Wigner, Husimi and GTMD at small-x

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Presentation transcript:

Wigner, Husimi and GTMD at small-x Yoshitaka Hatta (Yukawa institute, Kyoto U.) 1. Experimentally measuring 5D distributions at small-x 2. Computing 5D distributions in Color Glass Condensate YH, Bowen Xiao, Feng Yuan, Phys.Rev.Lett. 116 (2016) 202301, Yoshikazu Hagiwara, YH, Takahiro Ueda, arXiv:1609.05773

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

GTMD and Husimi GTMD Husimi Hagiwara, YH (2015) Meissner, Metz, Schlegel (2009) Hagiwara, YH (2015) Fourier transform Gaussian smearing in k, b PDF Form factor charge TMD GPD

Wigner/Husimi/GTMD model calculations, 1-loop calculations, evolution... Lorce, Pasquini Liu, Ma Mukherjee, Nair, Ojha Courtoy, Goldstein, Hernandez, Liuti, Rajan Hagiwara, YH Echevarria, Idilbi, Kanazawa, Lorce, Metz, Pasquini, Schlegel Wigner Husimi GTMD

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

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

Dipole gluon Wigner distribution at small-x YH, Xiao, Yuan (2016) Approximate ``Dipole S-matrix” Find a process sensitive to both and .

Diffractive dijet production in DIS Proton recoil momentum Dijet relative momentum Fourier transform of

`Elliptic’ Wigner distribution correlation between and expected at small-x

Wigner/Husimi/GTMD in the Color Glass Condensate Hagiwara, YH, Ueda (2016) Small-x evolution of dipole S-matrix including gluon saturation  Balitsky-Kovchegov (BK) equation Solve BK keeping the b-dependence

Hidden SO(3) symmetry BK equation conformally symmetric. Gubser (2011) Assume that a SO(3) subgroup of conformal group survives Realistic initial conditions break this symmetry… HOWEVER, the symmetry is dynamically restored by the equation! Berger, Stasto (2010) has a peak at

Wigner Peak at the saturation momentum insert a Gaussian factor to suppress the large-r region (mimic confinement) Peak at the saturation momentum

Rapidity evolution

Elliptic Wigner A few percent effect. Peak does not move with Y (no geometric scaling)

Husimi Positive everywhere  probability distribution of gluons in CGC Two Gaussian widths inversely related such that Large-r region naturally suppressed. Positive everywhere  probability distribution of gluons in CGC

GTMD Directly connected to dijet cross section! peak at , rapidly falls with increasing

Conclusions Let’s get 5 dimensional. Even richer physics than TMD+GPD combined, still largely unexplored. 5D distributions experimentally accessible in DIS Wigner, GTMD: subject to uncertainties due to confinement effects. A nonperturbative factor needed (like in TMD). Husimi can avoid this problem. The elliptic angular correlation—a few percent effect, different rapidity dependence.  challenging to measure at EIC?