ЯДЕРНАЯ ФИЗИКА, 2012, том 75, № 6, с. 735-738
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
CATALYTIC REACTIONS IN HEAVY-ION COLLISIONS
(©2012 E. E. Kolomeitsev1)*, B. Tomasik1) 2)
Received March 31, 2011
We discuss a new type of reactions of a <-meson production on hyperons, nY — <Y and anti-kaons KN — <Y. These reactions are not suppressed according to Okubo—Zweig—Iizuka rule and can be a new efficient source of < mesons in a nucleus—nucleus collision. We discuss how these reactions can affect the centrality dependence and the rapidity distributions of the < yield.
The study of <-meson production in different nucleus—nucleus collisions at various collision energies provides complementary information on collision dynamics and in particular on the evolution of the strange subsystem. Within the consitutent quark model the < meson is dominantly a spin-one bound state of 5 and s quarks. Hence, hadronic interactions of < mesons are suppressed due to the Okubo— Zweig—Iizuka (OZI) rule, which, in the strict implementation, would forbid an interaction of a pure (ss) state with non-strange hadrons. Indeed, the OZI-forbidden reactions are typically orders of magnitude smaller than the OZI-allowed ones.
Since the OZI suppression weakens the < production only by the ordinary hadronic matter and is lifted in the quark—gluon medium, the strong, order of magnitude, enhancement of the < yield was proposed in [1] as a signal of the quark—gluon plasma formation. An enhancement of the < yield was indeed observed experimentally at AGS and SPS energies albeit to a lesser degree [2, 3]. In [4] it was suggested that the main contribution to the < yields at these energies would be given by the OZI-allowed process with strangeness coalescence KK — <p and KK — <N.
Surprisingly strong enhancement of the < yield was observed at the beam energies about 2 GeV per nucleon [5, 6]. Such a large < abundance cannot be described by the transport model [7], where <s are produced in reactions BB — BB< and nB — <B (B = N, A) with the dominant contribution from pion—nucleon reactions. Note that the strangeness coalescence process could not contribute much to the < yield at these energies since kaons have a long mean
1)Matej Bel University, Banska Bystrica, Slovakia.
2)Czech Technical University in Prague, FNSPE, Czech Republic.
E-mail: e.kolomeitsev@gsi.de
free path and most likely leave the fireball right after they are created.
In [8] we propose a new mechanism of the < production — the catalytic reactions on strange particles
nY — <Y, KN — <Y, Y = K, E. (1)
In contrast to the strangeness coalescence reaction, here the strangeness does not hide inside the <s, but stays in the system, and the presence of K mesons is unnecessary. The efficiency of these reactions should be compared with the process nN — — <N, which is found to be dominating in [9]. The reactions (1) are OZI allowed, so we win in cross sections compared to nN — <N. We lose, however, in the smaller concentration of hyperons and anti-kaons compared to nucleons and pions.
The cross sections of reactions (1) were calculated in [8] according to tree-level diagrams (see Fig. 1) given by the effective Lagrangian of nucleons, hyperons and kaons, which incorporates the < meson as a heavy Yang—Mills boson. Then, one coupling constant fixed by the < — KK decay determines the
Y' Y'
K ^^ ^ K K\ +
I
N Y N
Y Y Y' b
ф K +
N Y Y
Fig. 1. Diagrams contributing to: (a) nY ^ reactions; (b) KN ^ reactions.
ф
+
ф
736
KOLOMEITSEV, TOMASIK
coupling of 0 to any strange hadron. The resulting isospin-averaged cross sections can be parameterized as
-фУ'(s) —
As1/2 \
РфУ'(s) ayy' + byy'
1 GeV J
aK N-фУ
: РфУ (s)
a-KY + Ьку f Qey 1 + dKY
As1/2 1 GeV
mb
GeV
mb
GeV
where p^Y(s) is center-of-mass momentum of the 0 meson and hyperon. For the hyperon channels we have: oaS = 4.24, 6as = 1-66; ass = 2.16, bss = = 0.851; osa = 1-40, bsA = 0.682; and for the kaon channels: aKA ~ aKS = 2.6, bKA ~ bKS = 1-2, and (ika ~ (ikS = 2.0.
In order to estimate the efficiency of reactions with the 0 production on hyperons and kaons, we model, first, the evolution of the strange subsystem in the course of a collision. We make two assumptions: (a) strangeness can be considered perturbatively; (b) the fireball matter is baryondominated. The first assumption allows us to introduce an effective parameterization for the time dependence of the fireball temperature and baryon density. We use the form of a scaling solution of hy-drodynamic equations T(t)/Tm = (pB(t)/pm)2/3 = = (t2/t2 + 1)_a, where Tm and pm are the maximal temperature and density of the fireball, and t0 is the typical time scale of the fireball expansion. In the baryon-dominated matter the particles carrying strange quarks, K = (K-,K°), A, £, and heavier hyperons have short mean free path and remain in thermal equilibrium with pions, nucleons and A's till the fireball breaks up. So, the density of a hadron of type i with mass mi is equal to
Pitt) = A^ (¿e9i^m2T/i 2 (m/T)/2vr2,
where Xs is the strangeness fugacity and si is the number of strange quarks in the hadron; jB is the baryon chemical potential and qi is the baryon charge of the hadron. The degeneracy factor (i is determined by the hadron's spin Ii and isospin Ti as (i = (2Ii + + 1)(2Ti + 1). We disregard the finite width of A's and treat them as stable particles with the mass m-A = 1232 MeV. The baryon chemical potential jB(t) is determined by the equation pN (t) + pA (t) = = pB(t), where we neglect the contributions of hyperons, heavier resonances, and anti-particles. The strangeness fugacity follows from the strangeness conservation relation: pk(t) + pA(t) + ps(t) w pK(t), where pK(t) is the number of produced kaons K = = (K +, K0) divided by the fireball volume. We do not
о 4
i—i
x
2
ftj
£
-&■ к
0
---nN
- Catalytic
----пЛ + nE
0.2 0.4 0.6 0.8 1.0
t/to
Fig. 2. 0-Meson production rates: solid curve is the sum of all catalytic reactions, dash-dotted curve is the reactions on hyperons. Dashed curve is the rate of the nN ^ reaction.
assume that K mesons are in thermal in chemical equlibrium with other species since they have large mean free paths and can leave the fireball at some earlier stage of the collision. The evolution of pK is described by the differential equation
PK(t)-pK(t)^=n(T(t),pB(t))
with the initial condition pK(0) = 0. The kaon production rate, R, is determined by the processes with nN, nA, NN, nn, and N A in the initial states; for the list of possible reaction channels and the corresponding cross sections see [10].
Now we are in position to analyze whether the catalytic reaction can be an efficient source of 0 mesons compared to conventional ones. As a baseline we take the ^-production rates in the nN ^
^ 0N reactions (t) = n^NpnPn. The transport coefficient nOd = (<Jcdvab)/(! + bab) is the cross section aCd(s) of the binary reaction a + b ^ c + + d averaged over the momentum distributions of colliding particles with the particle relative velocity
vab. We compare R^N with the catalytic reactions on
hyperons R^y = J2y,y=k,s KtYPnPy and on anti-
kaons RK n (t) = {kcKan + K) pk Pn . The rates of various processes are shown in Fig. 2 for the maximal temperature and density Tm = 130 MeV, pm = 5p0, a = 0.3, where p0 = 0.17 fm-3 is the nuclear saturation density. These parameters correspond roughly to a collision at beam energy 6 A GeV. The 0 production in nN collisions (dashed curve) starts, of course, at the very beginning and gradually falls off as the fireball cools down and expands. The rates of catalytic reactions increase initially (solid curve) as more strange particles are produced, reach the maximum
6
0.015
0.010 0.005 0
CATALYTIC REACTIONS IN HEAVY-ION COLLISIONS
a(NppjA) + b(Npp/A)
--a = 0, b = 1.2x10-2
---a = 1.0x10-2, b = 0
0.04
0.02
---a = 7x10-3, b = 3x10-3
J_i_I_i_I_i_I
- b'Npp/A)1'
^/Npp 0.04
a = 0, b = 0.028
a' = 0.035, b = 0 d = 0.017, b = 0.014
0.03 0.02 0.01
a(Npp/A)1/3 + b(Npp/A)2/3
-a = 0.017, b = 0.006
---a = 0.019, b = 0
NA60, InIn NA49, PbPb
0 50 100 150 200
0 50 100 150 200
N,
pp
N
pp
0.4 0.8 1.2 1.6
Npp/A
737
Fig. 3. Centrality dependence of ratios (a) and K + (b). Data points are for AuAu collisions at 11.7 A GeV [2]. (c) The 0/Npp ratio for InIn and PbPb collisions at 158 A GeV, the data are from [12].
0
RMSV
Fig. 4. Root mean square of the rapidity distributions of 0's produced in PbPb collisions versus the beam rapidity [3, 12]. Curves show the distribution widths from reactions nA ^ 0Y, K +A ^ 0N, and K+ K- ^ 0.
at (0.3—0.4)to and drop off later. The rates become comparable for times >0.6to. Note that the dominant contribution is given by reactions on hyperons (dash-dotted curve). The rates in Fig. 2 correspond to the fireball expansion time t0 = 10 fm. If the collision lasts longer, then the curves for catalytic reactions have to be scaled up by a factor t0/(10 fm), since the number of the strange particles is proportional to the expansion time. This will make the catalytic reactions efficient even at smaller temperatures. Our estimates show that the catalytic processes can contribute the 0 production in heavy-ion collisions.
We discuss now the centrality dependence of the 0 production. We will use the mean number of projectile participants, Npp, as a measure for the initial volume of the fireball created in the collision, V « Npp. If there is only one changing parameter with the unit of length as in the case of a symmetrical collision at the
fixed collision energy, l ~ V1/3 « Np1/3, the scaling properties of hydrodynamics imply that the collision
time is of the order t0 ~ l/c & N^3 [11]. Then the number of produced < mesons can be estimated as
N^ ~ aconvNp/3 + acatNpp3. The term proportional to
Np/3 is due to the conventional production reactions like nN — <N, whereas the term proportional to Np/3 corresponds to the catalytic reactions [8]. For the experimental ratios in [2] we find
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