details of ebac-dcc model
DESCRIPTION
Details of EBAC-DCC model. Hiroyuki Kamano. Informal EBAC meeting, May 24-26, 2010 (revised version of the talk at 2009 EBAC meeting). e.g.) D13 Total J = 3/2 , Isospin = 1/2 , Parity =. MB ( LS ). EBAC-DCC model: hadronic part. - PowerPoint PPT PresentationTRANSCRIPT
Details of EBAC-DCC modelDetails of EBAC-DCC model
Hiroyuki KamanoHiroyuki Kamano
Informal EBAC meeting, May 24-26, 2010(revised version of the talk at 2009 EBAC meeting)
Partial wave (LSJ) amplitude of a b reaction:
Reaction channels:
Potential:
EBAC-DCC model: hadronic part
2-body v potential(no N cut)
2-body v potential(no N cut) bare N* statebare N* state
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
2-body Z potential(with N cut)
2-body Z potential(with N cut)
e.g.) D13 Total J = 3/2 , Isospin = 1/2 , Parity =
MB( LS )
Meson-baryon Green’s functions
Stable channels = (, N), (, N), (K,), (K,) :
Unstable channels = (, ), (, N), (, N) :
() self-energy in the presence of spectator particle
Meson-baryon Green’s function
Branch point of unstable Green functions (MeV)
Unstable channels = (, ), (, N), (, N) :
Meson-baryon Green’s function
Model 2:
Unstable channels = (, ), (, N), (, N) :
Betz-Lee PRC23 375 (1981)
Simple s-wave (separable) model
Original Model 2
Branch points now have more realistic values.N Green function has two branch points.
2-body “v” potentials (non-strange channels)
5 diagramss-ch Nu-ch Nu-ch t-ch t-ch
2 diagramss-ch Nu-ch N
2 diagramss-ch Nu-ch N
3 diagramss-ch Nu-ch Nt-ch
2 diagramss-ch Nu-ch N
2 diagramss-ch Nu-ch N
4 diagramss-ch Nu-ch Nt-ch t-ch
2 diagramss-ch Nu-ch N
2 diagramss-ch Nu-ch N
2 diagramss-ch Nu-ch N
4 diagramss-ch Nu-ch Nu-ch t-ch
1 diagrams-ch N
1 diagrams-ch N
2 diagramss-ch Nu-ch N
2 diagramss-ch Nt-ch
Total 36 diagrams
2-body “v” potentials (channels with strange hadrons)
3 diagramss-ch Nu-ch t-ch K*
4 diagramss-ch Nu-ch t-ch t-ch
Total 18 diagrams
At present, KY couples to non-strange channelsthrough N channel only.
3 diagramss-ch Nu-ch u-ch t-ch K*
3 diagramss-ch Nu-ch t-ch
5 diagramss-ch Nu-ch t-ch t-ch t-ch
2-body “v” potentialsAll potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)
Partial wave decomposition
Plane wave matrix elementin helicity representationPlane wave matrix elementin helicity representation
Used for thecoupled-channelsequation
Unitary transformation (UT) method
e.g.) N N “v” potential (s-channel nucleon)
Independent of total scattering energy s1/2 !!
Potentials agree with usual Feynman diagram at on-shell. The off-shell behavior is uniquely defined within UT method.
UT methodUT method
See e.g., Ann. Phys. 322, 736 (2007)nucl-th/0102037for details of UT method
See e.g., Ann. Phys. 322, 736 (2007)nucl-th/0102037for details of UT method
Rules for attaching cutoff factors
Attach cutoff factors to each vertex (currently dipole form is used)
For s- and u-channel potential, use 3-momentum of external meson
For t-channel potential, use 3-momentum of exchanged meson
For contact potential, use product of two cutoff factors
2-body “Z” potentials
Feshbach projection:
2-body “Z” potentials
Numerical treatment of Z potentials
Z(E)(k,k’;E) potentials have logarithmic singularity.Z(E)(k,k’;E) potentials have logarithmic singularity.
N N, N, KY
Contour-rotation method
N N
Spline method
e.g., Larson et al, PRC9 699 (1974)
e.g., Matsuyama, PLB152 42 (1985); Matsuyama Lee, PRC34 1900 (1986)
Z as a function of kat k’=0.3 GeV, E=1.88 GeVZ as a function of kat k’=0.3 GeV, E=1.88 GeV
Bare N* MB vertex function
e.g.) D13 state ( I = 1/2, J = 3/2, Parity = minus) 18
# of parameters for a bare N* state
# of bare N* stateS11 2, S31 1P11 2, P13 1, P31 1, P33 2D13 1, D15 1, D33 1, D35 0F15 1, F17 0, F35 1, F37 1 total 16 bare N* state (as of today)
# of bare N* stateS11 2, S31 1P11 2, P13 1, P31 1, P33 2D13 1, D15 1, D33 1, D35 0F15 1, F17 0, F35 1, F37 1 total 16 bare N* state (as of today)
17
×
9
Use same cutoff
Meson-exchange amplitude:
Dressed N* propagating amplitude:
EBAC-DCC model: electromagnetic partFor details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
= hadronic process
gamma N MB potentials
7 diagramss-ch Nu-ch Nu-ch t-ch t-ch t-ch contact
2 diagramss-ch Nu-ch N
2 diagramss-ch Nu-ch N
4 diagramss-ch Nu-ch Nt-ch contact
Total 32 diagrams
5 diagramss-ch Nu-ch Nu-ch t-ch contact
6 diagramss-ch Nu-ch u-ch t-ch Kt-ch K*contact
6 diagramss-ch Nu-ch u-ch t-ch Kt-ch K*contact
gamma N MB potentialsAll potentials are described in Matsuyama, Sato, Lee, Phys. Rep. 439 193 (2007)
gamma N MB potentials
helicity-JLS mixed representation(angular projection of N part is not needed for our purpose)
gamma N N* bare vertex function
Bare N* helicity amplitude:
for transverse photon
for longitudinal photon
where
Parameterizations of bare helicity amplitudes
Introduce appropriate threshold behavior + dipole form factorIntroduce appropriate threshold behavior + dipole form factor
Plan for EBAC-DCC analysis in 2010
Full combined analysis (global fit) of:
N N (W < 2 GeV)
N N (W < 2 GeV)
N N (W < 1.6 GeV 2 GeV)
N N (W < 2 GeV)
N KY (W < 2 GeV)
N N (W < 2 GeV)
N N (W < 1.5 GeV 2 GeV)
EBAC second generation modelEBAC second generation model
~ End of 2010
2010 ~ 2011
pi- p K0 Lambda
Julia-Diaz, Saghai, Lee, Tabakin PRC73 055204
PreliminaryPreliminary
EBAC-DCC
gamma p K Lambda
PreliminaryPreliminary
gamma p K Lambda
PreliminaryPreliminary
Coupling effect of KY channels on piN PWA
PreliminaryPreliminary
Add KY channels5ch calc.SAID-EDS
P11 Re
P11 Im P13 Im
D13 Im
D15 Im F15 Im
F17 Im
S11 Re
P13 Re
D13 Re
F15 Re
F17 Re
S11 Im
D15 Re
Coupling effect of piN, pipiN, etaN channels on KY observables
Meson-exchange amplitudesMeson-exchange amplitudes
Amplitude with Dressed N*Amplitude with Dressed N*
Coupling effect of piN, pipiN, etaN channels on KY observables
Couplings to N, N, N channels off
Current EBAC-DCC result
PreliminaryPreliminary
(At least) about 20% reduction except backward angles is observed.(At least) about 20% reduction except backward angles is observed.
Back upBack up
pi N pi N PWAs
PreliminaryPreliminary
Add KY channels5ch calc.SAID-EDS
P11 Re
P11 Im P13 Im
D13 Im
D15 Im F15 Im
F17 Im
S11 Re
P13 Re
D13 Re
F15 Re
F17 Re
S11 Im
D15 Re
gamma p K LambdaKamano, Nakamura, Lee, Sato in preparation
Effect of N channels on p KEffect of N channels on p K
Couplings to N (D,N,N) channels are turned off
Current EBAC-DCC result
PreliminaryPreliminary
pi N pi N @ W=1232 MeV
V
Re(T)
Im(T)
EBAC
Juelich
Output is T,
not
pi N pi N @ W=1600 MeV
V
Re(T)
Im(T)
EBAC
Juelich
pi N pi @ W=1232 MeV
V
Re(T)
Im(T)
pi N pi @ W=1600 MeV
V
Re(T)
Im(T)
Meson-exchange amplitude:
Dressed N* amplitude:
EBAC-DCC model: hadronic partFor details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Parameters
29 + 247 (15 bare N*) = 271
nonresonantpotentialnonresonantpotential
N* parametersN* parameters
Hadronic part:
Electromagnetic part:
N* barehelicity amps.N* barehelicity amps.
2 + 39 (15 bare N*) = 41
& couplings & couplings
(roughly 20 parameters for each partial wave)
(roughly 3 parameters for each partial wave)
Pion-nucleon elastic scatteringJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
coupled-
channels is considered.
Fitted to the SAID N partial wave amplitudes up to 2GeV.
MINUIT library is employed for the numerical minimization.
Unitarity is satisfied in ~ 1 % !!Unitarity is satisfied in ~ 1 % !!
Re(T) with I = 1/2