Time dependence of SMparameters

Outline

• Dirac´s hypothesis

• SM parameters

• Experimental access to time dependence

laboratory measurements

Quasar absorption spectra

Oklo natural nuclear reactor

Big-Bang Nucleosynthesis

Dirac´s hypothesis

1937 after the publication of Hubble´s law. Dirac was convinced that “relativity will play only a subsidiaryrole in the subject of cosmology”

• Extrapolating Hubble´s law he concluded that the universe is some Ga old.• Searching for a new fundamental law he tried to connect cosmology with Atomic theory

Constructed out of atomic “constants” and cosmological quantities somethingwith Unit time and divided with Hubble constant to make it dimensionless again:

Dirac´s hypothesis

•relative strength of electric to gravitational force:

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c 3m

e2H≈1040

•Size of Universe compared to an electron:

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e2

G ⋅M ⋅m≈1040

•Number of particles in the universe:

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c 3

2G ⋅M ⋅H≈1080

Dirac´s hypothesisIf this are fundamental relations and for examplethe ratio

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c 4H

c 3G ⋅M ⋅mwhich is nowadays of order one is constant.

With:

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H ∝1/ t ⇒ Some of other constants not constant

For example:

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G∝1/ t

Standard model parameters

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α

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MW ,MZ

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mqi Quark masses

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mLi Lepton masses

+ Other parameters related to Symmetry breakingStrong Coupling, CKM Matrix, etc.

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ΛQCD,mP

Electroweak coupling

SM parametersIn principle different couplings can vary differently with time• But GUT theories offer connection between couplings:

SM MSSM

Experimental access to time dependence

The shorter the observed time scale is, the moreaccurate the measurement has to be!

Laboratory experiments (a)

Oklo (1Ga)

QSO (5Ga)

BBN (16Ga)

Laboratory experimentsFrequency of atomic clocks depends on alpha.But different clocks -> different alpha dependence:

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Rb87

00.15

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Cs133

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Rb87

today:

next year:00.16

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Cs133

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⇒α•

α=(4.2 ± 6.9) ⋅10−15 yr−1

Oklo

Natural nuclear fission reactor in West Afrika.Uranium composition indicates that it was active 1.7 Ga ago, using surface and groundwaters to moderate and reflect neutrons

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238U + n→239U→239Np+ β→235U +α

Absence of indicates that stopped at least 0.1 Ga ago

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236U(t1/ 2 = 2.3⋅107a)

Oklo

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n+149Sm→150Sm + γ

The Oklo abundance of is lower than what is foundelsewhere, which is due to neutron capture.

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149Sm

Capture cross-section depends on alpha (very narrow peak)and other constants.

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−6.7 ⋅10−171/a <α•

α< 5 ⋅10−171/a

-Shlyakhther-Damour, Dyson

QSO ConstraintsQSO (Quasi stellar object) is a extremely large blackhole in centre of galaxies. • When matter falls in light of all wavelengths is emitted• So brilliant, that can be observed at large distances• On way to earth light passes through absorbing gas clouds

Study fine structure splitting:

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E1 = E(S1/ 2 → P1/ 2)

E2 = E(S1/ 2 → P3 / 2)

ΔE = E1 − E2 ∝ Enα2

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⇒δλλ

∝α 2

QSO constraints

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δλ0

λ 0

∝α 02

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→δλz

λ z

∝α z2

Red shift

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α02 −α z

2 ∝δλ 0

λ 0

−δλ z

λ z

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α02 −α z

2

α 02 =

δλ 0 /λ 0

δλ z /λ z

−1

with

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α z =α 0 + Δα

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Δαα0

≈ 0.5(δλ 0 /λ 0

δλ z /λ z

−1)

= (−4.6 ± 4.3stat ±1.4syst) ⋅10−5

QSO constraints

More sophisticated analysis taking into account• Many electron effects• different transition lines like spin orbit coupling• different elements for line fitting (Mg, Al, Fe ...)• and statistics from 49 Quasar absorption systems...

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Δαα0

= (−0.72 ± 0.18) ⋅10−5

for 0.5<z<3.5

Murphy et al.Webb et al.

QSO constraints

BBN(Big-Bang Nucleosynthesis)

Question: “Where do heavy nuclei come from?”

• 1942 Gamow idea taking BBN as origin for heavy nuclei• 1957 Hoyle, Margaret, Burbidge, Fowler show that all elements beyond 4He can be made by stars• 1964 Hoyle and Tayler show abundance of 4He (around 25%) and suggest BBN• Several models follow until• around 1982 all primordial abundances of all four light elements are predicted in agreement with measurement by hot big-bang model.

BBN

Light elements that had to be explained are:

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D,3He,4He,7Li

• BBN takes place in non equilibrium during a few minutes in an expanding, radiation- dominated plasma.• Compare stellar nucleosynthesis takes place over billions of years• Assume general relativity, standard model -> dozen of cross sections -> calculate

(All astrophysical processes except BBN destroy D)

BBN

Statistical equilibrium->

formation oflight nuclei

Coulomb barriers and stability gaps at masses five and eight work against formation of larger nuclei

BBN

yields of primordial nucleosynthesis with 2 sigmatheoretical errors as function of baryon density:

BBNFurther implications from BBN:

(More neutrinos -> more 4He produced)

BBNBack to variation of SM parameters:

• Concordance of BBN rests on balance between

interaction rate and expansions rate

• Gives constraints on variation of almost all participating

parameters like:

-Particle types

-Particle masses

-Particle interactions

BBN

Especially D production rates seem to be very sensitiveto the change of this gives bounds on:

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W = ms /ΛQCD

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δW /W < 0.006

But this is strongly dependent on the used (simplified)model

Flambaum,Shuryak

Beane and Savage worked with an effective field theory (without s-quarks) and could not derive bounds on change of quark mass ratios.

Summary

Time dependence of fundamental constantsis still a riddle for theorists and a task forexperimentalists.

Time will reveal the existence oftime dependence. .