Nucleon tomography at small-x
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1 Nucleon tomography at small-x Yoshitaka Hatta (Yukawa inst. Kyoto U.)
2 Contents Introduction: Wigner distribution in QCD Measuring Wigner (unpolarized case) Wigner distribution and orbital angular momentum
3 Tomography CT = Computed Tomography See inside an object without cutting
4 Nucleon tomography
5 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
6 3D tomography: Transverse momentum dependent distributions (TMD) Relevant in semi-inclusive DIS (SIDIS), etc.
7 3D tomography: Generalized parton distributions (GPD) Fourier transform distribution of partons in impact parameter space Deeply Virtual Compton Scattering (DVCS)
8 5D tomography: Wigner distribution the mother distribution Belitsky, Ji, Yuan (2003); Lorce, Pasquini (2011) TMD GPD PDF Form factor charge
9 5D tomography: GTMD and Husimi GTMD Meissner, Metz, Schlegel (2009) Husimi Hagiwara, YH (2015) Gaussian smearing in k, b TMD GPD PDF Form factor charge
10 Wigner distribution and orbital angular momentum Nucleon spin decomposition Quarks helicity Gluons helicity Canonical Orbital angular momentum Lorce, Pasquini, (2011); YH (2011)
11 Electron-Ion Collider (EIC) A future (2025~?), high-luminosity the study of nucleon structure. experiment dedicated to Accardi et al. arxiv:
12 Wigner distribution: Is it measurable? In quantum optics, yes! What about in QCD? Go to small-x!
13 Gluon Wigner distribution There are two ways to make it gauge invariant Dominguez, Marquet, Xiao, Yuan (2011) Dipole distribution Weizsacker-Williams distribution
14 Dipole gluon Wigner distribution at small-x Approximate YH, Xiao, Yuan (2016) ``Dipole S-matrix correlation expected ``Elliptic Wigner distribution
15 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
16 How to measure 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
17 Probing Wigner (GTMD) in diffractive dijet production YH, Xiao, Yuan (2016) Jet 1 e Jet 2 Fourier transform of
18 Ultra-peripheral pa collisions! Hagiwara, YH, Pasechnik, Tasevsky, Teryaev, preferably small YH, Xiao, Yuan (2016) Use the Weiszacker-Williams photons in UPC! photon flux
19 Elliptic Wigner in DVCS YH, Xiao, Yuan (2017) Gluon transversity GPD Elliptic Wigner also relevant to: `elliptic flow in pa and pp collisions Hagiwara, YH, Xiao, Yuan (2017) correlation in quasielastic scattering Zhou (2016)
20 Nucleon spin puzzle and small-x Nonzero contribution from `large -x region de Florian, Sassot, Stratmann,Vogelsang (2014) Huge uncertainty in ΔG from the small-x region. Maybe after including the small-x contribution. OAM not needed?
21 Can we measure? A big challenge for the whole community. No observable proposed so far although OAM is the future of spin physics! Hint1: We need to introduce the x-distribution Hint2: cf., for OAMs Hagler, Schafer (1998) Harindranath, Kundu (1999) YH, Yoshida (2012) is related to the Wigner distribution. The gluon Wigner distribution is measurable at low-x. YH, Xiao, Yuan (2016) Recent progress small-x YH, Nakagawa, Yuan, Xiao, Zhao arxiv: moderate-x Ji, Yuan, Zhao arxiv: quark OAM Bhattacharya, Metz, Zhou arxiv: Liuti, talk in this workshop
22 OAM from the Wigner distribution Wigner distribution in QCD Need a Wilson line! Define Lorce, Pasquini (2011); YH (2011); Which OAM is this??
23 Canonical OAM from the light-cone Wilson line YH (2011) Kinetic (Ji s) OAM from the straight Wilson line Ji, Xiong, Yuan (2012) `Potential OAM Torque acting on a quark Burkardt (2012)
24 Jaffe-Manohar vs. Ji First lattice result Engelhardt, Staple length
25 OAM parton distribution function Define the x-distribution. YH, Yoshida (2012) Natural, because Jaffe-Manohar decomposition has a partonic interpretation.?? Go to the momentm space and look for the component Then
26 Deconstructing OAM Ji s OAM canonical OAM `potential OAM For a 3-body operator, it is natural to define the double density.
27 Ji s OAM canonical OAM `potential OAM doubly-unintegrate The gluon has zero energy, partonic interpretation! Canonical OAM density YH, Yoshida (2012) It coincides with defined via the Wigner distribution
28 Twist structure of OAM distributions YH, Yoshida (2012) Wandzura-Wilczek part Genuine twist-three part
29 `DGLAP equation of OAM PDF Hagler, Schafer (1998) YH, Nakagawa, Xiao, Yuan, Zhao (2016)
30 Spin dependence at small-x? Pomeron odderon cannot contain the structure forbidden by PT symmetry Lesson: All information about spin is lost in the eikonal approximation.
31 OAM as a next-to-eikonal effect YH, Nakagawa, Xiao, Yuan, Zhao (2016) Go to next-to-eikonal Can have spin-dependent matrix element. Involves half-infinite Wilson lines
32 Polarized gluon TMD Exactly the same matrix element appears. Linear relation between and Our conjecture: YH, Nakagawa, Xiao, Yuan, Zhao (2017)
33 DLA limit of the DGLAP equation Model calculation More, Mukherjee, Nair,
34 Dijet production at next-to-eikonal Green s function cf. Altinoluk, Armesto, Beuf, Martinez, Salgado (2014)
35 Longitudinal single spin asymmetry in dijet production Interference between eikonal (Pomeron, Odderon) and next-to-eikonal (OAM) contributions. OAM interferes with odderon, but Pomeron usually dominates.
36 Pomeron contributions suppressed in the kinematic regions Measurable at the EIC!
37 Conclusions Let s get 5-dimensional. Even richer physics than GPD and TMD combined. Nice addition to the EIC agenda! OAM: Holy grail in spin physics. Connection to Wigner crucial. 3D distributions do not give direct access to (canonical) OAM. Diffractive dijet events in ep (photoproduction) and pa (UPC) Promising channel to study Wigner. Look at and dependences Progress in the small-x evolution of helicity distributions. Kovchegov, Pitonyak, Sievert Possibly large spin content in the small-x region?
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