Babar anomaly and the pion form factors

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1 Babar anomaly and the pion form factors Adam Szczepaniak Indiana University Form-factors :: quark/gluon structure of hadrons

2 Babar anomaly and the pion form factors Adam Szczepaniak Indiana University Form-factors :: quark/gluon structure of hadrons high Q 2 :: LO pqcd (twist/αs expansion)

3 Babar anomaly and the pion form factors Adam Szczepaniak Indiana University Form-factors :: quark/gluon structure of hadrons high Q 2 :: LO pqcd (twist/αs expansion) Questions: 1. Role of hadronic vs partonic d.o.f 2. Is there indication that all-orders re-summation is needed with M.Gorshtein, P.Guo, J.L.Londergan, F.L.Estrada

4 BaBar anomaly e + e! 0 e + e B.Aubert et al. Phys.Rev. (2009) e e + (Q 2 ) F (Q 2 ) 0 + Q 2 ~ 1/r 2 + r theory: G.P.Lepage, S.Brodsky

5 BaBar anomaly e + e! 0 e + e B.Aubert et al. Phys.Rev. (2009) pointlike e e + (Q 2 ) F (Q 2 ) 0 harder + Q 2 ~ 1/r 2 + hard r soft theory: G.P.Lepage, S.Brodsky

6 problems with LO pqcd in exclusive reactions Φ Φ T H N.Isgur, C.H.Llewellyn Smith, Phys.Rev.Lett.(1983) Φ P z!1 z i P z,µ i,? O(1) t 1 t E = X i µ 2 i? z i P z valid for z i P z large i.e. NOT in the end-point region

7 similar final states but different asymptotic predictions t 1 QCD s = q 2 t 1 QCD + sf (s) O(1) 0 s = q 2 sf 2 (s) O( s (Q 2 ))... but it does look different on the Light Front S.Brodsky,P.Lepage A.Radyushkin, A.Efremov

8 Pion form factors : still a mystery Q 2 F (Q 2 ) F (0)! 8 2 f 2 factor of 2-4 Q 2 F 2 (Q 2 ) F 2 (0)! 8 f2 s (Q 2 ) 0.5 ( s =0.5)

9 ρmeson F 2 (s) e.m. transition BaBar transition CLEO transition Belle F (s) F (0) resonance tails or QCD (duality) 2 ρ meson s [GeV 2 ]

10 Dispersive analysis F (s) =F (0) + s Z s th ds 0 Im F (s0 ) s 0 (s 0 s) F = F 2,F

11 Dispersive analysis F (s) =F (0) + s Z s th ds 0 Im F (s0 ) s 0 (s 0 s) F = F 2,F EM F.Factor Im F 2 (s) =t 2,2 2 F 2 + t 2,K K 2KF 2K + X X t 2,X X F X t(s) = Z = t F 2 + R dz s t I=1 (s, t(z s ))P 1 (z s ) (s) =(1 s/s th ) 1/2

12 Dispersive analysis F (s) =F (0) + s Z s th ds 0 Im F (s0 ) s 0 (s 0 s) F = F 2,F EM F.Factor Im F 2 (s) =t 2,2 2 F 2 + t 2,K K 2KF 2K + X X t 2,X X F X t(s) = Z = t F 2 + R dz s t I=1 (s, t(z s ))P 1 (z s ) (s) =(1 s/s th ) 1/2 F 2 (s) =1+ 1 Z ds 0 t (s 0 ) (s 0 )F 2 (s 0 )+R(s 0 ) s th s 0 (s 0 s) (so far) Exact representation of the electromagnetic form factor

13 Dispersive analysis cont. solution F 2 (s) =1+ 1 Z elastic inelastic R(s 0 ) / (s 0 (4m ) 2 ) ds 0 t (s 0 ) (s 0 )F 2 (s 0 )+R(s 0 ) s th s 0 (s 0 s)

14 Dispersive analysis cont. F 2 (s) =1+ 1 Z elastic inelastic R(s 0 ) / (s 0 (4m ) 2 ) ds 0 t (s 0 ) (s 0 )F 2 (s 0 )+R(s 0 ) s th s 0 (s 0 s) solution F 2 (s) = N(s) D(s) inelastic cut elastic cut

15 Dispersive analysis cont. F 2 (s) =1+ 1 Z elastic inelastic R(s 0 ) / (s 0 (4m ) 2 ) ds 0 t (s 0 ) (s 0 )F 2 (s 0 )+R(s 0 ) s th s 0 (s 0 s) solution F 2 (s) = N(s) D(s) inelastic cut elastic cut N(s) =1+ s D(s) =exp Z ds 0 D(s 0 )Re R(s ) s i [1 it (s 0 ) (s 0 )]s 0 (s 0 s) Z s ds 0 (s 0 ) s th s 0 (s 0 s) = arctan Re t/(1 Im t )

16 Dispersive analysis cont. F 2 (s) =1+ 1 Z elastic inelastic R(s 0 ) / (s 0 (4m ) 2 ) ds 0 t (s 0 ) (s 0 )F 2 (s 0 )+R(s 0 ) s th s 0 (s 0 s) solution F 2 (s) = N(s) D(s) inelastic cut elastic cut input: on shell P-wave ππ amplitude t(s),r(s) N(s) =1+ s D(s) =exp on shell, exclusive ππ-> X amplitudes + associated form factors Z ds 0 D(s 0 )Re R(s ) s i [1 it (s 0 ) (s 0 )]s 0 (s 0 s) Z s ds 0 (s 0 ) s th s 0 (s 0 s) output: F 2 (s) = arctan Re t/(1 Im t )

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18 ππ P-wave amplitude t = e2i 1 2i 11 p s[gev ]

19 ππ P-wave amplitude t = e2i 1 2i 11 ρ is inelastic p s[gev ] Im t Re t fit to phase shift data below s 1/2 =1.9 GeV s[gev 2 ]

20 ππ P-wave amplitude t = e2i 1 2i 11 ρ is inelastic p s[gev ] Im t Re t Regge fit fit to phase shift data below s 1/2 =1.9 GeV s[gev 2 ]

21 ππ P-wave amplitude t = e2i 1 2i 11 ρ is inelastic p s[gev ] Im t Re t Regge fit unknown fit to phase shift data below s 1/2 =1.9 GeV s[gev 2 ]

22 ππ P-wave amplitude t = e2i 1 2i C.Hanhart 11 ρ is inelastic p s[gev ] Im t Re t Regge fit unknown fit to phase shift data below s 1/2 =1.9 GeV s[gev 2 ]

23 Inelastic contribution (I) R = t 2,K K 2KF 2K + X X t 2,X X F X

24 Inelastic contribution (I) R = t 2,K K 2KF 2K + X X t 2,X X F X ρ is inelastic

25 R = t 2,K K 2KF 2K + X X t 2,X X F X fit to phase shift data below s 1/2 =1.9 GeV and Regge above F K (w) 2 w = p s[gev ]

26 Inelastic contribution (II) R = t 2,K K 2KF 2K + X X t 2,X X F X

27 Inelastic contribution (II) R = t 2,K K 2KF 2K + X X t 2,X X F X s < μ 2 s >μ 2 t Im t q q, = (t)s q(t) s = q 2 t q q, (s, t) t q q, = Z dz t t q q, (s, t)p 1 (z s )

28 Inelastic contribution (II) R = t 2,K K 2KF 2K + X X t 2,X X F X s < μ 2 q t 4 (t)+1 2 q (t 0) 0.75 Mandelstam branchings s >μ 2 s X q q t 2,q q q q F q q s q(0) 1/2 t Im t q q, = (t)s q(t) s = q 2 t q q, (s, t) t q q, = Z dz t t q q, (s, t)p 1 (z s )

29 why reggezation enhances amplitudes leading Fock components soft γ * (s) no central plateau soft multi-particle production in e + e - soft Reggized quark soft

30 why reggezation enhances amplitudes soft leading Fock components soft γ * (s) rapidity γ * (s) no central plateau soft soft multi-particle production in e + e - soft Reggized quark soft

31 pion e.m form factor (summary) F 2 ρmeson F X=q q =1 t q q, = s q t 2,2 F 2 (s) e.m. transition µ 2 = 1 GeV 2 µ 2 = 10 GeV 2 possible (Q 2 ) α enhancement (from multi-particle production -- Reggized quark) ρ meson s [GeV 2 ] curves: dispersion relation solution with reggized quarks to describe large-s region

32 pion transition form factor (summary) resonances (ω,ρ) 100 BaBar CLEO Belle 1 Reggized quark F 2 (s) e.m. transition µ 2 = 1 GeV 2 µ 2 = 10 GeV s [GeV 2 ]

33 From the s-channel: ImF (s) = X X resonances (ρ,ω) at low energies t X(s) X (s)f X (s) -s F (s) [GeV] M.Gorchtein, P.Guo, A.P. Szczepaniak arxiv: (PRC in press) (Q 2 ) α enhancement from multi-particle production BaBar CLEO Belle µ 2 = 1 GeV 2 µ 2 = 5 GeV s [GeV 2 ] multi-particle ladder -- Reggized quark (aka diffractive dissociation) µ 2 = 10 GeV 2 curves: dispersion relation solution with reggized quarks to describe large-s region

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35 Summary In the available energy range f.factors dominated by resonances Complete analysis requires self consistency: (e.g kaon form factor, Im part of inelasticity ) Importance of Regge trajectories and not elementary particles