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### Dalitz decay:

lagrangian

eVdm

…to HADES experimental spectra

preliminary

B. Ramstein, IPN Orsay

In collaboration with J. Van de Wiele

GSI, HADES Collaboration Meeting , 05/07/08

- Dalitz decay in transport codes:C+C 2 GeV

IQMD

- Dalitz
pn

No medium effects

HSD

Me+e-(GeV/c2)

Thomère,Phys ReV C 75,064902 (2007)

E. Bratkovskaya nucl-th 07120635

Important issue for understanding intermediate mass dilepton yield

q2 = M2inv(e+e-) = M*2 > 0

Time Like - N transition:

Complementary probes of electromagnetic

structure of N - transition

Space Like N - transition :

extraction of electromagnetic

form factors

GE(q2), GM(q2), GC(q2)

e-

e-

q2 = M* = - Q2 < 0

*

p

D+

→Np

Lots of data, Mainz, Jlab

Pion electro/photo-production

Dalitz decay : intrinsic interest of the measurement Dalitz decay

p

D+

*

e+

Branching ratio not measured

experimental challenge

e--

e--

N- Dalitz decay dilepton yield: ingredients of the calculation

Strong interaction model

- 1) N N N :
- Mass dependent width Breit-Wigner, with possible cut-offs
- model for t dependence or angular distribution

QED

N

N

- 2 ) N e- e +
- exact field theory calculation
- 3 independent amplitudes:
- e.g. Electric, Magnetic and Coulomb

p

N

D+

*

QCD

e+

q2 = M*2 > 0

3) electromagnetic form factors

GM(q2),GE(q2),GC(q2)

Dalitz decay

e--

N- em transition : what do we know?« Photon point » : q2=0

GM(0)=3, GE(0)~0

- at q2=0, mainly M1+ (magnetic) transition

- At finite q2, many recent data points from Mainz, Jlab:
- multipole analysis of ° or + electroproduction

(%)

GM(q2)

related to GE(q2 )

(%)

related to GC( q2 )

Many models: dynamical models (Sato,Lee), EFT (Pascalutsa and Vanderhaeghen), Lattice QCD, two component modelQ. Wan and F. Iachello

What about time-like region ?

N- transition em structure: what about time-like region?

- Problems in Time-like region
- No data
- Electromagnetic form factors are complex

But,…

- decay width doesn’t depend on phases of form factors
- q2 stays small in Dalitz decay
at M =1232 MeV/c2 ,q2 < 0.09 GeV/c2

Space Like: q2<0

Time Like: q2>0

complex GTL(q2)

Analytic continuation :

real GSL(q2)

Models constrained by data

eg. GTL(q2) = GSL(-q2)

or GTL(q2) = GSL(-q2ei),…

- 2 options:
- take constant form factors
HSD, UrQMD, IQMD

- use models for form factors GE(q2),GM(q2),GC(q2) :
VDM,eVDM, (RQMD)two component Iachello model

GM(q2)

M=1.3 GeV/c2

0.6m2

M=1.1 GeV/c2

__ pure QED

__ Iachello FF

M=1.5 GeV/c2

M=1.7 GeV/c2

Sensitivity to Iachello form factor- two component model:
- Unified description of all baryonic transition form factors
- Direct coupling to quarks + coupling mediated by

- Analytic formula
- 4 parameters fitted on
- elastic nucleon FF (SL+TL)
- SL N- transition GM

PLUTO simulations: sensitivity to Iachello’s form factor in pe+e- events from Dalitz decay

E. Morinière, PHD thesis

pp @ 1.25 GeV

pe+e- events

Normalisation problem now solved →no sensitivity at E=1.25 GeV

N- in Dalitz decay dilepton yield: ingredients of the calculation

Strong interaction model

- 1) N N N :
- Mass dependent width Breit-Wigner, with possible cut-offs
- model for t dependence or angular distribution

QED

N

N

- 2 ) N e- e +
- exact field theory calculation
- 3 independent amplitudes:
- e.g. Electric, Magnetic and Coulomb

p

N

D+

*

QCD

e+

q2 = M*2 > 0

3) electromagnetic N- transition form factors GM(q2),GE(q2),GC(q2)

Dalitz decay

e--

Dalitz decay in « reference » papers in

Jones and Scadron convention

- form factor conventions
(including or not isospin factor of the amplitude)

- choices of form factors
- analytic formula for

differences

See Krivoruchenko et al. Phys.Rev.D 65, 017502

« remarks on radiative and Dalitz decays »

Comparing different Dalitz decay dilepton spectra:

- analytic formula for
- and form factors values at q2=0 from 4 papers
compare dilepton spectra for M=1232 MeV/c2

in mass dependence

factor 1.5

factor 1.7

factor 2.2

factor 2

Me+e-( GeV/c2)

Discrepancy increases with mass

But also off-shell effects problem at high mass

Branching in

Ratio

Expt

« Wolf »: HSD before 2007, IQMD,

UrQMD

« Ernst »

HSD after 2007

« Krivoruchenko »

RQMD

Zetenyi

PLUTO

Radiative

decay (10-3)

5.6± 0.4

6.0

8.7

7.05 (HSD)

5.6

5.6

Dalitz decay (10-5)

?

4.6

6.5

5.3 (HSD)

4.12 (const.GM)

4.25 (e-VDM)

4.12

4.4

Pretty

well!

Radiative decay width OK

Check: radiative decay width valuesM=1232 MeV/c2

For M* =0

radiative decay width

Dalitz decay width

Direct effect: in different normalisation of Dalitz decay dilepton spectrum

Same « Ernst » formula

Pluto BR(+→pe+e-) = 4.4 10-5

HSD BR (+→pe+e-) =5.3 10-5

Leptonic current

- Amplitude

Same as for →N

hadronic current

E,M,C : eg Krivoruchenko

« standard normal parity set »: eg Wolf

- Spin ½ projector (Dirac spinors)
- spin 3/2 projector (Rarita-Schwinger spinors)
- Traces of products of matrices

Calculation of

JH(..) JH ’*(..)* JL’(..) JL(…) *

phase space

From reference papers and Jacques Van de Wiele’s work

- Differential decay width:

- Electromagnetic hadronic current: 2 sets of covariants can be used:

in Dalitz decay width calculation: results

- Jacques Van de Wiele’s calculation → same analytical function as Krivoruchenko’s
- Can also be expressed in terms of g1,g2,g3:

- Shyam and Mosel; Kaptari and Kämpfer:
- g1=5.42, g2=6.61, g3=7 equivalent to GM=3.2 GE=0.04 GC~0.2
- Zetenyi and Wolf: g1=1.98, g2=0,g3=0
- fitted to reproduce radiative decay width
- →same Dalitz decay width as Van de Wiele/Krivoruchenko

q2 dependence negligible

for Dalitz decay

in Dalitz decay width calculation: results and suggestions for new PLUTO inputs

p

D+

*

e+

q2 = M*2

Dalitz decay

e--

- * angular distribution
- « helicity distribution »

- Krivoruchenko/Van de Wiele ( or « Zetenyi » ) expression for
- Electromagnetic N- transition form factors
- Branching ratio

Ok with E. Bratkovskaya, Phys. Lett. B348 (1995) 283

M=1232 MeV/c2

N- in Dalitz decay dilepton yield: ingredients of the calculation

Strong interaction model

- 1) N N N :
- Mass dependent width Breit-Wigner, with possible cut-offs
- model for t dependence or production angular distribution

QED

N

N

- 2 ) N e- e +
- exact field theory calculation
- 3 independent amplitudes:
- e.g. Electric, Magnetic and Coulomb

p

N

D+

*

QCD

e+

q2 = M*2 > 0

3) electromagnetic form factors

GM(Q2),GE(q2),GC(Q2)

Dalitz decay

e--

e in +

Same as in photoproduction

e--

N N N model: polarisation effects Dalitz decay

N

- polarization 4x4 density matrix
ms= -3/2,-1/2,1/2,3/2

N

N

D+

*

Anisotropy of * angular distribution

p

Spin-isospin excitation

1 exchange

+ exchange

Effective interaction,…

Long. polarization : (pure 1 exch.)

1/2 1/2 = -1/2 -1/2 =1/2

others ij=0

Transv. polarization :

( exch.)

3/2 3/2 = -3/2 -3/2 =1/2

others ij=0

Jacques Van de Wiele’s result

e in +

e-

p

p

, N

p

p

p

p

pD

p

e+

, N

e-

pp ppe+e- interference effects

Interference between all graphs including either a Delta or a nucleon

+ …..

+

,

cf Kaptari and Kämpfer,….

In PLUTO: factorization of NN → N cross section and (→Ne+e-):

p

p

1

No Bremstrahlung

two exit protons are distinguishable

p2

D+

p

e+

q2=M2inv(e+e-)=M*

e-

Origin of high dilepton mass tails in

HSD

HSDp+p 1.25 GeV

PLUTO

HSD

PLUTO

12C+12C

1 AGeV

tail at high dilepton mass: absent in PLUTO ?

absent in pp and pn ?

Different mass distributions ?

[email protected] in GeV

+ from p°

W. Przygoda’s talk

from e+e-p

M(e+e-)>140 MeV/c2

Ania Kozuch’s talk

q2=0.02 (GeV/c)2

q2=0.2 (GeV/c)2

Delta mass distribution in PLUTO:- Dmitriev’s mass distribution parametrisation
- but with Moniz vertex form-factors

Mass distribution

Teis = 300 MeV/c

Dmitriev = 200 MeV/c

M(MeV/c2)

d/dM

high mass dilepton yield is sensitive to

high mass

E. Morinière, PHD thesis

Quite well known, can be improved with our data in

N- Dalitz decay dilepton yield: ingredients of the calculationStrong interaction model

- 1) N N N :
- Mass dependent width Breit-Wigner, with possible cut-offs
- model for t dependence or angular distribution

QED

N

N

Exact calculation,

But offshell effects?

- 2 ) N e- e +
- exact field theory calculation
- 3 independent amplitudes:
- e.g. Electric, Magnetic and Coulomb

p

N

D+

*

QCD

e+

q2 = M*2 > 0

No sensitivity at E=1.25GeV,

Important at E=2.2 GeV

or in -p E=0.8 GeV/c

3) electromagnetic form factors

GM(q2),GE(q2),GC(q2)

Dalitz decay

e--

pp → pp ° E=1.25 GeV

Tingting’s talk

pp →pn+

E=1.25 GeV

- Experiment
- Simulation total
- Simulation D++
- SimulationD+
- SimulationN*

Normalized yield

simulation total

Marcin Wisniovski

pp → pp °

pp → pn +

E=2.2 GeV

Sexperiment =1.39*106 events

Ssimulation =1.37*106 events

Very good agreement

„pure in ”

pp→ppe+e-, pn →ppe+e-Challenging data ?Tetyana

Witold

+ (p,e+,e-) invariant mass

dilepton angle, helicity angle,…

Conclusion in

- A lot of different models to describe HADES data
- Different results , but we need to understand the reasons
- Some investigations for Dalitz decay
- A lot of other questions about other processes
- Let’s start the discussions…

Results of simulations for in Dalitz decay

Possibility to reduce ° background to 20%

1500 e+e-p events

In HADES acceptance

7 days of beam time

Better sensitivity to

discriminate pp bremstrahlung

M in D

Efficiency and acceptance corrected in pp data,comparison to transport model calculation

IQMD

preliminary

Δ→e+e-N seems to explain e+e- yield in p+p at 1.25 GeV

- Dalitz decay in transport codes: in p+p and pn at 1.25 GeV

Isospin effects

Time Like:

Space Like:

analytic continuation to Time-Like region:3) Intrinsic form factor:

Space Like:

Time Like:

Q2 - q2 ei

phase :

- removes singularity at q2=1/a2 (~ 3.45 (GeV/c)2)
- =53° fitted to elastic nucleon form factors Time Like data
- same value taken for N - transition

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