Atomic - PowerPoint Presentation

Slide1

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

:

1010.5108Slide2

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?

OutlineSlide3

The Big PuzzleSlide4

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 zSlide5

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!Slide6

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 dataSlide7

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. Slide8

Dark Energy

Field rolling down a runaway potential, reaching large values

now.Slide9

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. Slide10

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

:Slide11

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.Slide12

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:Slide13

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)Slide14

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

TestsSlide15

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: Slide16

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:Slide17

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

. Slide18

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:Slide19

Fitting with the data:

The

bound on M from the 1s-2s transition

implies

that

:

Is

it compatible with other tests?Slide20

Coupling to the Standard Model

The coupling involves two unknown coupling functions (gauge invariance):

At one loop the relevant vertices are: Slide21

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.Slide22

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:

STUVWXSlide23

The self energy parameters all involve quadratic divergences:

For instance:

The quadratic divergences cancel in

all

the precision testsSlide24

Experimental Constraints

mass

Inverse CouplingSlide25

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! Slide26

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:Slide27

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

. Slide28

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 eVSlide29

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 forceSlide30

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 shiftOnly compatible with data if the new forces are not flavour

blind. Other tests: optics

, Casimir, Neutron quantum

bouncer

…

Conclusions