Constraints on interaction from the process near threshold. V.F. Dmitriev and A.I. Milstein Budker Institute of Nuclear Physics

Transcription

1 NN Constraints on interaction from the process near ee threshold + NN V.F. Dmitriev and A.I. Milstein Budker Institute of Nuclear Physics

2 G E /G M.5 BABAR PS170 Ratio of electric and magnetic form factors in the threshold region GE F1 F 4 m p G = F + F M = + 1. q, R.Bijker, F.Jachello, Phys.Rev. C69 (004) Tp 10 MeV M pp (GeV/c ) Γ = Fγ F σ µ µ µν 1 m p p (Ν) q Γ _ -p (N) q ν

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5 General features of the process q p _ P P formation scale -p λ 1/ q 1/ m p 0.1 fm At distances 0.1 < r < 1.4 fm there is a strong interaction between slowly moving P and Pbar. This scale corresponds to the energies starting from few ten s MeV. Strong final state interaction in this energy scale is very likely responsible for the energy dependence of the form factors near threshold. QUANTUM NUMBERS of P Pbar state PHOTON P Pbar Isospin not fixed I=0,1 J=1, P=-1, C=-1 L+ 1 L+ S P ( 1), C ( 1), = = J=L+S L - even S = 1 S + D

6 Elementary amplitude of N Nbar production 1 E + ME EF MF ε T p ε 3 M p p p 3 ME ( + M) 1 () = ( E+ MF ) 1+ F ) e + 3( e ) e µ µλ µ λ λ λ F M proton mass, E nucleon energy, εµ F and F 1 and In the units of - spin-1 function of N Nbar pair F 1 e / q ( ) -Dirac form factors responsible for short distance behavior eλ - polarization of virtual photon are the smooth functions, nearly constants in threshold region

7 Accounting for N Nbar interaction I 3 I( ) εσ Tλ( p) Tσλ = d p' Ψ pσ ( p' ) Tλ( p' ) I is the isospin of N Nbar pair I ( ψ ) ( r) pσ - N Nbar scattering state with asymptotic behaviour ipr+ iη ln pr I( ) i i ln( pr(1 cos )) I () pr+ η θ e Ψ σ r e + p r εσ fσσ ' εσ '. r e η = v. For p pbar production For n nbar production p 1 0 T = T + T p 1 0 T = T T

8 Ψ () r Hˆ = ( E M) Ψ (), r I( ) I( ) pσ pσ ˆ p H = + U() r iw() r M Paris N Nbar potential, Phys.Rev. C50 (1994) 710 Phys. Rev. C59 (1999) 313 Real part - meson exchange for r > fm and fit a + ar+ a r + a r or b + br+ b r p π + n Coupled channels for r < fm. In both I=0,1 channels p n Imaginary part K ( ) 0 Mr W()~ r gc (1 + fctlab) r

9 Production amplitude becomes T = G 4 G m,1 11 Y ( p) I I I * ˆ σλ 0δσλ π σ λ m S-wave D-wave Electromagnetic form factors I I I I Q I I G GE = G0 + G, GM = G0 M G = G + G, G = G + G p 1 0 p 1 0 E E E M M M G = G G, G = G G n 1 0 n 1 0 E E E M M M

10 With these form factors the cross section p pbar or n nbar production has the usual form dσ α βc p = G ( ) M Q + θ + Q G E q dω 4M p ( ) 1 cos ( ) sin 4Q where v β = and C is the Coulomb distortion factor. c We omitted here effects of Coulomb-nuclear interference. θ

11 The amplitude depends on the wave function at short distances T + E M F F 3 M I I( ) 1 E ME µλ ~ Ψ p σ ( r=0) ( + ) 1+ ) eλ The second term I ( ) ~ i jψ p σ ( r=0) The process is sensitive to the short distance behavior of N Nbar wave function and N Nbar potential. It is not obvious that a pure phenomenological potential constructed to reproduce scattering phases in several partial waves in the restricted energy region will reproduce correctly the short range behavior of the N Nbar wave function.

12 A calculation with original Paris N Nbar potential Cross section (pb) BABAR FENICE DM DM1 ADONE73 BES M pp (GeV/c )

13 The only sensitive parameter in N Nbar potential is in the absorptive part of the potential K ( ) 0 Mr W()~ r gc (1 + fctlab) r fc is responsible for absorption rate at different energies. It is the same for all partial waves, which is probably oversimplified assumption. The coefficient is not well defined from the data. In two versions of the potential (1994) and (1999) it differs by factor ~. In our process we have s- and d-waves only and sensitivity to this coefficient is much higher due to short range origin of the process.

14 f Only when we reduced C by factor ~10 in both isospin channels we were able to reproduce the energy dependence of the cross section dσêdω HpbL σ HpbL E HGeVL E HGeVL

15 Without any additional fit we were able to reproduce the ratio of the proton electric and magnetic form factors..5»geêgm» E HGeVL

16 Summary We developed an approach to account for final state interaction (FSI) in P Pbar production near threshold. The effects of FSI are considerable; they lead to strong energy dependence near threshold. The process is sensitive to short range behavior of the N Nbar potential. It gives an additional constraint on the parameters of the potential.

17 There is an indication that the energy dependence of the absorptive part of the Paris N Nbar potential is too strong for s- and d-waves in J=S=1 channel.