Precision Tests and Light Scalar Couplings Philippe Brax IPhT S aclay The Proton Radius Puzzle Workshop Trento November 2012 PB and C Burrage arXiv 10105108 ID: 250708
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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