Possibilities to study physics beyond the standard model in solid state experiments. Oleg P. Sushkov Max-Planck Institute for Solid State Research, Stuttgart. On leave from University of New South Wales, Sydney

Electron Electric Dipole Moment (EDM) d e, T,P-violation. Nuclear Schiff Moment S, T,P-violation. Weinberg angle at q~30MeV, P-violation Present values: d e < e cm Reagan et al, 2002, atomic Tl beam. S( 199 Hg) < e cm 3 Romalis et al, 2001, Hg vapor. s 2 = Low energy value recalculated from Cs weak charge, Wood et al, 1997.

Solid state experiments Suggestions by Shapiro, 1968, electron EDM Lamoreaux, 2002, electron EDM Hunter, 2002, electron EDM Mukhamedjanov, Sushkov, 2004, Nuclear Schiff Moment Mukhamedjanov, Sushkov, 2005, Weinberg angle Lamoreaux: Gadolinium Gallium Garnet (GGG), Gd 3 Ga 5 O 12 Ionic crystal with cubic structure, ions: Cd 3+, Ga 3+, and O 2-, altogether 160 atoms in unit cell. Ga 3+ and O 2- are spinless while Gd 3+ has spin 7/2 (half filled 4f-shell) Eight nearest O around Gd ion.

Idea of the suggestion: apply external electric field E and measure induced magnetic field B. The energy shift due to electron EDM is Due to the Wigner Eckart theoremwhere S is spin of the ion =Gd ion, Z=64, the effect scales as Z 3 Applied electric field E Induced magnetic field B

The energy shift creates a macroscopic magnetization Gain is due to the large number density n and due to low temperature T An accurate calculation: Kuenzi, Mukhamedjanov,Dzuba, Cadogan, Sushkov: 2002,2003 Expected sensitivity B ~ G E ~ 10 kV/cm T ~ 2 K d e ~ e cm An order of magnitude gain compared to the present sensitivity. The problem is spin freezing that makes pointless cooling down below few kelvins.

Nuclear Schiff moment in PbTiO 3 ferroelectric. Mukhamedjanov, Sushkov, A similar idea: apply electric field and measure induced magnetic field. The ferroelectric has its internal electric field about E ~ 10 9 V/cm. In this compound all electrons spins are paired, so the experiment is aimed at nuclear Schiff moment (NSM) of 207 Pb. Hartree-Fock calculation Ludlow, Sushkov 2006 Compared to GGG: a) 5 orders of magnitude gain due to huge electric field b) Freezing temperature for nuclear spins is 10nK, so gain due to temperature is 8 orders of magnitude c) 3 orders of magnitude loss because nuclear magnetic moment is smaller than electron magnetic moment. The sensitivity estimate for NSM is S ~ e cm 3, this is by 9 orders of magnitude better than the present upper limit S ~ e cm3. The standard model prediction is S ~ e cm 3.

Weinberg angle and neutron skin Mukhamedjanov, Sushkov, 2005 A naive suggestion: apply external electric and magnetic field to a nonmagnetic solid with center of inversion and measure induced magnetization This is a T-even P-odd correlation and it might be induced by the weak interaction. However, one can show that the correlation is forbidden by Maxwell equations. PNC stays for Parity Non Conservation

One needs a crystal with center of inversion and with axis We suggest Dysprosium trifluoride DyF 3 that has a hexagonal structure. Correction to the crystal free energy is Q W is Dy weak charge and n is axis of the crystal. Induced PNC magnetization is

Dy has seven stable isotopes, four of them are even-even isotopes that are the best from the point of view of understanding of nuclear structure. Comparing effects for crystals with different isotopes one can extract value of the Weinberg angle. The estimated uncertainty comes from the nuclear neutron skin effect and the uncertainty is For B ext =1T, E ext =10kV/cm and temperature T=1K we found the following value of the expected induced PNC magnetic field Usually sited experimental sensitivity is B ~ G Alternatively one can use this effect to probe the nuclear neutron skin

Conclusions PNC in DyF 3 gives a possibility for precise measurement of Weinberg angle at low energy and for study of nuclear neutron skin. The most promising is the search for Nuclear Schiff Moment in PbTiO 3 ferroelectric that has a potential for improvement of sensitivity up to 9 orders of magnitude compared to the present level.