- Email: [email protected]
Flavour transfer and models of the Pomeron
Volume 67B, number 3
PHYSICS LETTERS
FLAVOUR TRANSFER
11 April 1977
AND MODELS OF THE POMERON M. JEZABEK
Institute of Physics, Jagellonian University, Cracow, Poland Received 22 February 1977 Distributions of flavours in multiparticle final states are discussed. It is pointed out that transfers of flavours in the quark exchange model of Brodsky and Gunion, and in the gluon exchange model of Low and Nussinov have different characteristics. Simple experimental tests to distinguish between these models are proposed. 1. Recently two different models of the particle production in hadron-hadron collisions have been proposed. These are also models of the Pomeron because of the unitarity. In the Low-Nussinov [1,2] model (GEM) an initial interaction proceeds via gluon exchange. This interaction sets up a system with separated colour octets near the ends of the rapidity ]axis (fig. 1a). On the other hand Brodsky and Gunion take the exchanged parton to be a quark [3]. Thus at first they have a system with separated 3 and 3 colour currents (fig. lb). The next assumption is that when two coloured quarks are separated in momentum, radiation of coloured gluons occurs. The radiated gluons materialize as hadrons in such a way that hadron multiplicity depends only on the gluon multiplicity i.e. on the underlying quark configuration. Thus the fact that hadron multiplicities have a universal parametrization [4] for hadron-hadron, e+e - and deep inelastic lepton-hadron scattering can be easily explained in this quark exchange model (QEM). It is purpose of this paper to discuss implications of these models for distributions of flavours in the hadronic final state. In QEM we start from q and ~ currents separated in rapidity (let Y be the length of the gap). This leads to long-range correlations between flavours. In the next step gluons are emitted. They turn into quarkantiquark pairs which recombine giving hadrons. Our essential assumption is that there are no correlations
between flavours o f quarks from different gluons. Furthermore, it is very probable thatY0, a gap between quark and antiquark from one gluon cannot be much more than 1 because of the well known local compensation of quantum numbers [5]. If this is the case (in general i f y 0 < Y) the transition 292
."
C*)
3
~b)
Fig. 1. Colour separation: (a) in the gluon exchange model of refs. [ 1,2] and (b) in the quark exchange model of ref. [3]. from gluons to hadrons does not disturbe the flavour correlation introduced to the system by quark which was exchanged. No such correlation can be expected in GEM because the gluon carries no flavour. Thus studying longrange correlations of charge, strangeness, charm etc., we can obtain informations about parton which is exchanged in hadron-hadron collisions. 11. Since the production of strange and charmed particles is small, it is a good approximation in the discussion of charge distribution to allow only u and d quarks to be produced. For the same reason we can neglect baryon-antibaryon pairs in the final multiparticle state *x . The right charge QRO') (left charge QL(Y)) is defined as a total charge of particles which have rapidity greater than y (smaller than - y ) . QRCV) = ~
Qi, QL(Y) = ~ Qi" yi>y yi < -y The charge correlation is defined as
(1)
C(y) = (OR)(QL ) - (QRQL) ,
(2)
where ( ) denotes averaging. If we take ½ Y >>y >>½Y0 ,l Moreover it is easy to show that these processes do not alter conclusions about the charge correlation at long distances.
Volume 67B, number 3
PHYSICS LETTERS
11 April 1977
ordering (figs. 2b and 2c) takes place, ~ = 2 and C(0) = ½. It is interesting that, as pointed out by Jadach and Dias de Deus [8], the squared dispersion of the charge transfer distribution is indeed equal to 0.5 for K - p (16 GeV/c) and pp (24 GeV/c) inelastic collisions, after correction for leading charges effect is performed.
Fig. 2. Examples of hadronization ofgluons: (a) baryonantibaryon pair production in the quark exchange model, (b) strong ordering in the quark exchange model and (c) strong ordering in the gluon exchange model.
we can write OR(Y) = q + R ,
QL(Y) = - q +L ,
(3)
where q denotes the charge of exchanged parton. R and L, as defined by eq. (3), are statistically independent. Consequently we have C(y) -- (q2) _ ( q ) 2 .
(4)
Thus for ½Y>>y >>½Y0 we obtain C O ' ) = ¼ in the quark exchange model (we assume the same probabilities for u and d quarks to be exchanged) and in the gluon exchange model C ( y ) = O. It is also interesting to study the charge correlation f o r y = 0 in the CM frame. This is related to the charge transfer [6] defined as AQ = QR(O) - Q~ ,
(5)
where Q/R denotes the right charge before the collision. At asymptotic energies C(0) equals to squared dispersion of the charge transfer. However at finite energies it is much less sensitive to effect of leading charges [7] than the moments of the charge transfer distribution and therefore more appropriate for studies of the central particle production. In both models we discuss here, the charge correlation for y = 0 can be expressed
Ill. To investigate transfers of other quantum numbers which are involved with exchanged parton, the same formalism as for the charge may be used. However, if we assume no more than one charmed-anticharmed (or strange-antistrange)pair of particles per collision it will be useful to study instead rapidity gaps distributions. In GEM a source of the rapidity gap between two charmed (strange) particles is a separation (~Y0)between c and E (or s and-g) quarks from the same gluon. Thus the gaps distribution for lengths much longer than Y0 should rapidly die out. In the quark exchange picture there is an extra source of the long gaps and a characteristic length of these gaps is Y. IV. Our conclusions can be summarized as follows. It is shown that the charge correlation and the rapidity gaps distributions for strange and charmed particles can provide information about partons which are exchanged in the hadron-hadron collisions. This follows from the observation that in hadronization of gluons only short order (~ 1 in rapidity) correlations of flavours should occur and consequently this process cannot alter the long order correlations implied by the exchanged parton. The author would like to thank Professor A. Biatas for helpful conversations and critical reading of the manuscript, and Dr. K. Fiatkowski for his constant encouragement and advice.
as
C(0) = ¼ ~,
(~ ~> 2 ) ,
(6)
where ~ denotes the mean number of quark-antiquark pairs separated by the cut (in QEM we must take the exchanged quark into account, e.g. ~ = 3 for a configuration as that in fig. 2a). To obtain a value of ~ and to compare predictions of QEM and GEM for the central region, more detailed assumptions about hadronization of gluons are needed. For example, if the strong
References [1] F.E. Low, Phys, Rev. D12 (1975) 163. [2] S. Nussinov, Phys. Rev. Lett. 34 (1975) 1286. [3] S.J. Brodsky and J.F. Gunion, Phys. Rev. Lett. 37 (1976) 402. [4] This universality seems to be controversial, cf.: P. Stix and T. Ferbel, Univ. of Rochester preprint UR-595 (1976). [5] For review and references see e.g.: D. Weingarten, Phys. Rev. DI3 (1976) 1494; A. Krzywicki, Orsay preprint LPTPE 76/25. 293
Volume 67B, number 3
PHYSICS LETTERS
[6] For review of applications of the charge transfer in phenomenology of particle production see e.g.: A. Bialas, in: Proc. of the IVth Intern. Syrup. of Multiparticle hadrodynamics, Pavia (1973); L. Fog, Phys. Reports 22C (1975) 1.
294
11 April 1977
[71 A. Biatas, K. Fiatkowski, M. Je~abek and M. Zielifiski, Acta Phys. Polon. B6 (1975) 59; R. Baier and F. Bopp, Bielefeld preprint Bi 75/11 (1975). [8] J. Dias de Deus and S. Jadach, Rutherford Lab. preprint RL-76-129/A.
PHYSICS LETTERS
FLAVOUR TRANSFER
11 April 1977
AND MODELS OF THE POMERON M. JEZABEK
Institute of Physics, Jagellonian University, Cracow, Poland Received 22 February 1977 Distributions of flavours in multiparticle final states are discussed. It is pointed out that transfers of flavours in the quark exchange model of Brodsky and Gunion, and in the gluon exchange model of Low and Nussinov have different characteristics. Simple experimental tests to distinguish between these models are proposed. 1. Recently two different models of the particle production in hadron-hadron collisions have been proposed. These are also models of the Pomeron because of the unitarity. In the Low-Nussinov [1,2] model (GEM) an initial interaction proceeds via gluon exchange. This interaction sets up a system with separated colour octets near the ends of the rapidity ]axis (fig. 1a). On the other hand Brodsky and Gunion take the exchanged parton to be a quark [3]. Thus at first they have a system with separated 3 and 3 colour currents (fig. lb). The next assumption is that when two coloured quarks are separated in momentum, radiation of coloured gluons occurs. The radiated gluons materialize as hadrons in such a way that hadron multiplicity depends only on the gluon multiplicity i.e. on the underlying quark configuration. Thus the fact that hadron multiplicities have a universal parametrization [4] for hadron-hadron, e+e - and deep inelastic lepton-hadron scattering can be easily explained in this quark exchange model (QEM). It is purpose of this paper to discuss implications of these models for distributions of flavours in the hadronic final state. In QEM we start from q and ~ currents separated in rapidity (let Y be the length of the gap). This leads to long-range correlations between flavours. In the next step gluons are emitted. They turn into quarkantiquark pairs which recombine giving hadrons. Our essential assumption is that there are no correlations
between flavours o f quarks from different gluons. Furthermore, it is very probable thatY0, a gap between quark and antiquark from one gluon cannot be much more than 1 because of the well known local compensation of quantum numbers [5]. If this is the case (in general i f y 0 < Y) the transition 292
."
C*)
3
~b)
Fig. 1. Colour separation: (a) in the gluon exchange model of refs. [ 1,2] and (b) in the quark exchange model of ref. [3]. from gluons to hadrons does not disturbe the flavour correlation introduced to the system by quark which was exchanged. No such correlation can be expected in GEM because the gluon carries no flavour. Thus studying longrange correlations of charge, strangeness, charm etc., we can obtain informations about parton which is exchanged in hadron-hadron collisions. 11. Since the production of strange and charmed particles is small, it is a good approximation in the discussion of charge distribution to allow only u and d quarks to be produced. For the same reason we can neglect baryon-antibaryon pairs in the final multiparticle state *x . The right charge QRO') (left charge QL(Y)) is defined as a total charge of particles which have rapidity greater than y (smaller than - y ) . QRCV) = ~
Qi, QL(Y) = ~ Qi" yi>y yi < -y The charge correlation is defined as
(1)
C(y) = (OR)(QL ) - (QRQL) ,
(2)
where ( ) denotes averaging. If we take ½ Y >>y >>½Y0 ,l Moreover it is easy to show that these processes do not alter conclusions about the charge correlation at long distances.
Volume 67B, number 3
PHYSICS LETTERS
11 April 1977
ordering (figs. 2b and 2c) takes place, ~ = 2 and C(0) = ½. It is interesting that, as pointed out by Jadach and Dias de Deus [8], the squared dispersion of the charge transfer distribution is indeed equal to 0.5 for K - p (16 GeV/c) and pp (24 GeV/c) inelastic collisions, after correction for leading charges effect is performed.
Fig. 2. Examples of hadronization ofgluons: (a) baryonantibaryon pair production in the quark exchange model, (b) strong ordering in the quark exchange model and (c) strong ordering in the gluon exchange model.
we can write OR(Y) = q + R ,
QL(Y) = - q +L ,
(3)
where q denotes the charge of exchanged parton. R and L, as defined by eq. (3), are statistically independent. Consequently we have C(y) -- (q2) _ ( q ) 2 .
(4)
Thus for ½Y>>y >>½Y0 we obtain C O ' ) = ¼ in the quark exchange model (we assume the same probabilities for u and d quarks to be exchanged) and in the gluon exchange model C ( y ) = O. It is also interesting to study the charge correlation f o r y = 0 in the CM frame. This is related to the charge transfer [6] defined as AQ = QR(O) - Q~ ,
(5)
where Q/R denotes the right charge before the collision. At asymptotic energies C(0) equals to squared dispersion of the charge transfer. However at finite energies it is much less sensitive to effect of leading charges [7] than the moments of the charge transfer distribution and therefore more appropriate for studies of the central particle production. In both models we discuss here, the charge correlation for y = 0 can be expressed
Ill. To investigate transfers of other quantum numbers which are involved with exchanged parton, the same formalism as for the charge may be used. However, if we assume no more than one charmed-anticharmed (or strange-antistrange)pair of particles per collision it will be useful to study instead rapidity gaps distributions. In GEM a source of the rapidity gap between two charmed (strange) particles is a separation (~Y0)between c and E (or s and-g) quarks from the same gluon. Thus the gaps distribution for lengths much longer than Y0 should rapidly die out. In the quark exchange picture there is an extra source of the long gaps and a characteristic length of these gaps is Y. IV. Our conclusions can be summarized as follows. It is shown that the charge correlation and the rapidity gaps distributions for strange and charmed particles can provide information about partons which are exchanged in the hadron-hadron collisions. This follows from the observation that in hadronization of gluons only short order (~ 1 in rapidity) correlations of flavours should occur and consequently this process cannot alter the long order correlations implied by the exchanged parton. The author would like to thank Professor A. Biatas for helpful conversations and critical reading of the manuscript, and Dr. K. Fiatkowski for his constant encouragement and advice.
as
C(0) = ¼ ~,
(~ ~> 2 ) ,
(6)
where ~ denotes the mean number of quark-antiquark pairs separated by the cut (in QEM we must take the exchanged quark into account, e.g. ~ = 3 for a configuration as that in fig. 2a). To obtain a value of ~ and to compare predictions of QEM and GEM for the central region, more detailed assumptions about hadronization of gluons are needed. For example, if the strong
References [1] F.E. Low, Phys, Rev. D12 (1975) 163. [2] S. Nussinov, Phys. Rev. Lett. 34 (1975) 1286. [3] S.J. Brodsky and J.F. Gunion, Phys. Rev. Lett. 37 (1976) 402. [4] This universality seems to be controversial, cf.: P. Stix and T. Ferbel, Univ. of Rochester preprint UR-595 (1976). [5] For review and references see e.g.: D. Weingarten, Phys. Rev. DI3 (1976) 1494; A. Krzywicki, Orsay preprint LPTPE 76/25. 293
Volume 67B, number 3
PHYSICS LETTERS
[6] For review of applications of the charge transfer in phenomenology of particle production see e.g.: A. Bialas, in: Proc. of the IVth Intern. Syrup. of Multiparticle hadrodynamics, Pavia (1973); L. Fog, Phys. Reports 22C (1975) 1.
294
11 April 1977
[71 A. Biatas, K. Fiatkowski, M. Je~abek and M. Zielifiski, Acta Phys. Polon. B6 (1975) 59; R. Baier and F. Bopp, Bielefeld preprint Bi 75/11 (1975). [8] J. Dias de Deus and S. Jadach, Rutherford Lab. preprint RL-76-129/A.