August 29, Riken Tokyo Office, Tokyo, Japan 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 ~ 2% ~ 98% Higgs boson Strong interaction Proton Quarks

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

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, …)

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

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

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

3+2D imaging TMDs GPDs Momentum transfer PDFs

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

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

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

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

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

Experimental efforts

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

Impact on high-energy physics GPDs and TMDs offer new opportunities Gluon TMD contributions to Higgs production Multiple parton scattering [Boer et al. (2012)] [Diehl et al. (2012)] Gluon linear polarization ratio Double PDF GPD2 GPD1

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

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

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

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

Nucleon spin decomposition Back to the fundamental questions Nucleon spin decomposition Phenomenological extraction [Nocera et al. (2014)] [DSSV (2014)] 25(10) % Sq SG 40(?) % Lattice estimate [Alexandrou et al. (2017)] 42,4(9,0) % Lq Sq 39,8(3,2) % JG 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)] [Jaffe, Manohar (1990)] [Chen et al. (2008)] [Hatta (2012)] ~ 20% ~ 25% ~ 25% ~ 29% Sq Lq Lq Sq LG LG ~ 15% SG SG ~ 6% ~ 40% ~ 40% « Inside » the nucleon « Outside » the nucleon Chromo Lorentz force Struck quark [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 !