Variation ofFundamental Constants from Big Bang to Atomic

Clocks V.V. Flambaum

School of Physics, UNSW, Sydney, AustraliaCo-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.CurranQuasar 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?

|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 e2/hc• Electron or quark mass/QCD strong interaction

scale, me,q/QCD

strong (r)=const/ln(r QCD /ch)

Variation of fine structure constant

Quasar absorption spectra

Earth QuasarGas cloud

Light

Quasar absorption spectra

Earth QuasarGas 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(2/02)

q is found by varying in computer codes:

q = d/dx = [(0.1)(0.1)]/0.2, x=2/02

=e2/hc=0corresponds to non-relativistic limit (infinite c).

Methods of Atomic CalculationsNve Relativistic Hartree-Fock + Accuracy

1 All-orders sum of dominating diagrams

0.1-1%

2-6 Configuration Interaction + Many-Body Perturbation Theory

1-10%

2-15 Configuration Interaction 10-20%

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 35051.217 86

Mg II 35760.848 211

Mg II 35669.298 120

Si II 55309.3365 520

Si II 65500.4492 50

Al II 59851.924 270

Al III 53916.540 464

Al III 53682.880 216

Ni II 58493.071 -20

Atom q

Ni II 57420.013 -1400

Ni II 57080.373 -700

Cr II 48632.055 -1110

Cr II 48491.053 -1280

Cr II 48398.862 -1360

Fe II 62171.625 -1300

Atom q

Fe II 62065.528 1100

Fe II 42658.2404 1210

Fe II 42114.8329 1590

Fe II 41968.0642 1460

Fe II 38660.0494 1490

Fe II 38458.9871 1330

Zn II 49355.002 2490

Zn II 48841.077 1584

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)

p

/35

/

1. Proton mass M 3 , measure /

2. Nuclear magnetic moments

/ 4 , /

3.Nuclear energy levels and resonances

QCD

QCD

QCD e p

p q QCD

m

m

m M

g e M c g g m

Nucleon magnetic moment

0 0(1 ...) (1 ...)qam b m Nucleon and meson masses

0 qM M am QCD calculations: lattice, chiral perturbation

theory,cloudy bag model, Dyson-Schwinger and

Faddeev equations, semiempirical.

Nuclear calculations: meson exchange theory of

strong interaction.

Measurements me / Mp or me / QCD

• Tsanavaris,Webb,Murphy,Flambaum,Curran 2005Hyperfine H/optical Mg,Fe,… , 8 quasar systems

X=2 gp me / Mp

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

• Reinhold,Bunnin,Hollenstein,Ivanchik,Petitjean

2006 , H2 molecule, 2 systems

(me / Mp )/ (me / Mp)=-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 byEr =0.1 eV resonanceShlyakhter;Damour,Dyson;Fujii et al Limits on variation of

Flambaum, Shuryak 2003 Er = 170 MeV X/X + 1 MeV X=ms/ QCD , enhancement 170 MeV/0.1 eV=1.7x109

Lamoreaux,Torgerson 2004 Er =-0.58(5) eV

X/X=-0.34(3) 10-9 two billion years ago2006 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: , (me, mq )/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)(me/Mp)2+ (mq/QCDV/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

Source Clock1/Clock2 d/dt/(10-15 yr-1)

Marion et al, 2003 Rb(hfs)/Cs(hfs) 0.05(1.3)a

Bize et al, 2003 Hg+(opt)/Cs(hfs) -0.03(1.2)a

Fisher et al, 2004 H(opt)/Cs(hfs) -1.1(2.3)a

Peik et al, 2004 Yb+(opt)/Cs(hfs) -0.2(2.0)

Bize et al, 2004 Rb(hfs)/Cs(hfs) 0.1(1)a

aassuming mq/QCD = Const

Combined results: d/dt ln 0.3(2.0) x 10-15 yr-1

d/dt ln(mq/QCD) -0.4(4.5) x10-14 yr-1 me /Mp or me/QCD 3(6)x10-15

yr -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 = 10-4 cm-1

Enhancement factor K = 108 (!), i.e.

Preliminary result (Berkeley,Los Alamos)

dln/dt =-2.9(2.6)x 10-15 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 10-4 Hz

PRL 2006

Nuclear/QCD calculation: Enhancement 105 -106,

105 Xq/Xq-10Xs/Xs )

Xq=mq/ QCD , Xs=ms/ QCD

235 U energy 76 eV, width 6 10-4 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.

• me /Mp : hyperfine H/optical – no variation, H2 - variation 4 . Space-time variation? Grand Unification model?

• Big Bang Nucleosynthesis: may be interpreted as variation of ms/ QCD (4 ?

• Oklo: variation of ms/ QCD (11 not confirmed, <10 -9• Atomic clocks: present time variation of , mq/ 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 nucleonsZ

e e

n n

H G2

C1pe 5ep pC1ne 5en n

• In atom with Z electrons and N neutrons obtain effective Hamiltonian parameterized by “nuclear weak charge” QW

C1p 12 1 4 sin2W ; C1n 1

2Standard model tree-level couplings:

hPV G2 2

QW(r)5

QW 2(NC1n ZC1p ) N Z(1 4 sin2W ) N

• APV amplitude EPV Z3 [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):

ha eA a

I (r) , a A2 3

[Flambaum,Khriplovich,Sushkov]

EPV Z2 A2/3 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.• 105 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.• 103 enhancement in Ra atom due to close opposite

parity state.

Atomic electric dipole moments• Electric dipole moments violate

parity (P) and time-reversal (T)

d

r

J

• T-violation CP-violation by CPT theorem

CP violation• Observed in K0, B0

• 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 suppressedTheories that go beyond the SM predict EDMs that are many orders

of magnitude larger!

Theory de (e cm)

Std. Mdl. < 10-38

SUSY 10-28 - 10-26

Multi-Higgs 10-28 - 10-26

Left-right 10-28 - 10-26

• Atomic EDMs datom Z2 , Z3 [Sandars]

Sensitive probe of physics beyond the Standard Model!

Best limit (90% c.l.): |de| < 1.6 10-27 e cm Berkeley (2002)

e.g. electron EDM [Commins ]

Atomic calculationsWe calculate:

EPV (1 2)2 HPV N N Dz 1

E2 EN

2 Dz N N HPV 1

E1 EN

N

• APV

• Atomic EDM

datom (1)21 Dz N N HPT 1

E1 ENN

PT

2

HPT 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 1999New 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

∑ = +

VHF VHF

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:

Electric field in cesium

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

1.0E-6 1.0E-4 1.0E-2 1.0E+0 1.0E+2

Radius (a.u.)

Ele

ctri

c fi

eld

(E

tot /E

ext )

Cesium APV

QW QWSM 0.9

Tightly constrains possible new physics, e.g. mass of extra Z boson MZ’ 750 GeV

EPV 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, EPV =W xE1/(Es-Ep)

[Flambaum,Ginges; Shabaev,Pachuki,Tupitsyn,Yerokhin]

7S

6S

• Best measurement [Boulder,1997]

-Im(EPV)/ = 1.5935(10.35%) mV/cm

• Best calculation [Dzuba,Flambaum,Ginges]

EPV = -0.897(10.5%)10-11 ieaB(-QW/N)

Enhancement of electron electric dipole moment

• Due to mixing of atomic levels of opposite parity electron EDM is enhanced in heavy atoms Z3times. Tl atom: d=-600 de

Measurements in Berkeley.

• Diatomic molecules : additional enhancement due to mixing of molecular rotational levels, d can reach 107 - 1010 de

YbF (London), PbO (Yale)

Screening of nuclear EDM.

• Nuclear EDM is screened by electrons (Schiff theorem). Explanation: external electric field E0does not accelerate neutral atom. Therefore, nucleus is at rest. Thus, total elecric field acting on nucleus Et=E0+Eelectron=0

Nuclear EDM has zero interaction with electric field, dN Et=0. Impossible to measure.

The Schiff theorem is violated by finite nuclear size. Nuclear and atomic calculations:

d(199Hg)=4x10-25 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

225 199

electronic enhancement nuclear enhancement[Dzuba,Flambaum,Ginges,Kozlov] [Auerbach,Flambaum,Spevak]

( Ra) / ( Hg) 3 200 d d

• Enhancement for EDM and APV in metastable states due to presence of close opposite parity levels

[Flambaum; Dzuba,Flambaum,Ginges]

d(3D2) 105 d(Hg)

EPV(1S0-3D1,2) 100 EPV(Cs)Anapole 1000• Measurements in preparation at

- Argonne National Laboratory, Chicago, USA

- Kernfysisch Versneller Instituut, Groningen, The Netherlands,

-Rn: TRIUMF (Canada)-University of Michigan

7s2 1S0

3D23P1

E=5 cm-1

3D1

3P0

7s6p7s6d

EPV(QW)EPV(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