lesson #2 asymmetry measurements and global fit

XXVIII Ph.D in Physics Ezio TorassaPadova, April 29th 2013

Lesson #2

Asymmetry measurements and global fit

Standard Model


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,


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


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


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


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


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


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


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


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)


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


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


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

QQ

aaQQ

sG

sGA

s00

Dominant term

s


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


Fit with Line shape and AFB


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)


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


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


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


- 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


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


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)


• 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


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 )


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


• 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


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


20 pseudo-osservables

5 fitted parameters

With the fitted parameters we can obtain

also the fitted pseudo-osservables


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


mH=81+52-33 GeV (2002)

mHiggs< 193 GeV 95% C.L.

mH=91+58-37 GeV (2003)


mH=96+60-38 GeV (2004)


MW

Ab FB

, Ac FB

, Rb , R

c

mH=96+31-24 GeV (2011)


GeV 96 3124HM


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)

lesson #2 asymmetry measurements and global fit

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