Volume 67B, number 1 PHYSICS LETTERS 14 March 1977

O N T H E D I F F R A C T I V E P R O D U C T I O N O F C H A R M E D B A R Y O N S *

G6sta GUSTAFSON and Carsten PETERSON Department of Theoretical Physics, University of Lund, Lund, Sweden

Received 4 January 1977

Arguments are presented in favour of observing charmed baryons in diffractive scattering at high energies. The cross section for production of charmed baryons is estimated to be ~ 10-100 ~b at ISR energies.

Much effort has been devoted to find charmed par- ticles in hadronic reactions. For associated production of a charmed baryon and a charmed meson, e.g. np CD, one expects a very strong suppression due to low intercepts of charmed meson trajectories [ 1,2]. Expe- rimentally an upper bound of O(1 ~b) is obtained [3]. Charmed meson pairs may be more frequently produced at high energies in collisions of charmed sea quarks. Theoretical estimates give results of the order 10 -100 /~b at ISR energies [4, 5].

In this paper we suggest that the diffractive produc- tion process

p + p - + p + X l~c~, (1)

should be suitable for producing charmed baryons and we estimate the total cross section for this process to be of the same order of magnitude as for D[) produc- tion. One would perhaps expect that this reaction is equivalent to the associated production process at s = M 2 :'This view is supported by duality arguments

[11. However if we study the production of strange par-

ticles we note that the cross section for inclusive pro- duction of A in pp collisions is as large as ~ 4 mb in the fragmentation region_at PLab = 300 GeV/c [6]. (Here the cross section for A-production (~0.5 rob) has been subtracted in order to correct for central production). This should be compared with inclusive neutron pro- duction, which in the fragmentation region is only about three times as large [7]. If on the other hand we study the production of strange particles in e.g. n+p scattering near threshold at 1.95 GeV/c we see that the total cross section for strange particle production

* Supported by the Swedish Atomic Research Council.

is only ~0 .7 mb [8] which could be compared with a total inelastic cross section of t 15 mb [8]. Thus it seems to be easier to produce the heavier strange quark in the decay of a diffractively produced heavy object X than in an ordinary scattering process. (We also note that the average multiplicity of the decaying system X is higher than the average multiplicity in 7rp collisions at s = 5'12 [9] .) This fact could be understood in a pic- ture where X is a system with the same three valence quarks as in the proton, which has been excited so that the quarks have large relative momenta. It decays through polarization of quark-antiquark pairs out of the vacuum, as shown in fig. la. I f M x is high enough it is also possible to produce heavy quarks.

In this picture it is possible to divide the problem of diffractive production of charmed particles into two parts; first the probability of diffractive production of a heavy object C and secondly the probability that this object decays into particles with heavy, strange or charmed, quarks. Concerning the first part it is well known that the cross section for diffractive production of an object with massM x scales in M2/s [9, 10] im- plying da/dM 2 ~ M x 2.

The necessary cut off for large M 2 increases with increasing energy. If we assume a cut off at x ~ 1 - M2/s ~ 0.8, independent of energy, we obtain a cut

2 off in M x at ~0.2 s. Thus the cross section for diffrac- tive production of an object with mass ~>M 0 is propor- tional to

0.2s f 2 2 d M x / M x = In (0.2s/M20) , (2)

l e t us now consider the decay of the diffractively produced system X. This excited system of three quarks may decay by polarizing a heavy quark-antiquark pair

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Volume 67B, number 1 PHYSICS LETTERS 14 March 1977

q

q

Fig. 1. %) Allowed diagram for X ~ CD, where X is an excited nucleon, q = u or d quark and Q is the vacuum polarized quark. (b) Dominant mechanism in fig. la when the massless gluons are almost on shell. (c) Realization of fig. I a in the case when one gluon is far off shell.

from the vacuum. I f M x is high enough additional quark-antiquark pairs will be created. However the energy available for pair creation is now smaller and will hence mainly give extra pions. Thus an estimate of the probability that the decay products contain a charmed quark should be obtained from a diagram like the one in fig. 1 a.

If the momenta of the exchanged particles in fig. 1 a depends more upon the initial energy than the quark masses, the main difference for polarizing different quarks Q should come from the propagator 1/(k - mQ). We thus expect the amplitude to contain a factor 1/mQ. In this picture the important part of the diagram for vacuum polarization is the part in fig. lb, with the gluons not far from mass shell. If on the other hand the diagram in fig. lc, with a gluon far off shell should be more important, then we would, for zero gluon mass, expect a dependence 1/m~ from the gluon pro- pagator. The first alternative is favoured by the cross section for A production (see below).

Assuming that fig. lb represents the dominant me- chanism, the cross sections will obtain a factor 1/rn 2 which gives the following probabilities for polarizing different quark-antiquark pairs (quark masses are as- sumed to be 150 MeV, 300 MeV and 1500 MeV respec- tively).

u : d : s : c ~ 1 : 1 : 1 / 4 : 1 / 1 0 0 . (3)

Let us assume that the charmed baryon, produced in fig. 1, is either a cqq (q = u or d quark) S-wave state, or a resonance which decays into a cqq S-wave system. Let us also assume that this cqq baryon is obtained by randomly picking 2 quarks from the proton and adding a c-quark having spin up or down with equal probabi- lities. The state of a proton with spin up can be written:

11 1 1 1 1 : )

• 00 v~ oo

where t~ I3) denotes a diquark system and II~ 3 denotes 0 3 ~ 3

the third quark. If we add a c-quark randomly to tile diquark system we obtain the following probabilities

for producing C0(=Ac), CI (=Ec) and C T (= YI*): (5)

C 0+ = 1/2, C 1++-- 1/9, C 1 += 1/18, ~1¢~*++-- 2/9, C~ += 1/9.

If the interpretation of the ~,37r(2250) and A4rr(2500) peaks discovered in photoproduction [11] as C O and a mixture o fC 1 and C~ respectively [12], is correct, then all the C 1 and CT states will decay into 7rC~, whereas the decay C~-* C 17r is forbidden. Thus in a search for C 1 and C~ in the 7r+C~ mass spectrum, we estimate that about I /9 of the C~ particles will

++ 7r+C~ and 2/9 from the come from the reaction C 1 --> decay C~ ++ ~ 7r+C~.

Results analogous to eq. (5) are obtained for the production of A, E and Y~, if a s-quark is produced instead of a c-quark. In this case the decay E -+ 7rA is forbidden by the masses, but I; 0 will rapidly decay electromagnetically into TA. Y~ decays into 7rA with a branching ratio 0.88. This implies that the fraction of A's will be 0.87.

If finally a u- or a d-quark is produced we expect the fraction of neutrons and protons to be about 1/3 and 2/3 respectively. With these estimates and eq. (3) we find

R ( X ~ A+.. . ) 0.87 1 - - " - ~- 0.3 . (6)

R ( X o n + . . . ) 2"1/3 4

This is in good agreement with the ratio of A- to n- production in the fragmentation region at NAL energies [6, 7]. Furthermore the energy dependence of the A- production seems to be fairly well described by the expression In (0.2 s/M20 ) with a threshold value M 0 2 GeV. (The sharp threshold at s = 5M02 has of course to be smoothed out.) We regard this agreement as a good support for the above ideas. With a threshold M 0 ~ 5 GeV for CD production we find from eqs. (2)

+ and (3) that the total cross section for C O production will be ~2% of the A production i.e. ~ 0.08 mb at PL TM 300 GeV/c. At ISR energies we obtain ~0.15 rob.

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Volume 67B, number 1 PHYSICS LETTERS 14 March 1977

Of course these numbers are uncertain. If the dia- gram in fig. 1 c were more important than that in fig. lb the cross section would be a factor of 25 smaller. Even if this alternative should be closer to the truth we expect the suppression of charmed particles to be much smaller for this process than in ordinary meson baryon scattering, where Regge exchange amplitudes contain the charmed meson mass in the exponent.

We also note ".hat if our estimate is correct a non negligible fraction of the direct produced leptons with low p± are decay products of charmed particles [ 13, 141.

If one wants to look for C in the mass spectrum of e.g. ATrTr~ one should expect a background of around 100 times as many A's produced directly. These latter would be accompanied by a kaon and, i f M x is restricted to M x ~> 5 GeV, usually many pions. Thus this back- ground could be suppressed if one observes a lepton from the decay of the charmed meson (D or D*), which is produced together with C.

References

[1] V. Barger and R.J.N. Phillips, Phys. Rev. D 12 (1975) 2623.

[2] R.D. Field and C. Quigg, FERMILAB-75/15 (1975), unpublished.

[3] K. Bunnel et al., SLAC-PUB-1747 (1976). [4] A. Donnachie and P.V. Landshoff, Nucl. Phys. B112

(1976) 233. [5] D.I. Sivers, Nucl. Phys. B106 (1976) 95~ [6] F.T. Dao et al., Phys. Rev. Lett. 30 (1973) 1151. [7] J. Engler et al., Nucl. Phys. B84 (1975) 70. [8] Particle Data Group: lr+p, n+n and ~r+d interactions - a

compilation, LBL53 (1973). [91 M.G. Albrow et al., Nucl. Phys. B102 (1976) 275.

[10l D. Leith, SLAC-PUB-1646 (1975). [11] B. Knapp et al., Phys. Rev. Lett. 37 (1976) 882. [12] B.W. Lee, C. Quigg and J.L. Rosner, FERMILAB-76/71-

THY (1976). [13] M. Bourquin and J.-M. Galliard, Nucl. Phys. B114 (1976)

334. [14] K. Kajantie, Helsinki preprint 19-76 (1976).

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