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

Lesson #1

Measurement of the Z e W bosons properties

Standard Model


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


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”


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 ]


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)


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)


• 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


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


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


=(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


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


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:


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)


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


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)


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


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_ _


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


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


(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


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 %


(4) Propagator correction (vacuum polarization)

f+ n loop

2

22

22

log3

)(1

)()(

Q

Q 22fmQ

)(1)(

202

QQ

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


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


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 %


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


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


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 ?


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.


• 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


LEP luminosities LEP2

From 1990 to 1994 about 170 pb-1


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


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


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).


2/NDoF =160/180 for the mediated ff data at LEPII


ZZ production at LEP2

ZZ(s)

Test at 5% precision


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


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


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


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:


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


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


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


MZ/MZ 2.3 10-5MW/MW 5.2 10-4

Measurements since 1989


Discrepancy observed in 1995 not confirmed after more precise Rb measurements

hadb /


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


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/

Documents

XXIX Ph.D in Physics Ezio TorassaPadova, April 28th 2014 Lesson #1 Measurement of the Z e W bosons properties Standard Model