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 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

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   ). 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.

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

Which Constants? Since variation of dimensional constants cannot be distinguished from variation of units, it only makes sense to consider variation of dimensionless constants. Fine structure constant  e 2 /hc   Electron or quark mass/QCD strong interaction scale, m e,q /  QCD   strong (r)=const/ln(r  QCD /ch)

Variation of fine structure constant 

Quasar absorption spectra Earth Quasar Gas cloud Light 

Quasar absorption spectra Earth Quasar Gas cloud Light  One needs to know E(  2 ) for each line to do the fitting

Use atomic calculations to find  For  close to  0  0  q(  2 /  0 2  ) q is found by varying  in computer codes: q = d  /dx = [  ( 0.1 )  (  0.1 )]/ 0.2, x=  2 /  0 2   =e 2 /hc=0  corresponds to non-relativistic limit (infinite c).

Methods of Atomic Calculations N ve Relativistic Hartree-Fock +Accuracy 1All-orders sum of dominating diagrams 0.1-1% 2-6Configuration Interaction + Many-Body Perturbation Theory 1-10% 2-15Configuration Interaction10-20% 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.

Results of calculations (in cm -1 ) Atom  q Mg I Mg II Mg II Si II Si II Al II Al III Al III Ni II Atom  q Ni II Ni II Cr II Cr II Cr II Fe II Atom  q Fe II Fe II Fe II Fe II Fe II Fe II Zn II Zn II Negative shifters Positive shifters Anchor lines Also, many transitions in Mn 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!

Results of the analysis Murphy et al, 2003: Keck telescope, Hawaii,143 systems, 23 lines, 0.2<z<4.2  x   VL telescope,Chile:  x   Quast et al, 2004: VL telescope,Chile, 1 system, Fe II, 6 lines, 5 positive q-s, one negative q, z=1.15  x   Srianand et al, 2004: VL telescope, 23 systems, 12 lines, Fe II, Mg I, Si II, Al II, 0.4<z<2.3  x   Systematic effect or spatial variation?

Spatial variation (C.L.Steinhardt)    Murphy et al North hemisphere -0.66(12) South (close to North) -0.36(19) Strianand et al (South) -0.06(06) No explanation by systematic effects have been found so far

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

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

Measurements m e / M p or m e /  QCD Tsanavaris,Webb,Murphy,Flambaum,Curran 2005 Hyperfine H/optical Mg,Fe,…, 8 quasar systems X=  2 g p m e / M p  X/X=1.17(1.01)10 -5 No variation Reinhold,Bunnin,Hollenstein,Ivanchik,Petitjean 2006, H 2 molecule, 2 systems  (m e / M p )/ (m e / M p )=-2.4(0.6)10 -5 Variation 4  ! Space-time variation? Grand Unification model?

Oklo natural nuclear reactor n+Sm capture cross section is dominated by E r =0.1 eV resonance Shlyakhter;Damour,Dyson;Fujii et al Limits on variation of  Flambaum, Shuryak 2003  E r = 170 MeV  X/X + 1 MeV  X=m s /  QCD, enhancement 170 MeV/0.1 eV=1.7x10 9 Lamoreaux,Torgerson 2004  E r =-0.58(5) eV  X/X=-0.34(3) two billion years ago 2006 results are consistent with zero (error bars larger)

Atomic clocks: Comparing rates of different clocks over long period of time can be used to study time variation of fundamental constants! Optical transitions:  Microwave transitions: , (m e, m q )/  QCD

Calculations to link change of frequency to change of fundamental constants: Microwave transitions: hyperfine frequency is sensitive to nuclear magnetic moments (suggested by Karshenboim) We performed atomic, nuclear and QCD calculations of powers  for H,D,Rb,Cd +,Cs,Yb +,Hg + V=C(Ry)(m e /M p )  2+  (m q /  QCD    V/V  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.  0  q(  2 /  0 2  )

Results for variation of fundamental constants SourceClock 1 /Clock 2 d  /dt/  ( yr -1 ) Marion et al, 2003Rb(hfs)/Cs(hfs)0.05(1.3) a Bize et al, 2003Hg+(opt)/Cs(hfs)-0.03(1.2) a Fisher et al, 2004H(opt)/Cs(hfs)-1.1(2.3) a Peik et al, 2004Yb+(opt)/Cs(hfs)-0.2(2.0) Bize et al, 2004Rb(hfs)/Cs(hfs)0.1(1) a a assuming m q /  QCD = Const Combined results: d/dt ln   0.3(2.0) x yr -1 d/dt ln(m q /  QCD )  -0.4(4.5) x yr -1 m e /M p or m e /  QCD 3(6)x yr -1

Dysprosium miracle Dy: 4f 10 5d6s E= … cm -1, q= 6000 cm -1 4f 9 5d 2 6s E= … cm -1, q= cm -1 Interval  = cm -1 Enhancement factor K = 10 8 (!), i.e.       Preliminary result (Berkeley,Los Alamos) dln  /dt =-2.9(2.6)x yr -1 Problem: states are not narrow!

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 Hz PRL 2006 Nuclear/QCD calculation: Enhancement ,     10 5   X q /X q -10  X s /X s ) X q =m q /  QCD, X s =m s /  QCD 235 U energy 76 eV, width Hz

Conclusions Quasar data: MM method provided sensitivity increase 100 times. Anchors, positive and negative shifters- control of systematics. Keck- variation of  VLT-no variation. Undiscovered systematics or spatial variation. m e /M p : hyperfine H/optical – no variation, H 2 - variation 4 . Space-time variation? Grand Unification model? Big Bang Nucleosynthesis: may be interpreted as variation of m s /  QCD (4  ? Oklo: variation of m s /  QCD (11  not confirmed, <10 -9  Atomic clocks: present time variation of , m q /  QCD Transitions between narrow close levels in atoms, molecules and nuclei – huge enhancement!

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

Atomic parity violation Dominated by Z-boson exchange between electrons and nucleons Z ee nn In atom with Z electrons and N neutrons obtain effective Hamiltonian parameterized by “nuclear weak charge” Q W Standard model tree-level couplings: APV amplitude E PV  Z 3 [Bouchiat,Bouchiat] Clean test of standard model via atomic experiments!

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] E PV  Z 2 A 2/3 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! B j  a

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 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 enhancement in Ra atom due to close opposite parity state.

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 K 0, B 0 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

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! Theoryd e (e cm) Std. Mdl.< SUSY Multi-Higgs Left-right Atomic EDMs d atom  Z 2, Z 3 [Sandars] Sensitive probe of physics beyond the Standard Model! Best limit (90% c.l.): |d e | < 1.6  e cm Berkeley (2002) e.g. electron EDM [Commins ]

Atomic calculations We calculate: APV Atomic EDM   PT     2     H PT 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!

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 !?

Method for atomic many-body calculations 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): External fields included using Time-Dependent Hartree-Fock (RPAE core polarization)+correlations ∑ = + In the lowest order  is given by: [Dzuba,Flambaum,Sushkov]

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

Cesium APV  Q W  Q W SM  0.9  Tightly constrains possible new physics, e.g. mass of extra Z boson M Z’  750 GeV E PV 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, E PV =W xE1/(E s -E p ) [Flambaum,Ginges; Shabaev,Pachuki,Tupitsyn,Yerokhin] 7S 6S Best measurement [Boulder,1997] -Im(E PV )/  = (1  0.35%) mV/cm Best calculation [Dzuba,Flambaum,Ginges] E PV = (1  0.5%)  iea B (-Q W /N)

Enhancement of electron electric dipole moment Due to mixing of atomic levels of opposite parity electron EDM is enhanced in heavy atoms Z 3   times. Tl atom: d=-600 d e Measurements in Berkeley. Diatomic molecules : additional enhancement due to mixing of molecular rotational levels, d can reach d e YbF (London), PbO (Yale)

Screening of nuclear EDM. Nuclear EDM is screened by electrons (Schiff theorem). Explanation: external electric field E 0 does not accelerate neutral atom. Therefore, nucleus is at rest. Thus, total elecric field acting on nucleus E t =E 0 +E electron =0 Nuclear EDM has zero interaction with electric field, d N E t =0. Impossible to measure. The Schiff theorem is violated by finite nuclear size. Nuclear and atomic calculations: d( 199 Hg)=4x e cm  strenght of T,P-odd interaction between nucleons. Measurements in Seattle – best limits on models of CP violation.

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( 3 D 2 )  10 5  d(Hg) E PV ( 1 S D 1,2 )  100  E PV (Cs) Anapole  1000 Measurements in preparation at - Argonne National Laboratory, Chicago, USA - Kernfysisch Versneller Instituut, Groningen, The Netherlands, -Rn: TRIUMF (Canada)-University of Michigan 7s 2 1 S 0 3D23D2 3P13P1  E=5 cm -1 3D13D1 3P03P0 7s6p7s6d E PV (Q W ) E PV (  a )

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