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EPJ manuscript No.
(will be inserted by the editor)
Inclusive meson production in peripheral collisions of
ultrarelativistic heavy ions
K.A.Chikin 1a , V.L.Korotkih 1b , A.P.Kryukov 1c , L.I.Sarycheva 1d , I.A.Pshenichnov 2e , J.P.Bondorf 3f , and
I.N.Mishustin 3g
1 Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia
2 Institute for Nuclear Research, Russian Academy of Science, 117312 Moscow, Russia
3 Niels Bohr Institute, DK-2100 Copenhagen, Denmark
Received: date / Revised version: date
Abstract. There exist several proposals to use Weizs?acker-Williams photons generated by ultrarelativistic
heavy ions to produce exotic particles in flfl fusion reactions. To estimate the background conditions for
such reactions we analyze various mechanisms of meson production in very peripheral collisions of ultra-
relativistic heavy ions at RHIC and LHC energies. Besides the flfl fusion they include also electromagnetic
flA interactions and strong nucleon-nucleon interactions in grazing AA collisions. All these processes are
characterised by low multiplicities of produced particles. The flA and AA events are simulated by corre-
sponding Monte Carlo codes, RELDIS and FRITIOF. In each of these processes a certain fraction of pions
is produced close to the mid-rapidity region that gives a background for the flfl events. The possibility of
selecting the mesons produced in the flfl fusion events via different p t cut procedures is demonstrated.
PACS. 25.75.-q Relativistic heavy-ion collisions -- 25.75.Dw Particle and resonance production
a E-mail: const@lav1.npi.msu.su
b E-mail: vlk@lav1.npi.msu.su
c E-mail: kryukov@theory.npi.msu.su
d E-mail: lis@alex.npi.msu.su
e E-mail: pshenichnov@nbi.dk
f E-mail: bondorf@nbi.dk
g E-mail: mishustin@nbi.dk
1 Introduction
According to the impact parameter b, different phenomena
take place in collisions of ultrarelativistic heavy ions. They
can be divided into the following three categories.

2 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
Central collisions (b п 0), i.e. the collisions with nearly
full nuclear overlap fall into the first category. Such colli-
sions provide conditions for the creation of very hot and
dense nuclear matter. It is the aim of future experimental
programs at the Large Hadron Collider (LHC) at CERN [1]
and the Relativistic Heavy Ion Collider (RHIC) at Brook-
haven National Laboratory [2] to study a possible phase
transition of the nuclear and hadronic matter into the so-
called quark-gluon plasma at high energy densities. Such
extreme conditions are believed to be similar to those ex-
isted in the Early Universe soon after the Big Bang.
The second category contains collisions with partial
overlap of nuclei (b ! R 1 +R 2 , R 1 and R 2 are the nuclear
radii). In such collisions the residual spectators remain
relatively cold. Short-range interaction via the strong nu-
clear forces is restricted mainly to the participant zone.
In the whole set of minimum-bias events the number of
peripheral nuclear collisions is significant due to the geo-
metrical factor 2пb. The general picture of ultrarelativis-
tic heavy-ion collisions at LHC and RHIC will be incom-
plete without considering such peripheral collisions. Non-
central heavy-ion collisions are considered as a place to
look for the disoriented chiral condensates [3] and ellip-
tic flow [4]. Combining the Hanbury-Brown-Twiss method
with the determination of the reaction plane [5] one is able
to study the size, deformation and opacities of the parti-
cle emission sources. With the aim to study central colli-
sions, one has to know the exact properties of the comple-
mentary peripheral collisions. A proper rejection of these
''background'' collision events will be crucial in the extrac-
tion of the events in which the quark-gluon plasma may
be created.
In the collisions of the third category the impact pa-
rameter exceeds the sum of nuclear radii (b ? R 1 + R 2 ).
Therefore, there is no overlap of nuclear densities, but
nevertheless, one or both nuclei may be disintegrated by
the long-range electromagnetic forces. This process of the
Electromagnetic Dissociation (ED) is a well-known phe-
nomenon [6--8]. The interaction can be treated in terms
of equivalent photons representing the Lorentz-boosted
Coulomb field of heavy ions. At ultrarelativistic energies
the ED cross section exceeds considerably the pure nuclear
cross section for heavy colliding nuclei. This fact was con-
firmed recently in experiments [9]. The electromagnetic
collision events are less violent then the collisions with nu-
clear interactions. Thus the average particle multiplicities
are essentially lower [10,11] and the main part of nucle-
ons and mesons is produced in the regions of projectile
and target fragmentation, very far from the mid-rapidity
region.
Besides the action of virtual (equivalent) photons on
colliding nuclei, the photons from two nuclei can collide
(fuse) and produce various secondary particles. Photon-
photon (flfl) physics may be investigated in such colli-
sions [7,8,12]. The idea to produce exotic particles via the
flfl fusion in heavy-ion colliders has been put forward more
then 10 years ago in Ref. [13]. Many authors have further
developed this idea since that time. The production of dif-
ferent particles from ? \Sigma , ? \Sigma leptons to Higgs bosons and

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 3
supersymmetric particles has been considered. The full list
of references can be found in the recent reviews [7,8].
As one can see, there exist several mechanisms of the
particle production in peripheral collisions of ultrarela-
tivistic heavy ions: the flfl fusion, flA interaction and graz-
ing nuclear collisions (see Figs. 1--3). In the present pa-
per we study the production of п \Sigma and п 0 mesons via
these mechanisms. We discuss the general features of the
pion production and calculate the contributions of differ-
ent mechanisms. Prior to investigating exotic particle pro-
duction in flfl collisions a certain ``calibration'' is necessary
for the theoretical methods and experimental techniques.
Similar investigations have been performed specially
for the STAR detector at RHIC [14,15] and the corre-
sponding acceptance cuts were applied from the begin-
ning. The CMS detector which will be installed at LHC [16]
can also be used for studying the meson production in
peripheral collisions. Even having in mind a plan to use
another experimental set-up for such studies one can esti-
mate first the flfl signal-to-background ratio without any
acceptance cuts. Such comparison of different mechanisms
provides a guide-line which is free of limitations and re-
strictions of existing experimental facilities. This is useful
for possible extensions and updates of the existing detec-
tors.
In the present paper we pay the main attention to the
inclusive cross sections of the meson production by differ-
ent mechanisms. This study is complementary to a very
recent one [17], which deals with the exclusive meson pro-
duction channels. As we expect, in order to select the rare
events with a single vector meson [17], one has to reject
the background due to the meson production (п + , п \Gamma , п 0 )
via the flA process. This background may be estimated in
the framework of the models used in the present paper.
A meson production event may be followed by a par-
tial disintegration of a nucleus. We study such reactions in
addition to the coherent meson production process consid-
ered in Ref. [17] when the colliding nuclei remain intact.
Different characteristics of the pion production by equiva-
lent photons are calculated by the RELDIS code [11] based
on the extended model of photonuclear reactions [18]. The
FRITIOF Monte Carlo event generator, version 7.1 [19] is
used to study the properties of grazing nuclear collisions.

4 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
2 Distant electromagnetic collisions
2.1 Equivalent photon spectra
Let us consider a point-like charge Ze moving with veloc-
ity v at impact parameter b. In the Weizs?acker-Williams
approximation [6--8] the spectrum of equivalent photons
is given by:
N(!; b) = Z 2 ff
п 2 b 2 fi 2 x 2
`
K 2
1 (x) + 1
fl 2 K 2
0 (x)
'
(1)
where x = !b=flv, fi = v=c and fl = (1 \Gamma fi 2 ) \Gamma1=2 is the
Lorentz factor of the moving charge. K 0 and K 1 are the
modified Bessel functions of zero and first order.
The total number of photons with the energies ! 1 and
! 2 colliding at the point P is obtained by the integration
of the equivalent photon spectra over the distances b 1 and
b 2 [20] (see Fig. 4):
F (! 1 ; ! 2 ) = 2п
Z 1
R1
b 1 db 1
Z 1
R2
b 2 db 2
\Theta
Z 2п
0
dOEN(! 1 ; b 1 )N(! 2 ; b 2 )\Theta(B 2 ); (2)
where R 1 and R 2 are the nuclear radii, \Theta is the step func-
tion and B 2 = b 2
1 + b 2
2 \Gamma 2b 1 b 2 cos OE \Gamma (R 1 +R 2 ) 2 .
The flfl luminosity calculated in the double equivalent
photon approximation [20] is:
d 2 L
dWdy = 2
W F ( W
2 e y ; W
2 e \Gammay ); (3)
where the energy squared W 2 = 4! 1 ! 2 and the rapidity
y = 1=2 ln(! 1 =! 2 ) of the flfl system were introduced.
The transverse momentum of a produced single meson
turns out to be small p t ? 1=R 1;2 [8,12]. Different nuclear
charge formfactors may be used in calculations [8,12], but
in any approximation the p t values for the produced meson
turns out to be less then 30 MeV/c in PbPb collisions. In
the following we shell see how this feature may be used to
disentangle flfl events from other processes.
2.2 Production of a single meson in flfl fusion
The production of a single meson in the flfl fusion is the
simplest process in our consideration. The calculation tech-
nique within the framework of the Weizs?acker-Williams
formalism for such a process is well-known [8,20].
The cross section to produce a meson with mass MR
is given by:
oe =
Z d! 1
! 1
Z d! 2
! 2
F (! 1 ; ! 2 )oe flfl!MR ; (4)
where the number of colliding photons, F (! 1 ; ! 2 ), is taken
from Eq. (2). Taking \Theta = 1 one can simplify the calcu-
lation, since in this case the integral of Eq. (2) may be
reduced to the product of the Weizs?acker-Williams spec-
tra, N(!), integrated over the impact parameter [6--8]. For
light mesons, MR ? fl=(R 1 +R 2 ), the resulting integral is
changed by several percent only. This simplification may
be not appropriate for heavy mesons, since they can only
be produced by a pair of photons from the high-energy
tail of the equivalent photon spectrum. Such mesons are
produced mainly in close collisions, where b п R 1 + R 2
and the region of nuclear overlap cannot be neglected.
The cross section of the elementary process flfl !MR
may be calculated [7,8,20] as:
oe flfl!MR = 8п 2 (2JR + 1)\Gamma MR!flfl ffi(W 2 \Gamma M 2
R )=MR ; (5)

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 5
where JR , MR and \Gamma MR!flfl are the spin, mass and two-
photon decay width of the meson R. W 2 is the c.m. energy
squared of the colliding photons.
The corresponding differential cross section for pro-
ducing a meson with the mass MR is given by
doe R
dy = 8п 2 (2JR + 1)\Gamma MR!flfl F ( MR
2 e y ; MR
2 e \Gammay )=M 3
R :
(6)
The exclusive cross sections for producing a single me-
son were calculated by many authors. In Ref. [7] the equiv-
alent photon cross section has been derived directly from
the first QED principles. Three types of nuclear formfac-
tors were used in the calculations [7] corresponding to a
homogeneously charged sphere, a Gaussian-shaped and
a point-like charge distributions. In this respect the ap-
proach of Ref. [7] is different from the more phenomenolog-
ical method of Ref. [20] which we basically follow. More-
over, even following the authors of Ref. [20] one can use
different values for the nuclear radii, R 1;2 . The real nu-
clear charge distribution with a diffuse boundary should
be approximated by a distribution with a sharp boundary
that leads to some uncertainties. A straightforward com-
parison of the results of different authors [7,8,20] seems
to be difficult due to different values of MR , \Gamma flfl!MR and
R 1;2 used in the different papers.
With the aim to understand the sensitivity of numeri-
cal results to the choice of parameters, we repeated the cal-
culations of the cross section for the single meson produc-
tion in ultrarelativistic heavy-ion collisions, see Tabs. 1--3.
We used the MR and \Gamma MR!flfl values according to the
corresponding papers [7,8,20]. All the cross sections were
calculated for the nuclear radii R 1;2 = 1:2A 1
3 .
As one can see from Tabs. 1--3, the different approaches
give quite similar results for the lightest mesons п 0 , j. On
the contrary, as it was expected, the difference is notice-
able for heavy mesons like j b , j c . Nevertheless this situa-
tion seems to be acceptable due to the following reasons.
First, in the present paper we will consider mainly the
production of the lightest п mesons. Second, because of
uncertainties in the Particle Properties Data on MR and
\Gamma MR!flfl for heavy mesons [35] 1 , it is difficult to predict
with confidence the exclusive cross section values for such
mesons. Therefore, the uncertainties of the method itself
become less important for heavy mesons.
2.3 Inclusive cross section of п 0 production in DRP
model
Pions can be produced not only in the direct process flfl !
п 0 . The flfl fusion produces several unstable heavy mesons
such as j; f 0 ,... and decay products of these mesons may
contain п 0 's. As one can see in the following, such two-
step processes, flfl ! R ! п 0 X , with the intermediate
meson R give a sizable contribution to the inclusive п 0
production cross section. In addition to the direct process,
reasonable estimation for the inclusive cross section flfl !
п 0 X should contain the sum of dominant contributions
from the intermediate meson resonances which contain at
1 This is particularly true for the scalar mesons f0(975) and
f0(1275) with large decay widths causing a strong overlap of
individual resonances, see details in Ref. [35].

6 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
least one п 0 meson in the final state. We call this approach
a Dominant Resonance Production (DRP) model.
The exclusive differential cross section, doe R =dy, to pro-
duce a single meson R with the mass MR is given by
Eq. (6). In the DRP approximation the inclusive cross
section of the п 0 production through the decay of inter-
mediate resonances is
doe incl
dy (п 0 ) =
X
R;k
doe R
dy B (k)
R (R ! п 0 ) n (k)
R (п 0 ); (7)
where B (k)
R (R ! п 0 ) is the branching ratio for the decay
of the resonance R to the channel k which contains at least
one п 0 . n (k)
R (п 0 ) is the number of п 0 's in the corresponding
channel k. If the first step decay products contain another
resonance, a similar expression may be written in turn
for the second step decays producing п 0 . Introducing the
value
B out
R =
X
k
B (k)
R (R ! п 0 ) n (k)
R (п 0 ); (8)
one can rewrite Eq. (7) in the following way:
doe incl
dy (п 0 ) =
X
R
doe R
dy B out
R : (9)
Particle Data information relevant to the calculation of
oe incl is given in Tab. 4. We selected the resonances with
relatively large widths \Gamma MR!flfl . The values of \Gamma tot and
B in
R = \Gamma MR!flfl =\Gamma tot from review [35] which are necessary
to calculate \Gamma MR!flfl are given for completeness. On the
contrary to Tabs. 1--3, the decay probabilities and meson
widths in Tab. 4 were taken according to the most recent
version of the Review of Particle Physics [35]. We assumed
that the decays f 0 (980) ! пп and f 0 (1370) ! пп take
place with 100% probability since there is no quantitative
information in Ref. [35] on other channels. Isospin con-
servation relations provide the probability of 1=3 for the
п 0 п 0 charge state in such пп channels.
The integrated inclusive cross section of the п 0 pro-
duction in PbPb collisions (R 1 = R 2 = 7:75 fm) at LHC
energies is found to be oe incl (п 0 ) = 106 mb in the DRP
model, while the exclusive one is only 36:3 mb. As one
can see, the contribution to the п 0 production via the in-
termediate resonances turns out to be essential. The cor-
responding rapidity distributions, doe=dy, will be discussed
in Sec. 4.
2.4 Pion production in flA collisions
The meson production induced by equivalent photons in
electromagnetic collisions of ultrarelativistic heavy ions
(Fig. 2) is a poorly explored phenomenon. To the best
of our knowledge, the first calculations of the total rate
of the pion production in electromagnetic collisions were
made in Ref. [22]. The first experimental evidence of the
electromagnetic dissociation accompanied by the pion pro-
duction was found in Ref. [23] for 200 AGeV 16 O ions. Due
to a small number of the pion production events detected
in nuclear emulsion, the absolute cross section for such
dissociation channel was not determined. To date only
the existence of the pion production in flA collisions is
demonstrated by the experiment [23].
Let us consider the absorption by a nucleus of an equiv-
alent photon leading to the pion production (Fig. 2). The
nucleus may absorb one or more virtual photons during a
collision. We follow Llope and Braun-Munzinger [24] in de-

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 7
scription of such multiple absorption processes. The dou-
ble differential cross section of the pion production via the
single photon absorption may be written first in the pro-
jectile rest frame. In such a frame the nucleus is at rest
prior to the absorption:
d 2 ~
oe (1)
p t dp t dy =
1
Z
!min
d! 1
! 1
N (1) (! 1 )oe A2 (! 1 ) d 2 W
p t dp t dy (! 1 ); (10)
where oe A2 is the total photoabsorption cross section for
the nucleus A 2 and d 2 W=p t dp t dy is the double differential
distribution of pions produced by the photon with the en-
ergy ! 1 . A spectral function N (1) is given by the following
expression:
N (1) (! 1 ) = 2п
1
Z
bmin
bdbe \Gammam(b) N(! 1 ; b); (11)
where N(! 1 ; b) is defined by Eq. (1) and m(b) is the mean
number of photons absorbed by the nucleus A 2 in a colli-
sion at the impact parameter b:
m(b) =
1
Z
!min
N(!; b)oe A2 (!) d!
! : (12)
Analogously, for the second order process with a pair of
photons absorbed by the nucleus A 2 the double differential
cross section is:
d 2 ~ oe (2)
p t dp t dy =
1
Z
!min
1
Z
!min
d! 1
! 1
d! 2
! 2
N (2) (! 1 ; ! 2 )
\Theta oe A2 (! 1 )oe A2 (! 2 ) d 2 W (! 1 )
p t dp t dy
d 2 W (! 2 )
p t dp t dy ; (13)
with the corresponding double photon spectral function:
N (2) (! 1 ; ! 2 ) = п
1
Z
bmin
bdbe \Gammam(b) N(! 1 ; b)N(! 2 ; b): (14)
In the above expressions b min is the minimal value of
the impact parameter which corresponds to the onset of
nuclear interaction. In pion production calculations the in-
tegration over the photon energy starts from !min п 140
MeV which corresponds to the pion emission threshold.
Finally, with the corresponding Lorentz boost from the
nucleus rest frame to the laboratory system one can ob-
tain the double differential distribution d 2 oe=p t dp t dy for
the produced pions suitable for measurements in experi-
ments. Further details of our approach may be found in
Refs. [10,11].
As it was shown in Ref. [11], the contribution to the
pion production from the double photon absorption is less
then 10% for heavy ions with fl AE 100. Since the con-
tribution from the third and fourth order processes are
expected to be even lower, these processes can be safely
disregarded for the ultrarelativistic energies.
Because of the coherent action of all the charges in the
nucleus, the virtuality of the emitted photon, Q 2 = \Gammaq 2 ,
is restricted. Such photons are almost real, Q 2 ? 1=R 2 ,
where R is the nuclear radius. Therefore, photonuclear
data obtained in experiments with monoenergetic photons
may be used, in principle, as an input for the Weizs?acker-
Williams calculations of pion production in flA collisions.
Since the spectrum of equivalent photons covers a very
wide range of the photon energies, one needs the double
differential distribution d 2 W (!)=p t dp t dy for the photon
energies ! starting from the pion emission threshold and
up to several tens or even hundreds of GeV.
In the region of interest, i.e. at ! ? 140 MeV, the pho-
ton de Broglie wavelength is comparable or even smaller
than the nucleon radius. A photon interacts, mainly, with

8 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
individual intranuclear nucleons. Experimental data on
the single pion photoproduction on the nucleon are accu-
mulated in compilations of Refs. [25,26]. The latter com-
pilation contains also the experimental data on photopro-
duction of baryon, B ? , and meson M ? resonances: flN !
пB ? and flN ! пM ? as well as on some channels of multi-
ple pion production: flN ! iпN , 2 ? i ? 8. Due to a long
mean free path, an equivalent photon may be absorbed
deeply in the nuclear interior. The mesons produced in a
photonucleon reaction interact with other intranuclear nu-
cleons inducing different reactions in the nuclear medium.
In other words, the process shown in Fig. 2 is followed
by the final state interaction of produced hadrons with
the residual nucleus A 2 . Beside the pions several nucleons
may be emitted and the residual nucleus may receive high
excitation energy.
Since the data on the pion photoproduction on nuclei
exist only for limited domains of ! and pion kinematical
variables, a theoretical model should be used in the cases
when the data are not available. A suitable tool for de-
scribing such multi-step photonuclear reactions is the In-
tranuclear Cascade Model, which is well-known for many
years [27].
As shown in Ref. [18], the extended Intranuclear Cas-
cade Model of photonuclear reactions describes reasonably
well available data on meson production and nucleon emis-
sion obtained in the last two decades with intermediate
energy quasi-monochromatic photons. With this in mind
one can use the INC model for the Weizs?acker-Williams
calculations, as it was demonstrated in Refs. [10,11]. For-
mally we use 1 TeV as the upper limit for the equivalent
photon energy in the flA process. Our model was not ini-
tially designed for such high energies when events with a
very high hadron multiplicity become possible and many
other channels, like baryon-antibaryon photoproduction,
may be open. Nonetheless, one can safely use the model to
investigate the flA processes with a low multiplicity which
mimic processes from the flfl fusion. The former processes
take place mainly at ! ! 10 GeV, where our model has
been verified in detail.
2.4.1 Simulation of flN interaction
The channels of the hadron photoproduction on the nu-
cleon which are taken into account in the model are listed
in Tab. 5. To describe the two-body photoproduction chan-
nels we have basically used the Monte Carlo event gener-
ator of Corvisiero et al. [28]. The contribution from the
two-body channel flN ! пN dominates up to ! п 0:5
GeV. Approximations of the total and differential cross
sections for such channels based on the model of Walker
and Metcalf [29] were used up to 2 GeV. The excitation
of six baryon resonances was taken into account. The con-
tributions from \Delta(1232), N ? (1520) and N ? (1680) are the
most important. The presence of these resonances explains
a well-known resonant structure in the total flN cross sec-
tion at ! ? 1:2 GeV.
The channels flN ! 2пN and flN ! 3пN play a
major role at 0:5 ? ! ? 2 GeV. These channels include
also the resonant contributions from п\Delta, jN , aeN and
!N channels (Tab. 5). Although the presence of these

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 9
contributions in the total flN cross sections is difficult
to trace, the angular distributions of these channels have
some specific features. Several examples may be given.
The flp ! jp channel has three important contributions
from S 11 (1535), S 11 (1700) and P 11 (1750) states. Due to
the dominance of S 11 (1535), the angular distribution of
the process is not far from isotropy. On the contrary, the
flp ! ae 0 p process has a prominent forward peak, since the
non-resonant diffractive contribution dominates.
Many channels in the multi-pion reactions, flN ! iпN ,
(2 ? i ? 8), were not suitable for measurements in spark,
bubble or streamer chamber experiments due to the pres-
ence of several neutral particles in the final state. How-
ever, one can reconstruct the integral cross sections of un-
detectable channels by applying isotopic relations to the
measured cross sections of channels with charged particles,
which can be found in compilation of Ref. [26]. A phe-
nomenological statistical approach for the exclusive de-
scription of the elementary flN interaction was applied
to multiple pion production channels in Ref. [18]. There
an isospin statistical model was used to connect unknown
cross sections with measured ones. Other details of the
method used for simulating the flN interaction may be
found elsewhere, see Ref. [18].
Since a huge number of multiple pion production chan-
nels is open at ! ? 2 GeV, the statistical description may
be the only way to estimate the cross sections of such
channels. Recently another kind of statistical assumptions
was used in the Monte Carlo event generator Sophia for
simulating photohadronic processes in astrophysics [30].
2.4.2 Secondary processes
According to our model, the fast hadrons produced in a
primary flN interaction initiate a cascade of successive
quasi-free hadron-nucleon collisions inside the nucleus. The
following elementary processes were taken into account:
пN ! пN; п(NN) ! NN; пN ! ппN ; пN ! (i+1)пN;
NN ! NN; NN ! пNN; NN ! iпNN; (i ? 2);
jN ! jN; jN * ) пN; jN ! ппN;
j(NN) ! NN; j(NN) ! пNN;
!N ! !N; !N * ) пN; !N ! ппN;
!(NN) ! NN; !(NN) ! пNN:
The empirical approximations for the measured integral
and differential cross sections of the NN and пN interac-
tions as well as the phenomenological estimations for the
total and partial cross sections of the jN and !N inter-
actions were used in the calculation [18].
The described Monte Carlo model is implemented into
the RELDIS code [11] which is especially designed for cal-
culating the electromagnetic dissociation processes in ul-
trarelativistic heavy ion collisions.
2.4.3 Characteristics of produced pions
The average number of pions, hn п i, produced in a flA
process is quite small. The values of hn п i for each pion
charge are given in Tab. 6 for AuAu and PbPb collisions
at RHIC and LHC energies, respectively. Even with the in-
clusion of multiple pion production channels (flN ! iпN ,

10 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
2 ? i ? 8), the average numbers of pions of each charge
are quite low (п 1). This can be explained by two reasons.
First, in a great part of the electromagnetic dissociation
events no pions are produced at all, due to the dominance
of soft photons (! ? 140 MeV) in the equivalent photon
spectrum, Eqs. (11),(14). Second, the most probable pro-
cesses of pion production are flN ! пN and flN ! п\Delta,
which produce one or two pions only.
As one can see from Tab. 6, in the flA process the
neutral pions are produced more abundantly as compared
with п + and п \Gamma mesons. A difference is noticeable also in
the differential distributions, doe=dy, shown in Fig. 5 for
each pion charge. The main deviations in the pion yields
appear at rapidities close to the beam rapidity. This fact
has a simple explanation. As already mentioned above, the
process flN ! пN dominates in the pion production by
equivalent photons and the corresponding pions are close
to the beam rapidity. This reaction can proceed on a pro-
ton: flp ! п + n, flp ! п 0 p and a neutron: fln ! п \Gamma p,
fln ! п 0 n. Thus, single neutral pions can be produced
both on the proton and the neutron, while п + on the neu-
tron and п \Gamma on the proton only. The total cross sections
of these four channels are close to each other. This gives
the rate of the п 0 production approximately twice as large
as the rate of п + or п \Gamma for a light nucleus with the equal
numbers of protons and neutrons. This feature of the sin-
gle pion photoproduction is confirmed by the measure-
ments of the inclusive cross sections and the calculations
made for carbon nucleus (see Fig. 15 of Ref. [18]).
Since a neutron excess exists in heavy nuclei like Pb
or Au, in this case the п \Gamma production will be enhanced
in comparison with п + , as it is shown in Fig. 5. The final
state interaction affects the absolute yields of the pions of
different charges, but does not essentially change the ratio
between them.
The detection of the pions produced close to the beam
rapidity is a complicated experimental task. Special zero-
degree detectors with proper identification of particle mass
and charge are necessary for this purpose. However, if a
forward detector located after a steering magnet is suit-
able for the determination of charges of nuclear fragments,
one may exploit it to detect the pion emission process in-
directly. If п \Gamma is produced in the reaction fln ! п \Gamma p, it
may be emitted while the recoil proton may be captured
by the residual nucleus. The deexcitation of such nucleus
may take place mainly via neutron emission. It means that
the initial charge of the nucleus will be increased by one
unit. The charge-to-mass ratio will be changed for such
ion and it will be separated from the beam. Depending on
the value of heavy-ion energy, the RELDIS code predicts
the cross section of such electromagnetic ``charge pick-up''
channels at the level of 10--100 mb. This process competes
with the nucleon pick-up process via the strong interac-
tion. Nevertheless, as it is known from Ref. [31], the cross
section of the latter process drops noticeably with increas-
ing beam energy. On the contrary, the cross section of the
electromagnetic charge pick-up increases gradually with
the beam energy and may essentially exceed the value of

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 11
the cross section for the nucleon pick-up due to the strong
interaction.
The photonuclear reactions (fl; п \Gamma xn), x = 0 \Gamma 9, in-
duced by bremsstrahlung photons were discovered many
years ago. We refer the reader to a recent paper where such
reactions were studied by radiochemical methods [32]. It
would be interesting to study the same type of reactions
induced by equivalent photons in ultrarelativistic heavy
ion collisions.
As mentioned above, the main part of pions is pro-
duced close to the beam rapidity. A small fraction of pi-
ons is produced by very-high energy photons with ! AE 10
GeV. Some of the pions produced in such interactions may
receive the momentum high enough to populate the cen-
tral rapidity region. As shown in Fig. 5, there are pions
with jyj ! 5 which may be confused with those from the
flfl process. Therefore some selection criteria are necessary
for the flfl processes (see Sec. 4).
3 Very peripheral nuclear collisions
Very peripheral (grazing) nuclear collisions with the par-
ticipation of the strong nuclear forces can be misiden-
tified as the electromagnetic interaction events. Both of
these types of interactions contribute to the events with
a low multiplicity of particles. To study the properties of
strong interaction events the Monte Carlo event generator
FRITIOF, version 7.1 [19] is used.
3.1 Basic processes considered by FRITIOF model
Let us recall the main statements of the extended FRITIOF
model [19] which is valid up to the TeV region. FRITIOF is
a Monte Carlo model for hadron-hadron, hadron-nucleus
and nucleus-nucleus collisions. The basic idea of the model
is in a simple picture that a hadron behaves like a relativis-
tic string with a confined color field. This field is equiva-
lent to that of a chain of dipoles lined up along the axis
line. The dipole links act as partons. During the soft in-
teraction many small transverse momenta are exchanged
between the dipole links and two longitudinally excited
string states result from the collisions. A disturbance of
the color field will in general initialise the gluonic radia-
tion according to QCD. The final state particles are ob-
tained by fragmentating the string states like in the e + e \Gamma
annihilation.
The large p t process can be treated by using QCD
directly. The hard interaction effects, which are considered
as the Rutherford parton scattering, become important
in the TeV range of c.m. energies and at large p t ? 1
GeV/c. The results of the model are in good agreement
with experimental hadron-hadron data up to the highest
energies currently available.
Nucleus-nucleus collisions are regarded in the FRITIOF
model as incoherent collisions between nucleons of collid-
ing nuclei. FRITIOF does not take into account collective
(coherence) effects when two nuclei interact as a whole.
Thus a nucleon from the projectile interacts independently
with the encountered target nucleons as it passes through
the nucleus. Each of these subcollisions can be treated as

12 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
a usual hadron-hadron collision. On the time scale of the
collision process, the exited nucleon does not fragment in-
side the nucleus, so there are no intranuclear cascades.
This assumption is reasonable at high energy since the
time scale associated with fragmentation is much longer
than the flight time of excited nucleons through the nu-
cleus.
3.2 Nuclear density distributions and total cross
section in PbPb collisions
One of important aspects of the collision is the nuclear
geometry. It is assumed that the projectile passes through
the target nucleus on a straight line trajectory. The nucle-
ons are distributed inside the nucleus according to the nu-
clear density distribution ae(r). Wood-Saxon density func-
tion for heavy nuclei was used in our calculations:
ae(r) = ae o
1 + exp( r\Gammar o A 1=3
C )
; (15)
where r o = 1:16(1 \Gamma 1:16A \Gamma2=3 ) is the radial scale pa-
rameter, C is the diffuseness parameter, it is slightly A-
dependent and its values used in the program ranging from
0.47 to 0.55 fm, and ae o is a normalisation constant. Then
for lead nucleus the radius defined at the half of the normal
nuclear density is equal to R = r o A 1=3 = 6:63 fm, while
the diffuseness parameter used by FRITIOF is equal to
C = 0:545 fm.
The total cross section of the strong lead-lead interac-
tion at LHC collider was estimated to be 7164 mb, accord-
ing to a simple geometrical formula used in Ref. [33]. This
estimation does not take into account the energy depen-
dence of the total nucleus-nucleus cross section due to the
increase of the total nucleon-nucleon cross section. Bas-
ing on extrapolations of the measured pp cross sections
to LHC energies one can obtain a higher value of about
10 barn, see Ref. [34]. For this value of the total nucleus-
nucleus cross section one has to rescale the plots given in
the present paper by 30% for grazing nuclear collisions.
3.3 Impact parameter distribution in nuclear collisions
Special efforts should be undertaken to find proper ranges
of the impact parameter b which divide nucleus-nucleus
collisions into different categories. These categories were
listed in the introduction, most important for us are very
peripheral nuclear collisions and electromagnetic interac-
tions, subsequently subdivided into the flfl and flA events.
The uncertainties associated with the diffuseness of
the nuclear density distribution affect grately the result-
ing ranges. We used the FRITIOF model to define these
ranges. The impact parameter distribution of events simu-
lated by the FRITIOF code is given in Fig. 6. The plotted
quantity dNAA (b)=db=NAA is a relative number of nuclear
collisions with a given b. As it is shown in the figure, the
events with a low multiplicity of pions correspond to the
collisions with 12 ? b ? 20 fm. It is the domain of b which
defines the grazing nuclear collisions with the participa-
tion of the strong nuclear forces. It should be stressed how-
ever, that this definition is essentially model dependent
and numerical results may be different if one uses another
code with a different treatment of the diffuse boundary

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 13
of the nucleus and another value of the elementary NN
cross section.
We see that the value which defines the onset of elec-
tromagnetic collision for PbPb ions, b min = 15:5 fm, used
in the paper [10] does not contradict the results of the
FRITIOF calculations given in Fig. 6. Following our pre-
vious papers [10,11], for consistency we define the end of
the nuclear overlap in lead-lead collisions at b min = 15:5
fm. This choice is also supported by the calculation of
Ref. [36] where the average number of interacting nucle-
ons, hN in i, was evaluated as a function of b for the case
of PbPb collisions. As it was found [36], hN in i п 1 at
b = 15:5 fm. According to the Wood Saxon density func-
tion for Pb nucleus, it corresponds to the overlap of those
boundary regions of the colliding nuclei which have the nu-
clear densities below 0.1 of the value at the center of the
nucleus. The total number of such events in the FRITIOF
simulation turns out to be 24%.
Fig. 7 demonstrates the distribution of pion multiplic-
ities for peripheral PbPb collisions (b ? 15:5 fm) at LHC
energies simulated by the FRITIOF code. The most prob-
able is the production of four pions and the distribution
is very broad. This conclusion is valid for all the charge
states of pions. The average pion multiplicities are given
in Tab. 6, where one can see that the multiplicities of the
pions produced in the above-defined grazing AA collisions
are generally greater than those for the flA process.
4 Comparison of different mechanisms of
pion production
Since most of the detectors used thus far in heavy-ion
experiments have very restricted acceptance on rapidity,
it is important to investigate the rapidity dependence of
the pion production cross section. Rapidity distributions
of neutral pions produced in peripheral PbPb collisions at
LHC energies are shown in Fig. 8.
Let us consider first the distributions without any ad-
ditional selection criteria. The distributions from the flfl
fusion and grazing nuclear collisions calculated by the
FRITIOF code with b ? 15:5 fm are very similar in shape.
The distributions of doe=dy for the single and inclusive п 0
production in the flfl fusion also have maximuma at y = 0.
But even in this region it is much lower then the contribu-
tion from grazing nuclear collisions. On the contrary, the
rapidity distribution for the flA production has peaks at
the beam and target rapidities. Nevertheless, its contribu-
tion at the midrapidity is comparable to one from the flfl
fusion.
This above-described picture is unfavourable for exper-
imental detection of the pions from flfl collisions. Nonethe-
less, one can improve the detection conditions by using
appropriate transverse momentum cuts. Indeed a single
meson from the flfl fusion has a very small transverse mo-
mentum. Selecting events with low values of p t one can
reject contributions from other processes. Following this
way, two different p t --cut procedures may be proposed.

14 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
According to the first procedure (b-criterion), one should
select the events with a small total transverse momentum
of the meson system jp t
(sum) j ? 75 MeV/c. The second
selection procedure (c-criterion) imposes more severe re-
strictions on the transverse momenta of the produced pi-
ons demanding each of them (including п 0 , п + , and п \Gamma )
to be small, jp t j ? 75 MeV/c, in this case. As one can see,
the b-criterion is equivalent to the c-criterion in the case
of the single pion production.
Let us investigate now to what extent the rapidity dis-
tributions are affected by the p t cuts. The distributions
obtained according to the b- and c-criteria are also given
in Fig. 8. One can see that the b-criterion reduces the con-
tribution from grazing nuclear collisions by three orders of
magnitude and gives some benefits for the detection of flfl
events. If this reduction is not sufficient, one can use the
c-criterion which is more efficient. Further suppression of
the pions from grazing nuclear collisions may be obtained
in the region \Gamma4 ! y ! 4. With this suppression even the
exclusive flfl ! п 0 channel may be clearly distinguished.
The difference in the b- and c-criteria applied to the flA
events calculated by the RELDIS code is less prominent.
This is explained by the fact that the single pion produc-
tion dominates in the flA collisions at ! ? 140 MeV while
the b- and c-criteria are equivalent for this case. Both of
the procedures may be recommended to reduce the con-
tribution from the flA process as it is shown in Fig. 8.
It should be noticed that the b-criterion does not af-
fect the inclusive distribution for the flfl fusion, while the
c-criterion suppresses the main part of the events of п 0
production due to heavy meson decays. This may be use-
ful for the extraction of the exclusive flfl ! п 0 process.
5 Conclusions
Only several hadrons are produced on average in very pe-
ripheral collisions of ultrarelativistic heavy ions. Because
of this feature such collisions can be considered as non-
violent events. The exact determination of the impact pa-
rameter in a collision event is beyond present experimen-
tal techniques. However, as it is shown in the present pa-
per, selecting the events with low multiplicity of produced
mesons, one can approximately identify a domain of large
impact parameters where the flfl fusion, flA or grazing
nuclear AA collisions takes place.
Calculations show that each of the mechanisms has a
specific distribution of the produced pions on the trans-
verse momentum, p t , and rapidity, y. One can use these
features for adjusting detectors to different regions of p t
and y with the possibility to disentangle pions produced
by different mechanisms. One can enhance the signal-to-
background ratio for the flfl fusion by selecting events with
a low p t by means of two procedures considered in the pa-
per. Our preliminary results confirm the importance of the
p t cut proposed in Ref. [12]. This procedure rejects the
background from flA and grazing AA collisions by sev-
eral orders of magnitude. Moreover, using p t cuts one can
avoid a pessimistic conclusion made in Ref. [37] that the
flfl fusion is indistinguishable from other processes since
the rapidity distributions for these processes are very sim-
ilar to each other.

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 15
6 Acknowledgments
L.I.S. and A.P.K. are grateful to Dr. Kai Hencken for use-
ful discussions and a possibility to use his code for compar-
ison. I.A.P. is indebted to INTAS for the financial support
from Young Scientists Fellowship 98-86 and thanks the
Niels Bohr Institute for the warm hospitality. The work is
supported in part by the Universities of Russia Basic Re-
search Fund, grant 5347, RFBR-DFG grant 99-02-04011
and by the Humboldt Foundation, Germany.
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K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 17
Table 1. Exclusive cross sections of single meson production in flfl fusion process in ultrarelativistic UU and PbPb collisions at
colliders. The values were calculated for comparison with Ref. [20]. The masses and two-photon decay widths for pseudoscalar
mesons were used according to Ref. [20].
cross section (mb)
Meson MR \Gamma MR!flfl Z=92 A=238 fl = 100 Z=82 A=208 fl = 4000
(GeV) (keV) [20] this work [20] this work
п 0 0.135 0.009 7.9 9.55 49 53.1
j 0.549 1 2.9 3.61 43 45.8
j 0 0.958 5 1.1 1.48 30 31.9
jc 2.981 6.3 2:5 \Delta 10 \Gamma3 4 \Delta 10 \Gamma3 0.59 0.644
j b 9.366 0.41 7\Delta 10 \Gamma9 3.36\Delta 10 \Gamma8 0.46 5 \Delta 10 \Gamma4
Table 2. Exclusive cross sections of single meson production in flfl fusion process in ultrarelativistic PbPb collisions at LHC.
The values were calculated for comparison with Ref. [8]. The masses and two-photon decay widths for c?c and b ? b mesons were
used according to Ref. [8].
cross section (mb)
Meson MR \Gamma MR!flfl Z=82 A=208 fl = 2750
(GeV) (keV) [8] this work
j 0 0.958 4.2 22 20.68
jc 2.981 7.5 0.59 0.552
и0c 3.415 3.3 0.16 0.145
j b 9.366 0.43 3.7\Delta10 \Gamma4 3.46\Delta10 \Gamma4
j 0b 9.860 2.5\Delta10 \Gamma2 1.8\Delta10 \Gamma5 1.62\Delta10 \Gamma5
j 2b 9.913 6.7\Delta10 \Gamma3 2.3\Delta10 \Gamma5 2.13\Delta10 \Gamma5

18 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
Table 3. Exclusive cross sections of single meson production in flfl fusion process in ultrarelativistic AuAu and PbPb collisions
at RHIC and LHC. The values were calculated for comparison with Ref. [7]. The masses and two-photon decay widths for
different scalar and pseudoscalar mesons were used according to Ref. [7].
cross section (mb)
Meson MR \Gamma MR!flfl Z=79 fl = 108 Z=82 fl = 2750
(GeV) (keV) this work [7] this work [7]
п 0 0.135 0.0077 4.744 5.721 37.701 42.937
j 0.547 0.51 1.127 1.285 18.744 19.897
j 0 0.958 4.5 0.826 0.989 22.152 24.780
f0(975) 0.974 0.25 0.042 0.0909 1.159 2.496
f0(1250) 1.25 3.4 0.177 0.332 6.360 11.728
f2 1.275 3.19 0.757 0.679 27.751 24.674
a2 1.318 1.14 0.230 0.252 8.784 9.542
п2 1.670 1.41 0.087 0.104 4.547 5.188
f4 2.05 1.4 0.053 0.0221 3.795 1.605
jc 2.98 6.3 3:18 \Delta 10 \Gamma3 3:66 \Delta 10 \Gamma3 0.464 0.555
и0c 3.42 5.6 1:21 \Delta 10 \Gamma3 1:36 \Delta 10 \Gamma3 0.243 0.290
j b 9.37 0.4 3:15 \Delta 10 \Gamma8 2\Delta10 \Gamma8 3:22 \Delta 10 \Gamma4 4:06 \Delta 10 \Gamma4

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 19
Table 4. Resonances, their decay modes and branching ratios (given in brackets) which were taken into account in inclusive
cross section calculation in the DRP model.
Channel MR \Gamma tot B in
R 1st decay step 2nd decay step B out
R
(GeV) (GeV)
flfl ! п 0 0.135 7.0\Delta10 \Gamma9 1. п 0 1
flfl ! j 0.547 1.18\Delta10 \Gamma6 0.388 j ! 3п 0 (0.32) 1.19
j ! п + п \Gamma п 0 (0.23)
flfl ! j 0 0.958 2.03\Delta10 \Gamma4 0.021 j 0 ! п 0 п 0 j (0.21) j ! 3п 0 (0.32) 1.18
j ! п + п \Gamma п 0 (0.23)
j 0 ! п + п \Gamma j (0.44) j ! 3п 0 (0.32)
j ! п + п \Gamma п 0 (0.23)
flfl ! f0 0.980 0.07 1.19\Delta10 \Gamma5 f0 ! п 0 п 0 (0.33) 0.66
flfl ! f2 1.275 0.185 1.32\Delta10 \Gamma5 f2 ! п 0 п 0 (0.28) 0.70
f2 ! п + п \Gamma 2п 0 (0.07)
flfl ! a2 1.318 0.107 9.4\Delta10 \Gamma6 a2 ! jп 0 (0.15) j ! 3п 0 (0.32) 0.33
j ! п + п \Gamma п 0 (0:23)
flfl ! п2 1.670 0.258 5.6\Delta10 \Gamma6 п2 ! f2п 0 (0.56) f2 ! п 0 п 0 (0.28) 1.10
f2 ! п + п \Gamma 2п 0 (0.07)
п2 ! f0(1370)п 0 (0.09) f0(1370) ! п 0 п 0 (0:33)

20 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
Table 5. Channels of elementary flN interaction taken into account in the INC model.
flp-interaction fln-interaction
flp ! п + n fln ! п \Gamma p
flp ! п 0 p fln ! п 0 n
flp ! п \Gamma \Delta ++ fln ! п \Gamma \Delta +
flp ! п 0 \Delta + fln ! п 0 \Delta 0
flp ! п + \Delta 0 fln ! п + \Delta \Gamma
flp ! jp fln ! jn
flp ! !p fln ! !n
flp ! ae 0 p fln ! ae 0 n
flp ! ae + n fln ! ae \Gamma p
flp ! п + п \Gamma p fln ! п + п \Gamma n
flp ! п 0 п + n fln ! п 0 п \Gamma p
flp ! п 0 п 0 п 0 p fln ! п 0 п 0 п 0 n
flp ! п + п \Gamma п 0 p fln ! п + п \Gamma п 0 n
flp ! п + п 0 п 0 n fln ! п \Gamma п 0 п 0 p
flp ! п + п + п \Gamma n fln ! п + п \Gamma п \Gamma p
flp ! iпN(4 ? i ? 8) fln ! iпN(4 ? i ? 8)
(35 channels) (35 channels)

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 21
Table 6. Average numbers of п + ,п \Gamma and п 0 mesons produced in flA and grazing AA collisions
flA AA
hn п +i hn п \Gamma i hn п 0 i hn п +i hn п \Gamma i hn п 0 i
100A+100A GeV 0.25 0.31 0.35 3.15 3.21 3.26
197 Au on 197 Au
2.75A+2.75A TeV 0.43 0.53 0.57 10.47 10.49 10.56
208 Pb on 208 Pb

22 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
A1
A2
fl
fl
п
X
Fig. 1. Meson production in flfl fusion.
A1
A2
fl
N
п
X
Fig. 2. Meson production in flA collision.
A1
A2
N
N
п
X
Fig. 3. Meson production in grazing AA collision.

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 23
R1
R2
B
b1 b2
E2
E1
A1 A2
P
Fig. 4. Effective flfl luminosity for heavy-ion collisions. The beam direction is perpendicular to the picture plane. b1 and b2 are
the distances from the nuclear centers to the photon interaction point P .

24 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
10 2
10 3
10 4
-10 -7.5 -5 -2.5 0 2.5 5 7.5 10
10 7
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Fig. 5. Rapidity and transverse momentum distributions of pions produced in flA process in PbPb collisions at LHC. The
results of the RELDIS code are given by solid, dashed and dotted histograms for п + , п \Gamma and п 0 mesons, respectively. Beam
rapidities are shown by arrows.

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 25
10
-3
10
-2
10
-1
0 2 4 6 8 10 12 14 16 18 20
10
-3
10
-2
10
-1
0 2 4 6 8 10 12 14 16 18 20
Fig. 6. Impact parameter distributions for nuclear PbPb collisions at LHC simulated by the FRITIOF code. The solid histogram
corresponds to all events. The doted and dashed histograms present the impact parameter distributions for events with N п 0 = 1
and N п 0 = 2, respectively.

26 K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions
Fig. 7. Pion multiplicity distributions for grazing nuclear PbPb collisions at LHC simulated by the FRITIOF code. The events
with impact parameter b ? 15:5 fm were selected.

K.A.Chikin et al.: Inclusive meson production in peripheral collisions of ultrarelativistic heavy ions 27
10
-3
10
-2
10
-1
1
10
10 2
10 3
10 4
-10 -8 -6 -4 -2 0 2 4 6 8 10
Fig. 8. Rapidity distribution of п 0 produced in peripheral PbPb collisions at LHC energies. The thick solid and dashed line
histograms labeled ``1'' are the inclusive (the DRP model) and exclusive cross sections for п 0 production in flfl fusion. The
histograms ``2a'',``2b'' and ``2c'' give the results of the RELDIS code for flA process. The FRITIOF results for peripheral
PbPb collisions with b ? 15:5 fm are given by the points ``3a'',``3b'' and ``3c''. The distributions with label ``a'' were obtained
without p t cuts. The label ``b'' corresponds to the selection of events with the total transverse momentum of meson system
jpt (sum) j ? 75 MeV/c. The label ``c'' corresponds to the selection of events with jpt j ? 75 MeV/c for each of the pions including
п 0 , п + , and п \Gamma .