Properties of neutral charmed mesons in pA interactions at 70 GeV

ISSN 1063-7788, Physics of Atomic Nuclei, 2011, Vol. 74, No. 2, pp. 324–331. c© Pleiades Publishing, Ltd., 2011.Original Russian Text c© V.N. Ryadovikov, 2011, published in Yadernaya Fizika, 2011, Vol. 74, No. 2, pp. 342–349.

ELEMENTARY PARTICLES AND FIELDSTheory

Properties of Neutral Charmed Mesonsin pApApA Interactions at 70 GeV

V. N. Ryadovikov*

(On behalf of the SVD-2 Collaboration1)1)1))Institute for High Energy Physics, ul. Pobedy 1, Protvino, Moscow oblast, 142281 Russia

Received May 28, 2010

Abstract—The results of data handling for the Е-184 experiment involving the irradiation of the activetarget, consisting of carbon, silicon, and lead plates by a 70-GeV proton beam are presented. When thetwo-prong neutral charmed meson decay signal was selected and the cross section for charm production ata near-threshold energy was estimated (σ(cc̄) = 7.1± 2.4(stat.)± 1.4(syst.) μb/nucleon), some propertiesof D0 and D̄0 were investigated. These include the atomic-weight dependence of the cross section onthe target mass number (its A dependence); the differential cross sections dσ/dp2

t and dσ/dxF; and thedependence of the parameter α on xF, p2

t , and plab. The experimental results are compared with thepredictions of the FRITIOF7.02 program.

DOI: 10.1134/S1063778811020189

INTRODUCTION

The SERP-Е-184 experiment “Investigation ofMechanisms of the Production of Charmed Particlesin Proton–Nucleus (pA) Interactions at 70 GeV andTheir Decays” [1] is being performed at the SVD-2 facility of the Institute for High Energy Physics(IHEP, Protvino). An active target, which consists ofcarbon, silicon, and lead plates, was irradiated witha 70-GeV proton beam. Upon separating a signalin the effective-mass spectrum of the Kπ system,an estimate of the cross section for charmed-mesonproduction in pA interactions at near-threshold en-ergy was given in [2]. The cross section for charmproduction proved to be

σ(cc̄) = 7.1 ± 2.4(stat.) ± 1.4(syst.) μb/nucleon.

*E-mail: [email protected])A.N. Aleev, E.N. Ardashev, A.G. Afonin, V.P. Balandin,

S.G. Basiladze, S.F. Berezhnev, G.A. Bogdanova,M.Yu. Bogolyubsky, A.M. Vishnevskaya, V.Yu. Volkov,A.P. Vorobiev, A.G. Voronin, G.G. Ermakov, P.F. Ermolov,S.N. Golovnia, S.A. Gorokhov, V.F. Golovkin, N.I. Grishin,Ya.V. Grishkevich, V.N. Zapolsky, E.G. Zverev,S.A. Zotkin, D.S. Zotkin, D.E. Karmanov, V.I. Kireev,A.A. Kiriakov, V.N. Kramarenko, A.V. Kubarovsky,N.A. Kouzmine, L.L. Kurchaninov, G.I. Lanshikov,A.K. Leflat, S.I. Lyutov, M.M. Merkin, G.Ya. Mitrofanov,V.S. Petrov, Yu.P. Petukhov, A.V. Pleskach, V.V. Popov,V.M. Ronjin, D.V. Savrina, V.A. Senko, M.M. Soldatov,L.A. Tikhonova, N.F. Furmanec, A.G. Kholodenko,Yu.P. Tsyupa, N.A. Shalanda, A.I. Yukaev, V.I. Yakimchuk.

The value obtained for the cross section exceedsthe predictions of hard QCD [1] (σ(cc̄) ∼ 1 μb).At the same time, variations in the parameters ofthe model within possible limits change the errorfield [3], with the result that this cross section doesnot seem overly large (Fig. 1a was taken from [4],and our point was added). Attempts to estimatethe cross section for charm production at energiesin the threshold region were undertaken more than20 years ago at the IHEP facility BIS-2 in irradiatinga carbon target with neutrons of energy in the range40–70 GeV [5]. In the kinematical region xF > 0.5,the measured cross section for D0-meson productionproved to be considerably larger than theoreticalpredictions—namely, σ(D0) = 28 ± 14 μb/nucleus.Upon rescaling it to the entire kinematical region thecross section for charm production proved to be about5 μb/nucleon. Approximately the same theoreticalestimate of this quantity was obtained by Kaidalov’sgroup in calculating the charm-production crosssection on the basis of the quark–gluon stringmodel [6]. Figure 1b shows the graph taken from [6]with addition of our point.

A detailed description of the SVD-2 facility can befound in [1]. The presence in the E-184 experimentof a target containing carbon, silicon, and lead platesmakes it possible to measure the dependence of thecharm-production cross section on the atomic weight(A) of target nuclei. In [2], it was shown that, in

324

PROPERTIES OF NEUTRAL CHARMED MESONS 325

10

1

10

2

10

3

10

–2

10

–1

10

0

σ

DD

, mb

–

(

b

)

SVD-2

s

GeV

,

10

1

10

2

10

3

10

0

10

3

σ

ccNN

,

μ

b

(

a

)

SVD-2

s

GeV

,

10

1

10

2

10

4

NLO supplemented with CTEQ6M

NLO within the range of parametervalues

UA2

pp

; PLB

236

, 488

–

MUON cosmic rays; NPB

122

, 353

PAMIR cosmic rays; NPB

122

, 353

NA32

pA

; PR

433

, 127

E769

pA

; PR

433

, 127

NA16

pA

; PR

433

, 127

NA27

pA

; PR

433

, 127

E743

pA

; PR

433

, 127

E653

pA

; PR

433

, 127

HERA-B

pA

; PR

433

, 127

NA50

pA

; PR

433

, 127

NA60 InIn (preliminary)

STAR

d

Au; PRL

94

, 062301

STAR AuAu (preliminary)

PHENIX

pp

; PRL

97

, 252002

PHENIX AuAu; PRL

94

, 082301

PHENIX AuAu; PRL

88

, 192303

Fig. 1. Experimental cross sections for charm production in pA interactions along with theoretical predictions based on (a)perturbative QCD [3] or (b) the quark–gluon string model [6].

PHYSICS OF ATOMIC NUCLEI Vol. 74 No. 2 2011

326 RYADOVIKOV

Table 1. Cross sections for D0-meson production for four p2t intervals (Δp2

t = 1.0 (GeV/c)2)

⟨p2

t

⟩,

(GeV/c)2εdet, %

dσ, μb/nucleus

carbon silicon lead average over nuclei

0.5 3.7 13 ± 13 83 ± 28 945 ± 285 218 ± 45

1.5 3.8 26 ± 18 63 ± 24 669 ± 237 157 ± 38

2.5 3.4 15 ± 15 30 ± 17 281 ± 162 72 ± 27

3.5 3.5 14 ± 14 10 ± 10 91 ± 91 20 ± 14

this experiment, the parameter α in the A dependence(σ ∼ Aα) is 1.08 ± 0.12, which is consistent withresults of other experiments [7–9].

A detailed simulation of processes accompany-ing the detection of charmed-particle decays at theSVD-2 facility on the basis of the FRITIOF7.02 andGEANT3.21 packages makes it possible to deter-mine the efficiencies of all procedures of the data-handling system and their dependence on the kine-matical parameters p2

t and xF; this in turn makes itpossible to estimate inclusive spectra of neutral Dmesons. Below, D0 denotes the sum of the particleand antiparticle.

LIFETIME OF NEUTRAL D MESONS

In order to verify whether the separated Kπ decaysare the decays of charmed mesons, we measured theirlifetime on the basis of the dependence of the crosssection for the reaction pA → D0 + X on the pathlength of the Kπ system. The visible path length

10

0.05

d σ

/

dL

,

μ

b/0.5 mm

L

, mm0.10 0.15 0.20 0.25

20

30

40

50

Fig. 2. Cross section for the production of neutral Dmesons as a function of their path length: (points) ex-perimental data and (curve) result of parametrizing databy an exponential function.

was corrected by multiplying it by the factor (p/M );that is, use was made of L = Lvis/(p/M), where p isthe momentum of the system and M is its measuredmass. The interval of path lengths was broken downinto subintervals (see Fig. 2); in each subinterval, theeffective-mass spectrum was constructed for the Kπsystem, and the cross section was determined fromthe number of events in the signal from D0-mesondecay. Because of the smallness of the statisticaldata sample, signals from D0 and D̄0 mesons wereunited into a single spectrum. In approximating thedependence of the cross section on the range (seeFig. 2) by a function of the form σ ∼ exp(−L/cτ),one obtains the fitted value of cτ = 0.123± 0.024 mm,which agrees with the tabulated value of 0.124 mmwithin the errors.

DIFFERENTIAL CROSS SECTION dσ/dp2t

The acceptance of the SVD-2 facility makesit possible to measure the transverse momentum

5

0 1 2 3 4

10

1

5

10

2

p

t

2

GeV

/

c

( )

2

,

2

2

d

σ

/

dp

t

2

μ

b

,

Fig. 3. Differential cross section dσ/dp2t for the produc-

tion of neutral D mesons: (points) experimental data and(curve) exponential function fitted to the data.



Table 2. Cross section for D0-meson production for various xF intervals (ΔxF = 0.2)

〈xF〉 εdet, %dσ, μb/nucleus

carbon silicon lead average over nuclei

–0.1 2.6 10 ± 10 13 ± 13 245 ± 173 40 ± 23

0.1 9.4 16 ± 9 55 ± 14 541 ± 135 123 ± 21

0.3 13.5 7 ± 5 15 ± 6 118 ± 52 39 ± 10

0.5 12.5 2 ± 2 6 ± 4 25 ± 25 6 ± 4

(pt) and the Feynman variable (xF = 2pL/√

s) ofcharmed mesons in wide intervals of p2

t between 0and 4 (GeV/c)2 and of xF between –0.2 and 0.6. Asimulation shows that 54% of D0 mesons and 23% ofD̄0 mesons then fall within the spectrometer aperture.

In order to obtain p2t spectra, we constructed

effective-mass spectra of the Kπ system in four p2t

intervals. In each spectrum, we determined thenumber of events, Ndet, with the decay of neutralD meson and calculated the inclusive partial crosssection for the respective p2

t interval by the formula

σ(D0)nucl = Kinstr · Ndet · A0.7/(Br · ε · Lint),

employing values determined previously for the effi-ciencies and other quantities (branching ratio, inte-grated luminosity, and instrumental factor) [2]. Forfour p2

t intervals, Table 1 gives values of respectivecross sections along with statistical errors in them.In order to calculate the cross-section value aver-aged over nuclei, we used the summed signal andthe averaged atomic weight of the nuclei in just thesame way as was described in [2]. The measuredaverage value of the transverse momentum of neu-tral D mesons is 〈pt〉 = 1.02 GeV/c. Approximatingthe transverse-momentum dependence of the exper-imental cross section for all nuclei by the expressiondσ/dp2

t ∼ exp−bp2t , we obtained the fitted exponent

value of b = 0.79 ± 0.15 (GeV/c)−2 (Fig. 3).In pA collisions, we investigated the behavior of

the A-dependence parameter α as a function of kine-matical variables. Despite small statistics of the sig-nal and large errors associated with this, we made anattempt at observing the p2

t dependence of α. Forfour p2

t intervals, Fig. 4a shows the differential crosssection as a function of the target atomic weight. Onecan see that the slopes of the respective straight linesare different for different values of p2

t . The experi-mental data indicate a decrease in the parameter α

with increasing p2t according to an exponential law

(see Fig. 4b).

DIFFERENTIAL CROSS SECTION dσ/dxF

We have studied the behavior of the cross sectionfor the reaction pA → D0 + X as a function of theFeynman variable xF. The cross sections for differ-ent xF intervals were calculated by a method similarto that used in studying the transverse-momentumdependence—that is, in constructing the effective-mass spectra of the Kπ system in four xF intervalsand in determining the number of events in the signalfor each interval (see Table 2). Figure 5 shows exper-imental values of the cross sections for the produc-tion of neutral charmed mesons versus the variablexF. In order to describe the respective dependence,we employed a standard parametrization of the formdσ/dxF ∼ (1 − |xF|)n. The fitted value of the param-eter n proved to be 6.8 ± 0.8, and the respective meanvalue was 〈xF〉 = 0.12.

Following the same line of reasoning as in study-ing the p2

t dependence of the parameter α, we haveanalyzed the dependence of this parameter on thevariable xF. For this, we estimated signals from D0

mesons and the corresponding cross sections for theirproduction in xF intervals for three materials of theactive target (see Fig. 6a). From Fig. 6b, one cansee that the parameter α decreases with increasingxF. If we describe the data in terms of an exponentialfunction, then, for xF → 1, the parameter α decreasesto the value of 0.55. This agrees with the theoreticalprediction made in [6].

It is noteworthy that Tables 1 and 2 present onlythe statistical errors in the cross sections; we estimatesystematic uncertainties in the cross sections at alevel of 20% of the statistical errors.


328 RYADOVIKOV

0 1 2 3 4

0.5

1.0

p

t

2

GeV

/

c

( )

2

,

1.5

α

(

b

)

2.5 3.5 4.5

1

3

d

σ

/

dp

t

2

( )

ln

5

ln

A

(

a

)

7

5.5

C

Si

Pb

y

= 0.40 + 0.73

x

0.03 + 1.04

x

0.37 + 1.14

x

–0.78 + 1.45

x

Fig. 4. (a) Differential cross section as a function of the atomic weight of target nuclei and (b) parameter α as a function of p2t :

(points) experimental data and (curve) exponential function fitted to the data.

0

–0.2

d σ

/

dx

F

,

μ

b/0.2

x

F

0 0.2 0.4 0.6

40

80

120

d

σ

/

dx

F

~ (1 –

|

x

F

|

)

n

n

= 6.8 ± 0.8

Fig. 5. Differential cross section for the production ofneutral D mesons, dσ/dxF: (points) experimental da-ta and (dotted curve) fitted parametrization of the formdσ/dxF ∼ (1 − |xF|)n.

FRITIOF CODE AND A DEPENDENCEOF CROSS SECTIONS

The Lund string model is used in the FRITIOFcode for simulating hadron–hadron and hadron–nucleus interactions. It is assumed that, after4-momentum exchange, hadrons become two excitedstring states, which, thereupon, emit gluons in theapproximation of QCD color dipoles. The ultimatehadronization is performed by using the Lund string-fragmentation model. A collision with a nucleusis treated as independent collisions of an incidentnucleon with constituent nucleons of the nucleusinvolved. The Fermi motion of nucleons, the de-formation of the nucleus, and multiple rescattering

are taken into account. The nucleon-distributiondensity in a nucleus is described by the Woods–Saxon potential. We employed this code to per-form a model investigation of the dependence of theparameter α on the kinematical parameters of D0

mesons and to compare the results obtained in thisway with experimental data. For three values of thetarget atomic weight (C, Si, and Pb), the availablenumbers of simulated (MC) events with D0 mesonswere weighed in such a way that the A dependencewith parameter α = 1 was satisfied on average forall events. From three distributions with respect toa given kinematical variable (xF, p2

t , and рlab), thedependence of the parameter α on this quantity wasthen calculated for D0 mesons.

According to [10], the xF dependence of α mustreflect the contribution to the cross section from var-ious nuclear subprocesses, such as final-state ab-sorption, interaction with closely flying hadrons (in-teractions with comovers), the shadowing of partondistributions, the parton energy loss in the medium,and the effect of intrinsic-charm components. Thisleads to an increase or a decrease in the parameter αas xF increases.

Figure 7a shows the input simulated distributionsof events in three targets (C, Si, Pb) with respectto the Feynman variable xF for D0 and D̄0 mesons.On the basis of these distributions, we calculate theparameter α. The graphs representing its dependenceon the variable xF are shown in Fig. 7b (solid anddashed curves). Also given in that figure are theexperimental values of α for four xF intervals.

It is worth noting that the variable xF may take“unphysical” values for MC events—those going be-yond the range [–1, 1]. This is because, in calculating



0 0.2 0.4 0.6 0.8

0.5

1.0

1.5

α

2.5 3.5 4.5

1

3

5

ln

A

7

5.5

C

Si

Pb

–1.35 + 0.87

x

–0.50 + 0.99

x

–1.01 + 1.20

x

–0.19 + 1.22

x

–1

ln(

d

σ

/

dx

F

)

1.0

x

F

0

2.0

1.32

e

–0.89

x

(

a

) (

b

)

Fig. 6. (a) Differential cross section dσ/dxF as a function of the target atomic weight for four intervals of xF (see Table 2) and(b) parameter α as a function of xF. The displayed points stand for experimental data, while the curve represents the fittedparametrization by an exponential function.

–0.8 0 0.4 0.8

0.4

0.8

1.6

α

x

F

0

2.0

–0.4

1.2

(

b

)

FRITIOF

D

0

FRITIOF

D

0

Experiment

–

–1.0 –0.5 0 0.5 1.0

x

F

(

a

)

D

0

D

0

–

10

3

10

2

10

1

10

1

10

0

10

2

10

3

N

event

Pb

PbSi

Si

C

C

Fig. 7. (a) Distributions of xF for D mesons and (b) parameter α as a function of xF. The displayed points stand for experimentaldata, and the curves represent the results of the simulation.

the Feynman variable xF = 2pL/√

s, the c.m. energy√s proves to be underestimated if the interaction of

the incident nucleon with several nucleons of the tar-get nucleus is not taken into account. In [11], it wasshown that, upon taking into account all interactingnucleons of the nucleus (in the case of the simulationon the basis of the FRITIOF code, this number isknown), the distribution of the variable xF falls withinthe range [–1, 1], as it must. Unfortunately, thenumber of interacting nucleons of the nucleus is un-known in the experiment; therefore, the c.m. energy iscalculated for two nucleons (incident and target), andone has to employ “unphysical” values of the variablexF for MC events. Thus, α decreases with increasing

xF over the entire range of xF, and the experimentqualitatively confirms this behavior.

Figure 8 shows p2t distributions for simulated D0

and D̄0 mesons (Fig. 8a) and the p2t dependence

of the parameter α (Fig. 8b). A comparison ofFRITIOF-simulated dependences and experimentalpoints reveals that there is not even qualitative agree-ment between the model and the experiment (experi-mental errors are large because of small statistics).

In Fig. 9, we present similar distributions withrespect to plab of neutral D mesons. In this case, thereis no problem in displaying data, in contrast to whatwe have for the Feynman variable xF, in which casethe number of interacting nucleons of the nucleus is


330 RYADOVIKOV

0 2 3 4

0.5

1.0

α

1

1.5

(

b

)

FRITIOF

D

0

FRITIOF

D

0

Experiment

–

10 2 3

(

a

)

D

0

D

0

–

10

3

10

2

10

1

10

2

10

3

N

event

Pb

Pb

Si

Si

C

C

p

t

2

GeV

/

c

( )

2

,

4

p

t

2

GeV

/

c

( )

2

,

Fig. 8. (a) Distributions of p2t for D mesons and (b) parameter α as a function of p2

t . The displayed points stand for experimentaldata, and the curves represent the results of the simulation.

0 20 30 40

0.4

0.8

α

10

1.2

(

b

)

FRITIOF

D

0

FRITIOF

D

0

Experiment

–

100 20 30

(

a

)

D

0

D

0

–

10

3

10

2

10

1

10

2

10

3

N

event

Pb

Pb

Si

Si

C

C

40

0

p

lab

, GeV/

c

p

lab

, GeV/

c

10

1

Fig. 9. (a) Distributions of plab for D mesons and (b) parameter α as a function of plab. The displayed points stand forexperimental data, and the curves represent the results of the simulation.

unknown. (The same dependence of the parameter αis presented in [12]). Here, we see qualitative agree-ment between the experiment and the model; that is,α decreases as plab of neutral D mesons increases.

CONCLUSIONS

In conclusion, we present Table 3, which givesthe results of some experiments devoted to studying

charm production in pA interactions. One can seethat, within the errors, our results are compatible withthose data. However, further investigations aimed atrefining the properties of charmed particles producedin pA interactions at near-threshold energy are re-quired.

In comparing the behavior of the A-dependenceparameter α of the cross section as a function of kine-



Table 3. Data on the production of neutral D mesons and on their properties in pA interactions

Experiment Beam energy,GeV

σ(D0),μb/nucleon

α(σ ∼ Aα)

n(dσ/dxF ∼ (1 − xF)n)

b(dσ/dp2

t ∼ exp(−bp2t ))

SVD-2 70 7.1 ± 3.8 1.08 ± 0.12 6.8 ± 0.8 0.79 ± 0.15

E769 [7] 250 12.0 ± 3.8 0.92 ± 0.08 4.1 ± 0.6 0.95 ± 0.09

NA16 [7] 360 20.4 ± 16.0 – – –

NA27 [7] 400 18.3 ± 2.5 – 4.9 ± 0.5 1.0 ± 0.1

Е-789 [8] 800 17.7 ± 4.2 1.02 ± 0.05 – 0.91 ± 0.12

E743 [7] 800 22.0 ± 14.0 – 8.6 ± 2.0 0.8 ± 0.2

E653 [7] 800 39.0 ± 15.0 – 11.0 ± 2.0 1.1 ± 0.2

HERA-B [9] 920 48.7 ± 10.6 0.97 ± 0.07 7.5 ± 3.2 0.84 ± 0.1

matical variables in FRITIOF-simulated events andexperimental data, we can see qualitative agreementfor the case of the Feynman variable xF of neutral Dmesons and their plab. In the case of the variable p2

t ,there is a significant discrepancy: within the model,α is virtually independent of p2

t , but the experimentalpoints indicate a decrease in α with increasing p2

t .

ACKNOWLEDGMENTS

This work was supported by the Russian Foun-dation for Basic Research (project no. 09-02-00445)and was funded by a grant (no. NSH-1456-2008-2)for support of leading scientific schools.

REFERENCES1. M. Yu. Bogolyubskii et al., Preprint No. 96-98, IFVE

(Inst. High Energy Phys., Protvino, 1996); http://web.ihep.su/library/pubs/prep1996/ps/96-98.pdf

2. E. N. Ardashev et al., Preprint No. 2009-9,IFVE (Inst. High Energy Phys., Protvino, 2009);http://web.ihep.su/library/pubs/prep2009/ps/2009-09.pdf

3. A. Shabetai, qm2008.bnl.gov/Program/8Feb/Ses-sion_XIV/qm08_shabetai.ppt

4. A. D. Frawket, T. Ullrich, and R. Vogt, Phys. Rep.462, 125 (2008).

5. BIS-2 Collab., Z. Phys. C 37, 243 (1988).6. A. B. Kaidalov and O. I. Piskunova, Yad. Fiz. 43, 1545

(1986) [Sov. J. Nucl. Phys. 43, 994 (1986)].7. J. A. Appel, in Proceedings of the 10th In-

ternational Conference on Physics in Collision,Durham, North California, Jun. 21–23, 1990.

8. M. Daniel Kaplan, http://arxiv.org/PS_cache/hep-ex/pdf/9610/9610003v1.pdf

9. S. Kupper, PhD Thesis (Univ. of Ljubljana, 2007).

10. R. Vogt, http://arxiv.org/PS_cache/hep-ph/pdf/9907/9907317v1.pdf

11. A. P. Vorob’ev et al., Preprint No. 2008-17,IFVE (Inst. High Energy Phys., Protvino, 2008);http://web.ihep.su/library/pubs/prep2008/ps/2008-17.pdf

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Translated by A. Isaakyan


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Properties of neutral charmed mesons in pA interactions at 70 GeV