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

Figure 1: (Left) Time evolution <strong>of</strong> the matter created in high-energy heavy-ion collisions. (Right) Noncentral collisions.
HIGH-ENERGY HEAVY-ION
COLLISIONS
As already mentioned, the main motivation <strong>of</strong> the HIC’s
is to create the QGP, a local equilibrium matter made <strong>of</strong>
quarks and gluons. In order to throw gigantic kinetic energies
into a small but finite volume, we need to collide
‘large’ objects, namely two heavy ions (bare nuclei without
electrons). Thus, the spatial extent <strong>of</strong> the created state
is, initially, <strong>of</strong> the order <strong>of</strong> that <strong>of</strong> colliding nuclei (e.g., for
Au nuclei, about 10 fm = 10 −14 m). If the energy density
is high enough to reach a very high temperature beyond
the critical value Tc ∼ 170 MeV, one can naively expect
that the QGP will be formed. In reality, however, the created
state with high-energy densities will show quite nontrivial
time evolution: It will quickly change into a hightemperature
QGP through interactions between quarks and
gluons. Then, the QGP will cool down to hadronic matter
as it rapidly expands (see Fig. 1, left). All these processes
take place during a very short time, and the life time <strong>of</strong>
QGP is, at most, <strong>of</strong> the order <strong>of</strong> 10 fm/c = 10 −22 sec.
In order to study the properties <strong>of</strong> QGP, we need to extract
information <strong>of</strong> QGP from the huge number <strong>of</strong> final
hadrons. Since particle production can, in principle, occur
at every stage <strong>of</strong> evolution, it is quite important to understand
the evolution history <strong>of</strong> the created matter in HIC’s.
In particular, the formation <strong>of</strong> QGP is one <strong>of</strong> the most difficult
problems in QCD (or maybe in theoretical physics) because
it requires non-perturbative description <strong>of</strong> non-linear
phenomena in non-equilibrium states. However, many people
believe that the strong field dynamics should be relevant
at least for the early time evolution. In fact, as already mentioned,
there emerge two different kinds <strong>of</strong> strong fields in
HIC’s, and the “color” electromagnetic fields are expected
to play important roles for the transition towards QGP. The
strong color electronic and magnetic fields give rise to the
quark-antiquark pair production (Schwinger mechanism)
and Nielsen-Olesen instability, respectively. We expect
both <strong>of</strong> them will contribute to drive the system towards
thermalization. On the other hand, ordinary magnetic fields
indeed have a significant influence on the created matter,
but would be irrelevant for thermalization, because it does
not appear in the central collision.
STRONG MAGNETIC FIELDS IN
NONCENTRAL HEAVY-ION COLLISIONS
How do they appear?
Note that the atomic nuclei used in HIC’s have large
electric charges 1 Ze and they are moving at very fast speed
close to the speed <strong>of</strong> light. Then, the Coulomb field (electric
field) <strong>of</strong> each nucleus is highly Lorentz contracted to a
strong spike. Time variation <strong>of</strong> the electric fields induces
magnetic fields <strong>of</strong> the same strength. For example, consider
a point charge moving on the z axis at rapidity (velocity)
Y . Then, the magnetic field at the position ⃗x is given by
e ⃗ B(⃗x) = Zα EM
−(⃗x⊥ × ⃗ez) sinh Y
[(⃗x⊥) 2 + (t sinh Y − z cosh Y ) 2 ,
3/2
]
which has a large enhancement factor sinh Y . One can
roughly estimate the magnetic field in noncentral HIC’s
(b ̸= 0) by simply summing the magnetic fields given
above assuming the trajectories <strong>of</strong> two colliding nuclei
shown in Fig. 1, right. Then, one finds the maximum
strength √ eB ∼ 100 MeV in noncentral Au-Au collisions
at RHIC ( √ sNN = 200 GeV) 2 when the impact parameter
b ∼ 10 fm [5]. In fact, such a crude estimate is numerically
confirmed by the UrQMD simulation [6]. As already
commented, this is quite a strong magnetic field, beyond 3
the “critical” value √ eBc = me = 0.5 MeV. Since this
magnetic field arises only from the kinematical configuration
<strong>of</strong> two charges, it becomes strongest when two charges
come closest, and decays rapidly as they recede from each
other. Typically, it lasts only for a few fm/c. However, it is
argued that the life time becomes longer in the presence <strong>of</strong>
the QGP, because the QGP has a large electric conductivity
[7]. If this is indeed the case, life time <strong>of</strong> the strong magnetic
field could be <strong>of</strong> the same order <strong>of</strong> that <strong>of</strong> the QGP,
namely, about 10 fm/c.
1 Z = 79 (Au) at RHIC, 82 (Pb) at LHC and we take e > 0.
2 √ sNN is the center-<strong>of</strong>-mass energy per nucleon-nucleon collision.
The total energy <strong>of</strong> the Au-Au collision is A × √ sNN with A = 197
being the mass number <strong>of</strong> Au.
3 It makes sense to discuss the magnetic field beyond the critical value,
because, unlike the electric field, the vacuum does not break down. However,
perturbative calculation ‘breaks down’ because the insertion <strong>of</strong> n
external magnetic fields in Feynman diagrams contributes as (eB/m 2 e )n
which becomes order 1 for B > Bc = m 2 e/e [3].