simonetta liuti university of virginia - home | jefferson lab
TRANSCRIPT
Realistic parameterization of GPDs and its
applications
Simonetta Liuti
University of Virginia
Jlab Theory Group SeminarNovember 10th, 2008.
Collaborations
Gary Goldstein (Tufts University)
Leonard Gamberg (Penn State, Berks)
Eric Voutier (Grenoble)
AHLT: Saeed Ahmad (U. Wisconsin), Heli Honkanen
(Iowa State), S.L., Swadhin Taneja
Graduate Students: Osvaldo Gonzalez, Chuanzhe Lin,
Huong Nguyen, Dan Perry
Outline
Unpolarized GPDs from proton and neutron data sets
New results using Jlab data constraints!
Access to Chiral-Odd GPDs
Practical method for the extraction of both
tensor charge: q “Burkardt's moment”: Tq
Nuclei: DVCS and p0 electroproduction on 4He
Conclusions/Outlook
No longer simple models (D. Muller)
Include Q2 dependence (M. Diehl)
Include all constraints from data DVCS, DVMP... (S.L.)
Include new data as they become available... (S.L.)
Use Lattice + Chiral Extrapolations (P. Hägler, A. Schaefer)
Connect various experiments, separate valence from sea,
flavors separation (T. Feldman)...
New! Representation in terms of dispersion relation only
necessary to measure imaginary part? Stronger polynomiality
constraint (Anikin, Teryaev, Diehl, Ivanov, Vanderhaeghen)
A more advanced phase of extracting GPDs from data
(a bit of summary from ECT*, June'08, and Jlab Hall B meeting, Aug.’08)
A similar program exists for TMDs (simpler partonic interpretation than
GPDs) see e.g. M. Anselmino and collaborators
GPDs give access to orbital angular momentum of partons!
DVCS and Generalized Parton Distributions
GPDs are hybrids of PDFs and FFs: describe simultaneously
x and t-dependences !
GPDs give access to spatial d.o.f. of partons !
“Generalized Parton Distributions Correlator”
t= 2
X. Ji
What goes into a theoretically motivated
parametrization...?
The name of the game: Devise a form combining
essential dynamical elements with a flexible model
that allows for a fully quantitative analysis
constrained by the data
Hq(X, t)= R(X, t) G(X, t)
“Regge” Quark-Diquark
Q2 Evolution is an essential element!!
S. Ahmad, H. Honkanen, S. Liuti and S.K. Taneja,
Phys. Rev. D 75, 094003 (2007)
Two different time orderings/pole structure!
Quark anti-quark pair describes similar physics (dual to) Regge t-channel exchange!!
DGLAP ERBL
X> X<
t
In DGLAP region partonic picture
PX
+
P'+=(1- )P+
k+=XP+k'+=(X- )P+
q q+
k' =k -k
P+
ReggeQuark-Diquark
Formulae extended to >0 in AHLT2 (arXiv:0708.0268).
Parton Distribution Functions
Notice! GPD parametric
form is given at Q2=Qo2
and evolved to Q2 of data.
Notice! We provide a
parametrization for
GPDs that
simultaneously fits
the PDFs:
q(x) = Hq(x,0,0)
Polynomiality
For higher moments (n=2,3,...) use lattice results
(consistency with data can be checked Juvs. J
d)
n=2
n=3
Chiral Extrapolations
Dorati, Gail and Hemmert (2007)
Wang, Thomas, Young (2008)Ashley et al. (2003)
-t (GeV2)
Summary of Constraints
Constraints from Form Factors
Dirac
Pauli
Constraints from PDFs
Further Theoretical Constraints:
● Sensible prediction for hadron shape at x 1
● Sensible prediction for kT
dependence (connection with TMDs!)
(SL and Taneja, 2004)
Constraints from Polynomiality
AHLT Parameterization
v1
v2
7 + 1 (Qo) parameters
10 + 1 (Qo) parameters
More details in AHLT, PRD 2007
0
use v1 for DGLAP region (X > )
0
The ERBL Region…partonic interpretation is not obvious
We know the area from
n=1 moment + constrained
DGLAP
We extract it from lattice QCD results
Hybrid Model (Dieter Mueller)
Weighted Average Value
Location of X-bin
Dispersion (error in X)
We know n 3 moments
Reconstruct GPDs from Bernstein moments
Comparison with Jlab Hall A data (proton)Munoz Camacho et al. (2006)
Im H from asymmetry
Note!!
Re H from x-section
VGG: crisis or not?
Cannot reproduce both!
Im F
Re
F
Guidal (2008)
Polyakov and Vanderhaeghen
(2008)
vanishes at X=0 as X
cusp
Fitted directly at Q
of data
(X- ) “DA type” shape needed to fit
“t”-dependence of Jlab data!!!
●Behavior determined by Jlab data on Real Part and Q2 dependence
S. Ahmad
●Consistent with lattice determination!
Viewed this way a quark + spectator cannot be on their
mass shell but hadronic jets must have some threshold.
This threshold (“physical threshold”) is much higher than what
required for the dispersion relations to be valid
Where is threshold?
Continuum starts at s =(M+m )2 lowest hadronic threshold.
How to fill the gap? Analytic continuation?
t
0 physical
phys ifmasses in the two-body
scattering problem are different!
Q2=1.0 GeV2Q2=2.0 GeV2
Q2=5.5 GeV2
-t -t
-t
-2.4>t>-7.4 GeV2
Physical region
has no gap for Q2=5.5 GeV2
-1.1>t>-2.7 GeV2
Physical region
has no gap for Q2=2.0 GeV2
-0.60>t>-1.34 GeV2
Physical region
has no gap for Q2=1.0 GeV2
Gaps in dispersion integrals
From Gary Goldstein, SPIN 2008
When deeply virtual processes involve directly final states
- like in exclusive or semi-inclusive processes - “standard kinematic
approximations should be questioned” (Collins, Rogers, Stasto, 2007)
Transversity
u
dET(x, , t,Q2) = T
q HT(x, , t,Q2)
h1(x,Q2) = q f1(x,Q2)
HT(x, , t,Q2) = q H(x, , t,Q2)
Related to Boer-Mulders function: h1
Simple Ansatzh1
JPC=1-- JPC=1+-
JPC=1--, 1+-
, ...HT, E
T, ...
Only chiral-odd GPDs!!!
JPC=1++, ... (a1-type exchange) H, E, ... ~ ~
What goes into the quark-hadron
amplitudes?
Generalized Form Factors
HT(X,0,0) = h
1(X) = transversity
h1(X,Q2) dX = q= tensor charge
h1
(X) dX d2k
T ~ -
T (A.Metz)
E2(X,0,0) dX =
T = Burkardt's moment
t-channel exchange
vertex
modeled as F (pseudoscalar-
meson transition form factor)
, b1, h
1
, , b1, h
1
JPC=1--
(3S
1)
JPC=1+-
(1P
1)
JPC=0-+
quark content:
Distinction between and b1, h
1exchanges
JPC=1--
JPC=1+-
o: qqbar from S, L S=0, L L
o: qqbar from (S=0, L=1) (S=0,L=0) L =1
“Vector” exchanges no change in OAM
“Axial-vector” exchanges change 1 unit of OAM!
Main Result: Tensor Charge and Anomalous Transverse Moment treated as
free parameters to be extracted from data
Fixed u
and d
GPDs & hadron tensor for Spin 0 nuclear target
(S.L. and SwadhinTaneja, PRC 2005)o production
(with G. Goldstein)
Spatial structure of quarks and gluons in nuclei
Burkardt-Soper
impact parameterquark's position
in nuclei
4He
o
0
0
+1/2
+1/2
-1/2
0
f 0,00(s,t,Q2) = g +,0- A0+,0 -
analogue of HT
JPC= 1+- exchange b1, h1
&
JPC= 1- - exchange 0,
mquark=0 has to flip helicity
for q +q and q q 0.
o
00
+1,0
b1 & h10 &
4He
0
4He 4Hestructure of p p
A+i(p +p) B 2 invariant amps,
2 independent helicity amps
o electro-production from 4He
Conclusions and OutlookComparison between GPD models and data is indeed possible...GPD extraction is possible!!!
Approaching “Global Analysis”
Interesting connections between TMDs and GPDs
Proposed extraction of tensor charge and transverse anomalous moment from neutral pion production data
Spatial structure of Nuclei