CHRX- CT93-0357 (DG 12 COMA). E On leave from St. Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188350, Russia. Elsevier Science B.V. PH S0550-3213(96)00155- 1

Testing place: event shapes Thrust: � i | ⃗ p i . ⃗ n T | , T = max � i | ⃗ p i | ⃗ n T T ≃ 2 / 3 3-jet event: 2-jet event: T ≃ 1 There exist many other measures of aspects of the shape: Thrust-Major, C-parameter, broadening, heavy-jet mass, jet-resolution parameters,. . . 3

Power corrections matter for event shapes Schematic picture: ⟨ 1 − T ⟩ v. e + e − centre of mass energy Q ⟨ 1 − T ⟩ ≃ 〈 1 − T 〉 0.18 DELPHI α 0 + B α 2 A α s + c T ALEPH s Q OPAL 0.16 ���� ���� L3 LO NLO NLO + 1/Q SLD several papers, notably 0.14 TOPAZ TASSO Dokshitzer, Marchesini PLUTO 0.12 CELLO & Webber ’95 MK II HRS 0.1 AMY JADE ◮ α 0 is non-perturbative 0.08 NLO but should be universal 0.06 ◮ c T can be predicted LO 0.04 through a calculation using a single 0.02 massive-gluon emission 0 20 30 40 50 60 70 80 90100 Q (GeV) 4

Power corrections matter for event shapes Schematic picture: ⟨ 1 − T ⟩ v. e + e − centre of mass energy Q ⟨ 1 − T ⟩ ≃ 〈 1 − T 〉 0.18 DELPHI α 0 + B α 2 A α s + c T ALEPH s Q OPAL 0.16 ���� ���� L3 LO NLO NLO + 1/Q SLD several papers, notably 0.14 TOPAZ TASSO Dokshitzer, Marchesini PLUTO 0.12 CELLO & Webber ’95 MK II HRS 0.1 AMY JADE ◮ α 0 is non-perturbative 0.08 NLO but should be universal 0.06 <(1-T)> Fit with Pythia hadronization: = 0.1192 0.0005 α ± ◮ c T can be predicted s 0.14 LO Fit with power corrections: = 0.1166 0.0015 α ± 0.04 s through a calculation 0.12 Pure NNLO prediction: = 0.1189 α s using a single 0.02 0.1 NNLO + 1/Q Gehrmann, Jaquier, & Luisoni 2010 massive-gluon emission 0.08 0 NNLO 20 30 40 50 60 70 80 90100 0.06 Q (GeV) 0 20 40 60 80 100 120 140 160 180 200 220 s (GeV) 4

universality of α 0 v. data (ellipses should all coincide…) 0.7 ρ 0.6 You could legitimately ask T (DW) the question: 0.5 C ρ h Given the complexity of real α 0 0.4 T (BB) hadronic events, could B T dominant non-perturbative 0.3 physics truly be determined B W from just a single-gluon 0.2 1- σ contours calculation? "Naive" massive gluon approach 0.1 0.110 0.120 0.130 α s (M Z ) The data clearly say something is wrong with this assumption initially, most clearly pointed out by the JADE collaboration 5

A first key result with Pino (+Yuri & A. Lucenti) Idea of “wise dispersive method”: probe non-perturbative e ff ects by integrating over virtuality of an infrared gluon. But such a “massive” gluon will necessarily decay to two gluons or q ¯ q that go in di ff erent directions. issue raised: Nason & Seymour ’95 So: explicitly include the calculation of that splitting. A very simple result: for thrust, non-perturbative correction simply gets rescaled by a numerical “Milan” factor M ≃ 1 . 49 Matrix elements from Berends and Giele ’88 + Dokshitzer, Marchesini & Oriani ’92 M first calculated for thrust: Dokshitzer, Lucenti, Marchesini & GPS ’97 n f piece for σ L : Beneke, Braun & Magnea ’97 calculation fixed: Dasgupta, Magnea & Smye ’99 6

2nd key observation with Pino et al. There are two classes of event shape 1) those that are a linear combination of contributions from individual emissions i = 1 . . . n = + n � p ti e − | η i | � � e.g. 1 − T ≃ i =1 2) those that are non-linear , e.g. B W , B T , ρ h = + for the latter, the non-perturbative correction cannot possibly be deduced just from a one-gluon calculation (2-gluon M diverges) 7

3rd key observation with Pino et al In the presence of perturbative emissions with p t � Λ QCD , then all the non-linear event shapes turn out to have an “emergent” linearity for non-perturbative emissions at scales ∼ Λ QCD = + ➥ non-perturbative (NP) e ff ects can still be deduced from the e ff ect of a single non-perturbative gluon, but its impact must be determined by averaging over perturbative configurations � [ d Φ pert . ] | M 2 ( pert . ) | × NP( pert . ) ⟨ NP ⟩ ≃ first such observation, for ρ h : Akhoury & Zakharov ’95 universality of “Milan” factor in e + e − : Dokshitzer, Marchesini, Lucenti & GPS ’98 PT and NP e ff ects together in jet broadenings: Dokshitzer, Marchesini & GPS ’98 universality of “Milan” factor in DIS: Dasgupta & Webber ’98 cross-talk between shape functions: moderate Λ / p t e ff ects: Korchemsky & Tafat ’00 8

comparing improvements to data 0.7 ρ Original results for fits of α s and the non-perturbative 0.6 parameter α s . T (DW) 0.5 → C ρ h Including all the “DLMS” α 0 0.4 T (BB) improvements B T Pino et al ’97-98 0.3 → B W 0.2 1- σ contours Taking care not just of gluon masses, but also "Naive" massive gluon approach hadron masses 0.1 0.110 0.120 0.130 GPS & Wicke ’01 α s (M Z ) 9

comparing improvements to data 0.7 Original results for fits of α s ρ and the non-perturbative ρ h 0.6 parameter α s . T 0.5 → C B T Including all the “DLMS” α 0 0.4 B W improvements Pino et al ’97-98 0.3 → 0.2 Taking care not just of gluon masses, but also Resummed coefficients hadron masses 0.1 0.110 0.120 0.130 GPS & Wicke ’01 α s (M Z ) 10

comparing improvements to data 0.7 Original results for fits of α s and the non-perturbative 0.6 parameter α s . T ρ 0.5 → C B T Including all the “DLMS” α 0 ρ h 0.4 B W improvements Pino et al ’97-98 0.3 → 0.2 Taking care not just of gluon masses, but also p-scheme hadron masses 0.1 0.110 0.120 0.130 GPS & Wicke ’01 α s (M Z ) 11