Atomic Precision Tests and Light Scalar Couplings

1. AtomicPrecision Tests and Light ScalarCouplings Philippe Brax IPhTSaclay P.B and C. Burrage , arXiv: 1010.5108 « The Proton Radius Puzzle » Workshop, Trento November 2012

2. Outline 1) Theacceleration of the expansion of the Universe and new forces 2) Screening mechanisms 3) Light scalarfields and atomicprecision tests 4) Compatibility withelectroweakprecision tests 5) BreakingUniversality?

3. The Big Puzzle

4. How do we know? measuring distances ! Absolute luminosity. acceleration parameter: we need large red-shift z Hubble parameter Received flux: what we see in the telescope …

5. Evidence: The Hubble Diagram The explosion of high red-shift SN Ia (standard candles): Within General Relativity, link to matter and dark energy Dark Energy must exist!

6. The Cosmic Microwave Background Fluctuations of the CMB temperature across the sky lead to acoustic peaks and troughs, snapshot of the plasma oscillations at the last scattering surface when the universe became transparent The position of the first peak: The universe is spatially flat WMAP data

7. The acceleration of the Universecouldbe due to either: In both cases, currentmodels use scalarfields. In modifiedgravitymodels, thisis due to the scalar polarisation of a massive graviton. In darkenergy, itis by analogywith inflation. The factthat the scalarfieldacts on cosmologicalscalesimpliesthatits mass must be large compared to solar system scales.

8. Dark Energy Field rolling down a runaway potential, reaching large values now.

9. DeviationsfromNewton’slaw are parametrised by: For fields of zero mass or of the order of the Hubble rate now, the tightestconstraint on β comes from the Cassini probe measuring the Shapiro effect (time delay): The effect of a long range scalarfield must bescreened to complywiththisbound.

10. Around a background configuration and in the presence of matter: The Vainshteinmechanismreduces the coupling in a dense environment by increasing Z The chameleonmechanismmakes the range becomesmaller in a dense environment by increasing m The Damour-Polyakovmechanismreducesβ in a dense environment

11. The effect of the environment When coupled to matter, scalar fields have a matter dependent effective potential Environment dependent minimum The field generated from deep inside is Yukawa suppressed. Only a thin shell radiates outside the body. Hence suppressed scalar contribution to the fifth force.

12. ϕ₊ ϕ₋ For all chameleon, dilaton, symmetronmodelswhereeither the potential and/or the couplingβ is a non-linear function of ϕ, thescreening criterion is simply:

13. Coupling to Photons When the coupling to matterisuniversal, and heavy fermions are integrated out, a photon couplingisinduced(from the top quark for instance)

14. AtomicPrecision Tests Light scalarscoupled to mattercandisplace the atomiclevels due to their interaction with the atomic nucleus. The scalarfieldfeels the presence of the nucleus as a point mass and the electricfieldgenerated by protons. The effective potential for the scalaris: This induces a scalar profile whichinteractwith the electrons or the muons orbitingaround the nucleus: This perturbation gives a shift to the energylevels.

15. In the electricfieldcreated by the nucleus, the scalarfieldsatisfies the Klein-Gordon equation, where the mass is suppose to bemuchsmallerthan the inverse size of the atom: The scalarfieldisthereforeobtained to be : Notice thatitdepends on both the coupling to matter and the coupling to photons. This gives a shift to the atomicenergylevels, to first order in perturbation theory:

16. This gives a shift to the 1s-2s differencedepending on the type of atom. Moreoverthisissignificantlylarger for muons compared to electrons: The contribution to the Lamb shift isalsoproportional to the mass of the fermion:

17. A stringentbound on the mattercouplingcanbededucedfrom the 1s-2s uncertainty, at the 1σ level (of order 1 per biilion): Atomicprecision tests simplyindicatethat if scalars are around, theybelong to beyond the standard model physics.

18. For electronicatomswith Z=1, the Lamb shift ismodified by: For muonicatoms, the shift isgiven by: Fittingwith the proton radius contribution to the Lamb shift: Wefindthat the scalarfieldreduces the proton radius by:

19. Fittingwith the data: The bound on M from the 1s-2s transition impliesthat: Is it compatible withother tests?

20. Coupling to the Standard Model The coupling involves two unknown coupling functions (gauge invariance): At one loop the relevant vertices are:

21. Z-Width Dark energy scalars being very light and coupling to the Z boson may lead to an increase of the Z width (similar to neutrinos). This leads to a weakbound on the photon couplingscalewhich must begreaterthan 60 GeV. Strongerboundsfollowfromprecision tests.

22. The corrected propagator becomes: Measurements at low energy and the Z and W poles imply ten independent quantities. Three have to be fixed experimentally. One is not detectable hence six electroweak parameters: STUVWX

23. The self energy parameters all involve quadratic divergences: For instance: The quadratic divergences cancel in all the precision tests

24. Experimental Constraints mass Inverse Coupling

25. Such a large value leads to an unobservableeffect of the scalar on the proton radius! Such a conclusion has been reached assumingthatmatter couples UNIVERSALLY to the scalarfield This is not necessaryat all!

26. In the standard model of particlephysics, the masses come fromunknownYukawacouplings: The coupling of a scalar to fermions couldfollow a similar pattern and beflavourdependent: The nucleon masses are essentially pure glue (gluons) and depend on the QCD scale:

27. Electronic and muonicatoms have different shifts: This impliesverydifferent conditions on the scales: The muoniccouplingscalewould have to bemuchlowerthan the electronic and photon couplings. This seemsunnaturalalthoughsuchhierarchies are not uncommon in nature. From an effective fieldtheory point of view, one must simplytry to confrontthispossibilitywith more data. From a theoretical point of view, only an embedding of the scalarfield model coupled to the standard model into a more fundamentaltheorycouldexplain a hierarchy of scales.

28. The coupling to photons canbetested in cavityexperimentswhere the Primakoffeffectisatplay: The original Primakoffeffect, creation of a pion as an intermediate state The Primakoffeffect for light scalarsin a staticmagneticfield No constraint for masses greaterthan a fraction of eV

29. The dark energy scale sets a typical scale: Casimir force experimentswill test up to a micron soon, henceapproaching the sensitivity to test the presence of a scalar force

30. Conclusions Scalar interactions couldgenerate the acceleration of the Universe and bescreened in local tests of gravity Theycouldpotentiallylead to a contribution to the muonic Lamb shift Only compatible with data if the new forces are not flavourblind. Other tests: optics, Casimir, Neutron quantum bouncer…