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

• 2015. 2. 14


HPNP 2015

based on
 arxiv:1304.4936, 1403.4951 
 with J.Gainer, J. Lykken, K. Matchev and S. Mrenna

• Higgs property-measurement within high mass

window

• Higgs property-measurement in a far off-shell

region 1

Higgs Properties @ RUN1

• H → ZZ → 4l signature
• Studied within a Higgs mass-

window, 106 < m4l < 141 GeV

CMS Collaboration , arxiv:1312.5353[hep-ex]

2

@LO, MELA, MEKD, …

• Based on a “general” amplitude of H to four

leptons, to study 7 degree of freedoms@Higgs resonance, various codes were developed.

{θ1, θ2, Φ1 − Φ2, Φ1 + Φ2, θ∗, MZ1, MZ2}

3

• General amplitude for transition up to

dimension five operators in effective Lagrangian will be

H → ZZ A(H → Z1Z2) = c1(✏∗

1 · ✏∗ 2) + c2(p1 · p2)(✏∗ 1 · ✏∗ 2)

+c3(p1 · ✏∗

2)(p2 · ✏∗ 1) + c4✏µνρσ✏∗µ 1 ✏∗ν 2 pρ 1pσ 2

+c5(p2

1 + p2 2)(✏∗ 1 · ✏∗ 2)

• 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

4

• :This operator represents a tree-level Standard Model Higgs boson coupling.


With a requirement of gauge invariance, this operator tells us that X has a
 vacuum expectation value as XhXiZµZµ

O1

5

• :With a linear combination of two operators, we can have an operator 


which is invariant under gauge-transformation, . 
 This operator comes from the new physics through the loop.

Zµ → Zµ + ∂µθ

• :This operator represents a tree-level Standard Model Higgs boson coupling.


With a requirement of gauge invariance, this operator tells us that X has a
 vacuum expectation value as XhXiZµZµ

O1 O2

6

• :With a linear combination of two operators, we can have an operator 


which is invariant under gauge-transformation, . 
 This operator comes from the new physics through the loop.

Zµ → Zµ + ∂µθ

• :This operator represents a tree-level Standard Model Higgs boson coupling.


With a requirement of gauge invariance, this operator tells us that X has a
 vacuum expectation value as XhXiZµZµ

O1

O2

• :This operator is CP odd coupling which is invariant under the 


gauge-transformation,

Zµ → Zµ + ∂µθ

O3

7

• These three operators are key operators at a Higgs resonance 


to study a property of a “Higgs”.

{O1, O2, O3}

• At resonance, since (e.o.m)

but it becomes important in a range of , 
 i.e., off-shell region.

m4` MX

O4 → O1

⇤X = M 2

X X

8

• A 5 dimensional basis,
• r

result without analysis cuts 9

• These three operators are key operators at the resonance to

study a property of a “Higgs”.

{O1, O2, O3}

L 3 M 2

Z

v HZµ ˆ

f (H)

µν Zν + 1 2HF µν ˆ

f (H)

µνρσF ρσ + 1 2AF µν ˆ

f (A)

µνρσF ρσ

• 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

CP even CP odd

O1 O2 O3

• In general, X is a linear combination as

10

κ3 κ2 κ1 0+ 0− 0+

m

• With measured total rate
• rij is a function of phase space, thus theoretically, 


from the phase space integrations we can calculate rij


• r13, r23 will be 0 since terms in 𝛥 proportional to k1 k3 or k2 k3 are parity odd.

R 1

−1 xdx = 0

• We have three degree of freedom, but these D.O.F. can be reduced by factoring
• ut overall normalization from the measured total rate.

11

• 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. rij will be changed.

• 2. There may be non-zero r13 ,r23 terms 


through incomplete phase- space integration.


• Analysis cuts are even under parity (pt cut, eta cut, invariant-mass cut), 


thus even after cuts, r13 ,r23 will be still 0. 


• What we observed at the LHC is the distorted image of

theoretical expectation by experimental procedures.

longitude latitude

Efficiency

=0.536

max

• =0.356

min

• (1,0,0)

(0,1,0) (0,0,1) (1,1,1)

Efficiency Map

R

cut xdx = 0

?

12

• 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. rij will be changed.

• 2. There may be non-zero r13 ,r23 terms 


through incomplete phase- space integration.


• Analysis cuts are even under parity (pt cut, eta cut, invariant-mass cut), 


thus even after cuts, r13 ,r23 will be still 0. 


• What we observed at the LHC is the distorted image of

theoretical expectation by experimental procedures.

longitude latitude

Efficiency

=0.536

max

• =0.356

min

• (1,0,0)

(0,1,0) (0,0,1) (1,1,1)

Efficiency Map

R

cut xdx = 0

?

12

• What we observed at the LHC is the distorted image of

theoretical expectation by experimental procedures.

→ ΓSM P

i,j

γ0

ijκiκj Theoretical shape After analysis cuts

cross-sectional shape of k3=0

• To consider cut-effects is very important for the precise

determination of higgs’ property.

13

• We simulated 1000 pseudo experiments. (300 events after analysis cuts.)

longitude latitude

)=(1,0,0)

3

• ,

2

• ,

1

• (

longitude latitude

)=(0,1,0)

3

• ,

2

• ,

1

• (

longitude latitude

)=(0,0,1)

3

• ,

2

• ,

1

• (
• A likelihood map:

14

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,

15

• Thus, previous CMS/ATLAS analysis can not have a sensitivity for 


(or along the -direction). To probe this operator we need to go beyond the resonant, i.e. off-shell production of Higgs.

κ4 κ4

• One concern is the production of Higgs, since we need to

consider ggH coupling in non-resonant region

gggX(M4`) = gggX(MX)

16

gggX(M4`) = gggX(MX)

Integrated cross sections in femtobarns (without cuts) 17

• 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

18

• One concern is the effect of Z-boson offshell especially operator

k5 (that depends on the momentum of Z-boson strongly)

19

• Thus we can not use NWA to calculate LO cross

section, especially for kappa5 operator. 20

• Another issue is the unitarity bound for O4.
• Based on XZZ analysis, we consider ZLZL → ZLZL

a0(s) = ✓ M 2

X

32πv2 ◆(s/M 2

X)2

6 ✓ (10−3s/M 2

X)κ2 4−20κ4

◆ − ✓ 3+ M 2

X

s − M 2

X

−2M 2

X

s log (1 + s M 2

X

) ◆

(here with kappa1 =1-kappa4)

21

• another approach is to use a “form” factor,

with fixed ggX, (varying ggX)

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.

22

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.