Perturbative QCD in Nuclear Environment Jianwei Qiu Iowa State University Student Lecture at Quark Matter 2004 Oakland – January 11, 2004 Table of Contents:

Slides:



Advertisements
Similar presentations
Target Fragmentation studies at JLab M.Osipenko in collaboration with L. Trentadue and F. Ceccopieri, May 20,SIR2005, JLab, Newport News, VA CLAS Collaboration.
Advertisements

1cteq ss 11 B. Properties of the PDFs -- Definitions First, what are the Parton Distribution Functions? (PDFs) The PDFs are a set of 11 functions, f i.
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.
1 PQCD Approach to Parton Propagation in Matter Ivan Vitev Hard Probes 2006, Pacific Grove, CA.
QCD-2004 Lesson 1 : Field Theory and Perturbative QCD I 1)Preliminaries: Basic quantities in field theory 2)Preliminaries: COLOUR 3) The QCD Lagrangian.
Academia Sinica, Taipei
May 2005CTEQ Summer School1 Global Analysis of QCD and Parton Distribution Functions Dan Stump Department of Physics and Astronomy Michigan State University.
Dijet Transverse Thrust cross sections at DØ Veronica Sorin University of Buenos Aires.
Lecture I: pQCD and spectra. 2 What is QCD? From: T. Schaefer, QM08 student talk.
Resummation of Large Logs in DIS at x->1 Xiangdong Ji University of Maryland SCET workshop, University of Arizona, March 2-4, 2006.
Cold nuclear matter effects on dilepton and photon production Zhong-Bo Kang Los Alamos National Laboratory Thermal Radiation Workshop RBRC, Brookhaven.
Ahmad Idilbi Uni. Regensburg TUM November 30, 2011 M. G. Echevarria, A. Idilbi, I. Scimemi, arXive: : [hep-ph] M. G. Echevarria, A. Idilbi, I.
QCD and Scaling violations
1 Methods of Experimental Particle Physics Alexei Safonov Lecture #14.
LEPTON PAIR PRODUCTION AS A PROBE OF TWO PHOTON EFFECTS IN EXCLUSIVE PHOTON-HADRON SCATTERING Pervez Hoodbhoy Quaid-e-Azam University Islamabad.
Xiangdong Ji University of Maryland/SJTU Physics of gluon polarization Jlab, May 9, 2013.
9/17/20151 Probing the Dense Medium in Cold Nuclei -- Gluon Saturation at small-x Bowen Xiao (CCNU) Feng Yuan (LBNL)
Electron-nucleon scattering Rutherford scattering: non relativistic  scatters off a nucleus without penetrating in it (no spin involved). Mott scattering:
Glauber shadowing at particle production in nucleus-nucleus collisions within the framework of pQCD. Alexey Svyatkovskiy scientific advisor: M.A.Braun.
9/19/20151 Nucleon Spin: Final Solution at the EIC Feng Yuan Lawrence Berkeley National Laboratory.
9/19/20151 Semi-inclusive DIS: factorization Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory.
Zhongbo Kang Los Alamos National Laboratory Transverse single spin asymmetry of the W production at RHIC RHIC-AGS Annual Users’ Meeting 2015 June 9-12,
High p T  0 Production in p+p, Au+Au, and d+Au Stefan Bathe UC Riverside for the Collaboration Topics in Heavy Ion Collisions McGill University, Montreal,
Jianwei Qiu Brookhaven National Laboratory Stony Brook University
1 Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 1 Wei Zhu East China Normal University.
Three lectures: Symmetries exact approximate Asymptotic freedom
J/ψ Production in pPb Collisions at the LHC Zhang, Hong-Fei Third Military Medical University.
Parton Model & Parton Dynamics Huan Z Huang Department of Physics and Astronomy University of California, Los Angeles Department of Engineering Physics.
Monday, Jan. 27, 2003PHYS 5326, Spring 2003 Jae Yu 1 PHYS 5326 – Lecture #4 Monday, Jan. 27, 2003 Dr. Jae Yu 1.Neutrino-Nucleon DIS 2.Formalism of -N DIS.
6/1/20161 TMD Evolution Feng Yuan Lawrence Berkeley National Laboratory.
May 18-20, 2005 SIR05 JLab 1 P ? Dependence of SSA -- from nonpert. to pert. Feng Yuan, RBRC, Brookhaven National Laboratory References: Ji, Ma, Yuan,
Zhongbo Kang Los Alamos National Laboratory QCD structure of the nucleon and spin physics Lecture 5 & 6: TMD factorization and phenomenology HUGS 2015,
Unintegrated parton distributions and final states in DIS Anna Stasto Penn State University Work in collaboration with John Collins and Ted Rogers `
Duality: Recent and Future Results Ioana Niculescu James Madison University Hall C “Summer” Workshop.
11/28/20151 QCD resummation in Higgs Boson Plus Jet Production Feng Yuan Lawrence Berkeley National Laboratory Ref: Peng Sun, C.-P. Yuan, Feng Yuan, PRL.
QCD-2004 Lesson 2 :Perturbative QCD II 1)Preliminaries: Basic quantities in field theory 2)Preliminaries: COLOUR 3) The QCD Lagrangian and Feynman rules.
Single-Spin Asymmetries at CLAS  Transverse momentum of quarks and spin-azimuthal asymmetries  Target single-spin asymmetries  Beam single-spin asymmetries.
PQCD mechanisms for single (transverse) spin asymmetry in Drell-Yan production PQCD mechanisms for single (transverse) spin asymmetry in Drell-Yan production.
Color Glass Condensate HIM MEETING( 광주 ) Dec. 4, 2004.
June 25, 2004 Jianwei Qiu, ISU 1 Introduction to Heavy Quark Production Jianwei Qiu Iowa State University CTEQ Summer School on QCD Analysis and Phenomenology.
Threshold Resummation for Top- Quark Pair Production at ILC J.P. Ma ITP, CAS, Beijing 2005 年直线对撞机国际研讨会, Tsinghua Univ.
Measurements with Polarized Hadrons T.-A. Shibata Tokyo Institute of Technology Aug 15, 2003 Lepton-Photon 2003.
David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Experimental Tests of QCD at Colliders: Part 1 David Milstead Stockholm University.
HERMES による パートン helicity 分布関数の QCD 解析 Tokyo Inst. of Tech. 1. Quantum Chromo-Dynamics (QCD) 2. Parton Helicity Distribution and Nucleon Spin Problem 3.
Thomas Jefferson National Accelerator Facility PAC-25, January 17, 2004, 1 Baldin Sum Rule Hall C: E Q 2 -evolution of GDH integral Hall A: E94-010,
DIS Conference, Madison WI, 28 th April 2005Jeff Standage, York University Theoretical Motivations DIS Cross Sections and pQCD The Breit Frame Physics.
Third TECHQM Collaboration Meeting, CERN July 6-10, 2009 Xin-Nian Wang Lawrence Berkeley National Laboratory The Brick Problem in High-Twist Approximation.
2/10/20161 What can we learn with Drell-Yan in p(d)-nucleus collisions Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory.
The Color Glass Condensate and Glasma What is the high energy limit of QCD? What are the possible form of high energy density matter? How do quarks and.
Understanding forward particle production Opportunities for Drell-Yan Physics at RHIC May 13 th, 2011 Roman Pasechnik Uppsala University, THEP group 1.
Single Transverse-Spin Asymmetries and Twist-3 Factorization J.P. Ma, ITP, Beijing Weihai,
Physics Potential of an ep Collider at the VLHC  Why ep? When?  Physics Results from the first ep Collider – HERA  Future ep Physics Priorities  Perturbative.
Single spin asymmetries in pp scattering Piet Mulders Trento July 2-6, 2006 _.
Tensor and Flavor-singlet Axial Charges and Their Scale Dependencies Hanxin He China Institute of Atomic Energy.
1. How to probe the quarks? Scatter high-energy electron off a proton: Deep-Inelastic Scattering (DIS) Highest energy e-p collider: HERA at DESY in Hamburg:
Parton showers as a source of energy-momentum deposition and the implications for jet observables Bryon Neufeld, LANL 1Neufeld Based on the preprint R.B.
11/19/20161 Transverse Momentum Dependent Factorization Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory.
Introduction to pQCD and TMD physics
QCD CORRECTIONS TO bb →h h
Lecture 2 Evolution and resummation
3/19/20181 Nucleon Spin: Final Solution at the EIC Feng Yuan Lawrence Berkeley National Laboratory.
Can We Learn Quark Orbital Motion from SSAs?
Unique Description for SSAs in DIS and Hadronic Collisions
TMDs in nuclei Jian Zhou Temple University
Deeply Virtual Neutrino Scattering at Leading Twist
Unique Description for Single Transverse Spin Asymmetries
Lecture 2: Invariants, cross-section, Feynman diagrams
Heavy-to-light transitions on the light cone
Factorization in some exclusive B meson decays
Y.Kitadono (Hiroshima ),
Presentation transcript:

Perturbative QCD in Nuclear Environment Jianwei Qiu Iowa State University Student Lecture at Quark Matter 2004 Oakland – January 11, 2004 Table of Contents: 1. QCD and Perturbative QCD 2. Factorization and Parton Distributions 3. Magic of Nuclear Targets 4. Multiple Scattering in QCD 5. Summary and Outlook See the mini-review by J.W. Qiu and G. Sterman (2003), and references therein

Quantum Chromodynamics (QCD)  Fields: Quark fields, Dirac fermions (like e - ) Color triplet: i = 1,2,3=N C Flavor: f = u,d,s,c,b,t Gluon fields, spin-1 vector field (like γ ) Color octet: a = 1,2,…,8 =N C 2 -1  Lagrangian density: Color matrix: + gauge fixing + ghost terms  Gauge invariance: where

Perturbative QCD  Physical quantities can’t depend on the renormalization scale - μ :  Asymptotic freedom: Larger Q 2, larger effective μ 2, smaller α s ( μ ) Perturbative QCD works better for physical quantities with a large momentum exchange Can we choose μ 2 as large as we want? No!

PQCD Factorization  Can pQCD work for calculating x-sections involving hadrons? Typical hadronic scale: 1/R ~ 1 fm -1 ~ Λ QCD Energy exchange in hard collisions: Q >> Λ QCD pQCD works at α s (Q), but not at α s (1/R)  PQCD can be useful iff quantum interference between perturbative and nonperturbative scales can be neglected Measured Short-distance Long-distance Power corrections Factorization - Predictive power of pQCD  short-distance part is Infra-Safe, and calculable  long-distance part can be defined to be universal  short-distance and long-distance are separately gauge invariant

Lepton-Hadron DIS  Kinematics:  Perturbative pinch singularities: “long-lived parton state if  Feynman diagram representation:

Factorization in DIS  Collinear approximation, if +UVC T Scheme dependence  DIS limit: Feynman’s parton model and Bjorken scaling  QCD corrections: pinch singularities in ++ +  resum leading logarithms into parton distributions + +…+ UVCT

Parton Distributions + UV CT  Gluon distribution in collinear factorization:  Integrate over all transverse momentum!  μ 2 -dependence from the UV counter-term (UVCT)  μ 2 -dependence determined by DGLAP equations Boundary condition extracted from physical x-sections  extracted parton distributions depend on the perturbatively calculated C q and power corrections  Leading order (tree-level) C q LO PDF’s  Next-to-Leading order C q NLO PDF’s  Calculation of C q at NLO and beyond depends on the UVCT the scheme dependence of C q the scheme dependence of PDFs

Factorization in hadronic collisions  Basic assumptions: X X 2 2  single parton  no interaction between A & B before hard coll.  no quantum interference between hard collision & distributions Hard coll. PDFs How well can we justify above assumptions?

Heuristic Arguments for the Factorizations  There are always soft interaction between two hadrons  Gauge field A μ is not Lorentz contracted Long range soft gluon interaction between hadrons  a “pure gauge field” is gauge-equivalent to a zero field Perturbation theory to “mask” factorization, except at the level of gauge invariant quantities  Field strength contracted more than a scalar field Factorization should fail at It does! factorize d Not factorized  Single parton interaction:  If x is not too small, hadron is very transparent!  Extra parton interaction is suppressed by 1/Q 2

Observed particle Target parton of Momentum xp Interaction region k Lepton or Beam parton P A

Multiple Scattering in QCD  Classical multiple scattering – cross section level: P in P out P2P2 P1P1 Kinematics fix only P 1 + P 2 either P 1 or P 2 can be ~ zero Finite  Parton level multiple scattering (incoherent/indep.) In pQCD, above k  parton distribution at x=0 is ill-defined  pinch poles of k in above definition  Quantum mechanical multiple scattering - Amplitude level P in k P out k’ P in P1P1 P1’P1’ P2P2 P2’P2’ y1y1 y2y2 y3y3 0 Need to include interference diagrams  3-independent parton momenta  no pinched poles  depends on 4-parton correlation functions

Classification of nuclear dependence  Universal nuclear dependence from nuclear wave functions (in PDFs):  Process-dependent nuclear dependence (power corrections):  Initial-state:  Final-state:  Separation of medium-induced nuclear effect (process-dependent) from that in nuclear PDFs (process-independent)

All twist contributions to shadowing X P xPxP … k k’ Variables: Lightcone gauge: Frame: - the DIS structure functions When x<x c, virtual photon probes more than one nucleon at the given impact parameter J.W. Qiu and I. Vitev, hep-ph/

Calculating power corrections  When x B < 0.1/A 1/3, the DIS probe covers all nucleons at the same impact parameter  Fully coherent multiple scattering Take all possible insertions and cuts U-quark, CTEQ5 LO  slope of PDF’s determines the shadowing  Valence and sea have different suppression

Comparison with existing data For  Characteristic scale of power corrections:

The Gross-Llewellyn Smith and Adler Sum Rules  Apply the same calculation to neutrino-nucleus DIS -- predictions without extra free parameter D.J.Gross and C.H Llewellyn Smith, Nucl.Phys. B 14 (1969) To one loop in Nuclear-enhanced power corrections are important Predictions are compatible with the trend in the current data S.Adler, Phys.Rev. 143 (1964)  Gross-Llewellyn Smith sum rule:  Adler sum rule:

Transverse momentum broadening Observed particle Lepton or Beam parton k L A  small kT kick on a steeply falling distribution Big effect  A 1/3 -type enhancement helps overcome the 1/Q 2 power suppression  Data are concentrated in small p T region, but, d σ /dQ 2 dp T 2 for Drell-Yan is Not perturbatively stable (resummation is necessary)  The moments are perturbatively stable (infrared safe)  Transverse momentum broadening

Drell-Yan transverse momentum broadening Q A Plus interference diagrams  Broadening:  Four-parton correlation functions:  Fermilab and CERN data  Predictions: A 1/3 -type dependence Small energy dependence to the broadening λ 2 ~ ξ 2 Show small energy dependence and give λ 2 ~ 0.01 GeV 2 X. Guo (2001)

Summary and outlook  Predictive power of QCD perturbation theory relies on the factorization theorem  The Theory has been very successful in interpreting data from high energy collisions  PQCD can also be used to calculate anomalous nuclear dependence in terms of parton-level multiple scattering, if there is a sufficiently large energy exchange in the collision  In nuclear collisions, we need to deal with both coherent inelastic as well as incoherent elastic multiple scattering  elastic scattering re-distribute the particle spectrum without change the total cross section  inelastic scattering changes the spectrum as well as the total cross sections  nuclear dependence is a unique observable to parton-parton correllations, the properties of the medium.