1. An Effective operators analysis associated with the Higgs
Fanrong Xu (徐繁荣)
National Tsing Hua University, Taiwan
Chang-Pan-Xu, arXiv: [hep-ph]
March 29, 2013
XS-2013, NCU, Taiwan

2. Content 1 2 3 4 5 Introduction Effective Operators Higgs Physics
Effective Operators 1
Higgs Physics 2
EDM, MDM 3
Discussion 4
Summary 5

3. Introduction
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4. NP? Strategy EFT Higgs data EDM, MDM GHO @ XS-2013, NCU,2013/03/29
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5. Higgs data New era started from July 4th, 2012.
Three rounds of data release up to now
since ICHEP2012, summer 2012
since HCP2012, winter 2012
latest data has been released in “Rencontres de Moriond 2013”
LHC Higgs XSWG 2012
excess or fluctuation?
Lots of paper
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6. Higgs data Moriond 2013, EW Moriond 2013, QCD
The data will be “unchanged” for 2 years;
What is hidden in current data: NP or SM?
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7. Cutoff Scale
Mass scale of exotic degrees of freedom: (0.4~8) TeV (cutoff)
Can we get a hint for the cutoff?
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8. Gauge-Higgs Operators1
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9. Effective Theory Bottom-up approach:
SM is the low energy effective theory;
The full Lagrangian can be expanded by (1/cutoff)
There are limited (59) gauge invariant independent dimension-6 operators
GIMR, JHEP10 (2010)085;
BW, NPB268 (1986) 621.
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10. Effective Operators
Motivated by diphoton excess and DOF(s) beyond SM, we
assume New Physics can be captured by the effective
gauge-Higgs operators
These operators form a subset, the other 3 gauge-Higgs operators are strictly constrained by EW precision tests.
The RG running effect will not be involved in this work.
Oblique correction: S
Manohar, Wise;
X. Zhang, B.-L. Young;
McKenn,Pospelov,Ritz ……
QCD theta term
GJMT, ;
MEMP,
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11. Effective interactions
CP even/odd tree level h-V-V’ interaction is brought in
Also anomalous gauge coupling is introduced
CP-even
CP-odd
Anomalous coupling
SM-like
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12. Higgs Physics 2
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13. Production and decay
Signal strength: co-determined by both production and decay
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14. Loop-level process production: gluon fusion dominates diphoton decay
unmeasured channel:
CP-even
CP-odd
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15. Tree-level process The tree level decay
SM contribution is contained in CP-even part,
phase space integral of 3-body decay needs to be treated.
Assumptions
All the final state fermions are summed up
All the fermions are massless
CP-even
CP-odd
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16. Numerical Analysis Numerical expressions at cutoff 1TeV
With latest experimental data as input
Rescaling:
The story of 6 numbers
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17. Pseudo global fit 68 % C.L. correlation among alpha’s:
Current LHC data agrees with SM;
Larger GF production  smaller Higgs decay width
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18. Constraints on Wilson coefficients
95 % C.L. correlation among Wilson coefficients: SM
LHC
Both CP-even and CP-odd Wilson coefficients have a boundary
CP-even Wilson coefficients are well constrained, a few
Constraints on CP-odd sector are poor,
There is still allowance for NP, from SM theoretical errors.
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19. Prediction The relation between ZZ and WW:SM
LHC
The boundary of decay width ratio and signal is obvious
A linear relation of alpha and mu between WW and ZZ is found
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20. EDM, MDM 3
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21. EDM
Current nEDM
Current eEDM
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22. AMDM
AMDM: the SM deviation from experimental measurement provides a room for NP
SM calculation:
QED (5-loop),
EW correction (2-loop),
hadronic contribution,
Measurement:
muon:
muon (g-2) collaboration, 2006
electron:
Hanneke et. al., PRA2011
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23. EDM and AMDM in EFT
One loop EDM and g-2 can be generated due to the effective operators
CP-odd (EDM); CP-even (g-2)
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24. Constraint on CP-odd sector
Neutron and electron EDM upper bound provides a constraint on 3D space.
Project to 2D plane by setting the third parameter in a certain region
EDM helps to further determine CP-odd sector
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25. Constraint on CP-even sector
With a best fit of muon and electron g-2, a linear relation is obtained
g-2 helps to further determine parameter space of CP-even sector.
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26. A global constraint on c
Take into account all the above experiments, we can get a limited region in Wilson coefficient space.
CP-odd sector are severely constrained, reduced to order of 1, which also gives an indication for NP models.
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27. Prediction The relation between ZZ and WW:
The interesting relation between WW/ZZ and AZ SM
LHC
But hard to detect
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28. Discussion 4
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29. 1. Discriminate c3 In the presence of effective operators, we have
One way to discriminate the degenerate solutions is by Higgs pair production in future LHC experiments.
The solution will bring a large deviation from SM, and would be easily checked (ruled out) by future experiments.
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30. 2. Wise-Manohar Model Wise-Manohar model: color-octet scalar
Custodial symmetry leads to
and
The physical CPV phase appears in potential, which is the source of CP-odd operators.
WM, PRD’06;
HVY,JHEP’11 ……
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31. 2. Wise-Manohar Model The mechanism to generate effective operators
From a naïve dimensional analysis, constraints on model parameters can be obtained from current LHC data
CP-even operators can be generated at 1-loop level;
CP-odd sector is at 2-loop level (why constraints are weak).
CP-even
CP-odd
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32. 3. Prediction for CPV decays
CP violation fraction
A not very predictive prediction (hard to analyze CP for photon)
The CPV fraction in WW/ZZ mode is small
There could be large CPV component in gamma-gamma/gamma-Z mode
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33. Summary 5
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34. Summary
We have provided an EFT approach to 125 GeV Higgs boson, and find even all Higgs decay channels agree with SM predictions, SM theoretical uncertainty still provides a room for NP.
From current LHC data we have got a global constraint of Wilson coefficients, which indicates NP models, and Wise-Manohar model is a typical example.
From current LHC data, we find a linear relation between WW and ZZ, and get the limits of signal strength for different di-boson decay modes.
When EDM and AMDM are taken into account, CP-odd operators are constrained severely. An interesting relation between ZZ(WW) and gammaZ is predicted.
The potentially interesting CPV fraction in diphoton and gammaZ mode is pointed out.
We also provide a way to discriminate a degenerated solution of c3.
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35. 谢谢