EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN{PPE/96{108

26 July 1996

A study of kinematical correlations between charmed particles

pro duced in

{Cu interactions at

p

s

= 26 GeV

The BEATRICE Col laboration

M. Adamovich

5)

, M. Adinol

3)

, Y. Alexandrov

5)

, C. Angelini

6)

, D. Barberis

3)

,

D. Barney

4)

, J. Batten

4)

, C. Bruschini

3)

, A. Cardini

6)

, F. Ceradini

8)

, C. Cianfarani

1)

,

G. Ciapetti

7)

, M. Dameri

3)

, G. Darb o

3)

, A. Duane

4)

, V. Flaminio

6)

,A.Forino

1)

,

B. R. French

2)

,A.Frenkel

7)

, C. Gemme

3)

, K. Harrison

7)

, N. Hummadi

4)

, R. Hurst

3)

,

A. Kirk

2)

, C. Lazzeroni

6)

, L. Malferrari

1)

, G. Martellotti

7)

,P. Martinengo

2)

,

P. Mazzanti

1)

, J. G. McEwen

9)

,P. Nechaeva

5)

, A. Nisati

7)

, D. Orestano

8)

, B. Osculati

3)

,

M. Palutan

7)

,M. Passaseo

2)

,G.Penso

7)

,L.Pontecorvo

7)

, A. Quareni

1)

, H. Rotscheidt

2)

,

C. Roda

6)

, L. Rossi

3)

,S.Veneziano

7)

,M. Verzocchi

7)

,D. Websdale

4)

, L. Zanello

7)

and

M. Zavertyaev

5)

.

Abstract

A sample of 475 events, in whichtwocharmed-particle decays are observed, is an-

alyzed to determine distributions of two-particle kinematic variables. One charmed

particle with

x

F

>

0 is fully reconstructed and the other is at least partially recon-

tructed. The distributions of

and

p

2

T

are compared with a next-to-leading order

QCD calculation.

(Tobe submitted to Physics Letters B)

1)

Universita di Bologna and INFN, Bologna, Italy.

2)

CERN, Geneva, Switzerland.

3)

Universita di Genova and INFN, Genoa, Italy.

4)

Blackett Lab oratory, Imp erial College, London, United Kingdom.

5)

Lebedev Physical Institute, Moscow, Russian Federation.

6)

Universita di Pisa and INFN, Pisa, Italy.

7)

Universita di Roma \La Sapienza" and INFN, Rome, Italy.

8)

Universita di Roma \Roma Tre" and INFN, Rome, Italy.

9)

University of Southampton, Southampton, United Kingdom.

1 Intro duction

Hadroproduction of heavy quarks is an important testing ground for Quantum Chro-

modynamics (QCD). Recent perturbative calculations to next-to-leading order (NLO),

i.e.

O

(

3

S

), are believed to be of sucient accuracy that useful comparisons can b e made be-

tween experimental data and theoretical predictions [1]. For charm production, however,

the mass is not suciently large for higher order p erturbative eects to be negligible,

thus signicant discrepancies with exp erimental results might still exist. The observed

experimental correlations between charmed particles provide a test of the NLO QCD

calculations.

In this letter we rep ort measurements of correlation variables which relate kinematic

quantities for twocharmed particles produced in a single eventby exp erimentWA92. We

have previously rep orted results on the azimuthal angle

between charmed particles

[2]. Nowwe improve our previous analysis in three ways. First, we include measurements

of kinematic correlation variables, in addition to the topological variable

. Second, we

use the full statistics of the exp eriment, increasing the sample size by approximately a

factor of 5; third, we include the corrections due to an improved study of the acceptance

of the detector.

The measurementof

does not require knowledge of the magnitudes of the two

charmed-particle momenta; however, this information is required for other kinematic cor-

relation variables and must b e either measured or estimated. The variables wehave mea-

sured, in addition to

, include the invariant mass

M

(

DD

), the rapidity dierence

y

=

y

(

D

)

y

(

D

), the Feynman

x

dierence

x

F

=

x

F

(

D

)

x

F

(

D

), the Feynman

x

of the

DD

system, and the square of the transverse momentum of the

DD

pair

p

2

T

(

DD

),

where

p

T

is relative to the incident b eam particle direction. These variables are useful in

subsequent comparisons with the predictions of charm pro duction models.

Data were collected using a 350 GeV/

c

beam incident on a 2 mm copper target

in the CERN Spectrometer. WA92 was conceived as a xed-target beauty hadropro-

duction exp eriment, so the apparatus was designed to study short-lived particles. The

main features of the experimental hardware are a fast online secondary vertex trigger

and a high precision silicon microstrip detector array which provides excellent track vi-

sualization. The trigger, although designed to select beauty decays, also has signicant

eciency for charm decays, which p ermits the present measurement. The silicon tracking

array is divided into a Decay Detector (DkD) consisting of 17 planes of 10

m pitch sili-

con microstrips covering the rst 2

:

5cm downstream of the target, followed byaVertex

Detector (VxD) consisting of 12 planes of 25

m pitch and 5 planes of 50

m pitch. The

DkD has analogue readout so that secondary interactions in the detector material may

be identied by their large energy deposits. Cuts on the recorded pulse heights in the

vicinity of secondary vertices reduce by

91% the number of vertices due to secondary

interactions in the material of the DkD. More details of the description and p erformance

of the exp erimental apparatus can b e found in Refs. [3, 4]. The exp eriment collected data

in 1992 and 1993 with a total luminosityof8

:

1nb

1

.

2 Event selection

Events are selected in which one charmed particle is fully reconstructed, while recon-

struction of the decayvertex is all that is required for the second. Requiring b oth charmed

particles to b e fully reconstructed would reduce the sample size by a factor

45 (

i.e.

to

10 events). This factor is consistent with charm branching fractions and with our ac-

1

ceptance and reconstruction eciency. Due to detector acceptance, all fully reconstructed

charmed particle decays have a p ositivevalue of Feynman

x

; the partially reconstructed

decays mayhave either p ositive or negative

x

F

. Only events with two secondary vertices

within 6 cm of the target are considered. The reconstructed positions of the secondary

vertices are required to be outside of the target and to be separated from the primary

vertex by at least 6

(1

:

2mmonaverage), where

is the r.m.s. precision in the vertex

separation. In addition, they are required to b e separated from each other by at least

100

m in the plane transverse to the beam direction. Since our vertex reconstruction has

a transverse accuracy of

3{10

m, this last requirement excludes with high probability

events in which a single vertex is split into twovertices by reconstruction errors.

As the fully reconstructed charm vertex must b e physically compatible with a

Cabibbo favoured decay

D

!

Kn

(

n

=1

;

2

;

3), its total charge is required to b e 0

or

1 and its total momentum vector is required to p oint to the primary vertex within

30

m. At this stage no cut is applied on the charmed candidate's invariant mass, except

that 2-prong vertices compatible with

K

0

or

0

decays are rejected.

Softer cuts are applied to the second vertex. Any pairs of tracks belonging to it which

have opp osite charge and whose momentum sum points to the primary vertex within

60

mmust be incompatible with

K

0

or

0

decays.

e

+

e

pairs from photon conversions

are automatically excluded as they would b e detected as a single track in the silicon

microstrip detectors which are lo cated in a zone of weak magnetic eld. The invariant

mass of the vertex, assuming pion mass for all particles, must be less than 1

:

9 GeV/

c

2

.

There is no requirement on the vertex charge, on the number of tracks, nor on p ointing

to the primary vertex.

From the events which satisfy the previous requirements, 690 (2251) in the 1992

(1993) data, we extract two samples: the signal sample if the mass of the fully recon-

structed vertex in the hypothesis

D

!

Kn

equals the

D

mass

15 MeV/

c

2

; and a

side-band sample if the invariant mass

M

is in the region 1

:

69

<M <

1

:

78 GeV/

c

2

or

1

:

96

<M <

2

:

05 GeV/

c

2

. The range and width of the side-bands has been chosen to allow

the subtraction of a linear background distribution and at the same time to minimize the

statistical error of this subtraction. There are 123 (441) events in the signal sample and

129 (407) events in the side-band sample for the 1992 (1993) data. Since our apparatus

cannot distinguish b etween

and

K

, mass assignments for 2- and 4-prong vertices are

ambiguous. All combinations are considered equally.Thus it is p ossible for a 2-prong

vertex, for example, to be used twice | once in the signal sample and once, with the

opposite mass assumptions, in the side-band sample. As the width of the side-bands is 6

times the width of the signal region, all combinations in the side-bands are given weight

1/6. The 1992 and 1993 experimental setups were slightly dierent so the two data sets

were analyzed indep endently. They were found to be compatible, so only the combined

results are presented.

3 Momentum estimator

As previously noted, the momenta of the charmed particles is not needed for the

measurementof

;however, it is required for the determination of the other correlation

variables. Thus it is necessary to have an estimator for the momentum of the partially

reconstructed vertex which takes into account the unseen decay products. We use a com-

bination of two metho ds that are based on dierentphysical considerations. The rst

method consists in closing the charm decayby adding a missing particle, assumed to have

2

Figure 1:

Error of the momentum estimator describedinSection 3. The dierencebe-

tween the reconstructed and the simulated charm momentum is displayed as a function

of the simulated momentum. The vertical error bars represent the r.m.s. width of the

reconstructed momentum distribution.

a pion mass. Requiring the vertex to have the charm mass and requiring that its total

momentum vector p oint to the primary vertex, a second order equation is obtained with

two possible solutions for the charm momentum. Wecho ose the lower of the twocharm

momentum solutions since the apparatus has no acceptance for low-momentum charged

particles (below

1 GeV

=c

) and, therefore, there is a greater probability that a missing

particle makes a small contribution to the total momentum. The second metho d has b een

used by other experiments [10, 11] and is based on the assumption that in the rest frame

of the charmed particle the unseen momentum is emitted on average in a direction per-

pendicular to the charm laboratory momentum. The Lorentz b oost

D

from the charm

rest frame to the lab oratory frame is then given by

D

=

E

vis

q

M

2

vis

+

p

2

T

vis

where

E

vis

is the visible energy,

p

T

vis

is the visible transverse momentum, and

M

vis

is the

mass of the visible system, calculated assigning the pion mass to all the detected particles.

The charm momentum can be deduced imp osing the charm mass:

p

D

=

D

D

M

D

:

A comparison b etween these two metho ds and the simulation indicates that both metho ds

give useful and independent information; however the rst metho d systematically under-

estimates the momentum while the second method systematically overestimates it. The

3

best estimator for the charm momentum is a weighted average of the results of the two

methods. The optimal weights are acceptance dependent; for our experimental setup equal

weights give a goo d result. Finally, a 10% correction comp ensates for the underestimation

of the visible mass due to the assignments of pion masses to kaons, yielding an accuracy

of

p

=p

=0

:

012 + 3

:

2

10

4

p

where

p

is in GeV

=c

(see Fig. 1). The resulting fractional errors on the correlation vari-

ables are well b elow 10% over most of the range of their measurements. Obviously,if

the secondary vertex momentum sum p oints to the primary vertex and the visible mass

is compatible with the

D

mass, neither of the two metho ds is applied, and the visible

momentum is used.

Figure 2:

Invariant mass distributions for: a) data; b) simulated

c

c

events.

4 Background subtraction and acceptances

The invariant mass distribution for the fully reconstructed vertex is shown in Fig. 2a.

Fitting the data mass distributions with a Gaussian peak above a linear background, we

nd that the background in the signal region is

15% for both the 1992 and 1993 data

sets.

The main contribution to the background is from poorly reconstructed vertices in

charm events and has b een estimated using a Monte Carlo simulation. The

c

c

events

were produced by a combination of Pythia 5.4 [5] for leading order QCD generation of

the initial

c

c

quark pair, Jetset 7.3 [6] for their hadronization, and Fluka [7] for nuclear

eects in the target; detector resp onses were simulated with Geant 3.21 [8] interfaced with

Fluka and Jetset 7.4 [9] as described in ref. [4]. Monte Carlo events were selected by the

4