7th International Symposium on Radiative Corrections
New Physics Search through
gg → t t → l X / b X
7/Oct./2005@Shonan Village
Kazumasa OHKUMA
Based on
hep-ph/0508183
PLB593 (2004) 189 &
(Fukui Tech.)
NPB689 (2004) 108
In collaboration with
B.Grzadkowski (Warsaw Univ.) , Z. Hioki （Tokushima Univ.）
J.Wudka （UC Riverside)
Plan of talk
I.
Introduction
II. Framework
III. Optimal-Observable Analysis
IV. Summary
I. Introduction
★Standard Model is composed by
Electro-weak theory and Quantum chromodynamics
Highly Successful Model
But!!
There are some unsolved problems
•Many parameters (Couplings, CKM, ‥‥)
•Origin of masses
•Hierarchy
New Physics beyond Standard Model
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How to search for the signal of new physics?
One of answers: Top quark physics.
Why?
Ans. There are some advantageous properties;
(1) Heaviest particle observed to date ! !
(i) Sensitive to SSB
Higgs
(ii) Decay as a free quark !
τ<<10-23[s]
Clear information about top quark
(2) On top quark sector, C P is negligible in SM ! !
Large CP indicates new physics contribution.
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In order to study non-standard effect, we focus on
at Photon Collider
Interesting option of ILC.
Initial CP parity is controllable !!
Only CP-even state at ee collider
• Couple to CP-odd scalar particles
We estimate
Statistical Significance of non-Standard Couplings
and probe
Optimal Beam Polarizations for New Physics Search
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II. Framework
★ Effective Lagrangian approach
Model Independent Analysis
Complementary relation
Model Dependent Analysis
Assumption
• New fields are not in existence under L scale.
• New heavy particles are decoupled.
SM Lagrangian is modified by
 dk
quantum effect of new physics.
: Energy scale of new physics
: SU(3) X SU(2) X U(1) invariant Dim.6 operators
: non-standard couplings
W.Buchmuller and D.Wyler, NPB268(1986)621
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Top Quark Production
Effective Operators for γγ→ t t
ｔｔg interaction (Top EDM)
ｔｔgg interaction (Contact Interaction)
We found relations between EDM operators and
Contact interaction operators.
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Relations of Operators
Bianchi identities and SM classical motion of
equations for quark and vector bosons lead us
to
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×
×
×
× ×
×
×
× ×
×
× : No contribution
Need not to consider Contact Interaction.
Effective Operators for gg→(H)→t t
ggH interaction (Higgs property)
Top Decay
Effective Operators for t → ｂ W
ｔｂW interaction
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Feynman rules for on-shell photos
★ Top Electric Dipole Moment interaction : ag
(1) C P-conserving ttg vertex
(2) C P-violating ttg vertex
★ Higgs Exchange interaction : ah
(1) C P-conserving ggH vertex
(2) C P-violating ggH vertex
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★ Decay Vertex
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Feynman Diagrams for gg → ｔ ｔ
S.Y.Choi and Hagiwara
PLB359(1995)369,
P.Poulos and S.D.Rindani
PRD56(1997)6835,
etc.
B.Grzadkowski and J.F.Gunion, PLB294(1992)316,
G.J.Gounaris and G.P.Tsirigoti,PRD56(1997)3030,
E.Asakawa, J.Kamoshita, A.Sugamoto and I.Watanabe,EPJC14(2000)335,
E.Asakawa, S.Y.Choi,K.Hagiwara and J.S.Lee, PRD62(2000)115005,
R.M.Godbole, S.D.Rindani and R.K.Shigh PRD67(2003)095009,
etc.
In actual experiment, their mixed signals will be observed !!
All possible non-standard interactions
are taken into account.
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III. Optimal Observable Analysis
What is Optimal Observable Analysis ?
Method for estimating the precision of
determination of relevant non-standard
couplings.
J. F. Gunion, et.al, PRL77 (1996) 5172
How to estimate these precision ?
Suppose following distribution:
Cross section
: final-state phase space
: known functions ← Calculable
: model-independent coefficients
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Extract C i using appropriate weighting
function
Extract
In general, different choice
for the
are possible.
There is a unique choice which minimizes
the resultant statistical uncertainty: DCi.
Such function is given by
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Inverse matrix of Mij :
Calculable
Statistical uncertainty of Ci is given by
: Event number
: Total cross section
Apply to analysis of final-lepton’s energy
and angular distribution for
.
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Application
e.g.
Final-lepton’s energy and angular distribution
EDM
Calculable
Higgs
Decay
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Matrix Element Mij
Inverse
where I,J=1,‥,6 correspond to
SM, g１,g２, h1, h2 and d, respectively.
EX.
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Parameters of Photon collider
High energy colliding beams of polarized photons
are generated by Compton backscattering
: Initial electron longitudinal polarization
: Degree of circular polarization of initial laser
: Degree of linear polarization of initial laser
with azimuthal angle
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Probing optimal photon beam polarizations
Estimate the uncertainty of
couplings
Search for the combinations that make
varying polarization parameters as
minimal,
Note
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Unfortunately !
Our results for Xij are very unstable
even a tiny fluctuation of Mij changes Xij significantly !
All the couplings cannot be determined
at the same time from only
.
Refrain from determining all the couplings
at once.
Assumption
Some non-standard couplings Ci have
been measured in other processes
e.g.
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Result
Under the conditions:
,
,
5 and 4 parameters analyses lead to
unstable solutions.
3 and 2 parameters analysis give stable
solutions within 10% ambiguity
3 parameter case :
3 combinations are OK
final lepton 1
final bottom 2
2 parameter case :
68 combinations are OK
final lepton 39
final bottom 29
Some results are presented hereafter.
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Results (3 parameter analysis)
Charged-lepton detection
(2 of 3)
Bottom-quark detection
Not so small !
with
with
: detection efficiency
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Results (2 parameter analysis)
There are 68 stable solutions.
However
All the stable solutions do not give us
good statistical precisions.
Two statistical uncertainties (
satisfy
,
)
is minimal
for each pair of
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and
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Results (2 parameter analysis)
mH=300 GeV
•Final lepton detection
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Results (2 parameter analysis)
mH=300 GeV
•Final bottom quark detection
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Results (2 parameter analysis)
Independent of Higgs mass
•Final lepton detection
Note
There are no combinations
which make ag2 small (ag2 < 0.1).
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IV. Summary
To study non-standard Effect in top quark
.
production,we focus on
Model independent analysis were performed
using effective low-energy Lagrangian.
Statistical uncertainties were estimated
- CP conserving and violating ttg coupling :ag1,ag2
- CP conserving and violating ggH coupling :ah1,ah2
- anomalous tbW coupling :ad
using Optimal Observable method.
Probe Optimal beam polarizations
for New physics search
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Adjusting beam polarization gives us
good statistical precisions:
in two parameter analysis
- all non-standard couplings （except for ag2）
could be determined with accuracy better
than 0.1 with a integrated luminosity of
500 fb-1.
It is useful to probe the proprieties
of Higgs boson couplings.
- the statistical uncertainty of
large in this analysis.
ag2 is still
We look for anther processes
to determine ag2.
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Back up
Comparing ee and gg colliders
Top quark productions
ee collider
gg collider
It is possible to measure ttg coupling at both colliders.
Within the framework of the effective
Lagrangian, we can estimate D a g .
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Appendix
Note!
In the ee
ag2
tt l / b X ,
could not be measured.
In gg tt
l / b X , ag2 could be measured
though it’s not to be measured precisely.
B.Grazkowski and Z. Hioki,
NP B484 (1997) 17, NP B585 (2000) 3
L. Brzezinski, Grzadkowski and Z. Hioki,
Int. J. Mod. Phys. A14 (1999) 1261
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Appendix
Comparison of ag1 measurement in ee and gg colliders
1 parameter Optimal Observable analysis
 ee
 gg
tt
tt
l X
l X
7th International Symposium on Radiative Corrections
ee colliders will give us
slightly good precision.
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Appendix
Comparing ee and gg colliders
ee collider ( e e



l / b X )
It seems to be slightly favored to
measure ag1.
ag2 could not measure in the process.
gg collider ( gg

tt
tt
l / b X )
ag2 could be measured in the process.
(precision is not good)
It seems to be very useful for testing
the Higgs coupling.
Looking for the processes or observable that make
statistical sensitivity small for the measuring ag2 is
important !
Circular polarization Asymmetry
(-)
(-)
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Appendix
Linear polarization Asymmetry
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Appendix
Results (2 parameter analysis)
mH=300 GeV
•Final bottom quark detection
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7/Oct./2005 Shonan Village
Appendix