Unexpected Features of Baryon Time-like Form Factors

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1 Unexected Features of Baryon Time-like Form Factors Rinaldo Baldini Ferroli Laboratori Nazionali di Frascati, Italy Simone Pacetti Perugia University and INFN Perugia, Italy 28 October - 2 November 203 Pahos, Cyrus

2 Agenda Sace-like region: Rosenbluth/Polarization conflict(?) Time-like region: definitions, data and more The ratio G E /G M Proton form factor at threshold Neutral Baryon Puzzle

q/2) q = (0, q) ] ρ q = J 0 = e [F + q2 F 4M 2 2 Jq = e u( ) γu() [F + F 2 ] N N 2Mu( )γ µ u() = u( )[( + ) µ + iσ µν q ν ]u() u( )u( ) =

3 Nucleon Form Factors definition Sace-like region (q 2 < 0) e time γ e µ γ(q) Γ µ (q) Electromagnetic current (q = ) [ ] J µ = N( ) j µ N() =eu( ) γ µ F (q 2 )+ iσµν q ν 2M F 2(q 2 ) u() Dirac and Pauli form factors F and F 2 are real In the Breit frame = (E, q/2) = (E, q/2) q = (0, q) ] ρ q = J 0 = e [F + q2 F 4M 2 2 Jq = e u( ) γu() [F + F 2 ] N N 2Mu( )γ µ u() = u( )[( + ) µ + iσ µν q ν ]u() u( )u( ) = E/M u ( )u( ) = Sachs form factors G E = F + G M = F + F 2 q2 4M 2 F 2 Normalizations F (0) = Q N G E (0) = Q N F 2 (0) = κ N G M (0) = µ N 2

4 QCD asymtotic behavior Sace-like region Lett. Nuovo Cim. 7 (973) 79 Phys. Rev. Lett. 3 (973) 53 JETP Lett. 96 (202) 6-2 q q q γ g g QCD: as q 2, asymtotic behaviors of F and F 2, and G E and G M must follow counting rules Valence quarks exchange gluons to distribute the momentum transfer q Non-helicity-fli current J λ,λ (q 2 ) J λ,λ (q 2 ) G M (q 2 ) Two gluon roagators G M (q 2 ) q 2 ( q 2 ) 2 Helicity-fli J λ, λ (q 2 ) J λ, λ (q 2 ) G E (q 2 )/ q 2 Two gluon roagators / q 2 G E (q 2 ) q 2 ( q 2 ) 2 Ratio of Sachs form factors Ratio: G E constant G M q 2 Dirac and Pauli form factors F (q 2 ) F 2 (q 2 ) q 2 q 2 ( q 2 ) 2 ( q 2 ) 3 3

5 Sace-like data 3

6 Rosenbluth searation Phys. Rev. 79 (950) 65 Laboratory frame e(e ) N e(e 2 ) θ e N Rosenbluth formula ( ) dσ dσ dω = dω τ [ GE 2 τ ] ɛ G2 M Mott Mott ointlike cross section ( ) dσ dω Mott Photon olarization ɛ = = 4α2 ( q 2 ) 2 E 3 2 E cos 2 (θ e/2) [ + 2 ( τ ) tan 2 (θ e/2) ] τ = q2 4M 2 N (dσ/dω) red /G 2 D Rosenbluth lot q 2 [PRD50,549] 2.5 GeV GeV GeV 2 Reduced cross section ( ) dσ ɛ(τ ) (dσ/dω) ex = GM 2 ɛ dω τ (dσ/dω) Mott τ G2 E = red (dσ/dω) red (ɛ) sloe G E (dσ/dω) red (ɛ) intercet G M ɛ Diole form: G D (q 2 ) = ( q 2 /0.7GeV 2) 2 4

7 G E and G M with Rosenbluth searation G E /G D G M /µ GD q 2 (GeV 2 ) RMP35,335(63) PLB3,40(70) PRD4,45(7) PLB35,87(7) NPB58,429(73) PRD8,753(73) NPB93,46(75) NPA333,38(80) PRD50,549(94) PRD49,567(94) PRC70,05206(04) PRL94,4230(05) q 2 (GeV 2 ) RMP35,335(63) PR42,922(66) PRL20,292(68) PLB3,40(70) PRD4,45(7) PLB35,87(7) PRD8,753(73) NPB58,429(73) NPB93,46(75) PRD48,29(93) PRD50,549(94) PRD49,567(94) PRC70,05206(04) PRL94,4230(05) 5

tensor: W µν = W µν(0) + W µν( P) + W µν( P ) + W µν( P, P ) }{{}}{{}}{{} no ol.

8 Polarization observables A.I. Akhiezer, M.P. Rekalo, Sov. Phys. Dokl. 3, 572 (968) e θ e x y z e h = + h = γ Elastic scattering of longitudinally olarized electrons (h = ±) on nucleon target Hadronic tensor: W µν = W µν(0) + W µν( P) + W µν( P ) + W µν( P, P ) }{{}}{{}}{{} no ol. ini. or fin. ol. of N ini. and fin. ol. of N In case of olarized electrons (h = ±) on unolarized nucleon target: P x = 2 τ(τ ) G 2 E τ ɛ G2 M ( ) θe G E G M tan 2 P z = (Ee +E e) ( ) τ(τ ) M ( GE 2 τ ) G 2 θe ɛ G2 M tan2 2 M P x P z 2M cot(θe/2) G E = E e + E e G M 6

G E /G M in olarization transfer exeriments µ G E /G M

agree with old Rosenbluth data ( ) New Rosenbluth data

9 G E /G M in olarization transfer exeriments µ G E /G M Polarization { PRL04,24230(0) PRL88,09230(02) PRL84,398(00) PRC7,055202(05) Rosenbluth { PRD50,549(94) PRC70,05206(04) PRL94,4230(05) Polarization data do not agree with old Rosenbluth data ( ) New Rosenbluth data (, ) from JLab still do not agree with olarization data q 2 (GeV 2 ) 7

10 Time-like region 9

Nucleon form factors Time-like region (q 2 > 0) γ N Crossing symmetry: N( ) j µ N() N( )N() j µ 0 time N Form factors are comlex functions of q 2 n n Otical theorem Im N( )N() j µ 0 N( )N() j µ n n j

11 Nucleon form factors Time-like region (q 2 > 0) γ N Crossing symmetry: N( ) j µ N() N( )N() j µ 0 time N Form factors are comlex functions of q 2 n n Otical theorem Im N( )N() j µ 0 N( )N() j µ n n j µ 0 = n n are on-shell intermediate states: 2π, 3π, 4π,... { ImF,2 0 for q 2 > 4M 2 π Time-like asymtotic behavior Phragmèn Lindelöf theorem: 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 this angle. lim q 2 } {{ } sace like G E,M G E,M (q 2 ) = lim G E,M (q 2 ) q 2 + } {{ } time like (q 2 ) 2 real q 2 + 8

Cross section and analyticity S NN = L NN = 0, 2 N N e e + θ Annihilation cross

nucleon velocity: β = Coulomb correction: C = /τ πα/β ex( πα/β) q 2 -comlex lane

Data region No data e + e BB FF s are comlex s th = 4Mπ 2 s hy = 4MN 2 Re[q 2 ] {

12 Cross section and analyticity S NN = L NN = 0, 2 N N e e + θ Annihilation cross section formula dσ dω = α2 βc [(+cos 2 θ) G 4q 2 M 2 + τ ] sin2 θ G E 2 Outgoing nucleon velocity: β = Coulomb correction: C = /τ πα/β ex( πα/β) q 2 -comlex lane Sace-like region en en FF s are real Im[q 2 ] Time-like region Unhysical region Data region No data e + e BB FF s are comlex s th = 4Mπ 2 s hy = 4MN 2 Re[q 2 ] { GE Only S-wave at threshold Hadronic helicity = 0 G M G E (4MN 2 ) = G M (4MN 2 ) 9

13 Time-like magnetic roton form factor G eff (q2 ) (γ)babar PRD73,02005(06) (γ)babar PRD73,02005(06) ()ADONE NC4A,(73) 0 - ()BES PLB630,4(05) (e + e )SPKR PLB64,475(76) (e + e )CALO PRL70,22(93) ()DM PLB86,395(79) (e + e )CALO PRD60,032002(99) ()DM2 NPB224,379(83) (e + e )CALO PLB559,20(03) ()DM2 ZPC48,23(90) ()FENICE PLB334,43(94) (e + e )WIRE NPB4,3(94) ()BES PLB630,4(05) q 2 (GeV 2 ) q 2 (GeV 2 ) Data obtained with G M = G E G eff (assumed true only at threshold) G eff 2 = 6πα 2 C 3 σ (q 2 ) ( ) /τ + 4q 2 2τ 0

Time-like G E /G M measurements [ ] dσ d cos θ = πα2 βc 2q 2 G M 2

EPJC46, 42 Scaling γγ exchange e e γ C = + γ γγ exchange interferes

14 Time-like G E /G M measurements [ ] dσ d cos θ = πα2 βc 2q 2 G M 2 (+cos 2 θ)+ 4M2 q 2 µ 2 sin 2 θ R 2 R(q 2 ) = µ G E (q2 ) G M (q2 ) G E (q2 )/G M (q2 ) BABAR (ISR) PRD73, WIRE ( e + e ) NPB4, 3 FENICE+DM2 E835 EPJC46, 42 Scaling γγ exchange e e γ C = + γ γγ exchange interferes with the Born term q 2 (GeV) Asymmetry in angular distributions [E. Tomasi-Gustafsson, M.P. Rekalo, PLB504,29(0)]

15 γγ exchange from e + e γ BABAR 203 data Phys. Lett. B659 (2008) 97 arxiv: [dσ/d cos(θ)] meas [dσ/d cos(θ)] fit..0 2M W 3 GeV Integrated over the -CM energy from threshold u to 3 GeV The MC-fit assumes one-hoton exchange 0.9 Sloe = 0.04±0.026± cos(θ) θ Integral asymmetry A cos θ = σ(cos θ > 0) σ(cos θ < 0) = ± 0.04 ± σ(cos θ > 0) + σ(cos θ < 0) σ(cos θ 0) is the cross section integrated with W 3 GeV and cos θ 0 2

16 The ratio R = µ G E /G M Disersion relation for the imaginary art Model-indeendent aroach First time-like G E G M searation Ratio in the whole q 2 comlex lane 5

17 Analytic R(q 2 ) Eur. Phys. J. A32 (2007) 42 R(q2 ) = R(0) + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) sace-like R(q 2 ) time-like Req 2 JLab+MIT-Bates 0 BABAR +DM2/FENICE+E q 2 (GeV 2 ) q 2 (GeV 2 ) 3

18 Analytic R(q 2 ) Eur. Phys. J. A32 (2007) 42 R(q2 ) = R(0) + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) sace-like R(q 2 ) time-like Req 2 JLab+MIT-Bates 0 BABAR +DM2/FENICE+E q 2 (GeV 2 ) q 2 (GeV 2 ) 3

19 Analytic R(q 2 ) Eur. Phys. J. A32 (2007) 42 R(q2 ) = R(0) + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) sace-like R(q 2 ) time-like Req 2 JLab+MIT-Bates 0 BABAR +DM2/FENICE+E DR Aroach 0 Sace-like zero t 0 = ( 0 ± ) GeV 2 PRD69,054022(04) /Q log 2 Q 2 /Q 2 Imr. log 2 Q 2 /Q 2 IJL q 2 (GeV 2 ) q 2 (GeV 2 ) 3

time-like Req 2 JLab+MIT-Bates 0 BABAR +DM2/FENICE+E835 JLab 200 [PRL04,24230] 0.

20 Analytic R(q 2 ) Eur. Phys. J. A32 (2007) 42 R(q2 ) = R(0) + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) sace-like R(q 2 ) time-like Req 2 JLab+MIT-Bates 0 BABAR +DM2/FENICE+E835 JLab 200 [PRL04,24230] 0.5 DR Aroach 0 Sace-like zero t 0 = ( 0 ± ) GeV 2 PRD69,054022(04) /Q log 2 Q 2 /Q 2 Imr. log 2 Q 2 /Q 2 IJL q 2 (GeV 2 ) q 2 (GeV 2 ) 3

Asymtotic G P E (q2 )/G M (q2 ) and hase G P E (q2

(GeV) QCD rediction G E (q2 ) G M (q2 ) q 2 Phase

21 Asymtotic G P E (q2 )/G M (q2 ) and hase G P E (q2 )/G M (q2 ) Sace Time Phase of G P E (q2 )/G M (q2 ) 2 0 Phragmèn Lindelöf hase limit zeros q 2 (GeV 2 ) q 2 (GeV) QCD rediction G E (q2 ) G M (q2 ) q 2 Phase from DR φ(q 2 ) = q 2 s th π ln R(s) ds Pr s sth (s q 2 ) s th 4

G E (q2 ) and G M (q2 ) from σ and DR 0 8 G eff (q2 ) q 4 G E = G M G eff (q2 ) 2 = σ (q 2 ) 4πα 2 βc 3s. ( + ) 2τ. 6 4 2 0 2 2.

22 G E (q2 ) and G M (q2 ) from σ and DR 0 8 G eff (q2 ) q 4 G E = G M G eff (q2 ) 2 = σ (q 2 ) 4πα 2 βc 3s. ( + ) 2τ q 2 (GeV) Usually what is extracted from the cross section σ(e + e ) is the effective time-like form factor G eff obtained assuming G E = G M i.e. R = µ Using our arametrization for R and the BABAR data on σ(e + e ), G E and G M may be disentangled 5

23 G E (q2 ) and G M (q2 ) from σ and DR 0 8 G E,M (q2 ) q 4 G E = G M G E ( R µ) G G M ( R µ) M (q2 ) 2 = σ (q 2 ) 4πα 2 βc 3s ( + R(q2 ) 2µ τ ) q 2 (GeV) Usually what is extracted from the cross section σ(e + e ) is the effective time-like form factor G eff obtained assuming G E = G M i.e. R = µ Using our arametrization for R and the BABAR data on σ(e + e ), G E and G M may be disentangled 5

24 Sommerfeld resummation factor needed? 8

25 I.S.R. versus c.m. Advantages All q at the same time = Better control on systematics c.m. boost = at threshold efficiency 0 + σ W MeV Detected ISR γ = full angular coverage Drawbacks L invariant mass bin w More background 6

26 Mass resolution Mass resolution (MeV/c 2 ) M (GeV/c 2 ) Incredibly good at threshold ( MeV/c 2 ), as e + e c.m. T / T 0.5% at GeV 7

The Coulomb Factor γ N N σ = 4πα2 β C 3q 2 [ ] G M (q2 ) 2 + 2M2

[Sommerfeld, Sakharov, Schwinger, Fadin, Khoze] Distorted wave

: β β = β β D-wave: C = πα ) β 0 β [he-h/05090089] No Coulomb

27 The Coulomb Factor γ N N σ = 4πα2 β C 3q 2 [ ] G M (q2 ) 2 + 2M2 q 2 G E (q2 ) 2 C describes the Coulomb interaction as FSI [Sommerfeld, Sakharov, Schwinger, Fadin, Khoze] Distorted wave aroximation C = Ψ Coul (0) 2 πα S-wave: C = β ex ( πα β Rel. corr.: β β = β β D-wave: C = πα ) β 0 β [he-h/ ] No Coulomb factor for boson airs (P-wave) Coulomb factor C q 2 (GeV) 8

28 Enhancement and Resummation Factors Coulomb factor C for S-wave only Partial wave FF G S = (2G M τ + GE )/3, G D = (G M τ GE )/3 Cross section σ(q 2 ) = 2πα 2 β [ τ q 2 C G S (q 2 ) G D (q 2 ) 2] Enhancement and Resummation factors C = E R Enhancement factor E = πα β Resummation factor R = e πα β It is resonsible for the one-hoton exchange FSI dominates close to threshold: C β 0 E cancels the hase-sace factor stewise cross section at threshold σ (4M) 2 = π2 α 3 β 2M 2 β G S (4M2 ) 2 = 0.85 G S (4M2 ) 2 nb It is resonsible for the multi-hoton exchange FSI becomes ineffective few MeV above threshold: R β>0 must account also for gluon exchange R R s = [ ex ( πα s/ β )] α s 0.5 β = β/( β) 9

29 Ste and lateau in BABAR data... another ossibility (Vladimir F. Dmitriev) Eur. Phys. J. A39 (2009) 35 Exected cross section with G S (4M2 ) = σ (b) BABAR (05) threshold At threshold σ (4M 2 ) = π2 α 3 2M β G β S (4M2 ) 2 σ (4M 2 ) = 0.85 G S (4M2 ) 2 nb q2 (GeV) G S (4M2 ) as ointlike fermion airs! 20

30 Ste and lateau in BABAR data... another ossibility (Vladimir F. Dmitriev) Eur. Phys. J. A39 (2009) 35 Exected cross section with G S (4M2 ) = σ (b) threshold BABAR (05) Prediction Assuming: G E (q2 ) = G M (q2 ) = R = R s α s = 0.5 in the region q 2 (2.GeV) 2 σ = (850 b) τ Rs At threshold σ (4M 2 ) = π2 α 3 2M β G β S (4M2 ) 2 σ (4M 2 ) = 0.85 G S (4M2 ) 2 nb q2 (GeV) G S (4M2 ) as ointlike fermion airs! 20

31 BABAR : G eff including threshold effects G no corr (q 2 ) 2 = ER 6πα2 3 σ (q 2 ) ) + 2τ ( β 4q 2 G eff (q2 ) 2 = ER s 6πα 2 3 σ (q 2 ) ) + 2τ ( β 4q 2 BABAR [PRD73, (05)] G no corr, G eff 0.5 threshold G no corr G eff 0 q2 (GeV)

32 BABAR : G eff including threshold effects G no corr (q 2 ) 2 = ER 6πα2 3 σ (q 2 ) ) + 2τ ( β 4q 2 G eff (q2 ) 2 = ER s 6πα 2 3 σ (q 2 ) ) + 2τ ( β 4q 2 BABAR [PRD73, (05)] G no corr, G eff 0.5 threshold G no corr G eff = e πα β R 0 q2 (GeV)

33 Integrated Sommerfeld factor W W [ ex( πα/β)]dw W (MeV) 22

34 e + e Λ + c Λ c and e+ e N(440)+c.c. [Belle PRL0, 7200] [BABAR PRD73, 02005] σ ΛcΛc (nb) 0.6 σ N* (nb) W ΛcΛc (GeV) W N* (GeV) 23

35 Λ + c Λ c cross section PRL0, 7200 σ (b) NO-COULOMB corr. (COULOMB corr.) + (G =) threshold Belle data M Λc Λ c (MeV/c 2 ) 24

36 BABAR 203: e + e PRD , arxiv: σ (nb) 0.5 L = 232 fb, W = 23, 25 MeV L = 469 fb, W = 23, 25 MeV L = 469 fb, W = 3.5, 5 MeV first bin W (GeV) 25

37 e + e : efficiency arxiv: Detection efficiency BABAR W (GeV) 26

38 Jum in the cross section! σ (b) BABAR [PRD87, (203)] BESIII reliminary BESIII reliminary E760 [PRL70, 22 (993)] W (GeV) 27

39 The neutral baryons uzzle 30 Pahos - October 29th, 203

40 Neutral Baryons uzzle (BABAR) [PRD76, ] σ(e + e N 0 N 0 )= 4πα2 βc 0 3q 2 [ G N0 M 2 + 2M2 N 0 q 2 G N0 E 2 No Coulomb correction at hadron level: C 0 = ] πα 2 β q 2 2M 2M 2 G N N 0 N σ(e + e ΛΛ) (b) BABAR 0.04 σ(e + e Σ 0 Σ 0 ) (b) 0.08 σ(e + e ΛΣ 0 ) (b) DM2 σ th = 200±50 b σ th = 30±3 b σ th = 47±23 b q 2 (GeV/c) q 2 (GeV/c) q 2 (GeV/c) Like a remnant of Coulomb interactions C 0 β at quark level? as q 2 2M N 0 For any neutral baryon σn 0 N 0 GN0 M N 0 28

41 Baryon octet and U-sin arxiv: n Y Σ Σ 0 Σ + - Λ Ξ Ξ 0 - I 3 (Y, I 3 ) (Y U, U 3 ) U 3 = 2 I Y Y U = Q Ξ 0 Ξ Y U Σ Λ = 3Λ+Σ 0 2 Σ + - Σ 0 = 3Σ 0 Λ 2 n U 3 U-sin relation: G Σ0 G Λ G ΛΣ0 = 0 M Σ 0 σσ M 0 Σ 0 Λ σλλ + 2 M ΛΣ 0 σλσ 0 = ( 0.06 ± 6.0)

42 Baryon octet and U-sin arxiv: n Y Σ Σ 0 Σ + - Λ Ξ Ξ 0 - I 3 (Y, I 3 ) (Y U, U 3 ) U 3 = 2 I Y Y U = Q Ξ 0 Ξ Y U Σ Λ = 3Λ+Σ 0 2 Σ + - Σ 0 = 3Σ 0 Λ 2 n U 3 U-sin relation: G Σ0 G Λ G ΛΣ0 = 0 M Σ 0 σσ M 0 Σ 0 Λ σλλ + 2 M ΛΣ 0 σλσ 0 = ( 0.06 ± 6.0)

43 BABAR : e + e ΛΛ [PRD76, ] σ ΛΛ (nb) 0.3 BESIII collected data at threshold and above W ΛΛ (GeV) 30

44 Neutral baryon non-zero cross section at threshold? Coulomb interaction at quark level! Unexected: hadron formation at short range and time Coulomb interaction at long range and time Hyerons at threshold in BESIII: non zero detection efficiency σ ΛΛ (nb) 400 BABAR BESIII? very good c.m. energy resolution (< MeV) Naive exectation: ( ) 2Q σ(4m 2 2 M Λ ) = σ(4m2 ) u + Qd 2 + Q2 s M Λ Qu 2 + Q2 u + = 400 b Q2 d ( πα ) eff ( 2 R eff = e β e πα ) eff 2 2 β ΛΛ threhsold ( 400 b ) Reff + βp QCD ΛΛ case: Cross section at threshold = 400 b σ(λλ) = 200 b 00 MeV above threshold = sike in the cross section, (if α S < α S) W ΛΛ (GeV) 3

45 e + e nn σ nn (nb) 2 nn threshold FENICE (988) Phys. Lett. B 33, 283 (93) SND (20) EPJ Web Conf. 37, (2) A very large cross section also at threshold Still room for β like rising G n M /G M Data.5 Naively Q d /Q u QCD < q2 (GeV) Soliton models VMD (Dubnicka) 32

46 Exeriments: now and future n GE at q 2 =.5 GeV2 (Pol. 3 He) GE and GM for q GeV2 Mainz Sace-like region n n [Hall A] GE /GM u to 0.2 GeV2 [Hall A] GE /GM u to 4 GeV2 n [Hall B] GM (deuterium) u to 4 GeV2 n [Hall A] GM (ratio) u to 8 GeV2 n [Hall C] GE u to 7 GeV2 at VEPP-2000 e+ e collider n Geff, Geff (scan) n GE, GM, Geff (scan and ISR) q 2 (4 GeV)2 Time-like region at BEPCII e+ e collider BESIII q 2 (3.5 GeV)2 at SuerKEKB e+ e collider at FAIR collider GE, GM, GE /GM hase ( olarization) (2.4 GeV)2 q 2 (3.7 GeV)2? GE, GM, (ISR) 2 q (4.5 GeV)2 33 Pahos - October 29th, 203

47 To do list Time-like G E - G M searation: DR and data Understanding threshold effect(s): Disersive analyses: integral equation, sum rule,... Exerimental observation in π 0 l + l [PRC75,045205(07)] Asymtotic behavior: DR and data for the hase Zeros hases: DR and data 34

48 To do list Time-like G E - G M searation: DR and data BESIII Understanding threshold effect(s): BESIII Disersive analyses: integral equation, sum rule,... Exerimental observation in π 0 l + l [PRC75,045205(07)] Asymtotic behavior: DR and data for the hase Zeros hases: DR and data 34

Baryon Form Factors at threshold. Rinaldo Baldini Ferroli and S. Pacetti PHIPSI11. BINP, Novosibirsk, 19 th -22 nd September 2011

Baryon Form Factors at threshold Rinaldo Baldini Ferroli and S. Pacetti PHIPSI BINP, Novosibirsk, 9 th -22 nd September 2 Outline Last News on Baryon FF near threshold The Neutral Baryon Puzzle Spacelike