From Jet Scaling to Jet Vetos

From Jet Scaling to Jet Vetos Heidelberg DESY, 2/202

LHC Higgs analyses Two problems for LHC Higgs analyses [talks Rauch, Englert] observe H b b decays [fat Higgs jets, Marcel s talk] 2 understand jet vetos [this talk] Understanding Jet Scaling and Jet Vetos in Higgs Searches E Gerwick, TP, S Schumann PRL 8 (202) Establishing Jet Scaling Patterns with a Photon C Englert, TP, P Schichtel, S Schumann arxiv:8.5473 Jets plus Missing Energy with an Autofocus C Englert, TP, P Schichtel, S Schumann PRD83 (20)

Exclusive jet counting Why count numbers of jets? hard event reconstruction crucial for LHC measurements [Higgs plus 0,,2 jets] utilize tagging and recoil jets in Higgs searches identify decay jets in BSM searches reduce t t and g g backgrounds dσ/dn jets just another distribution to cut on?

Exclusive jet counting Why count numbers of jets? hard event reconstruction crucial for LHC measurements [Higgs plus 0,,2 jets] utilize tagging and recoil jets in Higgs searches identify decay jets in BSM searches reduce t t and g g backgrounds dσ/dn jets just another distribution to cut on? Why avoid jet counting? [intro: arxiv:09.482, Springer Lecture Notes] soft gluon radiation infinitely likely [like soft photons] collinear parton splitting divergent [try qg Zq] parton densities defined including collinear jets [DGLAP] Z Z σ tot (s) = dx dx 2 0 0 X partons ij f i (x ) f j (x 2 ) ˆσ ij (x x 2 s) fiducial volume vs soft or collinear critical A jet or not a jet ill defined in perturbative QCD study features of n jets distributions

scaling Soft gluon radiation [Peskin & Schroeder] example: photons off hard electron [abelian diagrams, successive radiation] factorization of hard process and soft radiation eikonal approximation [cf E Laenen, next-to-eikonal] M n+ = g st a ɛ µ (k) q µ + O( /k) (qk) + O(k 2 ) Mn distribution [normalized pdf for n if n expected] σ n = nn e n n! R (n+)/n σ n+ σ n = n n + Ingredients of distribution radiation matrix element n n : abelian fine, non-abelian for leading log and color 2 phase space factor /n!: only combinatorics effect, matrix element ordered 3 normalization factor e n : /p T s /p T s /p T same expected for ISR at LHC? s

scaling From UA2 to ATLAS [Steve Ellis, Kleiss, Stirling; Berends scaling???]

scaling From UA2 to ATLAS many equivalent descriptions [Steve Ellis, Kleiss, Stirling; Berends scaling???] R (n+)/n = σ n+ σ n same for inclusive and exclusive rates = const R incl (n+)/n = confirmed by ATLAS and CMS P j=n+ σ(excl) j σ (excl) n + P j=n+ σ(excl) j = R excl (n+)/n

scaling From UA2 to ATLAS many equivalent descriptions [Steve Ellis, Kleiss, Stirling; Berends scaling???] R (n+)/n = σ n+ σ n same for inclusive and exclusive rates = const R incl (n+)/n = confirmed by ATLAS and CMS P j=n+ σ(excl) j σ (excl) n + P j=n+ σ(excl) j = R excl (n+)/n Theory [Englert, TP, Schichtel, Schumann] appropriate: CKKW/MLM merging [Sherpa] α s uncertainties? small scale uncertainties? tuning parameter dn dn jets variation 6 5 4 3 2 - L = fb p > 50 GeV T, j n j 2 W+jets W+jets, /4µ W+jets, 4µ 2 3 4 5 6.5 theoretical uncertainty statistical uncertainty n jets µ variation α s 2 3 4 5 6 n jets 2 3 4 5 6 n jets

scaling From UA2 to ATLAS many equivalent descriptions [Steve Ellis, Kleiss, Stirling; Berends scaling???] R (n+)/n = σ n+ σ n same for inclusive and exclusive rates = const R incl (n+)/n = confirmed by ATLAS and CMS P j=n+ σ(excl) j σ (excl) n + P j=n+ σ(excl) j = R excl (n+)/n Theory [Englert, TP, Schichtel, Schumann] appropriate: CKKW/MLM merging [Sherpa] α s uncertainties? small scale uncertainties? tuning parameter same thing for pure QCD jets correctly described by QCD simulations dn dn jets variation α s µ variation 9 8 7 6 5 4.2 0.8 2 - L = fb p > 50 GeV T, j n j 2 QCD QCD, /4µ QCD, 4µ 2 theoretical uncertainty 3 4 5 6 statistical uncertainty n jets 2 3 4 5 6 n jets 2 3 4 5 6 n jets

Induced scalings Scaling for photon plus jets [Englert, TP, Schichtel, Schumann] naively, no scaling at all [CMS, private complaint] staircase democratic γ and jet acceptance large separation [m or R, no large logs] dominant: non-abelian gluon splitting of ISR jet Rn+ n 0.4 0.3 0.2 0. R 0 =97 m γ,j > 70 GeV, dr =-0.0064 dn R 0 =0.488 m γ,j > 90 GeV, dr =-0.0007 dn R 0 =0.407 m γ,j > GeV, dr =0.0029 dn 0 2/ 3/2 4/3 5/4 6/5 7/6

Induced scalings Scaling for photon plus jets [Englert, TP, Schichtel, Schumann] naively, no scaling at all [CMS, private complaint] staircase democratic γ and jet acceptance large separation [m or R, no large logs] dominant: non-abelian gluon splitting of ISR jet 2 generate hard process [m, p T, R,...] lower standard p T for logarithm dominant: successive ordered ISR remaining: high-n staircase tail either staircase or and tunable! Rn+ n Rn+ n 0.4 0.3 0.2 0. 0 R 0 =97 m γ,j > 70 GeV, dr =-0.0064 dn R 0 =0.488 m γ,j > 90 GeV, dr =-0.0007 dn R 0 =0.407 m γ,j > GeV, dr =0.0029 dn 2/ 3/2 4/3 5/4 6/5 7/6 R 0 =0.03.5 p >0 GeV, T,j n=.738 R 0 =-0.0509 p >50 GeV, T,j n=2.36 R 0 =-0.0536 p >200 GeV, T,j n=2.6287 0 2/ 3/2 4/3 5/4 6/5 7/6 8/7

as Higgs analysis tool [Barger, Phillips, Zeppenfeld; Rainwater; Gerwick, TP, Schumann] implicit in LHC Higgs searches for exclusive fixed n jets particularly useful for WBF signals

as Higgs analysis tool [Barger, Phillips, Zeppenfeld; Rainwater; Gerwick, TP, Schumann] implicit in LHC Higgs searches for exclusive fixed n jets particularly useful for WBF signals in terms of jet counting avoid survival probability as one number [uncertainty?] 2 study exclusive n jets distributions 3 validate theory description 4 extrapolate to interesting regimes/processes

as Higgs analysis tool [Barger, Phillips, Zeppenfeld; Rainwater; Gerwick, TP, Schumann] implicit in LHC Higgs searches for exclusive fixed n jets particularly useful for WBF signals in terms of jet counting avoid survival probability as one number [uncertainty?] 2 study exclusive n jets distributions 3 validate theory description 4 extrapolate to interesting regimes/processes basic features staircase scaling for inclusive samples 2 scaling for radiation processes staircase scaling scaling σn σ 0 e bn e n n n σ tot R excl (n+)/n R incl (n+)/n e b e b 0 n n! n + @ (n + ) e n n (n+) Γ(n + ) nγ(n, n) n jets n 2 cosh b P veto e b e n + A

WBF Higgs production Example: WBF H ττ [Gerwick, TP, Schumann] staircase scaling before WBF cuts [QCD and e-w processes] e-w Zjj production with too many structures R (n+)/n R(! n+ /! n ).0 0.9 0.8 0.7 0.6 0.4 0.3 0.3 0.2 0. 0. Higgs gluon fusion ZQCD 0 - /0 0 2/ 3/2 2 4/3 3 5/4 4 6/5 5 6! /! n+ n n + n R (n+)/n R(! n+ /! n ).0 0.9 0.8 0.7 0.6 0.4 0.3 0.3 0.2 0. 0. ZEW Higgs WBF 0 - /0 0 2/ 3/2 2 4/3 3 5/4 4 6/5 5 6! /! n+ n n + n

WBF Higgs production Example: WBF H ττ [Gerwick, TP, Schumann] staircase scaling before WBF cuts [QCD and e-w processes] e-w Zjj production with too many structures WBF cuts: two forward tagging jets count add l jets to reduce backgrounds p veto T > 20 GeV min y,2 < y veto < max y,2 for QCD processes [ radiation pattern] R (n+)/n R(! n+ /! n ) 2.5 2.02.5.0 Higgs gluon fusion n(higgs gg fusion) =.80 n(z QCD) =.42 ZQCD 0 - /0 0 2/ 3/2 2 4/3 3 5/4 4 5! /! n+ n

WBF Higgs production Example: WBF H ττ [Gerwick, TP, Schumann] staircase scaling before WBF cuts [QCD and e-w processes] e-w Zjj production with too many structures WBF cuts: two forward tagging jets count add l jets to reduce backgrounds p veto T > 20 GeV min y,2 < y veto < max y,2 for QCD processes [ radiation pattern] (fairly) staircase for e-w processes [generic] n jets distributions understood cut on n jets fine R (n+)/n R(! n+ /! n ) 2.5 n(higgs gg fusion) =.80 n(z QCD) =.42 2.02.5 Higgs gluon fusion.0 ZQCD 0 - /0 0 2/ 3/2 2 4/3 3 5/4 4 5! /! n+ n R (n+)/n R(! n+ /! n ).0 0.9 0.8 0.7 0.6 ZEW 0.4 0.3 0.3 0.2 0. 0. Higgs WBF 0 - /0 0 2/ 3/2 2 4/3 3 5/4 4 5! /! n+ n

Effective mass [Englert, TP, Schichtel, Schumann] signal: measure for heavy masses backgrounds: m eff p T n jets - -2 3 L = fb [GeV] - [/0 GeV] S+B eff dm dn 5 signal 4 tt leptonic 3 tt hadronic W+jets 2 Z+jets QCD B 200 400 600 800 00 200 m 400 eff 2.5 n j = 3 2.5 200 400 600 800 00 200 m [GeV] 400 eff

Effective mass [Englert, TP, Schichtel, Schumann] signal: measure for heavy masses backgrounds: m eff p T n jets - -2 3 L = fb [GeV] - Mass vs color charge [/0 GeV] S+B eff dm dn 5 signal 4 tt leptonic 3 tt hadronic W+jets 2 Z+jets QCD B 200 400 600 800 00 200 m 400 eff 2.5 n j = 3 2.5 200 400 600 800 00 200 m [GeV] 400 eff effective mass for BSM masses 2 jet counting for BSM color charge [no octet decay to gluon] analysis in exclusive 2D likelihood m eff TeV.6.4 SPSa, inverse fb 6Σ SPSa, squarks squarks, inv. fb m eff TeV.6.4 4Σ SPSa, squarks gluino, inv. fb m eff TeV.6.4 3.2Σ SPSa, gluino gluino, inv. fb m eff TeV.6.4 0.6Σ.2.2.2.2.... 0.8 0.8 0.8 0.8 0.6 0.4 0Σ 0.6 0.4 0Σ 0.6 0.4 0Σ 0.6 0.4 0Σ 0.2 2 3 4 5 6 n j 0.2 2 3 4 5 6 n j 0.2 2 3 4 5 6 n j 0.2 2 3 4 5 6 n j

Exclusive jet counting Challenge for LHC-Higgs analyses described by appropriate QCD staircase scaling (non-abelian) vs scaling (ordered) waiting for dedicated ATLAS/CMS studies key to jet vetos