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Variation of Fundamental Constants from Big Bang to Atomic Clocks

Variation of Fundamental Constants from Big Bang to Atomic Clocks. V.V. Flambaum School of Physics, UNSW, Sydney, Australia Co-authors: Atomic calculations V.Dzuba,M.Kozlov,E.Angstmann,J.Berengut,M.Marchenko,Cheng Chin,S.Karshenboim,A.Nevsky

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Variation of Fundamental Constants from Big Bang to Atomic Clocks

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  1. Variation ofFundamental Constants from Big Bang to Atomic Clocks V.V. Flambaum School of Physics, UNSW, Sydney, Australia Co-authors: Atomic calculations V.Dzuba,M.Kozlov,E.Angstmann,J.Berengut,M.Marchenko,Cheng Chin,S.Karshenboim,A.Nevsky Nuclear and QCD calculations E.Shuryak,V.Dmitriev,D.Leinweber,A.Thomas,R.Young,A.Hoell, P.Jaikumar,C.Roberts,S.Wright,A.Tedesco,W.Wiringa Cosmology J.Barrow Quasar data analysis J.Webb,M.Murphy,M.Drinkwater,W.Walsh,P.Tsanavaris,S.Curran Quasar observations C.Churchill,J.Prochazka,A.Wolfe, thanks to W.Sargent,R.Simcoe

  2. Motivation • Extra space dimensions (Kaluza-Klein, Superstring and M-theories). Extra space dimensions is a common feature of theories unifying gravity with other interactions. Any change in size of these dimensions would manifest itself in the 3D world as variation of fundamental constants. • Scalar fields . Fundamental constants depend on scalar fields which vary in space and time (variable vacuum dielectric constant e0 ). May be related to “dark energy” and accelerated expansion of the Universe.. • “ Fine tuning” of fundamental constants is needed for humans to exist. Example: low-energy resonance in production of carbon from helium in stars (He+He+He=C). Slightly different coupling constants — no resonance –- no life. Variation of coupling constants in space provide natural explanation of the “fine tuning”: we appeared in area of the Universe where values of fundamental constants are suitable for our existence.

  3. Search for variation of fundamental constants • Big Bang Nucleosynthesis • Quasar Absorption Spectra 1 • Oklo natural nuclear reactor • Atomic clocks 1 |Dc|>0? |Dc|>0? |Dc|>0? 1 Based on analysis of atomic spectra

  4. Which Constants? Since variation ofdimensionalconstants cannot be distinguished from variation of units, it only makes sense to consider variation of dimensionless constants. • Fine structure constanta=e2/hc=1/137.036 • Electron or quark mass/QCD strong interaction scale, me,q/LQCD astrong (r)=const/ln(r LQCD /ch)

  5. Variation of fine structureconstanta

  6. Quasar absorption spectra Gas cloud Quasar Earth Light a

  7. Quasar absorption spectra Gas cloud Quasar Earth Light One needs to know E(a2) for each line to do the fitting a

  8. Use atomic calculations to find w(a). For aclose toa0w = w0 + q(a2/a02-1) qis found by varying a in computer codes: q = dw/dx = [w(0.1)-w(-0.1)]/0.2, x=a2/a02-1 a =e2/hc=0corresponds to non-relativistic limit (infinite c).

  9. Methods of Atomic Calculations These methods cover all periodic system of elements • They were used for many important problems: • Test of Standard Model using Parity Violation in Cs, Tl… • Predicting spectrum of Fr (accuracy 0.1%), etc.

  10. Results of calculations (in cm-1) Negative shifters Anchor lines Positive shifters Also, many transitions inMn II, Ti II, Si IV, C II, C IV, N V, O I, Ca I, Ca II, Ge II, O II, Pb II Different signs and magnitudes of q provides opportunity to study systematic errors!

  11. Results of the analysis • Murphy et al, 2003: Kecktelescope, Hawaii,143 systems, 23 lines, 0.2<z<4.2 Da/a=-0.543(116) x 10-5 VLtelescope,Chile: Da/a=0.02(21) x 10-5 • Quast et al, 2004: VL telescope,Chile, 1 system, Fe II, 6 lines, 5 positive q-s, one negative q, z=1.15 Da/a=-0.4(1.9)(2.7) x 10-6 • Srianand et al, 2004: VL telescope, 23 systems, 12 lines, Fe II, Mg I, Si II, Al II, 0.4<z<2.3 Da/a=-0.06(0.06) x 10-5 Systematic effect or spatial variation?

  12. Spatial variation (C.L.Steinhardt) No explanation by systematic effects have been found sofar 10 5 Da/a Murphy et al • North hemisphere -0.66(12) • South (close to North) -0.36(19) Strianand et al (South) -0.06(06)

  13. Variation of strong interaction Grand unification models (Marciano; Calmet, Fritzch; Langecker, Segre, Strasser; Dent)

  14. Nucleon magnetic moment Nucleon and meson masses QCD calculations: lattice, chiral perturbation theory,cloudy bag model, Dyson-Schwingerand Faddeev equations, semiempirical. Nuclear calculations: meson exchange theory of strong interaction.

  15. Measurements me / Mp or me / LQCD • Tsanavaris,Webb,Murphy,Flambaum,Curran 2005 Hyperfine H/optical Mg,Fe,… , 8 quasar systems X=a2 gpme / Mp DX/X=1.17(1.01)10-5 No variation • Reinhold,Bunnin,Hollenstein,Ivanchik,Petitjean 2006 , H2 molecule, 2 systems D(me / Mp )/ (me / Mp)=-2.4(0.6)10-5 Variation 4 s ! Space-time variation? Grand Unification model?

  16. Oklo natural nuclear reactor n+Sm capture cross section is dominated by Er =0.1 eV resonance Shlyakhter;Damour,Dyson;Fujii et al Limits on variation of a Flambaum, Shuryak 2003 DEr = 170 MeV DX/X + 1 MeV Da/a X=ms/ LQCD , enhancement 170 MeV/0.1 eV=1.7x109 Lamoreaux,Torgerson 2004 DEr =-0.58(5) eV DX/X=-0.34(3) 10-9 two billion years ago 2006 results are consistent with zero (error bars larger)

  17. Atomic clocks: Comparing rates of different clocks over long period of time can be used to study time variation of fundamental constants! Optical transitions:a Microwave transitions: a, (me, mq )/LQCD

  18. Calculationsto link change of frequency to change of fundamental constants: Optical transitions:atomic calculations (as for quasar absorption spectra) for many narrow lines in Al II, Ca I, Sr I, Sr II, In II, Ba II, Dy I, Yb I, Yb II, Yb III, Hg I, Hg II, Tl II, Ra II . w = w0 + q(a2/a02-1) Microwave transitions: hyperfine frequency is sensitive to nuclear magnetic moments (suggested by Karshenboim) We performed atomic,nuclear and QCD calculations of powers k ,bfor H,D,Rb,Cd+,Cs,Yb+,Hg+ V=C(Ry)(me/Mp)a2+k(mq/LQCD)b , Dw/w=DV/V

  19. Results for variation of fundamental constants aassuming mq/LQCD = Const Combined results: d/dt lna= -0.3(2.0) x 10-15 yr-1 d/dt ln(mq/LQCD) = -0.4(4.5) x10-14 yr-1 me /Mp or me/LQCD 3(6)x10-15yr -1

  20. Dysprosium miracle Dy: 4f105d6s E=19797.96… cm-1 , q= 6000 cm-1 4f95d26s E=19797.96… cm-1 , q= -23000 cm-1 Interval Dw = 10-4 cm-1 Enhancement factorK = 108(!), i.e.Dw/w0 =108 Da/a Preliminary result (Berkeley,Los Alamos) dlna/dt =-2.9(2.6)x 10-15 yr-1 Problem: states are not narrow!

  21. Nuclear clocks(suggested by Peik,Tamm 2003) Very narrow UV transition between first excited and ground state in 229 Th nucleus Energy 3-5 eV, width 10-4 Hz PRL 2006 Nuclear/QCD calculation: Enhancement 105 -106, Dw/w0 =105 (4 Da/a + DXq/Xq-10DXs/Xs ) Xq=mq/ LQCD , Xs=ms/ LQCD 235 U energy 76 eV, width 6 10-4 Hz

  22. Conclusions • Quasar data: MM method provided sensitivity increase 100 times. Anchors, positive and negative shifters-control of systematics. Keck- variation of a, VLT-no variation. Undiscovered systematics or spatial variation. • me /Mp : hyperfine H/optical – no variation, H2 - variation 4 s . Space-time variation? Grand Unification model? • Big Bang Nucleosynthesis: may be interpreted as variation of ms/ LQCD (4 s)? • Oklo: variation of ms/ LQCD (11 s not confirmed, <10 -9) • Atomic clocks: present time variation of a , mq/ LQCD • Transitions between narrow close levels in atoms, molecules and nuclei – huge enhancement!

  23. Violation of parity and time reversal • Atoms as probes of fundamental interactions • atomic parity violation (APV) - nuclear weak charge - nuclear anapole moment • atomic electric dipole moments (EDMs) • High-precision atomic many-body calculations • QED radiative corrections : radiative potential and low –energy theorem for electromagnetic amplitudes • Cesium APV • Radium EDM and APV • Summary

  24. e e Z n n Atomic parity violation • Dominated by Z-boson exchange between electrons and nucleons Standard model tree-level couplings: • In atom with Z electrons and N neutrons obtain effective Hamiltonian parameterized by “nuclear weak charge” QW • APV amplitude EPV  Z3 [Bouchiat,Bouchiat] Clean test of standard model via atomic experiments!

  25. j  a B Nuclear anapole moment • Source of nuclear spin-dependent PV effects in atoms • Nuclear magnetic multipole violating parity • Arises due to parity violation inside the nucleus • Interacts with atomic electrons via usual magnetic interaction (PV hyperfine interaction): [Flambaum,Khriplovich,Sushkov] EPV  Z2 A2/3 measured as difference of PV effects for transitions between hyperfine components Cs: |6s,F=3> – |7s,F‘=4> and |6s,F’=4> – |7s,F=3> Probe of weak nuclear forces via atomic experiments!

  26. Nuclear anapole moment is produced by PV nuclear forces. Measurements give the strength constant g. • Boulder Cs: g=6(1) in units of Fermi constant Seattle Tl: g=-2(3) New accurate calculations:Haxton,Liu,Ramsey-Musolf; Dmitriev,Khriplovich,Telitsin: problem remains. • 105 enhancement of the nuclear anapole contribution in diatomic molecules due to mixing of close rotational levels of opposite parity. Theorem: only anapole contribution to PV is enhanced. Experiment started in Yale. • 103 enhancement in Ra atom due to close opposite parity state.

  27. Atomic electric dipole moments   • Electric dipole moments violate parity (P) and time-reversal (T) • T-violation  CP-violation by CPT theorem CP violation • Observed in K0, B0 • Accommodated in SM as a single phase in the quark-mixing matrix (Kobayashi-Maskawa mechanism) However… not enough CP-violation in SM to generate enough matter-antimatter asymmetry of Universe!  Must be some non-SM CP-violation

  28. Excellent way to search for new sources of CP-violation is by measuring EDMs • SM EDMs are hugely suppressed • Theories that go beyond the SM predict EDMs that are many orders of magnitude larger! e.g. electron EDM [Commins ] Best limit (90% c.l.): |de| < 1.6  10-27 e cmBerkeley (2002) • Atomic EDMs datom  Z2 , Z3[Sandars] Sensitive probe of physics beyond the Standard Model!

  29.    PT   2 Atomic calculations • APV We calculate: • Atomic EDM HPT is due to nucleon-nucleon, electron-nucleon PT-odd interactions, electron, proton or neutron EDM. We performed nuclear and atomic calculations. Atomic wave functions need to be good at all distances! We check the quality of our wave functions by calculating: - hyperfine structure constants - energies - E1 transition amplitudes and comparing to measured values… there are also other checks!

  30. New accurate measurements of E1 amplitudes agree with calculations to 0.1% -theoretical accuracy in PV is 0.4% (instead of 1%) Bennet, Wieman 1999 New physics beyond Standard Model !?

  31. ∑= + Method for atomic many-body calculations [Dzuba,Flambaum,Sushkov] • Zeroth-order: relativistic Hartree-Fock. Perturbation theory in difference between exact and Hartree-Fock Hamiltonians. • Correlation corrections accounted for by inclusion of a “correlation potential” ∑ (self-energy operator): In the lowest order  is given by: • External fields included using Time-Dependent Hartree-Fock (RPAE core polarization)+correlations

  32. 1. electron-electron screening   … 2. hole-particle interaction    … 3. nonlinear-in-∑ corrections ∑ ∑ ∑ ∑ ∑   ∑ … The correlation potential Use the Feynman diagram technique to include three classes of diagrams to all orders:

  33. Cesium APV • Best measurement [Boulder,1997] -Im(EPV)/ = 1.5935(10.35%) mV/cm • Best calculation [Dzuba,Flambaum,Ginges] EPV = -0.897(10.5%)10-11 ieaB(-QW/N) 7S  QW QWSM  0.9 Tightly constrains possible new physics, e.g. mass of extra Z boson MZ’  750 GeV EPV includes -0.8% shift due to strong-field QED self-energy /vertex corrections to weak matrix elements [Kuchiev,Flambaum; Milstein,Sushkov,Terekhov] A complete calculation of QED corrections to PV amplitude includes also QED corrections to energy levels and E1 amplitudes, EPV =W xE1/(Es-Ep) [Flambaum,Ginges; Shabaev,Pachuki,Tupitsyn,Yerokhin] 6S

  34. Enhancement of electron electric dipole moment • Due to mixing of atomic levels of opposite parity electron EDM is enhanced in heavy atoms Z3a2 times. Tl atom: d=-600 deMeasurements in Berkeley. • Diatomic molecules : additional enhancement due to mixing of molecular rotational levels, d can reach 107 -1010 de YbF (London), PbO (Yale)

  35. Screening of nuclear EDM. • Nuclear EDM is screened by electrons (Schiff theorem). Explanation: external electric field E0does not accelerate neutral atom. Therefore, nucleus is at rest. Thus, total elecric field acting on nucleus Et=E0+Eelectron=0 Nuclear EDM has zero interaction with electric field, dN Et=0. Impossible to measure. The Schiff theorem is violated by finite nuclear size. Nuclear and atomic calculations: d(199Hg)=4x10-25 e cm h, h - strenght of T,P-odd interaction between nucleons. Measurements in Seattle – best limits on models of CP violation.

  36. Radium EDM and APV • Huge enhancement of EDM due to nuclear deformation • Enhancement for EDM and APV in metastable states due to presence of close opposite parity levels [Flambaum; Dzuba,Flambaum,Ginges] d(3D2)  105  d(Hg) EPV(1S0-3D1,2)  100  EPV(Cs) Anapole  1000 7s6d 7s6p E=5 cm-1 3D2 3P1 3D1 3P0 EPV(a) EPV(QW) 7s21S0 • Measurements in preparation at - Argonne National Laboratory, Chicago, USA - Kernfysisch Versneller Instituut, Groningen, The Netherlands, -Rn: TRIUMF (Canada)-University of Michigan

  37. Summary • Precision atomic physics can be used to probe fundamental interactions • unique test of the standard model through APV, now agreement • Nuclear anapole, probe of PV weak nuclear forces (in APV) • EDM, unique sensitivity to physics beyond the standard model. 1-3 orders improvement may be enough to reject or confirm all popular models of CP violation, e.g. supersymmetric models • A new generation of experiments with enhanced effects is underway in atoms, diatomic molecules, and solids

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