1. 1 On the total charm production cross section in hadronic interactions 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. 2 We assume that the charmed particles are produced in single diffractive dissociation single diffractive dissociation double diffractive dissociation double diffractive dissociation hard parton-parton collisions (p t > 1 GeV) hard parton-parton collisions (p t > 1 GeV) We estimate cross sections of these processes We estimate cross sections of these processes on the base of experimental data on the base of experimental data

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

4. 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: σ pN  cc+X (s) = C pN ln(s/s o ) σ  N  cc+X (s) = ⅔ σ pN  cc+X (3s/2) C pN = 28.84 ± 2.10 μb, √s o = 18.51 ± 0.36 GeV,  2 = 0.89 (1)

5. 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 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.

6. 6 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 processing of collider data on diffractive dissociation with use of The estimation of difractive production cross section is based on 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 --- √s = 200 GeV, 900 GeV (Ansorge et al., 1986) SPS --- √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) σ DD (pp  X) = C DD ln(s/s o ) σ DD (pp  X) = C DD ln(s/s o ) charm production cross section is extracted from charm production cross section is extracted from total cross section by quark statistics rules: total cross section by quark statistics rules: σ( pp  cc + X) ≈ k cc × σ DD (pp  X), k cc ≈ 0.025 ± 0.004 σ( pp  cc + X) ≈ k cc × σ DD (pp  X), k cc ≈ 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) λ q = ∑ 2J i +1 Mi2Mi2 i

7. 7 σ (pp  cc +X) at collider energies √s, GeV 200 546 900 1800 √s, GeV 200 546 900 1800 σ DD, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.44 σ DD, mb 4.8 ± 0.5 7.89 ± 0.33 7.8 ± 0.5 9.46 ± 0.44 σ (pp  cc +X) = k cc × σ DD, (2) σ (pp  cc +X) = k cc × σ DD, (2) σ pp  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. 8 Joint fit of low-energy and high-energy data on difractive charm production σ(pp  cc +X) = C*ln(s/s o ) C = 26.78 ± 1.44 μb √s o = 18.23 ± 0.23 GeV χ 2 /dof = 0.98 (3) Values of C and s o in (1) and (3) coincide within the limits of statistical errors Values of C and s o in (1) and (3) coincide within the limits of statistical errors The strip corresponds to 90 % CL

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

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

11. 11 3. Hard processes These data are fit very well (χ 2 /dof=0.092) by power functions dσ dt A Dx (t/μ 2 + 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 ≥ μ hard = ? ┴ ┴ D. Acosta et al, 2003 √s = 1.96 TeV dσ/dt, nb/GeV 2

12. 12 t o = μ hard ≈ m c t o = μ hard ≈ m c 2 (5) (6) 2

13. 13 A = 0.921 ± 0.106, 1/μ 2 = 1.346 ± 0.115 mb, K = 0.081 ± 0.005, Λ = 5.161 ± 1.361 GeV χ 2 /dof = 0.275 (7)

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

15. 15 (9) σ pN  cc+X (s) = σ DD (s) + σ 2DD (s) + σ hard (s) tot μ hard = 1.2 GeV The upper bound of the total charm production cross section

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