Nuclear Matrix Elements for Tensor Interactions that Violate Local - PowerPoint PPT Presentation

Nuclear Matrix Elements for Tensor Interactions that Violate Local Lorentz Invariance Alex Brown and Vladimir Zelevinsky Alex Brown and Vladimir Zelevinsky National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy Michigan State Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan Mi h Michael Romalis l R li Department of Physics, Princeton University, Princeton, New Jersey Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

CPT-even Lorentz violation L = –  ( m + a    + b   5   )  + a,b - CPT-odd c,d - CPT-even    + d   5   )    i 2  (   + c ( )   2 • Maximum attainable particle velocity Coleman and Glashow      ˆ ˆ ˆ ( ( 1 1 ) ) v v c c c c c c v v c c v v v v Jacobson Jacobson 00 0 MAX j j jk j k – Implications for ultra-high energy cosmic rays, Cherenkov radiation, etc – Best limit c 00 ~ 10 -23 from Auger ultra-high energy cosmic rays 10 23 f B t li it A lt hi h i – Many laboratory limits (optical cavities, cold atoms, etc) • Motivation for Lorentz violation (without breaking CPT) ( g ) – Doubly-special relativity – Horava-Lifshitz gravity Something special needs to happen when particle S hi i l d h h i l momentum reaches Plank scale!

Search for CPT-even Lorentz violation with nuclear spin • Need nuclei with orbital angular momentum and total spin >1/2 N d l i i h bi l l d l i 1/2 • Quadrupole energy shift proportional to the kinetic energy of the valence nucleon valence nucleon     2 2 2 ~ ( 2 ) 2 E c c c p p p 11 22 33 Q x y z • Previosly has been searched for in two experiments using 201 Hg and 21 Ne with sensitivity of about 0.5  Hz • Bounds on neutron c n ~10  – already most stringent bound on c 10  B d l d i b d coefficient! Suppressed by v Earth

M Magnetic field self-compensation i fi ld lf i

Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

Search for CPT-even Lorentz violation with nuclear spin • Need nuclei with orbital angular momentum and total spin >1/2 N d l i i h bi l l d l i 1/2 • Quadrupole energy shift proportional to the kinetic energy of the valence nucleon valence nucleon     2 2 2 ~ ( 2 ) 2 E c c c p p p 11 22 33 Q x y z • Previosly has been searched for in two experiments using 201 Hg and 21 Ne with sensitivity of about 0.5  Hz • Bounds on neutron c n ~10  – already most stringent bound on c 10  B d l d i b d coefficient! Suppressed by v Earth

e p =1 e n =0 1 0 Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

e p =1.37 e n =0.45 1 37 0 45 Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

e p =1 e n =0 1 0 Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

e p =1.37 e n =0.45 1 37 0 45 Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

Toi (Table of Ham Isotopes) p ) Hamiltonian Hamiltonian Input programs NuShellX@MSU wrapper Observables and Graphics NuShellX Outputs for energies .lpt Outputs for energies * lpt library of published <|a+|> *.lsf Hamiltonians <|a+ a|> *.obd (sps folder) <|a+ a+|> *.tna | | postscript (*.eps) (*.pdf) *.sp model space files figures *.int Hamiltonian files Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

The key is to optimize the sums in this equation for OpenMP and/or MPI Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries

jj55 model space

Search for Neutrinoless Double-Beta Decay in 136 Xe with EXO-200 Mihai Horoi (next week) – also requires addition of spin-orbit partners 137 Ba – first observation of double-gamma decay (D.J. Millener, R.J. Sutter, D.E. Alburger) Alburger)

(39) (10,052) 132 Te a b 2 +

(1333) (359,934) 132 I a b 2 +

(72) (74,311,166) 132 Xe a b

How small are these quadrupole momentum matrix q p elements in ab-initio and no-core approaches? For example 9 Be 3/2 ground state For example 9 Be 3/2- ground state Alex Brown, August 6, 2013 INT Program on Nuclei and Fundamental Symmetries