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Variation of Fundamental Constants from Big Bang to Atomic Clocks

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### 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

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.

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

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)

Quasar absorption spectra

Gas cloud

Quasar

Earth

Light

One needs to know E(a2) for each line to do the fitting

a

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).

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.

Fine structure anomalies and level crossing

Energies of “normal” fine structure triplets as functions ofa2

DE=A(Za)2

0 (a/a0)2 1

Problem: level pseudo crossing

Values ofq=dE/da2are sensitive to the position of level crossing

Energy levels of Ni II as functions ofa2

Solution:matching experimental g-factors

0 (a/a0)2 1

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!

= + (α2/α02 – 1)

ω0

q

Laboratory

Measurements

(London, NIST, Lund, etc.)

w0

Analysis (J.Webb, M.Murphy, et al.)

Atomic

Calculations

(V.A. Dzuba,

V.V. Flambaum, et al.)

Quasar

Observations

(Keck, VLT)

w

q

Da

Results of the analysis

- Murphy et al, 2003: Kecktelescope,143 systems, 23 lines, 0.2<z<4.2

Da/a=-0.543(116) x 10-5

- Quast et al, 2004: VLT telescope, 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: VLT 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?

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)

Variation of strong interaction

Grand unification models (Marciano; Calmet,

Fritzch;Langecker,Segre Strasser;Dent)

D(m/LQCD)/(m/LQCD)=35Da/a

- Proton mass Mp=3LQCD , measure me/Mp
- Nuclear magnetic moments m=g eh/4Mpc

g=g(mq/ LQCD)

3. Nuclear energy levels

Dependence on quark mass

- Dimensionless parameter is mq/LQCD . It is convenient to assume LQCD =const, i.e. measure mq in units of LQCD
- mp is proportional to (mqLQCD)1/2 Dmp/mp=0.5Dmq/mq
- Other meson and nucleon masses remains finite for mq=0. Dm/m=K Dmq/mq

Coefficients K are calculated for p,n,r,w,s.

Nuclear magnetic moments depends on p-meson mass mp

Nucleonmagnetic moment

p

n

p

p

Spin-spininteraction

between valence and

core nucleons

p

n

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 me / Mp or me / LQCD

- 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=a2 gpme / Mp

DX/X=1.17(1.01)10-5 No variation

- Reinhold,Bunnin,Hollenstein,Ivanchik,

Petitjean PRL 2006 , H2 molecule, 2 systems

D(me / Mp )/ (me / Mp)=-2.4(0.6)10-5 Variation 4 s !

Systematics or space-time variation?

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 alpha

Flambaum, Shuryak PRD 2003

DEr = 170 MeV DX/X + 1 MeV Da/a

X=ms/ LQCD , enhancement 170 MeV/0.1 eV=1.7x109

Lamoreax,Torgerson PRD(2004) DEr =-0.58(5) eV

DX/X=-0.34(3) 10-9 two billion years ago

Atomic clocks

Cesium primary frequency standard:

F=4

F=3

HFS of 6s:

n = 9 192 631 770 Hz

Also: Rb, Cd+, Ba+, Yb+, Hg+, etc.

E.g. n(Hg+) = 40 507 347 996.841 59(14)(41) Hz

(D. J. Berkeland et al, 1998).

Optical frequency standards:

Also: H, Al+, Sr, Ba+, Yb, Hg, Hg+, Tl+, Ra+,etc.

Accuracy about 10-15 can be further improved to 10-18!

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

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).

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 ,b for H,D,Rb,Cd+,Cs,Yb+,Hg+

V=C(Ry)(me/Mp)a2+k(mq/LQCD)b , Dw/w=DV/V

Results for variation of fundamental constants

aassuming mq/LQCD = Const

Combined results: d/dt lna= -0.9(2.9) x 10-15 yr-1

d/dt ln(mq/LQCD) = ...10-15 yr-1

me /Mp or me/LQCD …10-15yr -1

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 (Budker et al, Berkeley)

|dlna/dt| < 4.3 x 10-15 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.

w0 =Erotational -E hyperfine= E hyperfine /100-1000

Enhancement factorK = 102 -103,

Dw/w0 =KDa/a

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

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

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=me/Mp

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

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.

Alkali Doublet Method(Varshalovich, Potekhin, Ivanchik, et al)

Fine structure interval

DFS = E(p3/2) - E(p1/2) = A(Za)2

If DZ is observed at red shift Z and D0 is FS measured on Earth then

Ivanchik et al, 1999: Da/a = -3.3(6.5)(8) x 10-5.

Murphy et al, 2001: Da/a = -0.5(1.3)x 10-5.

Many Multiplet Method(Flambaum, Webb, Murphy, et al)

p3/2

p3/2

p1/2

p1/2

dw >> dDFS !

w

w

s1/2

s1/2

a1

a2

- Advantages:
- Order of magnitude gain in sensitivity
- Statistical: all lines are suitable for analysis
- Many opportunities to study systematic errors

Atoms of interest

1Nve– number of valence electrons

Fine structure unomalies and level crossing

Energies of “normal” fine structure doublets as functions ofa2

DE=A(Za)2

0 (a/a0)2 1

Fine structure unomalies and level crossing

Energies of strongly interacting states as functions ofa2

DE=A(Za)2

1D2

3P0,1,2

0 (a/a0)2 1

Implications to study of a variation

- Not every fine structure interval can be used in the analysis based on formulaDE=A(Za)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 ofa2

Values ofq=dE/da2are sensitive to the position of level crossing

0 (a/a0)2 1

Pb II: g-factors don’t help

Two 3D3/2 states are strongly mixed, but g-factors do not depend on mixing.

Energy levels of Pb II as functions ofa2

2D3/2

2D5/2

2D3/2

2D5/2

2S1/2

Solution:perform calculations with extremely high accuracy.

4P1/2

4P5/2

4P3/2

0 (a/a0)2 1

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)a2+k (mq/LQCD)b , Dw/w=DV/V

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