The microcanonical statistical approach is applied to study the production of
pentaquark states in pp collisions. We predict the average multiplicity and
average transverse momentum of Theta^{+}(1540) and Xi(1860) and their
antiparticles at different energies.Comment: 8 pages, 5 figure

Airapetian

Ansorge

Antinucci

Barmin

Barth

Bleicher

Chemtob

Cohen

Diakonov

F.M. Liu

Gazdzicki

Giacomelli

Greiner

H. Stöcker

Itzhaki

Jaffe

K. Werner

Letessier

Nakano

Praszalowicz

Randrup

Stepanyan

Strottman

Weigel

Werner

Physics Letters B

English

arXiv

The microcanonical statistical approach is applied to study the production of pentaquark states in pp collisions. We predict the average multiplicity and the average transverse momentum of Θ+(1540) and Ξ(1860) and their antiparticles at different energies

Liu, Fu-Ming

Stöcker, Horst

Werner, Klaus

Hochschulschriftenserver - Universität Frankfurt am Main

Production of pentaquark states in pp collisions within the microcanonical ensemble

The microcanonical statistical approach is applied to study the production of pentaquark states in pp collisions. We predict the average multiplicity and average transverse momentum of Theta+(1540) and Xi(1860) and their antiparticles at different energies

arXiv:hep-ph/0404156 v2   20 Apr 2004                                                                            1,2∗         1         3               1                                                                           2                                                                                           3                                                                                                                                                                                                                                                   Θ+(1540)    Ξ(1860)                                                            Θ+(1540)                        K+n                                             ℄     Θ+(1540)                                                (uudd¯ s)   q4¯ q                                                                                                                 ℄                                                                                                                                                             q4¯ q                                                                                                              ℄                                              10f, 12+)        mΘ = 1540MeV             Θ+(1540)                                                          10f, 12+)                                   N  Σ    Ξ                            ℄                                                                q4¯ q                                                                                ℄  Θ+(1540)                                                                     ud                         q4¯ q     ∗                                                      Θ+(1540)                N                                              uudd¯ u                   Θ+(1540)                          (27f)                                                                 ℄                                          Θ+(1540)                  Ξ          Ξ−−(ddss¯ u)  Ξ−(dssq¯ q)  Ξ0(ussq¯ q)   Ξ+(uuss¯ d)       q¯ q                             u¯ u   d¯ d                              ℄                                  Ξ−−(1860)    Ξ0(1860)                 Θ+(1540)    Ξ(1860)                                                                                                                                                                                                                                                                                                                                                                                                                              Θ+(1540)   Ξ(1860)                                                                                                    ℄                                                                                                                                                           4π                                                                                                                                                                                                                                                       Θ+(1540)    Ξ(1860)                                                                                                                                                                                                                                                                                                                 V                                            E                                                  Q =(Nu −N¯ u,Nd −N¯ d,Ns −N¯ s)                                                                                                          K = {h1,p1;...;hn,pn}          hi                pi                                         Ω(K) Ω(K) =V n(2π¯ h)3nn Yi=1giYα∈S1nα!n Yi=1d3pi δ(E − Σεi)δ(Σ  pi)δQ,Σqi,        εi =qm2i + p2i                     pi                       i  nα                             α     gi                        i         δQ,Σqi                                              Q = (4,2,0)  qi                         i           S                                                    S                                     (π,K,η,η′,ρ,K∗,ω,φ)                 12        32        (N,Λ,Σ,Ξ,∆,Σ∗,Ξ∗,Ω)                                                             K                                    Ω(K)                        ℄                          Θ+(1540)  Ξ(1860)                         S    Θ+                (uudd¯ s)     Ξ(1860)     Ξ−−(ddss¯ u)  Ξ−(dssq¯ q)  Ξ0(ussq¯ q)   Ξ+(uuss¯ d)                                                                                              12                                g = 2                                                                                                                                            Θ+(1540)  Ξ(1860)        32                                               12                                                                                                                                                                12             Ξ−(dssq¯ q)    Ξ0(ussq¯ q)     q¯ q     u¯ u   d¯ d                               Ξ              q3        Ξ−(dss)    Ξ0(uss)                                                           q3    q4¯ q                                                                                   q¯ q                                                                                                                                  (E, V )                            √s/GeV                       4π                                              p, ¯ p, π+, π−       ℄ E/GeV = −3.8 + 3.76ln√s + 6.4/√sV/fm3 = −30.0376 + 14.93ln√s − 0.013√s.                                                        4π               p, ¯ p, π+, π−                                                                                                                                                                                                                                                                                                  ℄                          1/3                            Λ    ¯ Λ                                                             ℄                             Ξ                                                              1/9          Ξ−                                     1/9                       ℄  10-210-111010 210 102 √s (GeV) average multiplicity   10xp+ p- p p_         p, ¯ p, π+, π−                                                            ℄                                                                                  10-210-1110 102 √s (GeV) multiplicityK+10-210-110 102 √s (GeV) multiplicityK-10-210-1110 102 √s (GeV) multiplicity K0+K----010-310-210-110 102 √s (GeV) multiplicityL10-210-110 102 √s (GeV) multiplicityaL10-410-210 102 √s (GeV) multiplicityX-                         1/3                            Λ    ¯ Λ                                                           ℄                              Ξ−                                     1/9                                         ℄                    Θ+                                                                                                        1/3    Θ+                                                                                Ξ(1860)                                                                   1/9                                                                                         Θ+                 Θ+                                         p + p → Θ+ + Σ+   ℄         4π                                                                                                                                      10-410-310-210 102 √s (GeV) multiplicityQ+ Q+                           Θ+                                          10-510-410-310 102 √s (GeV) multiplicityX-- X--10-510-410-310 102 √s (GeV) multiplicityX- X-10-510-410-310 102 √s (GeV) multiplicityX0 X010-510-410-310 102 √s (GeV) multiplicityX+ X+                           Ξ(1860)                                                                  ℄                                                Θ+(1540)    Ξ(1860)                                                                                                Ξ−−(ddss¯ u)  Ξ−(dss)  Ξ0(uss)    Ξ+(uuss¯ d)                                                                                                                                                                                                 ℄                Θ+    Ξ(1860)    2 ∼ 3                          Θ/p                                                                                                   ℄                             ℄                                   Ξ−−(1860)/Ξ−                            3 ∼ 4                               ℄                       σpp→Θ+                                                                             20 b   ℄                                                                                                                                                                       10−2                                   Θ+            Ξ                                        4  10−4                       0.40.50.60.70.810 102 √s (GeV) < pt > (GeV)Q+ Q+0.40.50.60.70.810 102 √s (GeV) < pt > (GeV)X X                                       Θ+(1540)    Ξ(1860)                                                                                                                                                                              ℄        etal                                  ℄                             etal                                ℄                                                    ℄                           etal                             ℄                               etal                   ℄                                           ℄                                                                                                  ℄                                                  SkyrmionsandAnomalies                                                                                                                                                                   ℄                                                   ℄                                  etal                                                  ℄                       etal                    ℄          etal                    ℄                                                    ℄                                                                                                         ℄                                                                                                                           ℄                                                                                  ℄                       ℄                                        ℄                                 ℄                              ℄                                                        ℄    ℄                                                                    

Albanian

Crossref

AbstractThe microcanonical statistical approach is applied to study the production of pentaquark states in pp collisions. We predict the average multiplicity and the average transverse momentum of Θ+(1540) and Ξ(1860) and their antiparticles at different energies

Liu, F.M.

Stöcker, H.

Werner, K.

Elsevier - Publisher Connector 

Production of pentaquark states in pp collisions within the microcanonical ensemble 

Physics Letters B 597 (2004) 333–337
www.elsevier.com/locate/physletb
Production of pentaquark states in pp collisions
within the microcanonical ensemble
F.M. Liu a,b,1, H. Stöcker a, K. Werner c
a Institut für Theoretische Physik, J.W. Goethe Universität, Frankfurt am Main, Germany
b Institute of Particle Physics, Central China Normal University, Wuhan, PR China
c Laboratoire SUBATECH, University of Nantes, IN2P3/CNRS, Ecole des Mines de Nantes, Nantes, France
Received 1 May 2004; accepted 17 July 2004
Available online 26 July 2004
Editor: J.-P. Blaizot
Abstract
The microcanonical statistical approach is applied to study the production of pentaquark states in pp collisions. We predict
the average multiplicity and the average transverse momentum of Θ+(1540) and Ξ(1860) and their antiparticles at different
energies.
 2004 Elsevier B.V. Open access under CC BY license.Recently, an exotic baryon, Θ+(1540), with the
quantum numbers of K+n has been reported in several
experiments [1–5]. The Θ+(1540) cannot be a three
quark state. Its minimal quark content is (uudds¯), a
so-called pentaquark state.
Pentaquark states have been theoretically investi-
gated since a long time in the context of the constituent
quark model [6,7]. Also other models have been em-
ployed to construct q4q¯ pentaquark states, predicting
different masses and quantum numbers. For example,
E-mail address: liufm@iopp.ccnu.edu.cn (F.M. Liu).
1 Research fellow of Alexander von Humboldt Foundation.0370-2693 2004 Elsevier B.V.
doi:10.1016/j.physletb.2004.07.032
Open access under CC BY license.the chiral soliton (Skyrme) model [8] predicts that
the lightest member of the SU(3)-flavor (10f , 12
+
)-
let has mΘ = 1540 MeV. The reported Θ+(1540)
agrees with the prediction remarkably well. The other
members of the (10f , 12
+
) antidecuplet are isospin-
multiplets of N , Σ and Ξ . In an uncorrelated quark
model [7], where all quarks are in the ground state of
a mean field, the ground state of q4q¯ has negative par-
ity. This is a striking difference to the chiral soliton
model. In Jaffe and Wilczek’s model [9], Θ+(1540) is
considered to be a bound state of an antiquark with
two highly correlated spin-zero ud diquarks. Hence
the lightest q4q¯ state cannot be Θ+(1540) but be-
longs to the N isospin-multiplets with minimal quark
334 F.M. Liu et al. / Physics Letters B 597 (2004) 333–337content, i.e., uuddu¯. Other models regard Θ+(1540)
as a member of the SU(3) flavor (27f )-let. Missing
members of the multiplet are assigned to reported par-
ticles [10].
The common members of above mentioned mod-
els are Θ+(1540) and the multiplets of Ξ , which
can be Ξ−−(ddssu¯), Ξ−(dssqq¯), Ξ0(ussqq¯) or
Ξ+(uussd¯), where qq¯ is a hidden quark–antiquark
pair uu¯ or dd¯ . Recently the NA49 Collaboration [11]
also presented the results of a search of Ξ−−(1860)
and Ξ0(1860).
The estimation of Θ+(1540) and Ξ(1860) yields at
different collision energies independent of the above-
mentioned models will be helpful for the search of
pentaquark states in proton–proton collisions in the
ongoing experiments at SPS and RHIC. Some work
has been done using the statistical hadronization ap-
proach within grandcanonical and canonical ensem-
bles. However, the system is small in proton–proton
collisions, and a microcanonical ensemble should be
employed.
The dynamical model NEXUS has also been used
to estimate the yields of Θ+(1540) and Ξ(1860), via
employing the microcanonical ensemble to hadronize
the remnants (formed by spectator quarks from the
collisions) [12].
In this Letter, we use an entirely microcanonical ap-
proach to study the production of pentaquark states
in pp collisions. The microcanonical parameters are
well studied already in previous work via fitting the
4π yields of charged pions, proton and antiproton. We
organize the Letter as followed: first we explain the
model, how pentaquark states are produced in pp col-
lisions, then we check how reliable the microcanonical
parameters are, then we present our results, the yields
and average transverse momentum of Θ+(1540) and
Ξ(1860) and their antiparticles, and finally we com-
pare our results to some other theoretical work and dis-
cuss our predictions on SPS and RHIC experiments.
We use the microcanonical ensemble to study the
production of pentaquark states in pp collisions. In
the microcanonical ensemble, we consider the final
state of a proton–proton collision as a “cluster” char-
acterized by its volume V (the sum of individual
proper volumes), its energy E (the sum of all the clus-
ter masses) and the net flavor content Q = (Nu −
Nu¯,Nd − Nd¯,Ns − Ns¯), decaying “statistically” ac-
cording to phase space. More precisely, the proba-bility of a cluster to hadronize into a configuration
K = {h1,p1; . . . ;hn,pn} of hadrons hi with four mo-
menta pi is given by the micro-canonical partition
function Ω(K),
Ω(K) = V
n
(2πh¯)3n
(1)
×
n∏
i=1
gi
∏
α∈S
1
nα !
n∏
i=1
d3pi
× δ(E − Σεi) δ(Σ pi) δQ,Σqi ,
with εi =
√
m2i + p2i being the energy, and pi the
3-momentum of particle i . nα is the number of
hadrons of species α, and gi is the degeneracy of
particle i . The term δQ,Σqi ensures flavor conserva-
tion and the net flavor content Q = (4,2,0); qi is
the flavor vector of hadron i . The symbol S repre-
sents the set of hadron species considered: the ordi-
nary S contains the pseudoscalar and vector mesons
(π,K,η,η′, ρ,K∗,ω,φ) and the lowest spin- 12 and
spin- 32 baryons (N,Λ,Σ,Ξ,∆,Σ
∗,Ξ∗,Ω) and the
corresponding antibaryons. We generate randomly
configurations K according to the probability distri-
bution Ω(K). For the details see Ref. [13].
We add the pentaquark states Θ+(1540), Ξ(1860)
and their antiparticles into S . The Θ+ has quark con-
tents (uudds¯). The Ξ(1860) can be Ξ−−(ddssu¯),
Ξ−(dssqq¯), Ξ0(ussqq¯) or Ξ+(uussd¯). The spin of
pentaquark states cannot be determined by experi-
ments yet, and it is generally accepted they are spin- 12
particles, so we take a degeneracy factor g = 2.
In our approach, because of the heavy masses of the
pentaquark states, the hadron configurations contain-
ing these particles appear very rarely. Therefore, if the
pentaquark states Θ+(1540), Ξ(1860) were spin- 32
particles, then their yields would be twice as big as the
results obtained for spin- 12 , according to Eq. (1), but
their average transverse momenta would be the same.
In the following, we report the results for spin- 12 parti-
cles.
In case of Ξ−(dssqq¯) and Ξ0(ussqq¯), the qq¯ can
be uu¯ or dd¯ , so these particles might be considered to
be three-quark states, Ξ−(dss) and Ξ0(uss). In the
microcanonical calculation, we do not need to distin-
guish between q3 and q4q¯ , the two cases give the same
results, when the masses and degeneracy factors are
the same, because the qq¯ of the same flavor does not
F.M. Liu et al. / Physics Letters B 597 (2004) 333–337 335Fig. 1. p, p¯, π+, π− excitation functions. The empty square points
are experimental data [16], solid lines are microcanonical calcula-
tion after adding the pentaquark states into the hadron set.
play any role in conserving flavors or charge in the mi-
crocanonical statistical hadronization approach.
The microcanonical parameters (E, V ) for pp col-
lisions at a given energy
√
s/GeV are obtained by
fitting the 4π multiplicities of the most copiously pro-
duced particles (p, p¯, π+, π−) [14,15]:
E/GeV = −3.8 + 3.76 ln√s + 6.4/√s,
V /fm3 = −30.0376 + 14.93ln√s − 0.013√s.
After adding pentaquarks states into the hadron set,
we have to verify whether the 4π multiplicities of
p, p¯, π+, π− still agree with the data, see Fig. 1. Ac-
tually, the yields of light particles are hardly changed,
except for antiproton. About 10% more antiprotons are
produced to compensate the net baryon numbers car-
ried by the pentaquark states.
The microcanonical calculation has no strangeness
suppression factor, so strange hadrons are overpro-
duced [15]. However, with a global factor 1/3 per
strange (anti)quark, strange hadrons yields (K , Λ and
Λ¯, Ξ ) agree roughly with the data, as shown in Fig. 2,
where microcanonical calculations (solid lines) are
compared with data [16–18] (empty squares).
In the following, we discuss the results for pen-
taquark hadrons. Also here we employ a strangeness
suppression factor 1/3 per strange (anti)quark. The
particle yields of Θ+ (solid line) and its antiparti-
cle (dashed line) from pp collisions at different col-Fig. 2. With a global factor 1/3 per strange (anti)quark, the microcanonical calculation (solid lines) can reproduce the data [16–18] (empty
squares) for strange hadrons such as K , Λ and Λ¯, Ξ− .
336 F.M. Liu et al. / Physics Letters B 597 (2004) 333–337Fig. 3. The particle yields of Θ+ (solid line) and its antiparticle
(dashed line).
lision energies are shown in Fig. 3. The yields of the
Ξ(1860) particles (solid lines) and the corresponding
antiparticles (dashed lines) are showed in Fig. 4. With
the increase of collision energy, more and more pen-
taquarks states are produces, except Θ+. We can see
in Fig. 3, Θ+ is favored at low energies because of the
channel p + p → Θ+ + Σ+ [19].
With the 4π yields of charged pions, protons and
antiprotons as input, the microcanonical calculation
can predict reliably the average transverse momenta of
both non-strange and strange hadrons [15]. In Fig. 5,
we also show the average transverse momentum of
Θ+(1540) and Ξ(1860) (solid lines) and their antipar-
ticles (dashed lines). The difference between the aver-Fig. 4. The particle yields of the Ξ(1860) particles (solid lines) and their antiparticles (dashed lines).
Fig. 5. The average transverse momentum of Θ+(1540) and Ξ(1860) (solid lines) and their antiparticles (dashed lines).
F.M. Liu et al. / Physics Letters B 597 (2004) 333–337 337age transverse momentum of Ξ−−(ddssu¯), Ξ−(dss),
Ξ0(uss) and Ξ+(uussd¯) from the microcanonical
calculation is very small antiparticles.
Now we compare our results to previous research
results at SPS and RHIC energies. It is expected that
the yields of pentaquark states should be higher as
compared to NEXUS calculations [12]. Indeed we find
2–3 times more Θ+ and Ξ(1860). We also compare
the particle ratio with the results from other models
even though these models are meant to describe heavy
ion collisions, corresponding to the large-system limit
of our microcanonical treatment. Our microcanonical
particle ratio Θ/p is about 0.7%, which agrees sur-
prisingly well with the prediction from a quark mole-
cular dynamics model prediction (0.6% [20]), while
the grandcanonical ensemble [21] gives about 6%. The
particle ratio Ξ−−(1860)/Ξ− is 2% at SPS and 3% at
RHIC, which is 3–4 times bigger than the grandcanon-
ical results [22].
The inclusive cross section σpp→Θ+ near the pro-
duction threshold, estimated with empirical coupling
constants and form factor, is 20 µb [19], which is about
ten times smaller than our results.
In conclusion, we presented a calculation of the
yields of different pentaquark states in pp collisions,
using the microcanonical approach. We obtain roughly
10−2 (almost independent of energy) for the Θ+,
whereas the Ξ yields increase strongly with energy,
reaching 4 × 10−4 at RHIC.
Acknowledgements
F.M.L. Thanks Prof. B.Q. Ma and Prof. M. Blei-
cher for the fruitful discussions and the Alexander von
Humboldt Foundation for the finance support.References
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8 pages, 5 figuresThe microcanonical statistical approach is applied to study the production of pentaquark states in pp collisions. We predict the average multiplicity and average transverse momentum of Theta^{+}(1540) and Xi(1860) and their antiparticles at different energies

Liu, F. M.

Stoecker, H.

HAL-Univ-Nantes

Production of Pentaquark States in pp Collisions within the Microcanonical Ensemble

HAL Mines Nantes

HAL-IN2P3

file:///data/remote/core/dit/data/elsevier/pdf/71e/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDM3MDI2OTMwNDAxMDcwNg==.pdf

Production of Pentaquark States in pp Collisions within the
  Microcanonical Ensemble

Production of Pentaquark States in pp Collisions within the Microcanonical Ensemble

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