Introduction to Quantum Chromodynamics (QCD)

Transcription

1 Introduction to Quantum Chromodynamics (QCD) Jianwei Qiu Theory Center, Jefferson Lab May 29 June 15, 2018 Lecture Four

2 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!

3 q Proton s mass: q Bag model: Hadron Mass ² QCD Lagrangian does not have mass dimension parameters, other than current quark masses ² Asymptotic freedom confinement: 1 A dynamical scale, QCD, consistent with R q Constituent quark model: q Lattice QCD: 200 MeV ² Kinetic energy of three quarks: K q 3/R ² Bag energy (bag constant B): T b = 4 ² Minimize : M p 4 3 R3 B R 4 K q + T b 0.88fm 912MeV ² Spontaneous chiral symmetry breaking: Ratios of hadron masses Massless quarks gain ~300 MeV mass when traveling in vacuum M p 3 m e q 900 MeV

4 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

5 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 /proton-mass-workshop-2016/

6 Hadron properties the spin? q Spin: ² Pauli (1924): two-valued quantum degree of freedom of electron S = s(s + 1) ² Pauli/Dirac: (fundamental constant ħ) 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 State: p = 1 18 Spin: S p p S p = 1 2, S = S i i $ % u u d +u u d 2u u d +perm. & ' Carried by valence quarks

7 q Spin of a nucleon QCD: Hadron spin in 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: S = f P, S z =1/2 Ĵ z f P, S z =1/2 = 1 2 q QCD Angular momentum operator: J i QCD = 1 2 ijk ² Quark angular momentum operator: Energy-momentum tensor d 3 xm 0jk QCD M µ QCD = T QCD x µ T µ QCD x 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

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

9 Polarization and spin asymmetry Explore new QCD dynamics vary the spin orientation q Cross section: Scattering amplitude square Probability Positive definite AB(Q, ~s) (2) AB (Q, ~s)+q s Q q Spin-averaged cross section: both beams polarized (3) AB (Q, ~s)+q2 s (4) Q 2 AB (Q, ~s)+ Positive definite q Asymmetries or difference of cross sections: Not necessary positive! one beam polarized A N = (Q, ~s T ) (Q, ~s T ) (Q, ~s T )+ (Q, ~s T ) Chance to see quantum interference directly

10 Polarized deep inelastic scattering q Extract the polarized structure functions: ² Define: \(ˆk, Ŝ) =, and lepton helicity ² Difference in cross sections with hadron spin flipped ² Spin orientation:

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

12 Polarized deep inelastic scattering ² General expansion of (x): (x) = 1 2 q(x) P + sk q(x) 5 P + q(x) P 5 S? ² 3-leading power quark parton distribution:

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

14 _ Determination of Δq and Δq 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

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

16 RHIC Measurements on ΔG q PHENIX π 0 : q STAR jet:

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

18 What is next? q JLab 12GeV upgrade project just completed: 12 GeV CEBAF Upgrade Project is just complete, and all 4-Halls are taking data CLAS12 Plus many more JLab experiments, COMPASS, Fermilab-fixed target expts

19 The Future: Challenges & opportunities q The power & precision of EIC: at EIC q Reach out the glue:

20 The future The Future: what Proton the EIC Spin can do? 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 Δg(x) extend to smaller x regime ² Orbital angular momentum contribution measurement of TMDs & GPDs!

21 Hadron s partonic structure in QCD q Structure a still picture Crystal Structure: Nanomaterial: NaCl, B1 type structure FeS2, C2, pyrite type structure Fullerene, C60 Motion of nuclei is much slower than the speed of light! q No still picture for hadron s partonic structure! Partonic Structure: Motion of quarks/gluons is relativistic! Quantum probabilities hp, S O(,,A µ ) P, Si 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,

22 Paradigm shift: 3D confined motion q Cross sections with two-momentum scales observed: Q 1 Q 2 1/R QCD ² Hard scale: ² Soft scale: Q 1 Q 2 localizes the probe to see the quark or gluon d.o.f. could be more sensitive to hadron structure, e.g., confined motion q Two-scale observables with the hadron broken: + + Two-jet momentum imbalance in SIDIS, SIDIS: Q>>P T DY: Q>>P T ² Natural observables with TWO very different scales ² TMD factorization: partons confined motion is encoded into TMDs

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

24 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: Elastic electric form factor Charge distributions q p p' 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

25 Paradigm shift: 2D spatial distributions q Cross sections with two-momentum scales observed: Q 1 Q 2 1/R QCD ² Hard scale: ² Soft scale: Q 1 Q 2 localizes the probe to see the quark or gluon d.o.f. could be more sensitive to hadron structure, e.g., confined motion q Two-scale observables with the hadron unbroken: J/Ψ, Φ, + + t=(p 1 -p 2 ) 2 GPD g-gpd + DVCS: Q 2 >> t DVEM: Q 2 >> t EHMP: Q 2 >> t ² Natural observables with TWO very different scales ² GPDs: Fourier Transform of t-dependence gives spatial b T -dependence

26 q The LO diagram: Deep virtual Compton scattering q Scattering amplitude: P 0 = P + q GPDs:

27 q GPDs of quarks and gluons: q Imaging (! 0 ): What can GPDs tell us? H q (x,, t, Q), E q (x,, t, Q), Evolution in Q H q (x,, t, Q), Ẽ q (x,, t, Q) gluon GPDs Z q(x, b?,q)= d 2?e i? b? 2 H q (x, =0,t=?,Q) q Influence of transverse polarization shift in density: EIC simulation

28 JLab12 valence quarks, EIC sea quarks and gluons Advantages of the lepton-hadron facilities q 3D boosted partonic structure: Momentum Space TMDs Confined d 2 b T Coordinate Space GPDs Why is diffraction so great? P motion distribution f(x,k T ) xp 3D momentum-space images k T b T Two-scales observables d 2 k T f(x,b T ) Spatial 2+1D coordinate-space images Semi-inclusive DIS Q >> P T ~ k T γ Exclusive DIS 1 z (1 z) r r V = J/ψ, φ, ρ z x x b t Q >> t ~ 1/b T p p

29 SIDIS is the best for probing TMDs q Naturally, two scales & two planes: l l 1 N N AUT ( ϕh, ϕs ) = P N + N Collins Sivers = A sin( φ + φ ) + A sin( φ φ ) UT Pretzelosity + A sin(3 φ φ ) UT h h S S UT h S q Separation of TMDs: Collins A sin( φ + φ ) h H A A UT h S Sivers UT sin( φ φ ) h S UT 1 1 1T sin(3 φ φ ) h H Pretzelosity UT h S UT 1T 1 UT f D 1 Collins frag. Func. from e + e - collisions Hard, if not impossible, to separate TMDs in hadronic collisions Using a combination of different observables (not the same observable): jet, identified hadron, photon,

30 EIC q Cross Sections: q Spatial distributions: Quark radius (x)!

31 Spatial distribution of gluons q Exclusive vector meson production: J/Ψ, Φ, d dx B dq 2 dt EIC-WhitePaper ² Fourier transform of the t-dep Spatial imaging of glue density t-dep q Gluon imaging from simulation: ² Resolution ~ 1/Q or 1/M Q Only possible at the EIC Gluon radius? Gluon radius (x)! How spread at small-x? Color confinement

32 Why 3D nucleon structure? q Spatial distributions of quarks and gluons: Static Boosted Bag Model: Gluon field distribution is wider than the fast moving quarks. Gluon radius > Charge Radius Constituent Quark Model: Gluons and sea quarks hide inside massive quarks. Gluon radius ~ Charge Radius Lattice Gauge theory (with slow moving quarks): Gluons more concentrated inside the quarks Gluon radius < Charge Radius 3D confined motion (TMDs) + spatial distribution (GPDs) Hints on the color confining mechanism Relation between charge radius, quark radius (x), and gluon radius (x)?

33 Why 3D hadron structure? q Rutherford s experiment atomic structure (100 years ago): Atom: J.J. Thomson s plum-pudding model Rutherford s planetary model Modern model Quantum orbitals 1911 Discovery of nucleus A localized charge/force center A vast open space Discovery of Quantum Mechanics, and the Quantum World! q Completely changed our view of the visible world: ² Mass by tiny nuclei less than 1 trillionth in volume of an atom ² Motion by quantum probability the quantum world! ² Provided infinite opportunities to improve things around us, What could we learn from the hadron structure in QCD,?

34 Paradigm shift: 3D imaging of the Proton q This is transformational! ² How color is confined? How far does glue density spread? How fast does glue density fall? ² Why there is preference in motion? JLab12 valence quarks, EIC sea quarks and gluons

35 Summary q QCD has been extremely successful in interpreting and predicting high energy experimental data! < 1/10 fm q But, we still do not know much about hadron structure work just started! q Cross sections with large momentum transfer(s) and identified hadron(s) are the source of structure information q QCD factorization is necessary for any controllable probe for hadron s quark-gluon structure! q TMDs and GPDs, accessible by high energy scattering with polarized beams at EIC, carry important information on hadron s 3D structure, and its correlation with hadron s spin! No still pictures, but quantum distributions, for hadron structure in QCD! Thank you!

36 Backup slides

37 q Mass intrinsic to a particle: Mass vs. Spin = Energy of the particle when it is at the rest ² QCD energy-momentum tensor in terms of quarks and gluons ² Proton mass: GeV X. Ji, PRL (1995) when proton is at rest! q Spin intrinsic to a particle: = Angular momentum of the particle when it is at the rest ² QCD angular momentum density in terms of energy-momentum tensor ² Proton spin:

38 Unified description of hadron structure q Wigner distributions in 5D (or GTMDs): Momentum Space TMDs Confined motion d 2 b T f(x,k T ) xp k T b T Two-scales observables d 2 k T f(x,b T ) Coordinate Space GPDs Spatial distribution q Theory is solid TMDs & SIDIS as an example: ² Low P ht (P ht << Q) TMD factorization: SIDIS(Q, P h?,x B,z h )=Ĥ(Q) f (x, k? ) D f!h (z,p? ) S(k s? )+O ² High P ht (P ht ~ Q) Collinear factorization: 1, 1 P h? Q SIDIS(Q, P h?,x B,z h )=Ĥ(Q, P h?, s ) f D f!h + O ² P ht Integrated - Collinear factorization: SIDIS(Q, x B,z h )= H(Q, 1 s ) f D f!h + O Q ² Very high P ht >> Q Collinear factorization: SIDIS(Q, P h?,x B,z h )= X Ĥ ab!c!a b D c!h + O abc 1 Q, Q P h? apple Ph? Q

39 q Quark form factor : Definition of GPDs P P 0 with H q (x,, t, Q), Ẽ q (x,, t, Q) Different quark spin projection q Total quark s orbital contribution to proton s spin: Ji, PRL78, 1997 q Connection to normal quark distribution: The limit when! 0

40 Orbital angular momentum OAM: Correlation between parton s position and its motion in an averaged (or probability) sense q Jaffe-Manohar s quark OAM density: L 3 q = q q Ji s quark OAM density: L 3 q = q h ~x ( i 3 q 3 h ~x ( i D)i ~ q q Difference between them: ² compensated by difference between gluon OAM density ² represented by Z different choice of gauge link for OAM Wagner distribution h i 3 L 3 q L 3 q = dx d 2 bd 2 k T ~b ~ kt Wq (x, ~ b, ~ n k T ) W q (x, ~ b, ~ o k T ) with W q {W q } (x, ~ b, ~ k T )= JM: staple gauge link Ji: straight gauge link Z d 2 Z T (2 ) 2 ei~ T ~b dy d 2 y T (2 ) 3 hp 0 q (0) between 0 and y=(y + =0,y -,y T ) + 2 Hatta, Lorce, Pasquini, e i(xp + y ~ kt ~y T ) JM{Ji} (0,y) (y) P i y + =0 Gauge link

41 Orbital angular momentum OAM: Correlation between parton s position and its motion in an averaged (or probability) sense q Jaffe-Manohar s quark OAM density: L 3 q = q q Ji s quark OAM density: L 3 q = q h ~x ( i 3 q 3 h ~x ( i D)i ~ q q Difference between them: ² generated by a torque of color Lorentz force Z dy d L 3 q L 3 2 y T q / (2 ) 3 hp 0 + Z 1 q (0) dz (0,z ) 2 y X 3ij yt i F +j (z ) (z,y) (y) P i y+ =0 i,j=1,2 Chromodynamic torque Hatta, Yoshida, Burkardt, Meissner, Metz, Schlegel, Similar color Lorentz force generates the single transverse-spin asymmetry (Qiu-Sterman function), and is also responsible for the twist-3 part of g 2

42 Transverse single-spin asymmetry (TSSA) q Over 50 years ago, Profs. Christ and Lee proposed to use A N of inclusive DIS to test the Time-Reversal invariance N. Christ and T.D. Lee, Phys. Rev. 143, 1310 (1966) S * They predicted: In the approximation of one-photon exchange, A N of inclusive DIS vanishes if Time-Reversal is invariant for EM and Strong interactions

43 A N for inclusive DIS q DIS cross section: q Leptionic tensor is symmetric: q Hadronic tensor: L µ = L µ q Polarized cross section: q Vanishing single spin asymmetry:?

44 A N for inclusive DIS q Define two quantum states: q Time-reversed states: q Time-reversal invariance:

45 q Parity invariance: A N for inclusive DIS Translation invariance: q Polarized cross section:

46 A N in hadronic collisions q A N - consistently observed for over 35 years! ANL 4.9 GeV BNL 6.6 GeV FNAL 20 GeV BNL 62.4 GeV q Survived the highest RHIC energy: A N Jets (x 0 -Jets (x EM-Jets (x F EM-Jets (x F > 0) F <0) F > 0) < 0) Graph STAR Preliminary s = 500GeV p EMJet > 2.0 GeV/c T 2.8 < EMJet < 4.0 s p Left photon-Jets-m >0.3 (x F > 0) Right EM-Jet Energy (GeV) Do we understand this?

47 q Early attempt: Cross section: Do we understand it? AB(p T, ~s) / Kane, Pumplin, Repko, PRL, 1978 m q Asymmetry: AB(p T,~s) AB(p T, ~s ) = / s p T q What do we need? Too small to explain available data! A N / i~s p (~p h ~p T ) ) i µ p hµ s p p 0 h Need a phase, a spin flip, enough vectors q Vanish without parton s transverse motion: A direct probe for parton s transverse motion, Spin-orbital correlation, QCD quantum interference

48 How collinear factorization generates TSSA? q Collinear factorization beyond leading power: p, ~s k (Q, ~s) / t 1/Q 2 Expansion Too large to compete! Three-parton correlation q Single transverse spin asymmetry: Efremov, Teryaev, 82; Qiu, Sterman, 91, etc. (s T ) / T (3) (x, x) ˆT D(z)+ q(x) ˆD D (3) (z,z)+... T (3) (x, x) / D (3) (z,z) / Qiu, Sterman, 1991, Kang, Yuan, Zhou, 2010 Integrated information on parton s transverse motion! Needed Phase: Integration of dx using unpinched poles

49 Interpretation of twist-3 correlation functions q Measurement of direct QCD quantum interference: T (3) (x, x, S? ) / Qiu, Sterman, 1991, Interference between a single active parton state and an active two-parton composite state q Expectation value of QCD operators: hp, s (0) + hp, s (0) + (y ) P, si 5 (y ) P, si apple Z hp, s (0) + (y ) P, si? s T dy 2 F + (y 2 ) apple Z hp, s (0) + ig? s T dy 2 F + (y 2 ) (y ) P, si How to interpret the expectation value of the operators in RED?

50 A simple example q The operator in Red a classical Abelian case: Qiu, Sterman, 1998 q Change of transverse momentum: q In the c.m. frame: q The total change: Net quark transverse momentum imbalance caused by color Lorentz force inside a transversely polarized proton

51 Transversity distributions q Transversity: q(x) or h 1 (x) Jaffe and Ji, UVCT with and q Unique for the quarks: No mixing with gluons! n? 5 = 0 Even # ofγ s No mixing with PDFs, helicity distributions q Perturbatively UV and CO divergent: + wave function renormalization DGLAP evolution kernels NLO - Vogelsang, 1998

52 Soffer s inequality q Relation between quark distributions: h 1 (x) apple 1 2 [q(x)+ q(x)] = q+ (x) Derived by using the positivity constraint of quark + nucleon -> quark + nucleon forward scattering helicity amplitudes Cautions: ² Quark field of the Transversity distribution is NOT on-shell ² Quark + nucleon -> quark + nucleon forward scattering amplitude is perturbatively divergent q Testing vs using as a constraint: It is important to test this inequality, rather than using it as a constraint for fitting the transversity Perturbatively calculated evolution kernels seem to be consistent with the inequality the scale dependence