Dalitz decay:

…to HADES experimental spectra

From theory…

eVdm

lagrangian

B. Ramstein, IPN Orsay

In collaboration with J. Van de Wiele

preliminary

GSI, HADES Collaboration Meeting , 05/07/08

Dalitz decay in transport codes: C+C 2 GeV

Important issue for understanding intermediate mass dilepton yield

HSDNo medium effects

E. Bratkovskaya nucl-th 07120635

Dalitz

pn

IQMD

Me+e-(GeV/c2)Thomère,Phys ReV C 75,064902 (2007)

Branching ratio not measured experimental challenge

Dalitz decay : intrinsic interest of the measurement

Dalitz decaye++

e--

p

Lots of data, Mainz, Jlab

extraction of electromagnetic form factors GE(q2), GM(q2), GC(q2)

e--

Pion electro/photo-production

p →N+

e-

e-

*

Time Like - N transition:

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

2 > 0

Space Like N - transition :

q2 = M* = - Q2 < 0

*

Complementary probes of electromagnetic structure of N - transition

N- Dalitz decay dilepton yield: ingredients of the calculation

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

+

q2 = M* 2 > 0

Dalitz decay

p

e+

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

*

N

N

N 2 ) N e- e +

• exact field theory calculation • 3 independent amplitudes: e.g. Electric, Magnetic and Coulomb

QED

Strong interaction model

QCD

N- em transition : what do we know? • at q2=0, mainly M1+ (magnetic) transition

N

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

What about time-like region ?

« Photon point » : q2=0 GM(0)=3, GE(0)~0

)Im(

)Im(

1

1

M

EREM

)Im(

)Im(

1

1

M

SRSM

• 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 )

(%)

(%)

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

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

No data Electromagnetic form factors are complex

Time Like: q2>0complex GTL(q2)Analytic continuation :

Space Like: q2<0

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 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

M=1.1 GeV/c2 M=1.3 GeV/c2

M=1.7 GeV/c2M=1.5 GeV/c2

__ pure QED__ Iachello FF

0.6m2

GM(q2)

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

pp @ 1.25 GeVpe+e- events

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

E. Morinière, PHD thesis

N- Dalitz decay dilepton yield: ingredients of the calculation

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

+

q2 = M* 2 > 0

Dalitz decay

p

e+

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

*

N

N

N 2 ) N e- e +

• exact field theory calculation • 3 independent amplitudes: e.g. Electric, Magnetic and Coulomb

QED

Strong interaction model

QCD

Dalitz decay in « reference » papersHSD before 2007, IQMD, UrQMD

Wolf, Nucl.Phys. A517 (1990) 615 GMWolf=2.7 GM=4.1

HSD after 2007

PLUTO

Ernst, Phys.Rev C 58, 447 (1998) GMErnst=3

(HSD 2.7)

GM=4.5

(HSD=4.1)

(PLUTO= 3.2)

RQMD Krivoruchenko Phys.Rev.D 65, 017502 e-VDM GM(0)~3

Zetenyi and Wolf Zetenyi and Wolf, nucl-th0202047 g1= 2 GM(0)~3

See Krivoruchenko et al. Phys.Rev.D 65, 017502« remarks on radiative and Dalitz decays »

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

choices of form factors

analytic formula for

32

2

)(

dq

eed

differences

Jones and Scadron convention

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

2

)(

dq

eed

X4 (misprint)

mass dependence

Discrepancy increases with massBut also off-shell effects problem at high mass

factor 2.2factor 2

factor 1.7

factor 1.5

Me+e-( GeV/c2)

Check: radiative decay width values

*)N(Δq 3πdq

)eNe(Δd22

-

5.65.68.7

7.05 (HSD)

6.05.6± 0.4Radiative

decay (10-3)

Dalitz decay (10-5)

Branching

Ratio

4.12

Zetenyi

4.44.12 (const.GM)

4.25 (e-VDM)

6.5

5.3 (HSD)

4.6 ?

PLUTO« Krivoruchenko »

RQMD

« Ernst »

HSD after 2007

« Wolf »: HSD before 2007, IQMD,

UrQMD

Expt

Prettywell!Radiative decay width OK

For M* =0radiative decay width

)N(Δ 2dq

2

--

dq

)eNe(Δd)eNe(Δ

Dalitz decay width

M=1232 MeV/c2

Pluto BR(+→pe+e-) = 4.4 10-5 HSD BR (+→pe+e-) =5.3 10-5

Direct effect: different normalisation of Dalitz decay dilepton spectrum

Same « Ernst » formula

From reference papers and Jacques Van de Wiele’s work

• Differential decay width:

Field theory calculation:

eNeMdddq

ds

e

s

e

ssN mmmmeq ,,,

2

2

5

4

1

2

1M

phase space

2

ssΔ

sΔN

sN

Hisospin

1p,m ,p,mJp,m,p,mJc

eeee qL

M

Leptonic current

hadronic currentSame as for

→N

• Amplitude

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

Calculation of JH(..) JH ’*(..)* JL

’(..) JL(…) *• Spin ½ projector (Dirac spinors)• spin 3/2 projector (Rarita-Schwinger spinors)• Traces of products of matrices

E,M,C : eg Krivoruchenko « standard normal parity set »: eg WolfC2

CE2

EM2

MH J)q(GJ)q(GJ)q(GJ 32

322

212

1H J)q(gJ)q(gJ)q(gJ

Jacques Van de Wiele’s calculation → same analytical function as Krivoruchenko’s

Can also be expressed in terms of g1,g2,g3:

Gmq

GGqmmqmmmmqmm

C

Δ

EM

/

NΔ

/

NΔ

NΔ

NΔ 2

2

2

222322

2122

23

2

23

22

2

2

-

isospinc

2

3

48πdq

)eNe(Δd

Dalitz decay width calculation: results

3

2

1

)( 2

g

g

g

qM

G

G

G

C

E

M

q2 dependence negligible for Dalitz decay

• 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

 Krivoruchenko/Van de Wiele ( or « Zetenyi » ) expression for

Electromagnetic N- transition form factors Branching ratio

isotropicddq

Nd

*2

3 *)(

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

+

q2 = M* 2

Dalitz decay

p

e+

e--

*

eedddq

Nd *2*

*2

5

cos1~*)(

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

2

-

dq

)eNe(Δd

* angular distribution

« helicity distribution »

2dq

2

--

dq

)eNe(Δd)eNe(Δ M=1232 MeV/c2

N- Dalitz decay dilepton yield: ingredients of the calculation

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

+

q2 = M* 2 > 0

Dalitz decay

p

e+

e-- 3) electromagnetic form factorsGM(Q2),GE(q2),GC(Q2)

*

N

N

N 2 ) N e- e +

• exact field theory calculation • 3 independent amplitudes: e.g. Electric, Magnetic and Coulomb

QED

Strong interaction model

QCD

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 =1/2others ij=0

N N N model: polarisation effects

ss mm '

qS

qS

.

+

Dalitz decay

p

e+

e--*

N

N

N polarization 4x4 density matrixm

s= -3/2,-1/2,1/2,3/2

Spin-isospin excitation1 exchange + exchangeEffective interaction,…

Anisotropy of * angular distribution

Same as in photoproduction

Jacques Van de Wiele’s result

q

+

pp

p

e+

+p

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

1

e-

pp ppe+e- interference effects

p

pp

p

e+

e-

, N

cf Kaptari and Kämpfer,….

pp

p

e+

p

e-

, N

+ …..

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

Interference between all graphs including either a Delta or a nucleon

,

No Bremstrahlungtwo exit protons are distinguishable

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 1.0 A GeVno medium effects

1/N d

N/dM

[1

/GeV

/c2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 1.0 A GeVin-medium effects: CB+DM

1/N d

N/dM

[1

/GeV

/c2 ]

M [GeV/c²]

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 1.0 A GeVno medium effects

1/N d

N/dM

[1

/GeV

/c2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 1.0 A GeVin-medium effects: CB+DM

1/N d

N/dM

[1

/GeV

/c2 ]

M [GeV/c²]

p+p 1.25 GeV

12C+12C1 AGeV

HSD

tail at high dilepton mass: absent in PLUTO ?absent in pp and pn ? Different mass distributions ?

PLUTO

HSDPLUTO

HSD

Origin of high dilepton mass tails

Delta mass distribution in PLUTO:

q2=0.2 (GeV/c)2q2=0.02 (GeV/c)2

22

223

k

k

k

k

M

MM r

r

rrDmitriev

22222

22

MMMM

MMM

r

2

22

223

k

k

k

k

M

MM r

r

rrTeis

Dmitriev’s mass distribution parametrisation but with Moniz vertex form-factors

Teis = 300 MeV/c Dmitriev = 200 MeV/c M(MeV/c2)

Mass distribution

high mass dilepton yield is sensitive to high mass

E. Morinière, PHD thesis

d/dM

Ani

a K

ozuc

h’s

talk

W. Przygoda’s talk+ from p°

from e+e-p

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

pp@1.25 GeV

N- Dalitz decay dilepton yield: ingredients of the calculation

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

+

q2 = M* 2 > 0

Dalitz decay

p

e+

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

*

N

N

N 2 ) N e- e +

• exact field theory calculation • 3 independent amplitudes: e.g. Electric, Magnetic and Coulomb

QED

Strong interaction model

QCD

Exact calculation,But offshell

effects?

No sensitivity at E=1.25GeV,

Important at E=2.2 GeVor in -p E=0.8 GeV/c

Quite well known, can be improved with

our data

• Experiment

• Simulation total

• Simulation

• Simulation

• Simulation N*

experiment =1.39*106 events

simulation =1.37*106 events

Very good agreement

simulation total

Nor

mal

ized

yie

ld

Tingting’s talk pp →pn+

E=1.25 GeV

Ania Kozuch’s talk

pp → pp ° E=1.25 GeV

Marcin Wisniovski

pp → pp °

pp → pn +

E=2.2 GeV

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

„pure ”+ (p,e+,e-) invariant massdilepton angle, helicity angle,…

Tetyana

Witold

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

1500 e+e-p eventsIn HADES acceptance 7 days of beam time

Possibility to reduce ° background to 20%

Better sensitivity to discriminate pp bremstrahlung

M

Efficiency and acceptance corrected pp data,

comparison to transport model calculation

preliminary

IQMD

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

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

Isospin effects

Transport codeor calculation

Form factors (different conventions)

Effective form factors at q2=0 using

convention of Jones and Scadron

Reference papers

HSD before 2007

GM=2.7GE=GC=0

GM=3.3GE=GC=0

WOLF,Nucl.Phys.A517(1990)615

HSD after 2007

GM=2.7GE=GC=0

GM=3.3GE=GC=0

Ernst,Phys.Rev C58,447(1998)

RQMD e-VMD GM=3.GE=GC=0

Krivoruchenko Phys.Rev.D 65, 017502

IQMD G=2.72GE=GC=0

GM=3.33GE=GC=0

WOLF,Nucl.Phys.A517(1990)615

Zetenyi and Wolf

g1=1.98, g2=0,g3=0

GM=3.33GE=GC=0

Zetenyi, nucl-th 0202047

 Kaptari and Kämpfer

g1= 5.4g2=6.6g3=7

GM=3.2

GE=0.04

GC=0.19

 Kaptari,Nucl.Phys. A764 (2006)338

Time Like:Space Like:

222

2

)1(

1

QaQg

2222

)1(

1

qeaqg

i

Space Like: Time Like:

Q2 - q2 ei

Analytic continuation :

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

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