QCD and Rescattering in Nuclear argets Lecture 5 Jianwei Qiu Iowa State University he 1 st Annual Hampton University Graduate Studies Program (HUGS 006) June 5-3, 006 Jefferson Lab, Newport News, Virginia 1
Incoherent Multiple Scattering Incoherent/independent rescattering Medium induced energy loss Jet quenching Important role of p(d)+a collision Calculation of Cronin effect Calculable transverse momentum broadening Summary and outlook
Incoherent/independent multiple scattering Weak quantum interference between scattering centers σ Jet Jet Modify jet spectrum without changing the total rate Nuclear dependence from the scattering centers density number momentum distribution and cut-off (new scale) etc 3
Parton level multiple scattering Classical multiple scattering cross section level: P in k P out Kinematics fix only P 1 + P P 1 P either P 1 or P can be ~ zero dσ σ ( p, p ) σ ( p, p ) dpdp δ( p + p + p p ) Double single single in 1 out 1 1 in out Parton level multiple scattering (incoherent/independent) In massless pqcd, above parton distribution at x=0 is ill-defined pinch poles of k in above definition single σ p1 p as or 0 double d p1 p σ as or 0 Need to include quantum interference diagrams 4
Multiple scattering in QCD Quantum mechanical multiple scattering - Amplitude level P in k P out k P 1 P 1 P P y 1 y y 3 0 3 1 P in Aφ + (0) φ + ( y ) φ( y ) φ( y) A 3-independent parton momenta no pinched poles depends on 4-parton correlation functions dσ C ( p, p, p, p, p, p ) ( p, p, p, p ) double double ' ' double ' ' in 1 1 out 1 1 dp dp dp dp δ ( p + p + p + p + p p ) ' ' ' ' 1 1 1 1 ( p, p, p, p ) A φ (0) φ ( y ) φ( y ) φ( y ) Adydydy double ' ' + + 1 1 3 1 1 3 It has no probability interpretation! in out 5
QCD Matter Hadronic matter: nuclei baryons QCD dynamics for a scale 1 ~00 MeV fm Q < mesons Hot matter produced in heavy ion collisions A B Initial hard collision should not be coherent with later multiple scattering of the high p jets 6
Jet omography High p jet suffers multiple scattering in medium Jet A B Prerequisites Calibrated source Calculable absorption cross sections Interpretation of the results Jet A change of single jet spectrum or two-jet correlation provides information on medium properties tomography 7
Calibrated probes Inclusive hadron distribution calculable in perturbative QCD Leading order pqcd phenomenology Next-to-Leading order pqcd c 3 ) - (mb GeV 3 σ/dp 3 E*d 1 10-1 10-10 -3 10-4 10-5 PHENIX Data KKP FF Kretzer FF a) 10-6 10-7 10-8 Δσ/σ (%) 40 b) 0 0-0 -40 E d σ h 3 d p ab cd (, ) (, ) ( *, ) a / A a D z b / B b h / c c Q f x Q f x Q Parton distribution functions 8 d σ dt Perturbative cross sections Fragmentation functions
Medium indenced rescattering Answer depends on the choice of source potential v(0,q 1) and the scattering phases Introduce approximation to make sense of the calculation 9
Medium induced QCD energy loss Approximation: G.Bertsch and F.Gunion, PRD5 (198) Induced gluon production: y = ln1/ x Where is interpreted as rapidity Gluon production in a medium: dn C k q dyd k k ( k ) BG g μ Aα s( ) = d q π ( q ) q transfer μ π q + CAα s( k ) μ π k ( k + μ ) 10 Screen mas μ Vitev,, QM004
Momentum distribution of induced gluon dn BG g dyd k 1/k he scattering scale does not follow from calculation μ 4 1/k = input screen mass k = μ k the scale will enlarge by the nuclear size 1/3 = μ = s k A Q 11
Reaction operator approach Gyulassy, Levai, Vitev, Nucl.Phys.B571 (000); Nucl.Phys.B594 (001) z z z n n z n n ˆ = R q n, a n q n, a + n q +, a qn, an n n q n, a n q n, a n k-q m k k-q m -q m k p+k-q m q m p p+k-q m - q n q m p Gluon Gluon polarization Parent parton Approximation: 1
QCD radiative energy loss Effective D Schroedinger equation Path integral formulation Reaction operator approach (1) C Rα s μ L E ΔE Log +..., 4 λg μ (L) L Stat ic m ed iu m 3 g (1) 9πCRαs 1 dn E ΔE L Log +..., 4 A dy μ (L) L 1+1D Bjorken Elastic energy lose: R.Baier et al., Nucl.Phys.B 483 (1997); ibid. 484 (1997) B.Zakharov, JEP Lett. 63 (1996) U.Wiedemann, Nucl.Phys.B588 (000 M.Gyulassy et al., Nucl.Phys.B594 (001); Phys.Rev.Lett.85 (000 J.D.Bjorken, SLAC preprint (198) unpublished elastic μ / μ ΔE 6α s e 1+ L ln 13 4 E μ jet
dσ Modified jet cross section jet quenching g* g rad parton Reduced partonic cross sections q 0 π dσ hadron Modified fragmentation functions ypical LHC Vitev,, QM004 vac dσ 1 qˆ L μ L, ω n c = = dp ( p ) λ Q( p ) exp CRα s g nω c π p Gluon transport coefficient: cold hot qˆ 0.045 GeV / fm, qˆ 1 GeV / fm 14 R AA = Quenching factor Q(p ) same as Leading parton R AA (p ) AA dσ ( b)/ dyd p pp Nbindσ / dyd p R.Baier et al., JHEP0109, (001)
Suppression of fragmentation functions Independent Poisson approximation for multiple gluon emission Kniehl, Kramer, Potter fragmentation functions Probability for fractional energy loss ε =ΔE/ Ejet P( ε ) n 1 dn( ωi ) = dωi n= 0 n! i= 1 dω dn dω d e ω δ ε n i= 1 ωi E jet Normalized for suppressed leading hadrons (no feedback) 1 med 1 vac z h/ q h/ q D (, z Q ) = dε P( ε) D, Q 1 ε 1 ε 0 15 z=p h /p c C.Salgado, U.Wiedemann, Phys.Rev.Lett. 89 (00)
E E ( ) x ( R ) xb = Q / p q, A = 1/ mn Δz γ * = C Q C α ( Q ) x 1 N Q x ( ) A s B 6ln c x A de / dl 0.5 0.6 GeV / fm cold 0 π A ν = Δz B Semi-inclusive DIS E E ' - energy transfer - radiative energy loss fraction ( ) Δ E = ν Δ z = E E Δ z L E.Wang, X.-N.Wang, PRL 89 (00) 16 F.Arleo, Eur.Phys.J. C30 (003)
Jet quenching in a dense medium Absolute scale Vitev and Gyulassy, Phys.Rev.Lett. 89 (00) μ ωpl, ρ, ε 3 4 PHENIX Collab., Phys.Rev.Lett. 91 (003) SAR Collab., Phys.Rev.Lett. 91 (003) 17
Centrality Dependence R Δp p AA ( p ) = (1 + c Δ / p ) ΔE E N p /3 part n 1+1D GLV Small number of semihard scatterings n = 1.5( peripheral) 3.5( central) scat X.-N.Wang, nucl-th/0305010 18 G.G.Barnafoldi et al., hep-ph/0311343
Broadening of the Jet Cone Jet cone opening angle: ρ( R) - fraction of the total energy within a jet subcone R = Δ φ +Δη ρ ρ vac med ( R) = 1 N jets jets ( R) = ρ ( R) vac Et ( R) E ( R = 1) ΔEt ( R) E ΔEt + 1 vac ( E t t ( ρ R) ) Very small effect even at the LHC t R = 0. 3 Et Et = 50 GeV, 5% effect = 100 GeV, 3% effect C.Salgado, U.Wiedemann, hep-ph/0310079 19
Di-hadron Correlation trig h1 Far Δφ Near Δφ Near h g rad g* Far h E E QGP d σ 3 3 d p d p g rad f ( x, Q ) f ( x, Q h h 1 a / A a b / B b 1 d σ ab cd / dt ) Qiu, Vitev, Phys.Lett.B570 (003) D ( z, j, Q ) D ( z, j δ Di-jet acoplanarity (insufficient) Away-side quenching 0 * * h / c c c h / d d d 1 ( pa p pc p ) 4 + b d, Q )
1
Assumptions: Jet quenching Soft interactions between the ions does not change the effective PDF s h A A Multiple scattering with the medium leads to energy loss Reduction of leading hadron momentum leads to suppression at high p Suppression is a final-state effect No suppression expected for da
Saturation and CGC Soft interactions between the ions alter the PDF s h A A Convolution of two universal saturated distributions at a saturation scale: Q s ~ GeV; or Solve classical Yang-Mills Equation gluon density from the AA collisions, then convert the gluons to the observed hadron Momentum of the GeV hadron h is balanced by many soft particles no back-to-back hadron correlation Suppression is a initial-state effect Large suppression expected for da R dau = R 1, R 0. 0.4 AuAu 3 AuAu
Comparison to the d+au Data RHIC Data from: B.Back et al. [PHOBOS], Phys.Rev.Lett. 91 (003) S.Adler et al. [PHENIX], Phys.Rev.Lett. 91 (003) J.Adams et al. [SAR], Phys.Rev.Lett. 91 (003) I.Arsene et al. [BRAHMS], Phys.Rev.Lett. 91 (003) heoretical predictions: I.Vitev and M.Gyulassy, Phys.Rev.Lett. 89 (00) D.Kharzeev, E.Levin,L.McLerran, Phys.Lett. B 561 (003) I.Vitev, Phys.Lett. B56 (003) Current Data from RHIC: - support Cronin type effect in d+au - disfavor the saturation picture in d+au Parton x is not small enough: - Increases collision energy the LHC - moves to the forward region lower x 4
Calculations of Cronin Effect B. Kopeliovich et al., Phys.Rev.Lett. 88, (00) Y. Zhang et al., Phys.Rev. C65, (00) k k k L = + Δ = μ / λ pa pp pa hese calculations have addressed the Y=0 total inclusive Cronin Effect at RHIC X.N. Wang, Phys.Rev. C 61, (000) All of the above find: at RHIC 5 RdAu 1.1 1.4
Power Corrections in p(d)+a Collisions Hadronic factorization fails for power corrections of the order of 1/Q 4 and beyond Medium size enhanced dynamical power corrections in p+a are factorizable to make predictions for p+a collisions, but, multiple hard scales, s, t, u. Single hadron inclusive production: Once we fix the incoming parton momentum from the beam and outgoing fragmentation parton, we uniquely fix the momentum exchange, q μ, and the probe size coherence along the direction of q μ p μ only t relevant. smaller t, larger coherent effect 6
Numerical results for power corrections Qiu and Vitev, hep-ph/0405068 Similar power correction modification to single and double inclusive hadron production increases with centrality and increase with rapidity disappears at high p because of the power suppression Power corrections to evolution equations will flatten the p dependence slower evolution 7
Systematics of P broadening 8
otal Q broadening Direct Q from multiple scattering is not perturbative: Drell-Yan Q average is perturbative: dσ dσ Q dq dq ( Q ) dq dq dq dq ha Drell-Yan Q broadening: Four-parton correlation: q dσ dσ α dq dq dq Q x A ( ) s, q 9 hn Δ Q Q A Q σ dy + ixp y ( x, A) = e dy1 dyθ ( y y1 ) ( y ) π θ + 1/3 + γ + 9 A pa Fα y y F y1 A F F q A x 16π R Characteristic scale: Single scale Q α + α + ( ) ψ ( 0) ψ ( ) ( ) p α ( ) + α + 1 + α + F Fα dy1 N F ( 0 ) Fα ( y1 ) N θ ( y + 1 ) p Guo, PRD 58 (1998) ( D)
Summary and outlook With all the data becoming available QCD and strong interaction physics will have a new exciting era hanks! 30