Accessing the gluon Wigner distribution in ep and pA collisions Yoshitaka Hatta (Yukawa inst. Kyoto U.) YH, B. Xiao, F. Yuan, PRL116 (2016) 202301 Y. Hagiwara, YH, R. Pasechnik, M. Tasevsky, O. Teryaev, PRD96 (2017) 034009

Contents Introduction: Phase space distributions in QCD Wigner distribution at small-x Diffractive dijet production in ep and pA.

Nucleon tomography

1D tomography: Parton distribution function (PDF) Probability distribution of quarks and gluons with longitudinal momentum fraction The nucleon is much more complicated! Partons also have transverse momentum and are spread in impact parameter space

3D tomography: Transverse momentum dependent distributions (TMD) Relevant in semi-inclusive DIS (SIDIS), etc.

3D tomography: Generalized parton distributions (GPD) distribution of partons in impact parameter space Fourier transform Deeply Virtual Compton Scattering (DVCS)

5D tomography: Wigner distribution— the “mother distribution” Belitsky, Ji, Yuan (2003); Lorce, Pasquini (2011) TMD GPD PDF Form factor charge

5D tomography: Generalized TMD and Husimi GTMD Husimi Meissner, Metz, Schlegel (2009) Hagiwara, YH (2015) Gaussian smearing in k, b Probabilistic interpretation! PDF Form factor charge TMD GPD

Wigner distribution and orbital angular momentum Nucleon spin decomposition Quarks’ helicity Gluons’ helicity Canonical Orbital angular momentum Lorce, Pasquini, (2011); YH (2011)

Electron-Ion Collider (EIC)  Abhay’s talk A future (2025~), high-luminosity　 experiment dedicated to the study of nucleon structure. arXiv:1212.1701

Wigner distribution: Is it measurable? In quantum optics, yes! What about in QCD? Go to small-x!

Gluon Wigner distribution There are two ways to make it gauge invariant Dominguez, Marquet, Xiao, Yuan (2011) Dipole distribution Weizsacker-Williams distribution

Dipole gluon Wigner distribution at small-x YH, Xiao, Yuan (2016) Approximate ``Dipole S-matrix” correlation expected ``Elliptic Wigner” ``OAM Wigner”

Gluon Wigner from Balitsky-Kovchegov equation Hagiwara, YH, Ueda (2016) Peak at the saturation momentum Small in magnitude (a few percent effect) Distinct functional dependence on

Elliptic Wigner in DVCS YH, Xiao, Yuan (2017) Gluon transversity GPD Elliptic Wigner (GTMD)

Elliptic Wigner in high-multiplicity pp and pA Hagiwara, YH, Xiao, Yuan (2017) see also, Kopeliovich et al. (2008), Levin Rezaeian (2011),.. Elliptic flow observed in high-multiplicity pp and pA. Initial state or final state effect? 1509.04776 Double parton scattering + Elliptic Wigner = Elliptic flow

Direct measurement of the Wigner distribution Find a process sensitive to both and …. Nontrivial! cf. Vector meson production One can study the dependence on Munier, Stasto, Mueller, 2001 but not on

Probing Wigner (GTMD) in exclusive diffractive dijet in ep YH, Xiao, Yuan (2016), see also Altinoluk, Armesto, Beuf, Rezaeian (2015) NLO calculation by Boussarie et al. (2016) Jet 1 Jet 2 𝑒 − Proportional to GTMD

Ultra-peripheral pA collisions! Hagiwara, YH, Pasechnik, Tasevsky, Teryaev, (2017) preferably small Use the Weiszacker-Williams photons in UPC! YH, Xiao, Yuan (2016) photon flux

Analytically invert these relations to get GTMD BK model MV model Can be done also for UPC in AA collisions

Nucleon spin puzzle and small-x Nonzero contribution from `large’-x region de Florian, Sassot, Stratmann,Vogelsang (2014) Huge uncertainty in from the small-x region. Maybe after including the small-x contribution. OAM not needed? Δ𝐺

- Longitudinal single spin asymmetry in diffractive dijet 2 2 YH, Nakagawa, Xiao, Yuan, Zhao (2016) 2 2 - ‘Odderon’ at small-x !?

Conclusions Physics of nucleon structure has literally expanded its dimensions, from 1D (PDF) to 3D (GPD/TMD) and 5D (Wigher/Husimi/GTMD). Exciting times ahead at the future EIC. First ideas to measure 5D gluon distributions: Diffractive dijet events in ep (photoproduction) and pA (UPC). Look for 　　　　 and angular dependences. Extension to spin-dependent part (OAM), moderate-x, quark Wigner. YH, Nakagawa, Xiao, Yuan, Zhao (2017) Ji, Yuan, Zhao (2017) Bhattacharya, Metz, Zhou (2017)

Homodyne Detection Two electromagnetic fields are incident on a beam splitter Photon count difference at detectors C and D : Probability distribution of (coherent state with phase ) c.f. Reconstruct via the inverse Radon transformation