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XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
Lesson #2
Asymmetry measurements and global fit
Standard Model
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
Forward-backward asymmetries
ForwardBackward
e+e-
f
f_
fB
fF
fB
fFf
FBA
cos)()cos1)((
4 22
1
22
sFsFs
NQ
d
dCF
EW
ff
Asymmetric term
1
0
cos2 dd
dfF
0
1
cos2 dd
dfB
2,0
2,
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
s)e+
e-
Z(s)e+
e-
cos2)(41sin)(4)cos1)((41
4 32
22
1
22
sGsGsGs
NQ
d
dfff
CFff
cos2)()cos1)((
4 32
1
22
sGsGs
NQ
d
dCFff
)/( 2 sm ff sf
22222221 |)(|))(())((Re2)( savavsvvQQQQsG offeeofefefe
23 |)(|4))((Re2)( savavsaaQQsG offeeofefe
ZZZ iMMs
ss
20 )(
0)(Re 20 ZM
Dominant term
s
2
220 |)(|
Z
ZZ
MM
WW
Vff
gv
cossin2
WW
Aff
ga
cossin2
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
BF G1(s)
G3(s)
1
1
2
3
8cos)cos1( d
BF 0cos)cos1(cos)cos1(
0
1
21
0
2
dd
1
1
0coscos2 d
22
1
2
12coscoscoscos2
1
0
0
1
dd
G1(s)
G3(s)
)(
)(4
3)(38
)(2
1
3
1
3
sG
sG
sG
sGA f
FB
For s ~ MZ2 I can consider only
the dominant terms feff
ff
ee
eef AAva
va
va
vaA
FB 4322
43
2222
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
cos2)()cos1)((
4 32
1
22
sGsGs
NQ
d
dCFff
cos2)(
)()cos1(
1
32
sG
sG
d
dff
222221 |)(|))(()( savavsG offee
23 |)(|4)( savavsG offee
cos2)cos1( 2
feff AA
d
d
Considering only the dominant terms the asymmetric contribution to the cross section is the product Ae Af
The cross section can be expressed as a function of the forward-backward asymmetry
cos3
8)cos1( 2
FBff A
d
d
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
cos3
8)cos1( 2
FBff A
d
d
The forward-backward asymmetry can be measured with the counting method:
or using the “maximum likelihood fit” method:
BF
BFFB NN
NNA
iiFBi AL cos
3
8)cos1( 2
With the counting method we do not assume the theoretical distributionWith the likelihood method the statistical error is lower
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
223
23
233
2222 )sin2()(
)sin2(222
Wfff
Wfff
VfAf
VfAf
ff
fff QII
QII
gg
gg
va
vaA
sin2W
0.95
0.70
0.15
0.23 0.24 0.25
Ad
Au
Ae
At the tree level the forward-backward asymmetry it’s simply related to the sin2W valueand to the fermion final state.
AFB measurement for different f comparison between different sin2W estimation
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
For leptons decays the angle is provided by the track direction.For quark decays the quark direction can be estimated with the jet axis
ForwardBackward
e+e-
Jet
Jet
The charge asymmetry is one alterative method where the final state selection is not required
forward
hemisphere
e+e-
Jet
Jet
fFB
ffB AqQ
backward
hemisphere
fFB
ffFB AqQ 2
had
ffFB
f
fFB AqQ
25
1
bFBA
cFBA
fFB
ffF AqQ
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
The relation between the asymmetry measurments and the Weinberg angle it depends to the scheme of the radiative corretions:
bFBAc
FBAlFBA FBQ
W2sin eff2sin
MS2sin
EffectiveMinimal
subtraction
00029.0sinsin 22 MSeff
Eur Phys J C 33, s01, s641 –s643 (2004)
On shell
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
sin2effW and radiative corrections
2
22 1sin
Z
WW M
M 2
22
2cossin
ZF
WWMG
We considered the following 3 parameters for the QEWD :
sinW GF
A better choice are the physical quantities we can measure with high precision:
measured with anomalous magnetic dipole moment of the electron GF measured with the lifetime of the muon MZ measured with the line shape of the Z sinW e MW becomes derived quantities related to mt e mH.
The Weinberg angle can be defined with different relations. They are equivalent at the tree level but different different when the radiative corrections are considered:
(1) (2)
(On shell) (NOV)
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
effWffeffVf
feffAf
QIg
Ig
2
3
3
sin2
Starting with the on-shell definition, including the radiative corerctions, we have:
WW
eff sW
2
22 sin)
tan1()(sin
=
...log4 2
2
2
2
Z
HZ
Z
tZ
m
mM
m
mM
22223
VfAf
VfAf
VeAe
VeAef
gg
gg
gg
ggA
FB
We can avoid to apply corrections related to mt mH in the final result simply defining the Weinberg angle in the “effective scheme”
HEW vertex
EW loops
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
Final Weinberg angle measurement:
sin2eff=0.23150±0.00016 P(2)=7% (10.5/5)
0.23113 ±0.00020 leptons0.23213 ±0.00029 hadrons
Larger discrepancy:
Al(SLD) –Afbb 2.9
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
ZZZ iMMs
ss
20 )(20 ))(Re(ZMs
ss
22222221 |)(|))(())((Re2)( savavsvvQQQQsG offeeofefefe
23 |)(|)4))((Re2)( savavsaaQQsG offeeofefe
AFB function of s
Outside the Z0 peak the terms with the function |0(s)|2 are not anymore dominant,they became negligible. The function Re(0(s)) can be simplified
222
1
32
43
)(
)(4
3Zfe
fefefFB Ms
s
aaQQ
sG
sGA
s00
Dominant term
s
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
With different AFB measurements for different √s we can fit the AFB(s) function.
We must choose the free parameters:
2222
0 3VfAf
VfAf
VeAe
VeAef
gg
gg
gg
ggA
FBZM Z
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
Fit with Line shape and AFB
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
We can decide the parameters to be included in the fit:
MZ , Z , 0h , Rl , AFB
0,lept5 parameters fit
assuming lepton universality
MZ , Z , 0h , Re , R , R ,
AFB0,e , AFB
0, , AFB0,
9 parameters fit leptons have been considered separately
(Rl=had/l)
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
The coupling constants between Z and fermions are identical in the SM. We can check this property with the real data.
Error contributions due to:- MH , Mtop
- theoretical incertanty on QED(MZ2)
Lepton universality
gV and gA for different fermions are compatible within errors
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
104/108/
007.0022.0
005.0014.0
009.0025.0
18.068.20
14.054.20
18.074.20
20.023.41
122483
991187
2
0
NDF
A
A
A
R
R
R
nb
MeV
MeVM
FB
FB
eFB
e
h
Z
Z
DELPHI 1990 (~ 100.000 Z0 hadronic) 1991 (~ 250.000 Z0 hadronic) 1992 (~ 750.000 Z0 hadronic)
LEP 1990-1995 ~ 5M Z0 / experiment
LEP accelerator !
MZ/MZ 2.3 10-5
GF/GF 0.9 10-5 (MZ) / 20 10-5
9 parameters fit
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
polarization measurement from Z
background
Z bosons produced with unpolarized beams are polarized due to parity violationfrom Z decay are polarized, we can measure P from the decays.
rest frame -
-
In the case of a decaying to a pion and a neutrino, the neutrino is preferably emitted opposite the spin orientation of the to conserve angular momentum, this is due to the left-handed nature of the neutrino. Hence, the pion will preferably be emitted in the direction of the spin orientation of the .* is defined to be the angle in the rest frame of the lepton between the direction of the and the direction of the pion. The distribution of is related to P:
spin
)cos1(2
1
cos
1 **
Pd
dN
N
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
- left-handled
- right-handled
dati
background
The 1/N dN/cos distribution can not be directly measured because it is not possible to determine the τ helicity on an event-by-event basis.We can anyway measure the polarization using the spectrum of the decay products:
rest frame -
-
direction in the laboratory
The pion tends to be produced- in the backward region for left-handled – - in the forward region for right handled – (forward/backward w.r.t. direction in the lab.)
backward
In the laboratory frame the p/ pbeam distribution is different for L and R
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
The polarization can be measured observing the final state particle distributions for different decays :
3 e
3232 8914953
11xxPxx
dx
dN
N beamppx /
In case of a leptonic decay the presence of two neutrinos in the final state makes this channel less sensitive to the tau helicity:
The p/ pbeam distribution is related to the polarization:
- left-handled - right-handled
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
cos2cos1
cos2cos1)(cos
2
2
AA
AAP
e
e
22AfVf
AfVff gg
ggA
Fit:eA A
Compared with AFB = ¾ Ae A
P (cos provides one independent measurement of Ae e A
The polarization is measured in several bin of the polar angle cos between the pion and the beam direction (within 3° is a good approximation of the angle between and beam direction)
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
• Compton Polarimeter
<Pe-> = 75 %
σ<Pe> = 0.5 %
• Quartz Fiber Polarimeter and Polarized Gamma Counter – run on single e- beam + crosschecks
• <Pe+> = -0.02 ± 0.07 %
Utilizza lo scattering Compton della luce polarizzata.L’angolo di scattering dipendente dallo spin dell’elettrone.
Luce polarizzata Circolarmente (YAG Laser, 532 nm)
elettroni diffusi
Misura della polarizzazione
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
With polarized beam we can measure the Left-Right asymmetry:
Cross section with ‘left-handed’ polarized beam:
eL-e+ ff
Cross section with‘right-handed’ polarized beam:
eR-e+ ff
Left-Right asymmetry at SLD
fR
fL
fR
fLf
LRA
fL
fR
To estimate the cross section difference betwnn e-L e+ and e-
R e+ we need a very precise luminosity control. The e- beam polarization was inverted at SLC at the crossing frequncy (120 Hz) to have the same luminosity for eL and eR
with Pe < 1 we measure only : AmLR = (NL-NR) / (NL+NR)
the left-right asymmetry is given by: ALR = AmLR / Pe
precise measurement Pe is needed
( Pe = 1 )
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
cos
73.0Pe
73.0Pe
0Pe
new
cos2)cos1(
cos2
feff AA
d
d
cos2)()cos1)(1(
cos2
feeeeff APAAP
d
d
Cross section for unpolarized beam
Cross section for partial polarization
Having the same luminosity and the same but opposite polarizations, the mean of P+ with P-
gives the same AFB like at LEP:AAA feff
fff
4
3
BF
BFFB
APA eemLRePP
RL
RL
APA femePP
ffff
fff
L
ff
4
3
)()(
)()(
BRFRBLFL
BRFRBFL
LRFB
new
Separating the two polarizations we can obtain new measurements:
AA eLR
AA ff
4
3LRFB
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
• Af with ALRFB
• Combined with Ae from ALR
0060.01544.0e A015.0142.0μ A015.0136.0τ A
00026.023098.0sin00207.015130.0
2
0
eff
LRA
Asymmetry results at SLD
SLD
LEPleptons 0005.02310.0sin2 eff
With only 1/10 of statistics, thanks to the beampolarization, SLD was competitive with LEPfor the Weinberg angle measurement:
0003.02310.0sin2 eff
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
From the experimental observables:
line shape (s) FB asymmetries AFB(s) polarization P(cos)
pseudo-osservables can be extrapolated:
MZ Z h AlFB etc..
Using a fit program (ZFITTER) with 2 loop QEWD and 3 loop QED the best fit can be obtained for the parameters of the model and for the masses having some uncertainty (mt, ,mH ). The current version of ZFITTER (in C++) is Gfitter.
Global fits are performed in two versions: the standard fit uses all the available informations except results from direct Higgs searches, the complete fit includes everything
Global Electroweak Fit
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
20 pseudo-osservables
5 fitted parameters
With the fitted parameters we can obtain
also the fitted pseudo-osservables
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
usage of latest experimental input:
Z-pole observables: LEP/SLD results [ADLO+SLD, Phys. Rept. 427, 257 (2006)]
MW and W: latest LEP+Tevatron averages (03/2010)[arXiv:0908.1374][arXiv:1003.2826]
mtop: latest Tevatron average (07/2010) [arXiv:1007.3178]
mc and mb: world averages [PDG, J. Phys. G33,1 (2006)]
had(5)(MZ
2): latest value (10/2010) [Davier et al., arXiv:1010.4180]
direct Higgs searches at LEP and Tevatron (07/2010)[ADLO: Phys. Lett. B565, 61 (2003)], [CDF+D0: arXiv:1007.4587]
Updated Status of the Global Electroweak Fit and Constraints on New Physics July 2011 arXiv:1107.0975v1
2min /DOF = 16.6 / 14
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
mH=81+52-33 GeV (2002)
mHiggs< 193 GeV 95% C.L.
mH=91+58-37 GeV (2003)
mHiggs< 211 GeV 95% C.L.
mH=96+60-38 GeV (2004)
mHiggs< 219 GeV 95% C.L.
MW
Ab FB
, Ac FB
, Rb , R
c
mH=96+31-24 GeV (2011)
mHiggs< 171 GeV 95% C.L.
GeV 96 3124HM
XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013
Z Physics at LEP I CERN 89-08 Vol 1 – Forward-backward asymmetries (pag. 203)
Measurement of the lineshape of the Z and determination of electroweak parameters from its hadronic decays - Nuclear Physics B 417 (1994) 3-57
Improved measurement of cross sections and asymmetries at the Z resonance - Nuclear Physics B 418 (1994) 403-427
Global fit to electroweak precision data Eur. Phys J C 33, s01, s641 –s643 (2004)
Measurement of the polarization in Z decays – Z. Phys. C 67 183-201 (1995)