Variation of Constants and

Violation of Symmetries,

Cairns, 2010

Radiative corrections and parity nonconservation in atoms

UNSW, Sydney, AustraliaMichael Kuchiev

Cairns, 24-25 July, 2010

Parity is not conserved,

, bosons interact

with left-handed fermions

W Z

only

Radiative corrections

Roughly speaking:

1. Vacuum polarization

2. Fermion self-interaction, self-energy and vertex correction

1. Vacuum polarization

m

m 1930

e

( ) ( )r U r

Uehling-Serber potential (1935)

22

1

2

2 2

2( ) 1 ( )

3

11( ) 1

2

m rZeU r e Y d

r

Y

Hesenberg-Euler problem (1935)

.Vacuum polarization is strong at small distances

How to find the correctio to

wave function at small distances?

Which parameters govern the pronblem?

Cr r

2 2

2

( 1/ 2), ( )

2 (2 1),

(4 1)

j Z

Za k

mc

Kuchiev, Flambaum (2002)

Parameters that govern wave function at small distances

22

2

| | conventional nonrelativistic parameter

| | ( ) relativistic parameterCompton

mV r

mV r r Z

Derivation (MK 2001)

Vacuum polarizationVacuum polarization correction to PNC correction to PNC

Kuchiev, Flambaum (2002)

Sushkov (2001)Johnson,Bednyakov, Soff(2001)

Vacuum polarizationVacuum polarizationcorrection in Cscorrection in Cs

0.4%

Sushkov, Milstein (2001)

Kuchiev, Flambaum (2002)

2001-2002: what we gonna do with Standard Model?

Michael Kozlov

Victor Flambaum

Oleg Sushkov

?

Alexander Milstein

Walter Johnson

2.Electron self-interaction for Lamb 2.Electron self-interaction for Lamb shiftshift

Self-interaction correction to PNCSelf-interaction correction to PNC

2.Analytical result2.Analytical result

Kuchiev (2002)Milstein, Sushkov, Terekhov (2002)

The thin dotted line, thick dotted line, and solid line: self-energy corrections to the PNC amplitude

Convergence of analytical results on self-energy correctionKuchiev (2002)Kuchiev, Flambaum (2002,2003)Milstein, Sushkov, Terekhov (2002)

Estimate for PNC based on available Estimate for PNC based on available data for Finite Nuclear Size (FNS)data for Finite Nuclear Size (FNS)

The correction to the PNC amplitude is equal to the average of the corrections to the FNS energy shifts for S1/2 and P1/2 levels. Kuchiev, Flambaum (2002)

Corrections to nuclear finite size:W.R.Johnson and G.Soff, At. Data Nuc. Data Tables 33, 405 (1985).S.A.Blundell, Phys. Rev. A 46, 3762 (1992).K.T.Cheng, W.R.Johnson and J.Sapirstein, Phys. Rev A 47, 1817 (1993).[I.Lindgren, H.Persson, S.Salomonson, and A.Ynnerman, Phys. Rev. A 47, 4555 (1993).

Corrections to the PNC amplitudeThe thin dotted line analitical result , thick dotted line (from comparison with FNS, solid line is an interpolation.

Kuchiev, Flambaum (2003)

•VA Dzuba, VV Flambaum, JSM Ginges - Physical Review D, 2002 – APS

•VV Flambaum, JSM Ginges - Physical Review A, 2005 – APS

•A Derevianko, SG Porsev - The European Physical Journal A-Hadrons, 2007

•SG Porsev, K Beloy, A Derevianko - Arxiv preprint arXiv:1006.4193, 2010

•VM Shabaev Physics-Uspekhi 51 1175 2008

•AV Maiorova, OI Pavlova, VM Shabaev, Journal of Physics B, 2009

Further reading

ConclusionsConclusions

Radiative corrections to PNC in heavy Radiative corrections to PNC in heavy atoms are large, of the order of 1%.atoms are large, of the order of 1%.

Similarly are large radiative Similarly are large radiative corrections related to any corrections related to any phenomenon which manyfests itslef phenomenon which manyfests itslef at small, nuclear scale, distancesat small, nuclear scale, distances

Lesson: before daring to amend a Lesson: before daring to amend a major theory do your calculations major theory do your calculations right.right.

Thanks:

To numerous colleagues (some of them pictured) for stimulating discussions and atmosphere

Internet community, which mostly tolerates my little follies

ARC for support Generous organisers and patient

listeners of the workshop