at smallx Yoshitaka Hatta Yukawa institute Kyoto U YH Yuya Nakagawa BoWen Xiao Feng Yuan Yong Zhao PRD95 2017 114032 YH DongJing Yang PLB781 2018 213 The proton spin problem ID: 830452
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Slide1
Parton orbital angular momentum at small-x
Yoshitaka Hatta(Yukawa institute, Kyoto U)
YH,
Yuya
Nakagawa, Bo-Wen Xiao, Feng Yuan, Yong Zhao,
PRD95 (2017) 114032
YH, Dong-Jing Yang,
PLB781 (2018) 213
Slide2The proton spin problem
The proton has spin ½.
Quarks’ helicity
Gluons’ helicity
Orbital angular
Momentum
(OAM)
with relativistic effects,
EMC result (1987)
Current value
In the quark model,
The proton is not an elementary particle.
Slide3HUGE
uncertainty
from
the
small-x region
Maybe , after all?What’s the role of OAM? Achenauer,
Sassot, Stratmann, 1509.06489
from
H. Gao’s talk on Monday
Global analysis for
Slide4Wigner distribution and OAM
Lorce, Pasquini, (2011);
YH (2011)
`PDF’ for OAM
Wigner distribution
Phase space distribution of quarks and gluons Naturally defines the orbital angular momentum.
How does behave as ?
I give two arguments that
at small-x.
Slide5Twist structure of OAM distributions
Wandzur
a-Wilczek
part
YH,
Yoshida (2012)
Genuine twist-three part
Slide6OAM at small-x
Approximate
YH, Xiao, Yuan (2016)
``Dipole S-matrix”
Gluon Wigner distribution
Slide7Where is spin dependence?
“Pomeron” “
o
dderon
”
c
annot depend on the longitudinal spin
…forbidden by PT symmetryLesson: All information about spin is lost in the
eikonal approximation.
“spin-dependent
odderon”
Jian Zhou (2013)
Slide8OAM as a next-to-eikonal
effect
Go to
next-to-
eikonal
YH, Nakagawa, Xiao, Yuan, Zhao (2017)
Can have spin-dependent matrix element.
Involves
h
alf
-infinite Wilson lines
Slide9Unintegrated polarized gluon distribution
Exactly the same matrix element appears.
Linear relation between and
YH, Nakagawa, Xiao, Yuan, Zhao (2017)
Slide10`DGLAP’ equation for
OAM
cf.
Hagler
, Schafer (1998)
Slide11Numerical
results
`Democratic model’
YH, Yang (2018)
helicity
total
Slide12`Helicity dominance model’
total
helicity
Slide13Analytical insights
Use the ansatz
At small-x, helicity and OAM distributions are
related to each other by the
Regge
parameter .
Slide14Conclusion
OAM is the holy grail of spin physics. A lot of recent progress, still there’s a long way to go.x-distribution for OAM can be defined. Significant cancelation between OAM and helicity at small-x.
Beyond `DGLAP’:
Resum
double logarithms
talk by Matt Sievert on ThursdayExperimental observable for ?
talk by Shohini Bhattacharya on Thursday