QCD Resum short

Slide1: 

Resummed QCD Power Corrections to Nuclear Shadowing Ivan Vitev (in collaboration with Jianwei Qiu) Iowa State University, Ames, IA 50011 Nuclear Theory Seminar, September 25, 2003 Iowa State University, Ames, IA Ivan Vitev, ISU

Outline of the Talk: 

Outline of the Talk Numerical results for the x-, A- and Q2-dependence of nuclear “shadowing”: Suppression of (process-dependent effect) Evidence for power in behavior versus DGLAP (comparison to a Gribov-Regge model) Test of via (a handle on the non- enhanced twist 4 contribution) A direct QCD calculation of in the collinear factorization approach: The source of nuclear enhancement, decomposition of multi-field correlators (2D (+,-) lightcone dynamics) The importance of separating process-dependent and process-independent nuclear dynamics: On the example of the nuclear modification factors at RHIC Ivan Vitev, ISU

Slide3: 

Predicted Elastic and Inelastic Multiple Scattering Effects in Au+Au I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002) RHIC prediction! Ivan Vitev, ISU

Predicted Cronin Effect in D+Au at RHIC via Elastic Scattering: 

Predicted Cronin Effect in D+Au at RHIC via Elastic Scattering I.V., Phys.Lett. B562 (2003) The Cronin peak is located at Antishadowing plays an important role for - an approximately constant contribution (experiments can constrain it) The maximum Cronin enhancement for the total invariant cross section is 20% There is a factor of ~2-3 difference between central (b=0 fm) and mid-peripheral (b=6 fm) reactions (30% versus 10%) What is not considered: Final state energy loss (expected to be small). From the kT-broadening we can estimate an effect 4-5 times smaller in d+Au than in Au+Au Approx. uniform reduction by 15% in central Ivan Vitev, ISU

Comparison to D+Au and Au+Au Data: 

Comparison to D+Au and Au+Au Data Suggested huge shadowing (not supported by authors after the data appeared) Theoretical predictions from: I.V., Phys.Lett. B562 (2003) I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002) Ivan Vitev, ISU Data from J.Adams et al. [STAR], Phys.Rev.Lett. 91 (2003) I.Arsene et al. [BRAHMS], Phys.Rev.Lett. 91 (2003) B.Back et al. [PHOBOS], Phys.Rev.Lett. 91 (2003) S.Adler et al. [PHENIX], Phys.Rev.Lett. 91 (2003) Combined evidence from all four experiments at RHIC: Cronin and quenching are result of multiple initial and final state elastic and inelastic scattering.

Comparison to p+p and Au+Au Data: 

Comparison to p+p and Au+Au Data Theoretical predictions from: I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002) Ivan Vitev, ISU Data from S.Adler et al. [PHENIX], Phys.Rev.Lett. 91 (2003) VERY IMPORTANT: The comparison holds on an absolute scale. This is NOT true for many recent models in d+Au and Au+Au

Correlations in D+Au and Au+Au: 

Correlations in D+Au and Au+Au Dijet acoplanarity Ivan Vitev, ISU J.W.Qiu and I.V., Phys.Lett. B570 (2003) Data from No monojets at RHIC J.Adams et al. [STAR], Phys.Rev.Lett. 91 (2003) J.Rak [PHENIX], nucl-ex/0306031 Additional evidence that is the process (or reaction) specific multiple scattering that leads to the broadening of the di-hadron correlation function in d+Au versus larger broadening and disappearance in Au+Au.

Nuclear Effects in Inclusive DeeplyInelastic Lepton-Nucleus Scattering : 

Nuclear Effects in Inclusive Deeply Inelastic Lepton-Nucleus Scattering Variables: Ivan Vitev, ISU k k’ - the DIS structure functions Used to determine the parton distribution functions (PDFs) Convenient to calculate in a basis of polarization stares of  Lightcone gauge: Breit frame: 2D lightcone dynamics

Nuclear Shadowing, Antishadowing, EMC Effect and the Fermi Motion : 

Nuclear Shadowing, Antishadowing, EMC Effect and the Fermi Motion Shadowing: Color dipole models Practical approach: parameterization of nPDFs K.Eskola,V.Kolhinen and C.Salgado, Eur.Phys.J. C9 (1999) EMC effect: Quark cluster models Fermi motion: Antishadowing: Constructive interference Gain from the momentum spread in the nucleus RHIC Ivan Vitev, ISU EMC Fermi Antishadowing Shadowing M.Hirari,S.Kumano and M.Miyama, Phys.Rev. D64 (2001) Assume only leading twist (LT) Parameterize all existing data at a scale Q0 Give the LT DGLAP evolution for Q A.Bodek and D.Ritchie, Phys.Rev. D23 (1981) H.Pirner and J.Vary, Phys.Rev.Lett 46 (1981) Partonic model A.Mueller and J.Qiu, Nucl.Phys. B268 (1986) N.Nikolaev and B.G.Zakharov, Z.Phys. C49 (1991) Gribov-Regge models B.Z.Kopeliovich, J.Raufeisen and A.Tarasov Phys.Rev. C62 (2000) L.Frankfurt and M.Strikman, JHEP 0202 (2002) Clash! S.Brodsky and H.Lu, Phys.Rev.Lett 64 (1990)

Lowest Order Contributions  to: 

Lowest Order Contributions to Ivan Vitev, ISU Transversely polarized couple directly to the struck quark Longitudinally polarized helicity conservation requires additional gluon R.Brock et al., Rep.Mod.Phys. 67 (1995) (Twist 2) q-propagator: J.W.Qiu, Phys.Rev. D42 (1990) Pole – on-shell, long distance No pole – contact, short distance

Twist Two Contribution to: 

Twist Two Contribution to Ivan Vitev, ISU Box diagram Bremsstrahlung diagram G.Altarelli and G.Martinelli, Phys.Lett. B76 (1978) M.Gluck and E.Reya, Nucl.Phys. 145 (1978)

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

Decomposition of Multi-Field Correlatorsvia 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) 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 TwistContributions 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

Resummed A1/3-Enhanced Power Corrections: 

Resummed A1/3-Enhanced Power Corrections Ivan Vitev, ISU Taking all possible insertions and cuts as in: J.W.Qiu and I.V., Phys.Lett. B570 (2003), M.Gyulassy, P.Levai and I.V., Nucl.Phys. B594 (2001) Insertions Cut The main result The series is dominated by its low order terms as in M.Gyulassy, P.Levai and I.V., Phys.Rev.Lett. 85 (2000) N - the number of quark-nucleon scatterings

The Effects of Isospin: 

The Effects of Isospin Ivan Vitev, ISU Very important at large Bjorken-x (e.g. JLab experiments) Even for the ratio may be modified by 5-7%. Conclusion: well accounted for by modern PDFs (e.g. CTEQ6) One needs to be careful since shadowing is extracted from .

Numerical Resultsfor the A- and Bjorken x-dependence: 

Numerical Results for the A- and Bjorken x-dependence Ivan Vitev, ISU J.W.Qiu and I.V., hep-ph/0309094 Favorable comparison for the x- and A-dependence NA37 (NMC) and E665 data M.Adams et al., Z.Phys. C67 (1995); Phys.Rev.Lett. 68 (1992) M.Arneodo et al., Nucl.Phys. B441 (1995); P.Amaudruz et al., Nucl.Phys. B441 (1995) NA37 E665 For we impose . (discussion of corrections will follow) Compares well to the EKS98 scale- dependent shadowing parameterization. Different physical interpretation: EKS98 QV Universal modification to the nPDFs Process-dependent modification ( )

Q2-dependence of the Resummed Nuclear-Enhanced Power Corrections : 

Q2-dependence of the Resummed Nuclear-Enhanced Power Corrections J.W.Qiu and I.V., hep-ph/0309094 Ivan Vitev, ISU N.Armesto et al., hep-ph/0304119 K.Eskola et al., Eur.Phys.J. C9 (1999) NMC data shows evidence for a power law in 1/Q2 behavior in Comparison to: 1. Gribov-Regge model calculation. Attributes the difference between data and theory to an insufficient strength of DGLAP evolution in the PDFs 2. EKS’98 scale-dependent shadowing parameterization M.Arneodo et al.,Nucl.Phys. B489 (1999)

A Direct Test of : 

A Direct Test of Ivan Vitev, ISU J.W.Qiu and I.V., hep-ph/0309094 Mott cross section: Polarization parameter: (spin ½ particle on a static Coulomb field) (the virtual photon ) The Leading Twist (LT) is not sensitive to modifications of the nPDFs Upper limit given since the 4-field correlator is approximated as a product of 2 x 2-field correlator. (J.W.Qiu and I.V., in preparation) K.Abe et al., Phys.Lett. B452 (1999)

Higher Corrections: 

Higher Corrections Ivan Vitev, ISU Box diagram It is the that modifies the simple (+,-) lightcone dynamics and significantly complicates the calculation of higher twist corrections Bremsstrahlung diagram

Higher Corrections andthe Dipole Approach: 

Higher Corrections and the Dipole Approach Ivan Vitev, ISU Mueller-Qiu correction to DGLAP (PDFs) If (very large gluon density or very small Q2) the factorization approach is not effective. Applicable if . A A.H.Mueller and J.W.Qiu, Nucl.Phys. B268 (1986) e.g. A.H.Mueller, Nucl.Phys. B558 (1999)

Slide22: 

Conclusions Combined evidence from p+p, d+Au, Au+Au - Au+Au reactions at RHIC differ significantly from lower energies or other systems (p+p, p+A). Most notably - strong final state interactions. Effects originate from dynamical multiple initial and final state scattering - not related to the nuclear wavefunction. Important question for modern nuclear physics – “How much is the true modification to the nPDFs?” First calculation of resummed QCD power corrections to nuclear shadowing. Process-dependent versus process-independent modification. Results consistent with the x-, Q2- and A- dependence of the small-x suppression in - process-independent part expected. Program of future experiments at RHIC, HERA, EIC, LHC – to separate the two contributions through signature observables. Ivan Vitev, ISU