Frank Linde, september 2005, BND summerschool, Texel Frank Linde, september 2005, BND summerschool, Texel Weak measurement s België Nederland BND summer school 2005 Deutschland he good news: an excellent LEP I paper Precision Electroweak Measurements on the Z Resonan e bad news: I did not study it (and yesterday did not
E lectro- W eak measurements. B elgië N ederland BND summer school 2005 D eutschland. The good news: an excellent LEP I paper “Precision Electroweak Measurements on the Z Resonance”. The bad news: I did not study it (and yesterday did not help). The night after . - PowerPoint PPT Presentation
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Frank Linde, september 2005, BND summerschool, TexelFrank Linde, september 2005, BND summerschool, Texel
Electro-
Weakmeasurement
sBelgiëNederland BND summer school 2005DeutschlandThe good news: an excellent LEP I paper
“Precision Electroweak Measurements on the Z Resonance”
The bad news: I did not study it (and yesterday did not help)
multiplicitycharged trackstopology jets planarity acoplanarityenergy total energy missing energy energy balance minimal energykinematic fitsverticingneural networks
AFB can be extracted using Born level prediction for the distribution:
cos-1 0 +1
d/d
cos combined
acceptanc& efficiency
fitted d/dcos
“data”
How to extract the asymmetry?
which real
world effects?
3333
counting or 2-fit or likelihood-fit
counting:
2-fit (correct for ):
Likelihood-fit:
3434
Results: cV & cA measurements
cA
cV
3636
3. Z-boson & W-bosondecay widths & masses
37
W-boson & Z-boson decay widths
px
p1
p2
e
e+
Z0
e
e+
W+
px
p1
p2
To be efficient, I perform calculation for X-boson with vertex factor: (gX/2)(cV-cA5)(in addition I work in X-boson rest frame and I mess around with u- and v-spinor states)
4-vectors:
Generic expression decay width:
X-boson polarization sum spin states:
Traces of -matrices:
38
The amplitude 5
2
1ccg AVX
px
p1p2
ee-
X
22
2
2
2
1
22 2+2
p·p1= p·p2=M2/2
p1·p2=M2/2
p·p=M2
39
px
p1
p2
e
e+
Z0
For the Z-boson:
The decay width
Plug into the decay width expression:
e
e+
W+
px
p1
p2
For the W-boson:
Use the 4-vectors: 2
2
40
W-boson
Z-boson
Z- & W-boson partial decay widths
41
Z- & W-boson partial decay widths
ee
eell
bbssdd
ttccuuqqZ-boson
tbcsudqq '
ee
W-boson
4242
Z-boson leptonic cross sections
“simple” (but correct!) counting and you get branching fractions
4343
W-boson cross section (LEP II)
e
e+
W
W+
e
e+
W
W+
Z0
e
e+
W
W+
e
4444
W+W event topologies
“simple” (but correct!) counting and you get branching fractions
“all hadronic”(4 jets)
“all leptonic”(no jets)
(2 jets)
4545
W-mass
bestaccuracy
:2 jets
no interplay between differentW-boson
decay products
4646
mW: screams for kinematic fit!
4-momentum conservation: (2Ebeam,0,0,0)(4)
2 W-bosons: equal mass? One condition.(1)
All hadronic: constraint improves E for jets2-jets: three constraints for neutrino
one constraint leftall leptonic: hopeless
(can also use the equal mass, but masses (width!) are not that equal
summing and averaging over the spin states look for the appropriate trace theorem integrate over the e(p’) + e(k’) + (k) phase space
-decay calculation
e
e
Wp
k
p’
k’
Kinematics:
With the standard Feynman rules you get for the amplitude:
Plugging this in the decay width “master” formula:
50
Spin:
Note: happily include in the summation non-existent -spin states
(0 contribution)
-decay: trace reduction
Kinematics & me20:
And finally the amplitude:
0: odd #
0: PL PR
51
Left with:
-decay: phase space integral
3-particle phase space yields 9-dimensional integral:
Using the -function yields a 6-dimensional
integral
Relevant variables: EeE’, E’ and angle between the electron and the anti-electron neutrino.
3-dimensional integral. The cos integration can be performed using:
52
-decay: what to measure?
’
E’
M/2
M/2
integration
region
M/2
M/2-E’
Experimentally only the electron can be observed. Hence integrate over ’ (and E’):
Maximum energy e , e en : M/2Minimal energy any particle pair: M/2
d/dE’
53-decay: measurements!
M/253 MeV
ee
54
-decay: for high schools
55-decay: equipment
56-decay: result
et/
constant background
dagelijks paar 100 -vervallen
57
The decay of the tau () ee
Calculation: just copy!
Rewards: lepton universalitynice experiment!
p
k
p’
k’
e
e
W
58
The tau lifetime
59
Lepton universality test-lifetime
+leptonic
branching ratio+
-mass
60
Another cute idea: -mass
+
KK+
KK++
select multi-prong -decays with lots of
visible mass
little room left for -mass
(in particular if you are lucky)
95% CL upper limit: 18.2 MeV
6161
5. inferringt-quark &H-bosoninformation
6262
t-quark mass: mt2 dependence
LEP’sfrustratio
ni.e. LEP should have
discovered the t-quark
6363
H-boson mass: ln(mH) dependence
LEP’s realfrustratio
ni.e. LEP should have
discovered the Higgs
6464
Higgs: the next discovery?
LEP
LHC ILC
6565
1. branching ratio
6666
Higgs to fermions: ff
H
f
f
H ff)()(2
fvfum
mg
W
fM
pm
mg
W
f 22
22
2M2
mm
pmg
m
p
WH
f
HffH 22
3222
2 48
M
6868
Higgs branching ratio’s
light Higgs: mH<150 GeVH bb, , cc
intermediate Higgs: 150<mH<350 GeV
H WW, ZZ heavy Higgs:
mH>350 GeVH WW, ZZ, tt
factortwo?
6969
2. LEP’s screw-up?
7070
Production process: Ecm>mZ+mH
H
Ze
e+ e+e-Z*ZH
HZ,W
e
e+
,e+
,e+
e+e- e+e-He+e- H
100 150 200 250
0.5 pb
1.0 pb
Ecm
607090
MH
(e
+e
- Z
H)
7171
ZH Analysis strategy: b-tagging
Hbb 4 jetsZqqH
2 jets + ee/Z ee/ H
2 jets + Z H
2 jets + EmissZ
H
7272
Higgs candidates or ZZ events
7373
Higgs candidates or ZZ events
H bbZ bb
Best Higgs fit:mH=113.4 GeV
7474
Higgs candidates or ZZ events
H bbZ
Best Higgs fit:mH=114.4 GeV
7575
Statistical analyses: 1-2 sigma’s
7676
3. discovery at LHC?
7777
m
100 fb-1
ppXH, HZZ4-leptons
“golden” channelmH: 4-lepton mass
7878
m
100 fb-1
ppXH, H (crazy coincidence)
Low mass HiggsmH: mass
7979
mbb
100 fb-1
ppttH, Hbb, tb(qq), tb(l)
Low mass HiggsmH: bb mass
e
e
q
q
qq
q
q
8080
4. self coupling at ILC?
8181mH
e+e- HHZHHZ
(fb)
ZHl+l-bbZHqqbb
Higgs at ILC
8282
Summary1st: find the one missing member: Higgs
2nd: better understanding of the “arbitrary” Standard Model parameters.3rd: lots of other open issues: monopoles, three families, gravity, dark matter, …