Charmed-particle production in hadronic and electromagnetic processes

P H Y S I C A L R E V I E W D V O L U M E 1 8 , N U M B E R 7 1 O C T O B E R 1 9 7 8

Charmed-particle production in hadronic and electromagnetic processes

Maurice Goldhaber and Ling-Lie Wang Physics Depurtment, Brookhaven National Laboratory, Upton, New York 11973.

(Received 26 May 1978)

Cross sections for the production of charmed particles In hadronic and electromagnetic interactions with hadrons are estimated in various energy regimes. Some implications of the results are discussed.

Direct evidence for charmed-meson production has so far not been observed in hadronic or electromagnetic interactions with hadrons. Recently "beam-dump" experiments a t CERN and calori- meter e'xperiments a t Fermilab have given results' which have been interpreted a s evidence for charm production in hadron-nucleus collisions. Charmed particles could be created either via the production of resonances such a s 1" (3772), which decays' nearly entirely into D and B, or by direct associated production.

We first concentrate on the production of q". We use a ptenomenological model which treats the hadronic production of massive mesons, such a s J / $ , $', and $", etc., on the same footing. We also estimate production of # I 1 by electromagnetic processes. The proton production of $I' turns out to be very small, rising steeply from threshold and reaching a few nonobarns per nucleon at a few hundred GeV laboratory energy. In photoproduction, a coherent process plays a role which in- creases the effective cross section for nuclei of large 11, leading also to an effective cross section of a few nanobarns per nucleon. Whenever thick targets a r e used, the secondary production by photons from no decay ought to be taken into consid- eration. A similar analysis could be applied to higher charmonium resonances once their decay parameters a r e established.

Finally we estimate associated production of charm by protons guided by the assumption that the ratio of charm associated production to that of J / $ is approximately equal to the ratio of strange as - sociated production to that of $. This leads to cross sections of a few microbarns for laboratory energies 2 100 GeV, which, considering the ap- proximate nature of the estimates, is compatible with the lower of the cross-section values for charm production deduced from experiment. '

A similar discussion would apply to states of heavier quarks. Once the width of 'Y is known, associated production of b-quark states can be estimated from the measured I" production cross section.

HAORONIC PRODUCTION OF \Ii"

The production cross sections of +" in hadronic processes a re estimated by using the conjecture4 that the cross section (I?')-'m3do/dk for massive meson production is a scaling function of s / r r z k d x only, i.e.,

where x= p ~ i / $ k ' s , m is the mass of the meson,

FIG. I. The plot of t h e scaling function of Eq. ( I ) tor J/P (open points) and a ' (solid points) production. Sources of the da ta points are given in Ref. 6.

C H A R M E D - P A R T I C L E P R O D U C T I O N I N H A D R O N I C A N D . . . 2365

and r' is the par t i a l width of the meson f o r decay The energy re lease in the decay 4" - DD is smal l . Thus the expected x distribution f o r D and IT would be nar rower than that f o r $". Taking the x distr i - bution f o r 4" to be - (1 - jx I)*, we obtain f o r D and F a distribution - (1 - 2 jx, 1 ) ' where x, goes f r o m 0- -0 .5 .

I t is seen f rom Fig. 2 that the production of $" by protons r i s e s steeply with energy and reaches a few nanobarns f o r laboratory energ ies 2 100 GeV. Therefore charmed-meson production by this p r o c e s s is very small . Fur ther contributions to charmed-part ic le production can be expected f r o m the higher charmonium resonance^.'^

into ordinary hadrons. The conjecture is based on dimensional arguments , and the division by r' is intended to eliminate the particle-type de-. pendence in the p r o d ~ c t i o n . ~ In Fig. 1 we update recen t compilations of J/$(3095) and $'(3684) production c r o s s section^,^ car r ied out in the f rame- work of th i s conjecture. Considering the vas t differences in the decay proper t i es and the production c r o s s sect ions of J / $ and $', the agree- ment with Eq. (1) appears good. (To obtain the points in Fig. 1 , we take I?;/,= 59 i 15 keV, I?;, = 9 & 5 keV, r ,,,a =4 .9*0 .3 keV, r,.+,z=1.9 i 0 . 3 keV.7) To obtain du/dx f rom Eq. (1) we need to know the value of r k . But s ince $# decays overwhelmingly into DD, l?;~ has not yet been measured . In the charmonium modelR i t i s reasonable to a s s u m e r i m = ( r J / rb-ez) r$n-ea Using rp-ea= 0.18 i 0 . 0 6 keV," we obtain I?$.- 0.9 keV. T h i s value and Eq. (1) determine

ELECTROMAGNETIC PRODUCTION O F \li" ON NUCLEI

We f i r s t calculate the photoproduction of $" and then apply it to the electroproductlon c r o s s section, using the vector-meson-dominance model." The photoproduction c r o s s sect ion of J / $ has been observed" to be

where B(GN-Dn) = 1. Using the empi r ica l data f r o m Fig. 1, Eq. (2) leads to the c r o s s section a t x = O a s shown in Fig. 2. where A i s the m a s s number of the nuclear t a rge t ,

and

In this production mechanism the photon converts virtually into J / $ , which then in te rac t s diffract- ively with the nucleus. The ra t io of photon-+" coupling to photon-J/$ coupling is given by

- ea/r J / o - e a ) 1 f 2 . The diffractive scat ter ing of 4'' on a nucleus i s assumed to be the s a m e as f o r J / $ . Thus we find f o r the photoproduction of a" on protons a t high energies

and on nuclei,

Integrating over t , we obtain FIG. 2. Predicted DB production in pp interaction

via $" .

M A U R I C E G O L D I I A B E R A N D L I N G - L I E W A N G - 18

FIG. 3. The observed inclusive production cross sections for the K meson (circles), the cp (triangles), and the J / # (squares). The dotted curve is the predicted single-charmed-particle inclusive cross sectionusing Eq. (7). The error bars are taken directly from experi- mental papers and do not include theuncertainties inour extrapolationsused to obtain the total cross sections. The formulasused in the extrap~lations and the references to the data points are given in Ref. 16.

and

Thus f o r a nucleus of sufficiently high A the photoproduction c r o s s section of D and B via $" may reach microbarn values p e r nucleus. Similar con- s iderat ions can be expected to hold for higher charmonium resonances a s well a s fo r the contin- uum . I 3

Using the vector-meson-dominance model, we obtain the electroproduction c r o s s section of DD via b",

where u is given by Eq. (5a) o r Eq. (5b) f o r a hy- drogen o r nuclear t a rge t , respectively, and

where Q ~ = ~ E E ~ s ~ ~ ~ ( B / ~ ) , v = E - E ' , a n d E , E l , and 8 a r e respectively the electron 's initial energy, final energy, and scat ter ing angle, measured in the laboratory .I4

Attempts to m e a s u r e the lifetime of D mesons using beams of protons, photons, o r muons have begun a t Fermi lab and CERN. Production of specific charmonium resonances which break up into D mesons may prove kinematically useful.

ASSOCIATED PRODUCTION OF CHARMED PARTICLES BY HADRONS

In addition to production of charmed mesons via specific charmonium s ta tes , d i rec t associated production h a s to be expected, s i m i l a r to the production of s t range par t i c les both via @ and by a s - sociated production. It is reasonable to conjecture that the rat io of the c h a r m associated production c r o s s section to that of J i $ i s approximately equal to the corresponding ra t io of K to ($.'51'8

In Fig. 3 we give the inclusive production c r o s s sections17 found f o r K, +, and J / $ . Using the above conjecture we obtain the c h a r m associated production c r o s s section.

shownl"n Fig. 3. At laboratory energ ies 2 100 GeV the c r o s s section reaches a few microbarns .

Since J/'+ production c r o s s sect ions a r e a few t i m e s l a r g e r f o r pions" than f o r protons, one might expect l a r g e r associated c h a r m productions f o r pions also.

ACKNOWLEDGMENTS

We would like to acknowledge useful discussions with D. Cutts , K. Gottfried, J . Sandweiss, A . J . S. Smith, and many colleagues a t Brookhaven.

*Under the auspices of the U. S. Department of Energy. 'P. Alibran et aL., Phys. Lett. E, 134 (1978); T. Hans1

et al. , ibid. E, 139 (1978); P. C. Bosetti et al., ibid. 74B, 143 (1978); B. Barish et al. , Caltech and Stanford -

experiment, reported at the Washington .4PS meeting, 1978 (unpublished).

'P. A. Rapidis et al. , Phys. Rev. Lett. 2, 526 (1977); I. Peruzzi et al., ibid. 39, 1301 (1977); W. Bacino et -

18 - C H A R M E D - P A R T I C L E P R O D U C T I O N I N H A D R O N I C A N D . .

al., ibid. 40, 671 (1978). 3 ~ . R. 1nneTet al . , Phys. Rev. Lett. - 39, 1240 (1977);

39, 1640(E) (1977). 'T-K. Gaisser, F . Halzen, and E . A. Paschos, Phys.

Rev. D 2, 2572 (1977); see also 3'. E. Paige, E. A. Paschos, D. P. Sidhu, and L.-L. Wang, BNL Internal Report No. PD 129 (unpublished).

'such hypotheses follow naturally from the Drell-Yan model; S. D. Drell and T.-M. Yan, Phys. Rev. Lett. 25, 316 (1970) and Ann. Phys. (N. Y.) 66, 578 (1971).

'~Tferences to the data points in Fig. 1 a r e 8: J . H. Cobb et al., Phys. Lett. 68B, 101 (1977); 0: F. W . Biisser et al., ibid. 56~ ,=2 (1975); 0: Yu. M. Anti- pov et al., ibid. =, 309 (1976); A: M. J. Corden et al . , ibid. 9, 96 (1977); 0,.: H. D. Snyder et al., Phys. Rev. Lett. 36, 1415 (1976) and B. C. Brown et al., Fermilab Report No. 77/54-exp (unpublished); V : M. Binkley et a l . , Phys. Rev. Lett. 2, 574 (1976); C;,

m: K. J. Anderson et al., ibid. 36, 237 (1976); A,& J. J. Aubert et al., ibid. 33, 1404 (1974). Corrections due to F e r m i motion a r e not included. They can be im- portant for checking scaling, especially in the energy region where the c ros s section r i s e s sharply with en-

ergy. 'see G. J. Feldman and M. L. Pe r l , Phys. Rep. 33C

(1977). 'see, for example, K. Gottfried, in Proceedings of the

International Symposium on Lepton and P hoton Inter- actions at High Energies, Hamburg, 1977, edited by F . Gutbrod (DESY, Hamburg, 1977).

$We take the value of f rom W. Bacino et al. in Ref. 2. P. A. Rapidis et al. in Ref. 2 give a value ap3 proximately twice a s large.

'Osee G. Goldhaber, in Proceedings of the 1977 European Conference on Particle Physics, Budapest, edited by L. Jenik and I. Montvay (CRIP, Budapest, 1978).

"c. A. Piketty and L. Stodolsky, Nucl. Phys. g, 571 (1970); J. J. Sakurai and D. Schildknecht, Phys. Lett. 40B, 121 (1972).

' ' B . ~ n a ~ ~ et al., Phys. Rev. Lett. E, 1040 (1975). 13see, for example, J.-M. Wang and L.-L. Wang, Phys.

Lett. s, 377 (1976). ''H. W. Kendall, in Proceedings of 1971 International

Symposiz4m on Electron and Photon Interactions at High Energies, edited by N . B. Mistry (Laboratory of Nu-

c lear Studies, Cornell University, Ithaca, N. Y., 1972).

his assumption was used to estimate the charm associated-production c ros s section at BNL energies; D. P. Sidhu, T. L. Trueman, and L.-L. Wang, Brook- haven Internal Report KO. PD-124, 1976 (unpublished).

I6There have been estimates of charm associative-production c ros s sections based upon various theoretical models, e.g., J. Babcock, D. Sivers, and S. Wolfram, Phys. Rev. D 2, 162 (1978); L. Jones and H. W. Wyld, ibid. 17, 759, (1978); 17, 1782 (1978); H. Fri tzsch, phys.Yett . E, 217 (1977); F. Halzen and S. Matsuda, Phys. Rev. D 17, 1344 (1978). After the completion of this manuscript, we saw another manuscript in this category by H. M. Georgi, S. L. Glashow, hl. E. Machacek, and D. V. Nanopoulos, Harvard University Report No. H U T P - ~ ~ / A O O ~ (unpublished). There a r e uncertainties involved in these model calculations. We take a different approach to estimate the charm associative-production c r o s s sections from a phenomeno- logical hypothesis, incorporating the most recent data.

ere we give references to the data points shown in Fig. 3. For w K , see Fig. 13 and Fig. 27 in the review by H. ~ b g g i l d and T. Ferbel, Annu. Rev. Nucl. Sci. 24, 451 (1974) and the references given therein [the distribution used to extrapolate for the highest-energy point i s ~ d a / d ~ p x (1 -x)4*06e3.93pl]; for a,: V , V. Blo- be1 et al., Phys. Lett. 3, 88 (1975); V: K. J. Ander- son et al . , Phys. Rev. Lett. 2, 799 (1976); 0: C. W. Akerlof, ibid. 2, 861 (1977) [the integrated c ros s section is obtained by taking ~ d a / d ~ p cr (1 -x)4.06e-3.93*l for Ip,l < 1 GeV, observed by K. J. Anderson et a1 ., inthis reference] ; r: A. J. Lankford, dissertation, Yale University, 1978 (unpublished) [the distributionusedfor extrapolation is the same]; for cr,;,: 0: J.H. Cobb et al., Ref. 6; 0 :B. C.Brownetal., Ref. 6 [the integratedcross sections for D and 0 a r e obtained using a distribution ~ & / d ~ ~ c (1 -x)3.5e-'.54P1]; 0 : K. J. Anderson et al., of this reference; D: M. J. Cordon et al., Ref. 6; 0: J. J . Aubert et al . , Ref. 6.

ere we ignore the possible effects on our estimates due to the difference in the suppression of the decay of 6 and J / $ to ordinary hadrons.

"J. G. Branson et al., Phys. Rev. Lett. 38, 1331 (1977). -

FIG. 1. The plot of the scaling function of Eq. (1) for J/O &pen points) and $' (solid points) production. ~ourcee of the data points are given i n ~ ~ e f . 6.

FIG. 2. Predicted DD production inpp interaction via #" .

10-26_

I I .

. a a l

. . .

a . . .

- - K \ $

- - f . . f - .

. .

10-2% - "4-p 1 : . .

.

. . .

. . .

. - -

- 10-29_ /, N . E . . /

/' : - . .

. / .

/ /'

/ I P! .

1 0 . ~ '

10-3Zr

-- . . - . . . / / + . . - . . - - c - /

/

. . -

- . ' -J~Y ___I f! h I I I I I 1

10 loZ 103 s I G ~ V ~ I

FIG. 3. The observed inclusive production cross sections for the K meson (circles). the @ (triangles). and the J / $ (squares). The dotted curve is the predicted single-charmed-particle inchsivecross sectionusing Eq. (7). The e r ro r bars are taken directly from experi- mental papers and do not includetheuncertaintles inour extrapolatioasused toobtalnthe totalcross sections. The farmulasused in the extrapolations and the referenoes to the data points are given in Ref. 16.

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Charmed-particle production in hadronic and electromagnetic processes