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Partonic Structure of Hadrons Theory

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Partonic Structure of Hadrons Theory Pre-workshop lecture (10/28/2013) Partonic Structure of Hadrons Theory Jianwei Qiu Brookhaven National Laboratory The International Conference on Electromagnetic Interactions with Nucleons and Nuclei (EINN 2013) October 28 – November 02, 2013, Pafos (Cyprus) Nobel Prize 2013 - discovery of Higgs boson François Engler Peter W. Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider" But, the Higgs mechanism generates mq ~ 10 MeV Too little to be relevant for the mass of our world of visible matter! mN ~ 1000 MeV Outline q Why do we care about the structure? Structure leads to the revolution in knowledge q Nucleon is not point-like and has internal structure Birth of QCD, partons (quarks and gluons) and their dynamics q How to “see” hadron’s partonic internal structure? QCD factorization links hadron cross sections to parton structures q Hadron properties and partonic structures Proton spin, mass, radius (EM charge, color, quark, gluon), … q Summary Atomic structure q Revolution in our view of atomic structure (100 years ago): Atom: J.J. Thomson’s Rutherford’s Modern model plum-pudding model planetary model Quantum orbitals 1911 Discovery of nucleus Discovery of A localized Quantum Mechanics, charge/force center and A vast the Quantum World! “open” space q Completely changed our view of the visible world: ² Mass by “tiny” nuclei – less than 1 trillionth in volume ² Motion by quantum probability – the quantum world! q Provided infinite opportunities to improve things around us: ² Nano materials, quantum computing, … Nuclear structure and nuclear physics q Since the Rutherford exp’t, Nuclear Binding Energy q Origin of nuclear force? Nucleon-nucleon, multi-nucleon, …? Hadrons – building blocks q Protons, neutrons, and pions: q “Historic” – as bound state: Fermi and Yang, 1952; Nambu and Jona-Lasinio, 1960 (dynamics) Yang-Mills theory, SU(2) Non-Abelian Gauge theory (1953) Nucleon structure q Nucleon is not elementary: Magnetic moment: gproton =2 gneutron =0 q The zoo of particles: Quark Model Proton Neutron Nobel Prize, 1969 A complete example: Proton q Flavor-spin part: q Normalization: q Charge: q Spin: Magnetic Moments q Quark’s magnetic moment: Assumption: Constituent quark’s magnetic moment is the same as that of a point-like, structure-less, spin-½ Dirac particle for flavor “i” q Proton’s magnetic moment: q Neutron’s magnetic moment: If How to “see” nucleon’s structure? Deep inelastic scattering (DIS) q Discovery of spin ½ quarks: SLAC 1968 E θ E’ The birth of QCD (1973) Quark Model + Yang-Mill gauge theory q Nucleon structure is complicate: Nobel Prize, 2004 Color Confinement Asymptotic freedom Q (GeV) 200 MeV (1 fm) 2 GeV (1/10 fm) Probing momentum QCD Landscape of the nucleon and atomic nuclei? Quantum Chromodynamics (QCD) A quantum field theory of quarks and gluons q Fields: Quark fields: spin-½ Dirac fermion (like electron) Color triplet: Flavor: Gluon fields: spin-1 vector field (like photon) Color octet: q QCD Lagrangian density: q QED Lagrangian density – force to hold atoms together: f 1 (φ,A)= ψ [(i∂ eA )γµ m ] ψf [∂ A ∂ A ]2 LQED µ − µ − f − 4 µ ν − ν µ f QCD is much richer in dynamics than QED Gluons are dark, but, interact with themselves, NO free quarks and gluons Role of QCD in the formation of hadronic matter QCD influenced how the universe evolve § the dynamics of early universe § the emergence of nucleons, and nuclei Accelerator technology allows us to: § recreate the condition of early universe § repeat the formation of hadronic matter QCD and hadron mass spectrum q Lattice QCD calculation of hadron masses: Hadrons are made of quarks and gluons bound together by QCD 13 Heavy flavors – new challenges q Particles discovered in 1964 – Now: H0 q New X, Y, Z particles: Heavy flavors – new challenges See talk by Yuan, … q Particles discovered in 1964 – Now: H0 q New X, Y, Z particles: States outside Quark Model q Charmonium quantum numbers: The complete list of allowed quantum numbers, , has gaps! q Exotic JPC : q Charmonium hybrids: – States with an excited gluonic degree of freedom q If it exists, ² Link QCD dynamics of quarks and gluons to hadrons beyond the Quark Model – new insight to the formation of hadrons ² Why one “quasi-stable” gluon? What is the penalty to have more? Questions? How to probe or “see” what is inside a hadron? Sub-femtometer scope? Need a well-controlled “tool” or ”probe” at sub-fermi scale! 17 QCD Asymptotic Freedom q ΛQCD: μ2 and μ1 not independent Weak coupling Reliable QCD perturbation theory (perturbative QCD) Controllable QCD dynamics at short-distance (large momentum transfer)! The challenges q BUT: Detectors only see hadrons and leptons, not quarks and gluons! How to probe quark-gluon structure of hadron without seeing them? q Facts: Hadronic scale ~ 1/fm ~ ΛQCD is non-perturbative Cross section involving identified hadron(s) is not infrared safe and is not perturbatively calculable! q Solution – QCD Factorization: ² Isolate the calculable dynamics of quarks and gluons ² Connect quarks and gluons to hadrons via non-perturbative but universal distribution functions – provide information on the partonic structure of the hadron Sub-femtometer “scope” q New DIS “Rutherford” experiment: 1 Q>2GeV ∆r<10− fm 2 2 2 Q Q =4EE sin (θ/2), xB = , ν = E E 2mN ν − q QCD Factorization - theory development in last thirty years: Sub-femtometer probe The structure 2 e(l) e(l) 2 xp, kT 2 h(p) xp, kT h(p) e(l) e(l) k ≈ ⊗ Cross section Asymptotic freedom Parton in a hadron Factorization (theoretical advances in recent years!) An example: Inclusive DIS q Process: q p e(k)+N(p) e(k)+X y = · k p −→ 2 2 2 Q · Q =4EE sin (θ/2), xB = , ν = E E 2mN ν − q Spin-averaged cross section: QCD Factorization! F (x, Q2)=F (x, Q2) 2xF (x, Q2) L 2 − 1 + (α )+ (1/Q2) O s O Cross section structure functions PDFs q Spin-averaged cross section: QCD Factorization! Helicity PDFs A few steps of details (3 slides) Hadronic tensor and structure functions q Hadronic tensor: 1 Wqp(, ,SSS )= dz4† eiq⋅ z p, JzJ () (0), p µν4π ∫ µν q Structure functions: EM current " % q q 2 1 " p ( q%" p ( q% 2 W = !$g ! µ ! 'F x ,Q + p ! q p ! q F x ,Q µ! $ µ! 2 ' 1 ( B ) $ µ µ 2 '$ ! ! 2 ' 2 ( B ) # q & p ( q # q &# q & ) , S p.q S ! S.q p +iM ! µ"#$ q + ! g x ,Q2 + ( ) ! ( ) ! g x ,Q2 . p ! + p.q 1 ( B ) 2 2 ( B ). *+ ( p.q) -. q Spin and polarization: 1 1 Spin-avg: σ = [σ(s)+σ( s)] Spin-dep: ∆σ = [σ(s) σ( s)] 2 − 2 − − Approximation and factorization 2 q Collinear approximation, if Q ! xp ! n ! kT , k – Lowest order: ⎛ k 2 ⎞ +O T +UVCT ≈ ⎜⎟2 ⊗ ⎝⎠Q Scheme dependence Same as elastic x-section Parton’s transverse momentum is integrated into parton distributions, and provides a scale of power corrections 2 q DIS limit: ν,,Qx→∞ whilefixed B Feynman’s parton model and Bjorken scaling ⎛⎞Λ2 FxQ(,22 )=++xe ϕ ()x O()α OQCD 2 BB∑ ffB s⎜⎟2 f ⎝⎠Q Factorization – two or more indentified hadrons q One hadron: + h(p) + X → ⎛⎞1 DIS + O σ tot : ⊗ ⎜⎟ ⎝⎠QR Now Past Connection Hard-part Parton-distribution Power corrections q Two hadrons: 0 h(p)+h(p) V (γ∗,Z ,...)+X → DY ⎛⎞1 σ tot : ⊗ s + O⎜⎟ ⎝⎠QR Predictive power: Universal Parton Distributions Parton distribution functions (PDFs) q Two parton correlations: p, s ψ (0) Γ ψ (y−) p, s | i ij j | +i +j ij p, s F (0) F (y−) p, s f | | q Cross section – Factorization: σ(Q,s) σ(Q, s ) p, s (ψ,Aµ) p, s p, s (ψ,Aµ) p, s ± − ∝ |O | ± − |O | − Factorized partonic part is independent of hadron spin q Parity and time-reversal invariance: µ µ 1 1 p, s (ψ,A ) p, s = p, s †(ψ,A ) − − p, s − |O | − |PT O T P | q Good operators: µ 1 1 µ p, s †(ψ,A ) − − p, s = p, s (ψ,A ) p, s |PT O T P | ± |O | Operator gives “+”: contribute to spin-averaged cross section Operator gives “–”: contribute to spin asymmetries Collinear quark and gluon distributions q Quark distributions – leading power spin projection: µ + (ψ,A )=ψ(0)γ ψ(y−) q(x) Number density O ⇒ µ + (ψ,A )=ψ(0)γ γ ψ(y−) ∆q(x) Net helicity O 5 ⇒ µ + Transversity (ψ,A )=ψ(0)γ γ s ψ(y−) δq(x) h(x) O · ⊥ ⇒ → q Gluon distributions – leading power spin projection: µ 1 +i ij +j (ψ,A )= F (0) δ F (y−) G(x) Number density O xp+ ⇒ µ 1 +i ij +j (ψ,A )= F (0) iε F (y−) ∆G(x) Net helicity O xp+ ⇒ q All operators for collinear PDFs are “local”: y− + U † ( , 0)U ( ,y−)=exp ig dy −A (y −) − ∞ − ∞ − 0 All operators are localized to “1/xp ~ 1/Q” (Not true for TMDs!) Scaling violation – “see” dark gluon q Physical cross sections should not depend on the factorization scale 2 d 2 µF 2 FxQ2 (,B )0= dµF Evolution (differential-integral) equation for PDFs ⎡⎤dxQ⎛⎞22 ⎛⎞ xQ d 2222CxCxB ,, ,B ,, , 0 ∑∑⎢⎥µFF22fff⎜⎟ααs ⊗ϕ( µµ)+ ⎜⎟ 2s ⊗FF 2ϕ f( µ) = ff⎣⎦dxµµFF⎝⎠ ⎝⎠ x µ F d µF q PDFs and coefficient functions share the same logarithms 22 22 PDFs: log(µµFF0QCD) or log( µΛ ) 22 22 Coefficient functions: log(QQµµF ) or log( ) DGLAP evolution equation: ∂ x 22(,xx2 )P ⎛⎞, (', ) µFF2 ϕiijjµ= ∑ / ⎜ αϕ sF⎟ ⊗ µ ∂µF j ⎝⎠x' Global QCD analysis – test of QCD Input DPFs at Q0 Vary a Minimize Chi2 x, a { j} ϕ fh( { j }) DGLAP Comparison with Data x at Q>Q QCD calculation ϕ fh( ) 0 at various x and Q Procedure: Iterate to find the best set of {aj} for the input DPFs Successes of QCD factorization Measure e-p at 0.3 TeV (HERA) Universal PDFs q Predict hadronic collisions at 0.2, 1.96, and 7 TeV: Puzzles and new challenges How to descript hadron properties in terms of parton dynamics? How to explore hadron structure beyond 1-D parton distributions? 31 The hadron mass puzzle q How does QCD generate energy for the proton’s mass? m ~ 10 MeV q Mass from nothing! mN ~ 1000 MeV Quark mass 1% proton’s mass ∼ Higgs mechanism is not enough!!! q Generation of mass: C.D.
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