The Top Quark and Precision Measurements
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![Page 1: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/1.jpg)
The Top Quark and Precision Measurements
S. Dawson
BNL
April, 2005
M.-C. Chen, S. Dawson, and T. Krupovnikas, in preparation
M.-C. Chen and S. Dawson, hep-ph/0311032
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Standard Model Case is Well Known
• EW sector of SM is SU(2) x U(1) gauge theory– 3 inputs needed: g, g’, v, plus fermion/Higgs masses– Trade g, g’, v for precisely measured G, MZ,
– SM has =MW2/(MZ
2c2)=1 at tree level• s is derived quantity
– Models with =1 at tree level include• MSSM• Models with singlet or doublet Higgs bosons• Models with extra fermion families
2
22
2 ZMGsc
2/122
22
2 24
'4
Gv
cg
sg
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We have a model….And it works to the 1% level
EW Measurements test consistency of SM
Consistency of precision measurements at multi-loop level used to constrain models with new physics
2005
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Models with 1 at tree level are different
• SM with Higgs Triplet
• Left-Right Symmetric Models
• Little Higgs Models
• …..many more
• These models need additional input parameter
• Decoupling is not so obvious beyond tree level
NEWSM LLL
As the scale of the new physics becomes large, the SM is not always recovered, violating our intuition
i
ii
NEW Oc
L2
Lore: Effects of LNEW become very small as
![Page 5: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/5.jpg)
Muon Decay in the SM
• At tree level, muon decay related to input parameters:
• One loop radiative corrections included in parameter rZ
• Where:
22222 22 WZ MsMcsG
2
2
2
22
2
2
s
s
c
sc
M
M
G
Gr
Z
Z
)1(2 222
rMcs
GZ
e
e
W
122
2
Z
W
Mc
M
If 1, there would be 4 input parameters
![Page 6: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/6.jpg)
Calculate top quark contribution to rZ
(mt2 dependence only)
• Muon decay constant:
• Vertex and box corrections, V-B small neglect
• Vacuum polarization, /, has no quadratic top mass dependence
• Z-boson 2-point function:
BVW
WW
MG
G
2
)0(
2
11)1(
4
32)0( 2
2
2
2
2
tt
cWW mm
QgN
1)1(
4
32 2
2
2
2
22
2
2
2
tZ
tc
Z
Z
m
Q
M
m
c
gN
M
M
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Calculate top quark contribution to rZ
(continued)
• Need s2/s2
• From SM relation using on-mass shell definition for s2
2
22 1
Z
W
M
Ms
2
2
2
2
2
2
2
2
2
2
2
2
2
2
64 W
tc
W
W
Z
Z
M
mNg
s
c
M
M
M
M
s
c
s
s
MW and MZ are physical masses
s2/s
2 not independent parameter
Includes all known corrections
2
2
2
282t
cSMt m
s
cNGr
Predict MW in terms of input parameters and mt
2005
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What’s different with a Higgs Triplet?
• SM: SU(2) x U(1)– Parameters, g, g’, v
• Add a real triplet, (+,0,-), 0=v
– Parameters in gauge sector: g, g’, v, v
– vSM2=(246 GeV)2=v2+4v
2
– Real triplet doesn’t contribute to MZ
• At tree level, =1+4v2/v21
• Return to muon decay:
2
2222 4
14 v
vvgMW
Blank & Hollik, hep-ph/9703392
2
2
2
22
2
2
s
s
c
sc
M
M
G
Gr
Z
Ztriplet
)1(2 222
rMcs
GZ
![Page 9: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/9.jpg)
Need Four Input Parameters With Higgs Triplet
• Use effective leptonic mixing angle at Z resonance as 4th parameter
• Variation of s:
241 sa
v
e
e
eZaveiL ee )( 5
2
22
2
222
22
2
2
2
2
log3
4
2
1
3
2
)()(
2)(
)(
t
e
ZzeeA
e
ZzeeVe
eeA
e
ee
Z
ZZ
m
Qs
s
a
M
v
M
cs
vm
a
av
M
M
s
c
s
s
2
1,2
2
1 2 ee asv
This is definition of s:
Proportional to meneglect
Contrast with SM where s2 is proportional to mt
2
* Could equally well have used as 4th parameter
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SM with triplet, cont.
2
2
2
22
2
2
s
s
c
sc
M
M
G
Gr
Z
Ztriplett
2
2
2
2
2
2
2
2
s
s
c
s
M
M
M
M
Z
Z
W
W
• Putting it all together:
• Finally,
mt2 dependence cancels
mt2 dependence cancels
rttriplet depends logarithmically on mt
2
If there is no symmetry which forces v=0, then no matter how small v is, you still need 4 input parameters
v 0 then 1
Triplet mass, M gv Two possible limits:
• g fixed, then light scalar in spectrum
• M fixed, then g and theory is non-renormalizable
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SU(2)L x SU(2)R x U(1)B-L Model
• Minimal model
• Physical Higgs bosons: 4 H0, 2A0, 2H
• Count parameters:
(g, g’, , ’, vR) (e , MW1, MW2, MZ1, MZ2)
'0
00,
2
1,
2
1
Czakon, Zralek, Gluza, hep-ph/9906356
EWSB
0
00)2,0,1(
LL v
0
00)2,1,0(
RR v
SU(2)R x U(1)B-L U(1)Y
Assume vL=0 (could be used to generate neutrino masses)
Assume gL=gR=g
![Page 12: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/12.jpg)
Renormalization of s in LR Model
2
22
2222222
22222
'21
2
1
)'(22
12
1
21
12
12
g
gvgMM
ggvgMM
vgMM
RZZ
RZZ
RWW
22222222
2
1
2
112 RRWW vgvgMM
2cos',
eg
s
eg
• Expand equations to incorporate one-loop corrections:
22222
222222
22222
22222222
2222
222222
))()((
)2()2(
2
1
))()((
))(())((
2
1
)()(
)()(2
1212
212121
1212
12121212
1212
1212
WWZZ
ZZZZZZ
WWZZ
WWZZZZWW
WWZZ
WWZZ
MMMM
MMMMMM
MMMM
MMMMMMMM
MMMM
MMMMcs
etc
• Gauge boson masses after symmetry breaking:
+2=2+’2
• Solve for s2 using
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Renormalization of s in LR Model, cont.
22222
222222
22222
22222222
2222
222222
))()((
)2()2(
2
1
))()((
))(())((
2
1
)()(
)()(2
1212
212121
1212
12121212
1212
1212
WWZZ
ZZZZZZ
WWZZ
WWZZZZWW
WWZZ
WWZZ
MMMM
MMMMMM
MMMM
MMMMMMMM
MMMM
MMMMcs
• Scale set by: 222
22
22222
121212 2cos
1
2cos2 WWRWWZZ MMvg
MMMM
• At leading order in MW12/MW2
2 v2/vR2:
)()(
24
)()(2
)()(
)()(2
22
2222
2
2
2
22
222
2
2
2222
2222
2
2
2
2
12
1
12
1
1212
1212
WW
WtcF
WW
W
WWZZ
WWZZ
MM
MmNsc
s
cG
MM
Msc
s
c
MMMM
MMMM
s
c
s
s
Very different from SM!
• As MW22, s2/s2 0
• The SM is not recovered!
![Page 14: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/14.jpg)
Thoughts on Decoupling
Limit MW22, s20
SM is not recovered
4 input parameters in Left-Right model: 3 input parameters in SM
No continuous limit from Left-Right model to SM
Even if vR is very small, still need 4 input parameters
No continuous limit which takes a theory with =1 at tree level to 1 at tree level
![Page 15: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/15.jpg)
Results on Top Mass Dependence
Scale fixed to go through data pointAbsolute scale arbitrary
Plots include only mt dependence
![Page 16: The Top Quark and Precision Measurements](https://reader038.fdocuments.us/reader038/viewer/2022110101/56812b88550346895d8fa574/html5/thumbnails/16.jpg)
Final example: Littlest Higgs Model
• EW precision constraints in SM require Mh light
• To stabilize Mh introduce new states to cancel quadratic dependence on higher scales– Classic model of this type is MSSM
• Littlest Higgs model: non-linear model based on SU(5)/SO(5)– Global SU(5) Global SO(5) with – Gauged [SU(2) x U(1)]1 x [SU(2) x U(1)]2SU(2) x U(1)SM
is complex Higgs triplet
22
22
1
x
x
I
I
fie /2
2/
2/2/
2/*
Th
hh
h
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Littlest Higgs Model, continued
• Model has complex triplet (1) at tree level
– Requires 4 input parameters
• Quadratic divergences cancelled at one-loop by new states• W, Z, B WH, ZH, BH
• t T
• H
• Cancellation between states with same spin statistics– Naturalness requires f ~ few TeV
• Just like in SM with triplet, dependence of r on charge 2/3 quark, T, is logarithmic!
T T T
T tb
2
2
(...)1f
v
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Littlest Higgs Model, continued
• One loop contributions numerically important– Tree level corrections (higher order terms in chiral perturbation
theory) v2/f2
– One loop radiative corrections 1/162
– Large cancellations between tree level and one-loop corrections
– Low cutoff with f 2 TeV is still allowed for some parameters.
– Contributions grow quadratically with scalar masses
Quadratic contributions cancel between these
Quadratic contribution remains from mixed diagrams
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Fine Tuned set of parameters in LH Model
Parameters chosen for large cancellations
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Models with triplets have Quadratic dependence on Higgs mass
• Mh0 is lightest neutral Higgs
• In SM:
• Quadratic dependence on Mh0 in LR Model:
• Quadratic dependence also found in little Higgs model
22
2
2
222
22 0
22
114)21(
224
1h
ZW
WFLRh M
M
c
M
scMG
sr
Czakon, Zralek J. Gluza, hep-ph/9906356
2
2
2
2
log192
11
W
hSMh M
Mgr
M.-C. Chen and S. Dawson, hep-ph/0311032
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Conclusion
• Models with 1 at tree level require 4 input parameters in gauge sector for consistent renormalization– Cannot write models as one-loop SM contribution plus tree level new
physics contribution in general
• Models with extended gauge symmetries can have very different behaviour of EW quantities from SM beyond tree level– Obvious implications for moose models, little Higgs models, LR
models, etc