Modeling hard scattering with LPM effect
H. Zaraket(1),(2)
(1) Laboratoire de Physique et d’´electronique, Lebanese University,
Faculty of Sciences (I), Hadath, Beirut Lebanon
(2) Laboratoire de Physique Subatomique et de Cosmologie, UJF,
CNRS/IN2P3, INPG, 53 avenue des Martyrs, 38026 Grenoble, France
hzaraket@ul.edu.lb
Abstract
We study the possibility of having hard scattering or background field effect besides multiple soft
scattering in nuclear medium or in quark-gluon plasma. The hard process affects the scaling of the
energy loss of a parton with its energy and the medium size.
INTRODUCTION
It is believed that during and after relativistic heavy ion collisions strong chromomagnetic field will form
that can be treated as a classical background. Numerical solutions [1, 2] indicate that ”just” after collision
transverse color electric and color magnetic fields change suddenly from being transverse in the initial
state, in the so-called Color-Glass-Condensate state, to being longitudinal. The latter are called glasma flux
tubes. Transverse fields then rise, and at some stage after the collision the transverse and longitudinal
components of color electric and color magnetic fields reach a ”steady” comparable
values. In this rich environment a fast parton escaping from the collision would feel the effect of such a
field besides multiple scattering. The two mechanisms are expected to be the dominant energy loss
mechanisms. Syncrotron radiation was analyzed for a longitudinal field in [3], and a transverse field in
[4,5] as an energy loss mechanism without coupling it to the radiation energy
loss considered extensively in the literature [6, 7]. It is reasonable to assume a simple factorization between
the two processes. However for a gluon radiation with long formation length it is possible that the strong
field that deviate the particle and multiple scattering from random scattering centers are ”felt” by the
coherent parton-gluon system. This is motivated by a recent work of Peigné et al [8]. The authors in [8]
considered a scenario where the incoming high energy (E) parton undergoing a hard, small angle, scattering
in the medium (a non-abelian possibility) with soft re-scattering has a medium-induced radiative energy
loss proportional to E. The medium-induced radiation spectrum arises from the interference between
initial and final state radiation. In our formalism the small angle (hard scattering) is replaced by the effect
of the passage through a region where a strong background field is present.
We consider special cases:
i)
an impulse field, a field that is nonzero in a verysmall region to mimic the single hard
scattering in[8],
ii)
a constant field.
A time varying field can be considered numerically as a succession of impulse field. Hence the impulse
field approximation can be seen as part of an iterative scheme.
Results
We have proposed a model to the propagation of an asymptotic parton in a medium where besides
scattering a remanent non-abelian background field is also present. In the impulse approximation field the
effect of the background can be related to the recently proposed model by Peigné et al where multiple soft
scattering are coupled to hard scattering. The later leads to a linear energy dependence in the energy loss.
However we have also considered a constant background field where synchrotron radiation is affected by
soft multiple scattering.
[1] R. J. Friesa, J. I. Kapustaa, and Yang Lia, Nucl. Phys. A 774, 861 (2006).
[2] T. Lappi, and L. McLerran, Nucl. Phys. A 772, 200 (2006).
[3] E. V. Shuryak and I. Zahed, Phys. Rev. D 67, 054025 (2003).
[4] B.G. Zakharov, JETP Letters 88, 475 (2008).
[5] Alaa Dbeyssi, Dima Al Dirani, and H. Zaraket, Phys. Rev.D 84, 105033 (2011).
[6] R. Baier, Y. L. Dokshitzer, A. H. Mueller, S. Peigné and D. Schiff, Nucl. Phys. B 483 , 291 (1997).
[7] B. G. Zakharov, JETP Lett. 65, 615 (1997).
[8] Stéphane Peigné, Francois Arleo, and Rodion Kolevatova, hep-ph/1402.1671v1.