L.P. Kaptari (BLTP JINR Dubna & FZ Rossendorf )

L.P. Kaptari (BLTP JINR Dubna & FZ Rossendorf)

L.P. Kaptari (BLTP JINR Dubna & FZ Rossendorf)

Propagation of broad meson resonances in a BUU type transport model: Application to di-electron production.H.W. Barz,B. Kampfer, Gy. Wolf, M. Zetenyi: nucl-th/0605036

Direct Dalitz decay

Bremssrahlung

“Bonn” with only four mesons

The (covariant, relat. inv. ) amplitude

Vertex Form Factors:

Coupling Constants (R. Shyam& U.Mosel, PRC67 (2003) 065202)

ISI + FSI (The Jost function formalism for FSI.Important only at the upper kinematical limitof the di-lectron mass)

2.

1.

VMD ? (double count.)

Bonn:

Electromagnetic FF’s:

-1.0 -0.5 0.0 0.5 1.00

2

4

6

8

10

Conv. + Brem.+FSI Conv.+FSI

pp -> pp

d/d* [

b sr

-1 ]

Cos *

-1.0 -0.5 0.0 0.5 1.05

10

15

20

25

30

pp -> pp

d/d* [n

b sr

-1 ]

Cos *

100 101 102 103

10-1

100

101

102 Tot(Brem.+Conv.+FSI) Conv. + FSI Brem.+Conv: No FSI

tot [

b]

s1/2 [MeV]

100 101 102 103

10-3

10-2

10-1

100

101

102

Tot(Brem.+Conv.+FSI) Conv. + FSI Brem.+Conv: No FSI

tot [

b]

s1/2 [MeV]

Fixing parameters

Gauge Invariance

a)

b)

Results for the neutron

Soft Photon Approximation:

(intermediate) summary: contact terms in pn bremsstrahlung are predominant!

Seagull and nucleonic currents

VMD

Delta contribution

Tagging the pn reaction in the spectator

SUMMARYAn effective model based on direct calculation of the Feynman diagrams is proposed to parametrize, in a consistent way, the amplitudes for the dielectron production in pp, pn and pD

Bremsstrahlung contribution is important in the whole kinematical region of the di-electron mass and at relatively low initial energies. Without the contact terms our results are compatible with the soft Photon Approximation and with calculations by other authors.

Contact terms, needed to restore the gauge invariance, play a predominant role in the bremsstrahlung amplitude in pn-reactions (in view of such circumstance, a moreconsistent investigation of the recipes of restoration the GI would be valuable here).

Our approach can be easily generalized to Dp reactions. Within a covariant Bethe Salpeter formalism by using the previously found solution of the BS equation(with the same OBE potential) we demonstrate that detecting the spectator protons with velocities close to the deuteron initial velocity and with momenta in the forward direction it is possible to study experimentally the pn sub-reaction with neutron targets.