symmetries and hadron form factorsbijker/franco70/talks/tomasigusta...egle tomasi-gustafsson irfu,...

Egle Tomasi-GustafssonIRFU, SPhN-Saclay, and

IN2P3- IPN Orsay France

Symmetries and

Hadron

Form Factors

Egle TOMASI-GUSTAFSSON IFAE, 29-V-2011 1

e-e-

p pe-

e+ p

p

Egle TOMASI-GUSTAFSSON 2

Hadron Electromagnetic Form factors

Cocoyoc, May 15, 2012

•

Characterize the internal structure of a particle (≠ point- like)

•

Elastic form factors contain information on the hadron ground state.

•

In a P- and T-invariant theory, the EM structure of a particle of spin S is defined by 2S+1 form factors.

•

Neutron and proton form factors are different.•

Deuteron: 2 structure functions, but 3 form factors.

•

Playground for theory and experiment•

- at low q2 probe the size of the nucleus,

•

- at high q2 test QCD scaling

IHEP


The proton vertex is parametrized in terms of FFs: Pauli and Dirac F1

,F2

Electromagnetic InteractionElectromagnetic Interaction

q2<0

e-e-

p p

)2q(2FM2qi

)2q(1Fνμνσ

μγμΓ +=

or in terms of Sachs FFs:GE=F1

-τ F2

, GM=F1

+F2

, τ=- q2/4M2

The electron vertex is known,γμ

The interaction is carried by a virtual photon of mass q2

What about high orderradiative corrections?

Egle TOMASI-GUSTAFSSON

Cocoyoc, May 15, 2012 4

AnalyticityAnalyticity

__

q2<0

e-e-

p p

q2>0

e-

e+ p

p

q2q2=4mp2

FFs are complexFFs are real Unp

hysi

cal r

egio

n

GE=GM

Space-like

Time-likeGE(0)=1

GM(0)=μp

Asymptotics- QCD-

analyticity

p+p ↔ e++e-e+p → e+p

p+p ↔

e++

e- +π


The polarization method (1967)


The polarization induces a term in the cross section proportional to GE GM

Polarized beam and target orpolarized beam and recoil proton polarization


Polarization experiments -

JlabA.I. Akhiezer and M.P. Rekalo, 1967

GEp collaboration1)

"standard" dipole function

for the nucleon magnetic FFs GMp

and GMn2) linear deviation

from the dipole function for the electric proton FF Gep

3)

QCD scaling not reached3) Zero crossing of Gep?4) contradiction between

polarized and unpolarized measurements

A.J.R. Puckett et al, PRL (2010)

PRC85 (2012) 045203Cocoyoc, May 15, 2012 6



Issues•

Some models predicted such behavior before the data appeared

•

Simultaneous description of the four nucleon form factors...•

...in the space-like and in the time-

like regions•

Consequences for the light ions

description•

When pQCD starts to apply?

•

Source of the discrepancy

BUT


Franco, 1973

Egle TOMASI-GUSTAFSSON Cocoyoc, May 15, 2012 8

Iachello, Jackson and Landé (1973)

Isoscalar and isovector FFs γ* ω,ρ,ϕ


)2

(GeV2Q0 1 2 3 4 5 6 7 8 9

p*G

Ep

/GM

pμ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

a

)2

(GeV2Q0 5 10 15 20 25 30

pμG

Mp

/GD

/

0.6

0.7

0.8

0.9

1

1.1

1.2

b

)2

(GeV2Q0.2 0.4 0.6 0.8 1 1.2 1.4

GE

n

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

c

)2

(GeV2Q0 2 4 6 8 10

n/G

Dμ

GM

n/

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

d

The nucleon form factors

VDM : IJLF. Iachello..PLB 43, 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC 66, 045501 2002)

HohlerNPB 114, 505 (1976)

BostedPRC 51, 409 (1995)

Electric Magneticne

utro

npr

oton

E. T.-G., F. Lacroix, Ch. Duterte, G.I. Gakh,

EPJA (2005)



Models in T.L. regionE. T-G., F. Lacroix, C. Duterte, G.I. Gakh EPJA 2005

VDM : IJLF. Iachello..PLB43 191 (1973)

Extended VDM (G.-K. 92): E.L.Lomon PRC66 045501(2002)

‘QCD inspired’

proton

neutron


R. Bijker and F. Iachello, Phys.Rev., C69 (2004) 068201 F. Iachello and Q. Wan, Phys.Rev., C69 (2004) 055204


Models in T.L. Region (polarization)

VDM : IJLExt. VDM

‘QCD inspired’

AngularAsymmetry

Ay Axx Ayy

AxzAzz

E. T-G., F. Lacroix, C. Duterte, G.I. Gakh, EPJA 2005


R. Bijker and F. Iachello, Phys.Rev., C69 (2004) 068201 F. Iachello and Q. Wan, Phys.Rev., C69 (2004) 055204


]2 [(GeV/c)2q4 6 8 10 12 14

R0

0.5

1

1.5

2

2.5

3

|GE| and |GM| individual determination up to large q2

PREDICTIONS

R=GE/GMBaBAR

PS170PANDA sim

L = 2x1032 cm-2.s-1, 107 s (~100 days)

]2|[(GeV/c)2|q0 5 10 15 20 25 30

D|/G

p|F

−110

1

10

GM(SL)

BaBarE835FenicePS170E760DM1DM2BES

GE(SL)

GM(TL)

CLEO

PANDASim

Symmetries

Egle TOMASI-GUSTAFSSON Cocoyoc, May 15, 201214

Crossing SymmetryCrossing SymmetryScattering

and annihilation channels:

-

Described by the same amplitude :

-

function of two kinematical variables, s and

t

k2

→ – k2

-

which scan different kinematical regions

p2

→ – p2

p + p e+ + e- + π0 and e- + p e- + p + π0


)+

p(p

)−p(p

)π(p0π

(k)*γ

)−(k−e

)+

(k+e

)1

p(p

)π(p0π

(k)*γ

)2

(k−e)1

(k−e

)2

p(p

Described in general by 6 amplitudeswhich depend

on 3 kinematical variables

π + N e+ + e- + Naccess the unphysical region

M. P. Rekalo (1967)


n(p2)

p̄(−p1)

γ∗(q)

�−(p−)

�+(p+)

π−(qπ)

p2 + p1

n(p2)

p̄(−p1)

π−(qπ)

�−(p−)

�+(p+)

p2 − qπ

γ∗(q)

n(p2)

p̄(−p1) π−(qπ)

γ∗(q)�−(p−)

�+(p+)

−p1 + qπ

(a) (b)

(c)

p + n e+ + e- + π-

Axial

Nucleon FFs

FFs in the unphysical region


Time-like electromagnetic form factors

IJL pQCD


C. Adamuscin, E. T-G,E. Santopinto, R. Bijker

DipoleBI

IJL

S=1 form factors




The IA deuteron structure: S=1, T=0

2) The S (u) and D (w) deuteron wave function

1) The nucleon form factors:


Deuteron VMD

Meson cloud: isoscalar vector meson only

Normalization

Intrinsic term

C. Adamuscin, G.I. Gakh and E.T-G. PRC 73, 045204 (2006)



ResultsFrom 12 to 6 parameters fit1) Constrains on the nodes: Q2

0C

=1.7 GeV2, Q20M

=2 GeV2

2) Intrinsic part common to the 3 FFs:

δ=1.04 ±0.03, γ=12.1 ± 0.5



Results

GCGQ

GM

C. Adamuscin, G.I. Gakh and E.T-G. PRC 73, 045204 (2006)



e+ + e- → d + d

PRC 74, 025202 (2006)-Imaginary part from the intrinsic term-No finite width for ρ,ω

mesons)

U&A (Dubnicka)

Parametrization I (real part)[Abbott, EPJA 2000]

|GM

|

|GQ

|

|GC

|



ρ−Meson

Form Factors

Analytical extension : imaginary part from the width (Γ ~ 1% or 10% M)

TL-parametrization:

…no experimental constraints, no new parameterCocoyoc, May 15,

2012 25Egle TOMASI-GUSTAFSSON

A=1, B=0.33 from the node of Gc at q2=-3 GeV2

Fit on light front calculation de Melo and Federico, PRC55,2043 (1997)

Space-like Time-like

ρ -

form factors : Observables

Spin 1



[n

b/s

r]Ω

/dσd

25

30

35

40

45 (a) σR

0.8

0.85

0.9

0.95

1 (b) xP

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1

-0 (c)

yP

-0.01

-0.005

0

0.005

0.01(d) z

P

-0.8-0.6-0.4-0.2

-00.20.40.60.8 (e) xx

P

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0 (f)

[deg]θ0 90 180

xzP

-1

-0.5

0

0.5

1(g)

[deg]θ0 90 180

zzP

0.8

1

1.2

1.4

1.6

1.8

2 (h)

[deg]θ0 90 180

yzP

0

0.1

0.2

0.3

0.4

0.5 (i)


)2 (GeV2q90 100 110 120

2|F

|

0

0.5

)2 (GeV2q-20 0 20

|G|

-310

-210

-110

1

10

A. Dbeyssi, E.T-G,G.I.Gakh,C.Adamuscin

|GM

|

|GC

||GM

|


Tanti Auguri, Franco!


The Rosenbluth separation

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

+Ω=

Ω)2(2)2(2

)1(1 QMGQEG

Mottdd

dd

ετ

τσσ

2M4

2Q,1

2e2)tan1(21 =

−++=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ τ

θτε

2MG2

EGR τεσ +=

→Holds for 1γ exchange only

Linearity of the reduced cross section

PRL 94, 142301 (2005)

→tan2θe dependenceε

Q2

fixed


From Space-Like to Time-Like

Phenomenological parametrizationsmust include an imaginary part

The sign is important for polarization observables



SL and TL generalized form factors


Definition:

space-time distribution of the electric charge in the space-time volume D

In SL-

Breit frame (zero energy transfer):

In TL-(CMS):

: time evolution of the charge distribution in the domain

E.A. Kuraev et al., arXiv:1106.1670


Time-like observables: | GE | 2 and | GM | 2 .

As in SL region:-

Dependence on q2

contained in FFs-

Even dependence on cos2θ (1γ

exchange)

-

No dependence on sign of FFs-

Enhancement of magnetic term

but TL form factors are complex!

A. Zichichi, S. M. Berman, N. Cabibbo, R. Gatto, Il Nuovo Cimento

XXIV, 170 (1962)B. Bilenkii, C. Giunti, V. Wataghin, Z. Phys. C 59, 475 (1993).G. Gakh, E.T-G., Nucl. Phys. A761,120 (2005).



The simultaneous measurement of Pt and Pl reducesthe systematic errors

The polarization method (exp)


C. Perdrisat et al, JLab- GEp collaboration (2000)

JLab, Hall A

Mpp=1.877Mpp=1.877--1.91.9A=0.01A=0.01±±0.020.02

Mpp=2.4Mpp=2.4--33

E. T.-G., E.A. Kuraev, S. Bakmaev, S. Pacetti, Phys. Lett. B (2008)




Phragmèn-Lindelöf theorem

Asymptotic properties for analytical functions

E. T-G. and G. Gakh, Eur. Phys. J. A 26, 265 (2005)

Δ=0.05, 0.1

If f(z) →a as z→∞along a straight line, and f(z) →b as z→∞along another straight line, and f(z) is regular and bounded in the angle between, then a=b and f(z) →a

uniformly in the angle.


The reaction p + p e+ + e- + π0


font[132]{q}

)+

p(p

)−p(p

)π(p0π

(k)*γV(q)

)−(k−e

)+

(k+e CMS system

γ∗NNπNN

VNN Vπγ∗

Thesis J. Boucher

V=ρ,ω,φ, J/Ψ, ..


1{g

1γ-2γ interference

2γ1γ

M. P. Rekalo, E. T.-G. and D. Prout, Phys. Rev. C60, 042202 (1999)


•

Differential cross section at complementary angles:

Symmetry relations (annihilation)

The DIFFERENCE enhances the 2γ contribution:

The SUM cancels the 2γ contribution:


Spin ObservablesAnalyzing power, A

Double spin observables


The reaction p + p e+ + e- + π0


γ∗NN

πNN

M. P. Rekalo


STATUS on Time-like EM Form factors

1)

No individual determination of |GE| and |GM|2)

Assume GE=GM

(valid only at threshold)

3)

TL

nucleon FFs are twice larger

than SL

FF

Λ QCD

=0.3 GeV

A(p)

= 56.3 GeV4

A(n)

= 77.15 GeV4

)]/(ln[ 2222 Λ+=

ssAGM π

VMD or pQCD inspired parametrizations (for p and n):

IHEP

symmetries and hadron form factorsbijker/franco70/talks/tomasigusta...egle tomasi-gustafsson irfu,...

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