Operators in H to four leptons with off-shell production Myeonghun - PowerPoint PPT Presentation

Constraining Higher Dimensional Operators in H to four leptons with off-shell production Myeonghun Park APCTP based on 
 arxiv:1304.4936, 1403.4951 
 with J.Gainer, J. Lykken, K. Matchev and S. Mrenna 2015. 2. 14 
 HPNP 2015

1 • Higgs property-measurement within high mass window • Higgs property-measurement in a far off-shell region

2 Higgs Properties @ RUN1 CMS Collaboration , arxiv:1312.5353[hep-ex] • H → ZZ → 4l signature • Studied within a Higgs mass- window, 106 < m4l < 141 GeV

3 @LO, MELA, MEKD, … { θ 1 , θ 2 , Φ 1 − Φ 2 , Φ 1 + Φ 2 , θ ∗ , M Z 1 , M Z 2 } • Based on a “general” amplitude of H to four leptons, to study 7 degree of freedoms@Higgs resonance, various codes were developed.

4 • General amplitude for transition up to H → ZZ dimension five operators in effective Lagrangian will be A ( H → Z 1 Z 2 ) = c 1 ( ✏ ∗ 1 · ✏ ∗ 2 ) + c 2 ( p 1 · p 2 )( ✏ ∗ 1 · ✏ ∗ 2 ) 1 ) + c 4 ✏ µ νρσ ✏ ∗ µ 2 p ρ + c 3 ( p 1 · ✏ ∗ 2 )( p 2 · ✏ ∗ 1 ✏ ∗ ν 1 p σ 2 + c 5 ( p 2 1 + p 2 2 )( ✏ ∗ 2 ) 1 · ✏ ∗ • Correspondence between amplitude and Lagrangian: • General amplitude is expressed as 
 a five dimensional space . • By taking five linearly-independent basis, 
 we cover the general amplitude of process. H → ZZ

5 • :This operator represents a tree-level Standard Model Higgs boson coupling. 
 O 1 With a requirement of gauge invariance, this operator tells us that X has a 
 vacuum expectation value as X h X i Z µ Z µ

6 O 2 • :With a linear combination of two operators, we can have an operator 
 which is invariant under gauge-transformation, . 
 Z µ → Z µ + ∂ µ θ This operator comes from the new physics through the loop. • :This operator represents a tree-level Standard Model Higgs boson coupling. 
 O 1 With a requirement of gauge invariance, this operator tells us that X has a 
 vacuum expectation value as X h X i Z µ Z µ

7 O 3 • :This operator is CP odd coupling which is invariant under the 
 Z µ → Z µ + ∂ µ θ gauge-transformation, O 2 • :With a linear combination of two operators, we can have an operator 
 which is invariant under gauge-transformation, . 
 Z µ → Z µ + ∂ µ θ This operator comes from the new physics through the loop. • :This operator represents a tree-level Standard Model Higgs boson coupling. 
 O 1 With a requirement of gauge invariance, this operator tells us that X has a 
 vacuum expectation value as X h X i Z µ Z µ

8 {O 1 , O 2 , O 3 } • These three operators are key operators at a Higgs resonance 
 to study a property of a “Higgs”. ⇤ X = M 2 O 4 → O 1 • At resonance, since (e.o.m) X X m 4 ` � M X but it becomes important in a range of , 
 i.e., off-shell region.

9 or • A 5 dimensional basis, result without analysis cuts

10 {O 1 , O 2 , O 3 } • These three operators are key operators at the resonance to study a property of a “Higgs”. L 3 M 2 f ( H ) f ( H ) f ( A ) v HZ µ ˆ µ ν Z ν + 1 2 HF µ ν ˆ µ νρσ F ρσ + 1 2 AF µ ν ˆ µ νρσ F ρσ Z • In effective theory point of view, we can think that form factors f as 
 infinite series expansions in terms of some new physics scale Λ O 1 CP even O 2 O 3 CP odd • In general, X is a linear combination as

11 • We have three degree of freedom, but these D.O.F. can be reduced by factoring out overall normalization from the measured total rate. κ 3 0 − • With measured total rate 0 + κ 2 0 + m κ 1 • r ij is a function of phase space, thus theoretically, 
 from the phase space integrations we can calculate r ij 
 - r 13 , r 23 will be 0 since terms in 𝛥 proportional to k 1 k 3 or k 2 k 3 are parity odd. R 1 − 1 x d x = 0

12 • What we observed at the LHC is the distorted image of theoretical expectation by experimental procedures. (1,0,0) Efficiency Map Efficiency (0,1,0) 0.52 (0,0,1) (1,1,1) 0.5 0.48 latitude 0.46 0.44 0.42 0.4 0.38 =0.536 � max 0.36 longitude =0.356 � min • It means that, with analysis cuts (In actual experimental observations) 
 There will be a limitation on the phase space integrations, 
 (also limitation comes from detector coverage.) 
 1. r ij will be changed. 
 2. There may be non-zero r 13 ,r 23 terms 
 ? R cut x d x = 0 through incomplete phase- space integration. 
 • Analysis cuts are even under parity (pt cut, eta cut, invariant-mass cut), 
 thus even after cuts, r 13 ,r 23 will be still 0. 


12 • What we observed at the LHC is the distorted image of theoretical expectation by experimental procedures. (1,0,0) Efficiency Map Efficiency (0,1,0) 0.52 (0,0,1) (1,1,1) 0.5 0.48 latitude 0.46 0.44 0.42 0.4 0.38 =0.536 � max 0.36 longitude =0.356 � min • It means that, with analysis cuts (In actual experimental observations) 
 There will be a limitation on the phase space integrations, 
 (also limitation comes from detector coverage.) 
 1. r ij will be changed. 
 2. There may be non-zero r 13 ,r 23 terms 
 ? R cut x d x = 0 through incomplete phase- space integration. 
 • Analysis cuts are even under parity (pt cut, eta cut, invariant-mass cut), 
 thus even after cuts, r 13 ,r 23 will be still 0. 


13 • What we observed at the LHC is the distorted image of theoretical expectation by experimental procedures. Theoretical shape After analysis cuts cross-sectional shape of k 3 =0 P γ 0 → Γ SM ij κ i κ j i,j • To consider cut-effects is very important for the precise determination of higgs’ property.

14 • A likelihood map: • We simulated 1000 pseudo experiments. (300 events after analysis cuts.) ( , , )=(1,0,0) � � � 1 2 3 80 Number of pseudo experiements (1,0,0) (0,1,0) 70 (0,0,1) (1,1,1) 60 latitude 50 40 30 20 10 0 longitude ( , , )=(0,1,0) � � � 1 2 3 Number of pseudo experiements (1,0,0) (0,1,0) 50 (0,0,1) (1,1,1) 40 latitude 30 20 10 0 longitude ( , , )=(0,0,1) � � � 1 2 3 Number of pseudo experiements (1,0,0) (0,1,0) 40 (0,0,1) 35 (1,1,1) 30 latitude 25 20 15 10 5 0 longitude

15 What else can we talk about Higgs measurement more than this? • We will have LHC Run 2 with 14TeV and possibly FCCs (Future Circular Colliders)… • With more energy,

16 • Thus, previous CMS/ATLAS analysis can not have a sensitivity for 
 (or along the -direction). To probe this operator we need to κ 4 κ 4 go beyond the resonant, i.e. off-shell production of Higgs. • One concern is the production of Higgs, since we need to consider ggH coupling in non-resonant region g ggX ( M 4 ` ) = g ggX ( M X )

17 Integrated cross sections in femtobarns (without cuts) g ggX ( M 4 ` ) = g ggX ( M X )

18 • One concern is the effect of Z-boson offshell especially operator k5 (that depends on the momentum of Z-boson strongly) • Z-boson off-shell contribution - with polarization vectors, 
 where s component is for the off-shell vector boson, usually 0 for the on-shell vector boson. Tanju Gleisberg, et.al., hep-ph/0306182

19 • One concern is the effect of Z-boson offshell especially operator k5 (that depends on the momentum of Z-boson strongly)

20 • Thus we can not use NWA to calculate LO cross section, especially for kappa5 operator.

21 • Another issue is the unitarity bound for O4. • Based on XZZ analysis, we consider Z L Z L → Z L Z L ✓ M 2 ◆ ( s/M 2 X ) 2 M 2 − 2 M 2 ✓ ◆ ✓ s ◆� (10 − 3 s/M 2 X ) κ 2 X X X a 0 ( s ) = 4 − 20 κ 4 3+ log (1 + ) − s − M 2 M 2 32 π v 2 6 s X X (here with kappa1 =1-kappa4)

22 • another approach is to use a “form” factor, cross section for SM ~ 0.009fb LHC may be sensitive ultimately to an off-shell cross section 5 to 10 times greater than the SM value. with fixed ggX, (varying ggX)

Conclusion • This study does not consider the interference effect between “Sig” and “Bkg”, but this points out the major issues for the off-shell analysis. • This study is only based on the very clean four lepton channel to have maximize efficiency. For different channels (WW for example) we will lose the efficiency through missing momentum from neutrino or sever bkg from QCD (hadronic W) • Higher dimensional operators can be severely constrained by the measurement of the off-shell H ∗ → ZZ rate and/or unitarity considerations.