1. Review of Anomalous Triple/Quartic gauge boson coupling measurements
Zhijun Liang
University of California,Santa Cruz

2. Diboson physics and Anomalous Triple gauge coupling
Diboson production cross-section measurements
Test of SM electroweak theory and perturbative QCD at TeV scale
Sensitivity to new particles decaying to dibosons (Technicolor, Little Higgs, SUSY, etc...)
Anomalous Triple Gauge Couplings (aTGCs)
The Higgs mechanism ≠ a Higgs boson !
Vector boson self-couplings fundamental prediction of the Electroweak Sector of SM
Its study is important to understanding electroweak symmetry mechanism

3. Diboson cross sections measurements overview
Summary of ATLAS and CMS have diboson cross section measurements at 7TeV and 8TeV
If there is any Anomalous couplings
increase of total cross sections
And differential cross sections at high invariant mass

4. Unfolded spectrum
Both ATLAS and CMS start providing unfolded spectrum in diboson processes.
Especially for transverse momentum spectum and invariant mass Spectrum

5. aTGCs model Charged aTGCs (WWV): in SM Neutral aTGCs (ZZV):
Forbidden in SM

6. aTGCs limit setting
Use reconstructed transverse momentum spectrum or invariant mass Spectrum for aTGCs limit setting
Most of the aTGCs sensitivity coming from the high pT/ high mass bins
The binning for aTGCs study is different from unfolded spectrum in some analyses.
Take ATLAS 7TeV WW analysis and CMS ZZ 8TeV analysis as example
aTGCs study is optimized to use more bins in high pT/high mass region.

7. Summary of charge aTGCs result
Provide 95% confidence intervals
aTGCs limits from ATLAS and CMS
Run 1 result Is comparable to LEP
and D0 results.

8. From aTGCs to EFT Effective field theory (EFT)
Including Higgs boson in SM fields
Both ATLAS and CMS are moving toward EFT model
to replace aTGCs model in longer run
The discussion between ATLAS/CMS diboson community is mainly focus on one of the basic of Dim 6 EFT model
CP even operator
CP odd operator
C. Degrande et al, axXiv:

9. Latest results basic on EFT models
ATLAS 7TeV WW/WZ analysis started to provide
Both the aTGCs limits
And the limits on one basic of Dimensional 6 EFT operators

10. Quartic Gauge Boson Couplings
Reminder of Quartic Gauge Boson Couplings (QGCs)
SM model predicts gauge boson self coupling
Four gauge boson vertex:
WWγγ , WWZγ , WWWW, WWZZ, ZZZZ …
QGCs can be studied in
Tri-boson processes
Vector boson scattering processes
Exclusive γγ->WW process

11. Modeling of aQGCs: Dim 8 EFT models
Extension of the effective SM-Lagrangian by introducing additional dimension-8 operators for QGCs
no effect on TGCs.
Higgs field
Higgs - Gauge boson field(LM)
Gauge boson field (LT)
O.J.P.Eboli, et.al. Phys.Rev.D74:073005,2006

12. Unitarity violation treatment
 EFT-predicted aTGC/aQGCs amplitudes
disrespect the gauge symmetry
and violate the unitarity once the √s goes sufficiently high
Unitarization with the k-matrix approach (arxiv: )
Unitarization by infinitely heavy and wide resonance
K-matrix amplitude
Form factor approach (arxiv: )
Unitarity can be preserved by introducing form-factor (FF)
energy-dependent form factors

13. The measurement of Vector boson scattering processes
O(α6EW)
Vector boson scattering (VBS) is one of the process to stduy QGCs.
Diboson + two forward jets in event topology
The scattering of longitudinally polarized vector bosons
violates unitarity at ~1TeV without higgs
Important to check
whether Higgs boson unitarizes it fully or only partially
The first VBS analysis :Same sign WW
Sensitive to WWWW vertex
Final state: W+W+jj or W-W-jj

14. aQGCs limits from VBS process
FS0 and FS1 in Dim 8 EFT model
is related to the Higgs field
ATLAS use K matrix unitarization
CMS result is without form factor
-> not easy to compare

15. aQGCs limits from Tri-boson processes
Tri-boson processes are sensitive to
FT and FM operators in Dim 8 EFT model.
CMS have results from WVγ

16. Summary
Measurements of diboson production in WW, WZ, ZZ, Wγ, Zγ have been performed
Contributions of aTGCs not observed
limits are set for aTGCs models and Dimension 6 EFT models
Measurements of tri-boson and Vector boson scattering production processes have been performed.
Contributions of aQGCs not observed
limits are set on aQGCs and Dimension 8 EFT models
Higgs and multi-boson studies often probe the same operators in EFT
We need a common basis of EFT operators if we want to combine
The choice of EFT model basic depends quite strongly on the availability in Generators

17. Backup: LEP convention for aQGCs
W+W−γγ , ZZγγ aQGCs
where Λ is the New Physics energy scale

18. CMS position on unitarization
All unitarization options modify the model and the measured couplings no longer correspond to EFT, but rather some ad-hoc model
when 95% CL limits cross unitarity violating regions it's just
means that the experimental measurement doesn't have much to say at the moment, but it's still valuable because:
a) it may avoid unitarity violation at lower confidence level
b) it can be easily combined with other measurements that together can lead to a more useful limit
c) it allows to estimate sensitivity for future measurements
When experimental measurements are well within the unitarity limit any reasonable unitarization scheme should lead to the result consistent with EFT as is without unitarization.