1. Atomic Precision Tests and Light Scalar Couplings Philippe Brax IPhT Saclay « The Proton Radius Puzzle » Workshop, Trento November 2012 P.B and C. Burrage, arXiv: 1010.5108

2. 1) The acceleration of the expansion of the Universe and new forces 2) Screening mechanisms 3) Light scalar fields and atomic precision tests 4) Compatibility with electroweak precision tests 5) Breaking Universality? Outline

3. The Big Puzzle

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

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 Universe could be due to either: In both cases, current models use scalar fields. In modified gravity models, this is due to the scalar polarisation of a massive graviton. In dark energy, it is by analogy with inflation. The fact that the scalar field acts on cosmological scales implies that its mass must be large compared to solar system scales. ϕ Dark Energy Modified Gravity

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

9. Deviations from Newton’s law are parametrised by: For fields of zero mass or of the order of the Hubble rate now, the tightest constraint on β comes from the Cassini probe measuring the Shapiro effect (time delay): The effect of a long range scalar field must be screened to comply with this bound.

10. The Vainshtein mechanism reduces the coupling in a dense environment by increasing Z The chameleon mechanism makes the range become smaller in a dense environment by increasing m The Damour-Polyakov mechanism reduces β in a dense environment Around a background configuration and in the presence of matter:

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₋ ϕ₊ϕ₊ For all chameleon, dilaton, symmetron models where either the potential and/or the coupling β is a non-linear function of ϕ, the screening criterion is simply:

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

14. Light scalars coupled to matter can displace the atomic levels due to their interaction with the atomic nucleus. The scalar field feels the presence of the nucleus as a point mass and the electric field generated by protons. The effective potential for the scalar is: This induces a scalar profile which interact with the electrons or the muons orbiting around the nucleus: This perturbation gives a shift to the energy levels. Atomic Precision Tests

15. In the electric field created by the nucleus, the scalar field satisfies the Klein-Gordon equation, where the mass is suppose to be much smaller than the inverse size of the atom: The scalar field is therefore obtained to be : Notice that it depends on both the coupling to matter and the coupling to photons. This gives a shift to the atomic energy levels, to first order in perturbation theory:

16. This gives a shift to the 1s-2s difference depending on the type of atom. Moreover this is significantly larger for muons compared to electrons: The contribution to the Lamb shift is also proportional to the mass of the fermion:

17. A stringent bound on the matter coupling can be deduced from the 1s-2s uncertainty, at the 1σ level (of order 1 per biilion): Atomic precision tests simply indicate that if scalars are around, they belong to beyond the standard model physics.

18. For electronic atoms with Z=1, the Lamb shift is modified by: For muonic atoms, the shift is given by: Fitting with the proton radius contribution to the Lamb shift: We find that the scalar field reduces the proton radius by:

19. Fitting with the data: The bound on M from the 1s-2s transition implies that: Is it compatible with other 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 weak bound on the photon coupling scale which must be greater than 60 GeV. Stronger bounds follow from precision 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 unobservable effect of the scalar on the proton radius! Such a conclusion has been reached assuming that matter couples UNIVERSALLY to the scalar field This is not necessary at all!

26. In the standard model of particle physics, the masses come from unknown Yukawa couplings: The coupling of a scalar to fermions could follow a similar pattern and be flavour dependent: The nucleon masses are essentially pure glue (gluons) and depend on the QCD scale:

27. Electronic and muonic atoms have different shifts: This implies very different conditions on the scales: The muonic coupling scale would have to be much lower than the electronic and photon couplings. This seems unnatural although such hierarchies are not uncommon in nature. From an effective field theory point of view, one must simply try to confront this possibility with more data. From a theoretical point of view, only an embedding of the scalar field model coupled to the standard model into a more fundamental theory could explain a hierarchy of scales.

28. The coupling to photons can be tested in cavity experiments where the Primakoff effect is at play: The original Primakoff effect, creation of a pion as an intermediate state The Primakoff effect for light scalars in a static magnetic field No constraint for masses greater than a fraction of eV

29. The dark energy scale sets a typical scale: Casimir force experiments will test up to a micron soon, hence approaching the sensitivity to test the presence of a scalar force

30. Scalar interactions could generate the acceleration of the Universe and be screened in local tests of gravity They could potentially lead to a contribution to the muonic Lamb shift Only compatible with data if the new forces are not flavour blind. Other tests: optics, Casimir, Neutron quantum bouncer… Conclusions