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

This is listed in Tab.1. The effect is sizable in ILC and is
dominant in colliders above a few TeV.
An example <strong>of</strong> the luminosity spectrum under strong
beamstrahlung is shown in Fig.1. It shows an extreme
case <strong>of</strong> a plasma collider. The peak at low energies comes
from the energy loss by multiple beamstrahlung. The spectrum
for ILC is by far clearly dominated by the high-energy
peak.
Figure 1: An extreme example <strong>of</strong> luminosity spectrum under
beamstrahlung and coherent pair creation. The parameter
Plasma1 is used.
COHERENT PAIR CREATION
When a high-energy photon (beamstrahlung in our case)
travels in an intense electromagnetic field, it can decay into
electron-positron pairs. The one that has the same sign <strong>of</strong>
charge as the oncoming beam is defected by a large angle
due to the Coulomb field and causes serious backgrounds
to the detector. The relevant Lorentz invariant quantity is
χ ≡ e
m3
(k µ Fµν) 2 = ω
m
B
B Sch
where kµ is the 4-momentum <strong>of</strong> the photon and ω its energy.
When Υ is O(1), χ can also be O(1). The beamstrahlung
and coherent pair creation come from the same
diagram seen in different channels as shown in Fig.2.
The spectrum (energy distribution <strong>of</strong> the pair particles)
is given by[3]
dW CP
dE+
= α m
√
3π
2
ω2 ∞
η
K1/3(η ′ )dη ′
E−
+
η = 2
3χ
ω 2
E+E−
+
E+
E+
E−
(5)
K2/3(η)
, E− = ω − E+, (6)
where α is the fine structure constant, E+(E−) the final
positron (electron) energy, Kν the modified Bessel function.
This spectrum (normalized to unity) is plotted in Fig.3
for various values <strong>of</strong> χ.
Figure 2: Beamstrahlung and Coherent Pair Creation. The
double solid line indicates electron in an external field.
Figure 3: Spectrum <strong>of</strong> the coherent pair creation.
There is another process, sometimes called ‘trident cascade’,
<strong>of</strong> creating pairs. The virtual photon associated with
an electron can create pairs under a strong field. This process
has been studied in early 1970’s[4]. When Υ is very
large (e.g., > 1000), the contribution <strong>of</strong> this process may
be even larger than the combination <strong>of</strong> beamstrahlung and
coherent pair creation.
Early studies on beamstrahlung and coherent pair creation
are reviewed in[5].
BEAM-BEAM DEPOLARIZATION
It is relatively easy to obtain polarized beams in linear
colliders than in ring colliders. The most important
source <strong>of</strong> depolarization comes from beam-beam interaction.
There are two mechanisms that causes depolarization,
namely the precession in magnetic field and the spin-flip
synchrotron radiation. Both <strong>of</strong> these processes are wellknown
except the correction <strong>of</strong> the precession formula under
strong field.
The relevant terms in the Thomas-BMT equation is
dS
dt
= e
mγ (γa + 1)B T × S (7)
where S is the spin vector (in the rest frame), B T the transverse
component <strong>of</strong> the magnetic field and a the coefficient
<strong>of</strong> the anomalous magnetic moment.