Parton Distributions and Transverse Momentum Broadening in Nuclei
Parton Distributions and Transverse Momentum Broadening in Nuclei Feng Yuan (fyuan@lbl. gov) Lawrence Berkeley National Laboratory 3/10/2021 1
n References for Parton Model ¨ G. Sterman, Partons, Factorization and Resummation, hep-ph/9606312 ¨ John Collins, The Foundations of Perturbative QCD, published by Cambridge, 2011 ¨ CTEQ, Handbook of perturbative QCD, Rev. Mod. Phys. 67, 157 (1995). n Pt-broadening ¨ Baier-Dokshitzer-Mueller-Peigne-Schiff, Nucl. Phys. B 483 (1997) 291, B 484 (1997) 26 3/10/2021 2
Quark model Gell-Man Nucleons, and other hadrons are not fundamental particles, they have constituents n Gell-Man Quark Model n ¨ Quark: n spin ½ Charges: up (2/3), down (-1/3), strange (-1/3) ¨ Flavor symmetry to classify the hadrons Mesons: quark-antiquark n Baryons: three-quark n Gell-Man-Okubo Formula n 3/10/2021 3
Deep Inelastic Scattering Discovery of Quarks Friedman Kendall Taylor Bjorken Scaling: Q 2 Infinity Feynman Parton Model: Point-like structure in Nucleon 4 3/10/2021
Understanding the scaling n Weak interactions at high momentum transfer ¨ Rutherford n formula rules Strong interaction at long distance ¨ Form factors behavior ¨ No free constituent found in experiment n Strong interaction dynamics is different from previous theory 3/10/2021 5
QCD and Strong-Interactions n QCD: Non-Abelian gauge theory ¨ Building blocks: quarks (spin½, mq, 3 colors; gluons: spin 1, massless, 32 -1 colors) n Asymptotic freedom and confinement ce n ta s i ive t d a rb ort u h t r S pe , Long distance: ? Soft, non-perturbative rd ha Clay Mathematics Institute Millennium Prize Problem ~1/Length Nonperturbative scale QCD~1 Ge. V 6
Quantum Chromodynamics n n n n There is no doubt that QCD is the right theory for hadron physics However, many fundamental questions… How does the nucleon mass? Why quarks and gluons are confined inside the nucleon? How do the fundamental nuclear forces arise from QCD? We don’t have a comprehensive picture of the nucleon structure as we don’t have an approximate QCD nucleon wave function … 3/10/2021 7
Feynman’s parton language and QCD Factorization n n If a hadron is involved in high-energy scattering, the physics simplifies in the infinite momentum frame (Feynman’s Parton Picture) The scattering can be decomposed into a convolution of parton scattering and parton density (distribution), or wave function or correlations ¨ QCD Factorization!
High energy scattering as a probe to the nucleon structure Drell-Yan DIS (Q>> QCD) k n Feynman Parton Momentum fraction DVCS Hadronic reactions Many processes: Deep Inelastic Scattering, Deeply-virtual compton scattering, Drell-Yan lepton pair production, pp jet+X ¨ ¨ ¨ Momentum distribution: Parton Distribution Spin density: polarized parton distribution Wave function in infinite momentum frame: Generalized Parton Distributions 9
Long distance physics (factorization) n Not every quantities calculated in perturbative QCD are infrared safe ¨ Hadrons in the initial/final states, e. g. Factorization guarantee that we can safely separate the long distance physics from short one n There are counter examples where the factorization does not work n 3/10/2021 10
Naïve Parton Model n the parton distribution describes the probability that the quark carries nucleon momentum fraction 3/10/2021 11
Naïve Parton Model n Partonic tensor is calculated n Structure functions ¨ Callan-Gross relation: ¨ Quark spin is ½ 3/10/2021 12
Quark model and parton distributions Point Particle 1 1 Gell-Man Zweig Three-quark (interaction) 1 Quark+antiquark +gluons 1 3/10/2021 13
Operator definition for PDFs n n Non-local operators to define the PDFs as functions of x They are expressions in the physical gauge invariant definition 3/10/2021 14
n The gauge invariant definition n In Feynman gauge 15
Where does the gauge link come from? n Factorizable multiple gluon interactions 16
Example: FSI in DIS ¨ This is just the leading order expansion of the exponential gauge link ¨ Summing all final state gluon interactions will lead to the final gauge link in the parton distribution definition 17
Initial state interaction in Drell. Yan ¨ This leads to the gauge link in Drell-Yan process goes to -infty, instead of +infty in DIS 18
PDFs on Lattice Only moments of PDFs become local operators, and can be calculated on lattice n There has been proposals to directly calculate PDFs on lattice n ¨ Quasi-PDFs, defined along z-direction, instead of light-cone direction ¨ Correlation functions 3/10/2021 19
Intuitive argument for the factorization (DIS) n In the Bjorken limit, nucleon is Lorentz contracted x. P k k’ x. P Hard interaction scale ~ 1/Q Hadron wave function scale ~ 1/Lambda ~1/Ge. V Hadronization scale ~1/Ge. V k 3/10/2021 20
Factorization formula n Factorization scale dependence n Scale dependence resummation anomalous dimension: 3/10/2021 21
Quark-quark splitting n n Physical polarization for the radiation gluon Incoming quark on-shell, outgoing quark offshell 3/10/2021 22
DGLAP evolutions 3/10/2021 23
These evolutions describe the HERA data CTEQ 6 3/10/2021 24
Reverse the DIS: Drell-Yan J. C. Peng 3/10/2021 25
Drell-Yan lepton pair production n The same parton distributions as DIS ¨ Universality n Partonic cross section 3/10/2021 26
Profound results u u Universality Perturbative QCD at work 3/10/2021 27
More general hadronic process Hadronic reactions n All these processes have been computed up to next-to-leading order, some at NNLO, few at N 3 LO 3/10/2021 28
PDG 2014 3/10/2021 29
Parton picture of the nucleon C. -P. Yuan@DIS 15 n n Beside valence quarks, there are sea and gluons Precisions on the PDFs are very much relevant for LHC physics: SM/New Physics 3/10/2021 DIS summary 30
PDFs in nucleus: Medium effects Inclusive vs 3/10/2021 Semi-inclusive 31
Pt-broadening in nuclei n Take BDMPS as an example ¨ Baier-Dokshitzer-Mueller-Peigne-Schiff, Nucl. Phys. B 483 (1997) 291, B 484 (1997) 26 ? 3/10/2021 32
Basic assumptions n Incoherence ¨ Each scattering is independent ¨ Formation time smaller than distance between the scatterings n Unitarity ¨ Conserve the total probability 3/10/2021 33
Quark-nucleon scattering 3/10/2021 34
Momentum distribution and evolution n Introduce dimensionless quantities 3/10/2021 35
Diffusion equation n Taking small Q expansion n Average Pt-broadening 3/10/2021 36
Fourier transform space n Evolution equation is simple n And solution is 3/10/2021 37
What is qhat? Transverse momentum broadening per distance traversed by the jet n Related to scattering property/gluon density of nucleon n Some time also called saturation scale n 3/10/2021 38
Modeling each scattering n Average Pt-broadening 3/10/2021 Gluon distribution function 39
Beyond the leading order picture n n Large logarithms resummation of high order corrections ¨ Liou, Mueller, Wu, Nucl. Phys. A 916 (2013) 102; Bin Wu, JHEP 1110, 029 (2011) Medium PT broadening (qhat) vs Sudakov (vacuum) ¨ Mueller-Wu-Xiao-Yuan, 1604. 04250; 1608. 07339 40
Jet quenching in heavy ion collisions 3/10/2021 41
Pt-broadening in Dijet imbalance n Dijet azimuthal angular correlation in heavy ion collisions PTjet=120 Ge. V PTjet=35 Ge. V Mueller-Wu-Xiao-Yuan, Ø 1604. 04250; 1608. 07339 Phenomenological relevance at RHIC/LHC Ø Different physics are well separated 42
Partonic cross section eq e’q’ n Cross symmetry with e+e- qq 3/10/2021 43
Inclusive and Semi-inclusive DIS Inclusive DIS: Q Partonic Distribution depending on the longitudinal momentum fraction Semi-inclusive DIS: Q Probe additional information for parton transverse distribution in nucleon 44
Back to DIS n Kinematics 3/10/2021 45
Structure functions (cross section) n EM factorization (photon exchange) n Hadronic tensor 3/10/2021 46
n Symmetry property for hadronic tensor ¨ Spin average ¨ Time-reversal invariance ¨ Current conservation ¨ Two independent structure functions 3/10/2021 47
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