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

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1 Baryon Form Factors at threshold Rinaldo Baldini Ferroli and S. Pacetti PHIPSI BINP, Novosibirsk, 9 th -22 nd September 2

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 2

3 Cross sections and analyticity Space-like region eb eb FF s are real Im[q 2 ] Time-like region Unphysical region Data region No data e + e BB FF s are complex Time-like: had. helicity = s th = 4Mπ 2 ( GE G M s phy = 4M 2 B Re[q 2 ] G E (4M 2 B ) = G M (4M 2 B ) e B B e θ Elastic scattering dσ dω = α2 E e cos 2 θ 2 4Ee 3 sin 4 θ 2»G 2E τ +2( τ ) tan 2 θ «GM 2 2 τ τ = q2 4MB 2 B e e + θ B Annihilation Coulomb correction r dσ dω = α2 βc»(+cos 2 4q 2 θ) G M 2 + τ β = sin2 θ G E 2 τ 3

4 The Coulomb Factor γ B pp Coulomb interaction as FSI [Sommerfeld, Sakharov, Schwinger, Fadin, Khoze] B Distorted wave approximation C = Ψ Coul () 2 πα S-wave: C = β exp D-wave: C = πα β πα β β Coulomb factor C No Coulomb factor for boson pairs (P-wave) p q 2 (GeV/c) 4

5 Sommerfeld Enhancement and Resummation Factors Coulomb Factor C for S-wave only: Partial wave FF: Cross section: G S = 2G p M q 2 /4M 2 + G E 3 G D = G p M q 2 /4M 2 G E 3 σ(q 2 ) = 2πα 2 β 4M2 (q 2 ) 2 h C G S (q 2 ) G D (q 2 ) 2i C = E R Enhancement factor: E = πα/β Step at threshold: σ(4m 2 ) = π2 α 3 β 2M 2 β G S(4M 2 ) 2 =.85 G S (4M 2 ) 2 nb Resummation factor: R = /[ exp( πα/β)] Few MeV above threshold: C σ(q 2 ) β G S (q 2 ) 2 5

6 The e + e τ + τ case σ ττ (nb).75 KEDR BES With Coulomb corr. Without Coulomb corr. With only enhancement factor W ττ (GeV) 6

7 Pointlike Baryons? R. Baldini Ferroli, S. Pacetti, A. Zallo and A. Zichichi 7

8 I.S.R. versus c.m. Advantages All q at the same time = Better control on systematics c.m. boost = at threshold efficiency + σ W MeV Detected ISR γ = full pp angular coverage Drawbacks L invariant mass bin w More background 8

9 Mass resolution Mass resolution (MeV/c 2 ) M pp (GeV/c 2 ) Incredibly good at threshold ( MeV/c 2 ), as e + e c.m. p T /p T.5% at GeV 9

10 BABAR : e + e pp [PRD73, 25] σ pp (nb) W pp (GeV)

11 Proton form factor at q 2 = 4M 2 p σ(e + e pp)(4m 2 p ) =.83 ±.5 nb σ(e + e pp)(4mp) 2 = π2 α 3 β 2Mp 2 β Gp (4Mp) 2 2 =.85 G p (4Mp) 2 2 nb G p (4M 2 p ) G p (4M 2 p) =.99 ±.4(stat) ±.3(syst)

12 Proton form factor at q 2 = 4M 2 p G p (4M 2 p ) At q 2 = 4MP 2 protons behave as pointlike fermions!

13 Sommerfeld Resummation Factor Needed? 2

14 Resummation Factor Needed? At threshold: G E /G M = σ(q 2 ), G E /G M G S, G D G S = exp( πα/β) No need of Resummation Factor { GS R G D = R For a wide energy range ( 2 MeV): Proton behaves as a pointlike particle e.m. dominance, no strong interaction? Mild sensitivity to BB invariant mass resolution 3

15 BABAR : G p E /Gp M and σ(e+ e pp) [PRD73, 25] G E p /GM p σ pp (nb) W pp (GeV) 4

16 BABAR : G p E /Gp M and σ(e+ e pp) [PRD73, 25] G S p, GD p p exp( πα/β) G S p G D p W pp (GeV) 5

17 BABAR : G S, G D and G eff [PRD73, 25] G S, G D.5 G p eff W pp (GeV) W pp (GeV) 6

18 Integrated Sommerfeld factor W Z W [ exp( πα/β)]dw W (MeV) 7

19 Other charged baryon FF s at threshold 8

20 e + e Λ + c Λ c and e+ e pn(44)+c.c. [Belle PRL, 72] [BABAR PRD73, 25] σ ΛcΛc (nb).6 σ pn* (nb) W ΛcΛc (GeV) W pn* (GeV) 9

21 e + e pn(44)+c.c. BABAR PRD73, 25 σ Coulomb = 6π2 α 3 M 3/2 p M 3/2 N(44) (M p + M N(44) ) 5 G pn(44) 2 = G pn(44) 2.49 nb Events/. GeV σ pn(44) (nb).6.4 Coulomb W pπ (GeV) p q 2 (GeV/c) G pn(44) =.4 ±.9 2

22 The neutral baryons puzzle 2 September 2st, 2

23 Neutral Baryons puzzle (BABAR) [PRD76, 926] σ(e + e B B )= 4πα2 βc 3q 2 " G B M 2 + 2M2 B q 2 G B E 2 No Coulomb correction at hadron level: C = # πα 2 β q 2 2M 2M 2 G B 2 B B 3 σ(e + e ΛΛ) (pb) BABAR 4 σ(e + e Σ Σ ) (pb) 8 σ(e + e ΛΣ ) (pb) 2 DM2 σ th = 2±5 pb 3 2 σ th = 3±3 pb σ th = 47±23 pb p q 2 (GeV/c) p q 2 (GeV/c) p q 2 (GeV/c) Like a remnant of Coulomb interactions C β at quark level? as p q 2 2M B For any neutral baryon p σb B GB M B 22

24 Baryon octet and U-spin arxiv: n Y p Σ Σ Σ + - Λ Ξ Ξ - I 3 (Y, I 3 ) (Y U, U 3 ) U 3 = 2 I Y Y U = Q Ξ Ξ Y U Σ Λ = 3Λ+Σ 2 Σ + - Σ = 3Σ Λ 2 p n U 3 U-spin relation: G Σ G Λ G ΛΣ = p M Σ σσ M Σ Λ σλλ + 2 p M ΛΣ σλσ = (.6 ± 6.)

25 Baryon octet and U-spin arxiv: n Y p Σ Σ Σ + - Λ Ξ Ξ - I 3 (Y, I 3 ) (Y U, U 3 ) U 3 = 2 I Y Y U = Q Ξ Ξ Y U Σ Λ = 3Λ+Σ 2 Σ + - Σ = 3Σ Λ 2 p n U 3 U-spin relation: G Σ G Λ G ΛΣ = p M Σ σσ M Σ Λ σλλ + 2 p M ΛΣ σλσ = (.6 ± 6.)

26 BABAR : e + e ΛΛ [PRD76, 926] σ ΛΛ (nb) W ΛΛ (GeV) 24

27 Time-like G n M measurements G n M (q2 ).8.6 No Coulomb correction FENICE DM2 DM2 extr. from G Λ G p M (q2 ) Q d /Q u G n M /Gp M Data.5 Naively Q d /Q u.4 pqcd < p q 2 (GeV) Soliton models VMD (Dubnicka) Only SND, CMD2(?) and BESIII can measure this cross section No other experiments at present and in near future will be able to perform such a measurement 25

28 e + e nn: preliminary result from SND σ nn (nb) e + e nn SND (2) FENICE (988) Scan 2 Maximum energy: 2 GeV Efficiency 3% Above nn threshold: σ nn =.8 ±.2 nb SND preliminary p q 2 (GeV) 26

29 Dispersive analysis of the ratio R = µ p G p E G p M Eur. Phys. J. A32, 42 R. Baldini, S. Pacetti and A. Zallo space-like unphysical region time-like Re(q 2 ) 27

30 Space-like G p E /Gp M measurements µpg p E (q2 )/G p M (q2 ) Space-like G p E = F p + q2 F p 4Mp 2 2 G p M = F p + F p 2 F / q 2 4Mp 2 F 2 cancellation G p E (q2 ) G p M (q2 ) < PRD5 549 q 2 (GeV 2 /c 2 ) Time-like F / q 2 4Mp 2 F 2 enhancement G p E (q2 ) G p M (q2 ) > Radiative corrections of polarization technique < Radiative corrections in Rosenbluth method 28

31 Space-like G p E /Gp M measurements µpg p E (q2 )/G p M (q2 ) Space-like G p E = F p + q2 F p 4Mp 2 2 G p M = F p + F p 2 F / q 2 4Mp 2 F 2 cancellation G p E (q2 ) G p M (q2 ) < PRL PRL PRD5 549 q 2 (GeV 2 /c 2 ) Time-like F / q 2 4Mp 2 F 2 enhancement G p E (q2 ) G p M (q2 ) > Radiative corrections of polarization technique < Radiative corrections in Rosenbluth method 28

32 Time-like G p E /Gp M measurements " # dσ d cos θ = πα2 βc 2q 2 G p M 2 (+cos 2 θ)+ 4M2 p q 2 µ 2 sin 2 θ R 2 p R(q 2 ) = µ p G p E (q2 ) G p M (q2 ) R(q 2 ) /µp BABAR (ISR) PRD73, 25 LEAR (pp e + e ) NPB4, 3 FENICE+DM2 E835 EPJC46, 42 Scaling γγ exchange e e γ C = + γ γγ exchange interferes with the Born term p p p q 2 (GeV/c) Asymmetry in angular distributions [PLB659, 97] 29

33 γγ exchange from e + e ppγ BABAR data E. Tomasi-Gustafsson, E. A. Kuraev, S. Bakmaev, SP PLB659, 97 dσ A(cos θ, q 2 ) = dω (cos θ, q2 ) dσ dω ( cos θ, q2 ) dσ dω (cos θ, q2 ) + dσ dω ( cos θ, q2 ). A cos θ -. A cos θ,q 2 =. ± p q2 (GeV/c) 3

34 R(q 2 ) in the complex plane G E, G M and also R, if G M has no zeros, are analytic on the q 2 plane with a cut (s th = 4M 2 π, ) [see e. g.: Eur. Phys. J. C, 79 (999)] R(q 2 ) experimental sheet Im(q 2 ) s th s phy Re(q 2 ) physical sheet unphysical sheet 3

35 R(q 2 ) in the complex plane R(q 2 ) experimental sheet Dispersion relation for the imaginary part (q 2 s th ) G(q 2 ) = I G(z)dz lim R 2πi C z q 2 = π Z s th ImG(s)ds s q 2 Im(q 2 ) s th s phy path C R physical sheet Re(q 2 ) unphysical sheet 3

36 R(q 2 ) in the complex plane R(q 2 ) Dispersion relation for R with subtraction at q 2 = experimental sheet R(q 2 ) = R() + q2 π Z s th ImR(s)ds s(s q 2 ) Im(q 2 ) s th s phy path C R physical sheet Re(q 2 ) unphysical sheet 3

37 R(q 2 ) EPJA32 42 R(q2 ) = R() + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) space-like R(q 2 ) time-like Req 2 JLab+MIT-Bates BABAR +DM2/FENICE+E q 2 (GeV 2 /c 2 ) q 2 (GeV 2 /c 2 ) 32

38 R(q 2 ) EPJA32 42 R(q2 ) = R() + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) space-like R(q 2 ) time-like Req 2 JLab+MIT-Bates BABAR +DM2/FENICE+E q 2 (GeV 2 /c 2 ) q 2 (GeV 2 /c 2 ) 32

39 R(q 2 ) EPJA32 42 R(q2 ) = R() + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) space-like R(q 2 ) time-like Req 2 JLab+MIT-Bates BABAR +DM2/FENICE+E835.5 DR Approach /Q log 2 Q 2 /Q 2 Impr. log 2 Q 2 /Q 2 IJL q 2 (GeV 2 /c 2 ) q 2 (GeV 2 /c 2 ) 32

40 R(q 2 ) EPJA32 42 R(q2 ) = R() + q2 π 4M 2 π ImR(s) s(s q 2 ) ds R(q 2 ) space-like R(q 2 ) time-like Req 2 JLab+MIT-Bates BABAR +DM2/FENICE+E835 JLab preliminary V. Punjabi DSPIN-9 Dubna, Russia.5 DR Approach /Q log 2 Q 2 /Q 2 Impr. log 2 Q 2 /Q 2 IJL q 2 (GeV 2 /c 2 ) q 2 (GeV 2 /c 2 ) 32

41 Asymptotic G P E (q2 )/G p M (q2 ) and phase G P E (q2 )/G p M (q2 ) 2 Space Time Phase of G P E (q2 )/G p M (q2 ) 2 Phragmèn Lindelöf phase limit zeros q 2 (GeV 2 /c 2 ) p q 2 (GeV/c) pqcd prediction G p E (q2 ) G p M (q2 ) q 2 Phase from DR φ(q 2 ) = p q 2 s π Z ln R(s) ds Pr s s s (s q 2 ) 33

42 J/ψ strong and electromagnetic phase G J/ψ 34

43 BESIII preliminary results: J/ψ pp, nn nn identification Events/5 MeV E(n) (GeV) Events/2 3 2 Events/ degree 5 5 Number of n in 5 o cone Bkg from MC J/ψ π nn Angle between n and recoil dir. of n (degree) BESIII B(J/ψ nn) = (2.7±.±.4) -3 B(J/ψ pp) = (2.2±.4±.27) -3 PDG B(J/ψ nn) = (2.2±.4) -3 B(J/ψ pp) = (2.7±.7) -3 B(J/ψ pp) B(J/ψ nn) suggests a phase 9 between strong and e.m. amplitudes! 35

44 J/ψ decays: strong and electromagnetic e γ J/ψ γ G N e γ J/ψ 3g N e A γ N cross section A γ + A 3g 2 = A γ 2 + A 3g Re[A γa 3g ] {z } interference term According to pqcd: A γ and A 3g are real interference e A 3g N On the contrary data suggest: J/ψ J P JP 2 A γ A 3g phase 6 o ± o 38 o ± 37 o 9 o ± o But these conclusions have been obtained modeling SU(3) breaking, or using poorly measured nn cross section outside J/ψ Interference with the continuum measures the relative phase in an independent way nn 89 o ± 5 o 36

45 Full interference as seen by PANDA or BESIII σ pp (nb) 2 PANDA ( p p /p p = 4 ) BESIII W pp (MeV) 37

46 Conclusions Pointlike Behavior at and well above threshold No Sommerfeld Resummation Factor Neutral baryon non zero cross section at threshold? G p E space-like asymptotically? Imaginary J/ψ strong decay amplitude? Perspectives Data from SND and CMD2 More data from BABAR ( 2) and Belle (?) BESIII: ISR now, scan PANDA could explore FFs below threshold through pp π l + l 38