INSIGHTS INTO THE ELECTROMAGNETIC N TRANSITION Jorge Segovia and - PowerPoint PPT Presentation

INSIGHTS INTO THE ELECTROMAGNETIC γ ∗ N → ∆ TRANSITION Jorge Segovia and Craig D. Roberts Argonne National Laboratory Chen Chen and Shaolong Wang University of Science and Technology of China Kent State University, Center for Nuclear Research (CNR) Kent (Ohio), May 1st, 2013 Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 1/37

The ∆ baryon Discovered more than 50 years ago E. Fermi et al. , Phys. Rev. 85 , 935 (1952). ↓ H. Anderson et al. , Phys. Rev. 85 , 936 (1952). By Fermi and collaborators ↓ In pion scattering off protons at the Chicago cyclotron (now Fermilab) Mass of 1232 MeV and width of 120 MeV . Lightest baryon resonance ⇒ 300 MeV heavier than the nucleon. Almost an ideally elastic π N resonance ⇒ 99% of times decaying to ∆ → π N . Only other decay channel: ∆ → γ N ⇒ less than 1% to the total decay width. The ∆ + and ∆ 0 can be viewed, respectively, as isospin- and spin-flip excitations of the proton and neutron Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 2/37

The γ ∗ N → ∆ reaction Two ways in order to analyze the structure of the ∆-resonances ւ ց π -mesons as a probe photons as a probe ↓ ↓ complex relatively simple BUT: B (∆ → γ N ) � 1% This became possible with the advent of intense, energetic electron-beam facilities Reliable data on the γ ∗ p → ∆ + transition: ☞ Available on the entire domain 0 ≤ Q 2 � 8 GeV 2 . Isospin symmetry implies γ ∗ n → ∆ 0 is simply related with γ ∗ p → ∆ + . γ ∗ p → ∆ + data has stimulated a great deal of theoretical analysis: Deformation of hadrons. The relevance of pQCD to processes involving moderate momentum transfers. The role that experiments on resonance electroproduction can play in exposing non-perturbative phenomena in QCD: ☞ The nature of confinement and Dynamical Chiral Symmetry Breaking. Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 3/37

QCD and hadron physics Quantum Chromodynamics is generally regarded as the non-Abelian gauge quantum field theory that describes quark and gluon physics (strong interactions). Successful at high energies → perturbative calculations are allowed. Some non trivial and unexpected properties of QCD have been well understood and confirmed experimentally. The nonperturbative regime of QCD, where the hadron properties are involved, remains to be understood. A rigorous proof is still lacking that QCD works as a microscopic theory of strong interactions that gives rise to the phenomenological properties of hadron spectra. Emergent phenomena ☞ Quark and gluon confinement. No matter how hard one strikes the proton, one cannot liberate an individual quark and gluon. ☞ Dynamical chiral symmetry breaking Very unnatural pattern of bound states. Current quark mass is small and still no degeneracy between parity partners is found. Neither of these phenomena is apparent in QCD’s Lagrangian yet! they are the dominant determining characteristics of real-world QCD Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 4/37

Emergent phenomena: Confinement (I) Usual result in Lattice QCD G.S. Bali, Phys. Rep. 343 , 1 (2001). Pure gluon dynamics 4 m ps + m s 3 Π u Multigluon exchanges produce an attractive 2 2 m ps linearly rising potential proportional to the [V(r)-V(r 0 )]r 0 1 distance between quarks. 0 + Σ g This idea has been confirmed, but not -1 rigorously proved, by quenched lattice gauge quenched -2 κ = 0.1575 calculations applied to heavy valence quark -3 systems. 0.5 1 1.5 2 2.5 3 r/r 0 G.S. Bali, Phys. Rev. D 71 , 114513 (2005). Sea light quarks 0.2 0 Sea quarks are also important ingredients of the strong interaction dynamics. [E(r) - 2 m B ]a -0.2 Included in the lattice calculations. -0.4 Contribute to the screening of the rising -0.6 potential at low momenta and eventually to state |1> the breaking of the quark-antiquark binding state |2> -0.8 string. 2 4 6 8 10 12 14 16 18 - r/a Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 5/37

Emergent phenomena: Confinement (II) Another point of view ☞ Novel feature of QCD: Tree-level interactions between gauge-bosons 3-gluon vertex O ( α s ) cross-section cf. O ( α 4 em ) in QED (b) fermion screening (c) gluon antiscreening 4-gluon vertex ... g 0 g 0 + + + s s (a) (b) (c) = g s ( Q 2 ) g s ( Q 2 ) ¯ ¯ − → (d) � α (0) Q 2 + 11 α (0) � 4 π ln Λ 2 4 π ln Λ 2 1 − 2 α s ( Q 2 ) = α (0) s s 3 n f s Q 2 ☞ This momentum-dependent coupling translates The confinement hypothesis: into a coupling that depends strongly on separation Color-charged particles cannot be ☞ The interaction becomes stronger as the isolated, they clump together in participants try to separate. color-neutral bound states. Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 6/37

Emergent phenomena: Confinement (III) Quantum field theory paradigm Dressed-propagator for a colored state Confinement is expressed through a dramatic change in the analytic structure of propagators for colored states. Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities. State described by rapidly damped wave and hence state cannot exist in observable spectrum. Dressed-gluon propagator Confined gluon. IR-massive but UV-massless. m G ∼ 2 − 4Λ QCD . Modification of the quark and gluon propagators Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 7/37

Emergent phenomena: Dynamical chiral symmetry breaking (I) In the Dirac basis, γ 5 is the chiral operator and one may represent: q + ( x ) = 1 Positive helicity (right handed) fermion: 2 ( I D + γ 5 ) q ( x ) = P + q ( x ) q − ( x ) = 1 Negative helicity (left handed) fermion: 2 ( I D − γ 5 ) q ( x ) = P − q ( x ) A global chiral transformation is enacted by: q ( x ) → q ′ ( x ) = e i γ 5 θ q ( x ) , q ′ ( x ) → ¯ q ( x ) e i γ 5 θ ¯ q ( x ) → ¯ with the choice θ = π/ 2, this transformation maps: q + → q + , q − → − q − helicity is conserved An example: θ = π/ 4 q ( x ) i γ 5 q ( x ) ¯ − − − − → − ¯ q ( x ) I D q ( x ) It turns a pseudoscalar into a scalar Spectrum of a theory invariant under chiral transformations ↓ should exhibit degenerate parity doublets J P = 0 − J P = 0 + π m = 140 MeV cf. σ m = 500 MeV J P = 1 − J P = 1 + ρ m = 775 MeV cf. a 1 m = 1260 MeV J P = 1 / 2 + J P = 1 / 2 − N m = 938 MeV cf. N (1535) m = 1535 MeV Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 8/37

Emergent phenomena: Dynamical chiral symmetry breaking (II) Current quark mass should be the responsible since it is the only piece in the QCD Lagrangian that breaks chiral symmetry This appears to suggest that the quarks are quite massive ↓ but quarks are very light: m u / m d ∼ 0 . 5 m d = 4 MeV ↓ splitting between parity partners is greater than 100-times this mass scale Dynamical chiral symmetry breaking Rapid acquisition of mass is Mass generated from the interaction of quarks 0.4 effect of gluon cloud with the gluon-medium. Quarks acquire a HUGE constituent mass. 0.3 m = 0 (Chiral limit) M(p) [GeV] m = 30 MeV Responsible of the 98% of the mass of the m = 70 MeV proton. 0.2 (Not) spontaneous chiral symmetry breaking Higgs mechanism. 0.1 Quarks acquire a TINY current mass. 0 Responsible of the 2% of the mass of the 0 1 2 3 p [GeV] proton. Modification of the quark propagator Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 9/37

Theory tool: Dyson-Schwinger equations The extraordinary phenomena of confinement and DCSB: Can be identified with properties of dressed-quark and -gluon propagators. Are expressed through QCD’s vertices. Dyson-Schwinger equations (DSEs) Well suited to Relativistic Quantum Field Theory. Generating tool for perturbation theory → No model-dependence. Nonperturbative tool for the study of continuum strong QCD → any model-dependence should be incorporated here. Allows the study of the interaction between light quarks in the whole range of momenta Analysis of the infrared behaviour of the strong coupling constant → β -function. The β -function behaviour at infrared momenta is crucial to disentangle confinement and DCSB. DSEs connect β -function to experimental observables Solutions of DSEs are Schwinger functions. All cross sections can be constructed from such n-point functions. Comparison between computations and observations of Hadron mass spectrum. Elastic and transition form factors ... can be used to illuminate QCD (at infrared momenta). Insights into the electromagnetic γ ∗ N → ∆ transition Jorge Segovia et al. , jsegovia@anl.gov 10/37