1. Theory Introduction to Semi-Inclusive Physics
Jianwei Qiu
Brookhaven National Laboratory
Jefferson Lab (Jlab) 2014 Joint Hall A/C Summer Meeting
JLab, Newport News, VA, June 4-5, 2014

2. DIS vs. SIDIS  E E’ Inclusive DIS – one scattering plane:
Localized probe:  E E’
Two independent variables:
Semi-inclusive DIS (SIDIS) – two scattering planes:
Leptonic plane:
Hadronic plane:
Path of the color flow
Angle between two planes:

3. Semi-inclusive DIS Naturally, two scales: Spin-motion correlation:
high Q – localized probe
To “see” quarks and gluons
Low pT – sensitive to confining scale
To “see” their confined motion
Theory – QCD TMD factorization
Confined
motion
Spin-motion correlation:
4 spin combinations
Various TMDs: vector, axial vector, tensor
Needs
4 spin combinations

4. TMDs – role of spin and motion
Rich quantum correlations:
8 leading power (twist) quark TMDs:
Similar for gluons

5. Quantum correlation between hadron and parton
Sivers effect – between hadron spin and parton motion:
Hadron spin influences
parton’s transverse motion
Sivers function o
Observed
particle
Parton’s transverse spin
influence its hadronization
Collins function
Transversity
Collins effect – between parton spin and hadronization:
Observed
particle
JLab12, COMPASS, and low energy EIC for valence,
covers the sea and gluon!

6. SIDIS – the best for probing TMDs
Naturally, two planes:
Separation of TMDs:
Collins frag. Func.
from e+e- collisions
Very hard, if not impossible, to separate TMDs in hadronic collisions
Using a combination of different observables (not the same observable):
jet, identified hadron, photon, …

7. QCD corrections Sources of parton kT at the hard collision:
Gluon shower
Confined motion
Emerge of a hadron
hadronization
Parton kT generated by the shower caused by the collision:
Has very little to do with the kT in hadron wave function – hadron structure
At large Q2 and collision energy (large phase space),
the shower generated kT could be perturbative
Q2 – evolution of the cross section
“True” parton structure:
Input distribution for the Q2 evolution - nonperturbative

8. Factorization for SIDIS
TMD fragmentation
Leading power contribution:
Soft factors
Low PhT – TMD factorization:
TMD parton distribution
High PhT – Collinear factorization:
PhT Integrated - Collinear factorization:

9. Modified Universality of TMDs
TMD distributions with non-local gauge links:
Parity + Time-reversal invariance:
The sign change is a critical test of TMD factorization approach

10. Evolution of TMDs Evolution in the b-space – Fourier transform of kT:
RG equations:
Boer, 2001, 2009, Idilbi, et al, 2004
Aybat, Rogers, 2010
Kang, Xiao, Yuan, 2011
Aybat, Collins, Qiu, Rogers, 2011
Sun, Yuan, 2013 …
Evolution equations for Sivers function:
CS:
RGs:

11. Numerical “prediction” for evolution
Aybat, Prokudin, Rogers, 2012:
Huge Q
dependence
Sun, Yuan, 2013:
Smaller Q
dependence
No disagreement on evolution equations!
Issue: extrapolation to non-perturbative large b-region
choice of the Q-dependent “form factor” – more work needed!!!

12. SIDIS Drell-Yan e–e+ to pions World effort on TMDs proton lepton
EIC
BNL
JPARC
FNAL
proton
lepton
antilepton
proton
lepton
pion
SIDIS
Drell-Yan
BESIII
Partonic scattering amplitude
Fragmentation amplitude
Distribution amplitude
electron
positron
pion
Test of the sign change!
e–e+ to pions

13. Transition from low pT to high pT
TMD factorization to collinear factorization:
Two factorization are
consistent in the overlap
region where
TMD
Collinear Factorization
Quantum interference – high pT region (integrate over all kT):
Non-probabilistic quark-gluon quantum correlation
Single quark state quark-gluon composite state
(Spin flip)
interfere with
Kang, Yuan, Zhou, 2010

14. Twist-3 correlation functions
Twist-2 parton distributions:
Kang, Qiu, PRD, 2009
Unpolarized PDFs:
Polarized PDFs:
Two-sets Twist-3 correlation functions:
Role of color magnetic force!

15. Evolution of twist-3 correlation functions
Kang, Qiu, 2009
Closed set of evolution equations (spin-dependent):
Plus two more equations for:
and

16. Sample scale dependence of twist-3 correlations
Kang, Qiu, 2009
Follow DGLAP at large x
Large deviation at low x (stronger correlation)
Matching between low pT (resum) and high pT (fixed)
Kang, Xiao, Yuan, 2011

17. Single-spin asymmetry in hadronic collisions
Consistently observed for over 35 years!
ANL – 4.9 GeV
BNL – 6.6 GeV
FNAL – 20 GeV
BNL – 62.4 GeV
BNL – 200 GeV
Definition:

18. Do we understand it? Early attempt: QCD factorization at twist-3: 2
Kane, Pumplin, Repko, PRL, 1978
Early attempt: 2
Cross section:
Asymmetry:
Too small to explain available data!
QCD factorization at twist-3:
Qiu and Sterman, NPB, 1991
Sivers - type
Collins - type

19. A sign “mismatch” if keeps only Sivers-type
Sivers function and twist-3 correlation:
Kang, Qiu, Vogelsang, Yuan, 2011
+ UVCT
“direct” and “indirect” twist-3 correlation functions:
Calculate Tq,F(x,x) by using the measured Sivers functions
direct
direct
indirect
indirect
Metz & Pitonyak, 2013
Important role of Collins’ effect to single pion production – twist-3 FFs
SIDIS – separate two effects by difference in angular distribution

20. Flavor structure of the proton sea
The proton sea is not SU(3) symmetric!
Violation of Gottfried sum rule
Confirmed by Drell-Yan exp’t
Why ?
Why does change sign?

21. Challenges for d(x) – u(x)
All known models predict no sign change!
Meson cloud
Chiral-quark soliton model
Statistic model
Future experiments:
Fermilab E906
Very important
non-perturbative physics
What is the ratio as
x increases?

22. Asymmetry between strange and up/down sea?
LO and NLO QCD global fitting to DIS data:
with
for x > 0.1
New LHC data on W/Z data:
HERMES data:
Does not follow the shape of u(x) + d(x)?
Why strange sea behave so different?
Need FFs
PT-integrated SIDIS:

23. Hadronization puzzle
Strong suppression of heavy flavors in AA collisions:
Emergence of hadrons:
How do hadrons emerge from a created quark or gluon?
How is the color of quark or gluon neutralized?
Need a femtometer detector or “scope”:
Nucleus, a laboratory for QCD
Evolution of partonic properties

24. Nucleus as a “detector”
The “vertex” detector
At a fermi scale
Nucleus in SIDIS is
an ideal “vertex” detector
Need a good control of the kinematics
of fragmenting parton
Almost impossible for a hadron machine

25. Color neutralization – energy loss
Unprecedented ν range at EIC: D0
Control of ν and
medium length!
Heavy quark energy loss:
Mass dependence of fragmentation
pion D0
semi-inclusive
DIS π
Need the collider energy of EIC
for heavy flavors

26. PT broadening of leading hadron in SIDIS
Definition:

27. Color fluctuation – azimuthal asymmetry
Preliminary low energy data:
Hicks, KEK-JPAC2013
Contain terms in cos(φpq) and cos(2φpq)
only statistical uncertainties shown
Classical expectation:
Any distribution seen in Carbon should be washed out in heavier nuclei
Surprise:
Azimuthal asymmetry in transverse momentum broadening
Spin-”orbital” correlation + soft multiple scattering
Qiu & Pitonyak
In preparation

28. SIDIS’ role in probing the gluon saturation
Strong suppression of dihadron correlation in
Theory
Simulation
ϕ12
Never been measured!
Directly probe Weizsacker-Williams (saturated) gluon distribution
in a large nucleus
A factor of 2 suppression of away-side hadron-correlation!
No-sat: Pythia + nPDF (EPS09)

29. Summary
SIDIS in eP offers many more better controlled observables to probe QCD’s confining features and hadron’s partonic structure
From 3D confined motion to quantum interference of different parton states
Best channel for probing TMDs
SIDIS in eA collision is ideal for probing “hadronization”,
“color neutralization”, QCD energy loss, …
JLab12 is excellent for the valence region, while a future
EIC will cover the sea and gluon
A future could help continue to keep the US’s leadership position in nuclear physics and …
Thanks!

30. Electron-Ion Collider (EIC)
A giant “Microscope”
To “see” quarks and gluons
A sharpest “CT”
To “cat-scan” nucleons and nuclei