BABAR Measurement of Baryon Form Factors Connecting Time and Space Regions

Transcription

1 BABAR Measurement of Baryon Form Factors Connecting Time and Sace Regions Centro Studi e Ricerche Enrico Fermi, Roma, Italy INFN Laboratori Nazionali di Frascati, Frascati, Italy Jefferson Lab, Newort News, Virginia May 21-23, 2007

2 Outline ISR main features, advantages and drawbacks BABAR candidates, selection and background BABAR stewise σ(e + e ) G E /G M time-like from e+ e angular distribution Sace and time G E /G M via disersion relations Asymtotic redictions on G E /G M BABAR results on G E and G M, F 1 and F 2, B S and B D Baryonium and dis in e + e hadronic channels? Λ and neutron time-like form factors 2

3 I.S.R. main features e + γ q 2 e < 0 dσ e + e γ d cos θγ (w) = de γ Eγ A(s, Eγ, θγ)σ 0 (w) e q 2 >4M 2 w = invariant mass for θ γ > 20 o I.S.R. Angular Accetance 15% ISR γ detected = no γγ interactions background Advantages All q at the same time = Better control on systematics c.m. boost = at threshold ɛ 0 + σ W 1 MeV Detected ISR γ = full angular coverage Drawbacks L invariant mass bin w More background 3

4 Events selection and background Analyzed 232 fb 1 Event selection: Tracks within Tracking and Particle ID accetance Very tight roton selector 30% good events loss γ kinematical fit E γ resolution not reroduced = 3C fit ɛ 18 ± 1 % 4025 selected events e + e π ± 32 estimated Background Summary M > 4 GeV signal overwhelmed π + π γ K + K γ π 0 π 0 γ uds γ data N 1 5.9± ± ±32 13±3 26±4 3737±

5 σ(e + e γ) BABAR stewise behaviour cross section [PRD73 (2006) ] σ(e + e )[b] BABAR FENICE DM2 DM1 ADONE73 q(gev ) q(gev ) 5

6 Nucleon form factors and cross sections e γ µ γ(q) Γ µ (q) N Nucleon current oerator (Dirac & Pauli) Γ µ (q) = γ µ F 1 (q 2 ) + i 2M N σ µν q νf 2 (q 2 ) Electric and Magnetic Form Factors e N G E (q 2 ) = F 1 (q 2 ) + τf 2 (q 2 ) τ = q2 G M (q 2 ) = F 1 (q 2 ) + F 2 (q 2 ) 4MN 2 e e θ Elastic scattering dσ dω = α2 E e cos 2 θ 2 4Ee 3 sin 4 θ 2»G 2E + τ 1 + 2(1 + τ) tan 2 θ «GM τ e e + θ Annihilation dσ dω = α2 1 1/τ 4q 2 C»(1 + cos 2 θ) G M 2 + 1τ sin2 θ G E 2 Coulomb correction: C y 1 e y y = παm βq 6

7 BABAR e + e angular distributions cos θ distributions from threshold u to 3 GeV Histograms show contribution from: G E (dashed) G M (dash-dotted) Transition from: sin 2 θ (G E dominant) to: 1 + cos 2 θ (G M dominant) Events/0.2 Events/0.2 Events/ cos θ cos θ Events/0.2 Events/0.2 Events/ cos θ cos θ cos θ cos θ 7

8 Time-like G E /G M measurements " # dσ d cos θ = πα2 βc 2q 2 G M 2 (1+cos 2 θ)+ 4M2 q 2 sin 2 θ R 2 µ R(q 2 ) = µ G E (q2 ) G M (q2 ) R(q 2 ) BABAR (ISR) PRD73(2006) Lear ( e + e ) NPB411(1994)3 Scaling γγ exchange e e γ γ γγ exchangeinterferes with the Born term q(gev ) Asymmetry in angular distributions 8

9 Sace-like G E /G M measurements Sace-like data µg E (q2 )/G M (q2 ) Sace like F 1 and Q2 4M 2 F 2 cancellation: R(Q 2 ) < 1 Time like (BABAR ) F 1 and Q2 4M 2 F 2 enhancement: R(Q 2 ) > 1 q 2 (GeV 2 ) 9

10 Analyticity constraints on the nucleon form factors 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 NN FF s are comlex s th = 4Mπ 2 s hy = 4M 8 2 Re[q 2 ] < 1 G E Crossing: tot. helicity = G : E (4M) 2 = G M (4M) 2 0 G M Perturbative QCD constrains the asymtotic behaviour QCD: q 2 F i (q 2 ) ( q 2 ) (i+1) "ln!# q Λ 2 QCD Analyticity: q 2 ± G E,M ( ) = G E,M (+ ) 10

11 Disersion relations connecting time and sace regions R(q 2 ) is analytic on the q 2 lane with a cut [s th = 4M 2 π, [, if G M has no zeros R Im(q 2 ) q 2 s th C Re(q 2 ) Subtraction at q 2 = 0 because of a non-vanishing asymtotic limit of the ratio For q 2 s th R is real For q 2 > s th R is comlex R(q 2 ) = R(0) + q2 π Z s th ImR(s)ds s(s q 2 ) Z ReR(q 2 ) = R(0) + q2 π Pr ImR(s)ds s th s(s q 2 ) 11

12 R(q 2 ) arametrization and constraints The imaginary art of R is arametrized by two series of orthogonal olynomials T i (x) 8 >< Pi C i T i (x) x = 2q2 s hy s th s ImR(q 2 ) I(q 2 s hy s 0 th q 2 s hy s th = 4Mπ 2 ) = >: Pj D j T j (x ) x = 2s s hy 1 q 2 hy = 4MN 2 > s q 2 hy Theoretical constraints on ImR(q 2 ) R(4M 2 π) is real = I(4M 2 π) = 0 R(4M 2 N ) is real = I(4M2 N ) = 0 R( ) is real = I( ) = 0 Theoretical constraints on R(q 2 ) Continuity at q 2 = 4M 2 π R(4M 2 N ) is real and ReR(4M2 N ) = 1 Exerimental constraints on R(q 2 ) and R(q 2 ) Sace-like region (q 2 < 0) data for R from TJNAF and MIT-Bates Time-like region (q 2 4MN 2 ) data for R from FENICE+DM2, BABAR, E835 and Lear 12

13 R(q 2 ) NPB(Proc.Su.)162(2006)46 Reconstructed R in sace and time regions R(q 2 ) sace-like R(q 2 ) time-like BABAR -Lear q 2 (GeV 2 ) 13

14 Asymtotic G P E (q2 )/G M (q2 ) NPB(Proc.Su.)162(2006)46 Asymtotic behaviour of G P E (q2 )/G M (q2 ) Sace Time BABAR -Lear QCD rediction G E (q2 ) G M (q2 ) q 2 1 q 2 (GeV 2 ) 14

15 G E (q2 ) and G M (q2 ) from σ and DR S.Pacetti, PANDA Worksho,Orsay 07 BABAR G E (q2 ) G M (q2 ) σ + DR G E = G M σ + DR G E = G M q 2 (GeV ) q 2 (GeV ) G M very stee at threshold = vector Baryonium? 15

16 Baryonium di in multihadronic rocesses P.J. Franzini and F.J. Gilman, 1985 γ γ γ V 1 + V 1 V 0 V 1 a + a V 1 V 0 V 1 V 0 V 1 a a a a A vector meson V 0 (J PC = 1 ), with vanishing e + e couling, which decays through an intermediate broad vector meson V 1 1 A s M1 2 A = For instance...! a s M0 2 a s M1 2 + s M 2 0 (s M 2 1 )(s M2 0 ) a2 M 0 = 1880MeV M 1 = 1850MeV Γ 0 = 20MeV Γ 1 = 300MeV +O(a 6 ) A 2 s(gev ) 16

17 Dis in multihadronic reactions σ(e + e hadrons)[nb] e + e annihilation rocesses 2.5 FENICE World average σ(e + e 3π + 3π )[nb] DM2 Diffractive hotoroduction E687 q 2 (GeV 2 ) q(gev ) e + e annihilation rocesses with ISR σ(e + e 3π + 3π )[nb] BABAR σ(e + e 2π + 2π 2π 0 )[nb] BABAR V 0 M(MeV ) Γ(MeV ) hadrons DM2 1930(30) 35(20) E (10) 37(13) BABAR 1880(50) 130(30) BABAR(π 0 ) 1860(20) 160(20) q(gev ) q(gev ) 17

18 Phases from DR: F 1 (q2 ) and F 2 (q2 ) S.Pacetti, PANDA Worksho,Orsay 07 BABAR F 1 (q2 ) = G M G E /G M τ 1 τ σ + DR F 2 (q2 ) = G M G E /G M 1 τ 1 σ + DR G E = G M G E = G M If G E = G M F 1 (q2 ) = G M (q2 ) F 2 (q2 ) = 0 q 2 (GeV ) q 2 (GeV ) 18

19 Phases from DR: B S (q2 ) and B D (q2 ) S.Pacetti, PANDA Worksho,Orsay 07 BABAR B S (q2 ) = 2 τg M + G E 3 σ + DR G E = G M B D (q2 ) = τg M G E 3 If B S (q2 ) = G M (q2 ) B D (q2 ) = G M (q2 ) (1 τ ) σ + DR G E = G M q 2 (GeV ) q 2 (GeV ) 19

20 Time-like G n M measurements Only two measurements by FENICE and DM2 G n M (q2 ) No Coulomb correction FENICE DM2 DM2 extr. from G Λ G M (q2 ) Q d /Q u G n M /G M Data 1.5 Naively Q d /Q u QCD < 1 Soliton models 1 VMD 1 q 2 (GeV 2 ) Threshold behaviour from angular distribution G n M (4M2 n) = G n E (4M2 n) = 0? Does BABAR agree with FENICE? Large G Λ U sin = large G n M 20

21 Conclusions BABAR : stewise σ(e + e ) BABAR : G E G M above threshold Sace and time G E /G M via disersion relations Asymtotic redictions on G E /G M BABAR results on G E and G M, F 1 and F 2, B S and B D Baryonium and dis in e + e hadronic channels? Λ and neutron time-like 21