Predictions for p + Pb Collisions at √ s NN = 5 TeV: Expectations vs. Data R. Vogt (with members and friends of the JET Collaboration) Lawrence Livermore National Laboratory, Livermore, CA 94551, USA Physics Department, University of California, Davis, CA 95616, USA Int. J. Mod. Phys. E 22 (2013) 1330007 [arXiv:1301.3395 [hep-ph]], update in progress Contributions to calculations in this talk from: J. Albacete et al. (rcBK, charged hadrons), F. Arleo et al. ( J/ψ , Υ ), G. Barnafoldi et al. (charged hadrons, for- ward/backward asymmetry), K. J. Eskola ( R p Pb , dijets), E. G. Ferreiro ( J/ψ , ψ ′ ) H. Fujii et al. ( J/ψ , Υ ) B. Kopeliovich ( R p Pb ), J.-P. Lansberg et al. ( J/ψ , Υ ), Z. Lin ( AMPT ), A. Rezaeian (b-CGC charged hadrons), V. Topor Pop et al. ( HIJINGBB ), R. Venugopalan et al. (IP-Sat), I. Vitev et al. (jets), RV ( J/ψ , Υ ), X.-N. Wang et al (charged hadrons), B.-W. Zhang et al (gauge bosons),
Outline We stick to results where data are already available Model descriptions are combined with available data • Charged particles – dN ch /dη – dN ch /dp T – R p Pb ( p T ) – Flow • Jets – Dijets – Single inclusive jets • J/ψ and Υ – R p Pb ( y ) – R F/B ( y ) , R F/B ( p T ) • Z bosons
Model Descriptions
Saturation
Saturation: rcBK (A. Rezaeian, J. Albacete et al ) Gluon jet production in pA described by k T -factorization � � � � � dσ = 2 α s 1 d 2 � x 1 ; � p T − � k T φ G φ G k T x 2 ; � k T p A p 2 dy d 2 p T C F T Here x 1 , 2 = ( p T / √ s ) e ± y and unintegrated gluon density, φ G A ( x i ; � k T ) , is related to color dipole forward scattering amplitude � � � 1 C F r T e i� r T ∇ 2 x i ; � d 2 � k T · � φ G b T d 2 � k T = T N A ( x i ; r T ; b T ) A (2 π ) 3 α s N A ( x i ; r T ; b T ) = 2 N F ( x i ; r T ; b T ) − N 2 F ( x i ; r T ; b T ) In k T -factorized approach, both projectile and target have to be at small x so that CGC formalism is applicable to both
rcBK Hybrid Approach Hybrid models that treat the projectile (forward) with DGLAP collinear factor- ization and target with CGC methods Hadron cross section is proportional to f g ( x 1 , µ 2 F ) N A ( x 2 , p T /z ) + f q ( x 1 , µ 2 F ) N F ( x 2 , p T /z ) modulo fragmentation functions � � 1 � dN pA → hX K dz F ) N A ( x 2 , p T x 1 f g ( x 1 , µ 2 = z ) D h/g ( z, µ Fr ) dηd 2 p T (2 π ) 2 z 2 x F � F ) N F ( x 2 , p T + Σ q x 1 f q ( x 1 , µ 2 z ) D h/q ( z, µ Fr ) � 1 � � 1 α in z 4 dz dξ s d 2 k T k 2 + T N F ( k T , x 2 ) p 4 2 π 2 z 2 ξ x F k 2 T <µ 2 x 1 T F � q,g w i/j ( ξ ) P i/j ( ξ ) x 1 f j ( x 1 × Σ i,j = q, ¯ ξ , µ F ) D h/i ( z, µ Fr ) . K factor introduced to incorporate higher order corrections Inelastic term is multiplied by α in s , different from running α s in rcBK equation – in hybrid formulation, strong coupling in dilute regime (proton) can differ from that in the dense system (nucleus) but appropriate scale of α in s cannot be determined without a NNLO calculation Factorization, renormalization and fragmentation scales assumed to be equal, µ F = µ R = µ Fr with µ F = 2 p T , p T and p T / 2 to form uncertainty range for given N and α in s
rcBK Equation N A ( F ) is 2-D Fourier transform of imaginary part of dipole scattering amplitude in the fundamental ( F ) or adjoint ( A ) representation N A ( F ) N A ( F ) calculated using JIMWLK which simplifies to BK in the large N c limit Running coupling corrections to LL kernel result in rcBK equation � ∂ N A ( F ) ( r, x ) � d 2 � r 1 K run ( � = r,� r 1 ,� r 2 ) N A ( F ) ( r 1 , x ) + N A ( F ) ( r 2 , x ) ∂ ln( x 0 /x ) � − N A ( F ) ( r, x ) − N A ( F ) ( r 1 , x ) N A ( F ) ( r 2 , x ) � �� � � γ � 1 r 2 Q 2 0 s N ( r, Y =0) = 1 − exp − ln Λ r + e 4 Last equation is initial condition with γ fixed from DIS data, γ = 1 is MV initial condition, γ ∼ 1 . 1 in fits 0 p ∼ 0 . 2 GeV 2 in MV initial condition, smaller for other values of γ Q 2 Q 2 0 A ∼ NQ 2 0 p with 3 < N < 7 in Rezaeian’s calculations, Albacete et al let nuclear scale be proportional to the number of participants at a given b to account for geometrical fluctuations in Monte Carlo simulations
Saturation: IP-Sat (Tribedy and Venugopalan) Here one starts as before with k T -factorization � � dN pA g ( b T ) d 2 k T dφ p ( x 1 , k T | s T ) dφ A ( x 2 , p T − k T | s T − b T ) = 4 α s 1 d 2 s T p 2 dy d 2 p T (2 π ) 5 d 2 s T d 2 s T πC F T Unintegrated gluon density is expressed in terms of the dipole cross section as � � 2 � ∞ dσ p,A dφ p,A ( x, k T | s T ) = k 2 T N c 1 − 1 d 2 r T e i � dip k T . � r T ( r T , x, s T ) d 2 s T 4 α s 2 d 2 s T 0 Dipole cross section is a refinement of Golec-Biernat–Wusthoff that gives the right perturbative limit for r T → 0 , equivalent to effective theory of CGC to LL � � �� dσ p − π 2 dip r 2 T α s ( µ 2 ) xg ( x, µ 2 ) T p ( b T ) 1 − exp ( r T , x, b T ) = 2 d 2 b T 2 N c µ 2 is related to dipole radius, r T , by µ 2 = 4 T + µ 2 r 2 0 The gluon density g ( x, µ 2 ) is LO DGLAP result without quarks � � T p ( b T ) is the gluon density profile function, T p ( b T ) = (2 πB G ) − 1 exp − ( b 2 T / 2 B G ) where � b 2 � = 2 B G , the average squared gluonic radius of the proton, obtained from HERA data
Event-by-Event Calculations
HIJING2 . 0 (X.-N. Wang et al ) Based on two-component model of hadron production, soft (string excitations with effective cross section σ soft ) and hard (perturbative QCD) components separated by cutoff momentum p 0 LO pQCD calculation with K factor to absorb higher-order corrections � dσ jet � T , b ) dσ ab → cd pA dy 2 d 2 b T A ( b ) x 1 f a/p ( x 1 , p 2 T ) x 2 f a/A ( x 2 , p 2 = K dy 1 d 2 p T dt a,b,c Effective 2 → 2 scattering, x 1 , 2 = p T ( e ± y 1 + e ± y 2 ) / √ s Default HIJING collisions decomposed into independent and sequential NN collisions – in each NN interaction, hard collisions simulated first, followed by soft Since hard interactions occur over shorter time scale, HIJING2 . 0 also uses decoherent hard scattering (DHC) where all hard collisions are simulated first, then soft, so available energy unrestricted by soft interactions Energy-dependent k T broadening in HIJING T � = [0 . 14log( √ s/ GeV) − 0 . 43] GeV 2 /c 2 � k 2
Shadowing in HIJING Shadowing treated as scale independent Versions before HIJING2 . 0 did not differentiate between quark and gluon shadowing f a/A ( x, µ 2 F , b ) = S a/A ( x, µ 2 F , b ) f a/A ( x, µ 2 F ) f a/A ( x ) S a/A ( x ) ≡ Af a/N ( x ) = 1 + 1 . 19 log 1 / 6 A [ x 3 − 1 . 2 x 2 + 0 . 21 x ] � � √ x 10 . 8 − s a ( A 1 / 3 − 1) n e − x 2 / 0 . 01 1 − log( A + 1) � � 1 − b 2 5 s a ( b ) = s a R 2 3 A In HIJING2 . 0 the ( A 1 / 3 − 1) factor is nonlinear ( n = 0 . 6 ) but n = 1 in earlier versions Previously s a = s g = s q = 0 . 1 In HIJING2 . 0 s g � = s q : s q = 0 . 1 and s g ∼ 0 . 22 − 0 . 23 to match LHC data The b dependence of s a gives some impact parameter dependence to S a/A
HIJINGBB (V. Topor Pop et al ) Differs from standard HIJING in treatment of fragmentation HIJING uses string fragmentation with constant vacuum value of κ 0 = 1 . 0 GeV/fm for string tension HIJINGBB allows for multiple overlapping flux tubes leading to strong longitudinal color field (SCF) effects SCF effects modeled by varying κ and momentum cutoff with √ s and A Fragmentation also modified, including baryon loops to explain baryon to meson anomaly and increase strange baryon production
AMPT : A Multi-Phase Transport (Z. Lin) AMPT is a Monte Carlo transport model for heavy ion collisions, montage of other codes • Heavy Ion Jet Interaction Generator ( HIJING ) for generating the initial condi- tions • Zhang’s Parton Cascade ( ZPC ) for modeling partonic scatterings • A Relativistic Transport ( ART ) model for treating hadronic scatterings AMPT − def treats the initial condition as strings and minijets and using Lund string fragmentation AMPT − SM treats the initial condition as partons and uses a simple coalescence model to describe hadronization
Perturbative QCD Calculations
Leading Order Calculations (I. Vitev et al ) LO single inclusive hadron production cross section � dx 1 � dx 2 � = K α 2 dσ s d 2 k T 1 f a/N ( x 1 , k 2 d 2 k T 2 f b/N ( x 2 , k 2 T 1 ) T 2 ) dyd 2 p T s x 1 x 2 a,b,c � dz c s, ˆ s + ˆ × D h/c ( z c ) H ab → c (ˆ t, ˆ u ) δ (ˆ t + ˆ u ) z 2 c Gaussian form of k T dependence in parton densities assumed 1 T � e − k 2 T 1 / � k 2 T � f a/N ( x 1 , k 2 T 1 ) = f a/N ( x 1 ) π � k 2 In pp collisions, � k 2 T � pp = 1 . 8 GeV 2 /c 2 Broadening increased in cold matter, � k 2 T � pA = � k 2 T � pp + � 2 µ 2 L/λ q,g � ζ Cold matter energy loss due to medium-induced gluon Bremsstrahlung, imple- mented as a shift in momentum fraction, f i/p ( x ) − → f i/p ( x/ (1 − ǫ i, eff )) where ǫ ∝ Σ i ∆ E i /E with the sum over all medium-induced gluons Dynamical shadowing shifts nuclear parton momentum fraction so that i ( A 1 / 3 − 1)) → f i/p (( x/ − ˆ t )(1 + C i ζ 2 f i/p ( x ) − Proton and neutron number (isospin) accounted for
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