3D Spatial Imaging: from JLab 12 GeV to the EIC Daria Sokhan University of Glasgow, Scotland Lecture course for the 33rd annual Hampton University Graduate Studies Programme (HUGS) 29th May - 15th June 2018 Jefferson Lab, Virginia, USA
General outline of lecture material: Imaging at the sub-nucleon scale, Generalised Parton Distributions and how to access them Deeply Virtual Compton scattering Deeply Virtual Meson Production Experimental measurements @ JLab What we have learned pre JLab-12 Tomography with JLab-12 and the EIC ( 5 lectures)
An abridged history of nucleon imaging Before 1956: the nucleon is 1960s: the Quark Model. Nucleons point-like and fundamental… are composed of three valence quarks! Gell-Mann (Nobel Prize 1969), Zweig. 1968: Deep Inelastic scattering at SLAC: scaling observed. The proton consists of point-like charges: partons! Friedman, Kendall, Taylor: Robert Hofstadter Nobel Prize 1990 1915 - 1990 (Wikipedia) 1972: Theory of QCD developed. 1956: Elastic scattering at SLAC: the proton has internal structure! Hofstadter: Nobel Prize 1961. 21st Century: High-precision imaging of quarks and gluons. 3D tomography of the 1970s-1990s: Deep nucleon: spatial and momentum Inelastic Scattering reveals a distributions inside it across all scales. rich structure: quark-gluon sea, flavour distributions, puzzles of spin… what you see depends on how closely you look!
Electron scattering: a reminder of terminology Elastic scattering: initial Deep inelastic scattering (DIS): and final state is the same, state of the nucleon changed, only momenta change. new particles created. e' e' e γ * e γ * N N' X N Measurements: ★ Inclusive — only the electron is detected Complementary ★ Semi-inclusive — electron and typically one information on the hadron detected nucleon’s structure ★ Exclusive — all final state particles detected
Scales of resolution – an elephantine analogy Lyuba, baby mamoth found in Siberia, imaged with visible light… International Mammoth Committee ? e − Q 2 ~ MeV 2
Scales of resolution – an elephantine analogy Lyuba, baby mamoth found in Siberia, imaged with visible light… … and X-rays. International Mammoth Committee Equivalent wavelength of the ? probe: e − e − 1 λ ≈ Q 2 ~ MeV 2 Q 2 >> GeV 2 2 Q What you see depends on what you use to look…
The 2D spatial image Lepton (eg: electron, neutrino) scattering off a nucleon reveals different aspects of nucleon structure. Elastic Scattering e ' e γ ∗ N N ' Cross-section parameterised Transverse quark in terms of Form Factors distributions: charge, (Pauli, Dirac, axial, pseudo- magnetisation. scalar)
Charge density inside a nucleon Proton Neutron negative positive outer inner core surface C. Carlson, M. Vanderhaeghen PRL 100, 032004 (2008)
A dynamical image Deep Inelastic Scattering e ' e γ ∗ N First experimental evidence of partons inside a nucleon Cross-section parameterised in terms of polarised and unpolarised Structure Functions Longitudinal momentum and helicity distributions of partons
Parton Distribution Functions Momentum distributions of quarks and gluons within a nucleon. x : longitudinal momentum of parton as a fraction of nucleon’s momentum.
A full “knowledge” of the nucleon… or your favourite representation… x : longitudinal momentum fraction carried by struck parton nucleon
… is hard to come by The story of the blind men and the elephant. Elastic scattering Deep Inealstic Scattering (DIS) Semi-inclusive DIS Deep exclusive reactions What you see depends also on how you look… G. Renee Guzlas, artist.
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon 2 d b ∫ Transverse T Semi-inclusive DIS Momentum Distributions (TMDs)
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon 2 d b ∫ Transverse T Momentum Distributions (TMDs) 2 d k ∫ T Parton Distribution Deep Inelastic Scattering Functions (PDFs)
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon d 2 k ∫ T Generalised Parton Distributions (GPDs) • relate, in the infinite momentum frame, transverse position of partons ( b ┴ ) to longitudinal momentum ( x ). Deep exclusive reactions, e.g.: Deeply Virtual Compton Scattering, Deeply Virtual Meson production, …
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon d 2 k ∫ Fourier Transform of electric Form T Factor: transverse charge density of a nucleon Generalised Parton Distributions (GPDs) ∫ dx Form Factors proton neutron eg : G E, G M C. Carlson, M. Vanderhaeghen PRL 100, 032004 (2008)
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon d 2 2 k d b ∫ ∫ Transverse T T Momentum Distributions Generalised Parton (TMDs) Distributions (GPDs) 2 ∫ dx d k ∫ T G. Renee Guzlas, artist. Form Factors Parton Distribution eg : G E, G M Functions (PDFs)
Images of the nucleon Wigner function: full phase space parton distribution of the nucleon d 2 2 k d b ∫ ∫ Transverse T T Momentum Distributions Generalised Parton (TMDs) Distributions (GPDs) 2 ∫ dx d k ∫ T Form Factors Parton Distribution eg : G E, G M Functions (PDFs)
Generalised Parton Distributions (GPDs) — proposed by Müller (1994), Radyushkin, Ji (1997). Directly related to the matrix element of the energy- momentum tensor evaluated between hadron states. In the infinite momentum frame, can be interpreted as relating transverse position of partons (impact parameter), b ┴ , to their longitudinal momentum fraction ( x ). Tomography: 3D image of the nucleon. First studies at JLab and DESY (HERMES), currently at JLab and CERN (COMPASS). A crucial part of the JLab12 programme — and, in the future, of the EIC.
Deeply Virtual Compton scattering Skewness:
Factorisation: allows to separate the “hard”-scattering of electron off a quark from the “soft” part of the interaction inside the nucleon. perturbative Factorisation only valid at high Q 2 non-perturbative At leading order, leading twist four GPDs for each quark-flavour q At sufficiently high Q 2 , can extract GPD information from cross-sections and asymmetries in DVCS and related processes.
Definitions: Order and Twist 1 Twist: powers of in the DVCS amplitude. Leading-twist p Q 2 (LT) is twist-2. Order: introduces powers of α s Next-to-leading order (NLO) Leading order (LO) LO requires Q 2 >> M 2 ( M : target mass)
A closer look at GPDs Independent of quark helicity, unpolarised GPDs Helicity-dependent, polarised GPDs
A closer look at GPDs The first Mellin moments of the GPDs reduce to Form Factors: Two distinct regions: x x − ξ + ξ The DGLAP region: scattering from quarks or anti-quarks t The ERBL region: scattering results in a qq pair. Fourier Transform of GPD w.r.t. gives the transverse spatial distribution at each given x . Small changes in transverse momentum carry sensitivity to transverse structure at large distances within the nucleon.
The Nucleon Spin Puzzle ✴ What contributes to nucleon spin? ✴ 1980’s: European Muon Collaboration (EMC) measures contribution of valence quarks to proton spin to be ~ 30 %. Subsequent deep inelastic scattering (DIS) experiments confirm. Where is the rest? Proton spin crisis! Quark spin : extracted from Gluon spin and OAM : helicity distributions measured measurements of DIS and in polarised DIS. polarised proton collisions indicate gluon spin 1 1 contribution is very small, J L J = = Σ + + although in a different N q q g 2 2 decomposition. Caveat: Quark orbital angular momentum (OAM) : can be In Ji’s decomposition of accessed, in Ji’s decomposition, via GPDs , which nucleon spin, the gluon spin contain information on total angular momentum, J q . and OAM terms cannot be separated.
GPDs and nucleon spin 1 1 J L J = = Σ + + N q q g 2 2 1 1 1 { } Ji’s relation: q g q ( ) q ( ) J J x dx H x , , 0 E x , , 0 ∫ − = − = ξ + ξ 2 2 1 Second Mellin moments of the GPDs contain information on the total angular momentum carried by quarks. Note that the contribution from GPD H is given by the quark momentum, already known from PDFs:
Experimental paths to GPDs Accessible in exclusive reactions, where all final cliparts.co state particles are detected. Trodden paths, or ones starting to be explored: Deeply Virtual Compton Scattering (DVCS) Deeply Virtual Meson Production (DVMP) Time-like Compton Scattering (TCS) Double DVCS DVCS TCS Virtual photon space-like Virtual photon time-like DDVCS DVMP One time-like, one space-like virtual photon
Measuring DVCS ✴ Process measured in experiment: γ e ' e ' e ' γ + + e e γ e γ * γ * γ * N ' N ' N ' N N N Bethe - Heitler DVCS 2 2 * * d T T T T T T σ ∝ + + + DVCS BH DVCS BH BH DVCS Interference term Amplitude Amplitude calculable parameterised in from elastic Form 2 2 terms of Compton T T Factors and QED << DVCS BH Form Factors
Recommend
More recommend
