Electroweak Symmetry
Breaking and Triple Gauge
Coupling Measurements
NCTS, Theory Division
Qi-Shu Yan
with S. Dutta, K. Hagiwara, K. Yoshida
NTHU, 14:00-15:00, 22, March, 2007
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Q.S. Yan - Constraints on the EWCL from the precision data
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NTHU, Seminar,
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z
z
z
z
z
Mass Origin and the
Elctroweak Symmetry
Breaking Mechanism
Three generations
Too many free
parameters
No dark matter
candidate
…
The SM is an effective description of a fundamental theory!
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Q.S. Yan - Constraints on the EWCL from the precision data
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EWSB and S Parameter
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How conclusively precision
data can rule out QCD-like
dynamics for EWSB sector?
Triple Gauge Couplings
¾Examining the non-Abelian
structure of the SM
¾Measuring the size of weak
bosons
¾Removing bkgd for new physics
¾…
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Outline
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S in QCD-like Theories
S parameter is postive!
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Q.S. Yan - Constraints on the EWCL from the precision data
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Precision of S in Evolution
1990(2)
1999
2004
2006
PDG
S = 119Sˆ
T = 129Tˆ
S parameter is negative!
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Q.S. Yan - Constraints on the EWCL from the precision data
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Theoretical Effort for Solution
‰ Produce a negative S in TCs
‰ Include extra vector bosons
‰ Decrease T
‰ Extra Dimensions
‰ ADS/CFT
‰…
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Q.S. Yan - Constraints on the EWCL from the precision data
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Shortages in Experimental
Uncertainty Analysis
Model independent analysis is favored!
It is necessary to have an integrated and general analysis
with two-, three-, and four-point functions data.
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Q.S. Yan - Constraints on the EWCL from the precision data
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What’s New in this Talk?
S can be either positive or negative!!
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2 Introduction to the EWCL
14 free parameters form the parameter space of the EWCL
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Operators
Two
Point
Function
Four
Point
function
Three
Point
Function
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Bosonic Vertices
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EWCL in Effective Field
Theory
We expect that S parameter should be a running parameter!
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Running Allowed by QFT
We assume that perturbation method
could be valid from Mz to UV Cutoff
with only dimension 2 and 4 operators.
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3 RGEs
Dimensional regularization,
Background field method,
Feynman-’t Hooft gauge,
Modified MS,
Heat kernel method
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Check Points
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4 Precision Data and Bounds
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Precision Data of STU
Inputs and formula to determine the two point chiral coefficients
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Precision Data of STU
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Q.S. Yan - Constraints on the EWCL from the precision data
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Precision Data of TGC
Proof of Non-Abelian Structure of the SM
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Precision Data of TGC
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Bounds of QGC
5 conditions (J=0 channel) to fix 5 free parameters
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Chiral Coefficients in EWCL
TGC errors are two order larger than those of
two-point chiral coefficients
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5 Uncertainty in S-T
TGC
Case
1
TGC
Case
2
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TGC
Case
3
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Uncertainty in T
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Summary
S
T
Λ
Λ
=
− 0 . 08
( − 0 . 02
) ±
0 . 20
=
+ 0 . 40
( + 0 . 52
) ±
0 . 22
When TGC & QGC uncertainty is taken into account
S
T
Λ
Λ
=
− 0 . 17
=
+ 0 . 38
( − 0 . 11
( + 0 . 50
) ±
0 . 10
) ±
0 . 14
When TGC & QGC uncertainty isn’t taken into account
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Conclusions
Q.S. Yan - Constraints on the EWCL from the precision data
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Backup
Discussions
Should S parameter run?
Subtracted dispersion relation without custodial symmetry
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Power counting problem
If the derivative power counting rule doesn’t hold, our results are the
most conservative perturbation calculation.
• High order operators can affect STU and TGC fitting and QGC
bounds significantly. Effective description might break down.
• High order operators can affect the RGEs running dramatically,
especially near the UV region.
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