Intr Introduc oduction tion to to Qua Quantum ntum Chr hrom - PowerPoint PPT Presentation

Intr Introduc oduction tion to to Qua Quantum ntum Chr hrom omodyna odynamic ics (QC (QCD) ) Jianwei Qiu Theory Center, Jefferson Lab May 29 – June 15, 2018 L ecture Four

Hadron properties – the mass? q How does QCD generate the nucleon mass? “… The vast majority of the nucleon’s mass is due to quantum fluctuations of quark-antiquark pairs, the gluons, and the energy associated with quarks moving around at close to the speed of light. …” The 2015 Long Range Plan for Nuclear Science q Higgs mechanism is not relevant to hadron mass! “Mass without mass!”

Hadron Mass q Proton’s mass: ² QCD Lagrangian does not have mass dimension parameters, other than current quark masses ² Asymptotic freedom confinement: 1 A dynamical scale, , consistent with R ∼ 200 MeV Λ QCD q Bag model: ² Kinetic energy of three quarks: K q ∼ 3 /R T b = 4 3 π R 3 B ² Bag energy (bag constant B): ² Minimize : M p ∼ 4 4 K q + T b 0 . 88 fm ∼ 912MeV R ∼ q Constituent ² Spontaneous chiral symmetry breaking: quark model: Massless quarks gain ~300 MeV mass when traveling in vacuum M p ∼ 3 m e ff ∼ 900 MeV q q Lattice QCD: Ratios of hadron masses

Hadron Mass in QCD q From Lattice QCD calculation: Input A major success of QCD – is the right theory for the Strong Interaction! How does QCD generate this? The role of quarks vs that of gluons? If we do not understand proton mass, we do not understand QCD

New community effort q Three-pronged approach to explore the origin of hadron mass ² Lattice QCD ² Mass decomposition – roles of the constituents ² Model calculation – approximated analytical approach https://phys.cst.temple.edu/meziani /proton-mass-workshop-2016/ http://www.ectstar.eu/node/2218

Hadron properties – the spin? q Spin: ² Pauli (1924): two-valued quantum degree of freedom of electron � ² Pauli/Dirac: (fundamental constant ħ ) S = � s ( s + 1) ² Composite particle = Total angular momentum when it is at rest q Spin of a nucleus: ² Nuclear binding: 8 MeV/nucleon << mass of nucleon ² Nucleon number is fixed inside a given nucleus ² Spin of a nucleus = sum of the valence nucleon spin q Spin of a nucleon – Naïve Quark Model: ² If the probing energy << mass of constituent quark ² Nucleon is made of three constituent (valence) quark ² Spin of a nucleon = sum of the constituent quark spin 1 $ & p ↑ = 18 u ↑ u ↓ d ↑ + u ↓ u ↑ d ↑− 2 u ↑ u ↑ d ↓ + perm. State: % ' S p ≡ p ↑ S p ↑ = 1 Spin: Carried by valence quarks 2, S = ∑ S i i

Hadron spin in QCD q Spin of a nucleon – QCD: ² Current quark mass << energy exchange of the collision ² Number of quarks and gluons depends on the probing energy q Angular momentum of a proton at rest: f | P, S z = 1 / 2 ⇥ = 1 � � P, S z = 1 / 2 | ˆ J z S = 2 f q QCD Angular momentum operator: Energy-momentum tensor � QCD = 1 d 3 x M 0 jk J i 2 � ijk M α µ ν QCD x µ − T α µ QCD = T αν QCD x ν QCD ² Quark angular momentum operator: Angular momentum density → ∆ q + L q ? − ² Gluon angular momentum operator: → ∆ g + L g ? − Need to have the matrix elements of these partonic operators measured independently

Proton spin – current status q How does QCD make up the nucleon’s spin? 2 = 1 1 2 ∆Σ + ∆ G + ( L q + L g ) Proton Spin Quark helicity Gluon he helic licity ity Best known Orbital Angular Momentum Start to know of quarks and gluons Little known ∼ 30% ∼ 20%(with RHIC data) Spin “puzzle” If we do not understand proton spin, we do not understand QCD

Polarization and spin asymmetry Explore new QCD dynamics – vary the spin orientation q Cross section: Scattering amplitude square – Probability – Positive definite s ) + Q 2 s ) + Q s s ) ≈ � (2) Q � (3) Q 2 � (4) s � AB ( Q, ~ AB ( Q, ~ AB ( Q, ~ AB ( Q, ~ s ) + · · · q Spin-averaged cross section: – Positive definite q Asymmetries or difference of cross sections: – Not necessary positive! § both beams polarized § one beam polarized A N = � ( Q, ~ s T ) − � ( Q, − ~ s T ) � ( Q, ~ s T ) + � ( Q, − ~ s T ) Chance to see quantum interference directly

Polarized deep inelastic scattering q Extract the polarized structure functions: ∠ (ˆ k, ˆ ² Define: , S ) = α and lepton helicity λ ² Difference in cross sections with hadron spin flipped ² Spin orientation:

Polarized deep inelastic scattering q Systematics polarized PDFs – LO QCD: ² Two-quark correlator: ² Hadronic tensor (one –flavor):

Polarized deep inelastic scattering ² General expansion of : φ ( x ) φ ( x ) = 1 ⇥ ⇤ q ( x ) γ · P + s k ∆ q ( x ) γ 5 γ · P + δ q ( x ) γ · P γ 5 γ · S ? 2 ² 3-leading power quark parton distribution:

Basics for spin observables q Factorized cross section: q Parity and Time-reversal invariance: q IF: or Operators lead to the “+” sign spin-averaged cross sections Operators lead to the “-” sign spin asymmetries q Example: Quark helicity: Transversity: Gluon helicity:

_ Determination of Δ q and Δ q q W’s are left-handed: q Flavor separation: Lowest order: Forward W + (backward e + ): Backward W + (forward e + ): q Complications: High order, W’s p T -distribution at low p T

Sea quark polarization – RHIC W program q Single longitudinal spin asymmetries: Parity violating weak interaction q From 2013 RHIC data: 15 – ∆χ 2 x ∆ u DSSV++ 0.02 incl. proj. W data Q 2 = 10 GeV 2 10 0 ∆χ 2 =2% in DSSV anal. -0.02 5 DSSV Q 2 = 10 GeV 2 DSSV+ -0.04 DSSV++ with proj. W data DSSV+ 0 -2 -1 -0.03 -0.02 -0.01 0 0.01 10 10 1 x ∫ ∆ u(x,Q 2 ) dx sign 0.05 – Q 2 = 10 GeV 2 x ∆ d 15 0.02 Q 2 = 10 GeV 2 ∆χ 2 DSSV++ incl. proj. W data 0 10 ∆χ 2 =2% in DSSV analysis -0.02 5 -0.04 DSSV+ 0 -2 -1 10 10 x -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 1 ∫ ∆ d(x,Q 2 ) dx 0.05

RHIC Measurements on Δ G q PHENIX – π 0 : q STAR – jet:

Global QCD analysis of helicity PDFs q Impact on gluon helicity: ² Red line is the new fit ² 90% C.L. areas ² Dotted lines = other fits ² Leads Δ G to a positive # with 90% C.L.

What is next? q JLa Lab 1 12Ge GeV – upg V – upgrade de pr proje oject just c t just com omple plete ted: d: CLAS1 S12 12 GeV CEBAF Upgrade Project is just complete, and all 4-Halls are taking data Plus many more JLab experiments, COMPASS, Fermilab-fixed target expts …

The Future: Challenges & opportunitie unities s q The power & precision of EIC: at EIC q Reach out the glue:

The future – what the EIC can do? The Future: Proton Spin q One-year of running at EIC: Wider Q 2 and x range including low x at EIC! Before/after No other machine in the world can achieve this! q Ultimate solution to the proton spin puzzle: ² Precision measurement of Δ g(x) – extend to smaller x regime ² Orbital angular momentum contribution – measurement of TMDs & GPDs!

Hadron’s partonic structure in QCD q Structure – “a still picture” Crystal Nano- Structure: material: NaCl, FeS2, Fullerene, C60 B1 type structure C2, pyrite type structure Motion of nuclei is much slower than the speed of light! q No “still picture” for hadron’s partonic structure! Motion of quarks/gluons is relativistic! Partonic h P, S |O ( ψ , ψ , A µ ) | P, S i Quantum “probabilities” Structure: None of these matrix elements is a direct physical observable in QCD – color confinement! q Accessible hadron’s partonic structure? = Universal matrix elements of quarks and/or gluons 1) can be related to good physical cross sections of hadron(s) with controllable approximation , 2) can be calculated in lattice QCD, …

Paradigm shift: 3D confined motion q Cross sections with two-momentum scales observed: Q 1 � Q 2 ⇠ 1 /R ⇠ Λ QCD ² Hard scale: localizes the probe Q 1 to see the quark or gluon d.o.f. ² “Soft” scale: could be more sensitive to Q 2 hadron structure, e.g., confined motion q Two-scale observables with the hadron broken: Two-jet momentum + + imbalance in SIDIS, … DY: Q>>P T SIDIS: Q>>P T ² Natural observables with TWO very different scales ² TMD factorization: partons’ confined motion is encoded into TMDs

TMDs: confined motion, its spin c spin cor orrela lation tion q Power of spin – many more correlations: s p k T Require two Physical scales More than one TMD contribute to the same observable! Similar for gluons q A N – single hadron production: Transversity Collins-type Sivers-type

Proton’s radius in color distribution? q The “big” question: How color is distributed inside a hadron? (clue for color confinement?) q Electric charge distribution: q p p' Elastic electric form factor Charge distributions q But, NO color elastic nucleon form factor! Hadron is colorless and gluon carries color Parton density’s spatial distributions – a function of x as well (more “proton”-like than “neutron”-like?) – GPDs