Diffractive heavy quark production in AA collisions at

Diffractive heavy quark production in AA collisions at the LHC at NLO* Maria Beatriz Gay Ducati GFPAE – IF – UFRGS beatriz. gay@ufrgs. br www. if. ufrgs. br/gfpae * Work with M. M. T. Machado and M. V. T. Machado First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 1

Outlook Motivation Diffractive Physics Hadroproduction of heavy quarks at LO Hadroproduction of heavy quarks at NLO Coherent heavy quark production Pomeron Structure Function Multiple Pomeron Scattering Results Conclusions 2 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

Motivation Heavy quarks will be produced in large quantities at LHC Very important for physics study and for understanding background processes Heavy flavoured hadrons may produce high momentum leptons Potential background to new physics signal background Estimate the inclusive, single and Double Pomeron Exchange (DPE) in heavy ion collisions Coherent and incoherent (single diffraction) production of heavy quarks in AA collisions Coherent DPE production of heavy quarks in AA collisions 3 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

Introduction 1 M. B. Gay Ducati, M. M. M, M. V. T. Machado, PRD 75, 114013 (2007) 2 M. B. Gay Ducati, M. M. M, M. V. T. Machado, PRD 81, 054034 (2010) Diffractive processes caractherized by a rapidity gap Pomeron and its reaction mechanisms is not completely known Regge Theory Pomerons with substructure DPDFs It does not describe hadron collider data Application of multiple Pomeron scattering suppress the diffractive cross section 1, 2 Gap Survival Probability (GSP) to AA collisions ? Studies Diffractive structure function Gap Survival Probability (GSP) First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 4

4 M. Heyssler, Z. Phys. C 73. (1997) 297. Z. Kopeliovich et al, Phys. Rev. Lett. 85, 507 (2000) 5 B. Diffractive events Absence of hadronic energy in angular regions Φ of the final state Rapidity gaps Hard diffractive factorization 4 Single diffraction DPE exchange Introduction of the appropriate absorptive effects which cause the suppresion of any LRG process 5 and nuclear effects as well First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 5

6 M. L. Mangano et al, Nucl. Phys. B 373, 295 (1992) Heavy quark hadroproduction o Focus on the following single diffractive processes o Diffractive ratios as a function of energy center-mass ECM o Diagrams contributing to the lowest order cross section 6 6 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

6 M. L. Mangano, P. Nason, G. Ridolfi Nucl. Phys. B 373 (1992) 295 Total cross section LO 6 x 1, 2 are the momentum fraction are the parton distributions inner the hadron i=1 and j=2 Partonical cross section factorization (renormalization) scale 7 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

6 M. L. Mangano, P. Nason, G. Ridolfi Nucl. Phys. B 373 (1992) 295 NLO Production 6 Running of the coupling constant n 1 f = 3 (4) charm (bottom) 8 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

8 NLO functions 8 a 0 0. 108068 a 4 0. 0438768 a 1 -0. 114997 a 5 -0. 0760996 a 2 0. 0428630 a 6 -0. 165878 a 3 a 7 -0. 158246 0. 131429 P. Nason, S. Dawson, R. K. Ellis Nucl. Phys. B 303 (1988) 607 Auxiliary functions 9 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

H 1 Coll. A. Aktas et al, Eur. J. Phys. J. C 48 (2006) 715 V. A. Khoze, A. D. Martin, M. G. Ryskin, Eur. Phys. J. C 18, 167 (2000) 9 10 Diffractive cross section Pomeron flux factor Pomeron Structure Function (H 1) 9 KKMR model <|S|2> = 0. 06 at LHC single diffractive events 10 Parametrization of the pomeron flux factor and structure function H 1 Collaboration 10 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

Gap Survival Probability (GSP) • Currently a subject of intense theoretical and experimental interest • GAP – region of angular phase space devoid of particles Large Rapidity Gap • Survival probability – fulfilling of the gap by hadrons produced in interactions of remanescent particles • A(s, b) is the amplitude (in the parameter space) of the particular process of interest at center-of-mass energy • PS(s, b) is the probability that no inelastic interaction occurs between scattered hadrons First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

KMR - GSP (*) Khoze-Martin-Ryskin Eur. Phys. J. C. 26 229 (2002) • The survival probability of the rapidity gaps (associated with the Pomeron, represented by the double vertical line) * single diffraction (SD) • Calculated * central diffraction (CD) * double diffraction (DD) • FPS or cal denotes “forward photon spectrometer” or “calorimeter”, and corresponds to the detection of isolated protons, or to events where the leading baryon is either a proton or a N* (symbolically, two lines emerging from the vertex) First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

KMR model • t dependence of elastic pp differential cross section in the form exp (Bt) • pion-loop insertions in the Pomeron trajectory • non-exponential form of the proton-Pomeron vertex (t) • absorptive corrections, associated with eikonalization, which lead to a dip in dσ/dt at |t| ~ 1 Ge. V 2, whose position moves to smaller |t| as the collider energy increases • (a) Pomeron exchange contribution; • (b-e) are unitarity corrections to the pp elastic amplitude. • (f) is a two pion-loop insertion in the Pomeron trajectory First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France (f)

KMR model • GSP KMR values • GSP considering multiple channels First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

GLM - GSP (*) Gotsman-Levin-Maor PLB 438 229 (1998) • Suppression due to secondary interactions by additional spectators hadrons a • Survival probability as a function of ν(s) = Ω (s, b = 0) (Ω is the opacity or optic density of interaction of incident hadrons and a, where a is the ratio of the radius in soft and hard interactions) a = Rs / Rh First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

GLM model • Eikonal model originally conceived so as to explain the exceptionally mild energy dependence of soft diffractive cross sections. • Considers that the s-channel unitarization enforced by the eikonal model operates on a diffractive amplitude in a different way than it does on the elastic amplitude • We consider the single-channel eikonal approach • Case where the soft input is obtained directly from the measured values of tot, el and hard radius RH <|S|>2 Tevatron LHC GLM 0. 126 0. 081 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

11 N. 12 M. Agababyan et al Phys. Atom. Nucl. 62, 1572 (1999) K. Tuchin, ar. Xiv: 0812. 1519 v 2 [hep-ph] (2009) Nuclear single diffractive Inclusive case 11 APb = 208 (5. 5 Te. V) Diffractive case Coherent process Incoherent process Pomeron emmited by the nucleus Pomeron emmited by a nucleon inner the nucleus 12 17 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

Heavy quarks production at the LHC Heavy quarks cross sections in NLO to pp collisions GSP value decreases the diffractive ratio (<|S|2> = 0. 06) Inclusive nuclear cross section at NLO difrativo A Pb. Pb = 208 (5. 5 Te. V); 40 (6. 3) Te. V 18 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

13 M. Gay Ducati, M. M. M, M. V. T. Machado, PRD. 81, 054034 (2010) 14 B. Kopeliovich et al, 0702106 [ar. Xiv: hep-ph] (2007) Diffractive cross sections @ LHC Inclusive cross section Diffractive cross sections Proton-Nucleus collision Similar results that 14 Nucleus-Nucleus collision Predictions to cross sections possible to be verified at the LHC 13 Very small diffractive ratio 19 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

p. A cross sections @ LHC Suppression factor σp. A ~ 0. 8 mb 20 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

13 M. Gay Ducati, M. M. M, M. V. T. Machado, PRD. 81, 054034 (2010) Diffractive cross sections @ LHC 13 No values to <|S|2> for single diffractive events in AA collisions Estimations to central Higgs production <|S|2> ~ 8 x 10 -7 Values of diffractive cross sections possible to be verified experimentally 21 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

15 A. Bialas and W. Szeremeta, Phys. Lett. B 296, 191 (1992) Bialas-Landshoff approach Double Pomeron Exchange nucleon form-factor 15 Differential phase-space factor mass of produced quarks First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 22

Bialas-Landshoff approach Sudakov parametrization for momenta two-dimensional four-vectors describing the transverse component of the momenta for the incoming (outgoing) protons momentum for the produced quark (antiquark) momentum for one of exchanged gluons 23 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

14 A. Bialas and W. Szeremeta, Phys. Lett. B 296, 191 (1992) Bialas-Landshoff approach Square of the invariant matrix element averaged over initial spins and summed over final spins 14 effect of the momentum transfer dependence of the non-perturbative gluon propagator 24 First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France

10 V. A. Khoze, A. D. Martin, M. G. Ryskin, Eur. Phys. J. C 18, 167 (2000) DPE results pp collisions at the LHC (14 Te. V) Ingelman-Schlein Bialas-Landshoff 10 Ingelman-Schlein > Bialas-Landshoff First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 25

Conclusions • Theoretical predictions for single and DPE heavy quarks production at LHC energies in pp, p. A and AA collisions • Diffractive ratio is computed using hard diffractive factorization and absorptive corrections (NLO) • There are no predictions to <|S|2> in p. A and AA collisions • Diffractive cross sections for AA collisions possible to be verified • Diffractive channel dominates over exclusive photoproduction channel in proton-proton case • Calculation of GSP values to AA collisions is highly important First Rete. Quarkonii Workshop, 25 -28 October, 2010, Nantes, France 26