Lesson #1 Measurement of the Z e W bosons properties

XXVIII Ph.D in Physics Ezio TorassaPadova, April 22th 2013

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

GeVGF510)00001.016637.1( GeVM 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


Produzione dei bosoni W+W- e misura di Mw a LEP II

MZ e sin2W misurati a LEPI MW permette la definizione di vincoli piu’ stringenti.W+

W -

e+

e-

W+

W -

+Z*

W+

W -

+ + rad.corr.

I vertici ZWW previsti come conseguenza della strutta non abeliana della teoria di gauge SU(2)L×U(1)Y esistono

Per ricavare WW occorre distinguere il segnale WW dal fondo: ff() ff(gg)

-

Le cancellazioni previste dalla teoria di gauge sono state verificate al livello dell’ 1 %.

-


Decadimenti adronici

La caratteristica è la ricostruzione di 4 jets. Talvolta anche gli eventi ff possono fornire 4 jets. I jets dovuti a radiazione di gluoni sono caratterizzati da un piccolo angolo e da una bassa energia. La variabile D è in grado di discriminare permettendo la riduzione del fondo:

-

Decadimenti semileptonici

La caratteristica è la ricostruzione di 2 jets ed un leptone energetico ed isolato.

Decadimenti totalmente leptonici

La caratteristicha è la ricostruzione di 2 leptoni energetici isolati di carica opposta. L’esempio in figura riporta solo 2 tracce cariche ma il leptone puo’ anche essere un Una variabile discriminante è la direzione del momento mancante che per il fondo ff ha piccoli angoli

)( minmax

min

max

min

EEE

ED


MW a LEP II

MW si può considerare una grandezza derivata da GF , il cui valore è conosciuto con precisione. La relazione è semplice a livello (r=0) mentre con le correzioni di

polarizzazione del vuoto risulta dipendente da mt ed MH.

Una precisa misura della massa del W permette una ulteriore verifica del modello

ed allo stesso tempo fornisce dei limiti per le masse del top e dell’Higgs.

All’inizio di LEP II le misure dirette di mt al Tevatron (18012 GeV) avevano ancora

errori piuttosto grandi.

La massa del W può essere ottenuta:

• dall’andamento WW(MW) che in prossimità della soglia s ~160 GeV varia rapidamente

• mediante la ricostruzione della massa invariante.

)),(1(

1

)/1(2 222HtZWW

F MmrMMMG


Determinazione della massa da WW

W+

W -

e+

e-

W+

W -

Z*W+

W -

Diagrammi CC03

Lo stato finale in 4 fermioni, oltre ai contributi dei diagrammi CC03, può ricevere contributi da altri diagrammi elettrodeboli. Tali contributi sono stati considerati con dei termini di correzione della sezione d’urto (v. Tabella). La sezione d’urto così corretta è stata confrontata con l’andamento previsto in funzione della massa MW

Dati 1996 a 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

Contributi, interferenza inclusa, di altri diagrammi che generano 4 fermioni mediante il coinvolgimento di 0,1 o 2 bosoni vettori massivi

Vengono selezionati 29 eventi (15 + 12 + 2) da cu si ricava:


Ricostruzione diretta della massa

Per s > 2 MW è possibile ricostruire direttamente la massa dai decadimenti.

La ricostruzione ottenuta solo con le tracce osservate non ha una sufficiente risoluzione. Applicando dei vincoli quali la conservazione dell’energia e dell’impulso del centro di massa la risoluzione migliora significativamente. La ricostruzione si effettua solo per i decadimenti adronici e semileptonici, per quelli totalmente leptonici non si dispone di sufficienti vincoli (rispetto ai semileptonici manca l’asse del jet che determina la direzione del W opposto).

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

I due W decadono a distanze di frazioni di fm

nel caso adronico contribuiscono le interazioni dei partoni nello stato finale

FSI


L’FSI riduce il peso del canale adronico rispetto al canale semileptonico

Risultato combinato LEP II

2/042.0412.80 cGeVMW

Contributi agli errori statistici e sistematici


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 LHC

LEP 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


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/2013/

Lesson #1 Measurement of the Z e W bosons properties

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