Inclusive hadron distribution in pp collision from saturation
Inclusive hadron distribution in p+p collision from saturation model of HERA DIS Prithwish Tribedy Variable Energy Cyclotron Centre, Kolkata Based on work in collaboration with Raju Venugopalan (BNL, NY) ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Outline – Saturation Models of the proton HERA DIS – Inclusive Gluon Distribution – Scaling of kinematic variables – Multiplicity distribution from ab initio CGC/Glasma approach ICPAQGP ' 2010, Goa, India, December 7 th, 2010
DIS Models of HERA DIS at HERA Probes hadron structure in the Regge-Gribov limit Rapid rise of gluon distribution xg(x, Q 2) high energy hadrons wave function Maximally occupied(~1/αS ) with wee gluons of k QS QS Dynamically generated semi-hard scale “Saturation Scale” Ref : F. Gelis et al, ar. Xiv: 1002. 0333 v 1 [hep-ph] ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Dipole Models : Good fits to inclusive, diffractive & exclusive HERA data Dipole cross section : is related to un-integrated gluon distribution (UNGDF) inside proton as : We use different saturation models IP-Sat , b-CGC and NLO-BK to extract UNGDF Kowalski et al. , hep-ph/0606272 ; Watt, Kowalski, ar. Xiv: 0712. 2670 ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Impact parameter dependent dipole models b-CGC Model IP-Sat Model xg(x, μ 2 ) evolved using LO DGLAP Impact Parameter dependence is introduced through proton profile function : Impact Parameter dependence is introduced through the functional form: ~ 4 Ge. V -2 R. M. S. gluonic radius of proton BG , μ 0 & xg(x, μ 0) → from fit to HERA data Proton profile has no explicit energy dependence A, B, BCGC , λ , γs → from fit to HERA data Proton shape has explicit energy dependence Kowalski et al. , hep-ph/0606272 ; Watt, Kowalski, ar. Xiv: 0712. 2670 ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Tribedy, Venugopalan ar. Xiv: 1011. 1895 Saturation scales Such that Dipole amplitude satisfies NLO-BK Model running coupling NLO-BK Kernel Initial condition Parameters σp , γ, Qso 2 are fixed from HERA data. Albacete, Kovchegov, Phys. Rev. D 75, 125021 (2007). Mc. Lerran-Venugopalan Model Step function proton profile. ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Inclusive gluon distribution p+p collision overlap of two wave functions k. T factorization to compute gluon dist. at a given impact parameter: Blaizot, Gelis, Venugopalan hep-ph/0402257 For x >10 -2 Phenomenological extrapolation of UNGDF. Regulation of Infrared Divergence. β = 4 (QCD) λ 0 = 0 -0. 2 Same mass term Pseudo-rapidity dist. Earlier treatment : Levin & Rezaeian ar. Xiv: 1005. 0631 ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Results : Inclusive Hadron Production and comparison to Data Gribov Diffusion IP-Sat & NLO-BK b 0 ~ 2 brms , C ~ 0. 2 Ge. V-1 b-CGC b 0 ~ 2 brms , C ~ 0. πbmax 2 ~ σInel cross section contributing to multiplicity (specially high energy ) 10 Te. V 14 Te. V Tribedy, Venugopalan ar. Xiv: 1011. 1895 Band mass term & parameters of HERA ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Tribedy, Venugopalan ar. Xiv: 1011. 1895 Fragmentation : NLO-BK → b dependence + Gribov diffusion → input by hand ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Saturation and scaling Kinematic variables scales with functions of QS(x, b) d. N/dη : ~ QS 2/αS(QS 2) p. T ~ A+ B×QS p. T → p. T /QS Energy dependence of QS Scaling of p. T distribution Mc. Lerran, M. Praszalowicz , 1006. 4293 ; Tribedy, Venugopalan, 1011. 1895 ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Multiplicity distribution from CGC/Glasma approach Multiplicity distribution: Derived to be the negative binomial distribution Gelis, Lappi, Mc. Lerran k = 1 : Bose-Einstein k = ∞ : Poisson Computed numerically to be O(1) Lappi, Srednyak, Venugopalan Avg. inclusive gluon multiplicity QS 2 S ~ No of flux tubes (interacting Hotspots) = Tribedy, Venugopalan 1011. 1895 ICPAQGP ' 2010, Goa, India, December 7 th, 2010
Thick flux tube p. B p. A Thin flux tube (~ 1/ QS 2) Multiplicity fluctuation due to impact parameter Eikonal approach : Extra parameter Our approach : ~ Inelastic collision probability b Tribedy, Venugopalan 1011. 1895
Multiplicity distribution from CGC/Glasma approach Dominant contribution Intrinsic fluctuations of gluon production from multiple glasma flux High multiplicity events high occupation numbers (1/αS). in the proton wave functions for k. T ≤ QS Tribedy, Venugopalan 1011. 1895
Summary - Impact parameter dependent wave functions extracted from HERA data in IP-Sat , b-CGC & NLO-BK models. - Inclusive p. T and rapidity distribution in k. T –factorization approach gives reasonable agreement with LHC data; multiple scattering effects can be included in future. - Scaling of different kinematic variables have been studied. - n-particle multiplicity distribution has been calculated in CGC approach and give good fit LHC data. - Approach can be used to study semi-hard final states at LHC.
Backup slides
Energy dependence of average d. N/d and ‹p. T›
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