Working group e + e - @ Frascati

Milan 4/11/05 Work group e+e- M. Radici - Time-like form factors 1

Working group e+e- @ FrascatiMilano 4 Nov. 2005

Time - like form factors

Marco Radici

INFN - Pavia


Outline

1. Why should we measure time-like (TL) form factors (FF) ?

2. What should we learn from TL FF with respect to SL FF ?

3. Which measurements are needed ?

4. Available data and calculations ?


1. Why TL FF ?2. What do we learn ?3. Which measurements ?4. Available data and models ?

1. Questions in SL region2. Surprise in SL $ TL 3. Few and poor TL data4. Better constrain models

elastic scatteringcross section

Rosenbluth separation

fixed Q2, varyGE slope , GM intercept

large errors in GE




polarizationtransfer




JLab – Hall A Qattan et al. P.R.L. 94 (05) 142301

Blunden et al. nucl-th/0506039

2?




pQCD

JLab polar. transfer data

where is onset of pQCD scaling ?


GEp

GMp

GEn

GMn

Lomon, P.R. C66 (02) 045501 : VMD

Miller, P.R. C66 (02) 032201(R) : LFCBM

Holzwarth, hep-ph/0201138

Ma, Qing, Schmidt, P.R. C65 (02) 035205 : LF diquark

from H. GaoInt. J. Mod. Phys. E12 (03) 1

erratum E12 (03) 567




SpaceLike TimeLike

analytic continuation by Dispersion Relations (DR)

But

fit to pQCD TimeLike

fit to pQCD SpaceLike




2Q

nMGpQCD + analyticity

But

fit to |GMp|




poor statistic

integrate dover wide

angular range

all data assume

it’s true only at where steep rise is observed




only 1 measurement for neutron (ADONE-1998) again with

scarce angular distributions and with low statistics

no polarization of protons and/or electrons




IJL

CQM

pQCD“improved”

Dispersive approach on BaBar and LearPacetti talk at Nucleon ’05 - Frascati

Brodsky et al. P.R. D69 (04) 054022



1. Form factors are complex2. |FF| from unpol. cross section3. Phases from polarization4. Unphysical region

Dispersion Relation (DR)

F(t) analytic function in t 2 C withcut [t0 = 4m

2, 1)

C

R

Im F(t’) 0 only in [t0=4m2, 1 )

vector-meson poles and multi-hadron continuum

dipole fit to F2 (q2e-i) / F1 (q2 e-i) ! R !




unpolarized cross section for

R angular asymmetry

q2<0 Rosenbluth plotchange E, e at fixed q2

) linear plot in

q2>0 measure 2 at fixed q2 ) get Rcos2 typical of Born diagram

measure 3 ) explore 2 mechanisms




polarized cross section for

Ax, Az require polarization of the electron beam: Pe 0




phases of FF from Final-State Interactions (FSI) of final baryon system : interference of channels with different phases ( Im (GE

*GM) )

pQCD : FSI ! 0 for Q2 ! 1 ) test transition to scaling and Color Transparency (CT)

FSI ! T-odd mechanisms are allowed : generates

not possible in elastic scattering

GE = F1 + F2 = |GE| ei E

GM = F1 + F2 = |GM| ei M

Im (GE*GM) = ( -1) Im F2

*F1

threshold t1=4M2 ! Im( )=0consistent with |GE|=|GM| from GT=1(t1)=0

ambiguity $ - solved by




discriminate among models that are close in SL region

IJL

CQM

pQCD“improved”




steep rise at threshold

tail of narrow resonance at t ≤ 4M2 (baryonium) ?

should show up as a dip in somehadronic cross section

E687 diffractive photoproduction of 6

Upcoming results from BaBar also

W » 1.9 GeV



measure angular dependence of unpol. cross section) angular asymmetry R and test 2 mechanisms

measure Ay / sin (E - M)

measure Ay / Ax / tan (E - M)

utopia : measure Ai j



ADONE Q2 = 4.4 GeV (1973)

CERN Q2 ~ 3.6 (1977)

Orsay-DM1 Q2 ~ 3.75-4.56 (1979)

Orsay-DM2 Q2 =4-5 (1983)

LEAR Q2 ~3.5-4.2 (1994)

E760 Q2 ~8.9-13 (1993)

FENICE Q2 ~3.7-6 (1994)

E835 Q2 ~8.8-18.4 (1999) 11.6-18.2 (2003)

CLEO Q2 ~11-12 (2005)

BES Q2 ~4-9 (2005)

BaBar Q2 ~2-20 (2005)

1. data : proton2. models



1. data : proton2. models



1. data : neutron2. models

2Q

nMG

but always assumed

|GEN| = |GM

N| N=p,n

FENICE Q2 ~3.7-6 (1994)



1. data2. models

• Dispersion Relations (DR): analyticity+unitarity+Vector Mesons (VM) (Drechsel, Meissner, Hammer, Hoehler,..) “ “ + input exp. data (Baldini, Pacetti, …)

• VM Dominance (VMD) based models (Iachello, Bijker, Lomon, …)

• Soliton (Holzwarth)

• CQM : Light Front Form (Pace, Salmè, Simula, …) “ “ “ + \pi cloud (Miller, Jennings, .. ) Point Form (Pavia + Graz collaboration) Diquark (Ma, …)

• pQCD “inspired” (Brodsky, Ji, Belitski, Yuan, ..)

• reviews: Brodsky et al. P.R. D69 (04) 054022 Tomasi-Gustafsson et al. E.P.J. A24 (05) 419


Possible logo ?

(from Pacetti talk at Nucleon’05)

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