1	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
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
4	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 a=e²/hc=1/137.036 Electron or quark mass/QCD strong interaction scale, m_e,q/L_QCD a_strong(r)=const/ln(r L_QCD /ch)
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7	Quasar absorption spectra
8	Quasar absorption spectra
9	"Use atomic calculations to find..." Use atomic calculations to find w(a). For a close to a₀ w = w₀+ q(a²/a₀²-1) q is found by varying a in computer codes: q = dw/dx = [w(0.1)-w(-0.1)]/0.2, x=a²/a₀²-1
10	Methods of Atomic Calculations
11	Fine structure anomalies and level crossing
12	Problem: level pseudo crossing Values of q=dE/da² are sensitive to the position of level crossing
13	Results of calculations (in cm^-1)
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17	Results of the analysis Murphy et al, 2003: Keck telescope, 143 systems, 23 lines, 0.2<z<4.2 Da/a=-0.543(116) x 10^-5
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19	Spatial variation (C.L.Steinhardt) 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)
20	Variation of strong interaction Grand unification models (Marciano; Calmet, Fritzch;Langecker,Segre Strasser;Dent) D(m/L_QCD)/(m/L_QCD)=35Da/a Proton mass M_p=3L_QCD, measure m_e/M_p Nuclear magnetic moments m=g eh/4M_pc g=g(m_q/ L_QCD) 3. Nuclear energy levels
21	Dependence on quark mass Dimensionless parameter is m_q/L_QCD . It is convenient to assume L_QCD=const, i.e. measure m_qin units of L_QCD m_pis proportional to (m_qL_QCD)^1/2 Dm_p/m_p=0.5Dm_q/m_q Other meson and nucleon masses remains finite for m_q=0. Dm/m=K Dm_q/m_q Coefficients K are calculated for p,n,r,w,s.
22	Nuclear magnetic moments depends on p-meson mass m_p
23	"Nucleon magnetic moment" Nucleon magnetic moment
24	Measurements m_e / M_por m_e / L_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=a²g_pm_e / M_p DX/X=1.17(1.01)10^-5No variation Reinhold,Bunnin,Hollenstein,Ivanchik, Petitjean PRL 2006 , H₂molecule, 2 systems D(m_e / M_p )/ (m_e / M_p)=-2.4(0.6)10^-5Variation 4 s ! Systematics or space-time variation?
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29	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 DE_r= 170 MeV DX/X + 1 MeV Da/a X=m_s/ L_QCD, enhancement 170 MeV/0.1 eV=1.7x10⁹ Lamoreax,Torgerson PRD(2004) DE_r=-0.58(5) eV DX/X=-0.34(3) 10^-9two billion years ago
30	Atomic clocks Cesium primary frequency standard:
31	Optical frequency standards:
32	Atomic clocks: Comparing rates of different clocks over long period of time can be used to study time variation of fundamental constants!
33	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).
34	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 k ,b for H,D,Rb,Cd⁺,Cs,Yb⁺,Hg⁺ V=C(Ry)(m_e/M_p)a²⁺^k(m_q/L_QCD)^b , Dw/w=DV/V
35	Results for variation of fundamental constants
36	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 factor K = 10⁸ (!), i.e. Dw/w₀= 10⁸Da/a
37	Molecular clocks Cancellations between rotational and hyperfine intervals in very narrow microwave transitions in LaS, LaO, LuS,LuO, etc. w₀=E_rotational-E_hyperfine= E_hyperfine/100-1000 Enhancement factor K = 10²-10³, Dw/w₀= KDa/a
38	Nuclear clocks (suggested by Peik,Tamm 2003) Very narrow UV transition between first excited and ground state in ²²⁹Th nucleus Energy 3-5 eV, width 10^-4 Hz Nuclear/QCD calculation: Enhancement 10⁵-10⁶, Dw/w₀= 10⁵(4 Da/a + DX_q/X_q-10DX_s/X_s) X_q=m_q/ L_QCD, X_s=m_s/ L_QCD ²³⁵U energy 76 eV, width 6 10^-4 Hz
39	Ultracold atomic and molecular collisions (in Bose condensate). Cheng Chin, Flambaum PRL 2006 Enhancement near Feshbach resonance. Variation of scattering length a/a=K D X/X , K=10² – 10¹² X=m_e/M_p
40	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. m_e/M_p: hyperfine H/optical – no variation, H₂ - variation 4 s . Undiscovered systematics or space-time variation. Big Bang Nucleosynthesis: may be interpreted as variation of m_s/ L_QCD? Oklo: variation of m_s/ L_QCD? Atomic clocks: present time variation of a , m_s/ L_QCD Transitions between narrow close levels in atoms, molecules and nuclei – huge enhancement!
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42	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, 034502 (2000). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, LNP 570, 564 (2001). J. K. Webb et al , PRL 87, 091301 (2001). V. A. Dzuba, V. V. Flambaum, M. T. Murphy, J, K. Webb, PRA 63, 042509 (2001). M. M. Murphy et al, MNRAS, 327, 1208 (2001). V. A. Dzuba et al, PRA, 66, 022501 (2002). V. A. Dzuba, V. V. Flambaum, M. V. Marchenko, PRA 68, 022506 (2003). E. J. Angstmann, V. A. Dzuba, V. V. Flambaum, PRA 70, 014102 (2004). J. C. Berengat et al, PRA 70, 064101 (2004). M. M. Murphy et al, LNP, 648, 131 (2004). V. A. Dzuba, PRA, 71, 032512 (2005). V. A. Dzuba, V. V. Flambaum, PRA, 71, 052509 (2005). V. A. Dzuba, V. V. Flambaum, PRA, 72, 052514 (2005). V. A. Dzuba, PRA, 71, 062501 (2005). S. G. Karshenboim et al, physics/0511180.
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57	Alkali Doublet Method (Varshalovich, Potekhin, Ivanchik, et al) Fine structure interval D_FS= E(p_3/2) - E(p_1/2) = A(Za)² If D_Z is observed at red shift Z and D₀ is FS measured on Earth then
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82	Text
83	Many Multiplet Method (Flambaum, Webb, Murphy, et al)
84	Atoms of interest
85	Fine structure unomalies and level crossing
86	Fine structure unomalies and level crossing
87	Implications to study of a variation Not every fine structure interval can be used in the analysis based on formula DE=A(Za)² (not good!). Strong enhancement is possible (good, but for atomic clocks only). Level crossing may lead to instability of calculations (bad!).
88	Problem: level pseudo crossing
89	Pb II: g-factors don’t help Two ³D_3/2 states are strongly mixed, but g-factors do not depend on mixing.
90	Microwave transitions