11

On the total charm On the total charm production cross section in production cross section in

hadronichadronicinteractions at high interactions at high

energies energies √s > 1 TeV √s > 1 TeV

Yu.F. NovoseltsevYu.F. Novoseltsev, , G.M. VereshkovG.M. Vereshkov

Institute for Nuclear Researsh of RAS,Physics Research Institute of Rostov State University

22

We assume that the charmed We assume that the charmed particles are produced inparticles are produced in

single single diffractive dissociationdiffractive dissociation double double diffractive dissociatiodiffractive dissociationn hard parton-parton collisions (phard parton-parton collisions (pt t > 1 GeV)> 1 GeV)

We estimate cross sections of these We estimate cross sections of these processesprocesses

on the base of experimental dataon the base of experimental data

33

1. Single 1. Single diffractive diffractive dissociationdissociation

Data on Data on σσtottot( pp ( pp cc + X cc + X)) at at s = 20 − 40 GeV s = 20 − 40 GeV

The assumption about the dominating The assumption about the dominating

contributioncontribution of of

single single dissociationdissociation processes into the total cross processes into the total cross section of charm production at low energies.section of charm production at low energies.

Additive Additive quark model and quark model and quark statistics rulesquark statistics rules The additional set of experimental data:The additional set of experimental data:

SPS, SPS, TEVATRON data on TEVATRON data on σσDDDD(pp (pp X) X)

at at s = 200, 546, 900 and 1800 GeVs = 200, 546, 900 and 1800 GeV

44

Data on total cross section of charm Data on total cross section of charm production production

at at s = 20 − 40 GeVs = 20 − 40 GeV

First of all, we clear up the opportunities of AQM and

logarithmic dependence for cross section in the description of data on charm production in pN and N interactions at low

energies:

σpNcc+X (s) = CpN ln(s/so)

σNcc+X(s) = ⅔ σpNcc+X(3s/2)

CpN = 28.84 ± 2.10 μb, √so = 18.51 ± 0.36 GeV , 2 = 0.89 (1)

55

The fit result enables us to make an assumption The fit result enables us to make an assumption about about

the dominating contribution of diffractive the dominating contribution of diffractive processes into processes into

the total cross section of charm production at low the total cross section of charm production at low energiesenergies

in the region of low energies the probability of double in the region of low energies the probability of double

dissociation processes is low,dissociation processes is low, the contribution of hard processes is small, because the contribution of hard processes is small, because

partons with small values of Bjorken's variable x (those partons with small values of Bjorken's variable x (those

are many) do not participate in the c-quark production.are many) do not participate in the c-quark production.

66

At high energies we use an additional set of experimental data. At high energies we use an additional set of experimental data. The estimation of difractive production cross section is based on The estimation of difractive production cross section is based on

processing of collider data on diffractive dissociation with use of processing of collider data on diffractive dissociation with use of quark statistics rules.quark statistics rules.

Cross section of diffractive dissociation in pp-interactons:Cross section of diffractive dissociation in pp-interactons: SPS --- SPS --- √s = 200 GeV, 900 GeV (Ansorge et al., 1986)√s = 200 GeV, 900 GeV (Ansorge et al., 1986) TEVATRON --- √s = 546 GeV, 1800 Gev (Abe et al., 1994)TEVATRON --- √s = 546 GeV, 1800 Gev (Abe et al., 1994)

σσDDDD(pp (pp X) = C X) = CDDDD ln(s/s ln(s/soo))

charm production cross section is extracted fromcharm production cross section is extracted from total cross section by quark statistics rules:total cross section by quark statistics rules:

σσ( pp ( pp cc + X) ≈ k cc + X) ≈ kcccc× × σσDDDD(pp (pp X), k X), kcccc ≈ 0.025 ± 0.004 ≈ 0.025 ± 0.004 uu : dd : ss : cc = 1 : 1 : (0.38 ± 0.07) : (0.06 ± 0.01)uu : dd : ss : cc = 1 : 1 : (0.38 ± 0.07) : (0.06 ± 0.01)

λλqq = ∑ = ∑2Ji +1

Mi2

i

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σσ(pp (pp cc +X) at collider energies cc +X) at collider energies

√√s, GeV 200 546 900 1800s, GeV 200 546 900 1800

σσDDDD, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± , mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.440.44

σσ(pp (pp cc +X) cc +X) = k= kcccc × × σσDD DD ,, (2)(2)

σσpp pp cc +X cc +X, , μμb 120 ± 21 197 ± 32 195 ± 32 236 ± 38b 120 ± 21 197 ± 32 195 ± 32 236 ± 38

The obtained values of charm production cross section have the statusof model dependent processing collider data

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Joint fit ofJoint fit of low-energylow-energy and high-energy data and high-energy data on difractive charm productionon difractive charm production

σσ(pp (pp cc +X) = C*ln(s/s cc +X) = C*ln(s/soo))

C = 26.78 ± 1.44 μb√so = 18.23 ± 0.23 GeVχ2/dof = 0.98

(3)

Values of C and sValues of C and soo in in (1) and (3) coincide (1) and (3) coincide within the limits of within the limits of statistical errorsstatistical errors

The strip correspondsThe strip correspondsto 90 % CLto 90 % CL

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2. 2. Double diffractive Double diffractive dissociationdissociation

√√s, GeV s, GeV 200 200 900 900

σσ2DD2DD, mb , mb 3.53.5 ± ± 2.22.2 4.0 4.0 ±± 2.5 2.5

Ansorge et al (CERN-UA-005 Collaboration), 1986

1010

σσ2DD2DD(s)(s)

σσDDDD(s)(s)

const + O(1/sn), n > 0, s ∞

1. σσ2DD2DD(s)(s) can not rise faster than ln s

2.

σσ2DD2DD(pp X) = C(pp X) = C2DD 2DD ln s/sln s/so o , C, C2DD 2DD = 584 = 584 ± 263 ± 263 μμb b

If

then

Using the quark statistics rules gives

σ(pp cc+X) = Cpp cc ln s/so

Cpp cc = 14.6 ± 7.0 μb, √so = 18.23 ± 0.33 GeV

(2DD)(2DD)

(2DD)

(4)

1111

3. Hard processes3. Hard processes

These data are fit very well

(χ2/dof=0.092) by power functions

dσdt

ADx

(t/μ2 + 1)n, t = ( p )2=

The parameters μ = 2.451 ± 0.143 GeV and n = 3.275 ± 0.031

are the same to all channels

p ≥ μhard = ?

┴

┴

D. Acosta et al , 2003 √s = 1.96 TeV

dσ/d

t, n

b/G

eV2

1212

tto o = = μμhard hard ≈ m≈ mcc22

(5)

(6)

22

1313

A = 0.921 ± 0.106, 1/μ2 = 1.346 ± 0.115 mb,K = 0.081 ± 0.005,Λ = 5.161 ± 1.361 GeV

χ2/dof = 0.275

(7)

1414

The upper bound of the cross section σσ pp pp cc + X cc + X is obtained with the assumption

(8)

hard

1515

(9)

σpNcc+X (s) = σDD(s) + σ2DD (s) + σhard (s)tot

μhard = 1.2 GeV

The upper bound of the total charm production cross section

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“1” – present workσpNcc+X = 1210 ± 400 μb at √s = 1.96 TeV,

σpNcc+X = 1590 ± 540 μb at √s = 14 TeV,

2 -- R.Vogt. NLO pQCD (2003)3 – L.Volkova, G.Zatsepin (2001)

μhard = 1.0 GeV

μhard = 1.5 GeV

μb