Proceedings of International Conference on Physics in ... - KEK

theory provides a natural explanation why the observed
dark energy is so small without any fine tuning. This predicts
decaying Λ with t −2 as a function <strong>of</strong> the age <strong>of</strong> the
universe t. The present age <strong>of</strong> the universe is t = 10 60 in
Planckian unit. Thus it naturally explains why Λ is 10 −120
at present in the same unit. The uniqueness <strong>of</strong> the theory
from an experimental point view is that it can give us a
testable prediction with the explicit allowed mass and coupling
strength. As a result <strong>of</strong> the theory we expect a scalar
field with mass <strong>of</strong> neV range by allowing a few orders <strong>of</strong>
latitudes which couples to matter via gravitational strength.
In past experiments probing a deviation from Newtonian
potential form, massive and huge bodies were used as a test
probes [5]. However, when they measure the gravitational
effects in a short distance, they must suffer from the background
physical process like Coulomb force. In contrast, if
we could use photon-photon scattering as a probe for such
a new kind <strong>of</strong> force, the experiment would be free from the
background physical process, since the total photon-photon
elastic cross section in the optical energy is only 10 −42 b at
most [6].
However, the biggest issue appears, because the huge
and massive probes were actually demanded to have a sensitivity
to the gravitational coupling strength. Nevertheless,
if we could overcome this drawback to use photons
as the test probe, the method opens up a new window to
probe weakly coupling and low-mass fields (finite long
range force). As long as the field has a finite mass and coupling
to matter, we can directly produce low-mass fields as
resonance states such as higgs particle production in high
energy colliders. The production cross section is in principle
free from the constraints by the weak coupling, if the
center <strong>of</strong> mass system energy Ecms <strong>of</strong> two colliding photons
is adjusted to the top <strong>of</strong> the resonance point. In the
following sections we discuss how to realize the photonphoton
collision system and the sensitivity to the coupling
as weak as gravitational coupling for the mass range well
below optical frequency 1 eV.
QUASI-PARALLEL SYSTEM OF
PHOTON-PHOTON COLLISIONS
If we are interested in extremely low-mass ranges even
below meV, we have to reduce the CMS energy <strong>of</strong> photonphoton
collisions compared to the incident photon energy if
optical laser fields are assumed. As long as the resonance is
allowed to decay into only two photons, the scattering process
looks like elastic scattering even if a low-mass field
is exchanged via the resonance state in CMS. Thus there is
no frequency shift in the final state in CMS. However, if we
boost this system to the direction perpendicular to the colliding
axis, the frequency shift takes place along that boost
axis. In the forward direction on the boost axis we expect a
frequency up shift to close to the double <strong>of</strong> the incident frequency,
while a zero frequency photon must be emitted to
the backward direction due to the energy-momentum conservation
independent <strong>of</strong> the dynamics <strong>of</strong> the exchanged
field. We refer this boosted system as the quasi-parallel
system (QPS). This may be interpreted as if the second harmonic
photon is generated from the nonlinear vacuum response.
This could be an interesting analogy to second harmonic
generation due to the nonlinear response <strong>of</strong> a crystal
with a laser injection which was pioneered by Franken
et al. [7]. Inversely if we realize the QPS as a laboratory
frame, the corresponding CMS energy can be very much
lowered. The CMS energy with variables in QPS can be
defined as
Ecms ∼ 2ϑω, (1)
where ϑ is defined as a half incident angle between two
incoming photons with ϑ ≪ 1 and ω is the beam energy
in unit <strong>of</strong> ¯h = c = 1. This relation indicates that we have
two experimental handles to adjust Ecms. If we take the
head-on collision geometry, we have to introduce very long
wavelength as the incident photons. However, it is not too
difficult to introduce the very small incident angle. In such
a case Ecms can be lowered by keeping ω constant. We
also know that the cross section <strong>of</strong> photo-photon scattering
in QED process σqed in QPS is quite suppressed due to the
fourth power dependence on the incident angle which is
expressed as σqed ∼ (α 2 /m 4 e) 2 ω 6 ϑ 4 with the fine structure
constant α and electron mass me [8]. Therefore, the low
frequency photons in QPS is the best system to probe such
a low-mass field.
QPS BY FOCUSING WITH SINGLE
GAUSSIAN LASER BEAM
However, it is difficult to introduce two colliding photon
beams which satisfy the small incident angle based on the
simple geometrical optics due to the wavy nature <strong>of</strong> photons
in the diffraction limit <strong>of</strong> photons. Below meV range
we are naturally led to introduce a geometry by focusing a
single laser beam as illustrated in Fig.1. What is important
here is that in the diffraction limit there are uncertainties on
the incident momentum due to the uncertainty principle, in
other words, there are uncertainties on the incident angles
between two photons among the single beam, even though
photons are in the degenerated state at the output <strong>of</strong> the
laser crystal. This should be contrasted to the case <strong>of</strong> high
energy collider where the momentum spread <strong>of</strong> each colliding
particle or the uncertainty based on the de Broglie
length is negligibly small compared to the magnitudes <strong>of</strong>
relevant momentum exchanges they are interested in. This
different initial condition becomes critically important for
the following discussions.
DYNAMICS OF PHOTON-PHOTON
SCATTERING
As the simplest coupling between two photons and a
low-mass field we focus on the quantum anomaly type coupling
g 2 /M which includes square <strong>of</strong> electric charge g to
couple virtual fermion loops to two external photons and a
dimensional coupling 1/M to low-mass neutral fields [9].