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Variation of Fundamental
        Constants
                  Pinghan Chu


             Department of Physics
    Universi...
Dimensionless Constants

In 1937(Nature 139, 323), Dirac pointed out the interest of time-varying fundamental
constants, l...
Variation of Coupling Constants

The variations of EM, weak and strong couplings should be related at high energy.
The inv...
Variation of Fundamental Constants

GUT predicts the variation of QCD scale ΛQCD in terms of variation of α(fine structure
...
Search for Variation of Fundamental Constants

    Deuteron binding energy.
    Quasar Absorption Spectra.
    Oklo natura...
Variation of Deuteron Binding Energy

Deuteron binding, Qnow , is well measured to be 2.22 MeV(25.82 × 109 K) at the
prese...
Variation of Deuteron Binding Energy

Dmitriev et. al. (Phys. Rev. D 69, 063506 (2004)) used big bang nucleosynthesis
calc...
Variation of Deuteron Binding Energy(cont’)

                                                   8




   1σ contour ellips...
Variation of Deuteron Binding Energy (cont’)

   From previous slide, ∆Q/Q = −0.019 ± 0.005. It can be interpreted as
   X...
Optical Spectra

Compare cosmic and laboratory optical spectra to measure the time variation of α.
The relative value of a...
Observations of the Variation of α

Spectroscopic observations of gas clouds seen in absorption against background
quasars...
Observations of the Variation of α
                  α1                                      α2
   P3/2                   ...
Observations of the Variation of α (cont’)

 Webb et al. (Phys.Rev.Lett.82, 884, 1999 and 87, 091301, 2001) report observa...
Oklo Natural Nuclear Reactor

The discovery of the Oklo natural nuclear reactor in Gabon (West Africa) was in 1972.
About ...
Oklo Natural Nuclear Reactor (cont’)

                   Fujii et. al. (Nuclear Physics B, 573, 377 (2000)) showed
       ...
Atomic clocks

Compare rates of different clocks over long period of time. Optical transitions are
related to α and microw...
Summary

Big Bang Nucleosynthesis: may be interpreted as a variation of mq /ΛQCD .
Quasar data : MM method provided sensit...
Conclusion

The experiments and observations mentioned here are related to different time
intervals and there is no reliab...
Parameters of the Standard Model(Variations?)

    There are 19 parameters in SM, determined by experiments.
    Mass of t...
References

E. W. Kolb and M. S. Turner, The Early Universe, Westview Press (1990).
J. P. Kneller and G. C. McLaughlin, Ph...
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Variation of Fundamental Constants

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Variation of Fundamental Constants, alpha and me/mp.

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  1. 1. Variation of Fundamental Constants Pinghan Chu Department of Physics University of Illinois at Urbana-Champaign Sack Lunch Talk, April 5, 2010 Variation of Fundamental Constants – p. 1/2
  2. 2. Dimensionless Constants In 1937(Nature 139, 323), Dirac pointed out the interest of time-varying fundamental constants, like fine structure constant and the mass ratio of the proton to the electron. Many theories suggest that time variation in fundamental constants can be correlated to each others (e.g. Langacker, et. al. Phys. Lett. B, 528, 121(2002)) If these constants were different at early universe than they are today, their relative shifts can only be determined by the underlying theory which causes the changes. For example, in the grand unifies theories, all couplings are correlated to the GUT scale parameter, which varies with time. Since variation of dimensional constants cannot be distinguished from variation of units, it only makes sense to consider variation of dimensionless constants. e2 1 Fine structure constant α = c = 137.036 . me,q me Electron or quark mass/QCD strong interaction scale, ΛQCD ,or mp since mp ∼ 3ΛQCD where me,q are proportional to Higgs vacuum (weak scale). Variation of Fundamental Constants – p. 2/2
  3. 3. Variation of Coupling Constants The variations of EM, weak and strong couplings should be related at high energy. The inverse coupling constants have the following dependence on the scale µ and normalization point µ0 (∼ 3 × 10−16 GeV): α−1 (µ) = α−1 (µ0 ) + bi ln(µ/µ0 ) i i (1) Variation of Fundamental Constants – p. 3/2
  4. 4. Variation of Fundamental Constants GUT predicts the variation of QCD scale ΛQCD in terms of variation of α(fine structure constant): αs (r) ∼ 1/ ln(rΛQCD / c) → δΛQCD /ΛQCD ≈ +34δα/α. (2) The variation of quark mass and electron masses are given by δm/m ∼ +70δα/α, so that δ(m/ΛQCD ) δm δΛQCD δα ∼ − ∼ 35 . (3) (m/ΛQCD ) m ΛQCD α The big coefficient implies the running strong-coupling constant and Higgs constants run faster than α. If these models are correct, the variation of mq /ΛQCD can be searched for experimentally. Variation of Fundamental Constants – p. 4/2
  5. 5. Search for Variation of Fundamental Constants Deuteron binding energy. Quasar Absorption Spectra. Oklo natural nuclear reactor. Atomic clocks (based on atomic and molecular calculations). Variation of Fundamental Constants – p. 5/2
  6. 6. Variation of Deuteron Binding Energy Deuteron binding, Qnow , is well measured to be 2.22 MeV(25.82 × 109 K) at the present time. Deuteron binding energy at the time of big bang necleosynthesis can be deduced from the isotope abundances of D, 4 He, Li, and the baryon to photon ratio η. η has been accurately measured by WMAP, and Yp =4 He/H, YD = D/H and YLi = Li/H have also been well measured. Need model for big bang nucleosynthesis to relate QBBN to η and Yp , YD and YLi . Variation of Fundamental Constants – p. 6/2
  7. 7. Variation of Deuteron Binding Energy Dmitriev et. al. (Phys. Rev. D 69, 063506 (2004)) used big bang nucleosynthesis calculations and light element abundance data to constrain the relative variation of the deuteron binding energy = Q, so that ∆Q = Q(BBN ) − Q(now) . The vertical line shows the present value of Qnow = 25.82 × 109 K. The shaded regions illustrate the 1σ range in the data of the element abundance, Yi . Calculate the light elements abundances as a function of the deuteron binding energy QBBN using ηwmap = 6.14 × 10−10 . Variation of Fundamental Constants – p. 7/2
  8. 8. Variation of Deuteron Binding Energy(cont’) 8 1σ contour ellipse shows the QBBN and η by fitting YD , Yp and YLi . 7 The lighter shaded region shows CMB-WMAP data for ηwmap . Η 1010 6 The darker shaded region is the 1σ-range for η from BBN calculations using the present-day value of the deuturon binding energy, Qnow . 5 Using ηwmap , ∆Q/Q = −0.019±0.005. 4 24 24.5 25 25.5 26 Q 109 K Variation of Fundamental Constants – p. 8/2
  9. 9. Variation of Deuteron Binding Energy (cont’) From previous slide, ∆Q/Q = −0.019 ± 0.005. It can be interpreted as X ≡ ms /ΛQCD of the strange quark mass and strong scale δX/X = (1.1 ± 0.3) × 10−3 . The reason that the deuteron binding energy is sensitive to the strange quark mass are (Flambaum and Shuryak, Phys. Rev. D 67, 083507 (2003) ): there is strong cancellation between σ-meson and ω-meson contributions into nucleon-nucleon interaction (Walecka model), therefore, a minor variation of σ-meson mass leads to a significant change in the strong potential. the σ-meson contains valence s¯ quarks which give large contribution to its mass. s Variation of Fundamental Constants – p. 9/2
  10. 10. Optical Spectra Compare cosmic and laboratory optical spectra to measure the time variation of α. The relative value of any relativistic corrections to atomic transition frequencies is proportional to α2 . The relativistic corrections vary very strongly from atom to atom and can have opposite signs in different transitions. Relativistic many-body calculations are used to reveal the dependence of atomic frequencies on α for a range of atomic species (like Mg, Mg II, Fe II, Cr II, Ni II, Al II, Al III, Si II, Zn II, etc.). The transition frequencies can be presented as ω = ω0 + qx, (4) where x = (α/α0 )2 − 1 and ω0 is a laboratory frequency of a particular transition. Three classes: positive shifters, q > 1000 cm−1 . negative shifters, q < −1000 cm−1 . anchor lines with small values of q. It gives us an excellent control of systematic errors. Variation of Fundamental Constants – p. 10/2
  11. 11. Observations of the Variation of α Spectroscopic observations of gas clouds seen in absorption against background quasars. The alkali doublet method. The fine structure splitting is proportional to α2 . E(p3/2 ) − E(p1/2 ) = A(Zα)2 . (5) Simple but inefficient. It compares transitions with respect to the same ground state. Si IV alkali doublet P3/2 6 1393.8Å P1/2 6 1402.8Å S1/2 Varshalovich et. al.(Astron. Lett., 22, 6(1996)) showed δα/α = (0.2 ± 0.7) × 10−4 and |α/α| < 1.6 × 10−14 yr −1 . ˙ Variation of Fundamental Constants – p. 11/2
  12. 12. Observations of the Variation of α α1 α2 P3/2 P3/2 6 6 P1/2 P1/2 6 6 S1/2 S1/2 The many-multiplet method. It allows the simultaneous use of any combination of transitions from many multiplets, comparing transitions relative to different ground-states. Relativistic correction to electron energy En : En 1 ∆n = (Zα)2 [ − C(Z, j, l)], (6) ν j + 1/2 where C ≈ 0.6 is the contribution of the many-body effect and ν is effective principal quantum number. Compare heavy (Z ≈ 30) and light (Z < 10) atoms, or, compare s → p and d → p transitions in heavy atoms. Shifts can be of opposite sign. Variation of Fundamental Constants – p. 12/2
  13. 13. Observations of the Variation of α (cont’) Webb et al. (Phys.Rev.Lett.82, 884, 1999 and 87, 091301, 2001) report observations of quasar absorption lines at redshift of z = 1 − 2 that suggest the variation of the fine structure constant is at the level of 10−5 . The fit of the data (over 12 billion years) (Mon. Not. R. Astron. Soc. 345, 609, 2003) is δα α ˙ = (−0.543 ± 0.116) × 10−5 and = (6.40 ± 1.35) × 10−16 year −1 . (7) α α Variation of Fundamental Constants – p. 13/2
  14. 14. Oklo Natural Nuclear Reactor The discovery of the Oklo natural nuclear reactor in Gabon (West Africa) was in 1972. About 1.8 billion years ago within a rich vein of uranium ore, the natural reactor went critical, consumed a portion of its fuel and then shut down. Measure the number of atoms per unit volume NA for 149 Sm, 147 Sm, 235 U, etc. The 149 Sm concentrations is due to the yields from the fissions and the effect of neutron captures. Solve the neutron capture cross section of 149 Sm, n +149 Sm →150 Sm + γ by using the observed abundances ratio 149 Sm/235 U, etc. The neutron capture cross section can be described by the Breit-Wigner formula, Γn (E)Γγ σ(E) ∝ g 1 . (8) (E − Er )2 + 4 Γ2 A. I. Shlyakhter (Nature, 264, 5584, 340 (1976)) and Damourb, Dyson (Nuclear Physics B, 480, 37 (1996)) showed that the resonance Er for the neutron capture cross section is sensitive to the value of the fine structure constant (Oklo) (now) ∆ ≡ Er − Er = −|αdEr /dα|(αOklo − αnow )/α so that the final result is α ˙ −6.7 × 10−17 yr −1 < < 5.0 × 10−17 yr −1 . (9) α Variation of Fundamental Constants – p. 14/2
  15. 15. Oklo Natural Nuclear Reactor (cont’) Fujii et. al. (Nuclear Physics B, 573, 377 (2000)) showed (−0.2 ± 0.8) × 10−17 yr −1 < α/α < (4.9 ± 0.4) × 10−17 yr −1 . ˙ Assuming the reactor temperature (200 − 400◦ C), use the measured cross section from the abundance of 149 Sm to estimate ∆Er upper and lower bounds. 200 600 20°C Calculated resonance shift for n + 149Sm n+ 149 Sm Capture Cross Section σ (kb) 100°C 200°C 500 150 300°C ^ 500°C Temperature T (°C) 1000°C 400 100 300 200 50 100 0 0 − 200 − 150 − 100 − 50 0 50 100 150 200 − 20 − 10 0 10 20 Resonance Position Change ∆Er (meV) Resonance Position Change ∆Er (meV) Variation of Fundamental Constants – p. 15/2
  16. 16. Atomic clocks Compare rates of different clocks over long period of time. Optical transitions are related to α and microwave transitions are related to α and mq /ΛQCD . Very narrow lines, high accuracy of measurements. Flexibility to choose lines with larger sensitivity to variation of fundamental constants. Simple interpretation (local time variation). For example, Blatt et. al. (Phys. Rev. Lett. 100, 140801 (2008)) measured (a) [15] (c) 1 S −3 P clock transition frequency in 75 0 0 87 Sr related to the Cs standard. 2.1 Hz neutral [12] [13] [14] They showed the variations are 72 5/06 11/06 5/07 11/07 [18] 85 (b) [15] α ˙ νSr − ν0 (Hz) [13] [14] = (−3.3 ± 3.0) × 10−16 /yr, 75 α [22] [23] [12] 65 [17] Tokyo (10) Paris 55 Boulder 45 1/05 7/05 1/06 7/06 1/07 7/07 1/08 Need detailed atomic, nuclear and QCD Date calculations. Refer to Dinh, et. al.’s work (Phys. Rev. A 79, 054102 (2009)). Variation of Fundamental Constants – p. 16/2
  17. 17. Summary Big Bang Nucleosynthesis: may be interpreted as a variation of mq /ΛQCD . Quasar data : MM method provided sensitivity increase 100 times. Anchors, positive and negative shifters–control of systematics. Oklo : no positive conclusion. Atomic clocks : present time variation of α, mq /ΛQCD . Variation of Fundamental Constants – p. 17/2
  18. 18. Conclusion The experiments and observations mentioned here are related to different time intervals and there is no reliable method for their model-independent comparison. The lab results on optical measurements in terms of the effective rate ∂α/∂t are the most reliable since they are related to optical clocks. A possible variation of the fine structure constant is at the level of 10−15 per year? Variation of Fundamental Constants – p. 18/2
  19. 19. Parameters of the Standard Model(Variations?) There are 19 parameters in SM, determined by experiments. Mass of three leptons, me , mµ , mτ . Mass of six quarks, mu , md , ms , mc , mt , mb . CKM three angle, θ12 , θ23 , θ13 . CKM phase, δ. Three coupling constants, g1 , g2 , g3 . QCD vacuum angle, θQCD . Higgs quadratic coupling µ and Higgs self-coupling strength λ. We only discuss the variation of the coupling constants (fine structure constant) and mass ratio. Is it possible other parameters are also varied? Variation of Fundamental Constants – p. 19/2
  20. 20. References E. W. Kolb and M. S. Turner, The Early Universe, Westview Press (1990). J. P. Kneller and G. C. McLaughlin, Phys.Rev. D68 (2003) 103508. Jean-Philippe Uzan, Rev. Mod. Phys. 75, 403 (2003). S. G. Karshenboim, A. Yu. Nevsky, E. J. Angstmann, V. A. Dzuba and V. V. Flambaum, J.Phys.B.At.Mol.Opt.Phys.39:1937-1944,2006. V. V. Flambaum, AIP Conf.Proc.869:29-36,2006. V. V. Flambaum and V. A. Dzuba, Can. J. Phys. 87, 25-33 (2009). B. Fields, Lecture Notes for Astronomy 596 NPA, Fall 2009. V. V. Flambaum, Variation of Fundamental Constants, Workshop at University of Adelaide, February 2010. Variation of Fundamental Constants – p. 20/2

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