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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

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- 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
 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

X4 (misprint) in

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
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


Check radiative decay width values

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 values

M=1232 MeV/c2

For M* =0

radiative decay width

Dalitz decay width


Dalitz decay

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


Dalitz decay

Field theory calculation: in

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

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


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 dalitz decay dilepton yield ingredients of the calculation2
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--


N n n model polarisation effects

e in +

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 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-


Dalitz decay

Origin of high dilepton mass tails in

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

pp@1.25 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


N dalitz decay dilepton yield ingredients of the calculation3

Quite well known, can be improved with our data in

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 in

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 in ”

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

Tetyana

Witold

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

dilepton angle, helicity angle,…


Conclusion
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 dalitz decay
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


Dalitz decay

M in D


Efficiency and acceptance corrected pp data comparison to transport model calculation
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

Isospin effects


Analytic continuation to time like region

Analytic continuation in :

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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