charm production from proton–proton collisions

e

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sntsergy ofhadron

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Nuclear Physics A 728 (2003) 457–470

www.elsevier.com/locate/np

Charm production from proton–proton collisions

Wei Liu ∗, Che Ming Ko, Su Houng Lee1

Cyclotron Institute and Physics Department, Texas A&M University, College Station, TX 77843-3366, USA

Received 7 August 2003; received in revised form 5 September 2003; accepted 19 September 200

Abstract

We evaluate the cross sections for charmed hadron production from proton–proton reactionpp →pD̄0Λ+

c and pp → pD̄∗0Λ+c using a hadronic Lagrangian. With empirical coupling consta

and cutoff parameters in the form factors, sum of their cross sections at center-of-mass en11.5 GeV is about 1 µb and is comparable to measured inclusive cross section for charmedproduction from proton–proton reactions. The cross section decreases to about 1 nb at 40 Methreshold. 2003 Published by Elsevier B.V.

PACS: 25.75.-q; 13.75.Lb; 14.40.Gx; 14.40.Lb

1. Introduction

For reactions involving hadrons that consist of charm quarks, a hadronic modeinteraction Lagrangian based on the SU(4) flavor symmetry was first introduced in ReWith empirical coupling constants and introducing form factors at interaction verticesmodel gives aJ/ψ absorption cross section by pion or rho meson [2–4] that is compato that needed in the comover model for understanding the observed suppressionJ/ψ

production in relativistic heavy ion collisions [5,6]. Extending the Lagrangian to incthe interactions between charmed hadrons and baryons, the model has also beenstudy J/ψ absorption by nucleons [7] and charm photoproduction on nucleons [8both cases, the theoretical cross sections are comparable to those known empiricamodel has further been used to calculate the cross section for charm production fromπ–N

* Corresponding author.E-mail address: [email protected] (W. Liu).

1 Permanent address: Department of Physics and Institute of Physics and Applied Physics, Yonsei University,Seoul 120-749, Korea.

0375-9474/$ – see front matter 2003 Published by Elsevier B.V.doi:10.1016/j.nuclphysa.2003.09.011

y ion11,12].

hadronosedstudies

due toprevious

uction

ctionn from

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ons ismary

nearnsudying

SU(4)ssible,nowns with

sities

458 W. Liu et al. / Nuclear Physics A 728 (2003) 457–470

interactions [9], which is relevant to charmed meson production in relativistic heavcollisions [10], and the cross sections for charmed meson scattering by hadrons [In the present paper, the same hadronic Lagrangian is used to evaluate charmedproduction from proton–proton collisions. Motivated by future experiments at propaccelerator facility at the German Heavy Ion Research Center [13], there are alreadyon these reactions based on the meson-exchange model [14,15]. However, effectsoff-shellness of exchanged mesons have been neglected in these studies. As in ourstudies ofJ/ψ absorption by nucleon [7] and photoproduction ofJ/ψ on nucleons [8],we do not make the on-shell approximation in evaluating the charmed meson prodcross section from proton–proton collisions.

This paper is organized as follows. In Section 2, we introduce the interaLagrangians that are needed to evaluate the cross sections for charm productioproton–proton collisions. The two reactionspp → pD̄0Λc andpp → pD̄∗0Λc are thendiscussed in Section 3. We show in this section the amplitudes for these reactiocalculate their cross sections due to contributions from pion, rho meson,D, and D∗exchanges. The total cross section for charm production in proton–proton collisigiven in Section 4 and compared to available experimental data. Finally, a brief sumis given in Section 5.

2. The hadronic model

Possible reactions for charmed hadron production in proton–proton collisionsthreshold arepp → pD̄0Λ+

c and pp → pD̄∗0Λ+c . Cross sections for these reactio

can be evaluated using the same Lagrangian introduced in Refs. [7,8,11,12] for stcharmed meson scattering by hadrons. This Lagrangian is based on the gaugedflavor symmetry but with empirical masses. The coupling constants are taken, if pofrom empirical information. Otherwise, the SU(4) relations are used to relate unkcoupling constants to known ones. Form factors are introduced at interaction verticeempirically determined cutoff parameters.

2.1. Interaction Lagrangians

From the formalism described in Refs. [7,8,11,12], the interaction Lagrangian denthat are relevant to present study are given as follows:

LπNN = −igπNN N̄γ5�τN · �π,LρNN = gρNN N̄

(γ µ�τ · �ρµ + κρ

2mN

σµν �τ · ∂µ �ρν)N,

LπDD∗ = igπDD∗D∗µ �τ · (D̄∂µ �π − ∂µD̄ �π) + H.c.,

LρDD = igρDD

(D�τ∂µD̄ − ∂µD�τ D̄) · �ρµ,

LρD∗D∗ = igρD∗D∗[(∂µD

∗ν �τD̄∗ν −D∗ν �τ∂µD̄∗

ν

) · �ρµ

+ (D∗ν �τ · ∂ �ρν − ∂ D∗ν �τ · �ρ )

D̄∗µ
µ µ ν
+D∗µ(�τ · �ρν∂µD̄∗ν − �τ · ∂µ �ρνD̄∗

ν

)],

ho,

U(4)

actionons,

those

W. Liu et al. / Nuclear Physics A 728 (2003) 457–470 459

LDNΛc = igDNΛc

(N̄γ5ΛcD̄ +DΛ̄cγ5N

),

LD∗NΛc = gD∗NΛc

(N̄γµΛcD̄

∗µ +D∗µΛ̄cγµN),

LπΛcΣc = igπΛcΣc Λ̄cγ5 �Σc · �π + H.c.,

LρΛcΣc = gρΛcΣc Λ̄cγµ �Σc · �ρµ + H.c.,

LDNΣc = igDNΣc

(N̄γ 5�τ · �ΣcD̄ +D�τ · �̄Σcγ

5N),

LD∗NΣc = gD∗NΣc

(N̄γ µ�τ · �ΣcD̄

∗µ +D∗

µ �τ · �̄ΣcγµN

). (1)

In the above,�τ are Pauli spin matrices, and�π and �ρ denote, respectively, the pion and rmeson isospin triplet, whileD = (D+,D0) andD∗ = (D∗+,D∗0) denote, respectivelythe pseudoscalar and vector charmed meson doublets.

2.2. Coupling constants

For coupling constants, we use the following empirical values:gπNN = 13.5 [16],gρNN = 3.25, andκρ = 6.1 [17], andgπDD∗ = 5.56 [18], andgρDD = gρD∗D∗ = 2.52[12]. Other coupling constants, which are not known empirically, are obtained using Srelations [3,7,8,12], i.e.,

gD∗NΛc = −√3gρNN = −5.6,

gDNΛc = 3− 2αD√3

gπNN gπNN = 13.5,

gπΛcΣc −2αD√3gπNN , gDNΣc (1− 2αD)gDNΛc ,

gD∗NΣc = −gρNN , (2)

whereαD =D/(D+F) 0.64 [19] withD andF being the coefficients for usualD-typeandF -type couplings.

2.3. Form factors

To take into account finite sizes of hadrons, form factors are introduced at intervertices. In previous studies onJ/ψ absorption and charmed hadron scattering by hadrmonopole form factors have been used. Following the work onJ/ψ absorption bynucleons [7], the form factors atπNN andρNN vertices are taken to have the form:

F1(t) = Λ2 −m2

Λ2 − t, (3)

with t being the squared four momentum of exchanged pion or rho meson, whileat πDD∗ , ρDD, ρD∗D∗, DNΛc , D∗NΛc , DNΣc , andD∗NΣc vertices, that involveheavy virtual charm mesons or baryons, are

F2(q2)= Λ2

Λ2 + q2 , (4)

rsutoff

section

irtualerentn oractions

three

e

lefthe


with q being the three-momentum transfer in the center-of-mass frame fort andu channelsor momentum of initial or final particles in center-of-mass frame fors channel [12]. As inRefs. [16,17], we takeΛπNN = 1.3 GeV andΛρNN = 1.4 GeV. For the cutoff parametein F2(q2), they are taken to be 0.42 GeV. As discussed later in Section 3, this cparameter is needed in a similar hadronic model to reproduce the empirical crossfor pp → pK+Λ reaction at center-of-mass energy from threshold to a few GeV.

The reason we use noncovariant form factors at interaction vertices involving vcharm hadrons is to avoid introduction of many different cutoff parameters at diffinteraction vertices. This is in contrast with interaction vertices involving virtual piorho meson, where covariant form factors have been extensively used in hadronic reand their cutoff parameters are already known empirically.

3. Charmed hadron production from proton–proton collisions

In proton–proton collisions at low energies, charm production is dominated byparticle final states. Two possible reactions arepp → pD̄0Λc andpp → pD̄∗0Λc. In thefollowing, we discuss their contributions separately.

3.1. pp → pD̄0Λ+c

Diagrams for the reactionpp → pD̄0Λ+c are shown in Fig. 1. They involve th

exchange of pion ((1a)–(1c)), rho meson ((2a)–(2c)),D ((3a)–(3b)), andD∗ ((4a)–(4b)).Amplitudes for the four processes are given by

M1 = −igπNN p̄(p3)γ5p(p1)1

t −m2π

(M1a +M1b +M1c),

M2 = gρNN p̄(p3)

[γ µ + i

κρ

2mN

σαµ(p1 − p3)α

]p(p1)

×[−gµν + (p1 − p3)µ(p1 −p3)ν

m2ρ

]1

t −m2ρ

(Mν

2a +Mν2b +Mν

2c

),

M3 = igDNΛcΛ̄c(p3)γ5p(p1)1

t −m2D

(M3a +M3b),

M4 = gD∗NΛc Λ̄c(p3)γµp(p1)

[−gµν + (p1 − p3)µ(p1 − p3)ν

m2D∗

]

× 1

t −m2D∗

(Mν

4a +Mν4b

), (5)

wherep1 andp3 are, respectively, four momenta of initial and final baryons on theside of a diagram, andt = (p1 − p3)

2 is the square of baryon momentum transfer. TamplitudesMia , Mib, andMic are for the subprocessesπ0p → D̄0Λ+

c , ρ0p → D̄0Λ+c ,

D̄0p → D̄0p+, andD̄∗0p → D̄0p involving exchanged virtual mesons, and they are givenexplicitly by


Fig. 1. Charmed hadron production frompp → pD̄0Λ+c .

M1a = −gπDD∗gD∗NΛc

1

q2 −m2D∗

(k1 + k3)µ

×[gµν − (k1 − k3)

µ(k1 − k3)ν

m2D∗

]Λ̄cγνp,

M1b = gπNNgDNΛc

1

s1 −m2N

Λ̄c(mN − /k1 − /k2)p,

M1c = gπΛcΣcgDNΣc

1

u−m2Σc

Λ̄c(/k2 − /k3 −mΣc)p,

Mµ2a = igDNΛcgρDD

1

q2 −m2D

(2k3 − k1)µΛ̄cγ

5p,

f

lar and

ssal crossns

ections


Mµ2b = igρNNgDNΛc

1

s1 −m2N

Λ̄cγ5(/k1 + /k2 +mN)

(γ µ + i

κρ

2mN

σβµk1β

)p,

Mµ2c = igρΛcΣcgDNΣc

1

u−m2Σc

Λ̄cγµ(/k2 − /k3 +mΣc)γ

5p,

M3a = g2DNΛc

1

s1 −m2Λc

p̄(/k1 + /k2 −mΛc)p,

M3b = g2DNΛc

1

u−m2Λc

p̄(/k2 − /k3 −mΛc)p,

Mµ4a = igD∗NΛcgDNΛc

1

s1 −m2Λc

p̄γ 5(/k1 + /k2 +mΛc)γµp,

Mµ4b = igD∗NΛcgDNΛc

1

u−m2Λc

p̄γ µ(/k2 − /k3 +mΛc)γ5p. (6)

Here,k1 andk3 are momenta of initial and final mesons, whilek2 andk4 are momenta oinitial and final baryons in the two-body subprocesses; andq2 = (k1 − k3)

2 is the squareof meson momentum transfer.

There is no interference between amplitudes involving exchange of pseudoscavector mesons. Interferences between amplitudes involving exchange of pion andD mesonas well as those between rho meson andD∗ are unimportant due to the large madifference between light and heavy mesons. Neglecting these interferences, the totsection for the reactionpp → pD̄0Λ+

c is then given by the sum of the cross sectiofor the four processes in Fig. 1 and can be expressed in terms of off-shell cross sfor the subprocessesπ0p → D̄0Λ+

c , ρ0p → D̄0Λ+c , D̄0p → D̄0p, andD̄∗0p → D̄0p.

Following the method of Ref. [8] for the reactionJ/ψN → D(D∗)D̄(D̄∗)N , the spin-averaged differential cross section for the reactionpp → pD̄0Λ+

c can be written as

dσpp→pD̄0Λ+c

dtds1= g2

πNN

16π2sp2i

k√s1(−t)

1

(t −m2π)

2σπ0p→D̄0Λ+c(s1, t)

+ 3g2ρNN

32π2sp2i

k√s1

1

(t −m2ρ)

2

[4(1+ κρ)

2(−t − 2m2N

) − κ2ρ

(4m2N − t)2

2m2N

+ 4(1+ κρ)κρ(4m2

N − t)]σρ0p→D̄0Λ+

c(s1, t)

+ g2DNΛc

16π2sp2i

k√s1

[−t + (mN −mΛc)2] 1

(t −m2D)

2σD̄0p→D̄0p(s1, t)

+ 3g2D∗NΛc

32π2sp2i

k√s1

1

(t −m2D∗)2

[−4t + 4(mΛc −mN)

2

− 8mΛcmN + 2(m2N −m2

Λc− t)(m2

N −m2Λc

+ t)

m2D∗]

+ 2((mΛc −mN)2 + t)t

m2D∗

σD̄∗0p→D̄0p(s1, t). (7)

imental

andtum offactor of

cutoffns andlusiveng, weuction

s in

f-nstants, the

wn in

sroton–


Fig. 2. Cross section for kaon production from the reactionpp → pK+Λ with cutoff parameterΛ = 0.42 GeVin the form factors at interaction vertices involving exchange of strange mesons. Filled circles are experdata taken from Ref. [21].

In the above,pi is the center-of-mass momentum of two initial protons,t is the squaredfour-momentum transfer of exchanged meson,s is the squared center-of-mass energy,s1 andk are, respectively, the squared invariant mass and center-of-mass momenexchanged meson and the nucleon in the subprocesses. We have also included atwo to take into account contributions from interchanging two initial protons.

Since the charmed hadron production cross sections is sensitive to the value ofparameters in the form factors at interaction vertices involving virtual charmed mesobaryons, it is necessary to constraint this cutoff parameter empirically. Without exccross sections available for charmed hadron production from proton–proton scatteriresort to strange hadron production. Using the same hadronic model for kaon prodfrom the reactionpp → pK+Λ, this reaction can be described by similar diagramFig. 1 for the reactionpp → pD̄0Λ+

c with D0 andΛc replaced byK+ andΛ, respectively,in the final states. Also, the exchangedD̄0 in diagrams (3a) and (3b) as well as̄D0∗ indiagrams (4a) and (4b) are replaced byK andK∗, respectively, while intermediate ofshell charmed baryons are replaced by strange baryons. With empirical coupling cogπKK∗ = 3.25 andgρKK = 3.25, as well as others determined via SU(3) relations [20]measured cross section can be reproduced with a cutoff parameterΛ = 0.42 GeV in theform factorsF2(q2) at vertices involving virtual strange mesons and baryons, as shoFig. 2.

Assuming that the same cutoff parameterΛ = 0.42 GeV is applicable at verticeinvolving virtual charmed mesons and baryons in charmed hadron production from pproton reactions, resulting cross sections for the reactionpp → pD̄0Λc from the four
possible processes of pion (solid curve), rho (dashed curve),D (dotted curve), andD∗(dash-dotted curve) exchanges as functions of center-of-mass energy are shown in Fig. 3.

,

e fromchange

tarevy

wt thenergiesfromxcepthe on-

,

urnd they


Fig. 3. Cross sections for charmed hadron production from the reactionpp → pD̄0Λ+c due to pion (solid curve)

rho meson (dashed curve),D (dotted curve), andD∗ (dash-dotted curve).

It is seen that contributions from light meson exchange are more important than thosheavy meson exchange. Although we consider diagrams (1a) and (2a) in Fig. 1 as exof pion and rho meson, respectively, they actually involve exchange of heavyD∗ andDmesons in the subprocessπ0p → D̄0Λ+

c andρ0p → D̄0Λ+c , respectively. Our results tha

main contributions to the reactionpp → pD̄0Λ+c are due to exchange of light mesons

not inconsistent with conclusions in Ref. [14] that this reaction is dominated by heaD

meson exchange.To see the relative contributions froms, t , andu channel diagrams in Fig. 1, we sho

in Fig. 4 the partial cross sections due to diagrams (1a), (1b), and (1c). It is seen thatchannel diagram (1a) dominates charmed hadron production cross section at high ewhile thes channel diagram (1b) is most important near threshold. The contributiontheu channel diagram (1c) is much smaller than those from other two diagrams. Enear threshold, our results are thus similar to those found in Ref. [14], which uses tshell approximation for the subprocessπp → D̄0Λ+

c and does not includes andu channeldiagrams.

3.2. pp → D̄∗0pΛ+c

For charm production from proton–proton collisions withD̄∗0pΛ+c in the final state

relevant diagrams are shown in Fig. 5. As for the reactionpp → pD̄∗0Λ+c , this reaction

can proceed through pion, rho meson,D, andD∗ exchanges. Amplitudes for the foprocesses can be evaluated with the interaction Lagrangians given in Section 2, aare given by

M5 = −igπNN p̄(p3)γ5p(p1)1

t −m2π

(Mα

5a +Mα5b +Mα

5c

)εα

the


Fig. 4. Partial cross sections forpp → pD̄0Λ+c due to contributions from different channels.

M6 = gρNN p̄(p3)

[γ µ + i

κρ

2mN

σαµ(p1 − p3)α

]p(p1)

×[−gµν + (p1 − p3)µ(p1 −p3)ν

m2ρ

]1

t −m2ρ

(Mνα

6a +Mνα6b +Mνα

6c

)εα,

M7 = igDNΛcΛ̄c(p3)γ5p(p1)1

t −m2D

(Mα

7a +Mα7b

)εα,

M8 = gD∗NΛc Λ̄c(p3)γµp(p1)

×[−gµν + (p1 − p3)µ(p1 −p3)ν

m2D∗

]1

t −m2D∗

(Mνα

8a +Mνα8b

)εα, (8)

wherep1 andp3 are again, respectively, four momenta of initial and final baryons onleft side of a diagram andεα denotes the polarization vector ofD∗ meson in final state.

Expressions for individual amplitudes can be written as follows:

Mµ5a = −igπDD∗gDNΛc

1

q2 −m2D

(2k1 − k3)µΛ̄cγ5p,

Mµ5b = −igπNNgD∗NΛc

1

s1 −m2N

Λ̄cγµ(/k1 + /k2 +mN)γ

5p,

Mµ5c = igπΛcΣcgD∗NΣc

1

u−m2Σc

Λ̄cγ5(/k2 − /k3 +mΣc)γ

µp,

Mµν6a = gD∗NΛcgρD∗D∗

1

q2 −m2

[gαβ − (k1 − k3)α(k1 − k3)β

m2

]Λ̄cγ

αp

D∗ D∗

× [2kν1g

βµ − (k1 + k3)βgµν + 2kµ3 g

βν],


Fig. 5. Charmed hadron production frompp → pD̄∗0Λ+c .

Mµν6b = gρNNgD∗NΛc

1

s1 −m2N

Λ̄cγν(/k1 + /k2 +mN)

(γ µ + i

κρ

2mNσβµk1β

)p,

Mµν6c = gρΛcΣcgD∗NΣc

1

u−m2Σc

Λ̄cγµ(/k2 − /k3 +mΣc)γ

νp.

Mµ7a = igDNΛcgD∗NΛc

1

s1 −m2Λc

p̄γ µ(/k1 + /k2 +mΛc)γ5p,

Mµ7b = igDNΛcgD∗NΛc

1

u−m2Λc

p̄γ 5(/k2 − /k3 +mΛc)γµp,

Mµν8a = g2

D∗NΛc

1

s1 −m2Λc

p̄γ ν(/k1 + /k2 +mΛc)γµp,

Mµν8b = g2

D∗NΛc

1

u−m2Λc

p̄γ µ(/k2 − /k3 +mΛc)γνp. (9)

ell

have

eactionesonpion

s

hown-masscharmr [22].reshold.)


As in the case of charmed hadron production from the reactionpp → pD̄0Λ+c , total

cross section for the reactionpp → pD̄∗0Λ+c can be expressed in terms of off-sh

cross sections for the subprocessesπ0p → D̄∗0Λ+c , ρ0p → D̄∗0Λ+

c , D̄0p → D̄∗0p, andD̄∗0p → D̄∗0p. In this case, the spin averaged differential cross section is

dσpp→pD̄∗0Λ+c

dt ds1

= g2πNN

16π2sp2i

k√s1(−t)

1

(t −m2π)

2σπ0p→D̄∗0Λ+c(s1, t),

+ 3g2ρNN

32π2sp2i

k√s1

1

(t −m2ρ)

2

[4(1+ κρ)

2(−t − 2m2N

) − κ2ρ

(4m2N − t)2

2m2N

+ 4(1+ κρ)κρ(4m2

N − t)]σρ0p→D̄∗0Λ+

c(s1, t)

+ g2DNΛc

16π2sp2i

k√s1

(−t + (mN −mΛc)2) 1

(t −m2D)

2σD̄0p→D̄∗0p(s1, t)

+ 3g2D∗NΛc

32π2sp2i

k√s1

1

(t −m2D∗)2

[−4t + 4(mΛc −mN)

2 − 8mΛcmN

+ 2(m2N −m2

Λc− t)(m2

N −m2Λc

+ t)

m2D∗

+ 2((mΛc −mN)2 + t)t

m2D∗

]σD̄∗0p→D̄∗0p(s1, t). (10)

Using coupling constants and cutoff parameters introduced in Section 2, weevaluated the cross section for the reactionpp → pD̄∗0Λ+

c . In Fig. 6, we showcontributions from pion (solid curve), rho meson (dashed curve),D (dotted curve), andD∗(dash-dotted curve) exchanges as functions of center-of-mass energy. As for the rpp → pD̄0Λ+

c , light meson exchanges are more important than those from heavy mexchanges. However, the contribution from rho exchange is larger than that fromexchange, which is opposite to that in the reactionpp → D̄0Λ+

c , as a result of couplinginvolving three vector mesons, which are absent in the latter reaction.

4. Total cross section for charmed hadron production in proton–proton collisions

The total cross section for charm production from proton–proton collisions is sin Fig. 7 as a function of center-of-mass energy (solid curve). It is value at center-ofenergy of 11.5 GeV is about 1 µb and is within the uncertainty of measured inclusiveproduction cross section, which is about 2 µb as shown by solid circles with error baThe cross section decreases as energy drops and is about 1 nb at 40 MeV above thAlso shown in Fig. 7 are the cross section for the reactionspp → pD̄0Λ+

c (dashed curve
andpp → pD̄∗0Λ+
c (dotted curve), and it is seen that the former is somewhat larger thanthe latter.

n

curvesolidymeter


Fig. 6. Cross sections for charmed hadron production frompp → pD̄∗0Λ+c due to pion (solid curve), rho meso

(dashed curve),D (dotted curve), andD∗ (dash-dotted curve).

Fig. 7. Cross sections for charmed hadron production from proton–proton collisions. Dashed and dottedare forpp → pD̄0Λ+

c andpp → pD̄∗0Λ+c , respectively, while the total cross section is shown by the s

curve. The threshold energys0 refers to that of the reactionpp → pD̄0Λ+c . Experimental data are shown b

filled circles [22]. Also shown by dash-dotted curve is the total cross section obtained with cutoff para
Λ = 1.0 GeV in the form factors at interaction vertices involving virtual charmed hadrons, in contrast with othercurves which are based onΛ = 0.42 GeV.

ederac-those ofheir in-ameter,roduc-ss

adronons is

iricalproton–

n

ons.angearmedeV isaboveout at

statesmuch

r Grantalso

Korea


The cutoff parameterΛ = 0.42 GeV at interaction vertices involving virtual charmhadrons is obtained from fitting strange hadron production with similar hadronic inttion Lagrangians and form factors. Since charmed hadrons have smaller sizes thanstrange hadrons, harder form factors with larger cutoff parameters are expected at tteraction vertices. To see how the results obtained here are affected by the cutoff parwe show in Fig. 7 by dash-dotted curve the total cross section for charmed hadron ption from proton–proton reactions usingΛ = 1 GeV. It is seen that the resulting crosection is almost two order of magnitude larger than that given byΛ = 0.42 GeV and de-viates strongly from the experimental data. Within our present model for charmed hproduction, a large cutoff parameter at interaction vertices involving charmed hadrthus excluded.

5. Summary

Using a hadronic model based on SU(4) flavor-invariant Lagrangian with empmasses and coupling constants, we have studied charmed hadron production fromproton collisions through the reactionspp → pD̄0Λ+

c and pp → pD̄∗0Λ+c . These

reactions involve exchange of pion, rho meson,D, andD∗, and their cross sections cabe expressed in terms of the cross sections for the off-shell processesMp → D̄0Λ+

c

and Mp → D̄∗0Λ+c , whereM denotes one of the above exchanged off-shell mes

With cutoff parameters of form factors adjusted to fit the cross section for strhadron production in proton–proton reactions, the resulting cross section for chhadron production from proton–proton collisions at center-of-mass energy of 11.5 Gconsistent with available experimental data. The predicted cross section at 40 MeVthreshold is about 1 nb. Our results will be useful for the experiments to be carriedproposed accelerator at the German Heavy Ion Research Center [13].

It is worthy to mention that we have not considered in the present study finalinvolvingΣ+

c insteadΛ+c as the cross sections for such reactions are expected to be

smaller due to both largerΣ+c thanΛ+

c masses and smallergDNΣc andgD∗NΣc couplingconstants thangDNΛc andgD∗NΛc coupling constants.

Acknowledgements

This paper is based on work supported by the National Science Foundation undeNo. PHY-0098805 and the Welch Foundation under Grant No. A-1358. S.H.L. issupported in part by the KOSEF under Grant No. 1999-2-111-005-5 and by theResearch Foundation under Grant No. KRF-2002-015-CP0074.

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charm production from proton–proton collisions

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