Gavin P. Salam, CERN Giuseppe Marchesini Memorial Meeting GGI

POWER CORRECTIONS FROM MILAN TO LHC Gavin P. Salam, CERN

Giuseppe Marchesini Memorial Meeting GGI, Florence, 19 May 2017

1 CERN-TH/95-281 Cavendish-HEP-95/12 hep-ph/9512336

Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes1

Yu.L. Dokshitzer 2 Theory Division, CERN, CH-1211 Geneva 23, Switzerland G. Marchesini Dipartimento di Fisica, Universitàdi Milano and INFN, Sezione di Milano, Italy and B.R. Webber Cavendish Laboratory, University of Cambridge, UK NUCLEAR A PIVOTAL ARTICLE PHYSICS B ELSEVIER Nuclear Physics B 469 (1996) 93-142 Abstract set out systematics of power Wecorrections consider power-behaved for almost any contributions to hard processes in QCD arising from non-perturbative effects at low scalesDispersive which approach can be desc to ribedpower-behaved by intro- --k ducingQCD the notion observable of an infrared-finite effcontributionsective coupling. in QCD Our hard method processes is based on a dispersive treatment which embodiesYu.L. running Dokshitzer couplinga,1, G. Marchesini effects b B.R. in Webber all or- c “Wise Dispersive Method” a Theory Division, CERN, CIt-121! Geneva 23, Switzerland ders. The resulting power behaviourb isDipartimento consistent di Fisica, Universit~ with di Milano, expe and ctationsINFN, Sezione di Milano, based haly on the operator product expansion, but our approachc Cavendish Laboratory, is more University of w Cambridge,idely UK applicable. The dispersively-generated power contributionsReceived 25 January to 1996; di ffacceptederent 18 March observables 1996 are given by (log-)moment integrals of a universal low-scaleeffective coupling, arXiv:hep-ph/9512336v3 29 Jan 1996 with process-dependent powers andAbstract coe fficients. 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,bative effects at low scales and which show can be howdescribed th byepowercontri- introducing the notion of an infrared- finite effective coupling. Our method is based on a dispersive treatment which embodies running butions are specified in lowest ordercoupling effects by thein all orders. behaviour The resulting power of one-behaviourloop is consistent Feynman with expectations based diagrams containing a gluon of smallon the operator virtual product mass.expansion, but We our approach discus is sbothcollinearmore widely applicable. The dispersively generated power contributions to different observables are given by (log-)moment integrals of + safe observables (such as the e ea −universaltotal low-scale cross effective section coupling, andwith process-dependentτ hadronic powers width, and coefficients. We + analyze a wide variety of quark-dominated processes and observables, and show bow the power DIS sum rules, e e− event shapecontributions variables are specified and in thelowest Drell-Yanorder by the behavioarK-factor) of one-loop Feynman and diagrams containing a gluon of small virtual mass. We discuss both collinearosafe+ observables (such as the collinear divergent quantities (suche+e - astotal DIScross section structure and z hadronic func width,tions, DIS sum erules,e −e+efragmen- - event shape variables and the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e+e - tation functions and the Drell-Yanfragmentation cross functions section). and the Drell-Yan cross section).

2 CERN-TH/95-281 1. Introduction December 1995 1 Power-behaved contributions to hard collision observables are by now widely rec- Research supported in part by the UK Particleognized both Physics as a serious and difficulty Astronomy in improving Research the precision Council of tests and of perturbative by the EC Programme “Human Capital and Mobility”, Network “PhysicsatHighEnergyColliders”,contract * Research supported in part by the UK Particle Physics and Astronomy Research Council and by the EC CHRX-CT93-0357 (DG 12 COMA). Programme "Human Capital and Mobility", Network "Physics at High Energy Colliders", contract CHRX- 2 CT93-0357 (DG 12 COMA). On leave from St Petersburg Nuclear PhysicsEOn leave Institute, from St. Petersburg Gatc Nuclearhina, Physics St Institute, Petersburg Gatchina, St. Petersburg 188350, 188350, Russia. Russia.

Elsevier Science B.V. PH S0550-3213(96)00155- 1 Best place to check: event shapes TestingFirst discussion place: goes event back shapes to 1964. Serious work got going in late’70s. Various proposals to measure shape of events. Most famous example is Thrust:

|⃗pi .⃗n | T =max i T , ⃗nT ! i |⃗pi | !

2-jet event: T ≃ 1 3-jet event: T ≃ 2/3 There exist many other measures of aspects of the shape: Thrust-Major, C-parameter, broadening, heavy-jet mass, jet-resolution parameters,. . .

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 33 / 15 PowerClear corrections need for matter contributions for event beyond shapes perturbation theory

Schematic picture: ⟨1 − T ⟩ v. e+e− centre of mass energy Q

〉 0.18 T

T ⟨1 − ⟩≃

− DELPHI 1 〈 α0 ALEPH 2 Aαs + Bαs + cT 0.16 OPAL Q L3 LO NLO + 1/Q SLD NLO 0.14 TOPAZ several papers, notably TASSO !"#$ !"#$ PLUTO 0.12 Dokshitzer, Marchesini CELLO MK II & Webber ’95 0.1 HRS AMY JADE ! 0.08 α0 is non-perturbative NLO but should be universal 0.06 ! LO cT can be predicted 0.04 through a calculation 0.02 using a single

0 massive-gluon emission 20 30 40 50 60 70 80 90100 Q (GeV)

4 Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 4 / 15 PowerClear corrections need for matter contributions for event beyond shapes perturbation theory

Schematic picture: ⟨1 − T ⟩ v. e+e− centre of mass energy Q

〉 0.18 T

T ⟨1 − ⟩≃

− DELPHI 1 〈 α0 ALEPH 2 Aαs + Bαs + cT 0.16 OPAL Q L3 LO NLO + 1/Q SLD NLO 0.14 TOPAZ several papers, notably TASSO !"#$ !"#$ PLUTO 0.12 Dokshitzer, Marchesini CELLO And today? MK II & Webber ’95 0.1 HRS AMY JADE ! 0.08 α0 is non-perturbative NLO but should be universal 0.06 Fit with Pythia hadronization: α = 0.1192 ± 0.0005 0.14 ! s LO Fit with power corrections:cT can be predicted = 0.1166 0.0015 Some people had objected that <(1-T)> α ± 0.04 s 0.12 Pure NNLO prediction:through αs a= 0.1189 calculation 0.020.1 using a single Q NNLO + 1/Q combing NLO + 1/ was incon- 0.08 Gehrmann, Jaquier, & Luisoni 2010 0 massive-gluon emission 20 30 40 50 60 70 80 90100 0.06 NNLO Q (GeV)

0 20 40 60 80 100 120 140 160 180 200 220 sistent, because NNLO might eas- (GeV)s 4 Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 4 / 15 > 2 ily account for all the discrepancy 0.025 Fit with Pythia hadronization: αs = 0.1272 ± 0.0008 Fit with power corrections: αs = 0.1202 ± 0.0018 <(1-T) 0.02 NNLO with αs = 0.1189 between NLO and data. 0.015

0.01

0.005 0 20 40 60 80 100 120 140 160 180 200 220 In the past few years, thanks to (GeV)s > 3 Fit with Pythia hadronization: α = 0.1306 ± 0.0010 0.005 s Fit with power corrections: αs = 0.1233 ± 0.0021 <(1-T) 0.004 NNLO with = 0.1189 epic calculations, NNLO has be- αs 0.003 come available. 0.002 0.001

0 20 40 60 80 100 120 140 160 180 200 220 Gehrmann-De Ridder, Gehrmann (GeV)s > 4 0.0012 Fit with Pythia hadronization: αs = 0.1339 ± 0.0011

0.001 Fit with power corrections: αs = 0.1267 ± 0.0024 Glover & Heinrich ’07 <(1-T) NNLO with = 0.1189 0.0008 αs

0.0006 Weinzierl ’09 0.0004 0.0002

00 20 40 60 80 100 120 140 160 180 200 220 (GeV)s

-3 ×10

> 0.35 5 Fit with Pythia hadronization: α = 0.1367 ± 0.0013 AﬁtwithNNLOshowsclearneed 0.3 s Fit with power corrections: αs = 0.1294 ± 0.0027

<(1-T) 0.25 0.2 NNLO with αs = 0.1189 still for 1/Q component. 0.15 0.1 0.05 Gehrmann, Jacquier & Luisoni ’09 0 0 20 40 60 80 100 120 140 160 180 200 220 (GeV)s

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 11 / 15 universality of α0 v. data (ellipses should all coincide…)

0.7 ρ

0.6 You could legitimately ask T (DW) the question: 0.5 C ρh

Given the complexity of real 0

α 0.4 T (BB) hadronic events, could BT dominant non-perturbative 0.3 physics truly be determined BW from just a single-gluon 0.2 1-σ contours calculation? "Naive" massive gluon approach 0.1 0.110 0.120 0.130

αs(MZ)

The data clearly say something is wrong with this assumption initially, most clearly pointed out by the JADE collaboration 5

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 5 / 15 A first key Aresult ﬁrst with key resultPino (+Yuri with Pino & A. Lucenti) (+ Yuri & A. Lucenti)

Idea of “wise dispersive method”: probe non-perturbative eﬀects by integrating over virtuality of an infrared gluon.

But such a “massive” gluon will necessarily decay to two gluons or qq¯ that go in diﬀerent directions. issue raised: Nason & Seymour ’95

So: explicitly include the calculation of that splitting. Averysimpleresult:forthrust,non-perturbativecorrection 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

nf piece for σL: Beneke, Braun & Magnea ’97 calculation ﬁxed: Dasgupta, Magnea & Smye ’99

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 6 / 15 6 2nd key observation with2nd Pino key et observational. 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 −|ηi | e.g. 1 − T ≃ pti e ! "i=1 #

2) those that are non-linear, e.g. BW , BT , ρh =+

for the latter, the non-perturbative correction cannot possibly be deduced just from a one-gluon calculation (2-gluon M diverges)

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 7 / 15 7 3rd key observation with Pino3rd keyet al observation with Pino et al

In the presence of perturbative emissions with pt ≫ ΛQCD ,thenall the non-linear event shapes turn out to have an “emergent” linearity for non-perturbative emissions at scales ∼ ΛQCD =+

➥ non-perturbative (NP) effects can still be deduced from the effect of a single non-perturbative gluon, but its impact must be determined by averaging over perturbative configurations

2 ⟨NP⟩≃ [dΦpert.] |M (pert.)| × NP(pert.) ! ﬁrst such observation, for ρh:Akhoury&Zakharov’95 universality of “Milan” factor in e+e−:Dokshitzer,Marchesini,Lucenti&GPS’98 PT and NP eﬀects together in jet broadenings: Dokshitzer, Marchesini & GPS ’98 universality of “Milan” factor in DIS: Dasgupta & Webber ’98

cross-talk betweenmoderate shapeΛ/ functions:pt eﬀects: Korchemsky & Tafat ’00 8 Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 8 / 15 comparing improvements to data

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

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 9 / 15 comparing improvements to data

0.7 Original results for ﬁts of αs ρ and the non-perturbative 0.6 ρh parameter αs. T 0.5 → C B T Including all the “DLMS” 0

α 0.4 BW improvements Pino et al ’97-98 0.3 →

0.2 Taking care not just of Resummed coefficients gluon masses, but also 0.1 hadron masses 0.110 0.120 0.130 GPS & Wicke ’01 αs(MZ) 10

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 9 / 15 comparing improvements to data

0.7 Original results for ﬁts of αs 0.6 and the non-perturbative T parameter αs. ρ 0.5 → C B T Including all the “DLMS” 0 ρ α 0.4 h BW improvements Pino et al ’97-98 0.3 →

0.2 Taking care not just of p-scheme gluon masses, but also 0.1 hadron masses 0.110 0.120 0.130 GPS & Wicke ’01 αs(MZ) 11

Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 9 / 15 calculation obtained with nlojet++ [11], and leading 1/Q NP corrections computed with the dispersive method [8, 9]. Events with three separated jets are selected by requiring the three-jet resolution parameter y3 in the Durham algorithm to be larger than ycut.Itisthen many other investigationsclear that different values of ycut correspond to different event geometries. A rich field: many investigations in e+e−Figureand 1 shows DIS the result of a simultane- 1.1 ous fit of αs(MZ )andα0(µI =2GeV)forthe ycut = 0.1 Banfi, Dokshitzer 0.65 D-parameter distribution at Q = MZ cor- 1 ycut = 0.05 10 OPAL 91 GeV α0 Distributions ALEPH 2-jet responding to y =0.1andy =0.05. NLO + NLL 0.6 cut cut Marchesini, 0.9 Zanderighi + hadronisation 0.9 a) BW MH The 1-τzEσ contour plots in the αs-α0 plane 0.55 analysis 0.8 of 3-jet shapes are plotted together with results for other 0.8 τtE B T B 0.5 zE 0.7 T distributions of two-jet event shapes. There (2GeV) /dB (D-parameter)0 0

σ 0.7 α

α 0.45 is a remarkable consistency among the var- d 1 0.6 σ CE 1/ 0.6 D ious distributions, thus strongly supporting 0.5 average 0.4 1-T 0.5 2 the ideaρ that universality of 1/Q power cor- MH, MH C 1-T 0.35 E 0.4 B 0.4 T Q > 30rections GeV holds also for three-jet variables. BW 0.3 0.3 C This leads to the non-trivial implication 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13(a) 0.1 0.08 0.1α 0.12(M ) 0.25 that leading power corrections are indeed 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 s z 0.11 0.115 0.12 0.125 0.13 αS(MZ) Total Broadening (BT) sensitiveαs to the colour and the geometry

2.5 Figure 1: Contour plots in the αs-α0 plane of the hard underlying event, and more- Combined result SU(5) for the Overall,D-parameter many differential analyses distributions in lateover ’90s this and dependence is the one predicted 2 SU(3) QCD corresponding to two different values of ycut. by eq. (5). SU(4) OPAL N gg early ’00s paint a picture of general success DELPHI FF The comparison to data is less satisfac- 1.5 OPAL 4-jet tory forofT them,ascanbeseenfromFig.2. simple physical idea of probing 1000 NP NLO+NLL+1/Q CF Event Shape There one notices a discrepancy between ALEPH ycut=0.1 (x 100) 1 ALEPH 4-jet physics with perturbative tools. 100 theory and data at large values of Tm.To SU(2) track down the origin of the problem, one ycut=0.05 (x 10) 10 0.5 U(1)3 can look at hadronisation corrections pro- 86% CL error ellipses Even if there are “corners” where it doesn’t /dL ycut=0.025 SU(1) duced by MC programs, defined as the ra- σ 1 d

0 σ 0123456tio of the MCwork results as at hadron well as and we’d par- like.1/ . . C A ton level. From the plots in [10] one can 0.1 see that hadronisation corrections for the D- 0.01 Gavin Salam (CERN/Princeton/CNRS) parameterPino and are Power always Corrections larger than one, corre-Pino2012 May 29 2012 10 / 15 sponding to a positive shift, consistent with 0.001 -2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6

our predictions. On the contrary, hadro- L=ln(Tm) nisation corrections for Tm become smaller than one at large Tm,afeaturethatwill Figure 2: Theoretical predictions for Tm dis- never be predicted by a model based on a tribution plotted against ALEPH data for single dressed gluon emission from a three three diﬀerent values of ycut. hard parton system. This issue is present also in the heavy-jet mass and wide-jet broadening distributions, and requires further theoretical investigation.

3Extensiontootherhardprocesses

Observables that measure the out-of-event-plane radiationinthree-jeteventscanbeintro- duced also in other hard processes. In DIS two observables have been already measured. One is a variant of Tm [12], where

DIS 2007 NOW MOVE FORWARDS 15-20 YEARS

many NNLO calculations have become available + – (for e e , DIS and pp) LHC physics is reaching high precision, not just for QCD physics, but also e.g. today for “dark-matter” searches, & in the future for Higgs physics NNLO hadron-collider calculations v. time

�� explosion of calculations �� in past 24 months ��

��

�� as of April 2017, let me know of omissions �� 14 indirect constraints on Hcc coupling

impact of modiﬁed Hcc joint limits on κc & κb 2 coupling on Higgs+jet pT @ HL-LHC 4 momenta pT . mh/2. This partly compensates for the by CMS [66] show that the residual experimental sys- 2 2 SM

quadratic mass suppression m /m appearing in (1). As ) Q h tematic uncertainty will be reduced to the levelc =- of10 a few 2 h 1.4 2 percent, at the HL-LHC. Therefore, it is natural to study a result of the logarithmic sensitivity and of the  de- T Q =-5 pendence in quark-initiated production, one expects de- the prospects of the method in future scenariosc assuming dp a reduced/ theory uncertainty given that this = error0 may viations of several percent in the pT spectra in Higgs 1.2 c 1 × production for (1) modiﬁcations of  .IntheSM, becomed the limiting factor. Q c = 5 O In order to investigate the future prospects of our the light-quark e↵ects are small. Speciﬁcally, in compar- / 1 method, we need a more precise assessment of the non- b

ison to the Higgs e↵ective ﬁeld theory (HEFT) predic- )/( perturbative1.0 corrections to the pT,h distribution. To esti-

h 0 tion, in gg hj the bottom contribution has an e↵ect , ! mate theseT e↵ects, we used MG5aMC@NLO and POWHEG [67] of around 5% on the di↵erential distributions while the showered with Pythia 8.2 and found that the correc- dp

/ 2 2 impact of the charm quark is at the level of 1%. Like- tions can reach up to 2% in the relevant p region. = 2.3 = 5.99 0.8 T,h -1 wise, the combined gQ hQ, QQ¯ hg channels (with This ﬁndingd agrees with recent analytic studies of non- LHC Run II

! ! Q = b, c) lead to a shift of roughly 2%. Precision mea- perturbative/ corrections to pT,h (see e.g. [68]). With im-

1 HL-LHC proved( perturbative calculations, a few-percent accuracy surements of the Higgs distributions for moderate pT values combined with precision calculations of these ob- in this observable0 will20 therefore40 be reachable.60 80 100 -6 -4 -2 0 2 4 6 We study two benchmark cases. Our LHC Run II sce- servables are thus needed to probe (1) deviations in yb 1 p , [GeV] O nario employs 0.3 ab of integratedT h luminosity and as- c and yc. Achieving such an accuracy is both a theoretical sumes a systematic error of 3% on the experimental ± and experimental challenge, but it seems possible in view side and a total theoretical uncertainty of 5%. This Figure 3: Projected future constraints in the c –b plane. of foreseen advances in higher-order calculations and the Figuremeans 1: that The we normalised envision thatpT,h thespectrum non-statistical of± inclusive uncer- HiggsThe SM point is indicated by the black cross. The figure production at ps = 8TeV divided by the SM prediction forshows our projections for the LHC Run II (HL-LHC) with large statistics expected at future LHC runs. tainties presentFady at LHCBishara, Run Ulrich I can beHaisch, halved Pier in the Francesco Monni1 and1 Emanuele Re, arXiv:1606.09253 di↵erent values of  .Only is modified, while the remain-0.3ab (3 ab ) of integrated luminosity at ps =13TeV. coming years, whichc seems plausible.c Our HL-LHC sce- Theoretical framework. Our goal is to explore ing Yukawa couplings aresee kept also at their Y. Soreq, SM values. H. X. Zhu, andThe J. remaining Zupan, assumptionsJHEP 12, 045 entering (2016), our future 1606.09621 predictions 1 15 the sensitivity of the Higgs-boson (pT,h) and leading- nario instead uses 3 ab of data and foresees a reduc- are detailed in the main text. tion of both systematic and theoretical errors by an- jet (pT,j) transverse momentum distributions in inclusive Higgs production to simultaneous modifications of the other factor of two, leading to uncertainties of 1.5% and 2.5%, respectively. The last scenario is illustrative± feature that they are controlled by the size of systematic light Yukawa couplings. We consider final states where are obtained from HIGLU [38], taking into account the of the± reach that can be achieved with improved the- uncertainties that can be reached in the future. Also, at the Higgs boson decays into a pair of gauge bosons. To NNLOory uncertainties. corrections Alternative in the HEFT theory [39 scenarios–41]. Sudakov are dis- loga-future LHC runs our method will allow one to set relevant avoid sensitivity to the modification of the branching ra- rithmscussed ln in ( thepT /m appendix.h) are resummed In both benchmarks, up to NNLL we employ order bothbounds on the modifications of yb. For instance, in the tios, we normalise the distributions to the inclusive cross forpsp=T,h 13[42 TeV–44 and] and thepT,jPDF4LHC15[45–47],nnlo treatingmc set mass [69–72 correc-], HL-HLC scenario we obtain  [0.7, 1.6] at 95% CL. b 2 section. The e↵ect on branching ratios can be included in tionsconsider following the range [27].p The[0 latter, 100] GeV e↵ects in will bins be of significant,5 GeV, Finally, we also explored the possibility of constrain- T 2 the context of a global analysis, jointly with the method onceand takethe spectra into account haveh been precisely, h ZZ measured⇤ 4` downand toing modifications of the strange Yukawa coupling. Under ! ! ! proposed here. ph valuesWW of⇤ (52` GeV).2⌫`. We The assumegQ thathQ, future QQ¯ measure-hg contri-the assumption that yb is SM-like but profiling over c, T ! !O ! ! The gg hj channel was analysed in depth in the butionsments will to be the centred distributions around the are SM calculated predictions. at NLO These withwe find that at the HL-LHC one should have a sensitiv- HEFT framework! where one integrates out the domi- MG5aMC@NLOchannels sum[48 to] a and branching cross-checked ratio of 1 against.2%, butMCFM given. The the ob-ity to ys values of around 30 times the SM expectation. large amount of data the statistical errors per bin will Measurements of exclusive h decays are expected nant top-quark loops and neglects the contributions from tained events are showered with PYTHIA 8.2 [49] and jets be at the 2% ( 1%) level in our LHC Run II (HL- to have a reach that is weaker! than this by a factor of ± ± lighter quarks. While in this approximation the two areLHC) reconstructed scenario. We with model the the anti- correlationkt algorithm matrix [50 as] in as im-order 100 [11]. spectra and the total cross section were studied exten- plementedthe 8 TeV case. in FastJet [51]usingR =0.4 as a radius Conclusions. In this letter, we have demonstrated parameter. 2 sively, the e↵ect of lighter quarks is not yet known with The results of our fits are presented in Figure 3, that the normalised pT distribution of the Higgs or of the same precision for pT . mh/2. Within the SM, showingOur default the constraints choice for in the the renormalisationc –b plane. The (µR un-), fac-jets recoiling against it, provide sensitive probes of the the LO distribution for this process was derived long torisationshaded contours (µF ) and refer the to the resummation LHC Run II (Q scenarioR, for gg with hjbottom,) charm and strange Yukawa couplings. Our new 2 ! ago [17, 19], and the next-to-leading-order (NLO) cor- scalesthe dot-dashed is mh/2. (dotted) Perturbative lines corresponding uncertainties to are estimated = proposal takes advantage of the fact that the di↵eren- 2.3(5.99). Analogously, the shaded contours with the rections to the total cross section were calculated in [20– by varying µR, µF by a factor of two in either direc-tial Higgs plus jets cross section receives contributions solid (dashed) lines refer to the HL-LHC. By profiling from the channels gg hj, gQ hQ, QQ¯ hg 24]. In the context of analytic resummations of the Su- tion while keeping 1/2 µR/µF 2. In addition, for ! ! ! over b, we find in the LHC Run II scenario the follow- that feature two di↵erent functional dependences on Q. dakov logarithms ln (pT /mh), the inclusion of mass cor- the gg hj channel, we vary QR by a factor of two ing 95% CL bound on the yc modifications We have shown that in the kinematic region where the rections to the HEFT were studied both for the p while keeping! µ = µ = m /2. The final total theo- T,h R F h transverse momentum p of emissions is larger than the and pT,j distributions [25–27]. More recently, the first retical errorsc are[ then1.4, 3. obtained8] (LHC by Run combining II) , the(3) scale ? 2 relevant quark mass mQ, but smaller than the Higgs resummations of some of the leading logarithms (1)were uncertainties in quadrature with a 2% relative error as-mass m , both e↵ects can be phenomenologically rele- while the corresponding HL-LHC bound± reads h accomplished both in the abelian [28] and in the high- sociated with PDFs and ↵s for the normalised distribu-vant and thus their interplay results in an enhanced sen- energy [29] limit. The reactions gQ hQ, QQ¯ hg tions. We stress that the normalised distributions usedsitivity to  . This feature allows one to obtain unique ! ! c [ 0.6, 3.0] (HL-LHC) . (4) Q were computed at NLO [30, 31] in the five-flavour scheme in this study are2 less sensitive to PDFs and ↵s varia-constraints on yb, yc and ys at future LHC runs. that we employ here, and the resummation of the loga- tions,These therefore limits compare the above well not2% only relative with the uncertainty projected is a We derived constraints in the c –b plane that arise rithms ln (p /m )inQQ¯ h was also performed up to realisticreach of estimate.other proposed We strategiesobtain± the but relative also have uncertainty the nice infrom LHC Run I data and provided sensitivity projec- T,h h ! next-to-next-to-leading-logarithmic (NNLL) order [32]. the SM and then assume that it does not depend on Q. In the case of gg hj, we generate the LO spectra While this is correct for the gQ hQ, QQ¯ hg chan- with MG5aMC@NLO [33!]. We also include NLO corrections nels, for the gg hj production! a good assessment! of ! to the spectrum in the HEFT [34–36]usingMCFM [37]. the theory uncertainties in the large-Q regime requires The total cross sections for inclusive Higgs production the resummation of the logarithms in (1). First steps in 36 1. Quantum chromodynamics τ

36 1. QuantumBaikov chromodynamics -decays Davier Pich

Boito τ

BaikovSM review -decays Davier PichHPQCD (Wilson loops) BoitoHPQCD (c-c correlators) lattice SMMaltmann review (Wilson loops) JLQCD (Adler functions) 36HPQCDPACS-CS1. Quantum (Wilson (vac. pol. loops) fctns.) chromodynamics ETM (ghost-gluon vertex)

HPQCD (c-c correlators) lattice BBGPSV (static energy)

Maltmann (Wilson loops) τ Baikov -decays PACS-CS (SF scheme)Davier functions structure ABM Pich ETMBBG (ghost-gluonBoito vertex) SM review BBGPSVJR (static potent.) NNPDF HPQCD (Wilson loops)

HPQCD (c-c correlators) functions structure lattice ABMMMHT Maltmann (Wilson loops) JLQCD (Adler functions)

BBG annihilation e+e- PACS-CS (vac. pol. fctns.) JRALEPH (jets&shapes)ETM (ghost-gluon vertex) NNPDFOPAL(j&s) BBGPSV (static energy) Extracting αs from e+e- event shapes and jet MMHTJADErates(j&s) ABM functions structure (3j) BBG

Dissertori e JR ➤ ALEPHJADE (3j) (jets&shapes)NNPDF + Two “best” determinations are from same group e MMHT OPALDW (T)(j&s) – e+e- annihilation e+e- (Hoang et al, 1006.3080,1501.04111) jets & shapes JADEAbbate(j&s) (T) ALEPH (jets&shapes) OPAL(j&s) αs(MZ) = 0.1135 ± 0.0010 (0.9%) [thrust] DissertoriGehrm. (T) (3j) JADE(j&s) Hoang Dissertori (3j) αs(MZ) = 0.1123 ± 0.0015 (1.3%) [C-parameter] JADE (3j) (C) JADE (3j) DW (T) DW (T) electroweak GFitter (T) ➤ Abbate (T) Abbate Similar result from Gehrmann, Luisoni & Monni (1210.6945) Gehrm. (T) precision fts Gehrm. (T) Hoang hadron α (M ) = 0.1131 ± 0.0028 (2.5%) [thrust] CMS (C) s Z Hoang electroweak (tt cross section) GFitter collider (C) precision fts ➤ CMS electroweakhadron lattice: GFitter (tt cross section) precisioncollider fts αs(MZ) = 0.1183 ± 0.0007 (0.6%) [HPQCD] CMS hadron (tt cross section) αs(MZ) = 0.1186 ± 0.0008 (0.7%) [ALPHA prelim.] collider

30 2 Figure 1.2: Summary of determinations of αs(MZ )fromthesixsub-fields2 dependence on fit range Figure 1.2: Summarydiscussed in the of text. determinations The yellow (light shaded) of α bandss(M and)fromthesixsub-fields dashed lines indicate the 5 thrust & “best”± lattice2 are 4-σ apart Z 0 0" 38 ')& :ELQV αs(mZ ) (pert.Aprilpre-average error) 2016χ /(dof) values of each sub-field. The dotted line and grey(darkshaded)band Q Rgapdiscussed in the text. The yellow (light shaded)2 bands and dashed lines indicate the %<& ττPLQ0 PD[ 3 ′ ± represent the final world average value of αs(M ). !"*! 0" 090 0" 33 N LL with Ω1 0.1135 0.0009 0.91 Z 3 ′ MSpre-average values of each sub-field. The dotted line and grey(darkshaded)band N LL with Ω¯ 1 0.1146 ± 0.0021 1.00 " ! 5 '#( 2 0 0" 33 3 ′ representmod the± final world average value of αs(M ). Q N LL without Sτ 0.1241 0.0034 1.26 Z 2 +*H9/ 6 '&' Comments: So far, only one analysis is available which involves the determination of αs from 0 0" 38 O 3 Figure 1.2: Summary of determinations of αs(M )fromthesixsub-fields Q 8 (αs)fixed-order Z 0 0" 33 &&$ 0.1295 ± 0hadron.0046 collider 1.12 data in NNLO of QCD: from a measurement of the tt cross section at !")! Q mod discussed in the text. The yellow (light shaded) bands and dashed lines indicate the 6 without Sτ %<$ &%% ➤ 0 0" 25 vary0 0" 33 thrust & C-parameter are highly correlated observables Q VWULFW pre-average values of each sub-field.February The 22, dotted 2016 10:28 line and grey(darkshaded)band TABLE VII: Comparison of global fit results for our full anal- 6 &*) 0 0" 33 So far, only one analysis¯ is available which involves2 the determination of αs from Q VWULFW ysis➤ to a fit where therepresent renormalon the is not final canceled world with averageΩ1,a value of αs(M ). Analysismod valid far from 3-jet region, but not too deepZ into !"(! fit without Sτ hadron(meaning collider without power data corrections in NNLO with of QCD: from a measurement of the tt cross section at mod Sτ (2-jetk)=δ( kregion)), and a fit— at at fixed LEP, order not without clear power how cor- much of distribution rections and logusing resummation. the transverse All results include energy-energy bottom correlation function (TEEC) and its associated 8 mass andsatisfies QED corrections. this requirement February 22, 2016 10:28 0 0" 33 &$) !"'! Q VWULFW azimuthal asymmetry (ATEEC), respectively [247]. All theseresultsareatNLOonly, 8 %%' 39% CL 0 0" 25 ➤ Q VWULFW thrusthowever fit shows they noticeable provide valuable sensitivity new values to fit of regionαs at energy scales now extending up to 68% CL effect of power corrections is a shift of the distribution in τ,(C-parameter we have estimated in doesn't) Sec. I that a 300 MeV power !"&! correction will lead to an extraction of α from Q = m May 5, 2016 21:57 !"### !"##$ !"##% !"##& !"##' !"##( s Z data that is δαs/αs ( 9 3)% lower than an analysis without power corrections.≃ − ± In our theory code we 16 can easily eliminate all nonperturbative effects by set- FIG. 17: The smaller elongated ellipses show the experimental ting Smod(k)=δ(k)and∆¯ = δ =0.AtN3LL′ or- 39% CL error (1-sigma for αs)andbestfitpointsfordifferent τ global data sets at N3LL′ order in the R-gap scheme and der and using our scan method to determine the per- including bottom quark mass and QED effects. The default turbative uncertainty a global fit to our default data set theory parameters given in Tab. III are employed. The larger yields αs(mZ )=0.1241 (0.0034)pert which is indeed ± ellipses show the combined theoretical plus experimental error 9% larger than our main result in Eq. (68) which ac- for our default data set with 39% CL (solid, 1-sigma for one counts for nonperturbative effects. It is also interesting dimension) and 68% CL (dashed). to do the same fit with a purely fixed-order code, which we can do by setting µS = µJ = µH to eliminate the summation of logarithms. The corresponding fit yields experimental error ellipses, hence to larger uncertainties. αs(mZ )=0.1295 (0.0046)pert, where the displayed error ± It is an interesting but expected outcome of the fits has again been determined from the theory scan which in this case accounts for variations of µ and the numerical that the pure experimental error for αs (the uncertainty H uncertainties associated with ϵ2 and ϵ3. (A comparison of αs for fixed central Ω1) depends fairly weakly on the τ range and the size of the global data sets shown in with Ref. [22] is given below in Sec. IX.) Fig. 17. If we had a perfect theory description then we These results have been collected in Tab. VII together would expect that the centers and the sizes of the error with the αs results of our analyses with power corrections ellipses would be statistically compatible. Here this is in the R-gap and the MS schemes. For completeness we 2 not the case, and one should interpret the spread of the have also displayed the respective χ /dof values which ellipses shown in Fig. 17 as being related to the theo- were determined by the average of the maximal and the retical uncertainty contained in our N3LL′ order predic- minimum values obtained in the scan. tions. In Fig. 17 we have also displayed the combined (experimental and theoretical) 39% CL standard error ellipse from our default global data set which was al- VIII. FAR-TAIL AND PEAK PREDICTIONS ready shown in Fig. 11a (and is 1-sigma, 68% CL, for either one dimensional projection). We also show the The factorization formula (4) can be simultaneously used 68% CL error ellipse by a dashed red line, which corre- in the peak, tail, and far-tail regions. To conclude the sponds to 1-sigma knowledge for both parameters. As discussion of the numerical results of our global analysis we have shown above, the error in both the dashed and in the tail region, we use the results obtained from this solid larger ellipses is dominated by the theory scan un- tail fit to make predictions in the peak and the far-tail certainties, see Eqs. (68). The spread of the error ellipses regions. from the different global data sets is compatible with the In Fig. 18 we compare predictions from our full N3LL′ 1-sigma interpretation of our theoretical error estimate, code in the R-gap scheme (solid red line) to the accurate and hence is already represented in our final results. ALEPH data at Q = mZ in the far-tail region. As input for α (m )andΩ we use our main result of Eq. (68) Analysis without Power Corrections s Z 1 and all other theory parameters are set to their default Using the simple assumption that the thrust distribution values (see Tab. III). We find excellent agreement within in the tail region is proportional to αs and that the main the theoretical uncertainties (pink band). Key features Non-perturbative effects in Z pT – (issues hold also for Higgs pT)

17 Non-perturbative effects in Z pT

18 Non-perturbative effects in Z pT

19 impact of 0.5 GeV

Non-perturbative effects in Z pT ��shift�� of�� Z�� p��T � �� ➤ � Inclusive Z cross section should have �� 2 2 -4 �� ~Λ /M corrections (~10 ?)

�� ➤ Z pT is not inclusive so corrections

can be ~Λ/M. �� ➤ Size of eﬀect can’t be probed by � �� turning MC hadronisation on/oﬀ �� [maybe by modifying underlying MC �� 0.5 GeV is perhaps parameters?] �� conservative(?)

➤ Shifting Z pT by a ﬁnite amount �� illustrates what could happen ��

A conceptually similar problem is present for the W momentum in top decays

20 Closing remarks

This is just one of several fun physics topics that were pushed forwards in the late ’90s with Pino in Milan. small x,resummationswereothers

Pino wrote ∼ 15 articles with the students and postdocs then (including Banﬁ, Dasgupta, GPS, Smye, Zanderighi)

Many of the collaborations that formed between them then have continued to this day, easily having produced another ∼ 15X articles. 24

21 Gavin Salam (CERN/Princeton/CNRS) Pino and Power Corrections Pino2012 May 29 2012 15 / 15 EXTRAS

22 V+jet @ 13 TeV V+jet ratios @ 13 TeV 5

10 R 4 1000 x g+ jet 10 NLO QCD nNLO EW 3 ⌦ 10 NNLO QCD nNLO EW 10 2 ⌦ [pb/GeV] 1 PDF Uncertanties (LUXqed) 10 1 + + V 100 x (` n)+ jet , W

T 1 p 1 10 + +

/d 2 + W(`n¯) / W (` n)

s 10 Z(` `) / Z(nn¯)

d 3 + 10 Z(` `)+ jet 4 10 1 + 5 10 Z(` `) / W(`n) 10 6 10 7 NLO QCD nNLO EW 10 ⌦ + 8 NNLO QCD nNLO EW Z(` ` ) / g 10 ⌦ 9 PDF Uncertanties (LUXqed) 10 10 x W(`n¯)+ jet 10 10 2 10 1.2 1.1 1.15 1.1 1.05 EW

1.05 ⇥

NLO QCD 1.0 1.0 QCD s

0.95 R /d /

s 0.95 0.9 R d 0.85 + + Z(` `)+ jet 0.9 Z(` `) / W(`n) LHC PRECISION: PERTURBATION0.8 THEORY 1.2 1.1 1.15 1.1 1.05 EW

1.05 ⇥ V+jet @ 13 TeV V+jet ratios @ 13 TeV

NLO QCD 1.0 1.0 QCD s 5 R 010.95 R /d Z+jet process is main 4 1000 x g+ jet / 10 NLO QCD nNLO EW

s 0.95 0.93 R

d ⌦ 10 + 0.852 W (` n¯)+ jet Z(` ` ) / g NNLO QCD nNLO EW background for LHC 10 0.9 ⌦ [pb/GeV] 1 PDF Uncertanties (LUXqed) 100.81 + + V 100 x (` n)+ jet , W

T 1 dark-matter searches. p 1.21 10 1.1 + +

/d 1.152 + W(`n¯) / W (` n)

s 10 Z(` `) / Z(nn¯) d 101.13 Z(`+` )+ jet 1.05 EW 4 And powerful input for 101.05 ⇥ 1 + 5 10 Z(` `) / W(`n) NLO QCD 101.0 1.0 QCD s 6 100.95 NLO QCD nNLO EW R /d PDF ﬁts. 10 7 ⌦ / s 0.95 R + 0.98 NNLO QCD nNLO EW d Z(` ` ) / g 10 ⌦ (` n¯) / +(`+n) 0.859 PDF Uncertanties+(`+ )+ (LUXqed) W W 10 W n jet 10 x W(`n¯)+ jet 0.9 0.108 Perturbative results are 10 2 10 11..22 11..11 very precise… 11..1515 11..11 1.05

EW 1.05 EW ⇥ 11..0505 ⇥

± % NLO QCD 2 NLO QCD 11..00 11..00 QCD s QCD s R 00..9595 R /d / /d /

s 0.95

s 0 95

R . 00..99 R d d + 00..8585 g+ +jet Z(` +`) / Z(nn¯) Z(` `)+ jet 00..99 Z(` `) / W(`n) 00..88 1.2 100 200 500 1000 3000 100 200 500 1000 3000 1.1 1.15 pT,V [GeV] pT,V [GeV] 1.1 1.05 EW

1.05 Lindert, Pozzorini et al, 1705.04664 ⇥ 23

NLO QCD 1.0 1.0 QCD s

0.95 R /d Figure 17: Predictions at NLO QCD nNLO EW/ and NNLO QCD nNLO EW for V + jet

s 0.95 0.9 R

d ⌦ ⌦ 0.85 W (` n¯)+ jet Z(`+` ) / g spectra (left) and ratios (right) at 13 TeV. The0 lower.9 frames show the relative impact of 0.8 1.2 NNLO corrections and theory uncertainties normalised1.1 to NLO QCD nNLO EW. The 1.15 ⌦ green bands1.1 at NLO QCD nNLO EW correspond1.05 to the combination (in quadrature) EW

1.05 ⌦ ⇥

of the perturbativeNLO QCD 1.0 QCD, EW and mixed QCD-EW1.0 uncertainties, according to Eq. (45), QCD s

0.95 R /d /

s 0.95 while the0.9 NNLO QCD nNLO EW bands (red)R display only QCD scale variations. PDF d + + 0.85 + + W(`n¯) / W (` n) W (` n)+⌦jet 0.9 uncertainties0.8 are shown as separate hashed orange bands. 1.2 1.1 1.15 1.1 1.05 EW

1.05 ⇥

based onNLO QCD 1.0 NLO QCD. PDF uncertainties are below1.0 the perturbative uncertainties in all QCD s

0.95 R /d +/

s 0.95 nominal0 distributions.9 and all but the W /W R ratio. Clearly, a precise measurement of d + 0.85 + Z(` `) / Z(nn¯) + g jet 0.9 the W /W0.8 ratio at high pT, where perturbative uncertainties almost completely cancel, 100 200 500 1000 3000 100 200 500 1000 3000 will help to improve PDF fits. pT,V [GeV] pT,V [GeV] Our predictions are provided in the form of tables for the central predictions and for theFigure diff 17:erent Predictions uncertainty at sources. NLO QCD EachnNLO uncertainty EW and source NNLO is to QCD be treatednNLO as EW a 1 for-standardV + jet ⌦ ⌦ deviationspectra (left) uncertainty and ratios and (right) pragmatically at 13 TeV. associated The lower with frames a Gaussian-distributed show the relative impact nuisance of parameter.NNLO corrections and theory uncertainties normalised to NLO QCD nNLO EW. The ⌦ greenThe bands predictions at NLO are QCD given atnNLO parton EW level correspond as distributions to the combination of the vector (in boson quadrature)pT, with ⌦ looseof the cuts perturbative and inclusively QCD, over EW other and mixed radiation. QCD-EW They uncertainties,are intended to according be propagated to Eq. to (45), an experimentalwhile the NNLO analysis QCD usingnNLO Monte EW Carlo bands parton (red) display shower only samples QCD whose scale inclusive variations. vector- PDF ⌦ bosonuncertaintiespT distribution are shown has as been separate reweighted hashed to orange agree bands. with our parton-level predictions. The impact of additional cuts, non-perturbative effects on lepton isolation, etc., can then be deduced from the Monte Carlo samples. The additional uncertainties associated with the based on NLO QCD. PDF uncertainties are below the perturbative uncertainties in all + nominal distributions and all but the W /W ratio. Clearly, a precise measurement of + the W /W ratio at high pT, where perturbative35 uncertainties almost completely cancel, will help to improve PDF fits. Our predictions are provided in the form of tables for the central predictions and for the different uncertainty sources. Each uncertainty source is to be treated as a 1-standard deviation uncertainty and pragmatically associated with a Gaussian-distributed nuisance parameter. The predictions are given at parton level as distributions of the vector boson pT, with loose cuts and inclusively over other radiation. They are intended to be propagated to an experimental analysis using Monte Carlo parton shower samples whose inclusive vector- boson pT distribution has been reweighted to agree with our parton-level predictions. The impact of additional cuts, non-perturbative effects on lepton isolation, etc., can then be deduced from the Monte Carlo samples. The additional uncertainties associated with the

35 ] ]

-1 -1 -1 -1 −1 ATLAS s=8 TeV, 20.3 fb −1 ATLAS s=8 TeV, 20.3 fb 10 12 GeV ≤ m < 20 GeV, |y | < 2.4 10 20 GeV ≤ m < 30 GeV, |y | < 2.4 ll ll ll ll [GeV [GeV ll 10T −2 ll 10T −2 /dp /dp σ −3 ee-channel σ −3 ee-channel d 10 d 10 σ µµ-channel σ µµ-channel 1/ 1/ 4 10− Combined 10−4 Combined Statistical uncertainty Statistical uncertainty −5 10 Total uncertainty 10−5 Total uncertainty

1.2 2 2 10 1.1 10 1.1 1 1

Channel 0.9 Channel Combined χ2/NDF= 8/8 Combined 0.9 χ2/NDF= 6/8 0.8 ] 2 ] 2 σ 2 10 σ 2 10 0 0

Pull [ −2 Pull [ −2 50 100 500 50 100 500 pll [GeV] pll [GeV] T T ] ] -1 s=8 TeV, 20.3 fb-1 -1 s=8 TeV, 20.3 fb-1 −1 ATLAS 1 ATLAS 10 30 GeV ≤ m < 46 GeV, |y | < 2.4 46 GeV ≤ m < 66 GeV, |y | < 2.4 ll ll ll ll −1

[GeV [GeV 10 ll 10T −2 ll T −2 /dp /dp 10 σ σ −3 ee-channel ee-channel d 10 d −3 σ µµ-channel σ 10 µµ-channel 1/ 1/ 10−4 Combined 10−4 Combined Statistical uncertainty Statistical uncertainty 10−5 10−5 Total uncertainty Total uncertainty 10−6 102 1 10 102 1.1 1.05 1 1 Channel Channel Combined 0.9 χ2/NDF= 7/8 Combined 0.95 χ2/NDF=13/20

] 2 ] 2 σ 2 10 σ 2 1 10 10 0 0

LHCPull [ −PRECISION:2 EXPERIMENT Pull [ −2 50 100 500 1 10 102 pll [GeV] pll [GeV] T T ] ] -1 1 ATLAS s=8 TeV, 20.3 fb-1 -1 1 ATLAS s=8 TeV, 20.3 fb-1 −1 66 GeV ≤ m < 116 GeV, |y | < 2.4 Experimental116 GeV results ≤ m < 150 GeV, |y | < 2.4 10 ll ll ll ll −1

[GeV −2 [GeV 10 ll 10T arell T equally precise. −3 −2 /dp 10 /dp 10 σ ee-channel σ ee-channel d 10−4 d σ µµ-channel σ 10−3 µµ-channel 1/ −5 1/ 10 Combined Combined −6 −4 10 Statistical uncertainty 10 Statistical uncertainty −7 10 Total uncertainty 10−5 Total uncertainty 10−8 1 10 102 1 10 102 1.01 1.05 1 ±1%1 Channel Channel

Combined 0.99 Combined χ2/NDF=43/43 0.95 χ2/NDF=27/20

] 2 ] 2 σ 2 1 10 10 σ 2 1 10 10 0 0

Pull [ −2 Pull [ −2 1 10 102 1 10 102 pll [GeV] pll [GeV] T T 24 `` Figure 6: The Born-level distributions of (1/)d/dpT for the combination of the electron-pair and muon-pair channels, shown in six m regions for y < 2.4. The central panel of each plot shows the ratios of the values from `` | ``| the individual channels to the combined values, where the error bars on the individual-channel measurements represent the total uncertainty uncorrelated between bins. The light-blue band represents the data statistical uncertainty on the combined value and the dark-blue band represents the total uncertainty (statistical and systematic). The 2 per degree of freedom is given. The lower panel of each plot shows the pull, deﬁned as the di↵erence between the electron-pair and muon-pair values divided by the uncertainty on that di↵erence.

18 REMARKS

➤ Non-pert. eﬀects are always relevant at Analytic v. MC

accuracies we’re interested in hadronisationhadronisation pt shift (scaled by R CF/C)

➤ Monte Carlo tune jet radius, flavour Watch out for cancellation between 0.1 Herwig 6 R=0.2, quarks “hadronisation” and MPI/UE (separate (AUET2) 0 R=0.4, quarks physical effects) Pythia 8 R=0.2, gluons -0.1 (Monash 13) R=0.4, gluons ➤ Definition of perturbative / non- /C [GeV] /C pp, 7 TeV, no UE perturbative is ambiguous F -0.2

× R C -0.3 ➤

Alternative to MC: analytical hadr t

p -0.4 estimates. Δ MC’s have strong pT dependence, -0.5 simple analytical estimate missing in analytical estimates -0.6 100 200 500 1000

pt (parton) [GeV] 25

non-perturbative effects may becomeFigure 11 a. key The average limitation shift in at jet p1%t induced by hadronisation in a range of Monte Carlo tunes, for R =0.4 and R =0.2 jets, both quark and gluon induced. The shift is shown as a function of jet pt and is rescaled by a factor RCF /C (C = CF or CA) in order to test the scaling expected from Eq. (5.1). The left-hand plot shows results from the AUET2 [48] tune of Herwig 6.521 [22, 23] and the Monash 13 tune [49] of Pythia 8.186 [21], while the right-hand plot shows results from the Z2 [50] and Perugia 2011 [51, 52] tunes of Pythia 6.428 [20]. The shifts have been obtained by clustering each Monte Carlo event at both parton and hadron level, matching the two hardest jets in the two levels and determining the di↵erence in their pt’s. The simple analytical estimate of 0.5 GeV 20% is shown as a yellow band. ±

and Pythia 8 Monash 2013 both having somewhat smaller than expected hadronisation corrections. Secondly there is a strong dependence of the shift on the initial jet pt,with a variation of roughly a factor of two between pt = 100 GeV and pt =1TeV.Suchapt dependence is not predicted within simple approaches to hadronisation such as Refs. [19, 43, 46, 47]. It was not observed in Ref. [19] because the Monte Carlo study there restricted its attention to a limited range of jet p , 55 70 GeV. The event shape studies that t provided support for the analytical hadronisation were also limited in the range of scales they probed, speciﬁcally, centre-of-mass energies in the range 40 200 GeV (and comparable photon virtualities in DIS). Note, however, that scale dependence of the hadronisation has been observed at least once before, in a Monte Carlo study shown in Fig. 8 of Ref. [53]: e↵ects found there to be associated with hadron masses generated precisely the trend seen here in Fig. 11.Thept dependence of those e↵ects can be understood analytically, however we leave their detailed study in a hadron-collider context to future work.13 Experimental insight into the pt dependence of hadronisation might be possible by examining jet-shape measurements [55, 56] over a range of pt, however such a study is also beyond the scope of this work. In addition to the issues of pt dependence, one further concern regarding the analytical approach is that it has limited predictive power for the ﬂuctuations of the hadronisation

13Hadron-mass e↵ects have been discussed also in the context of Ref. [54].

– 20 – STANDARD MODEL TODAY

Gauge interactions well tested. Higgs sector mostly an assumption

ASSUMPTION KNOWLEDGE 26 STANDARD MODEL TODAY

t b τ c s μ u s e

Gauge interactions well tested. Higgs sector mostly an assumption

ASSUMPTION KNOWLEDGE 27 STANDARD MODEL BY END OF LHC (~2035)

t b τ c s μ u s e

Gauge interactions well tested. Higgs sector mostly an assumption

ASSUMPTION KNOWLEDGE 28 N3LO

Anastasiou et al, 1602.00695 Dreyer & Karlberg, 1606.00840

N3LO ggF Higgs N3LO VBF Higgs 4

[pb] d/dpt,H [pb/GeV] 100 10-1 PDF4LHC15_nnlo_mc LO NNLO Q/2 < µR , µF < 2 Q NLO N3LO

10-2

10 N3LO 10-3 LHC 13 TeV LO NNLO Q/2 < µR , µF < 2 Q NLO N3LO PDF4LHC15_nnlo_mc 1 10-4

1.02 1.02

NNLO 1.01 N3LO 1.01

ratio to N3LO 1 1

0.99 NNLO 0.99 7 10 13 20 30 50 100 0 50 100 150 200 250 300 Figure 2: E↵ective theory production cross section of a scalar particle of mass m [50, 150] GeV S 2 s [TeV] pt,H [GeV] through increasing orders in perturbation theory. For further details see the caption of Fig. 1. FIG. 4. Cross section as a function of center-of-mass energy (left), Higgs transverse momentum distribution (center) and Higgs mass around 770 GeV. This feature is not shared with individual PDF sets. We therefore rapidity distribution (right). use, conservatively, the envelope of CT14, NNPDF30 and PDF4LHC, which leads to an uncertainty due to the lack of N3LO parton densities at the level of 0.9% 3% for scalars 29 t-/u-channel interferences which are known to con- in the range 50 GeV 3 TeV. This uncertainty remains of the order of a few percent also • (13 TeV) [pb] (14 TeV) [pb] (100 TeV) [pb] tribute (5 ) at the fully inclusive level and at lower masses, but it increases rapidly to (10%) for mS . 20 GeV. O O +0.051 +0.037 +6.45 (0.5 ) afterh VBF cuts have been applied [10]. We present the cross section values and uncertainties for this range of scalar masses in LO 4.099 0.067 4.647 0.058 77.17 7.29 O +0.025 +0.032 +1.73 h Appendix A. In particular, in Tab. 6 we focus on the range between 730 and 770 GeV. NLO 3.970 0.023 4.497 0.027 73.90 1.94 Contributions from s-channel production, which • +0.015 +0.018 +0.53 have been calculated up to NLO [10]. At the inclu- NNLO 3.932 0.010 4.452 0.012 72.44 0.40 3. Finite width e↵ects and the line-shape 3 +0.005 +0.006 +0.11 sive level these contributions are sizeable but they N LO 3.928 0.001 4.448 0.001 72.34 0.02 are reduced to (5 ) after VBF cuts. The results of the previous section hold formally only when the width of the scalar is set to O TABLE I. Inclusive cross sections at LO, NLO, NNLO and h zero. In many beyond the Standard Model (BSM) scenarios, however, finite-width e↵ects Single-quark line contributions, which contribute to N3LO for VBF Higgs production. The quoted uncertainties • cannot be neglected. In this section we present a way to include leading finite-width e↵ects the VBF cross section at NNLO. At the fully inclu- correspond to scale variations Q/2 <µR,µF < 2Q,while sive level these amount to corrections of (1%) but into our results, in the case where the width is not too large compared to the mass. statistical uncertainties are at the level of 0.2 . are reduced to the permille level afterO VBF cuts The total cross section for the production of a scalar boson of total width S can be h have been applied [11]. obtained from the cross section in the zero-width approximation via a convolution order in QCD, where we observe again a large reduction Q (Q) (Q, =0, ⇤ ) Loop induced interferences between VBF and (m , , ⇤ )= dQ2 S S S UV + ( (m )/m ) , (3.1) of the theoretical uncertainty at N3LO. • S S S UV ⇡ (Q2 m2 )2 + m2 2(m ) O S S S gluon-fusion Higgs production. These contribu- Z S S S A comment is due on non-factorisable QCD corrections have been shown to be much below the per- where Q is the virtuality of the scalar particle. This expression is accurate at leading order tions. Indeed, for the results presented in this letter, we mille level [36]. in S(mS)/mS. For large values of the width relative to the mass, subleading corrections have considered VBF in the usual DIS picture, ignor- ing diagrams that are not of the type shown in figure 1. Furthermore, for phenomenological applications, one These e↵ects neglected by the structure function approx- also needs to consider NLO electroweak e↵ects [10], which imation are known to contribute less than 1% to the total amount to (5%) of the total cross section. We leave a detailed studyO of non-factorisable and electroweak e↵ects –6– cross section at NNLO [7]. The e↵ects and their relative corrections are as follows: for future work. The code used for this calculation will be published in the near future [37]. Gluon exchanges between the upper and lower ha- In this letter, we have presented the first N3LO calcula- • dronic sectors, which appear at NNLO, but are tion of a 2 3 hadron-collider process, made possible by kinematically and colour suppressed. These contri- the DIS-like! factorisation of the process. This brings the butions along with the heavy-quark loop induced precision of VBF Higgs production to the same formal ac- contributions have been estimated to contribute at curacy as was recently achieved in the gluon-gluon fusion the permille level [7]. channel in the heavy top mass approximation [12]. The WH at large Q2 with dim-6 new physics isn’t BSM effect just a single number that’s

3000 fb-1 �� wrong (think g-2) ��

�� but rather a � � ��

�� distinct scaling ��

� pattern of ��

�� 2

� deviation (~ pT ) ��

�� moderate and high ��

� pT’s have similar �� schemati statistical GPS 2016-10 �� signiﬁcance — so �� it’s useful to 30 understand whole

pT range