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A light-cone wavefunction approach to heavy meson dynamics in the QGP Ivan Vitev Credit goes to my collaborators R. Sharma and B. W. Zhang Phys. Rev. C 80, 054902 (2009), Rishi Sharma, IV, Ben-Wei Zhang • Phys. Lett. B 649, 139 (2007), Azfar Adil, IV • Heavy Quark Production in Heavy Ion Collisions Purdue, January 4-6, 2010 Outline of this Talk Motivation, light particle quenching and the nonphotonic electron puzzle An alternative mechanism for open heavy flavor suppression Heavy mesons near the phase transition Distribution and fragmentation functions for open heavy flavor at zero and finite T Calculation of the in-medium heavy meson dissociation probability (GLV approach). Heavy flavor dynamics at RHIC and the LHC, examples for inclusive D/B and decay e± I. Light Particle Quenching So far has worked very well versus pT, root(s), centrality, … Gyulassy-Levai-Vitev (GLV) formalism Gyulassy et al, (2001) • RAA: provides useful information for the hot / dense medium T [MeV] RHIC LHC 370 720 .75-1. 1.4-1.8 .75-.42 .39-.25 qˆ 0.35 0.85 GeV . fm 2 1 qφ 0.40 0.99 GeV 2 . fm1 IV 2005 I. Leading Particle Suppression at the LHC K. Amadot et al, (2011) IV, (2005) 1 ET Observable Observable ~ n , RAA 1 ET ET n (2 m ') I.V., M. Gyulassy (2002) The pT dependence and magnitude of the ~ suppression is consistent with predictions form 2002 and 2005 I. The Open Heavy Flavor Quenching Puzzle Calculations include Cronin effect, coherent power corrections (shadowing), IS energy loss, E-loss in the QGP (FS) The real problem comes form B mesons that dominate at intermediate / high pT R. Sharma et al. (2009) II. The Space-Time Picture of Hadronization • Inside-outside cascade • Outside-inside cascade String models Hadron Parton Bjorken (1984) Bialas et al. (1987) QGP extent B D Perturbative QCD 6 20 fm 1.5 fm 0.4 fm II. The Mass and Momentum Dependence of Particle Formation Markert et al. (2008) For particle masses ~ > 1 GeV one has to consider their formation and dissociation in the medium II. Collisional Dissociation of D / B Mesons An alternative D-mesons, B-mesons c Simultaneous fragmentation and dissociation call for solving a system of coupled equations • Example: radioactive decay chain u Time evolution • Both emulate energy loss and lead to suppression of the final observable spectra Adil, IV (2007) dN i i 1 N i 1 i N i dt III. Quarkonia Near the Phase Transition The quark-antiquark potential can be extracted form the lattice One particular parametrization • Mocsy, Petreczky (2007) Non-relativistic – Schroedinger J/ψ J/ψ can survive (color screening) to ~ 2 Tc. ϒ can survive to much higher temperatures ϒ III. D and B Mesons Near the Phase Transition • Relativistic – Dirac equation M. Avila (1994) Coulomb Linear 1 4 V , s r 3 S br b dG k 1 V ' S ' m F G dr r 2M dF k 1 b F V ' S ' m G r 2M dr B, D can survive color screening to ~ 1.5 – 2 Tc depending on the effective light quark mass IV. Light Cone Wave Functions • Expansion P , P , S , S z 2 in Fock components n n 2,3 i1 dxi d 2 k i 2xi 2 3 n i, j,k n x,k , a i i i i n n xi 1 k i i1 i1 r r r a a ...a (xi P k i )...b j (x j P k j )... d k (xk P k k )... 0 a i Composite hadron creation operator: ' ' '2 ' ' z 2 P , P , S , S P , P , S , S z r r ' s s ' 2P 2 P P z z 3 3 r a (P ) † sz H The normalization then becomes 1 1 2 2 3 n n 2,3 i1 dxi d 2 k i 2xi 2 3 n xi , k i , i ai 2 n n xi 1 k i i1 i1 IV. Parton Distribution Functions at Non-zero T Even though the physical situation of mesons in a co-moving plasma is nor realized it is interesting to investigate theoretically the PDFs and FFs at finite temperature Distribution function dy ixP y a a q / P (x) e P (y , 0) (0, 0) P 2 2 • Light cone gauge A+=0 , 0<x<1 (k , x) 2 k2 4mQ2 (1 x) 4mq2 (x) : Exp 42 x(1 x) Sharma, IV, Zhang (2009) IV. Heavy Quark Fragmentation Functions at Non-zero T Fragmentation function At tree level: # (x 1). # 0 The leading contribution: dy iP / z y 1 1 DH /q (z) z e Trcolor TrDirac 2 3 2 2 0 a (y , 0)aH† (P )aH (P ) a (0, 0) 0 Ma (1993), Braaten et al. (1995) • Keep the leading qT dependence in the meson wavefunction. Complexity ~10^3 terms Sharma et al. (2009) Includes: 3 S0 1 S0 The only calculation of “modified fragmentation functions”. The shape is the same as in the vacuum. Quenching comes from energy loss - not universal. IV. The Inapplicability of Simple Mesons in Equilibrium Models • Incompatible with equilibrium + boost assumption AdS/CFT The J/ψ yield suggests that the LQCD based results with the equilibrium dissociation Theoretically • rmed t form . Leads to “instant” wavefunction approximation It is not the screening, but the subsequent collisional dissociation that reduce the rates of open heavy flavor and quarkonia V. Calculating the Heavy Meson Dissociation Probability Calculate the kernel for the system evolution in the GLV approach Opacity (mean # scatterings): L One can resum the interactions in impact parameter space Rutherford tail enhancement Master equation ( 3 5) V. The Physics of In-medium Heavy Meson Scattering k m (1 x ) m2 x 1 2 4 x(1 x )2 x(1 x ) 2 i (k , x) (K ) Norm e e 2 2 Initial condition: 2 2 2 K2 k2 m 2 (1 x ) m22 x 2 1 e 4 2 2 2 2 x(1 x) 2 f (k , x) Norm e 4( x(1 x ) ) e x(1 x ) 2 2 2 x(1 x) 4 2 Result: Two physics effects arise form meson broadening • Heavy meson acoplanarity: K 2 L 2 2 2 q K • Broadening (separation) the q-qbar pair: k f (k , x) a M (k , x) (1 a) qq dissociated (k , x) 16 VI. Coupled Rate Equations and Initial Conditions t f Q ( pT ,t) 1 form ( pT ,t) f Q ( pT ,t) 1 + diss ( pT / x ,t) t f H ( pT ,t) + 1 dx 0 1 (x) f H ( pT / x,t) 2 Q/ H x 1 f H ( pT ,t) diss ( pT ,t) 1 form ( pT / z ,t) 1 dz 0 1 DH / Q (z) f Q ( pT / z,t) 2 z Adil, IV (2007) • • • The subtlety is how to include partonic energy loss It cannot be incorporated as drag/diffusion We include it approximately as MODIFIED INITIAL CONDITION f Q ( pT ,t 0) d Q f ( pT ,QUENCHED) 2 dyd pT f H ( pT ,t 0) 0 Sharma et al. (2009) VI. Numerical Results for D/B mesons at RHIC • D/B mesons (and non-photonic electrons): show similar suppression Au+Au, Cu+Cu at RHIC • • Cronin effect is very important. Reduces the suppression at intermediate pT M. Aggarwal et al. (2010) VI. RHIC Results on Non-photonic Electrons • Employ a full simulation of the D and B meson semi-leptonic decay,. PYTHIA subroutin.e T. Sjostrand et al (2006) • • • The predicted suppression is still slightly smaller than the quenching of inclusive particles It is compatible with the experimental data within the error bars Improved direct measurements are needed to pinpoint the magnitude and relative contribution of B/D R. Sharma et al. (2010) VI. Open Heavy Flavor Suppression at the LHC • • • • The main effect is the increased suppression in the intermediate pT range 5 GeV to 30 GeV At low pT the predicted D/B (electron) suppression is smaller than the one for light particles At pT > 40 GeV they become comparable. (Residual matching model dependence) LHC is critical to cover the pT range needed for b-quark, Bmeson dynamics Conclusions Theoretical predictions of leading light particle suppression in the GLV approach have worked very well from SPS to the LHC In contrast, the suppression of non-photonic electrons is significantly underpredicted. The problem is in the B mesons. Common to all e-loss approaches Color screening by itself does not imply disappearance of quarkonia to ~ 2Tc and heavy mesons to 1.5- 2 Tc Presented first calculations of heavy meson distribution and fragmentation functions at zero and finite temperature (beyond the point like approximation) There is no universal (T) medium modification of fragmentation functions. Suppression comes from processed that are/emulate energy loss Conclusions (continued) Theoretical and phenomenological considerations suggest that for energetic mesons fragmentation may not be affected by the thermal medium. Calculated the dissociation probability of mesons moving through the medium associated with its collisional interactions Partonic energy loss and meson dissociation are now combined. This is not straightforward – as quenched quark initial conditions The main prediction remains equal and large B and D meson suppression. Matches smoothly onto the quenching region. Compatible with RHIC results. Predictions for LHC presented IV. QCD on the Light Front The free theory r (x ) a • Quarks r (x ) a • Anti-quarks • Gluons r A (x ) a dp d 2 p a r ipx †a r ipx a ( p )u ( p)e b ( p )v ( p)e 2 p 2 3 dp d 2 p a r ipx †a r ipx b ( p )v ( p)e a ( p )u ( p)e 2 p 2 3 |x 0 dp d 2 p a r ipx †a r * ipx d ( p ) ( p)e d ( p ) ( p)e 2 p 2 3 |x 0 |x 0 Commutation relations and normalization of states a a' ' r r r r 3 ( p ' ), a† a ( p ) 2 p 2 3 p p ' aa ' ' b a' ' r r r r 3 ( p ' ),b† a ( p ) 2 p 2 3 p p ' aa ' ' r r r r ba'' ( p ' ),b†a ( p ) 2 p 2 3 3 p p ' aa ' ' • States: a r n, pn , n n r r r ... a†a,i ( pi)...b†a, j ( pj )...d†a,k ( pk ) 0 i, j,kn • Implicit: quark flavor, (anti)symmetrization • Normalization trivially obtained from above I. High pT (ET) Observables Understanding high pT particle suppression (quenching) Power laws: n n( s, pT , system) m-Particle Observable ~ Observable RAA ET 1 ET d A A d 2 pT pT p0 n pT n Quenching factor correlated to spectra 1 ETn n (2 m ') • Some models’ RAA varies with the underlying power law spectrum • High pT suppression at the LHC can be comparable and smaller than at RHIC • Complete absorption models produce a constant RAA 24 I. The Open Heavy Flavor Quenching Puzzle Large suppression of nonphotonic electrons – incompatible with radiative/collisional e-loss … one can fit heavy flavor only (no doubt) M. Djordjevic et al. (2006) But it doesn’t work. Data favors B meson suppression comparable to that of D mesons M. Aggarwal et al. (2010) “Instant” Approximation • • Compatible with measured multiplicities Full treatment of cold nuclear matter effects Results from the LHC So far has worked very well versus pT, root(s), centrality, … Advantage of RAA : providing useful information of the hot / dense medium, with a simple physics picture. Gyulassy-Levai-Vitev(GLV) formalism Gyulassy, Levai, IV, NPB 594(2001)371 Leading particles Gluon Feedback to Single Inclusives • Note that Nbin / (Npart/2) = 0.11 • The redistribution of the lost energy is very important at the LHC. 100% correction and pT<15 GeV affected • Can quickly eliminate some models or indicate very interesting new possibilities for modeling 28 Calculating the Meson Wave Function • Relativistic Dirac equation 3 VS m S' S V 2 MQ MQ V'S 2 1 S m S 2 MQ MQ l 1, l, j l 1/ 2 j l 1/ 2 Reduces to: • Radial density: 1 (r) ~ (F 2 G 2 ) D0 , D0 , D _ D , Ds ... The*, .... Same for B S0 3 S1 Coulomb Linear S br 1 4 V , s r 3 Reduces to: b dG k 1 V ' S ' m F G dr r 2M dF k 1 b F V ' S ' m G dr r 2M Boost with large P+ - end up at the same longitudinal rapidity (k , x) 2 k2 4mQ2 (1 x) 4mq2 (x) : Exp 42 x(1 x) M. Avila, Phys. Rev. D49 (1994) 29 Heavy Quark Production and Correlations D D • Fast convergence of the perturbative series • Possibility for novel studies of heavy , k, 30 D quark-triggered (D and B) jets: hadron composition of associated yields Quenching of Non-Photonic Electrons • Full semi-leptonic decays of C- and B- mesons and baryons included. PDG branching fractions and kinematics. PYTHIA event generator RAAe ( pT ) • Similar to light d AAe / dyd 2 pT N coll d pp e / dyd 2 pT 0, however, different physics mechanism • B-mesons are included. They give a major contribution to (e++e-) Note on applicability D-, B-mesons to RAA (D) RAA (B) (e++e-) to 25 GeV 31 Light Front Quantization • Advantages of light front quantization: simple vacuum, the only state with p+=0 • Full set of operators, commuting: M 2 2 p p p2 , p , p S 2 , Sz S.Brodsky, H.C.Pauli, S.Pinsky, Phys. Rep. (1998) 32 From Low to High Fock Components • Perturbative generation of the higher Fock states s d 2 d dPa dzPa bc ( z ) 2 2 2 At the QCD vertexes: conserve color, momentum, flavor, … • The lowest lying Fock state (non-perturbative) – the most important Correct quantum #s carry over to higher states 33 Medium-Induced Radiation: Theory • Includes interference with the radiation from hard scattering d el d 2 q 1 el 2 ( q ) 2 1 el 2 ( q ) 2 φn Vφn φn Dφn V Rφn D n CR s n L ji1 z j d zi k k 2 2 2 dk d k n 1 dk d k n 1 i 1 0 g ( zi ) dN g dN n g n -2C1...n Bm1...n m...n cos m 1 Color current propagators 1 d el 2 d qi el d 2 qi (qi ) 2 k 2 k ...nzk cos m Momentum transfers Number of scatterings k 1k ...nzk m Coherence phases (LPM effect) The Soft Medium • Local thermal equilibrium PHOBOS • Local parton-hadron duality • Gluon-dominated soft sector • Bjorken expansion / approximate boost invariance Au + Au 2 g g T , g 2 2 . 5 ( 0 . 3 0 . 5 ) D s 4 2 1 g g 9 s 2 , g g g 2 D w h e r e # D o F 2 ( p o l a r i z a t i o n ) 8 ( c o l o r ) ,[ 3 ] 1 . 2 2 1 4 p d p # D o F 3 ( T ) # D o F 2 [ 3 ] T t h e o r y p / T 3 0 e 1 ( 2 ) T [MeV] RHIC LHC 370 720 .75-1. 1.4-1.8 .75-.42 .39-.25