Particle physics: precision, precision and precision…

Mihail ChizhovSofia University, Bulgaria

…or three decades without unexpected discoveries

C L Y

3

SU(3) SU(2) U(1)

g g g2

S3

WW

2

g e e = g = g =

4 cos

e

sin

= 4

22 22 2sin2 sin cos2W Z

F

W W WM MG

; 22 2 F

W Z

F

M MG G

Spontaneous Symmetry Breaking

…contains ones more independent parameter: the Higgs mass HM

H. Fritzsch, Murrey Gell-Mann, H. Leutwyler,Advantages of the Color Octet Gluon Picture,Phys. Lett. B 47 (1973) 365-368

I.Khriplovich’68

37.3 GeV; 2 74.6 GeV2 2F

W Z

F

M MG G

T. Kinoshita & A. Sirlin, Phys. Rev. 113 (1959) 1652

T. van Ritbergen & R. G. Stuart, Phys. Rev. Lett. 82 (1999) 488

Theoretical uncertainty in the determination of GF is less than 0.3 ppm,the final goal of MuLan experiment is 0.5 ppm.

Choosing the third constant

2 2

2 2 2

PDG 1988:

92.4 1.8 GeV

Phy

/ 3.9%

sin

s. Lett. 204B

0.230 0.005 sin / sin 2

(1 8

.

8)

2

9

%

Z Z Z

W W W

M M M

2 2 2

PDG 1982:

sin 0.229 0.01

Phys. Lett. 111

0 sin

B (1982)

/ sin 4.4%W W W

2

91.1876 0.0021 GeV

Jo

urna

l of Phy

23 pp

sics G 33, 1 (20PDG 2006:

sin 0.23152 0.00014 605

06)

m

pp

mW

ZM

2

0.0007 ppm 5 ppm 46 ppmF ZG M

1( ) 128.91 0.02

155 ppm ZM

2

2W 2

4 sin 2 =

sin 0.21215 0.00001 80.939 0.0

cos2

02 GeV

W Z W

W W

F Z

M MG M

M

while direct W-boson mass measurements give 80.398 0.025 GeV

> 20WM

2 2W Wsin (PDG) si > 3 8n 1

Quantum corrections !!!

2 3s

1

in 0.231

08 0.00005

79.961 0.006 V 8 GeW

WM

Electroweak Quantum corrections (mt and MH)All coupling constants are functions of a scale (by the way, definition of the massis also scale dependent). Therefore, different definitions of the sin2 W, whichare equivalent in the Born (tree) approximation, depend on the renormalizationprescription. There are a number of popular schemes leading to values which differ

by small factors depending on mt and MH. 2 2

W 2

0 0

2

2 2 2

2

2

2

W W

sin : 2 (1 )

, where 1 / ( ) 0.06654(14)

3

On-shell sc

tan 8 2 tan

1heme W

F W

H Zt

tt

W

t

W Z

F

r

mr

MG s r

r r r r M

s M M

G

2

( )

172.7 GeV

0.03630 0.00014 0.0001

0.03256

1Z tm

t

M

m

r

2tm dependence?

What about Appelquist--Carazzone decoupling theorem?T. Appelquist & J. Carazzone, Phys. Rev. D 11 (1975) 2856

In QED and QCD the vacuum polarization contribution of a heavy fermion pair is suppressed by inverse powers of the fermion mass. At low energies, the information on the heavy fermions is then lost. This ‘decoupling’ of the heavy fields happens in theories with only vector couplings and an exact gauge symmetry, where the effects generated by the heavy particles can always be reabsorbed into a redefinition of the low-energy parameters.

The SM involves, however, a broken chiral gauge symmetry. Therefore,the electroweak quantum corrections offer the possibility to be sensitive to heavy particles, which cannot be kinematically accessed, through their virtual loop effect.The vacuum polarization contributions induced by a heavy top generate corrections to the W± and Z propagators, which increase quadratically with the top mass [M. Veltman, Nucl. Phys. B 123 (1977) 89]. Therefore, a heavy top does not decouple. For instance, with mt = 171 GeV, the leading quadratic correction to amounts to a sizeable 3% effect. The quadratic mass contribution originates in the strong breaking of weak isospin generated by the top and bottom quark masses, i.e., the effect is actually proportional to .

Owing to an accidental SO(3)C symmetry of the scalar sector (the so-called custodial symmetry), the virtual production of Higgs particles does not generate any quadratic dependence on the Higgs mass at one loop [again M. Veltman]. The dependence on MH is only logarithmic. The numerical size of the corresponding correction to varies from a 0.1% to a 1% effect for MH in the range from 100 to 1000 GeV.

2 2btm m

2WM

2WM

2 2

22

W 2 2

22

2 2

0

W

0

ˆˆ sin ( )

ˆ ( )ˆ sin ( )ˆ ˆ( ) ( )

1 : ˆ ˆ ˆ2 (1 )

ˆ 0.06969(4)(14) , where 1 /

Modified minimal substraction MS scheme

WW

ZZ Z

F Z W

W

s M

g

g g

MM

M G s r

r r r

( ) 0.06654(14)

ˆ 1.01043(34) 1 Z

t

M

2 ˆsin ( )W

[GeV]

ms

mc

mb

MW

Atomic parity violation (APV)5 5

1 2 (1)2

eh FNC q q

q

GC q q C q q

L

At tree level, For atomic parity violation and the SLAC polarized electron experiment,

51 1 2 2

ˆ ˆ 0.9876, 1.0006, 1.0026, 1.0299,

2 3.6 10 , 0.0121 and 0.0026.

eq eq eq eq

d u u d

For heavy atoms one determines the “weak charge”

21 12 2 2 1 4sinu d WW C Z N C Z NQ Z N

The parity-nonconserving measurements (PNC) are interpreted in terms of the weak nuclear charge QW, which quantifies the strength of the electroweak coupling between atomic electrons and quarks in the nucleus. The relation between QW and the PNC amplitude, EPNC, can be represented as

EPNC = k QW, where k is an atomic-structure factor. Apparently, the interpretation requires atomic-structure calculations of k with an accuracy that matches the experimental uncertainty in EPNC. So far the most accurate measurement has been carried out in 133Cs. 133

exp agrees with the SM valuCs 72.65(28) (36) 73.19(13)e

within 1 level

W thQ

The theoretical uncertainties for the other atoms, thallium, lead and bismuth are largerthan 3%.

From arXiv:0704.2618 [hep-ph]

Parity-violating electron scattering (PVES) on nuclear targetsThe right-left asymmetry, ARL, in parity violating deep inelastic electron scatteringis given by,

2

1 1 2 22

32 ( ) 2

10 2F

RL u d u d

G QA C C g y C C

Q

where (Q2) is the electromagnetic coupling at squared momentum transfer, Q2, and g(y) is a function of the fractional energy transfer, y, from the electron to the hadrons. The relative weights of up and down quarks is given by their electric charge ratio -- a consequence of interfering individual quarks with the photon amplitude as is typicalin the deep-inelastic regime. The first experiment of this type was the celebrated E–122 experiment at SLAC which was crucial to establish the SM even before the discovery of the W and Z bosons (searches for atomic parity violation at the time gave conflicting results).

exp

1 1

exp

1 1

0.1526(13)

0.513(15)

u d

u d

C C

C C

1 1

1 1

0.1529(1)

0.5297(4)

th

u d

th

u d

C C

C C

Polarized Møller (electron-electron) Scattering

2

2 2 2W2

ˆ, , where = 1 4sin e e ePV W W W

Z

QA Q y Q Q Q Q

M A

An experiment free of QCD issues has been completed recently by the E–158 Collaboration. They obtained the first measurement of the parity violating Møller asymmetry,

The resulting QeW = −0.0403±0.0053, is in reasonable agreement with the SM

prediction.

2 74 ( 2.68 0.05 0.04 ) 10 .4 2

pFPV W s s st

ptat yQA B

GQ Q

Q-weakA very similar experiment, in fact using the same kind of target (hydrogen), willmeasure the analogous weak charge of the proton, Qp

W = 2C1u +C1d at average Q2= 0.03 GeV2. With an expected polarization of 85±1% the Q-weak Collaboration anticipates to measure the parity violating asymmetry,

7 2 2( 1.31 0.14 0.10 ) 10 at 0.026 GeV .PV stat systA Q

NuTeV

5

12

5 5

2 2 2 22 2

2 2 2 22

0

2

(1 ) (1 ) (1 ) ;2

( ) ( / ) ( / ),

3 3 11

3 3( ) /

( ) ( / ) ( / ) 1,

( ) /

where

3

3

3

fo

q q qFNC L R

q

L R R LL R

R L L RL R

Gg q q g q q

X g g q g g qR g rg

X q q

X g g q g g qR g g

X q q r

y dy

L

NN

NN

2 2 2 22 2 4 2 4

r an isoscalar target, ( ) / 2,

( ) / 1 and

( ) / 2

1 5 5sin sin , sin

2 9 9

3

3

u d u dL L L W W R R R W

q u d

X q qr

X q q

g g g g g g

NN

NuTev Collaboration, Phys. Rev. Lett. 88 (2002) 091802

2exp

2exp

2

2

0.3042

0.03

0.3916 0.0007 0.3005 0.0014

0.4050 0.0016 0.0310 0.0011 01

L SM

R R S

L

M

R g

R

g

gg

22sin 0.2277 0.0013 0.0 sin 0.2227 0.00009 04W sta Wt syst

S. Davidson et al., JHEP 02 (2002) 037

SM electroweak fit(status of March 2007)

2 2leptonic effective mixing angle sin lepteffs

Higgs mass constraints

114.4 GeV < 144 GeV (95% C.L.)HM

332476 GeV

144 GeV (95% C.L.)

H

H

M

M