The flavouring of a gluon jet

Volume 236, number 4 PHYSICS LETTERS B 1 March 1990

T H E FLAVOURING OF A G L U O N J E T

Bo ANDERSSON, G~sta GUSTAFSON and Leif L O N N B L A D Department of Theoretical Physics, University of Lund, S61vegatan 14.4, S-223 62 Lund, Sweden

Received 13 October 1989; revised manuscript received 27 November 1989

We show that the hard qcl production is very sensitive to the details of the parton shower and that our treatment based on the dipole approximation gives significantly larger production than "conventional" patton showers. For our model we find qualitative agreement with experimental data for the K/n ratio and D-meson production in high-/rr jets.

We have in an earlier publication [ 1 ] considered the possibilities o f introducing the process of gluon splitting into the dipole approximation to the QCD cascades [ 2 ]. The results are that we obtain an essen- tially larger rate for the process g ~ Q 0 compared to g ~ g g than in other approaches, e.g. ref. [3] (2 -4 times larger).

In this note we will consider the implications o f these results for gluon jets obtained in high-pT (Ruth- erford) scatterings o f partons. It is well known that due to the cross sectional sizes, there is in general a large amount o f such gluonic jets. At e.g. the SppS collider the main part of the large jets stems from gluonic scattering, and this is also believed to be the case over the ISR region.

Our main results are that we obtain an essential increase in the production o f strange, charmed and bot- tom mesons in gluon jets compared to earlier approaches. For the charmed meson production we obtain qualitative agreement with recent results from the FNAL and CERN 13p colliders. Also for bot tom mesons we find a substantially larger rate in our ap- proach than in conventional cascades. We also find that the ratio o f e.g. K/Tt increases to around 0.5 for fast fragments of the gluon jets. This is an observed [ 4 ] and until now phenomenologically very puzzling phenomenon. It has led to speculations that the present description in the Lund model o f a strange to nonstrange q~l production ratio of about 0.3 in the hadronization processes may be entirely wrong.

We feel that our results confirm the general picture of the low-pT string fragmentation together with a

hard Q 0 production component from gluon splitting. Although our hard rate is larger than in earlier approaches, it is for u, d and s quarks very much smaller than the soft fragmentation production o f such pairs. Therefore it will influence the K / n ratio in the "t ips" o f the gluon jets where the hard production is kinematically favoured.

Before we consider the detailed results, we will present a brief description o f the reasons why we obtain a larger gluon splitting rate in the dipole approximation than what has been found in the other schemes.

We note that if we start with an original qodlo pair (a colour 33) produced e.g. in an e÷e - annihilation reaction with large W, then there will be dipole emission of bremsstrahlung gluons (colour 8's) when the qo~lo starts to go apart. The phase space limits to emit a gluon g~ with transverse momentum kT~ and (pseudo-)rapidi ty y~ is in the CMS

lY~ I<,% l n ( W / k T : ) . (1)

The dipole approximation is built upon the observa- tion [5] that the cross section to obtain this gluon together with a second softer (smaller kT) gluon (g2) can be factorized. The first gluon is emitted according to eq. ( 1 ) from the (qoClo) pair and the second stems from the emission from a dipole spanned either between the q0 and gl or between gl and the dlo. These latter dipoles emit independently to a very good approximation. In the dipole approximation as imple- mented in the Monte Carlo simulation model A R I A D N E [6], this factorization property is ex-

0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland ) 461


ploited systematically. New gluons are emitted one after the other "downwards" in kT, all the time pro- ducing new and smaller mass dipoles.

For all of these emissions there are similar restric- tions as in eq. ( 1 ), and these conditions are equiva- lent to the requirements of "strong angular ordering" in other cascade approximations [3,7].

If we now introduce the possibility of gluon splitting, then there will be a competition between emitting a second gluon g2 or to split the already emitted gluon gl--'QQ. The way to handle such a situation is to introduce a Sudakhov form factor.

If the gluon emission cross section is dah and the splitting cross section is da2, then the probability that neither process occurs inside the phase space region f~is

P(~2) = e x p l - ! (dal + d a 2 ) ] (2)

(with ao a normalization cross section). The probability that the process 1 occurs in the phase space point Pj on the border o f ~ is

dal(Pl) - - P ( O ) , (3)

ao

etc. It is, however, necessary to determine some "or-

dering variable" in this connection, i.e. to start at the phase space boundary [as in eq. (1)] and go "in- wards" in some ordered fashion according to eqs. (2) and (3).

In earlier approaches one has used as an ordering variable either the virtual mass Q2 [3] of each parton or the variable ~--- EO/xS2 [ 7 ], where E is the energy of the parton and 0 is the opening angle of the decay. These variables are related to the transverse momentum kv and the energy fractions z and 1 - z of the decay products by the following relations:

Q2~ k2 ~_~ 1 kT (4) z ( 1 - z ) ' x / ~ z ( 1 - z ) "

In the dipole approximation the natural ordering variable is k~ instead.

The choice of ordering variable is very important due to the different pole structures in the cross section for gluon emission and gluon splitting

d z da~ gluon emission

z ( 1 - z ) '

daz ~ dz, gluon splitting. ( 5 )

Thus the competition between the two processes de- pend strongly on the kinematically allowed range in z. For a fixed value ofk~ this is given by

k~ k~ M-- 5 < z < 1 - M~5, (6)

where M is the mass of the emitting dipole. The ratio between the gluon emission and the gluon splitting is proportional to 2 ln M2/k~. If the largest value of k~- is chosen by a Sudakhov form factor this quantity is never very large.

If, on the other hand, we use an ordering in e.g. Q2

we see from eqs. (4) and (6) that for fixed Q2 also very small z and k 2 are allowed. For massless decay products the z range is 0 < z < 1 and the cross section for gluon emission diverges. The gluon emission cross section therefore depends on the (virtual) mass of the decay products and is sensitive to the allowed lower limit of these masses and to the exact defini- tion chosen for the z variable. Normally this ap- proach gives a much larger relative propability for gluon emission.

It should also be noted that in particular for heavy (QQ) production the emission of an earlier (soft or collinear) gluon effectively prohibits such emission due to lack of energy in the dipoles. The conclusion is that the ordering in k 2 instead of Q2 will increase the splitting process and this is the main reason that we obtain a larger rate.

It is also known, that by the use of different kine- matics in the extrapolation from the pole regions into other allowed parts of phase space, one may obtain rather different results. The way we have chosen to implement the gluon splitting process is to refer half of the cross section to each of the two dipoles sur- rounding the gluon and we have also extrapolated the cross section in terms of the CMS energy fraction [ 1 ]. This procedure gives a (minor) increase in the rate as compared to e.g. the procedure used in ref. [ 3 ].

Before we discuss the high-pv gluon jets it is necessary to consider the emission of bremsstrahlung from extended sources. In ref. [8] we have devel- oped a simple model, of which we will make use here

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(it is built into the MC simulation program ARIADNE [6 ] ). Most of our results are, however, insensitive to the details.

It is well known that the bremsstrahlung emission of wavelengths shorter than the size of the emitting region is generally suppressed. Consider as a first ex- ample the gluon emission in relation to an inelastic leptoproduction event, in case a hadron behaves like a vortex line in a colour superconducting vacuum, i.e. like a string. Then the "hi t" quark (colour 3) moves away with energy momentum W+ in the direction of the momentum transfer while the remainder of the hadron (all in all a colour 3 state) in general moves in the opposite direction with the energy momentum W_. [The indices ( _+ ) indicate positive and negative lightcone components.] I f a gluon with transverse momentum kv and rapidity y is emitted from this dipole, then we expect that only a region of the order of the wavelength 2 ~ k~ ~ of the remainder will be involved and radiate coherently. In particular for the negative lightcone component

k_ =kT e -y (7)

we will then have an upper limit

¢t k_<~w_ (S)

with/~ and hadronic size parameter. Instead of eq. ( 1 ) we obtain from eq. (8)

2 WT In k~- < y < l n (9)

/tW_ kv

We have found [ 8 ] that all the final state properties of the leptoproduction events in the present energy regions are well described by this "softening" of the spectrum with ~t ~ 1 GeV. For the much larger energies in the HERA regime this condition will, however, mean essential differences as compared to e.g. the results of the well known MC simulation program LEPTO [9,10].

To model what happens in high-px gluon scattering events, we use the Monte Carlo program PYTHIA 5.3 [ 11 ]. This program uses by default an initial and final state parton shower as described in ref. [3 ]. In our calculations this option is turned off and we per- form a dipole cascade on the partonic state produced by PYTHIA modeling only the hard interaction. Here, the partons which have actually participated in the

hard interaction are considered to be pointlike, all others are treated as extended objects. We would like to point out that this is not intended to he a "com- plete" model for hadroproduction, but we think that it is sufficient for the investigations of the properties of high Pr jets presented in this paper.

The QCD leading log calculations are only trust- worthy when the gluons are strongly ordered (kT~>>kT2>>kT3...). Closer to the kinematical boundaries, i.e. when two gluons have approximately the same kT, it is not possible to calculate the result because many diagrams contribute and interfere. Therefore different options are available in the A R I A D N E MC. In the default option the gluons are strictly ordered so that always ka-t > kT2 > kx3 .... Op- tionally the full phase space for gluon emission is allowed in each dipole, which implies that the gluons are only ordered on the average. In e+e - annihilation this option gives considerably larger multiplicity at LEP-SLC energies and beyond.

When allowing for the gluon splitting process the amount of ambiguity is further increased. In the default option (DO) all the ka-'s are strictly ordered. However, even if the gluons are strictly ordered, there is a priori no reason that the kT o f a qq pair could not be larger than the ka- of the parent gluon. Thus we have investigated the possibility that the gluons are strictly ordered while for the q~l pairs the full phase space is available (called the IO option). This will give an increase in the heavy quark production while the increase in multiplicity is negligible.

We have used this ( IO) option and the default option (DO) in our calculations. We have also used the Parton Shower Program which is default in PYTHIA [11] for comparison. In all cases the JETSET 7.1 [ 12 ] program was used for fragmentation.

First we will consider the situation where the gluons from the hard scattering in a lop collision have a fixed kT and lie in the (pseudo) rapidity interval I q I < 0.5. We then study the K + / ~ + ratio as a function of Z=PT(K +, 7t+)/kT(g) for Ir/I < 1. The results are presented in fig. 1 where we have used 10p collisions with a center of mass energy of 500 GeV.

In fig. la we show the result for kT= 10 GeV using the dipole cascade with DO and IO. There is also a curve for the case where the QQ splitting is turned off in the cascade. Here we see that the QQ production in the cascade contributes considerably to the

463


0,6

0,4

-,e

0,2

0,0 U,O

I i I I

a oo Io

I l i I I I

0 , 2 0 , 4 Z 0 , 6 0 , 8 1 , 0

I=

0,6

0,4

0,2

I

C I I I I

b . . ::.'. :" :........-..-.-

'=:" . . . . . 40 GeV . . . . . . . . 20 GeV

10 GeV I I I l

0,2 0,4 0,6 0,8 z

0,4

v

0,2

0,0 0,0 o,O 1,0 U,O

0,6

f . . . . . 40IGev

. . . . . . . . 20 GeV

10 GeV i i | | i

0,2 0,4 0,6 0,8 Z

,0

Fig. 1. K + /n + as a function of z. (a) For different options in ARIADNE for kx (g) = 10 GeV. (b) For different k T of the hard gluon using ARIADNE (DO). (c) The same as (b) using Parton Shower.

K / n ratio for large z, especially in the IO case. In fig. I b we see the result for DO for different kT and in fig. lc the same for the Parton Shower. Comparing these figures demonstrates clearly the differences between different ways of introducing the g--,QQ process into QCD cascades.

In fig. 2 we compare our model with the Parton Shower and with the data on K + / n + from the C D H W Collaboration at ISR [4] for pp collisions at 62 GeV. Because o f the low statistics in the MC calculations we show only the lowest PT bins, where the statistical errors are acceptable. For higher px there are also large systematic uncertainties because the choice o f the angle where the measurements are made (50 ° ). Here the MC calculations are very sensitive to the gaussian width of the PT for primary hadrons in the Lund fragmentation model [ 12 ].

We see that the hard qq production is very essential for the results and that our model is much closer to the experimental data than the "conventional"

Parton Shower, in particular the IO option, even if it does not completely reach the experimental values.

In fig. 3 we show results for the D + / n ÷ and B+ / n ÷ ratios using ARIADNE (DO) in the same situa-

0,5

÷

"- 0,4 ÷

5L

I I

o ARIADNE DO

• • ARIADNE IO

x Parton Shower T I • ISR data

! 0 , 3 I I I | ~ I I

3,0 3,2 3,4 3,6 3,8 4,C PT

Fig. 2. K+ /n + at 0~ 50 ° at ISR energies as a function Of PT.

464


0,5

0,4

0,2

0,0 0,0

u u u I a

P-r (g) . . ~¢ i I , " °

/ J _ _ _ _ ~ o" 40 GeV / , ."

. . . . . 20 GeV / ' -" /f i / °° . . . . . . . . 10 GeV / , , .."

5 GeV / • "" i t °° A,'...""

0,2 0,4 0,6 0,8 Z

1,0

for ou t mode l , w i thou t cons ider ing the specif ic cuts

and biases used in the e x p e r i m e n t are 0.07 ( I O ) and

O.O4 (DO).

O u r conc lus ion is that the " h a r d " qcl p r o d u c t i o n is

very sensi t ive to the details o f the par ton cascade. O u r

t r e a t m e n t based on the d ipo le a p p r o x i m a t i o n gives

s igni f icant ly larger p r o d u c t i o n than " c o n v e n t i o n a l "

pa r ton showers. We thus f ind a qua l i t a t ive a g r e e m e n t

wi th expe r imen ta l da ta for the K/n ra t io and D - m e -

son p roduc t i on in high-px jets.

0,6

0,4

0,2

0,0 0,0

b | m u u

/ o PT (g) / , '

40 GeV / e **

. . . . . 20 GeV / , ..

. . . . . . . . 10 GeV / ' 5 GeV 17 . '"

/ / ," /¢s '~ . "

/ . / " ..." ~-- -~- - .~ . ' r '" , '" ,

0,2 0,4 0,6 0,8 Z

,0

Fig. 3. (a) D+/n + and (b) B+/n + as a function ofz for different kr of the hard gluon using ARIADNE (DO).

t ion as in fig. I, and we no te the spec tacu la r rise in

these rat ios for large kT. We also note, especial ly in

the B + / n + rat io, that there are (as e x p e c t e d ) typical

th resho ld effects. T h e p r o d u c t i o n o f D and B mesons ,

using the defaul t pa r ton shower o f P Y T H I A , is neg-

l igible in g luon je ts at these energies.

The re are recent results f r o m U A 1 [ 13 ] and C D F

[ 14 ] on D* p roduc t ion where they have found a va lue for the n u m b e r o f D *-+ per je t o f 0.1 1 + 0.05 + 0.06

and 0.10_+0.03_+0.03 for je t s wi th a m e a n PT o f 43

G e V and 40 G e V respect ively . C o r r e s p o n d i n g va lues

R e f e r e n c e s

[1] B. Andersson, G. Gustafson and L. L6nnblad, Gluon splitting in the colour dipole formulation, Lund preprint LU TP 89-9.

[2] G. Gustafson, Phys. Len. B 175 (1986) 453; G. Gustafson and U. Pettersson, Nucl. Phys. B 306 (1988) 746.

[3]M. Bengtsson and T. Sj6strand, Phys. Lett B 185 (1987) 435.

[4] A. Breakstone et al., Phys. Lett. B 135 (1984) 510. [5] Ya.I. Azimov et al., Coherence effects in QCD jets,

Leningrad preprint 1051 ( 1985 ); Phys. Lett. B 165 (1985) 147.

[6]L. I_6nnblad, ARIADNE-3, a Monte Carlo for QCD Cascades ..., Lund preprint LU TP 89-10.

[ 7 ] G. Marchesini and B.R. Webber, Nucl. Phys. B 310 ( 1988 ) 461.

[ 8 ] B. Andersson, G. Gustafson, L. L~nnblad and U. Pettersson, Z. Phys. C 43 (1989) 625.

[ 9 ] G. Ingelman, DESY preprint in preparation. [ 10 ] M. Bengtsson, G. Ingelman and T. Sj/Sstrand, Nucl. Phys. B

301 (1988) 554. [ 11 ] H.-U. Bengtsson and T. Sj6strand, private communications. [ 12 ] T. Sj~strand, Comput. Phys. Commun. 39 (1986) 347;

T. Sj~Sstrand and M. Bengtsson, Comput. Phys. Commun. 43 (1987) 367.

[ 13 ] S. Wimpenny, talk presented at the EPS High Energy Physics Conf. (Madrid, 1989).

[14] A.F. Garfinkel, talk presented at the EPS High Energy Physics Conf. (Madrid, 1989).

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The flavouring of a gluon jet