Cherenkov Radiation from Jets in Heavy-ion Collisions Page: 3 of 4
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..p=1.5T ... Im[f(s)]
I \ - - Re[H21(s)
- - --------S
-I -. . .. I
FIG. 2: The real (solid) and imaginary part (dotted) of the
full self-energy and the first two contributions (dashed and
dot-dashed) from Eq. (4).
which approaches the light-cone as (p0, p) is increased.
Even though we have studied a simple scalar theory, the
attraction leading to Cherenkov-like bremsstrahlung has
its origin in resonant scattering. Thus, the result is gen-
uine and only depends on the masses of the bound states
and their excitations.
-I ' * ' I 1 '
o 2 4
e r i
paFI.3:e dispersion relation Toe imainaryheralt aea-m
wihastionalcln to twomastivehn prtclne.Then in-
dAnater esseial isste is. he beaior of te imagi-h
diae damin of 4 th0oe.6 InFi.8 1epo h
real and imaginary parts of the self-energies for values of
(pop) which satisfy the in-medium dispersion relation.
The two sets of curves correspond to the first two sets
of parameters in Fig. 3. One notes that the real part
has only moderate variation in this range of momentum.
) In contrast, the imaginary part seems to rise in magni-
tude. A large imaginary part indicates that the mode
experiences strong damping and will not propagate far
in the medium. However, there seems to exist a range
of soft energies and momenta in the dispersion relation
where the imaginary part is very small allowing the pos-
sibility for long range propagation of Cherenkov-like glu-
ons. Even in the region where the imaginary part is large
and the mode is considerably damped, there could still
be a unique angular distribution of Cherenkov-like gluon
bremsstrahlung  except that the energy of these glu-
ons is absorbed by the medium. The propagation of this
30 energy through the medium can also cause sonic shock
waves, however, with modified Mach cone angles.
0.4 0.6 0.8 1 1.2 1.4
FIG. 4: The real and imaginary parts of II(p ,p) for p ,p
which satisfy the quasi-particle dispersion relation. The
choice of parameters and the legends for the real parts are
the same as in Fig. 3.
Cherenkov-like gluon bremsstrahlung may be observed
as conical structures in two-particle correlations in jets.
Shown in Fig. 5 is the dependence of the Cherenkov an-
gle cos O, = 1/n(p) on the gluon momentum, as deter-
mined from the dispersion relation in Fig. 3. It has a
strong momentum dependence and vanishes quickly at
large gluon momentum as the dispersion relation ap-
proaches the light-cone. Such a momentum dependence
of the emission angle is in contradistinction with that of
a Mach cone, which is independent of the momentum of
the emitted particle.
The normal Cherenkov radiation (without multiple
scattering of the propagating energetic parton) also con-
tributes to the parton energy loss. Adopting the results
obtained for photon Cherenkov radiation  we can es-
timate this energy loss by
dE fn [ 4
4r,, po 1 - ( dpo, (4)
dx J(po)>1 n2(po)
.- . -
- Re(H),m1=1T,m2=3T *.
Im(H),m1=1T,m2=3T .' *
. I . I I I
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Koch, Volker; Majumder, Abhijit & Wang, Xin-Nian. Cherenkov Radiation from Jets in Heavy-ion Collisions, article, July 26, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc884824/m1/3/: accessed May 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.