Dalitz decay :
description
Transcript of Dalitz decay :
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
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: