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Introduction to pQCD and TMD physics
Lecture 3: TMD physics (I)
Zhongbo Kang
Los Alamos National Laboratory
Spinfest 2016
University of California, Riverside
July 25 – 26, 2016
The proton in QCD
 Proton is made of



2 up quarks + 1 down quarks
u
+ any number of quark-antiquark pairs
u
+ any number of gluons
d
Infinite many …
 Fundamental questions for proton structure (what is the internal
landscape of the nucleons?)




What are the momentum distributions of quarks, antiquarks, and gluons?
How are quarks and gluons distributed spatially?
How do partons carry the proton spin-1/2? (spin and orbital angular momentum)
How are these quark and gluon distributions correlated with overall nucleon
properties, such as spin direction?
2007 nuclear physics long range plan
EIC white paper
Parton distribution functions (PDFs), Transverse momentum
dependent distributions (TMDs), …
2
2 ep eX
2
2
d
4
y
2
e.m.
Collinear
one-dimensional
picture
Deep Inelastic
ScatteringPDFs:
:
=
1
y
+
F
(x,Q
)
2
2
4
dxdQ
xQ
2
• Scaling violation: dF 2/dlnQ2 and
linear DGLAP
Universal (measured)
calculableEvolution
G(x,Q2)
em
F2 -log10(x)
ZEUS
x=6.32E-5 x=0.000102
x=0.000161
x=0.000253
x=0.0004
x=0.0005
x=0.000632
x=0.0008
5
ZEUS NLO QCD fit
tot. error
ZEUS 96/97
x=0.0013
BCDMS
E665
x=0.0021
NMC
4
y2
FL (x,Q2 )
2
Gluons dominate
low-x wave function
x=0.0032
x=0.005
x=0.008
xG ( 1
3
x=0.013
)
xd v
x=0.021
x=0.032
2
20
xu v
xS ( 1
x=0.05
20
)
x=0.08
x=0.13
x=0.18
1
x=0.25
x=0.4
3
x=0.65
0
1
10
10
2
10
3
10
4
10
2
Q2(GeV )
5
3
Recent advance in hadron structure
 Hadron 3D structure: both longitudinal + transverse momentum
dependent structure (confined motion in a nucleon)
Transverse Momentum Dependent parton distributions (TMDs)
 Transversely polarized scattering provides new structure of proton
Longitudinal motion only
Longitudinal + transverse motion
4
Parton’s transverse motion
 Parton’s transverse momentum is usually smaller than the longitudinal
component in the proton, which moves very fast in the longitudinal
direction, how do we probe the parton’s transverse motion?
k~xp
q
p
 Use transverse spin as a probe: transverse-spin dependent
observables are sensitive probes of the partons transverse
momentum as they can correlate with each other
Transverse spin physics
5
Spin physics: excellent laboratory for QCD
 We are looking into both the partonic dynamics at the short distance,
as well as the nucleon structure at long distance
QCD Factorization
6
Transverse spin physics: birth and growth
 Remarkable development of this field


From the sidelines in strong interaction physics
To center stage in our efforts to figure out QCD
 Numerous exciting new developments over recent years

Differential citation grows exponentially as a function of time
Sivers
Collins
250
200
150
100
50
0
1990 - 1993 1994 - 1997 1998 - 2001 2002 - 2005 2006 - 2011
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Example: experimental observable
 Consider a transversely polarized proton scattering with an
unpolarized proton or lepton
0.03
p+
p-
e + 3He­ ® p± + X
0.02
3
ANHe
0.01
0
JLab Hall A
-0.01
-0.02
-0.03
0.6
0.65
0.7
p [GeV/c]
T
sp
Left
Right
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SSA vanishes with collinear momentum only
 If one assumes partons are purely collinear
Kane-Pumplin-Repko, 1978
 AN≠0: result of parton’s transverse motion
 A new window: much richer QCD dynamics
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How many distributions are needed
 In order to fully characterize the proton structure, how many parton
distribution functions are actually needed
TMD parton
distribution
TMD fragmentation
function
U
Quark Polarization
L
T
Pion
Collins
10
Good textbooks
 Understand C, P, T discrete symmetry properties of the correlation
function

Most textbooks on quantum field theory will give discussion (somewhat limited) on
this topic, such as Peskin, Sterman

If you want extensive discussion, see this book
11
Operator analysis
 Operator analysis to figure out how many distributions are needed to
characterize the nucleon structure
 I provide a detailed study for spin-0 particle
 For details, see



Mulders, Tangerman hep-ph/9403227
Mulders, Tangerman hep-ph/9510301
Mulders, http://www.nat.vu.nl/~mulders/correlations-0new.pdf
 The next slide continues after I mentioned gauge link
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Sivers function: non-universal
 Sivers function: unpolarized quark distribution inside a transversely polarized
proton
Spin-independent
Spin-dependent
Sivers effect
left-right asymmetry
sp
Look closer
Left
Right
 Naïve time-reversal-odd:
recall momentum and spin
change sign under T
 Forbidden?: such kind of
correlation is forbidden in Tinvariant theory (QCD),
unless there is a phase
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Where does the phase come from
 Existence of the Sivers function relies on the interaction between the
active parton and the remnant of the hadron

σ=
=

σ=
=
DIS: final-state interaction
+
+
+…
+
+…
⊗
Drell-Yan: initial-state interaction
+
⊗
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Sivers function: sign change
 Light-cone trajectory
DY
−∞
⊥"
DIS
y⊥
0
y−
+∞
!"
 Parity and time-reversal invariance
NSAC milestone: most important property of the Sivers function,
need to be tested
15
Sivers effect: QCD version of Aharonov-Bohm effect
 Pure quantum effect: different paths lead to interference
 Physics today, September 2009
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The history of Sivers function
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