inclusive yields and transverse spectra of non-strange mesons

Nuclear Physics B128 (1977) 397-407 © North-Holland Publishing Company

INCLUSIVE YIELDS AND TRANSVERSE SPECTRA OF NON-STRANGE MESONS Comparisons with the quark model, and an estimate of the fraction of "direct" pion production

Aachen-Berlin-Bonn-CERN-Cracow-London- Vienna- Warsaw Collaboration

H. KIRK and G. RUDOLPH III. Physikalisches Insitut der Technischen Hochschule, Aachen

U. KRIEGEL and H. VOGT Insitut flit Hochenergiephysik der Akademie der Wissenschaflen der DDR, Zeuthen- Berlin

K. BC)CKMANN and H.G. ZOBERNIG Physikalisches lnstitut der Universitllt, Bonn

H. BOHR *, V.T. COCCONI, M.J. COUNIHAN **, P.K. MALHOTRA ***, D.R.O. MORRISON, H. SAARIKKO + and P. SCHMID CERN, European Organization for Nuclear Research, Geneva

D. KISIELEWSKA Institute of Nuclear Physics and Techniques of the Academy of Mining and Metallurgy, Cracow

K.W.J. BARNHAM and R.M. EASON Physics Department, Imperial College, London

F. MANDL and M. MARKYTAN Institut fflr Hochenergiephysik der ~)stereichischen Akademie der Wissenschaflen, Vienna

K. DOROBA and A. PARA Institute of Experimental Physics, Warsaw University, Warsaw

Received 13 June 1977

* Now at the Niels Bohr Inst., Copenhagen. ** Now at the Rutherford Laboratory, Chilton, Didcot.

*** Now at the Tata Inst. of Fundamental Research, Bombay. + Now at the Institute of Nuclear Physics, University of Helsinki.

397

398 H. Kirk et al. / Inclusive yields

Recent data on the production of n, P 0, to and other mesons in hadron-hadron collisions at intermediate energies are studied. Their transverse spectra da]dp 2 are all found to be approximately exponential, with similar slopes, ~3.4 (GeV/c)-Z, up to about p~ = 2(GeV/c) 2. The inclusive yields of the mesons are broadly in agreement with quark model predictions. In the case of pions, a distinction is made between those directly produced and those produced indirectly via resonance decay. It is estimated that between 10% and 30% of pions are directly produced.

1. Introduction

We shall discuss in this paper three main points related to the inclusive production of hadrons (in particular the non-strange mesons) in hadronic collisions at intermediate and high energies. Firstly, in sect. 2 it is shown that the available data suggest the existence of a common transverse momentum (PT) dependence for the production of r/(549), p°(770), 60(780) and f(1270) in a number of different experiments, i.e.

do/dp~ cx e x p ( - B p 2 ) , (1)

with the slope B = 3.4 + 0.1 (GeV/¢) -2 . This parametrization appears to hold at least up to about p~ = 2(GeV/e) 2 . The main exception to eq. (1) is the pion spec-

trum, which is strongly influenced at low PT by the fact that many pions are produced by the decays of heavier hadrons.

Secondly, in sect. 3, the total inclusive yields of the various mesons are compared with the predictions of the quark model as calculated by Anisovich and Shekhter [1 ]. Such a model implies a distinction between "directly" produced hadrons and those "indirectly" produced from the decays of heavier particles. This distinction is especially important for understanding the production characteristics of pions. The third main topic of this paper (sect. 4) concerns the problem of estimating how many pions are "directly" produced. Finally, in sect. 5, our conclusions are summarized.

2. Transverse spectra

The/9 o is the resonance which has been studied most exhaustively in multiparticle interactions, for the reason that its decay products can be readily detected, with negligible bias from particle misidentification. Inclusive/90 production has thus been investigated in a number of recent papers on pp [2 -4 ] and rrp [5 -10 ] interactions in bubble chambers, with beam momenta ranging from 6 GeV/c up to 205 GeV/c, and it has been noticed that an exponential of the form of eq. (1) is generally a good parametrization of the PT distribution. An example is provided by the pO production in n+p interactions at 16 GeV/c shown in fig. la. It should be emphasized that this behaviour has been observed up to about p~ = 2(GeV/c) 2 ; it may well be that a more complicated expression will be necessary to fit also the higher Px regions.

In the case of pO production in 7rp collisions, an exception to the distribution of

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400 H. Kirk et al. / Inclusive yieMs

eq. (1) occurs at low PT values, i.e. below the region of p~ = 0.I (GeV/c) 2 . This comes about because of certain quasi-two-body processes such as lr+p ~ p°A++(1236) which are not of interest to the present discussion. Where necessary, the 1ow-PT region for pO production is therefore excluded when fitting data with eq. (1).

The slope B of the p2 distribution for po production is found to have approximately the same value in a variety of different experiments. The available results are summarized in table 1. It is particularly noteworthy that the slope does not seem to depend on whether the p0 is produced by" beam fragmentation or by central production, in the sense of ref. [8]. Thus, in the process rr+p ~ p0 + anything, which is dominated by beam fragmentation at moderate energies, the slope is unchanged if

Table 1 Slopes o f p ~ distr ibutions and relative yields found for the non-strange mesons in a variety o f

i

different exper iments

Reaction Incident Slope o f Relative yields Ref. m o m e n t u m do/dp2T (where applicable) (GeV/c) (GeV/c) -2

+ ~r+p -* n + charged 16 3.33 -+ 0.24 ~r+p ~ co + charged 16 3.33 ± 0.13 n p ~ p 0 + c h a r g e d 16 4.2 +0 .35 n - p ~ n + charged 16 n - p ~ co + charged 16 K - p ~ ~,Pn + charged 10 K - p ~ Kpco + charged 10 K - p --, An + charged 10 K - p --, Ato + charged 10 n+p --, p0 + anything 16 3.45 -+ 0.1

+ n p ~ f + anything 16 3.45 ± 0.3

+ 7r p ~ n + anything 16 ~3.45 a) pp ~ p0 + anything 12 3.6 ± 0.4

--, p0 + anything 24 3.6 - 0.4 pp +

p~ + charged 12 PP pp --, PU + charged 24 pp ~ co + charged 12 3.4 ± 0.2 pp ~ to + charged 24 3.7 -+ 0.3 n~-p ~ p0 + anything 6 3.9 ± 0.4 rr+p ~ p0 + anything 22 3.0 -+ 0.6 7r-p ~ p0 + anyth ing 16 2.95 ± 0.2 n - p ~xo 0 + anyth ing 147 2.7 ± 0.5 PP ~ P0u+ anyth ing 205 3.0 ± 1.0 pp ~ n + anyth ing ~1500 pp ~ ?2 + anything ~1500 (n ±, p)p ~ lr 0 + anyth ing 1 0 0 - 3 0 0

+

(n , p)p ~ n + anyth ing 1 0 0 - 3 0 0

n/co = 0.38 ± 0.04

¢o/p ° ~ 0.9

??/to = 0.44 + 0.12 [111

n/co = 0.38 + 0.05

n/co = 0.6 +0 .2

f/pO = 0.21 + 0.03 [6]

n-/p 0 ~ 1 .0 a)

co/pO= 1.0 ± 0.1

n /n O = 0.55 + 0¢11 a)

n/n 0 = 0.5 +0.1 a)

[2]

[5]

[8) 19) [4l

1191

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a) Result found for the large PT region.

H. Kirk et aL/ Inclusive yields 401

one looks only at the "central" p°'s produced with low c.m. rapidity. This is illustrated in fig. la. Moreover, the slope found for the mainly central pO production in pp collisions is again the same (table 1).

Apart from the p0, attempts have been made to study the inclusive production of a number of other mesons. Inclusive f(1270) production in 16 GeV/c 7r+p interactions has been found [6] to follow eq. (1) with a slope equal to that for the pO. Work on the production of the r/and co has appeared in pp [2] and rrp [11 ] reactions (see also the review by BGckmann [12]), but the analysis in these cases is not so straight- forward: to detect the r/and co through their decays into lr+~r-Tr °, conventional bubble chamber experiments require that the rr ° be reconstructed through energy- momentum balance, all other particles being charged. Consequently, one is restricted to quasi-inclusive reactions of the type

beam + target ~ lr+Tr-rr ° + charged particles. (2)

The resulting p~ distributions from ref. [11] are reproduced in fig. lb, and once again the data are compatible with a simple exponential for both the 7/and the ~, with a slope of 3.3(GeV/c) -2 . Fig. lb also includes the corresponding distribution for quasi-inclusive p°'s, i.e. for p°'s which are accompanied only by charged particles. Except for the low-pr region (mentioned above), there is similarity between the p0 and w transverse spectra. It seems likely that the p} slope for quasi-inclusive r~ and w production is not very different from that for fully inclusive production, i.e. that the requirement that the meson be accompanied by charged particles does not affect things. This point has been discussed at some length in ref. [11 ].

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The transverse momentum spectra shown in fig. 1 are merely a representative set of recent data, and a more complete list is given in table 1. All the slopes in table 1 are displayed as a Gaussian ideogram in fig. 2. They can be fitted to a common value of 3.40 -+ 0.06 (GeV/c) -2 , with ×2/NDF = 16.6/13, i.e., with good consistency. While the precision of the data is such that .we cannot exclude variations of order 10% from this "universal" slope, it is remarkable that such close agreement is seen for different hadrons in a diversity of experiments, over a wide energy range.

Although we have restricted ourselves to non-strange mesons in the data of fig. 1, results are accumulating on other inclusive reactions such as K - p ~ K,*(890) + anything [13], n+p ~ A++(1236) + anything [14] and K - p ~ ~±(1385) + anything [15], which seem to indicate that at these energies and in this mass range around 1 GeV, also strange mesons, as well as non strange and strange baryons, have similar p~ dependence. This apparent "universality" o fp~ slopes is, however, to be taken with caution, considering the limitations of the data available. The possibility of small mass and/or energy dependences is not ruled out.

As was mentioned earlier, the most obvious exception to eq. (1) is the transverse spectrum of pions. This is illustrated by the upper set of data points in fig. la, which are for lr+p -~ 7r- + anything at 16 GeV/c. The pion spectrum is grossly different from that of the heavier particles, at least up to about P r = 1 GeV/c. For higher PT values, it appears that the pions have the same slope as other mesons.

The different shape of the pion transverse spectrum is not surprising when one considers that many pions are likely to originate from the decay of resonances such as the 0 °. Their transverse spectra, therefore, must differ from those of the parent resonances, as a consequence of the decay kinematics which will generally tend to "kick down" the decay products to PT values lower than those of the parent. Thus, the excess of pions at low PT (fig. la) may be tentatively ascribed to the pions produced indirectly by the decays of heavier particles. We shall return to this point la- ter, when discussing the amount of "direct" pion production.

3. The relative yields of the mesons

It is now of great interest to establish the ratios among the inclusive cross sections for producing the various hadrons in high-energy interactions. One reason for this is that the inclusive cross section ratios provide a s0nsitive test for models of multiparticle production. Predictions have been made by Anisovich and Shekhter [1] and by Bjorken and Farrar [16] for the yields of the pseudoscalar and vector mesons, and of other particles, using two simple quark-counting models. We shall take the results of ref. [1] for the purpose of comparison with experimental data, although the models are similar to each other and the experimental results do not favour one over the other.

In table 2 we list ratios of experimental cross sections together with quark model predictions for the central region. Experimental errors are not always included, since

H. Kirk et al. / Inclusive yields 403

Table 2 Ratios of the inclusive cross sections for the production of non-strange mesons at high energy and comparison with the quark-model predictions

Ratio Cross section ratio Ref.

quark model experimental prediction [ 1 ], result central region

co/o o I 0.9 [2,11 ]

~/a ° ~ =0.11 <~0.I [111

n/to 11 gi = 0.14 0.39 +- 0.03 [11] "r/'/r/ 19 Ti = 1.7 -0.05 - 0.10 [11]

7rOir/~ 27 Ti -= 2.5 -2 a) [18,19]

ndir/'a'all 1~ = 0.07 ~0.1 a)

a) Results found for the large PT region and subject to the assumptions mentioned in the text.

in many cases the ratios are qualified by strong assumptions. The 60/pO ratio, for example, appears to be close to unity, but the ~ is only detected "quasi-inclusively" and an extrapolation is made when the data are assunted to behave in a similar way in the fully inclusive case.

The 1 : 1 ratio which appears to hold between the 60 and the p0 is what one ex- pects from quark-model arguments. Simply because they have the same spin and are constructed in similar ways from non-strange quarks, the pO and 6o should have similar inclusive cross sections. For the r//60 ratio, the measured value of about 0.39 is three times larger than predicted. Both the r/' and the ¢ mesons are strongly suppressed in their inclusive cross sections: the r~'/r/ratio is more like 0.1 than the predicted 1.7. The q~ is strongly suppressed relative to the p0 because of its strange quark con- tent, in agreement with the model.

The suppression of ~ production may be regarded as a consequence of the Okubo- Zweig-Iizuka rule [17], and it is tempting to explain the 77' suppression in the same way. To do this it would be necessary to postulate that the r/' is dominantly com- posed of strange quarks, in contradiction to the simple quark model. However, this is an attractive hypothesis because it explains not only why the r/' should be rare, but also why the 77 should be strongly produced. In the limits, a form of r//r/' mixing by which all the strange quarks are concentrated in the r/' would lead to the prediction r//60 = 0.33 (to be compared with 0.39 -+ 0.03, experimentally).

The quark-model predictions in table 2 refer to the mesons produced b2r some "direct" process, and take no account of those produced indirectly by the decays of heavier objects. While this is a reasonable approximation in the case of r/, pO, 60, etc.,

404 11. Kirk et al. / Inclusive yields

it is surely a poor approximation in the case of pions, which are frequently produced as resonance decay products. Indeed, the work of Anisovich and Shekhter [1 ] indicates that at high energies in the central region only about 7% of pions will be "direct". The experimental estimation of this fraction poses a difficult problem.

4. The amount of direct pion production

A way of estimating the level of direct pion production is to look at the number of pions produced at large PT, exploiting the argument (see sect. 2) that indirect pions will become relatively unimportant with increasing PT- In the case of rr- and pO production in 16 GeV/c 7r+p collisions [6], fig. la indicates that the l r - /p ° ratio ap- proaches unity at large PT. It may then be conjectured, assuming that production of 7rdi r has a similar PT dependence as pO, that the ~ r / p 0 ratio is of that order. Actual- ly, detailed studies [18] of the sources of large PT pions have recently suggested that about ~- of the pions in this region are indirectly produced. Hence, using the result that 7r°/p-~l = 0.19 -+ 0.02, one obtains an estimate that the ffdir/ffall ratio is ~10%.

Another approach to estimating the direct pion yield comes from measurements of the r//Tr ° ratio at large PT which have been made at the CERN ISR [19] and at Fermilab [20]. These measurements give r~/rr ° = 0.5 + 0.1, which we may interpret as an estimate of the 1"//ffd0ir ratio. Using the 77 and rr- total cross section results in 16 GeV/c n+p collisions [6,11], we are therefore led to a rough value of ffdir/ffaU of 12%.

It is to be stressed that the conclusions of the two previous paragraphs are of an approximate nature, and may easily be in error of a factor of two. Also, the numbers quoted above refer to the large PT region only, the corresponding particle ratios at lower PT values remaining a puzzle.

Even if the p~ distributions are really exponential as in eq. (1), a small increase of the average transverse momentum with the mass of the produced particle (not incompatible with the existing data) would cause an increase in the estimate 7rdir/Tral I ~ 0.1 given above. Similarly, a correction in that same direction would be caused by the more complicated PT dependendes that have been suggested in refs. [21,22]. On the other hand, about 50% of the 7r-'s produced in n+p interactions at 16 GeV/c come from well known meson decays alone [18], so the ratio 7r~r/Tr~l must be well below 0.5 to allow some production of the n - ' s v/a less known meson decays and via baryon decays. A realistic conclusion would be that 7rdir/ffal I lies between 0.1 and 0.3.

The experimental values of the r'//71"di r and ffdir/ffall given above are included in table 2, together with the corresponding quark-model predictions, and it can be seen that there is rough agreement.


5. Conclusions

The experimental data presently available suggest very strongly that the transverse spectra of p, co, ~ and f mesons produced in high-energy collisions have a common dependence on p~, in the PT range investigated, well represented by the exponential formula of eq. (1). The assumption of an "universal" slope for direct particle production lends credibility to the idea that the relative yields of the different particles are determined only by the quark combinatorics governing the particles' con- struction. Indeed, the data are in reasonably good agreement with the predictions of such a quark model. Within this scheme, a distinction must be made between "direct" particle production and "indirect" production by resonance decay: this is especially important in the case of pions, and an interesting parameter in any model for multiparticle production is the ratio lrdir/li'al 1. However, this ratio is difficult to determine experimentally and we can suggest only that the 7r~r/Tr~l ratio is likely to lie between 0.1 and 0.3.

It has been found that at large PT the quantum numbers of produced particles are more strongly influenced by those of the incident particles than is the case at small PT [23,24]. For example, in pp collisions there is a preponderance of positive over negative particles, which becomes more marked as PT increases. This can be explained by the fact that, as PT increases, the proportion of directly produced particles becomes greater. At low PT, on the other hand, indirectly produced pions from resonance decays will tend to "wash out" the charge asymmetry, so that in pp collisions, the Ir+/Tr - ratio falls towards unity as PT increases. Thus charge conservation, together with the kinematics of resonance decay, may explain the observed large PT asymme- tries. This problem has previously been discussed in terms of models which involve the hard-scattering of partons [25].

It should be mentioned that the quark-model predictions which we have referred to represented the first attempts to calculate the high-energy relative yields of the hadrons. There are several ways in which improvements may be made. Firstly, the work of Anisovich and Shekhter involves a strange-quark suppression factor X which is an adjustable parameter in their model. Here, we have used the predictions calculated with X = ½ as was originally suggested in ref. [1], but it has been pointed out [26] that a value ;k = 0.2 is in closer agreement with recent data on strange-meson production. However, the predictions in table 2 are relatively insensitive to the X parameter and our conclusions would be unaffected by taking X = 0.2 instead of ½.

Secondly, it is possible to modify the Anisovich-Shekhter model so that it cor- rectly allows for leading particle effects and the limited phase space available at finite energies. However, such models [27,28] contain several new adjustable parameters and/or assumptions, and demand refined experimental data for testing them.

Finally, we want to point out that other modifications to the models may be re- quired by the observation that the ~k(3100) produced in lr and p interactions on nu- clei has p~ dependence with slope B much smaller than the value of ~3.4(GeV/c) -2 reported here. Recent results for ~b production in the forward hemisphere at ~40


GeV/c [29] repor t B ~ 1.5 (GeV/c) - 2 , and a value B ~ 1 (GeV/c) - 2 has been found

at 150 and 225 GeV/c [30]. Dependences o f the average transverse m o m e n t u m on

the mass o f the particle p roduced and/or on the incoming energy have to be included

in the model . It could also be that the mass o f the quarks involved affects the aver-

age transverse m o m e n t u m .

We are indebted to our numerous colleagues who have assisted this work with

valuable crit icism and encouragement .

References

[ 1 ] V.V. Anisovich and V.M. Shekhter, Nucl. Phys. B55 (1973) 455. [2] V. Blobel et al., Phys. Letters 48B (1974) 73. [3] V.V. Ammosov et al., paper submitted to Int. Conf. on high-energy physics, Palermo 1975. [4] R. Singer et al., Argonne preprint (1975) ANL-HEP-PR-75-48. [5] H.A. Gordon et al., Phys. Letters 34 (1975) 284. [6] Aachen-Berlin-Bonn-CERN-Cracow-Heidelberg-Warsaw Collaboration, M. Deutschmann et

al., Nucl. Phys. B103 (1976) 426. [7] J. Brau et al., Nucl. Phys. B99 (1975) 232. [8] Aachen-Berlin-Bonn-CERN-Cracow-Heidelberg-Warsaw Collaboration, J. Bartke et al., Nucl.

Phys. B107 (1976) 93. [9] D. Fong et al., Phys. Letters 60B (1975) 124.

[10] F.C. Winkelman et al., Phys. Letters 56B (1975) 101. [11] Aachen-Berlin-Bonn-CERN-Cracow-London-Vienna-Warsaw Collaboration, J. Bartke et al.,

Nucl. Phys. Bl18 (1977) 360. [12] K. BSckmann, Talk presented at Int. Conf. on high-energy physics, Palermo 1975. [13] Aachen-Berlin-CERN-London-Vienna Collaboration, H.G. Kirk et al., Nucl. Phys. Bl16

(1976) 99; R.L. Eisner et al., Nucl. Phys. Bl19 (1977) 1.

[14] Inclusive £x ++ (1236) production in 7r+p, 7r-p interactions at 16 GeV/c, Aachen-Berlin- Bonn-CERN-Cracow-Heidelberg-London-Vienna-Warsaw Collaboration, paper submitted to Int. Conf. on high-energy physics, Tbilisi 19"i6.

[15] Aachen-Berlin-CERN-London-Vienna Collaboration, H. Gr/issler et al., Nucl. Phys. Bl18 (1977) 189.

[16] J.D. Bjorken and G.R. Farrar, Phys. Rev. D9 (1974) 1449. [17] G. Zweig, CERN-TH-412 (1964);

S. Okubo, Phys. Letters 5 (1963) 165; I. Iizuka, Prog. Theor. Phys. Supp. 37-38 (1966) 21.

[ 18] A study of indirect pion production in ~r+p interactions at 16 GeV/c, Aachen-Berlin-Bonn- CERN-Cracow-Heidelberg-Warsaw Collaboration, paper submitted to Int. ConL on high- energy physics, Tbilisi, 1976.

[19] F.W. Biisser et al., Phys. Letters 55B (1974) 73. [20] I. Stumer et al., private communication, BNL-Caltech-LBL Collaboration. [21] Aachen-Berlin-Bonn-CERN-Cracow-Heiderlber-London-Vienna-Warsaw Collaboration, M.

Deutschmann et al., Nucl. Physics B70 (1974) 189. [22] H. B6ggild et al., NucL Phys. B57 (1973) 77. [23] W.B. Fretter et al., Phys. Letters 57B (1975) 197;

B. Alper et al., Report given at Int. Conf. on elementary particle physics, London 1974.


[24] Aachen-Berlin-Bonn-CERN-Cracow-Heidelberg-Warsaw Collaboration, J. Bartke et ah, Nucl. Phys. Bl17 (1976) 293.

[25] B.L. Combridge, Phys. Rev. D10 (1974) 3849 and references therein. [26] K. B6ckmann, private communication. [27] V. Cerny, P. Lichard and J. Pisut, Multiparticle production in a simple Monte-Carlo quark-

patton model, paper presented at 2nd Adriatic Meeting on particle physics, Dubrovnik, 1976.

[28] H. Bohr and H.B. Nielsen, Nucl. Phys. B128 (1977) 275. [29] Yu. M. Antipov et al., Dimuon production by 43 GeV/c negative particles, Tbilisi-Moscow

preprint; M.J. Corden et ah, Phys. Letters 68B (1977) 96.

[30] K.J. Anderson et al., Phys. Rev. Letters 36 :(1976) 237; H.D. Snyder et al., Phys. Rev. Letters 36 (1976) 1415.

inclusive yields and transverse spectra of non-strange mesons

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