Scaling properties in multijet events towards high multiplicities - PowerPoint PPT Presentation

Scaling properties in multijet events –– towards high multiplicities –– Peter Schichtel Durham University @ Higgs plus Jets 2014

Content Introduction ➝ theoretical uncertainties in multi-jet observables ➝ jet scaling patterns Jet radiation in QCD (FSR) ➝ a simple QED example ➝ generating functionals ➝ scaling limits & beyond Hadron colliders ➝ pdf effects ➝ learning from data ➝ understanding Higgs (vetoes, using BDTs) ➝ data driven background stud

Theoretical uncertainties pdf uncertainties & scale choice (smaller at NLO) jet sprectrum effective mass X m e ff = / p T + p T,jet all jets 6 6 10 10 -1 -1 -1 -1 -1 -1 -1 -1 L = 1 fb L = 1 fb L = 1 fb L = 1 fb L = 1 fb L = 1 fb L = 1 fb L = 1 fb p p p p > 50 GeV > 50 GeV > 50 GeV > 50 GeV p p p p > 50 GeV > 50 GeV > 50 GeV > 50 GeV 5 5 10 10 [1/100 GeV] [1/100 GeV] T, j T, j T, j T, j T, j T, j T, j T, j 5 5 10 10 n n n n ≥ ≥ ≥ ≥ 2 2 2 2 n n n n ≥ ≥ ≥ ≥ 2 2 2 2 j j j j j j j j jets jets 4 4 10 10 dN dN 4 4 10 10 dn dn W+jets W+jets W+jets W+jets W+jets W+jets W+jets W+jets 3 3 10 10 eff eff dN dN W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 W+jets, 1/4 µ µ µ µ µ µ µ µ dm dm 3 3 10 10 2 2 10 10 W+jets, 4 W+jets, 4 W+jets, 4 W+jets, 4 W+jets, 4 W+jets, 4 W+jets, 4 W+jets, 4 µ µ µ µ µ µ µ µ 1.5 1.5 2 2 3 3 4 4 5 5 6 6 200 200 400 400 600 600 800 800 theoretical uncertainty theoretical uncertainty 1.1 1.1 variation variation variation variation statistical uncertainty statistical uncertainty 1 1 1 1 s s s s α α α α 0.9 0.9 0.5 0.5 2 2 3 3 4 4 5 5 6 6 200 200 400 400 600 600 800 800 variation variation variation variation 10 10 10 10 1 1 1 1 µ µ µ µ 2 2 3 3 4 4 5 5 6 6 200 200 400 400 600 600 800 800 n n m m [GeV] [GeV] jets jets eff eff uncertainties highly correlated understand jets ➝ controll jet dependent observables [Englert, Plehn, P .S., Schumann: Phys.Rev. D83 (2011) 095009]

W/Z plus jets in the past discoverd at SPS observed at Tevatron and LHC CDF ATLAS UA1 [Aad et al. Phys. Rev. D 85 092002 (2012)] [Alioli et al, JHEP (2011) 095] [Ellis,Kleis,Stirling(1985)] staircase like jet spectrum

Aside: exclusive cross section ratios ratios: cancel systematics exclusive: statistically independent visualization exclusive: challenge for uncertainty estimation

Scaling patterns staircase scaling Poisson scaling [Steve Ellis,Kleis,Stirling(1985); Berends(1989)] [Peskin & Schroeder; Rainwater, Zeppenfeld(1997)] n n e − ¯ ¯ n σ excl. = σ 0 e − bn σ excl. = σ 0 n n n ! falling ratios constant ratios n ¯ = σ n +1 = σ n +1 R n +1 = R 0 R n +1 = n + 1 σ n n σ n n same for exclusive and inclusive [Phys. Rev. D 83 095009 (2011)] Can we understand these from basic principles?

LHC: 7 TeV data confirmed at LHC [1304.7098] staircase small tilt Poisson flattens out needs high jet p T Can we understand these from basic principles?

Bremsstrahlung in QED schematic Peskin & Schröder

Bremsstrahlung in QED soft collinear limit: factorization theorem d σ n +1 = d σ n × dt t dz α s 2 π P i → jl ( z ) resolvable unresolvable n independet emissions resummed P ( n ) = ¯ n n e − ¯ n normalization n ! bosonic phase space 2 t 3 Z dt 0 X ∆ i ( t ) = exp Γ i ! jl 4 − 5 jl t 0 Sudakov form factor: non splitting prob. phase space boundary Peskin & Schröder

Bremsstrahlung in QCD more complicated: gluon self interaction formal way to deal with QCD: generating functional formalism [Konishi te al. (1979); Ellis, Stirling, Webber (1996); Gerwick, Gripaios, Schumann, Webber (2012) ] jet rate � P ( n ) = 1 d n X � Φ ( u ) := u n P ( n ) du n Φ ( u ) � n ! � u =0 n

Bremsstrahlung in QCD 2 t ◆3 evolution equation ✓ Φ j ( t 0 ) Φ l ( t 0 ) Z dt 0 X Φ i ( t ) = u exp − 1 Γ i ! jl 4 5 Φ i ( t 0 ) jl t 0 Φ i ( t ) = u ∆ i ( t ) large log limit: t � t 0 ∆ i ( t ) u primary emissions dominate → Poisson scaling 1 democratic limit Φ g ( t ) = t → t 0 1 − u 1 + u ∆ g ( t ) exact solution [JHEP 1210 (2012) 162] → staircase scaling additional effects: 1 ➝ breaking terms ✔ Φ g ∼ 1 + 1 − u u ∆ g − R ( u ) ➝ phase space ✔ φ ( n ) ➝ finite jet radius ✘ [Gerwick, PS: 1412.1806]

Bremsstrahlung in QCD n+1 n ← simulation of e + e − → q ¯ q + n × g 6 R R = 0.5, e = 10 6 (n) naive phase space Poisson phase space φ 5 n = 5.2 10 R = 0.5 staircase phase-space × naive φ R = 0.747, B = 4.8 4 0 R = 0.3 8 dR naive 0 φ = -0.0177 dn 3 6 2 4 1 2 1/0 6/5 11/10 16/15 21/20 n+1 n 10 20 30 40 50 60 70 n ✓  � ◆ 1 × φ ( n + 1) + dR 0 = 1 + dn ( n + 1) R n +1 R 0 B + ( n + 1) φ ( n ) n small & vanishing as [Gerwick, PS: 1412.1806] R → 0

PDF effects threshold approximation r ⇣ ⌘ m 2 p p 2 T + m 2 Z + p 2 Z + 2 p T m Z T x (0) ≈ x (1) ≈ 2 E beam 2 E beam 1.1 Drell-Yan kinematics effects factorize at LL 1 0.9 characterised by d quark initial state 0.8 lead p 100 GeV ≥ n B T 2 0.7 f ( x ( n +1) ,Q ) � � ← all jets recoil � � f ( x ( n ) ,Q ) � � B n = 0.6 � � f ( x ( n +2) ,Q ) � � f ( x ( n +1) ,Q ) balanced in p ← � � 0.5 T 0.4 1 2 3 4 5 6 7 n pdf suppresion of additional jets [Gerwick, Plehn, P .S., Schumann: JHEP 1210 (2012) 162]

Callibrate your jets from data 0.5 R =-0.0092 0 1.5 p >100 GeV, R =0.149 T,j1 n =1.7197 0 dR 0.4 =-0.0004 R =-0.0461 dn 0 p >150 GeV, T,j1 n =2.2197 R =0.0387 0 0.3 p >200 GeV, 1 T,j1 n =2.1449 Z plus jets n+1 n+1 n n R R 0.2 0.5 0.1 0 0 2/1 3/2 4/3 5/4 6/5 7/6 2/1 3/2 4/3 5/4 6/5 7/6 8/7 0.5 R =0.1437 R =0.0131 min 0 R >1.0, 0 1.5 p >100 GeV, ,j γ dR T,j1 n =1.7138 =-0.005 dn 0.4 R =-0.0509 R =0.1266 0 p >150 GeV, min 0 R >1.3, T,j1 n =2.361 γ ,j dR =0.0001 dn R =-0.0536 0 0.3 p >200 GeV, 1 R =0.1087 T,j1 n =2.6287 min 0 R >1.6, photons plus jets n+1 n+1 γ ,j dR n n =0.0053 R dn R 0.2 0.5 0.1 0 0 2/1 3/2 4/3 5/4 6/5 7/6 2/1 3/2 4/3 5/4 6/5 7/6 8/7 exact same jet spectrum! [Englert, Plehn, P .S., Schumann: JHEP 1202 (2012) 030]

Understanding Higgs veto efficiencies [Gerwick, Schumann, Plehn: Phys.Rev.Lett. 108 (2012) 032003] WBF Higgs p min | y j | < 4 . 5 T,j = 20 GeV | y 1 − y 2 | > 4 . 4 y 1 y 2 < 0 1 . 0 1 1 . 0 1 0 . 9 0 . 9 0.9 0.9 0 . 8 0 . 8 0.8 0.8 R ( n +1) /n R ( n +1) /n 0 . 7 0 . 7 0.7 0.7 0 . 6 0 . 6 0.6 0.6 before cut 0 . 5 0 . 5 0.5 0.5 Z EW m jj Higgs gluon fusion 0 . 4 0 . 4 0.4 0.4 0 . 3 0 . 3 0.3 0.3 0 . 2 0 . 2 0.2 0.2 Z QCD Higgs WBF 0 . 1 0 . 1 0.1 0.1 0 0 -1 0 1 2 3 4 5 6 -1 0 1 2 3 4 5 6 1 / 0 2 / 1 3 / 2 4 / 3 5 / 4 6 / 5 1 / 0 2 / 1 3 / 2 4 / 3 5 / 4 6 / 5 1 . 0 1 2 . 5 2.5 Y-axis scale → note n (Higgs gg fusion) = 1 . 80 ¯ 0 . 9 0.9 n (Z QCD) ¯ = 1 . 42 0 . 8 0.8 2 . 0 2 R ( n +1) /n R ( n +1) /n 0 . 7 0.7 0 . 6 0.6 1 . 5 1.5 0 . 5 0.5 Z EW Higgs gluon fusion 0 . 4 0.4 1 . 0 1 after cut 0 . 3 0.3 m jj 0 . 2 0.2 0 . 5 0.5 Z QCD 0 . 1 Higgs WBF 0.1 0 0 -1 0 1 2 3 4 5 -1 0 1 2 3 4 5 1 / 0 2 / 1 3 / 2 4 / 3 5 / 4 1 / 0 2 / 1 3 / 2 4 / 3 5 / 4

Know you backgrounds: jets & BDT B WBF Higgs 0.98 ∈ 1 - FWMs, y-selection Δ FWMs, p -selection [Bernaciak, Mellado, Plehn, Ruan, PS: Phys. Rev D89 2014] T 0.97 jet veto 0.96 0.95 jet veto 0.94 0.3 0.35 0.4 ∈ S cuts veto more jets S/B 0. 014 0. 047 0. 083 p T selection 0. 026 0. 045 0. 071 ∆ y selection

Know you backgrounds: jets & BDT invisible Higgs (WBF) [Bernaciak, Plehn, PS, Tattersall: 1411.7699] cuts BDT more jets Γ inv / Γ SM 47 % 28 % 16 % 10 fb − 1 6.9% 3.5% 2.1% 3000 fb − 1

Conclusions ➝ multi-jet observables are plagued by huge theoretical uncertainties (LO) ➝ jet spectra follow simple scaling patterns ➝ staircase scaling is a firm QCD prediction (& observed) @ LHC: low multiplicities due to PDF effects ➝ controll uncertainties & understand backgrounds from data ➝ QCD high multiplicity predictions possible [difficult with NLO] ➝ use in subsequent applications (Higgs studies, BSM, ...) thanks for listening