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.

Fine structure anomalies and level crossing Energies of “normal” fine structure triplets as functions of  2 0 (  0 ) 2 1  E=A(Z  ) 2

Problem: level pseudo crossing Values of q=dE/d  2 are sensitive to the position of level crossing Energy levels of Ni II as functions of  2 0 (  0 ) 2 1 Solution: matching experimental g- factors

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!

= + (α 2 /α 0 2 – 1)ωω0ω0 q Analysis ( J.Webb, M.Murphy, et al.)   q  Laboratory Measurements (London, NIST, Lund, etc.) Quasar Observations (Keck, VLT) Atomic Calculations (V.A. Dzuba, V.V. Flambaum, et al.)

Results of the analysis Murphy et al, 2003: Keck telescope, 143 systems, 23 lines, 0.2<z<4.2  x   Quast et al, 2004: VLT telescope, 1 system, Fe II, 6 lines, 5 positive q-s, one negative q, z=1.15  x   Srianand et al, 2004: VLT 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)  m/  QCD )/(m/  QCD  1.Proton mass M p =3  QCD, measure m e /M p 2.Nuclear magnetic moments  g eh/4M p c g=g(m q /  QCD ) 3. Nuclear energy levels

Dependence on quark mass Dimensionless parameter is m q /  QCD. It is convenient to assume  QCD =const, i.e. measure m q in units of  QCD m  is proportional to (m q  QCD ) 1/2  m   m   m q  m q Other meson and nucleon masses remains finite for m q =0.  m/m=K  m q  m q Coefficients K are calculated for p,n, 

Nuclear magnetic moments depends on  -meson mass m  p n p p n  Nucleon magnetic moment Spin-spin interaction between valence and core nucleons

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

Measurements m e / M p or m e /  QCD Tsanavaris,Webb,Murphy,Flambaum, Curran PRL 2005 Hyperfine H/optical, 8 quasar absorption systems with Mg,Ca,Mn,C,Si,Zn,Cr,Fe,Ni Measured X=  2 g p m e / M p  X/X=1.17(1.01)10 -5 No variation Reinhold,Bunnin,Hollenstein,Ivanchik, Petitjean PRL 2006, H 2 molecule, 2 systems  (m e / M p )/ (m e / M p )=-2.4(0.6)10 -5 Variation 4  ! Systematics or space-time variation?

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 alpha Flambaum, Shuryak PRD 2003  E r = 170 MeV  X/X + 1 MeV  X=m s /  QCD, enhancement 170 MeV/0.1 eV=1.7x10 9 Lamoreax,Torgerson PRD(2004)  E r =-0.58(5) eV  X/X=-0.34(3) two billion years ago

Atomic clocks Cesium primary frequency standard: = Hz HFS of 6s: F=4 F=3 Also: Rb, Cd +, Ba +, Yb +, Hg +, etc. E.g. (Hg + ) = (14)(41) Hz (D. J. Berkeland et al, 1998).

Optical frequency standards: Z AtomTransition FrequencySource 20Ca 1S0-3P11S0-3P (5.3) HzDegenhardt et al, Sr +1S0-3P11S0-3P (10) kHzFerrari et al, In +1S0-3P01S0-3P (230) Hzvon Zanthier et al, Yb +2 S 1/2 - 2 F 7/ (600) HzHosaka et al, 2005 Also: H, Al +, Sr, Ba +, Yb, Hg, Hg +, Tl +, Ra +, etc. Accuracy about can be further improved to !

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

Advantages: Very narrow lines, high accuracy of measurements. Flexibility to choose lines with larger sensitivity to variation of fundamental constants. Simple interpretation (local time variation).

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   0.9(2.9) x yr -1 d/dt ln(m q /  QCD )  yr -1 m e /M p or m e /  QCD … 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 (Budker et al, Berkeley)  dln  /dt  < 4.3 x yr -1 Problem: states are not narrow!

Molecular clocks Cancellations between rotational and hyperfine intervals in very narrow microwave transitions in LaS, LaO, LuS,LuO, etc.   =E rotational -E hyperfine = E hyperfine / Enhancement factor K = ,      

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 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

Ultracold atomic and molecular collisions (in Bose condensate). Cheng Chin, Flambaum PRL 2006 Enhancement near Feshbach resonance. Variation of scattering length  a/a=K  X/X, K=10 2 – X=m e /M p

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 . Undiscovered systematics or space-time variation. Big Bang Nucleosynthesis: may be interpreted as variation of m s /  QCD ? Oklo: variation of m s /  QCD ? Atomic clocks: present time variation of , m s /  QCD Transitions between narrow close levels in atoms, molecules and nuclei – huge enhancement!

More suggestions … AtomState 1 State 2 K Ce I 5H35H D21D H43H D23D Nd I 5K65K L57L Nd I 7L57L K67K Sm I 5D15D G27G Gd II 8 D 11/ F 9/ Tb I 6 H 13/ G 9/ E. J. Angstmann et al, submitted to J. Phys. B

Publications: V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRL 82, 888 (1999). V. A. Dzuba, V. V. Flambaum, J, K. Webb, PRA 59, 230 (1999). V. A. Dzuba, V. V. Flambaum, PRA 61, (2000). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, LNP 570, 564 (2001). J. K. Webb et al, PRL 87, (2001). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, PRA 63, (2001). M. M. Murphy et al, MNRAS, 327, 1208 (2001). V. A. Dzuba et al, PRA, 66, (2002). V. A. Dzuba, V. V. Flambaum, M. V. Marchenko, PRA 68, (2003). E. J. Angstmann, V. A. Dzuba, V. V. Flambaum, PRA 70, (2004). J. C. Berengat et al, PRA 70, (2004). M. M. Murphy et al, LNP, 648, 131 (2004). V. A. Dzuba, PRA, 71, (2005). V. A. Dzuba, V. V. Flambaum, PRA, 71, (2005). V. A. Dzuba, V. V. Flambaum, PRA, 72, (2005). V. A. Dzuba, PRA, 71, (2005). S. G. Karshenboim et al, physics/

Alkali Doublet Method (Varshalovich, Potekhin, Ivanchik, et al) Fine structure interval  FS = E(p 3/2 ) - E(p 1/2 ) = A(Z  ) 2 If  Z is observed at red shift Z and  0 is FS measured on Earth then Ivanchik et al, 1999:  x  . Murphy et al, 2001:  x  .

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Many Multiplet Method (Flambaum, Webb, Murphy, et al) p 3/2 s 1/2 p 1/2  >>  FS ! Advantages: Order of magnitude gain in sensitivity Statistical: all lines are suitable for analysis Many opportunities to study systematic errors    

Atoms of interest ZAtom / IonTransitionsN ve 1 6C I, C II, C IIIp-s4, 3, 2 8O Ip-s4 11Na Is-p1 12Mg I, Mg IIs-p2, 1 13Al II, Al IIIs-p2, 1 14Si II, Si IVp-s3, 1 16S IIs-p4 20Ca IIs-p1 22Ti IIs-p, d-p3 24Cr IId-p5 25Mn IIs-p, d-p1 26Fe IIs-p, d-p7 28Ni IId-p9 30Zn IIs-p1 1 N ve – number of valence electrons

Fine structure unomalies and level crossing Energies of “normal” fine structure doublets as functions of  2 0 (  0 ) 2 1  E=A(Z  ) 2

Fine structure unomalies and level crossing Energies of strongly interacting states as functions of  2 0 (  0 ) 2 1  E=A(Z  ) 2 1D21D2 3 P 0,1, 2

Implications to study of  variation Not every fine structure interval can be used in the analysis based on formula  E=A(Z  ) 2 (not good!). Strong enhancement is possible (good, but for atomic clocks only). Level crossing may lead to instability of calculations (bad!).

Problem: level pseudo crossing Energy levels of Ni II as functions of  2 0 (  0 ) 2 1 Values of q=dE/d  2 are sensitive to the position of level crossing

Pb II: g-factors don’t help Two 3 D 3/2 states are strongly mixed, but g-factors do not depend on mixing. Energy levels of Pb II as functions of  2 0 (  0 ) 2 1 Solution: perform calculations with extremely high accuracy. 2 D 5/ 2 2 D 3/2 2 S 1/2 2 D 5/2 2 D 3/2 4 P 5/2 4 P 3/2 4 P 1/2

Microwave transitions Hyperfine frequency is sensitive to nuclear magnetic moments (suggested by Karshenboim) We performed atomic, nuclear and QCD calculations of powers k,b for H,D,Rb,Cd+,Cs,Yb+,Hg+ V=C(Ry)(me/Mp)  2+k (mq/LQCD)b, Dw/w=DV/V