Observing the proton off the light-cone
Transcript Observing the proton off the light-cone
Observing the proton
Off the light-cone
University of Maryland/SJTU
JLab Physics Colloquium,
April 23, 2013
Collaborators and papers
Feng Yuan, LBL
Jianhui Zhang, Shanghai Jiao Tong University
Xiaonu Xiong, Peking University
Yong Zhao, U. Maryland
1. Phys. Rev. Lett. 109, 152005 (2012)
2. Phys.Lett. B717 (2012) 214-218
3. Parton picture for longitudinal polarization, Phys. Rev. D
4. Physics of gluon helicity
5. parton distribution from Euclidean lattice
Frame dependence in relativistic quantum
Two special frames for understanding the
proton structure: the lab frame and infinite
momentum frame (IMF)
The proton spin structure in IMF
Lattice QCD calculation of parton physics in
An important mission of Jlab 12 GeV upgrade
and EIC is to study the internal structure of
proton and neutron at a new level.
A complex system of the quarks and gluons
Strong interactions, relativistic
Test the fundamental theory: QCD
Constraints of Relativity
The proton wave function is a frame
Boost operators, Ki, are interactiondependent
|P˃ = U(Λ(p)) |p=0>
U is not just kinematical, it is dynamical!
Wave functions in Relativistic QM
Wave function is not a Lorentz invariant
concept as it is defined by observations of
different space points in a fixed time
(simultaneously) at a particular frame.
Simultaneity for two events in one frame does
not mean simultaneity in a different frame.
In general, WF has not been very a popular
concept in field theory. However, it is an
important and intuitive concept.
Two special frames
Lab frame: where the proton is at rest, or low
momentum, relatively speaking
Probe frame: in which the electron or virtual
photon has the smallest momentum.
In high-energy limit, the probe frame reaches
the infinite momentum frame (IMF), i.e., the
proton is probed as it travels at the speed of
four momentum transfer qµ = (v, q) is a space
like vector v2-q2 < 0 and fixed.
smallest momentum happens when v=0, Q2=q2
Pq = P3Q = Q2/2x, thus P3 = Q/2x.
In the scaling limit, P3 -> infinity.
Reconcile physics in two frames
Physics shall be frame-independent!
In the rest frame, one probes the light-cone, timedependent correlations (light-front)
In the IMF, one probes the static correlations.
The two different correlations are related by
If one uses the light-front quantization in the
rest frame (an effective theory), one gets
the same physics as IMF!
Proton WF in the IMF is what high-energy
IMF and parton physics
In the IMF, the interactions between
particles are Lorentz-dilated, and thus the
systems appear as if interaction free: the
proton is made of free partons.
This is only true to a certain degree: leading
twist. The so-called higher-twist
contributions are sensitive to parton offshellness, transverse momentum and parton
Partons provide a useful language to
understand the proton structure.
Spin of the proton in QCD
The spin of the proton is generated from the
angular momentum of the internal quarks and
From general consideration,
one can write down,
J 1/ 2 J q ( ) J g ()
The quark orbital contribution
can be probed through GPDs
These are frame-independent
The spin structure in IMF
How is the spin of the proton generated from
the AM of the underlying partons?
Quark orbital AM:
Orbital AM is nominally a leading twist,
however, it is actually a high-twist
contribution because it involves the parton
The total contribution can be probed through
the GPD sum rule (L=J-ΔΣ. However, the
individual parton contributions do not yet
have a simple parton picture.
OAM parton distribution can be probed
through twist-three GPDs. (Ji, xiong, & yuan)
In IMF, however, the gluon partons have welldefined helicity ± 1 and densities g±(x)
+1 or -1
Gluon helicity distribution is
g(x) = g+(x) – g-(x) and
G = ʃdx g(x)
Total gluon helicity
The total gluon helicity ΔG is gauge invariant,
and has a complicated expression on the rest
In light-cone gauge A+=0, it reduces to a
, which is the spin of
the gluon, but has no gauge-symmetric notion
ALL from RHIC 2009
p0 p (GeV/c)
Q = 10 GeV
PHENIX Prelim. p , Run 2005-2009
PHENIX shift uncertainty
DSSV++ for p 0
STAR Prelim. jet, Run 2009
Dc = 2% in DSSV analysis
STAR shift uncertainty
DSSV++ for jet
PHENIX / STAR scale uncertainty 6.7% / 8.8% from pol. not shown
Jet p (GeV/c)
Dg(x) = 0.1±
Dg(x,Q ) dx
Perspective on Delta G
Q2 = 10 GeV 2
RHIC 200 GeV
in units of h
ò g(x,Q2) dx
Q = 10 GeV
Dg(x) = 0.1±
Total gluon helicity in the IMF
A gauge potential can be decomposed into
longitudinal and transverse parts (R.P.
The transverse part is gauge covariant,
One can define the gauge-symmetric gluon
spin as ExA┴ (X.Chen et al, 2009)
It be shown that ΔG is the matrix element of
about operator in the IMF. (Ji, Zhang, Zhao)
Reproducing the light-cone gauge
result by boost
In fact, transforming to the rest frame
Which in the light-cone gauge, reduces to the
standard expression ExA.
Transverse polarization in term of the
polarization vector S is of subleading, thus
does not seem to have a simple parton picture
However, this is incorrect.
There are many misconceptions and pitfalls
about transverse pol.
The best language is not the transverse AM,
rather, it shall be transverse Pauli-Lubanski
spin. [Transverse AM does not commute with
There is a leading twist-contribution, the
subleading contributions either are cancelled
or related to the leading one by symmetry.
The leading contribution has a partonic
First pointed out by Burkardt (2005), but the
connection to the spin sum rule was not
A plane-wave derivation of transversespin parton sum rule
Consider parton momentum density
It has a “distribution” term depending on
Calculating its contribution to the transverse
The Feynman momentum is easier to understand in the
infinite momentum frame: fraction of the longitudinal
momentum carried by quarks x = kz/Pz, 0<x<1
Lattice QCD calculation
Current approach is based on the rest frame
To compute light-cone correlation difficult
because the lattice cannot handle real time
One can calculate the moments (2-3) of
parton distributions: local operators.
Lattice QCD calculations
Parton distributions are calculated using the
rest-frame formalism, the corresponding
operators are light-cone correlations
Since lattice cannot handle real-time
dependence, only moments are calculated on
Usually only a few moments (2-3) are
A new proposal
Using the IMF formalism.
Start with static correlation in the zdirection.
X. Ji, to be published
This can be proved using the local matrix
Approaching the light-cone through boost
One-loop calculation demonstrates how this
The extension of the approach
The extension of the approach
Light-cone wave functions, higher-twists….
In high-energy scattering, one probes parton
physics, which can be understood both in the
rest frame and IMF formulation
Understanding the spin structure of the
proton in term of partons needs more
theoretical and experimental efforts
Parton physics is best calculated in lattice
QCD using IMF formalism.