Modern Hadron Spectroscopy : Challenges and Opportunities Adam Szczepaniak, Indiana University/Jefferson Lab Lecture 1: Hadrons as laboratory for QCD: • Introduction to QCD • Bare vs effective effective quarks and gluons • Phenomenology of Hadrons Lecture 2: Phenomenology of hadron reactions • Kinematics and observables • Space time picture of Parton interactions and Regge phenomena • Properties of reaction amplitudes Lecture 3: Complex analysis Lecture 4: How to extract resonance information from the data • Partial waves and resonance properties • Amplitude analysis methods (spin complications) INDIANA UNIVERSITY
Why QCD and Hadron Spectroscopy 2 • A single theory describing nuclear phenomena at distance scales O(10 15 m) as well as O(10 4 m). • It builds from objects (quarks and gluons) that do not exist. Gluons are responsible for mass generation and color confinement. • ~99% mass comes from interactions! • Complex ground state (vacuum) and excited (hadrons) states (monopoles, vortices, …) • Predicts existence of exotic matter, e.g. matter made from radiation (glueballs, hybrids) and novel plasmas. • A possible template for physics beyond the Standard Model F = -k x • It is challenging ! INDIANA UNIVERSITY
Stranger Things (of the Nuclear World) 3 What are the constituents of hadrons, (quarks and gluons) ? small world (10 -15 m) of fast (v~c) particles exerting ~1T forces !!! ~ = c = 1 Unit energy = 1GeV [length] = [time] = [energy] -1 = [momentum] -1 Unit lengt = 1GeV -1 = 0.197 fm INDIANA UNIVERSITY
Particle vs Fields 4 In relativistic quantum mechanics (QFT) particles are emergent phenomena (i.e. fields are not physically measurable but their “consequences” are, cf. potential vs electric field density) “excitation of the collective motion aether” → field → particle H = H h.o = (coupled) harmonic oscillators “bare” particles : eigenstates of H h.o. INDIANA UNIVERSITY
5 The only physical mass parameter is the distance between “beads” a y i y i +1 a i i + 1 N − N dim [ p ] = 1 dim [ q ] = 0 [ p ( x ) , q ( y )] = − i δ ( x − y ) In the continuum limit q i = y i a → 0 a H = 1 Z H = 1 i + 1 � ⇥ p 2 ( x ) + ( ∂ q ( x )) 2 ⇤ dx X a 2 ( q i − q i +1 ) 2 p 2 2 a 2 i Z Z Fourier transform linearize Hamiltonian dxe ikx q ( x ) dxe ikx p ( x ) q ( x ) → q ( k ) = p ( x ) → p ( k ) = Particles associated with creation and annihilation operators | k i = a † ( k ) | 0 i | k, q i = a † ( k ) a † ( q ) | 0 i , · · · q ( k ) = a ( k ) + a † ( k ) INDIANA UNIVERSITY
Renormalization 6 • The distance scale a was the only mass scale, e.g. E = O(a -1 ) and there is now continuum limit for energy. This a reflation of scaling invariance of the x → λ x H → H continuum Hamiltonian. λ • A calculable QCD “scheme” (e.g. lattice, S-D equations, etc) needs a distance scale. (aka anomalous symmetry breaking). • All physical quantities are determined w.r.t to his scale, (e.g. pion mass in QCD, or electron mass in QED) • Renormalizable QFT : scale is there, but it is arbitrary, i.e. the theory predicts how observables change with scale. • Non-renormalizable (effective) QFT : scale if fixed, i.e. the theory is only valid (predictive) at a particular scale. INDIANA UNIVERSITY
Example: 7 In 0+1 dimension (Quantum Mechanics in 1 special dimension) find bound states of the Hamiltonian p 2 + λδ ( x ) p H = p + λδ ( x ) = INDIANA UNIVERSITY
Particles vs Fields: Hamiltonian vs Lagrangian 9 Legendre transformation H ( p i , q i ) Quantization Quantization Probabilistic interpretation Semiclassical Picture: Quantum picture: path integral, particles, states, classical solution operators, etc. (solitons), etc. INDIANA UNIVERSITY
Bare particles are eigenstates of free Hamiltonian 10 “Bare (free)” particles of QCD: quarks and gluons e.g. because of asymptotic freedom measured in high energy collisions • Gluon ~ 8 copies of a photon • Photons do not cary electric charge : they only interact the matter (e.g.) electrons that do carry charge • Gluons carry charge, i.e. interact with each other and with quarks. INDIANA UNIVERSITY
Discovery of quarks e.g. the J/ ψ 11 A narrow resonance was discovered in the 1974 November revolution of particle physics" in two reactions: Proton + Be => e + e - + anything e + e - annihilation to hadrons at the BNL J. J. Aubert et al., “Experimental in the SPEAR storage ring at Stanford observation J. E. Augustin et al., “Discovery of a narrow of a heavy particle J," Phys. Rev. Lett. 33, 1404 resonance in e + e - annihilation," Phys. Rev. Lett. 33, 1406 (1974). (1974). J/ ψ = c ¯ c mass = 3096 . 87 MeV Γ = 87 keV 10 3 longer lifetime ! (weak interactions 10 12 ) typical hadronic width = O (100 MeV) INDIANA UNIVERSITY
Charmonium spectrum 12 J/ ψ J/ ψ is a bound state of c c INDIANA UNIVERSITY
QED vs QCD 13 • Bare particles are eigenstates of free Hamiltonian. If interactions are weak (QED) the “bare particle” ~ observed particle = (interacting particles) H QED = H c.h.o. + eV e ~ 0.303 |electron> = + O(e 2 ) + |bare electron> eV|bare electron> e QCD ~ 10 e QED • Quarks in hadrons have effective color quarks charge e > 3-4. There is no reason why bound quarks should retain their identify in in hadrons presence of strong interactions … …but it seems they do “free” quarks inverse distance between quarks INDIANA UNIVERSITY
“Evidence” for Constituent Quarks:Light Quark Hadrons 14 Spectrum of mesons containing u,d,s quarks from numerical QCD simulations (lattice) resembles spectrum of quark models. J.Dudek et al. INDIANA UNIVERSITY
Emergence of constituent quarks 15 H = H kin + V = H h.o + V (Color) charge density (Color) charge density Z V = d x d y ρ ( x ) V ( | x − y | ) ρ ( y ) Instantaneous potential between (color) charges, e.g. Coulomb + Linear The ground state contains condensate of quarks | k i = a † k | Ω i δ m k = h k | V | k i k Z � Z d x e i kx δ m k = d y V ( | x � y | ) h Ω | ρ ( y ) | Ω i + · · · | Ω i Hartree + Fock INDIANA UNIVERSITY
QCD vacuum and Constituent Quarks 16 Where do constituent quarks come from m const ~ 0.1-0.3 GeV E Current quark levels Cooper pairs from Chromoelectric Coulomb attraction near Fermi-Dirac surface. Fermi-Dirac sea BCS vacuum Meson = INDIANA UNIVERSITY
space time QCD vacuum and Constituent Gluons 17 Gluons are responsible for confinement (aka effective potential between color charges) and are confined (aka contribute to the color charge) Coulomb gauge r A a ( x ) = 0 ⟨ A ⊥ A ⊥ ⟩ short range long range interaction interaction INDIANA UNIVERSITY
Confining Potential and the gluon condensate 18 H = H kin + V K ⇥ � g 2 α ⌅ 2 = | x � y | = • Coulomb “Potential” between external (i.e. quark charges) depends on the distribution Coulomb string tension of gluons. • In presence of a gluon condensate it produces a Confining force been external without vortices color charge J.Greensite, et al. | Ω i h Ω | long range, + · · · = + + Confining interaction Ω contains condensate of monopoles, vortices, … INDIANA UNIVERSITY
How to Probe Gluons 19 1. Gluons in the vacuum: 2. Gluons in a physical e.g. quark- antiquark state: • Insert a quark pair and measure energy the • Insert a quark pair, wait until it instantaneous energy. polarizes the vacuum and measure energy the state. Q QCD vacuum _ Q Expectation value of QCD Hamiltonian in the Coulomb state 1 r ! h 0 | V c [ A ] | 0 i = V c ( r ) Coulomb state = QCD eigenstate \ Wilson state = QCD eigenstate Q i = Q † ¯ Q † | 0 i + Q † ¯ | Q ¯ Q † g † | 0 i + · · · Coulomb state Coulomb state + extra gluons INDIANA UNIVERSITY
Quasi-Gluon Properties 20 K.Juge, J.Kuti, Morningstar G.Bali Q J PC =1 +- ¯ Q glue-lump Potential energy curves for the excited Adiabatic potentials map out distribution of valence states of Ca 2 exited gluons: Gluons behave as quasiparticles with J PC =1 +- INDIANA UNIVERSITY
Quark Model (without quasi-gluons) 21 quark model states S 2 S = S + S 2 1 S 1 L J = L + S NEW states L + 1 P = (-1) C = (-1) L + S ρ π J.Dudek et al. JLab INDIANA UNIVERSITY
Lattice Charmonium Spectrum 22 ψ (4415) X,Y,Z states TERRA INCOGNITA ψ (4260) ψ (4040) η c ’ ϰ 1 ϰ 2 h c ψ ’ ϰ 0 J/ ψ η c J.Dudek et al. 0-+ 1-+ 2-+ 1- - 0++ 1++ 2++ 0+- 1+- 1+- 1+- 2+- 2+- 3+- INDIANA UNIVERSITY
Quark Model with Gluons : Hybrid States 23 q = ( − 1) L +1 P q ¯ q = ( − 1) L + S C q ¯ J PC glue _ J PC QQ 1 −− _ J PC = 1 -+ is not a qq state exotic quantum numbers INDIANA UNIVERSITY
Meson Spectrum on the Lattice 24 large overlap with new multiplets from lattice gluonic operators includes 1 -+ exotic quark model states NEW states 0 -+ 1 -+ 2 -+ 1 -- lowest-mass hybrid multiplet ρ π J.Dudek et al. JLab INDIANA UNIVERSITY
Hunting for Resonances 25 In 1952, E. Fermi and collaborators peak in intensity measured the cross section π + p → π + p (cross section) for and found it steeply raising. ∆ ++ width Γ 180 0 phase change in the amplitude INDIANA UNIVERSITY
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