Slide1 :
Parton Energy Loss in Ultrarelativistic Heavy Ion Collisions
14-th Jyvaskyla Summer School,
August 9 - August 27 2004, Jyvaskyla, Finland
Ivan Vitev, LANL
Lecture (III) : Lecture (III) A direct QCD calculation of
in the collinear pQCD factorization approach:
The source of nuclear enhanced corrections
Photo-nuclear reactions. Ivan Vitev, LANL Nuclear shadowing in neutrino-nucleus DIS:
Interplay of mass and nuclear enhanced power corrections
Shadowing in F2 and xF3 and valance quarks. QCD sum rules
Dynamical power corrections in p+A collisions:
High Twist modification to the low pT region
Disappearance of the effect at high pT. Contrast with saturation
Application to dihadron correlations
Ivan Vitev, LANL Coherent multiple scattering:
Differences with Glauber
pQCD in Nuclear Collisions : pQCD in Nuclear Collisions Universal nuclear dependence:
from nuclear wave functions
Process-dependent nuclear
effects:
● Initial-state:
● Final-state:
Nuclear PDF’s versus
medium-induced nuclear effect Data from: NMC K.Eskola,V.Kolhinen and C.Salgado,
Eur.Phys.J. C9 (1999)
M.Hirari,S.Kumano and M.Miyama,
Phys.Rev. D64 (2001)
Shadowing (Will be discussed) Ivan Vitev, LANL
Deviations from the Hard Scattering Regime : Ivan Vitev, LANL AA AA /sinelp+p nucleon-nucleon
cross section Deviations from the Hard Scattering Regime p+A collisions are ideal since the
deviations from the QCD
factorization can be
systematically computed Rapidity dependence, centrality dependence Ivan Vitev, LANL
Predictive Power of pQCD : Predictive Power of pQCD Factorization theorem:
Scale of hadron wave function:
Scale of hard partonic collision:
Factorization:
Process-dependent:
Process-independent:
Predictive power: Universality of
Infrared safety of
Address the deviations:
Power corrections
J.Collins, D.Soper, G.Sterman,
Nucl.Phys.B223 (1983)
Ivan Vitev, LANL (dynamical nuclear shadowing) Ivan Vitev, LANL
Nuclear Effects in Lepton-Nucleus DIS : Nuclear Effects in Lepton-Nucleus DIS Ivan Vitev, LANL - the DIS structure functions Used to determine the parton distribution
functions (PDFs) Convenient to calculate in a
basis of polarization stares of Ivan Vitev, LANL Kinematics
LO Contributions to : LO Contributions to Ivan Vitev, LANL (Twist 4) Short distance, not A1/3-enhanced G.Altarelli and G.Martinelli,
Phys.Lett. B76 (1978) M.Gluck and E.Reya,
Nucl.Phys. 145 (1978) Bremsstrahlung
diagram Box
diagram Genuinely new higher twist contribution The old and known Leading Twist contribution Ivan Vitev, LANL
Multiple Final State Scattering : Multiple Final State Scattering Ivan Vitev, LANL Lightcone gauge: Breit frame: 2D lightcone dynamics Pole – on-shell, long distance No pole – contact, short distance J.W.Qiu, Phys.Rev. D42 (1990) Ivan Vitev, LANL The brick wall frame (Breit) Don’t leak out
of the nucleon
The Technology of Power Corrections : The Technology of Power Corrections Ivan Vitev, LANL The small-x limit of the leading
twist gluon distribution function Only one contributing uniquely defined sequence: Hard part Matrix element Ivan Vitev, LANL Pomeron Color singlet approximation
Resumming the Power Corrections : Resumming the Power Corrections Ivan Vitev, LANL Simple analytic formula: QM shift operator Scale of power corrections (geometric and
vertex factors, two gluon correlation function) Ivan Vitev, LANL Physics: dynamical generation of the parton’s mass
Results : Results Ivan Vitev, LANL J.W.Qiu and I.V., hep-ph/0309094 Q2 dependence,
Longitudinal SF
Generated by the
multiple final
state scattering
of the struck quark Compares well to the EKS98 scale-
dependent shadowing parameterization.
Ivan Vitev, LANL
Modifications to Scattering : Modifications to Scattering Ivan Vitev, LANL Similarly for the neutral current The NuTeV experiment claims: Based on: Beware: Monte Carlo with many effects taken on average Motivation Axial and vector part (weak current) Recall the tensorial decomposition Ivan Vitev, LANL
New Contribution to : Ivan Vitev, LANL On-shell paricle (M) New Contribution to Even if one neglects mass
effects show up due to the mixing of electroweak
and mass eigenstates J.W.Qiu, I.V., Phys.Lett.B 587 (2004) |V| - the CKM matrix elements xi Along the way we will develop techniques that
may be useful in the discussion of charm
production at RHIC
(Cuts fix kinematics) Ivan Vitev, LANL
Mass and Nuclear Enhanced Power Corrections : Ivan Vitev, LANL Equations of motion - nuclear enhanced power corrections and mass corrections
commute Mass and Nuclear Enhanced Power Corrections Special propagator structure: Ivan Vitev, LANL
Results: F2(x,Q2) and xF3(x,Q2) : Results: F2(x,Q2) and xF3(x,Q2) Approximate analytic formula Framework: Collinear factorized pQCD Ivan Vitev, LANL J.W.Qiu, I.V., Phys.Lett.B 587 (2004) Valance quark shadowing and QCD sum rules: examples where dipole models will fail Ivan Vitev, LANL Similarly in a gedanken DIS on gluons on would measure much bugger shadowing.
The Gross-Llewellyn Smith and Adler Sum Rules : 1 10 20 3 Q2 The Gross-Llewellyn Smith and Adler Sum Rules To one loop in Nuclear-enhanced power corrections
are very important Ivan Vitev, LANL D.J.Gross and C.H Llewellyn Smith ,
Nucl.Phys. B 14 (1969) S.Adler , Phys.Rev. 143 (1964) Can set a limit on the 4-point parton
correlation function Leading twist shadowing does not contribute to GLS Ivan Vitev, LANL
Inclusive Spectra Revisited : Inclusive Spectra Revisited Ivan Vitev, LANL I. Arsene et al., nucl-ex/0403050 GCG GCG ~ 0.4 – 0.5 Looks like 0.5! Power corrections It makes no sense to try and fit the charded hadrons at low pT and these rapidities Ivan Vitev, LANL
p+A Collisions : p+A Collisions Ivan Vitev, LANL Isolate all the xb 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 Interested in the maximum coherent rescattering of the small xb
parton in the nucleus
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
Power Correction Contributions to LO pQCD : Power Correction Contributions to LO pQCD Ivan Vitev, LANL J.W.Qiu, I.V., hep-ph/0405068 The results look like LO pQCD with the substitution: Cd = 1 for quarks, CA/CF = 9/4 for gluons c d Driven by the Mandelstam invariant (-t) the resulting suppression will be
sensitive to pT and rapidity y. 1. Recall that the two gluon ladder generates
the scale of higher twist - 2. For a fixed number of interactions (2N) we
take all possible cuts 3. Sum over all possible N I.B.P New contributions to
the cross section Ivan Vitev, LANL
Numerical Results : Numerical Results J.W.Qiu, I.V., hep-ph/0405068 Similar power corrections
modification to single and double
inclusive hadron production - increases with rapidity and centrality disappears at high pT in accord with
the QCD factorization theorems Ivan Vitev, LANL
Forward Rapidity : Statistical errors only 25
Summary (III) : Summary (III) Deeply inelastic scattering. The pQCD
factorization approach.
Ivan Vitev, LANL Photo-nuclear reactions. Nuclear shadowing.
Neutrino-nucleus scattering and QCD sum rules.
Coherence in p+A collisions. Single inclusive
particle spectra and particle correlations.
Dynamical effects come from multiple coherent
final state scattering.
Calculating Power Corrections : Calculating Power Corrections Ivan Vitev, ISU Only even number of gluon insertions survive between the vertex and the cut Short distance interactions can be
paired in an effective scalar vertex Finite length Note: it is that gives The small-x limit of the leading twist gluon distribution function
Decomposition of Multi-Field Correlators via a Density Matrix : Decomposition of Multi-Field Correlators via a Density Matrix Needed correlator: So far Lattice QCD cannot
calculate the correlators. (open exciting problem) We approximate: For the FL the 4-field correlator - replaced
by a product a 2-correlators in the same
nucleon state: Normalization of the nucleon states: Model of a constant density nucleus: Nucleon momentum: (pole-separated, long-distance) Ivan Vitev, ISU
The Scale of the High Twist Contributions to : Ivan Vitev, ISU Vertex factor From D. matrix One parameter: Physical meaning: X.F.Guo, Phys.Rev. D58 (1998),
M.Luo, J.W.Qiu and G.Sterman, Phys.Rev. D49 (1994) The Scale of the High Twist Contributions to mod. norm. Constraints on the value of 1. Drell-Yan kT-broadening 2. Momentum imbalance in dijet photoproduction Lowest order
Through a kT-derivative term can potentially become large if the gluon density increases too fast