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XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Lesson #1
Measurement of the Z e W bosons properties
Standard Model
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
in approssimazione di massa nulla per tutte le particelle di stato iniziale e finale (m 0, E |p| )
p1 = [E, p, 0, 0]; p2 = [E, -p, 0, 0]; p3 = [E, p cos, p sin, 0]; p4 = [E, -p cos, -p sin, 0];
s = ( p1 + p2 )2 = ( p3 + p4 )2 = 4E2; t = ( p1 - p3 )2 = ( p4 - p2 )2 = - ½ s (1 - cos); u = ( p1 - p4 )2 = ( p2 - p3 )2 = - ½ s (1 + cos);
s + t + u = m12 + m2
2 + m32 + m4
2 0 (2 variabili indipendenti).
s,t,u – le variabili invarianti di Mandelstam
e-
b
a
e+
e-
b
ae+
1
2
3
4
Introduzione
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
e++
e-
-canale “s”
e+
e+
e+
e+
canale “t”
• si chiamano processi di “canale s” quelli, come e+e- +-, in cui la particella emessa e riassorbita ( in questo caso) ha come quadrato del quadri-momento il valore s, la variabile di Mandelstam che caratterizza il processo;
• viceversa, si chiamano processi di “canale t” quelli, come e+e+ e+e+, in cui la particella scambiata ( anche in questo caso) ha come quadrato del quadri-momento il valore t;
• talvolta, il processo (ex. e+e- e+e-) è descritto da più diagrammi di Feynman, di tipo s e t; in tal caso si parla di somma di “diagrammi di tipo s” o di “tipo t”
(+ interferenza).
Canale “s” e canale “t”
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Luminosity definition and measurement
dt
dNtL eventsproduced _)(
dttLN eventsobserved )(_
Integrated luminosity
dt
dNtL eventsobserved _)(
Efficiency (trigger + reconstruction +selection)
collisionxy
ee
fArea
NNL
[cm -2 sec -1 ]
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Based on low angle Bhabha scattering event counting
e- e+
e+
e-
e+e- e+e-
Dominated by the photon exchange “t cannel”:
(deg)
d
d
45. 90.Region used by the luminometer: 1-10 deg
e+
e-
“s channel”
e+
e-
Luminosity measurement LEP
Bhabha Homi Jehangir, indian theoretica physicist (Bombay 1909 – monte Bianco 1966)
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
cos1
)cos1(2
)cos1(
4)cos1(2)cos1(
4
2
2
22
2
sd
d QED
e+
e-
t) s)
e+
e-
(s)-(t)
21cos 4
2 14
sd
d QED
(t)-(t)(s)-(s)
Z(s)-(s) Z(s)-(t) Z(t)-(s) Z(t)-(t) Z(s)-Z(s) Z(s)-Z(t) Z(t)-Z(t)
Z(s)e+
e-
e+
e-
Zt)
(non polarized emectrons)
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
• Coasting beams with crossing angle and beam currents
x
y
x
z
yo
Luminosity (rate) insensitive to offsets in x and z, but sensitive to offsets in y:
See S. Van der Meer, ISR-PO/68-31, June 18th, 1968
Now the trick: scan the offset while measuring the rate, over the whole non-zero range, then integrate the result:
Rate vs offset, taken from Potter in Yellow report CERN 94-01 v1
Van der Meer scan
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
The standard Model is our particle interaction theory
It’s based on the two non –abelian gauge groups:
QCD (Quantum CromoDynamics) : color symmetry group SU(3)
QEWD (Quantum ElectroweakDynamics) : symmetry group SU(2)xU(1)
We have one theory but many Monte Carlo programs because the cross section for every possible process is not a trivial calculation also starting from the “right” Lagrangian.
Standard ModelStandard Model
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Standard Model
The QEWD Lagrangian (cfr. Halzen, Martin, “Quarks & leptons”, cap.13 - 15):
LQEWD = Lgauge + Lfermioni + LHiggs + LYukawa
=> Fermions – Vector bosons interaction term
)()(2
1 2 VDLHiggs
BBWWLgauge 4
1
4
1
2
1
LRRLGL TiYukawa
*
Lfermioni = Llept+ Lquark
=> Fermions – Scalar boson interaction term
BY
igWg
iD2
'2
42 baV
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
=(1,2,3) : Pauli matrixes
g g’ a b
v = |
Gi
2
vGm e
e
,,
___
2'
2'
2),(
elRR
L
Llept BY
igBY
igWg
iL
bsddtcuu
RR
L
Lquark uBY
igud
uB
YigW
giduL
,,,,
___
2'
2'
2),(
amH 2
b
a
2
Parameters of the model
Removing the mass of the fermions and the Higgs mass
we have only 3 residual free parameters: g g’ v
RR dB
Yigd
2'
_
is the minimum of the Higgs potential
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
2
21
WWW
2
21
WWW
22
3
'
'
gg
gBWgA
22
3
'
'
gg
BggWZ
vgMW 2
10AM
22 '2
1ggvM Z
,, 21 Small oscillation around the vacuum.
For
we neglect terms at order > 2nd
42 baV 22221
2
1
After the symmetry breaking :
2 complex Higgs fields 1 real Higgs field - 3 DOF
4 massless vector bosons 1 massless + 3 massive vector bosons + 3 DOF
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
W Weinberg angle
g g’ v 22 '
'
gg
gge
22 '
'sin
gg
gW
2
12v
GF
e Millikan experiment (ionized oil drops)
GF lifetime W Gargamelle (1973) asymmetry from scatteringp p
WF
WG
eM
2
22
sin24
W
WZ
MM
cos
electron charge Fermi constant
sin2W 0.23 ( error 10 % )
MW 80 GeV MZ 92 GeV
UA1 pp √s = 540GeV (1993) MW = 82.4±1.1 GeV MZ = 93.1±1.8 GeV
Before the W and Z discovery we had strong mass constraints:
Historical measurements:
The mass of the vector bosons are related to the parameters:
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
The Z° boson can decay in the following 5 channels with different probabilities:
p=0,20 (invisible)e- e+ p=0,0337 pv= 0,0421
Z° - + p=0,0337 pv= 0,0421- + p=0,0337 pv= 0,0421qq p=0,699 pv= 0,8738
The differences can be partially explained with the different number of quantum states:
includes the 3 different flavors: e , , qq includes the 5 different flavors: uu , dd , ss , cc , bb
for every flavor there’re 3 color states ( tt is excluded because mt >MZ)
“partially explained” : 0,20 > 3 × 0,0337 and 0,699 > 15 × 0,0337
we will see later they are depending also to the charge and the isotopic spin
Z0 boson decay (channels and branching ratios)
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Z0 boson decay (selection criteria)
e+e- Z0 e+e-
Efficiency 96 %
Contamination 0.3 % ( + - events)
e+e- Z0 hadrons
• Charged track multiplicity 3
• E1ECAL > 30 GeV E2
ECAL > 25 GeV
• < 10 o
Efficiency 98 %
Contamination 1.0 % (+ - events)
Nucl. Physics B 367 (1991) 511-574
150.000 events(hadronic and leptonic)
collected betweenAugust 1989 - August 1990
NchFraction of √s
a) Charged track multiplicity 5
b) Energy of the event > 12 % s
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
e+e- Z0 +-
e+e- Z0 +-
• Charged track multiplicity 6
• Etot > 8 GeV , pTmissing > 0.4 GeV
• > 0.5 o
• etc.
• Charged track multiplicity = 2
• p1 e p2 > 15 GeV
• IPZ < 4.5 cm , IPR < 1.5 cm
• < 10 o
• Association tracker- muon detector
• EHCAL < 10 GeV (consistent with MIP)
• EECAL < 1 GeV (consistent with MIP)
Efficiency 99 %
Contamination: ~1.9 % (+ - events)
~1.5 % (cosmic rays)
Efficiency 70 %
Contamination: ~0.5 % (+ - events)
~0.8 % (e+e- events)
~0.5 % (qq events)
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
19 input variables:
• P and Pt of the most energetic muon
• Sum of the impact parameters
• Sphericity , Invariant mass for different jets
3 output variables:
• Probability for uds quarks
• Probability for c quarks
• Probability for b quarks
Quark flavor separation
Classification using neural network
MC uds MC c
MC b Real data
h
bbR
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
s)e+
e-
(s)-(s)
Z(s)e+
e-
Z(s)-Z(s)weak
ffff
em
ff
EW
ff
d
d
d
d
d
d
d
d
int
Z0 line shape
The line shape is the cross section (s) e+e- ff with √s values arround MZ
Can be observed for one fermion or several together (i.e. all the quarks)
_
f
ffTOT
)cos1(4
222
s
NQ
d
dCf
em
ff
f
f
f
f_ _
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
gVf = I3f - 2 Qf sin2W gAf = I3f
s
NQ
s
MsI
MMs
ss CfZ
ZZZ
ZEW
3
4
)()(
222
02222
2
Resonance term (Breit – Wigner) ( I QeQf )
)(26
223
AfVfZF
Cf ggMG
N 220
12
ZZ
fe
M
f
fZ
( terms proportional to ( mf / Mz )2 have been neglected )
The expected line shape from the theory is a Breit-Wigner function characterized by 3 parameters:
Mass (MZ) – Width (Z) – Peak cross section (0)
With unpolarized beams we must consider the mean value of the 4 different helicity
Branching ratios f / Z are related to Qf and I3f
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
We can take the values of the parameters reported in the PDG
and calculate the expected value of the partial widths f
MeVMG ZF 01.088.165)4/14/1(
26
3
3 families
MeVMG ZF
l 005.0419.83)4/10014.0(26
3
2510)00001.016637.1( GeVGFGeVM Z 0021.01876.91
3 families
MeVMG ZF
cu 015.0446.285)4/10368.0(26
33
.
)(26
223
AfVfZF
Cf ggMG
N
2 families
gVf = I3f - 2 Qf sin2W gAf = I3f
MeVMG ZF
bsd 02.095.367)4/11197.0(26
33
,.
3 families
MeVZ 07.064.2422 MeVsperZ 3.22.2495
00013.023116.0sin2 W
%3
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
(s) e+e- hadrons
Born(s)
(s) experimental cross section0
Branching ratios
e+ e-
Process ff / Z (%)
B.R. exp. (%)
Neutrinos 20.54 20.00±0.06
Leptons 10.33 10.10±0.02
Hadrons 69.13 69.91±0.06
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Radiative corrections
The radiative corrections modify the expected values at the tree level:
Z*,
Relevant impact: • decreases the peak cross section of ~30%• shift √s of the peak of ~100 MeV
QED corrections
s
Born dsssGszss0
'),'()'()(
1-z = k2/s fraction of the photon’s momentum
(1) Initial state radiation (QED ISR)
(2) Final state radiation (QED FSR)
f
fQED
fh )1(0
Z*,
4
3 2ff
QED
Q
G(s’,s) = function of the initial state radiation
Initial state radiation correction:
~ 0.17 %
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
(4) Propagator correction (vacuum polarization)
f+ n loop
2
22
22
log3
)(1
)()(
Q
Q 22fmQ
)(1)(
202
137
10
128
1)( ZM
610)88()95( GeVGeV
064.0)( ZM
s
Born dsssssHszss0
')',()',()'()(
(3) Interference between initial state radiation and final state radiation
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
EW corrections
Z/f+ n loop
)(1)(
ss
)(1
)(sincossin)(sinsin 222
s
ss Z
WWWWW
2
)(ZM
ss
)(1)(
s
GsGG
Z
FFF
(1) Propagator corrections
Photon exchange
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
QCD corrections
f
QCDf
QEDf
h )1)(1(0
%17.04
3 2
ff
QED
Q%8.3
)( 2
ZsfQCD
M
(1) Final state radiations (QCD FSR)
(2) Vertex corrections
W/fZ*, WffftVfVf QImsgg 2
3 sin2),(
fftAfAf Imsgg 3),(
Contributions from virtual top terms
Z*, g
2
2
1Z
tZf m
mM
Z*, W/f
~ 1 + 0.9 %
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Z
ZZZ
Z
MsMs
ss
22222
2
0 )/'()'(
')'('
s
dsssssHszss0
')',()',()'(')(
Line shape
220
12
ZZ
fe
f M
)1)(1)((26
223
QCDf
QEDfAeVe
ZFCf gg
MGN
Interference EW- QED
WfffVf
ffAf
QIg
Ig
2
3
3
sin2
MZ Z 0
QED ISR QED Interference IS-IF
Photon exchange
QED FSR QCD FSR
EW vertex
Breit-Wigner modified by EW loops
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Padova 4 Aprile 2011
Ezio Torassa
MZ
Z
0h , 0
e , 0 , 0
MZ
Z
eh , ee , e , e
%06.000.20/
%06.091.69/
%008.0367.3/
%007.0366.3/
%004.0363.3/
0023.04952.2
0021.01876.91
Z
Zh
Z
Z
Ze
Z
Z
GeV
GeVM
PDG
2010
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Padova 4 Aprile 2011
Ezio Torassa
inv = Z – had - 3lept - 3
The number of the neutrino familiescan be added in the fit. The result is compatible only with N=3
We can also extract the width for new physics (emerging from Z decay):Z , had , lept can be measured can be estimated from the SMThe result is compatible with zero orvery small widths.
Number of neutrino families
We can suppose to have a 4th generation family with all the new fermions heavier than the Z mass (except the new neutrino) . How to check this hypothesis ?
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Gamma-gamma interactions
The gamma-gamma interactions produce two leptons with small energy (W << Ebeam) and small angles, most of them are not detected.
At the Z0 peak the gamma-gamma cross section is about 150 nb. After the selection (pT , cuts)is reduced to a non resonant 6 nb background.
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
• QED was assumed for the ISR function H(s,s’) and the interference IF-FS function (s,s’)• QEWD was assumed for the interference QED-EW function Z(s)• QCD was assumed for the QCD FSR correction
With the cross section measurements at higher energies (s= 130-200 GeV), the interference term can estimate from the data.
Residual dependence from the model
s
MsI
MsMs
s Z
ZZZ
Z2
022222
2
)/()(
s
NQ Cf
3
4 22
)(sEW
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
LEP luminosities LEP2
From 1990 to 1994 about 170 pb-1
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
qq()
WW
ZZ
s
Center of mass energy after the initial state radiation
Relevant ISR contributions (radiative return to the Z0 peak)
Searches beyond the Standard Model have more sensitivity to the non radiative events: s /s > 0.85
ff() production at LEP2
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Jet
Jet
|| 1p || 2p
|| p
Identification of ISR photon and s´ estimation (SPRIME)
Search of ISR candidates:
Sarch of signal inside calorimeters, luminometer included, with E>10 GeV (not associated to charged tracks)
Jet 1 and Jet 2 reconstruction
Photon inside the beam pipe hypothesys
Energy and momentum conservation:
None ISR photon detected
1221
12
sinsinsin
sin
sinsinsin
sin
s
CBA
Asp
2222 )()(' EEspEss
ISR photons are emitted at low angle, they mainly induce polar angle unbalance (R unbalance is neglected)
R
z
A
Bpp
sin
sin|||| 1
A
Cpp
sin
sin|||| 2
|||||| 21 ppps
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
One ISR photon detected
If the photon is coplanar with the two jets ( > 345o ) his direction is used.
Considering the low resolution of the calorimeters the energy momentum balance is used to estimate the energy of the photon
otherwise a second undetected photon inside the
beam pipe is considered.
1212
12
sinsinsin
sin
sp
22 )()(' hh ppEEss
ISR photon spectrum s = 130 GeV
22)(' pEss
The photon emission at the energy of s – 91 GeV increases because the process is traced back to the Z0 (cross section peak).
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
2/NDoF =160/180 for the mediated ff data at LEPII
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
ZZ production at LEP2
ZZ(s)
Test at 5% precision
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Produdction of W+W- bosons and Mw a LEP II
MZ e sin2W measured at LEPI MW meas. useful for more stringent constraints .W+
W -
e+
e-
W+
W -
+Z*
W+
W -
+ + rad.corr.
ZWW vertices are expected as a consequence of the non abelian structure of the SU(2)L×U(1)Y gauge theory
For the WW measurement the main backgrounds are:
- interactions
- Z*, * decays
Cancellations expected from the gauge theory have been verified with 1 %. of precision
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Hadronic decays
The characterisctic is the reconstruction of 4 jets. Sometime also two fermions from a Z decays can produce 4 jets due to gluon emission but radiative jets have small angle and energy. Variable D can discriminate this background.
-
Semileptonic decays
The characteristic is the reconstruction of 2 jets and one energetic and isolated lepton.
Total leptonic decays
The characteristic is the reconstruction of 2 energetic and isolated leptons with opposite charge. The example in figure shows only two tracks but the lepton can also be the One discriminant variable is the direction of the missing momentum (ff background has small angles)
)( minmax
min
max
min
EEE
ED
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
MW a LEP II
MW can be considered a derived parameter from GF . The relation has two components: the tree level and the radiative corrections (r).
The radiative corrections are dependent from mt ed MH.
The precise measurement of the W mass is important to verify the SM theory and
to provide limits for the top and Higgs masses. At the beginning of LEP II direct
measurement of mt at Tevatron (18012 GeV) still had large errors.
The W mass can be obtained:
• from the WW(MW) trend having a rapid variation close to the threshold (s ~160 GeV)
• through the invariant mass reconstruction
)),(1(
1
)/1(2 222HtZWW
F MmrMMMG
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Determination of the mass from WW
W+
W -
e+
e-
W+
W -
Z*W+
W -
Diagrams CC03
The 4 decay modes in the table have been considered.
1996 data at 161 GeV L = 10 pb -1
WW decay mode Corr (CC03)
qqqq eqq ()qq
ll
0.996 1.087 1.006 1.045
pbtotWW 19.067.3 97.0
85.0
2/09.044.040.80 cGeVmW DELPHI
Corrections to the CC03 diagrams due to othe contributions
With only 29 selected events the obtained measurement is:
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Direct reconstruction of the W mass
Per s > 2 Mwi is possibile to reconstruct directly the invariant mass.
The reconstruction can be obtained in the hadronic decay and in semileptonic decay.
In the semileptonic decay the momentun and the center of mass energery constraints are used.
DELPHI Dati 1998 a 189 GeV L = 150 pb -1
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
2/)(035.0)(017.0)(034.0)(087.0387.80 cGeVFSILEPsysstatmW
FSI: Final State Interaction
The distance decay between the two W is fraction of fm
In the hadronic decay channel the interatcion between partons in the final state are relevant
FSI
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
The FSI reduces the hadronic channel weight with respect to the semileptonic channel
LEP II combined result
2/042.0412.80 cGeVMW
Contribution to the statistical and systematic errors
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
MZ/MZ 2.3 10-5MW/MW 5.2 10-4
Measurements since 1989
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Discrepancy observed in 1995 not confirmed after more precise Rb measurements
hadb /
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
EWK physics at LHCLEP 170 pb-1 at the Z0 peak e+e-~ 3 104 pb → 5 M Z0 / experiment
LHC 25 fb-1 pp~ 3 104 pb → 750 M Z0 / experiment
WZ
WWWZ
ZZ
XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014
Quarks & Leptons – Francis Halzen / Alan D. Martin – Wiley International Edition
The Experimental Foundation of Particle Physics – Robert N. Cahn / Gerson Goldhaber
Cambridge University Press
Determination of Z resonance parameters and coupling from its hadronic and leptonic decays - Nucl. Physics B 367 (1991) 511-574
Z Physics at LEP I CERN 89-08 Vol 1 – Radiative corrections (p. 7) Z Line Shape (p. 89)
Measurement of the lineshape of the Z and determination of electroweak parameters from its hadronic decays - Nuclear Physics B 417 (1994) 3-57
Measurement and interpretation of the W-pair cross-section in e+e- interaction at 161 GeV Phys. Lett. B 397 (1997) 158-170
Measurement of the mass and width of the W boson in e+e- collision at s =189 GeV Phys. Lett. B 511 (2001) 159-177
http://www.pd.infn.it/~torassa/dottorato/2014/