Simonetta Liuti University of Virginia “ Garyfest 2010 ” Jefferson Lab October 29, 2010
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Simonetta LiutiUniversity of Virginia
“Garyfest 2010”Jefferson Lab
October 29, 2010
Generalized Parton Distributions Interpretationof Exclusive Deep Inelastic Processes
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Generalized Parton Distributions are a new way of interpretinga “growing” class of exclusive deep inelastic phenomena (X.Ji, D. Müller, A. Radyushkin)
Prototype Process: “Deeply Virtual Compton Scattering”
q
k'+=(X- Δ)P+, kT- Δ T
q'=q+Δ
k+=XP+, kT
P'+=(1- Δ )P+, - Δ TP+
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Amplitude
GPDs are embedded in soft matrix elements for deeply virtual Compton scattering
p+=XP+ p ’+=(X-Δ)P+
P’+=(1- Δ)P+
P+
p+q
q q ’=q+Δ
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GPDs – using the fact that factorization works at the amplitude level -provide a key to interpreting a number of “exclusive” DIS processes, other than DVCS
GPDs with Gary
Transversity and Tensor ChargeFrom exclusive DIS πo electroproduction
Studies of strange and charm content ofnucleon at Jlab/12 Gev and future ElectronIonCollider transversity
Deeply Virtual Neutrin
o Production of
πo from Nucleon and Nuclear Targets
Hyperon and charmed hyperon
transverse polarizationin unpolarized scattering
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Re k-
Im k-
3'1'
2'Re k-
Im k-
2' 3'
1'
X>ζ X<ζ
3
1
2
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P+
k’+=(-X)P+
P’+=(1- )P+
In ERBL region struck quark, k,is on-shell
k+=XP+
P+
k’+=(X-)P+
P’+=(1- )P+
PX+=(1-X)P+
In DGLAP region spectator with diquark q. numbers is on-shell
Analysis done for DIS/forward case by Jaffe NPB(1983)
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P+
k’+=(-X)P+
P’+=(1- )P+
ERBL region corresponds to semi-disconnected diagrams: no partonic interpretation
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(1) GPDs in ERBL region seem to be described withinQCD, consistently with factorization theorems, only by multiparton configurations
(2) Dispersion relations cannot be applied straighforwardly to DVCS. The “ridge” does not seem to contain all the information
borrowed from D. Mueller
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The next decade…role of QCD at the LHC
LHC results from multi-TeV CM energy collisions will open new horizons but many “candidate theories” will provide similar signatures of a departure from SM predictions…
Precision measurements require QCD input
QCD: A background for “beyond the SM discovery”
Interesting dynamical questions for QCD at untested high energies
Measured x-section Parton distributions Hard process x-section
σij
P2
P1
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Most important points for EIC
1) Our understanding of the structure of hadrons is … disconcertingly incomplete
2) Rich dynamics of hadrons can only be accessed and tested at the desired accuracy level in lepton DIS
Uncertainties from different PDF evaluations/extractions(ΔPDF)
are smaller than the differences between the evaluations(ΔG)
ΔPDF < ΔG
d-bar
u-valence d-valence
Gluon
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Strange and charm components studied through hard exclusive processes
Why exclusive processes?
LHC processes are sensitive to charm content of the proton Higgs production: SM Higgs, charged Higgs,
Precision physics (CKM matrix elements, Vtb ….): single top production, …
C.P.Yuan and collaborators
IC
IC
Electroproduction
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Data are at very low x where they cannot discriminate whether IC is there
10-2
x
10-3
IC/no-IC
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-Λc, Do, and Do exclusive production is governed by chiral-odd soft
matrix elements ( Generalized Parton Distributions, GPDs) which cannot evolve from gluons!
Λc, Do, and Do used as triggers of “intrinsic charm content”!
P+
p+q
q q’=q+γ
Chiral-odd GPDs: HT,ET,..
Λc, Do, …
Focus e.g. on heavy flavor production at EIC kinematics
-
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Intrinsic Charm (IC)
Gluon Fusion (GF)
vs.
IC content of proton can be large (up to 3 times earlier estimates) but PDF analyses are inconclusive (J.Pumplin, PRD75, 2007)
Inclusive
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Intrinsic Charm (IC)
“Light Cone” based Processes
Hadronic Processes
Meson Cloud: Thomas, Melnichouk …
Brodsky, Gunion, Hoyer, R.Vogt, …
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strangeγ*p K+ Λ 2Hu - Hd + Hs
γ*p Ko Σ+ Hd – Hs
γ*n Ko Σo Hu - Hs
(s)
p Hc
c
p
u
u Hc
p u + ud cud = Λc p ccuud (u u) cud = Λc - -
( 2 )( 1 )
What Observables? Spin Asymmetries from Exclusive Strange/Charm Quark Meson Production!
charmγ*p Do Λc
+ 2Hu - Hd + Hc
γ*p Do Σc+
Hd – Hc
γ*n Do Σco Hu - Hc
SU(3) (SU(4) for charm) relations allow one to extract Hs
(Hc)
(Λ)
(K+)
“di”quark“tetra”quark
(s)
(K+)
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Slice SU(4) weight diagrams to obtain SU(3) subgroup weight diagrams This replaces u,d,s by u,d,c octet relations
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Pseudoscalar Mesons Electroproduction and Chiral Odd GPDs(S. Ahmad, G. Goldstein and S.L., PRD (2008))
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LAB
e'
e γ*
Unpolarized Cross Section
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Q2 dependence in exclusive meson production
Jlab
Unexpected dominanceof transverse components
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“Regge factorization” QCD factorization
π o vertex is described by current operators: γ5 or γμ γ5
chiral-even structure
chiral-odd structure
GPDs: H, E,…~
~GPDs: HT, ET, HT, ET…
~
~
JPC=1--
JPC=1+-
ρ, ω, ..
b1, h
1
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t-channel exchange vertex
modeled as pseudoscalar-meson transition form factorIslam Bedir’s talk
ρ, ω b1, h1
ρ, ω, b1, h1
JPC=1-- (3S
1)
JPC=1+-
(1P1)
JPC=0-+
mesons quark content:
Q2 dependence
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Chiral Even Sector: M. Diehl and D. Ivanov (2008)
Only combination good for πo
production
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GPDs: H, E, and Weak Form factors~ ~
gP(t) = pseudoscalar form factor dominated by pion pole
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E~
Goeke et al.
1) For o production the pion pole contribution is absent!
2) The non-pole contribution is very small!
“non-pole” contribution
pion pole contribution
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πo,ηc electroproduction happens
mostly in the chiral-odd sector
it is governed by chiral-odd GPDs
issue overlooked in most recent literature on the subject
Since chiral-odd GPDs cannot evolve from gluons we have proven that charmed mesons production uniquely single out the “intrinsic charm content”!
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Helicity Amplitudes formalismfrom Goldstein and Owens
photon initial proton
final proton
pion
Factorized form
P’, ’
k’, ’
P,
k,
“quark-proton helicity amp.” quark scattering amp.
6 “f” helicity amps
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Rewrite helicity amps. expressions using new GFFs
Q2 dependent pion vertexGFFs
elementary subprocess
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Standard approach (Goloskokov and Kroll, 2009)
leading twist contribution within OPE, leads to suppression of transverse vs. longitudinal terms twist-3 contribution is possible
However… suppression is not seen in experiments
Need to devise method to go beyond the collinear OPE: considera mechanism that takes into account the breaking of rotational symmetry by the scattering plane in helicity flip processes (transverse d.o.f.)
See also
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Distinction between ρ,ω (vector) and b1,h1 (axial-vector)exchanges
JPC=1--
JPC=1+-
transition from ρ,ω(S=1 L=0) to πo(S=0 L=0) L =0
transition from b1,h1 (S=0 L=1) to πo(S=0 L=0) L =1
“Vector” exchanges no change in OAM
“Axial-vector” exchanges change 1 unit of OAM!
This yields configurations of larger “radius” in b space (suppressed with Q2)
Because of OAM axial vector transition involves Bessel J1
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At this point we need a sensible parametrization…
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In doing so … a large set of increasingly complicated and diverse observations is involved, from which PDFs, TMDs, GPDs, etc…are extracted and compared to patterns predicted theoretically
What goes into a theoretically motivated parametrization for GPDs...?
The name of the game: Devise an analytical form combining essential dynamical elements with a flexible model whose parameters can be tuned
However…for a fully quantitative analysis that is constrainedby the data it is fundamental to evaluate both the number and type of parameters
Multi-dimensional phase space (Elliott Leader)
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“Conventional” based onmicroscopic properties of the theory(two body interactions)
“Neural Networks” study the behavior of multiparticle systems as they evolve from a large and varied number of initial conditions.
Two main approaches
“Regge”Quark-Diquark
+ Q2 Evolution
Proceed conventionally at first:
Ahmad et al.,
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LSS06
New GPDs“physically motivated”ParametrizationG.Goldstein, O. Gonzalez Hernandez, S.L.
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Predict Ju and Jd
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Covariant quark diquark model
Re k-
Im k-
2' 3'
1'
X>ζ
3
1
2
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Skip some neat details, derivation from helicity amps. and connection withChiral Odd GPDs (Kubarovsky’s pi0 data)
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/2
H-
H+
(H+ + H-)/2=Hq
Q2 dependent
dominated by valence
Implement Crossing Symmetries in ERBL region
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ERBL Region Ahmad et al., EPJC (2009)
Determined from lattice moments up to n=3
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Recursive Fitting Procedure vs. Global Fits
In global fits we apply constraints simultaneously calculate χ2 (and covariance matrix) once including all constraints Need to find the solution for a system with n equations
Everytime new data come in the fit needs to be repeated from scratch
In a recursive fitting procedure (Kalman) one applies constraints sequentially
Need to update solution after each constraint Find solutions for < n systems, each one with fewer equations
Better control at each stage
Mandatory for GPDs (some of this is implicit in Moutarde’s approach)
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7 parameters per quark flavor per GPD, but we have not constrained the ζ dependence yet….. DVCS data
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Hall A
Hall B
GGL’s prediction based on our choice of physicalmodel, fixing parametersfrom “non-DVCS” data
Hall A
ζ=0.25
xBj=ζ
ζ=0.36
ζ=0.45
ζ=0.13
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For strange and charm Replace PDF used for light quarks GPDs with NP strange/charm based one
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HAPPEx+E734 G0 + BNL E734
Replace FF used for light quarks GPDs with upper limit on charm based one
Pate, McKee, Papavissiliou, PRC78(2008)
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G.Goldstein, S.L. (preliminary)
Ratio ηc/πo
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Problem of Transverse Polarization of Hyperons and Charmed Baryons in unpolarized pp collisions
p Λ
p What generates polarization?
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Spin degrees of freedom in pp scattering
Outstanding puzzle!
Collinear Factorization
Polarizing Fragmentation Function
Non Collinear Factorization
D. Boer, DIS 2010
Set of all data compiled by K. Heller
Go beyond collinear factorization,Insert kT and polarization dependent
Fragmentation function
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1.Gluon fusiondominant mechanismfor producing polarizedmassive quark pair2. Low pT phenomenon3. Recombination rules
Model of hyperon polarization
Dharmaratna & GRG (1990,96,99)
PΛ
pT (GeV)
PΛ
pT (GeV)+pC+X Polzn(ΛC) E791
Large mass scale
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Hyperon and Charmed Hyperon Polarization work with G. Goldstein and P. Di Nezza (ALICE)
ud
anti-c
Λc
+
Dharmaratna and Goldstein
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Interpretation in new language of GPDs:Generalized Fracture Functions
Next, new frontier…..
H
T
h hpp
See also work by•F. Ceccopieri and L.Trentadue Phys.Lett.B (2006)•D. Sivers, PRD81(2010)•O.Teryaev, Acta Phys. Polonica (2002)•A. Kotzinian, PLB (2003)
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Finally, somewhat unrelated…
Work in progress with K. Kathuria,and S.Taneja (BNL) What observables?
AUT.....
Taneja and S.L., arXiv:1008.1706
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Conclusions and Outlook
My own interaction with Gary has given me ”lots of courage”
Together we keep on generating ideas, students are getting involved, more projects, collaborations….