Experimental tests of the Standard Model 0. Standard Model ...
Transcript of Experimental tests of the Standard Model 0. Standard Model ...
Experimental tests of the Standard Model
0. Standard Model in a Nutshell
1. Discovery of W and Z boson
2. Precision tests of the Z sector
3. Precision test of the W sector
4. Radiative corrections and prediction of the
Higgs mass
5. Higgs searches
Literature for (2):
Precision electroweak measurement on the Z resonance,
Phys. Rept. 427 (2006), hep-ex/0509008.
http://lepewwg.web.cern.ch/LEPEWWG/1/physrep.pdf
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0. Standard Model in a Nutshell
2
RRR
LLL
e
e
e
LH weak iso-
spin doublets
RH singlets
W )( 21
2
1i
Symmetry:
Additional fieId W3 which corresponds to the 3rd isospin operator 3.
W3 only couples to the particles of the weak isospin doublet!
In addition we have two more fields:
• Photon which couples to the LH and RH fermions with same strength.
• Z boson which couples to LH and RH fermions with different couplings gL
and gR
How can we associate the observed fields to W3?
weak isospin: T, T3
3
3,2,1iW i
,~ ii WigJiJ
Corresponding to J and J3 there are fields
321 and )(2
1WiWWW
g
BYJ
2
g
BJg
i Y
2~
convention
g, g are coupling
constants.
Additional gauge field B
Gauge field B couples to hyper-charge: Y = 2 [Q-T3]
couples to LH and RH fermions
T.Plehn
4
While the charged boson fields W correspond to the observed
W bosons, the neutral fields B and W3 only correspond to
linear combinations of the observed photon and Z boson:
WW
WW
WBZ
WBA
cossin
sincos
3
3
WW
WW
ZAW
ZAB
cossin
sincos
3
massless photon
massive Z boson
The weak mixing angle w (Weinberg angle) follows from coupling constants:
WW
eg
eg
cossin
W
W
W
Z ggg
gcos
sin
cos
Coupling to the
photon field ~e
e
e
W
Vertex factors
)1(2
1
2
5gi
e
e
Z
)(2
1
cos
5
AV
W
ggg
i
e
e
ie
Propagator
(unitary gauge)
22
2
Z
Z
Mq
Mqqg
22
2
W
W
Mq
Mqqg
2
1
q
Feynman rules
:02qW28 2
2
F
W
G
M
g
:02qZ2cos8 22
2
NC
ZW
G
M
g
22
NCF GGAssuming
universality follows 2
22cos
Z
WW
M
M
=0
= 1- =1
2
22cos
Z
WW
M
M
1. Discovery of the W and Z boson1983 at CERN SppS accelerator,
s 540 GeV, UA-1/2 experiments
1.1 Boson production in pp interactions
p
pu
d
Ws
q,
q, p
pu
u
Zs
q,
q,
XWpp XffZpp
Similar to Drell-Yan: (photon instead of W)
10 1001 ZWMs ,ˆ
)( ZW
nb1.0
nb1
nb10
12.0x mitˆqsxxs qq
22
q )GeV65(014.0xˆ sss
Cross section is small !7
1.2 Event signature:
p p
High-energy lepton pair:
222 )( ZMppm
XffZpp
GeV91ZM
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1.3 Event signature: XWpp
p p
High-energy lepton:
Large transverse
momentum pt
Undetected :
Missing momentum
Missing pT vector
How can the W mass be reconstructed ?
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W mass measurement
In the W rest frame:
•
•
2WM
pp
2WT M
p
Tp
Tdp
dN
2WM
In the lab system:
• W system boosted only
along z axis
• pT distribution is conserved:
maximum pT= MW / 2
Jacobian Peak:
• Trans. Movement of the W
• Finite W decay width
• W decay not isotropic
GeV80WM
21
22
4
2~ T
W
W
T
T
pM
M
p
p
dN
10
Jacobian Peak
21
22
4
2cos
cosT
W
W
T
TT
pM
M
p
dp
d
d
dN
dp
dN~
Assume isotropic decay of the W boson in its CM system:
.cos
constd
dN
(Not really correct: W boson has spin=1 decay is not isotropic!)
2sin
w
TT
M
p
p
p
2
2
2cos1
w
T
M
p
cos2~cos
2T
w
T dp
M
pd
11Jacobian
W candidate from the LHC – they still exist!
eeWdu Anti-quarks from the sea! 12
Z bosons are alos produced at the LHC
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14
Z and W production at LHC
P.Harris,
Moriond 2011
Instead of EeT
use ET (i.e. E T)
W-boson production at LHC
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Valence quark +
sea quark
valence quark ratio u/d = 2 more W+ than W-
ATLAS 2010:
1.4 Production of Z and W bosons in e+e- annihilation
Precision tests
of the Z sector Tests of the W sector
qqW
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2. Precision tests of the Z sector (LEP and SLC)
21sin
32
21
21sin
34
21
21sin2
21
21
21
2
2
2
W
W
W
AV
quarkd
quarku
gg
Z
f
f
5
2
1
cos
fA
fV
w
ggig
22
2
Mq
Mqqgi
)(2
1)(
2
1AVRAVL gggggg
32
3 and sin2 TgQTg AWV
w
eg
sin
Standard Model
2
22 1
Z
ww
M
Msin
17
WW
A
V QT
Q
g
g 22
3
sin41sin21
Cross section for ffZee /
2M
2
Z
eeA
eVe
ZZZ
Z
AV
W
Z
ee
uggviMMq
Mqqgvggu
giM
uvq
gvuieM
)(2
1
)()(
2
1
cos
)()(
5
22
25
2
2
2
2
ee for
Z propagator considering a
finite Z width (real particle)
With a “little bit” of algebra similar as for M ….18
One finds for the differential cross section:
2222
2
2222
22
)()(cos
)(
)()(cos)(cos
2cos ZZZ
Z
ZZZ
ZZ
MMs
sF
MMs
MssFF
sd
d
/Z interference Z
)cos1()cos1()(cos 2222QQF e
cos4)cos1(2cossin4
)(cos 2
22 A
e
AV
e
V
WW
e
Z ggggQQ
F
cos8)cos1)()((cossin16
1)(cos 22222
44 AV
e
A
e
VAV
e
A
e
V
WW
Z ggggggggF
Vanishes at s MZ
known
e e
19
At the Z-pole s MZ Z contribution is dominant
interference vanishes
222
22222
44
2
)()()()()()(
cossin163
4
ZZZ
AVeA
eV
ww
ZtotMMs
sgggg
s
2222 )()()()(3
AV
AVeA
eV
eA
eV
FBgg
gg
gg
ggA
cos3
8)cos1(~
cos
2
FBAd
d BF
BFFBA
Forward-backward asymmetry
with
coscos
)0(1
)1(0
)( dd
dBF
20
22
12
Z
e
Z
ZZM
Ms
22
22)()(
cossin12
fA
fV
ww
Zf gg
M
i
iZ
With partial and total widths:Cross sections and widths
can be calculated within the
Standard Model if all
parameters are known
222
22222
44
2
163
4
)()()()()()(
cossin ZZZ
AV
e
A
e
V
ww
ZMMs
sgggg
s
22222 )(12)(
ZZZZ
e
MMs
s
Ms
Breit-Wigner Resonance:
BW description is very general
Z
iiiZBR )(
21
Z Resonance curve:
220
12
Z
e
ZM
Initial state Bremsstrahlung corrections
22222 )(12)(
ZZZZ
e
MMs
s
Ms
s
EzdzzszG
sm
ffff
f
21)()(
1
/4
0
)(2
Peak:
2.2 Measurement of the Z lineshape
• Resonance position MZ
• Height e
• Width Z
E
Leads to a deformation of the resonance: large (30%) effect ! 22
Resonance shape is the same, independent of final state: Propagator the same!
hadronsee ee
23
e e
e e
k k
p p
e
e e
e
k
p p
k
channel schannel t
eeee t channel contribution forward peak
Effect of t
channel
s-channel contribution ~ ( e)2
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MZ = 91.1876 0.0021 GeV
Z = 2.4952 0.0023 GeV
had = 1.7458 0.0027 GeV
e = 0.08392 0.00012 GeV
= 0.08399 0.00018 GeV
= 0.08408 0.00022 GeV
Z = 2.4952 0.0023 GeV
had = 1.7444 0.0022 GeV
e = 0.083985 0.000086 GeV
Z line shape parameters (LEP average)
Assuming lepton
universality: e = =
3 leptons are treated
independently
23 ppm (*)
0.09 %
*) error of the LEP energy determination: 1.7 MeV (19 ppm)
http://lepewwg.web.cern.ch/ (Summer 2005)
test of lepton
universality
(predicted by SM: gA and gV
are the same)
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LEP energy calibration: Hunting for ppm effects
Changes of the circumference of the LEP
ring changes the energy of the electrons
and thus the CM energy (shifts MZ) :
• tide effects
• water level in lake Geneva
1992 1993
Changes of LEP circumference
C=1…2 mm/27km (4…8x10-8)
ppm100
Effect of moon Effect of lake
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Effect of the French “Train a Grande Vitesse” (TGV)
In conclusion: Measurements at the ppm level are difficult to
perform. Many effects must be considered!
Vagabonding currents from trains
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