WG 9 Working Group on International Cooperation in

WG. 9: Working Group on International Cooperation in Nuclear Physics (ICNP) The Structure of the Nucleon Cédric Lorcé CPHT August 29, Riken Tokyo Office, Tokyo, Japan

Outline • • • Fundamental questions Hadron imaging Impact on other fields Current pictures Conclusions

Fundamental questions about the nucleon Nucleons are key building blocks of all matter around us, and yet we do not know that much about them ! Origin of mass and spin ? Mproton = Mquarks + Ekinetic + Einteraction Proton Quarks ~ 2% ~ 98% Higgs boson Strong interaction

Fundamental questions about the nucleon But also … Size ? 2010 Shape ? Structure ?

Approaches to the problem Hadron spectroscopy Lattice prediction of light meson spectrum • • [J. Dudek et al. (2011)] Meson spectrum better known than baryon spectrum Missing resonances (other production channel ? ) Exotic states (glueballs, hybrids, tetraquarks, pentaquarks, …) Nature (bound state, molecule, mixing, …)

Approaches to the problem Hadron imaging « Quantum billiard » Charge distribution [Carlson, Vanderhaeghen (2008)] Electron Proton • • • Large number of distributions (charge, spin, flavor, momentum, …) Requires high luminosities Intensity frontier Essential input for high-energy physics (electroweak, BSM, dark matter, …)

1 D imaging Electrocardiogram Parton distribution functions (PDFs) Perturbative QCD evolution Momentum fraction Deep inelastic scattering (DIS) [PDG (2016)]

3 D imaging 3 D model of heart Transverse momentum PDFs (TMDs) Polarized target Unpolarized target Courtesy of A. Bacchetta Semi-inclusive DIS (SIDIS)

1+2 D imaging 1+2 D model of heartbeat Generalized PDFs (GPDs) x-dissected charge distribution Sea quarks & Pion cloud Valence quarks gluons Deeply virtual Compton scattering (DVCS) Nucleon transverse extent [Dupré et al. (2017)]

3+2 D imaging TMDs GPDs Momentum transfer PDFs

3+2 D imaging TMDs GPDs Form factors PDFs FFs Elastic scattering Charges

3+2 D imaging Generalized TMDs Phase-space (Wigner) distribution GTMDs GPDs PDFs [Meissner, Metz, Schlegel (2009)] [C. L. , Pasquini, Vanderhaeghen (2011)] Charges FFs

Rich spin structure Quark polarization Nucleon polarization Spin-orbit Spin-spin GPDs TMDs [C. L. , Pasquini (2016)]

Multipole decomposition UU LU [C. L. , Pasquini (2016)]

Multipole decomposition UU Density mode Inflation mode Orbital mode Spiral mode LU [C. L. , Pasquini (2016)]

Experimental efforts

Impact on high-energy physics Main uncertainty on precision SM and BSM studies comes from PDFs [Forte, Watt (2013)] [LHe. C Study Group (2012)]

Impact on high-energy physics GPDs and TMDs offer new opportunities Gluon TMD contributions to Higgs production [Boer et al. (2012)] Multiple parton scattering [Diehl et al. (2012)] Gluon linear polarization ratio Double PDF GPD 2 GPD 1

Connections with other fields Quantum optics Solid-state physics Twisted beams of photons and electrons Spin Hall effect Astrophysics General relativity Hydrodynamical picture Gravitational memory effect quark pressure gluon pressure Before After

Back to the fundamental questions Nucleon momentum decomposition Phenomenological extraction [Harland-Lang et al. (2015)] Pq Lattice estimate 27, 3(2, 3) % 54, 6(5) % [Alexandrou et al. (2017)] PG Pq 74(10) %

Back to the fundamental questions Nucleon mass decomposition Phenomenological extraction 11(1) % [Gao et al. (2015)] Em Eq Lattice estimate 29, 1(1, 5) % 33(1) % [Bali et al. (2016)] [Alexandrou et al. (2017)] Em Eq 33, 7(7, 5) % EG 20, 5(1, 7) %

Back to the fundamental questions Nucleon mass decomposition Trace decomposition Ji’s decomposition [Shifman et al. (1978)] New decomposition [Ji (1995)] ~ 11% [C. L. (2017)] ~ 11% Em ~ 11% ~ 33% Em ~ 22% Eq Ea Ea ~ 89% Trace anomaly EG ~ 34% ~ 14% Ea Em EG ~ 42% ~ 33% Eq

Back to the fundamental questions Nucleon spin decomposition Phenomenological extraction [Nocera et al. (2014)] [DSSV (2014)] Sq 25(10) % SG 40(? ) % Lattice estimate 42, 4(9, 0) % [Alexandrou et al. (2017)] Lq Sq JG 39, 8(3, 2) % 27, 2(? ) %

Back to the fundamental questions Reviews: [Leader, C. L. (2014)] [Wakamatsu (2014)] [Liu, C. L. (2016)] Nucleon spin decomposition Kinetic decomposition Canonical decomposition [Ji (1997)] [Wakamatsu (2010)] ~ 20% ~ 25% ~ 29% LG ~ 25% Lq Sq Lq ~ 6% [Jaffe, Manohar (1990)] [Chen et al. (2008)] [Hatta (2012)] ~ 15% Sq LG SG SG ~ 40% « Inside » the nucleon ~ 40% « Outside » the nucleon Struck quark Chromo Lorentz force [Burkardt (2013)] [Burkardt, C. L. (in preparation)]

Hot topics for the near future • Gluon distributions • Orbital angular momentum • QCD trace anomaly • Transverse polarization effects • Saturation effects • Higher-twists effects • Quark flavor decomposition • Medium modifications • … Lattice QCD

Conclusions • Understanding nucleon structure is a fundamental problem • Nucleon imaging offers key insight • Rich spin structure with numerous effects • Gluon contributions and OAM still missing • Electron-ion collider and Lattice QCD will play an essential role • Connections with other fields should be further explored !