On the total charm production cross section in hadronic interactions at high energies √s > 1 TeV

1. On the total charm production cross section in hadronicinteractions at high energies √s > 1 TeV Yu.F. Novoseltsev, G.M. Vereshkov Institute for Nuclear Researsh of RAS, Physics Research Institute of Rostov State University

2. We assume that the charmed particles are produced in • single diffractive dissociation • double diffractive dissociation • hard parton-parton collisions (pt > 1 GeV) • We estimate cross sections of these processes on the base of experimental data

3. 1. Single diffractive dissociation • Data on σtot( pp  cc + X) at s = 20 − 40 GeV • The assumption about the dominating contributionof single dissociation processes into the total cross section of charm production at low energies. • Additive quark model and quark statistics rules • The additional set of experimental data: SPS, TEVATRON data on σDD(pp  X) at s = 200, 546, 900 and 1800 GeV

4. Data on total cross section of charm production at s = 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: σpNcc+X (s) = CpN ln(s/so) σNcc+X(s) = ⅔ σpNcc+X(3s/2) CpN = 28.84 ± 2.10 μb, √so = 18.51 ± 0.36 GeV , 2 = 0.89 (1)

5. The fit result enables us to make an assumption about the dominating contribution of diffractive processes into the total cross section of charm production at low energies • in the region of low energies the probability of double dissociation processes is low, • the contribution of hard processes is small, because partons with small values of Bjorken's variable x (those are many) do not participate in the c-quark production.

6. At high energies we use an additional set of experimental data. The estimation of difractive production cross section is based on processing of collider data on diffractive dissociation with use of quark statistics rules. • Cross section of diffractive dissociation in pp-interactons: SPS --- √s = 200 GeV, 900 GeV (Ansorge et al., 1986) TEVATRON --- √s = 546 GeV, 1800 Gev (Abe et al., 1994) σDD(pp  X) = CDD ln(s/so) • charm production cross section is extracted from total cross section by quark statistics rules: σ( pp  cc + X) ≈ kcc× σDD(pp X), kcc ≈ 0.025 ± 0.004 uu : dd : ss : cc = 1 : 1 : (0.38 ± 0.07) : (0.06 ± 0.01) 2Ji +1 λq = ∑ Mi2 i

7. σ(pp  cc +X) at collider energies √s, GeV 200 546 900 1800 σDD, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.44 σ(pp  cc +X) = kcc× σDD ,(2) σpp  cc +X, μb 120 ± 21 197 ± 32 195 ± 32 236 ± 38 The obtained values of charm production cross section have the status of model dependent processing collider data

8. Joint fit oflow-energyand high-energy data on difractive charm production • Values of C and so in (1) and (3) coincide within the limits of statistical errors The strip corresponds to 90 % CL σ(pp  cc +X) = C*ln(s/so) C = 26.78 ± 1.44 μb √so = 18.23 ± 0.23 GeV χ2/dof = 0.98 (3)

9. 2. Double diffractive dissociation √s, GeV 200 900 σ2DD, mb 3.5± 2.2 4.0± 2.5 Ansorge et al (CERN-UA-005 Collaboration), 1986

10. 1. σ2DD(s) can not rise faster than ln s σ2DD(s) σDD(s) If 2. const + O(1/sn), n > 0, s∞ σ2DD(pp X) = C2DD ln s/so , C2DD = 584 ± 263 μb then Using the quark statistics rules gives (2DD) σ(pp cc+X) = Cpp cc ln s/so Cpp cc = 14.6 ± 7.0 μb, √so = 18.23 ± 0.33 GeV (2DD) (4) (2DD)

11. 3. Hard processes D. Acosta et al , 2003 √s = 1.96 TeV These data are fit very well (χ2/dof=0.092) by power functions dσ/dt, nb/GeV2 dσ dt 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 = ? ┴

12. to = μhard ≈ mc 2 2 (5) (6)

13. (7) 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

14. (8) The upper bound of the cross section σ pp  cc + X is obtained with the assumption hard

15. (9) μhard = 1.2 GeV The upper bound of the total charm production cross section tot σpNcc+X (s) = σDD(s) + σ2DD (s) + σhard(s)

16. 2 -- R.Vogt. NLO pQCD (2003) 3 – L.Volkova, G.Zatsepin (2001) μb μhard = 1.0 GeV μhard = 1.5 GeV “1” – present work σpNcc+X = 1210 ± 400 μb at √s = 1.96 TeV, σpNcc+X = 1590 ± 540 μb at √s = 14 TeV,