Nucleon Spin Decomposition and Proton Spin Problem

 
N
ucleon spi
n decomposition
 
Yoshitaka Hatta
(Yukawa institute, Kyoto U.)
 
 
The proton spin problem
 
The proton has spin ½.
 
The proton is not an elementary particle.
 
Longitudinal double spin asymmetry in polarized DIS
 
           from polarized DIS
 
`Spin crisis’
 
In 1987, EMC (European Muon Collaboration) announced a very small value
of the quark helicity contribution
 
Recent value from NLO QCD global analysis
 
!?
 
Gluon polarization
 
DeFlorian, Sassot,
 Stratmann, Vogelsang (2014)
 
Note that the
 uncertainty 
from
the small-x region
 is huge!
 
R
esult from the NLO global analysis
after the RHIC 200 GeV
 
pp
 data
 QCD angular momentum tensor
QCD Lagrangian 
 Lorentz invariant 
                              
 Noether current
 
Jaffe-Manohar decomposition 
(1990)
 
Based on the 
canonical
 energy momentum tensor
 
Operators 
NOT
 gauge invariant.
 
Partonic interpretation in the light-cone gauge
Ji  decomposition 
(1997)
Improved (Belinfante) 
energy momentum tensor
 
 One can add a total derivative.
 
Generalized parton distributions (GPD)
 
Non
-forward proton matrix element
 
Twist-
two
 GPDs, accessible 
in
Deeply Virtual Compton Scattering (DVCS)
 
Lattice test of spin sum rule
 
Alexandrou et al. (2013)
 
Deka et al. (2015)
 
`Disconnected insertions’ included
Two spin communities divided
Jaffe-Manohar
Ji
 
Complete decomposition
 
Chen, Lu, Sun, Wang, Goldman (2008)
                                   Wakamatsu (2010)
                                                 Y.H. (2011)
 
Gauge invariant completion of Jaffe-Manohar
 
    where
 (
my
 choice)
OAM from the Wigner distribution
Lorce, Pasquini (2011)
Wigner distribution in QCD
Belitsky, Ji, Yuan (2003)
 
Which
 OAM is this??
Define
 
Engelhardt, talk at POETIC VI (2015)
 
Jaffe-Manohar
 
Ji
 
 vs.         on a lattice
 
s
taple length
Density of OAM
Understand 
this relation 
at the 
density
 level
Deconstructing
 OAM
 Ji’s OAM                         canonical OAM                    `potential OAM’        
 
``
D-type
 
``F
-type
Eguchi, Koike, Tanaka (2006)
The D-type and F-type correlators are related.
Relation to twist-three GPD
 twist-2
 YH. Yoshida (2012)
 
Quark canonical OAM density
 
First moment:
 
Wandzur
a-Wilczek 
part
 
g
enuine
twist-three
 
 
The b
ridge between JM and Ji
 
G
luon canonical OAM density
 
 twist-three gluon GPD
Transverse spin decomposition
U
se the 
Pauli-Lubanski vector
                    
instead of the angular momentum tensor              . 
        
Ji
 (1996)
Ji, Xiong, Yuan (2012)
 
Complete transverse 
spin
decomposition?
 
Longitudinal
 
 
 
 
Transverse
 
c
annot be separated in a
frame-independent way
s
ame!
 
YH, Tanaka, Yoshida (2012)
Computing
         
on a lattice?
Consider the usual quark distribution function
Nonlocal operator along the light-cone 
 
Real
-time problem
Becomes local
 after taking the x-moment.
Compute the naïve gluon helicity in 
some 
gauge
…gauge dependent, frame dependent.
 
Preliminary lattice study by 
xQCD collaboration
 
Conclusions
 
Complete gauge invariant decomposition of nucleon spin
now available in QCD, even at the density level
 
 
 
Relation between Jaffe-Manohar vs Ji fully understood
in terms of twist and GPD
.
Can we measure          in experiment?
    Hint: Wigner distribution measurable
 
 
YH, Xiao, Yuan (2016)
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Explore the complex realm of nucleon spin decomposition and the enigmatic proton spin problem, delving into concepts like orbital angular momentum, quarks and gluons' helicity, and longitudinal double spin asymmetry in polarized deep inelastic scattering. Learn about the spin crisis, gluon polarization, QCD angular momentum tensor, Jaffe-Manohar and Ji decompositions, generalized parton distributions, and lattice tests of spin sum rule.

  • Nucleon Spin
  • Proton Spin Problem
  • Quarks
  • Gluons
  • QCD Angular Momentum

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  1. Nucleon spin decomposition Yoshitaka Hatta (Yukawa institute, Kyoto U.)

  2. The proton spin problem The proton has spin . The proton is not an elementary particle. Orbital angular Momentum (OAM) Quarks helicity Gluons helicity In the quark model, with relativistic effects,

  3. from polarized DIS Longitudinal double spin asymmetry in polarized DIS p X

  4. `Spin crisis In 1987, EMC (European Muon Collaboration) announced a very small value of the quark helicity contribution !? Recent value from NLO QCD global analysis

  5. Gluon polarization Result from the NLO global analysis after the RHIC 200 GeV pp data DeFlorian, Sassot, Stratmann, Vogelsang (2014) Note that the uncertainty from the small-x region is huge!

  6. QCD angular momentum tensor QCD Lagrangian Lorentz invariant Noether current QCD angular momentum tensor quark helicity gluon helicity canonical energy momentum tensor Quark OAM Gluon OAM

  7. Jaffe-Manohar decomposition (1990) Based on the canonical energy momentum tensor Operators NOT gauge invariant. Partonic interpretation in the light-cone gauge

  8. Ji decomposition (1997) Improved (Belinfante) energy momentum tensor One can add a total derivative. Further decomposition in the quark part (but not in the gluon part)

  9. Generalized parton distributions (GPD) Non-forward proton matrix element Twist-two GPDs, accessible in Deeply Virtual Compton Scattering (DVCS)

  10. Lattice test of spin sum rule Alexandrou et al. (2013) Deka et al. (2015) `Disconnected insertions included

  11. Two spin communities divided measured by PHENIX, STAR, COMPASS, HERMES Nonexistent in Ji s scheme Jaffe-Manohar common and well-known not measured yet not even well-defined? Ji Define rigorously. Must be related to GPD! accessible from GPD measured at JLab, COMPASS, HERMES, J-PARC also calculable in lattice QCD

  12. Complete decomposition Chen, Lu, Sun, Wang, Goldman (2008) Wakamatsu (2010) Y.H. (2011) where (my choice) Gauge invariant completion of Jaffe-Manohar

  13. OAM from the Wigner distribution Wigner distribution in QCD Belitsky, Ji, Yuan (2003) Need a Wilson line ! Define Lorce, Pasquini (2011) Which OAM is this??

  14. Canonical OAM from the light-cone Wilson line YH (2011) Ji s OAM from the straight Wilson line Ji, Xiong, Yuan (2012) `Potential OAM Torque acting on a quark Burkardt (2012)

  15. vs. on a lattice Engelhardt, talk at POETIC VI (2015) Ji Jaffe-Manohar staple length

  16. Density of OAM Understand this relation at the density level ??

  17. Deconstructing OAM Ji s OAM canonical OAM `potential OAM ``F-type For a 3-body operator, it is natural to define the double density. ``D-type

  18. The D-type and F-type correlators are related. Eguchi, Koike, Tanaka (2006) doubly-unintegrate Canonical OAM density The gluon has zero energy partonic interpretation! YH. Yoshida (2012)

  19. Relation to twist-three GPD YH. Yoshida (2012) twist-2 twist-3 Penttinen, Polyakov, Shuvaev, Strikman (2000) integrate

  20. Quark canonical OAM density Wandzura-Wilczek part genuine twist-three First moment: The bridge between JM and Ji

  21. Gluon canonical OAM density twist-three gluon GPD WW part genuine twist-three first moment:

  22. Transverse spin decomposition Use the Pauli-Lubanski vector instead of the angular momentum tensor . Ji (1996) Ji, Xiong, Yuan (2012) YH, Tanaka, Yoshida (2012) Leader (2012) Frame dependent!

  23. Complete transverse spin decomposition? YH, Tanaka, Yoshida (2012) Longitudinal Transverse same! cannot be separated in a frame-independent way

  24. Computing on a lattice? Consider the usual quark distribution function Nonlocal operator along the light-cone Real-time problem Becomes local after taking the x-moment. nonlocal even though it is a moment. Local only in the light-cone gauge.

  25. Compute the nave gluon helicity in some gauge gauge dependent, frame dependent. Boost it to large momentum and do the matching Ji, Zhang, Zhao (2013) The limits and do not commute Not all gauges are allowed. The allowed gauges form a universality class. YH, Ji, Zhao (2013) Preliminary lattice study by xQCD collaboration Even the parton densities (PDF, , etc.) can be directly calculable? Ji (2013)

  26. Conclusions Complete gauge invariant decomposition of nucleon spin now available in QCD, even at the density level Relation between Jaffe-Manohar vs Ji fully understood in terms of twist and GPD. Can we measure in experiment? Hint: Wigner distribution measurable YH, Xiao, Yuan (2016)

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