rinaldo baldini ferroli and s. pacetti - infn · rinaldo baldini ferroli and s. pacetti phipsi11...

Baryon Form Factorsat threshold

Rinaldo Baldini Ferroli and S. Pacetti

PHIPSI11

BINP, Novosibirsk, 19th-22nd September 2011

2

Outline

Last News on Baryon FF near threshold

The Neutral Baryon Puzzle

Spacelike - Timelike Relationship

Interference Pattern in J/ψ → pp

Conclusions and Perspectives

September 21st, 2011 Baryon Form Factors at threshold

3

Cross sections and analyticity

Im[q2]

Re[q2]

Space-like regioneB → eB

FF’s are realFF’s are real

Time-like regionUnphysical region

No dataData regione+e−↔BB

FF’s are complexFF’s are complex

sth = 4M2π sphy = 4M2

B

Time-like: had. helicity =

(1 ⇒ |GE |

0 ⇒ |GM | GE (4M2B) = GM(4M2

B)

θe− Be−

B

Elastic scattering

dσdΩ

=α2E′

e cos2 θ2

4E3e sin4 θ

2

»G2

E −τ„

1+2(1−τ ) tan2 θ

2

«G2

M

–1

1−ττ =

q2

4M2B

θ

e− e+

B

B

Annihilation

dσdΩ

=α2βC4q2

»(1+cos2 θ)|GM |2+

1τ

sin2 θ|GE |2–

Coulomb correctionβ =

r1 −

1τ


4

The Coulomb Factor

γ∗

B

B

pp Coulomb interaction as FSI[Sommerfeld, Sakharov, Schwinger, Fadin, Khoze]

Distorted wave approximation

C = |ΨCoul(0)|2

S-wave: C =

παβ

1−exp“−πα

β

” −→β→0

πα

β

D-wave: C =1

No Coulomb factor for boson pairs (P-wave)

1

1.25

1.5

1.75

2

2 2.2 2.4pq2 (GeV/c)

Cou

lom

bfa

ctor

C


5

Sommerfeld Enhancement and Resummation Factors

Coulomb Factor C for S-wave only:

Partial wave FF: GS =2GM

pq2/4M2 + GE

3GD =

GMp

q2/4M2 − GE

3

Cross section: σ(q2) = 2πα2β4M2

(q2)2

hC |GS(q2)|2 + 2|GD(q2)|2

i

C = E × R

Enhancement factor: E = πα/β

Step at threshold: σ(4M2) =π2α3

2M2β

β|GS(4M2)|2 = 0.85 |GS(4M2)|2 nb

Resummation factor: R = 1/[1 − exp(−πα/β)]

Few MeV above threshold: C ' 1 ⇒ σ(q2) ∝ β |GS(q2)|2


6

The e+e− → τ+τ− case

0

0.25

0.5

0.75

1

3.55 3.555 3.56 3.565

Wττ (GeV)

σ ττ (

nb)

KEDR

BES

With Coulomb corr.

Without Coulomb corr.

With only enhancement factor


7

PointlikeBaryons?R. Baldini Ferroli, S. Pacetti,

A. Zallo and A. Zichichi


8

I.S.R. versus c.m.

Advantages

All q at the same time =⇒ Better control on systematics

c.m. boost =⇒ at threshold efficiency 6= 0 + σW ∼ 1 MeV

Detected ISR γ =⇒ full pp angular coverage

Drawbacks

L ∝ invariant mass bin ∆w

More background


9

Mass resolution

0

5

10

15

20

2 3 4Mpp (GeV/c2)

Mas

sre

solu

tion

(MeV

/c2)

Incredibly good at threshold (∼ 1 MeV/c2), as e+e− c.m.∆pT /pT ∼ 0.5% at 1 GeV


10

BABAR : e+e− → pp [PRD73, 012005]

0

0.25

0.5

0.75

1

1.8 2 2.2 2.4

Wpp (GeV)

σ pp (

nb)


11

Proton form factor at q2 = 4M2p

|Gp(4M2p)| ≡ 1

At q2 = 4M2P protons behave

as pointlike fermions!


12

SommerfeldResummation Factor

Needed?


13

Resummation Factor Needed?

At threshold: GE/GM = 1 ⇒

GS ∈ RGD = 0 ∈ R

σ(q2), |GE/GM | → GS, GD

GS =√

1 − exp(−πα/β)

No need of Resummation Factor

For a wide energy range (∼ 200 MeV):

Proton behaves as a pointlike particle

e.m. dominance, no strong interaction?

Mild sensitivity to BB invariant mass resolution


14

BABAR : |GpE/Gp

M| and σ(e+e− → pp) [PRD73, 012005]

0

0.5

1

1.5

2

2.5

1.9 2 2.1

|GEp /G

Mp|

0

0.5

1

1.5

1.9 2 2.1Wpp (GeV)

σ pp (

nb)


15

BABAR : |GpE/Gp

M| and σ(e+e− → pp) [PRD73, 012005]

0

0.25

0.5

0.75

1

1.9 2 2.1Wpp (GeV)

|GSp |,

|GDp

|

|GSp|

|GDp |

p1− exp(−πα/β)


16

BABAR : GS, GD and Geff [PRD73, 012005]

0

0.5

1

1.5

2 2.5 3 3.5 4

Wpp (GeV)

|GS|

,|GD

|

0

0.5

1

1.5

2 2.2 2.4

Wpp (GeV)|G

p e ff|


17

Integrated Sommerfeld factor

0.4

0.6

0.8

1

0 2 4

∆W (MeV)

1∆W

Z ∆W

0[1 − exp(−πα/β)]dw


18

Other charged baryon FF’sat threshold


19

e+e− → Λ+c Λ

−c and e+e− → pN(1440)+c.c.

[Belle PRL101, 172001]

0.2

0.4

0.6

4.6 4.7 4.8 4.9 5

WΛcΛc (GeV)

σ ΛcΛ

c (n

b)

[BABAR PRD73, 012005]

0

0.2

0.4

0.6

2.5 3 3.5 4

WpN* (GeV)

σ pN*

(nb)


20

e+e−→ pN(1440)+c.c. BABARPRD73, 012005

σCoulomb =16π2α3M3/2

p M3/2N(1440)

(Mp + MN(1440))5

˛GpN(1440)

˛2=

˛GpN(1440)

˛2×0.49 nb

0

50

100

1 1.5 2 2.5 3 3.5

Wpπ (GeV)

Eve

nts/

0.1

GeV

0

0.2

0.4

0.6

2.5 3 3.5 4

Coulomb

pq2 (GeV/c)

σpN

(144

0)(n

b)

|GpN(1440)| = 1.04 ± 0.09


21

The neutral baryons puzzle


22

Neutral Baryons puzzle (BABAR ) [PRD76, 092006]

σ(e+e−→ B0B0)=

4πα2βC0

3q2

"|GB

0

M |2+2M2

B0

q2|GB

0

E |2#

−→√q2→2MB0

πα2β

2M2B0

|GB0|2 → 0

No Coulomb correction at hadron level: C0 = 1

0

100

200

300

2.5 3 3.5pq2 (GeV/c)

σ(e+e− → ΛΛ) (pb)

BABAR

DM2

σth =200±50 pb

0

10

20

30

40

3 4 5

σ(e+e− → Σ0Σ0) (pb)

pq2 (GeV/c)

σth =30±13 pb

0

20

40

60

80

3 4 5

σ(e+e− → ΛΣ0) (pb)

pq2 (GeV/c)

σth =47±23 pb

Like a remnant ofCoulomb interactions

at quark level?⇒ C0 ∝ β−1

asp

q2 → 2MB0⇒ For any neutral baryonp

σB0B0 ∝|GB0 |MB0


23

Baryon octet and U-spin arXiv:0812.3283

Y

I3

pn

Σ− Σ+Σ0

Λ

Ξ− Ξ0

-1

1

1-1

(Y , I3) → (YU ,U3)

U3 = − 12 I3 + 3

4 Y

YU = −Q

YU

U3

Σ−Ξ−

Ξ0

n

Σ0 =√

3Σ0−Λ2

Λ=√

3Λ+Σ02

Σ+ p-1

1

U-spin relation: GΣ0 − GΛ + 2√3

GΛΣ0= 0

MΣ0p

σΣ0Σ0 − MΛ

√σΛΛ +

2√3

MΛΣ0p

σΛΣ0 = (−0.06 ± 6.0) × 10−4


24

BABAR : e+e− → ΛΛ [PRD76, 092006]

0

0.1

0.2

0.3

2.2 2.3 2.4 2.5 2.6

WΛΛ (GeV)

σ ΛΛ (

nb)


26

e+e− → nn: preliminary result from SND

e+e− → nn

pq2 (GeV)

σnn

(nb) SND (2011)

FENICE (1988)

SND preliminary

Scan 2011Maximum energy: 2 GeVEfficiency ∼ 30%Above nn threshold:σnn = 0.8 ± 0.2 nb


27

Dispersive analysis of the ratio R = µpGp

E

GpM

Eur. Phys. J. A32, 421R. Baldini, S. Pacetti and A. Zallo

Re(q2)time-like

unphysicalregion

unphysicalregion

space-like


28

Space-like GpE/Gp

M measurements

−q2 (GeV2/c2)

µpG

p E(q

2)/

Gp M(q

2)

PRD50 5491

GpE = F p

1 +q2

4M2p

F p2

GpM = F p

1 + F p2

F1 / q2

4M2pF2 cancellation

GpE(q2)

GpM(q2)

< 1

Spa

ce-li

ke

F1 / q2

4M2pF2 enhancement˛

˛ GpE(q2)

GpM(q2)

˛˛ > 1

Tim

e-lik

eRadiative corrections ofpolarization technique << Radiative corrections in

Rosenbluth method


28

Space-like GpE/Gp

M measurements

−q2 (GeV2/c2)

µpG

p E(q

2)/

Gp M(q

2)

PRD50 5491

PRL84 1398PRL88 092301

GpE = F p

1 +q2

4M2p

F p2

GpM = F p

1 + F p2

F1 / q2

4M2pF2 cancellation

GpE(q2)

GpM(q2)

< 1

Spa

ce-li

ke

F1 / q2

4M2pF2 enhancement˛

˛ GpE(q2)

GpM(q2)

˛˛ > 1

Tim

e-lik

eRadiative corrections ofpolarization technique << Radiative corrections in

Rosenbluth method


29

Time-like |GpE/Gp

M | measurements

dσd cos θ

=πα2βC

2q2 |GpM |2

"(1+cos2 θ)+

4M2p

q2µ2p

sin2 θ|R|2#

R(q2) = µpGp

E (q2)

GpM(q2)

0

0.5

1

1.5

2

2.5

4 5 6 7 8 9 10

|R(q

2)|/µ

p

pq2 (GeV/c)

LEAR (pp → e+e−)NPB411, 3

BABAR (ISR)PRD73, 012005

FENICE+DM2E835EPJC46, 421

Scaling

γγ exchange

e

e p

p

γ

γ

C =+1

γγ exchange interfereswith the Born term

Asymmetry inangular distributions

[PLB659, 197]


30

γγ exchange frome+e−→ ppγ BABAR data

E. Tomasi-Gustafsson,E. A. Kuraev, S. Bakmaev, SP

PLB659, 197

A(cos θ, q2) =

dσdΩ

(cos θ, q2) −dσdΩ

(− cos θ, q2)

dσdΩ

(cos θ, q2) +dσdΩ

(− cos θ, q2)

-0.1

0

0.1

2 2.25 2.5 2.75 3pq2 (GeV/c)

〈A〉 c

osθ

〈A〉cos θ,q2 = 0.01 ± 0.02


31

R(q2) in the complex plane

Re(q2)

Im(q2)

|R(q2)|

sthsphy

physical sheet

unphysical sheet

experimental sheetGE , GM and also R, if GM hasno zeros, are analytic on the q2

plane with a cut (sth = 4M2π, ∞)

[see e. g.: Eur. Phys. J. C 11, 709 (1999)]


31


Re(q2)

Im(q2)

|R(q2)|

sthsphy

physical sheet

path C R

unphysical sheet

experimental sheet

Dispersion relation for the imaginary part (q2 ≤ sth)

G(q2) = limR→∞

12πi

IC

G(z)dzz − q2 =

1π

Z ∞

sth

ImG(s)dss − q2


31


Re(q2)

Im(q2)

|R(q2)|

sthsphy

physical sheet

path C R

unphysical sheet

experimental sheetDispersion relation for R with subtraction at q2 = 0

R(q2) = R(0) +q2

π

Z ∞

sth

ImR(s)dss(s − q2)


32

R(q2) EPJA32 421

R(0) +q2

π

∫ ∞

4M2π

ImR(s)

s(s − q2)dsR(q2) =

Req2

0

0.5

1

-10 -8 -6 -4 -2 0

R(q2) space-like

q2 (GeV2/c2)

JLab+MIT-Bates

1

10

4 5 6 7 8 9 10

|R(q2)| time-like

BABAR +DM2/FENICE+E835

q2 (GeV2/c2)


32

R(q2) EPJA32 421

R(0) +q2

π

∫ ∞

4M2π

ImR(s)

s(s − q2)dsR(q2) =

Req2

0

0.5

1

-10 -8 -6 -4 -2 0

R(q2) space-like

q2 (GeV2/c2)

JLab+MIT-Bates

1

10

4 5 6 7 8 9 10

|R(q2)| time-like


q2 (GeV2/c2)

DR Approach1/Qlog2 Q2/Q2

Impr. log2Q2/Q2

IJL


32

R(q2) EPJA32 421

R(0) +q2

π

∫ ∞

4M2π

ImR(s)

s(s − q2)dsR(q2) =

Req2

0

0.5

1

-10 -8 -6 -4 -2 0

R(q2) space-like

q2 (GeV2/c2)

JLab+MIT-Bates

JLab preliminaryV. Punjabi DSPIN-09Dubna, Russia

1

10

4 5 6 7 8 9 10

|R(q2)| time-like


q2 (GeV2/c2)

DR Approach1/Qlog2 Q2/Q2

Impr. log2Q2/Q2

IJL


33

Asymptotic GPE(q2)/Gp

M(q2) and phase

-1

0

1

2

-10000 -5000 0 5000 10000

q2 (GeV2/c2)

GP E(q

2)/

Gp M

(q2)

Space Time

0

1

2

0 2 4 6 8 10pq2 (GeV/c)

Pha

seof

GP E(q

2)/

Gp M

(q2)

Phragmen Lindelof

phase limit ↔ zeros

pQCD prediction

GpE (q2)

GpM(q2)

−→|q2|→∞

−1

Phase from DR

φ(q2) = −p

q2 − s0

πPr

Z ∞

s0

ln |R(s)|ds√

s − s0(s − q2)


34

J/ψJ/ψ

GG

J/ψ strong and

electromagnetic phase

J/ψ strong and


J/ψ strong and



35

BESIII preliminary results: J/ψ → pp, nn

nn identification

0 50 100 1500

1000

2000

3000

Number of n in 50o cone

Eve

nts/

20.0 1.0 2.00

1000

2000

3000

E(n) (GeV)

Eve

nts/

50M

eV

Angle between n and recoil dir. of n (degree)

Eve

nts/

1de

gree

Bkg from MCJ/ψ → π0nn

BE

SIII B(J/ψ→nn)=(2.07±0.01±0.14)·10-3

B(J/ψ→pp)=(2.112±0.004±0.027)·10-3 PD

G B(J/ψ→nn)=(2.2±0.4)·10-3

B(J/ψ→pp)=(2.17±0.07)·10-3

B(J/ψ→pp)' B(J/ψ→nn)

suggests a phase ∼ 90 between strong and e.m. amplitudes!


36

J/ψ decays: strong and electromagnetic

e

eγ∗ J/ψ γ∗

N

N

G

Aγ e

eγ∗ J/ψ 3g

N

N

A3g

cross section ∼ |Aγ + A3g |2 = |Aγ |2 + |A3g |2 + 2 Re[A∗γA3g ]| z

interference term

According to pQCD: Aγ and A3g are real ⇒ interference

On the contrary data suggest:

J/ψ → JP1 JP

2AγA3g

phase

1−0− 106o ± 10o

1−1− 138o ± 37o

0−0− 90o ± 10o

nn 89o ± 15o

But these conclusions have been obtainedmodeling SU(3) breaking, or using poorlymeasured nn cross section outside J/ψ

Interference with the continuum measuresthe relative phase in an independent way


37

Full interference as seen by PANDA or BESIII

10-5

10-4

10-3

10-2

10-1

1

10

10 2

3000 3025 3050 3075 3100Wpp (MeV)

σ pp (

nb)

PANDA

BESIII

(∆pp/pp = 10−4)


38

ConclusionsPointlike Behavior at and well above threshold

No Sommerfeld Resummation FactorNeutral baryon non zero cross section at threshold?Gp

E space-like → −1 asymptotically?Imaginary J/ψ strong decay amplitude?

PerspectivesData from SND and CMD2More data from BABAR (×2) and Belle (?)

BESIII: ISR now, scan 2012-2013

PANDA could explore FFs below threshold throughpp → π0l+l−


rinaldo baldini ferroli and s. pacetti - infn · rinaldo baldini ferroli and s. pacetti phipsi11...

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