Please visit Jefferson Lab Event Policies and Guidance before planning your next event: https://www.jlab.org/conference_planning.

# Light Cone 2018

14-18 May 2018
Jefferson Lab - CEBAF Center
US/Eastern timezone

## Dynamical observables for a J=1/2 system within a fully Poincare'-covariant framework

17 May 2018, 14:00
20m
F113 (Jefferson Lab - CEBAF Center)

### Speaker

Dr Giovanni Salme' (Istituto Nazionale di Fisica Nucleare -)

### Description

The formalism based on the Poincare' covariant spin-dependent spectral function, recently introduced [1] within the light-front (LF) Hamiltonian dynamics, allows one to develop a phenomenological tool for investigating three-fermion bound systems, in particular their dynamical observables. As it is well-known, several and quite relevant efforts are underway at JLAB with the aim of getting information on both the nucleon transverse-momentum distributions [2] and $^{\rm 3}$He and $^{\rm 3}$H structure functions [3]. In this contribution, it will be presented some new relations among the six T-even leading-twist transverse-momentum distributions (TMDs) of a three-fermion system, e.g. the nucleon in valence approximation. Such relations can be formally obtained once the valence contribution to the correlator for a J=1/2 bound system is expressed in terms of the spin-dependent spectral function, whose diagonal terms yield the probability distributions to find a constituent with given spin and LF momentum. Moreover, within the same framework, some preliminary results of the EMC effect for the three-nucleon system will be also provided. The spin-dependent spectral function is defined through the overlaps between the ground state wave function of the three-body system and the states given by a Cartesian product of a plane wave of LF momentum $\tilde{ \kappa}$ (describing the struck particle in the intrinsic reference frame of the cluster [1,(23)]) and a state describing the intrinsic motion of a fully interacting two-particle spectator subsystem. As an example of the rich wealth of information one can extract and check against the experimental outcomes, one could mention the decomposition of the spin-dependent momentum distributions, obtained after properly integrating the spectral function on the relative intrinsic momentum $k_{23}$ of the interacting spectator pair, viz $$n^\tau_{\sigma \sigma '}(x,{\bf k}_{\perp};{\cal M},{\bf S}) ~ = ~ {2 (-1)^{{\cal M} + 1/2} \over (1- x)}~ \int d { k}_{23}~ %k^2_{23} ~{E_{23}~E({\bf k_1})\over k^+_1}~ \left \{ ~{\cal Z}_{\sigma \sigma'}(k_{23}, L=0) ~ + ~ {\cal Z}_{\sigma \sigma'}(k_{23}, L=2) ~ \right \} ~$$ where $L$ is the orbital angular momentum of the one-body off-diagonal density matrix. By exploiting a similar result, but for the T-even leading twist TMDS, it will be shown that the linear relations proposed in Ref. [4] between the transverse parton distributions, i.e. $$\Delta f(x, |{\bf p}_{\perp}|^2 )= \Delta'_T f(x, |{\bf p}_{\perp}|^2 ) ~ + ~ {|{\bf p}_{\perp}|^2 \over 2 M^2}~ h^{\perp}_{1T}(x, |{\bf p}_{\perp}|^2 ) \quad \quad g_{1T}(x, |{\bf p}_{\perp}|^2 ) = - h^{\perp}_{1L}(x, |{\bf p}_{\perp}|^2 )$$ exactly hold in valence approximation when the contribution to the transverse momentum distributions from the angular momentum $L=2$ is absent. **References** [1] A. Del Dotto, E. Pace, G. Salme', S. Scopetta, Phys. Rev. C **95**, 014001 (2017). [2] Hall A, H. Gao et al, PR12-09-014: Target Single Spin Asymmetry in Semi-Inclusive Deep-Inelastic $(e, e' \pi^\pm)$ Reaction on a Transversely Polarized $^{3}$He Target; J.P. Chen et al, PR12-11-007: Asymmetries in Semi-Inclusive Deep-Inelastic $(e, e' \pi^\pm)$ Reactions on a Longitudinally Polarized $^{3}$He Target''. [3] MARATHON Coll., P. Gerassimov et al E12-10-103: MeAsurement of the $F_{2n}/F_{2p}$, d/u Ratios and A=3 EMC Effect in Deep Inelastic Electron Scattering Off the Tritium and Helium MirrOr Nuclei''. [4] R. Jacob, P.J. Mulders, and J. Rodrigues, Nucl. Phys. A **626,** 937 (1997); B. Pasquini, S. Cazzaniga, S. Boffi, Phys. Rev. D **78**, 034025 (2008); C. Lorce', B. Pasquini, Phys. Rev. D **84**, 034039 (2011).

### Primary author

Dr Giovanni Salme' (Istituto Nazionale di Fisica Nucleare -)

### Co-authors

Prof. Emanuele Pace (Rome Univ. "Tor Vergata" and INFN) Prof. Sergio Scopetta (Perugia University)

 Slides