Simonetta LiutiUniversity of Virginia

“Garyfest 2010”Jefferson Lab

October 29, 2010

Generalized Parton Distributions Interpretationof Exclusive Deep Inelastic Processes

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+

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

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

Re k-

Im k-

3'1'

2'Re k-

Im k-

2' 3'

1'

X>ζ X<ζ

3

1

2

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)

P+

k’+=(-X)P+

P’+=(1- )P+

ERBL region corresponds to semi-disconnected diagrams: no partonic interpretation

(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

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

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

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

Data are at very low x where they cannot discriminate whether IC is there

10-2

x

10-3

IC/no-IC

-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

-

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

Intrinsic Charm (IC)

“Light Cone” based Processes

Hadronic Processes

Meson Cloud: Thomas, Melnichouk …

Brodsky, Gunion, Hoyer, R.Vogt, …

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+)

Slice SU(4) weight diagrams to obtain SU(3) subgroup weight diagrams This replaces u,d,s by u,d,c octet relations

Pseudoscalar Mesons Electroproduction and Chiral Odd GPDs(S. Ahmad, G. Goldstein and S.L., PRD (2008))

LAB

e'

e γ*

Unpolarized Cross Section

Q2 dependence in exclusive meson production

Jlab

Unexpected dominanceof transverse components

“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

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

Chiral Even Sector: M. Diehl and D. Ivanov (2008)

Only combination good for πo

production

GPDs: H, E, and Weak Form factors~ ~

gP(t) = pseudoscalar form factor dominated by pion pole

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

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”!

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

Rewrite helicity amps. expressions using new GFFs

Q2 dependent pion vertexGFFs

elementary subprocess

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

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

At this point we need a sensible parametrization…

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)

“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.,

LSS06

New GPDs“physically motivated”ParametrizationG.Goldstein, O. Gonzalez Hernandez, S.L.

Predict Ju and Jd

Covariant quark diquark model

Re k-

Im k-

2' 3'

1'

X>ζ

3

1

2

Skip some neat details, derivation from helicity amps. and connection withChiral Odd GPDs (Kubarovsky’s pi0 data)

/2

H-

H+

(H+ + H-)/2=Hq

Q2 dependent

dominated by valence

Implement Crossing Symmetries in ERBL region

ERBL Region Ahmad et al., EPJC (2009)

Determined from lattice moments up to n=3

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)

7 parameters per quark flavor per GPD, but we have not constrained the ζ dependence yet….. DVCS data

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

For strange and charm Replace PDF used for light quarks GPDs with NP strange/charm based one

HAPPEx+E734 G0 + BNL E734

Replace FF used for light quarks GPDs with upper limit on charm based one

Pate, McKee, Papavissiliou, PRC78(2008)

G.Goldstein, S.L. (preliminary)

Ratio ηc/πo

Problem of Transverse Polarization of Hyperons and Charmed Baryons in unpolarized pp collisions

p Λ

p What generates polarization?

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

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

Hyperon and Charmed Hyperon Polarization work with G. Goldstein and P. Di Nezza (ALICE)

ud

anti-c

Λc

+

Dharmaratna and Goldstein

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)

Finally, somewhat unrelated…

Work in progress with K. Kathuria,and S.Taneja (BNL) What observables?

AUT.....

Taneja and S.L., arXiv:1008.1706

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….