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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
7
PointlikeBaryons?R. Baldini Ferroli, S. Pacetti,
A. Zallo and A. Zichichi
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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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)
September 21st, 2011 Baryon Form Factors at threshold
11
Proton form factor at q2 = 4M2p
σ(e+e− → pp)(4M2p) = 0.83 ± 0.05 nb
σ(e+e− → pp)(4M2p) =
π2α3
2M2p
β
β|Gp(4M2
p)|2 = 0.85 |Gp(4M2p)|2 nb
|Gp(4M2p)| ≡ 1
|Gp(4M2p)| = 0.99 ± 0.04(stat) ± 0.03(syst)
September 21st, 2011 Baryon Form Factors at threshold
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Proton form factor at q2 = 4M2p
|Gp(4M2p)| ≡ 1
At q2 = 4M2P protons behave
as pointlike fermions!
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
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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|
September 21st, 2011 Baryon Form Factors at threshold
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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
September 21st, 2011 Baryon Form Factors at 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)
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
25
Time-like |GnM | measurements
0
0.2
0.4
0.6
0.8
1.8 2 2.2 2.4
No Coulombcorrection
pq2 (GeV)
|Gn M
(q2)|
FENICE
DM2
DM2 extr. from GΛ
|GpM (q2) · Qd/Qu|
|GnM/Gp
M |
Data ∼ 1.5
Naively ∼ |Qd/Qu|
pQCD < 1
Soliton ∼ 1models
VMD 1(Dubnicka)
Only SND, CMD2(?) and BESIII can measure this cross section
No other experiments at present and in near futurewill be able to perform such a measurement
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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]
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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)]
September 21st, 2011 Baryon Form Factors at threshold
31
R(q2) in the complex plane
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
September 21st, 2011 Baryon Form Factors at threshold
31
R(q2) in the complex plane
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)
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
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)
DR Approach1/Qlog2 Q2/Q2
Impr. log2Q2/Q2
IJL
September 21st, 2011 Baryon Form Factors at threshold
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
BABAR +DM2/FENICE+E835
q2 (GeV2/c2)
DR Approach1/Qlog2 Q2/Q2
Impr. log2Q2/Q2
IJL
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
34
J/ψJ/ψ
GG
J/ψ strong and
electromagnetic phase
J/ψ strong and
electromagnetic phase
J/ψ strong and
electromagnetic phase
September 21st, 2011 Baryon Form Factors at threshold
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!
September 21st, 2011 Baryon Form Factors at threshold
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
September 21st, 2011 Baryon Form Factors at threshold
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)
September 21st, 2011 Baryon Form Factors at threshold
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−
September 21st, 2011 Baryon Form Factors at threshold