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June 20, Back-to-Back Correlations in p+p, p+A and A+A Reactions 2005 Annual AGS-RHIC User's Meeting June 20, BNL, Upton, NY Ivan Vitev, LANL Ivan Vitev

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June 20, Outline of the Talk Ivan Vitev, LANL A+A jet triggered correlations: Phase space distribution of non-Abelian energy loss Redistribution of the lost energy in jet triggered correlations Broadening of the away-side correlation function p+A reactions at RHIC: Understanding initial and final state multiple scattering Dynamical gluon "shadowing" - yields and correlations, including open charm E-loss in cold nuclear matter Open charm production and correlations: Partonic subprocesses and cross sections D meson triggered correlations and hadrochemistry

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June 20, Theoretical Approach Ivan Vitev, LANL Collinear factorization approach: can be systematically expanded to include nuclear corrections Non-perturbative matrix elements: Twist 2, 4, 6,... Other phenomenologies: data = model NLO correction at LT Twist: from Opertaor Product Expansion (OPE) Higher twist (elastic) corrections: dynamical shadowing Energy loss - enhanced by the nuclear size T = Dimension - Spin

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June 20, I. Open Charm Production Ivan Vitev, LANL Popular belief In practice to LO (NLO) Many of the interesting features that follow are related to the scattering Time direction from PDFs

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June 20, D 0 and D + at the Tevatron Ivan Vitev, LANL D.Acosta et al., Phys.Rev.Lett. 91 (2003) Data from: Fragmentation functions: From heavy quark effective field theory (Vector and Pseudoscalar) E.Braaten et al., Phys.Rev.D 51 (1995) Very reasonable K-factor: K NLO = 1.7 Slightly stiffer power law Branching ratios taken into account...

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June 20, Contribution of Partonic Subprocesses Ivan Vitev, LANL Define partial cross sections Clearly one expects 2 things: Dynamical shadowing comparable to light pions Trigger dependent hadrochemistry How to test this? - di-hadron correlations Gluon fussion is not the dominant mechanism for open charm production

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June 20, D Triggered Correlations Ivan Vitev, LANL Never measured before: T.Goldman et al., in preparation Real possibility for RHIC experiments to discover D meson triggered correlations Constrain D meson production, c quark fragmentation Very strong dependence of particle species in the away side jet on p T2 Non-monotonic behavior on the away side yields: anti D at p T2 = p T1

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June 20, II. Shadowing in DIS and p+A Ivan Vitev, LANL Decompose Hard part Matrix element Non-perturbative Lightcone gauge: Breit frame: Perturbative Long distance Short distance Contribution of single scatter:

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June 20, Numerical Results J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004) Favorable comparison for the x- and A-dependence NA37 (NMC) and E665 data For we impose. Finite resolution: same for all models (r max ) Numerical A- and x B -Dependence Ivan Vitev, LANL Purely quantum effect The scale of higher twist per nucleon is small

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June 20, p+A Collisions are not DIS Ivan Vitev, LANL p+A collisions do not carry direct information about PDFs (unfortunately all effects) Forward (backward) physics not equal small x (large x) 1) Initial state energy loss and broadening - DY 2) Shadowing - DIS 3) Final state e-loss is added in p+A

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June 20, p+A Collisions Ivan Vitev, LANL Isolate all the x b dependence of the integrand: Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus p A Starting point: LO pQCD Other interactions are less coherent (elastic) and sppressed at forward rapidity by a large scale 1/u, 1/s - standard parton distribution functions - standard parton distribution functions Ivan Vitev, LANL

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June 20, Numerical Results J.W.Qiu, I.V., hep-ph/ Similar power corrections modification to single and double inclusive hadron production - increases with rapidity and centrality Ivan Vitev, LANL

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June 20, STAR Statistical errors only 25

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June 20, Dynamical Shadowing to Inclusive D 0 +D + Ivan Vitev, LANL Increases with centrality: (dynamical shadowing has little to do with A but with the local path length through nuclear matter) Increases with rapidity: (slightly) Disappears at high p T : (power correction type, coherent elastic) Quite similar to light pions (even slightly larger)

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June 20, (D 0 +D + ) - (D 0 +D - ) Triggered Correlations Ivan Vitev, LANL Experimentally probably biased to p T1 = p T2 Similar results for the D meson triggered correlations We know for a fact that the c quark rescatters (as in DIS) In light hadrons Naively expected that the partonic composition will matter but apparently what dominates is: -

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June 20, Energy Loss in Cold Nuclear Matter Ivan Vitev, LANL Before jumping to conclusions investigate existing data Leading twist shadowing: (phenomenology) clearly insufficient (in fact antishadowing) T.Goldman et al., in preparation Power corrections (theory) : clearly insufficient (~13%) Leaves additional effects: enegy loss NA35 collaboration: d+Au (interestingly enough) data - Same rapidity asymmetry as at h-h-

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June 20, One Implementation of Energy Loss Ivan Vitev, LANL Where energy loss arguably plays a role Bertsch-Gunion bremsstrahlung: Implemented as "Sudakov Form Factors": B. Kopeliovich et al., hep-ph/ This is one way of implementing energy loss (large rapidity gap events, amplification near kinematic bounds)

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June 20, III. Non-Abelian Energy Loss Ivan Vitev, LANL Naive picture Solution to first order in the mean # of scatterings The physics is more interesting than a Brownian motion of the gluon In reality I.V., hep-ph/ Re 2 x

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June 20, Angular and Frequency Behavior Ivan Vitev, LANL The small angle and small frequency behavior of the radiative spectrum is under perturbative control I.V., hep-ph/ Radiation is moderately large angle. Finite gluon number

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June 20, Depletion of high-p T hadron multiplicities in Au+Au relative to the binary collision scaled p+p result Jet Tomography Ivan Vitev, LANL D.d'Enterria, nucl-ex/ (EJP) Predicted nuclear modification Non-Abelian energy loss (GLV formalism) Room for improvement

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June 20, Deriving the Fragmentation Contributions Ivan Vitev, LANL Define a measure for nuclear modifications to di-hadron correlations: Use energy conservation to verify the fragmentation sum rule But the formation length is ~ L/2. May fragment outside the medium Quenched parent parton Feedback gluons (not DGLAP)

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June 20, Numerical Results Ivan Vitev, LANL Data is from: J.Adams et al., nucl-ex/ I.V., hep-ph/ For large energy loss - the radiative gluons dominate to unexpectedly high The redistribution of the energy is a parameter free prediction The amount of energy depends on the trigger p T Very interesting as a function of trigger

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June 20, Superposition of Jet Cones Ivan Vitev, LANL Trigger particle Some mechanism of jet cone production One has to filter through the di-jet rapidity distribution Surprisingly flat dijets in a wide rapidity range Experiments measure in the plane (to make the life of theorists difficult)

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June 20, Independent Verification Ivan Vitev, LANL Practically flat at all angles except very close to the beam pipes The distribution of away-side jets comes form How broad is broad? R.Bellwied, RHIC II presentation, April 2005 It is there in p+p Has nothing to do with random walk

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June 20, Projected Medium-Induced Radiation Ivan Vitev, LANL From this The double hump structure is partly gone to that Additionally: acoplanarity and incomplete jet energy loss Approximation

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June 20, Angular Di-Hadron Distribution Ivan Vitev, LANL Because: The width of the large-angle correlations is dominated by medium induced gluon radiation I.V., hep-ph/ Reasessment of the origin of small and moderate p T away triggered hadrons The quenched parton is not wider

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June 20, Results in Au+Au: STAR Ivan Vitev, LANL STAR preliminary: Talk by F.Wang, March 2005

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June 20, The Rapidity Story is Known Ivan Vitev, LANL Rapidity coverage J.Adams et al., nucl-ex/ , submitted to Phys.Rev.Lett. Slicing in and slicing in is the same No (curious) structure in rapidity or azimuth

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June 20, Conclusions Charm triggered correlations are new - p T dependent hadron composition (light hadrons and charm mesons). It will be interesting to test experimentally. Ivan Vitev, LANL Dynamical power corrections lead to shadowing and suppression of yields and correlations. Has very well defined p T dependence. Additional effects are related to energy loss. Low energy. Medium induced radiation converts the high p T suppression enhancement produces large angle correlations. However there are a number of effects that tend to dilute these signatures. If one looks for topological structures one has to do event by event analysis in more detail

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