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From theory….  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.

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Dalitz decay

From theory…

 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

  • 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


Dalitz decay intrinsic interest of the measurement

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

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

N

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 ?


Dalitz decay

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


Sensitivity to iachello form factor

GM(q2)

M=1.3 GeV/c2

0.6m2

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

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 dalitz decay dilepton yield ingredients of the calculation1

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

 Dalitz decay

e--


Dalitz decay in reference papers

 Dalitz decay in « reference » papers

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

X4 (misprint)

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


Mass dependence

 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


Check radiative decay width values

Branching

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 values

M=1232 MeV/c2

For M* =0

radiative decay width

Dalitz decay width


Dalitz decay

Direct effect: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


Dalitz decay

Field theory calculation:

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

JH(..) 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:


Dalitz decay

 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


Dalitz decay

 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 dalitz decay dilepton yield ingredients of the calculation2

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 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--


N n n model polarisation effects

e+

Same as in  photoproduction

e--

N N N model:  polarisation effects

 Dalitz decay

N

  • polarization 4x4 density matrix

    ms= -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


Dalitz decay

e+

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-


Dalitz decay

Origin of high dilepton mass tails

HSD

HSD

p+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 ?


Delta mass distribution in pluto

[email protected] 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


N dalitz decay dilepton yield ingredients of the calculation3

Quite well known, can be improved with our data

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

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--


Dalitz decay

Ania Kozuch’s talk

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


Pp ppe e pn ppe e challenging data

„pure ”

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

Tetyana

Witold

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

dilepton angle, helicity angle,…


Conclusion

Conclusion

  • 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 dalitz decay

Results of simulations for  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


Dalitz decay

MD


Efficiency and acceptance corrected pp data comparison to transport model calculation

Efficiency and acceptance corrected 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

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

Isospin effects


Analytic continuation to time like region

Analytic continuation :

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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