Download - L(1405) の光発生反応
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(1405)L の光発生反応
中村 聡 (阪大理)
共同研究者: 慈道 大介 ( 首都大)
Prog. Theor. Exp. Phys. (2014) 023D01
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Introduction(1405) : L 1st excited state of L
EpS K N
_
1330 1430
(MeV)
(1405, -25)(1405) L
* Existence “predicted” by Dalitz and Tuan (1960)
in analysis of KN scattering length with - KN pS model
* First experimental evidence in K -p pppS (1961)
_ _
Alston et al., PRL 6 (1961)
K -p pppS
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Controversial (1405) L structure
• 3-quark + mass splitting term Collins & Georgi, PRD 59 (1999) Schat et al., PRL 88 (2002)
• 5-quark Strottman, PRD 20 (1979) Zou, NPA 835 (2010) too many states
• Meson-baryon molecule Dalitz & Tuan, PRL 2 (1959) Oset & Ramos, NPA 635 (1998)
Too light to interpret as naïve 3-quark state
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(i,j,k : meson-baryon channel)
(1405) L as pole of Scattering amplitude
Coupled-channel scattering equation for T-matrix (scattering amplitude)
Near pole position :
T-matrix for real energy W is used to calculate observables (cross sections, etc.)
Analytic continuation to complex energy W
Resonance is identified by : mass width
Resonance pole can be extracted from analyzing data
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Why want to know (1405) L pole(s) ?
• Internal structure of (1405)L
constraint on hadron structure models
• Nuclear structure of deeply bound kaonic nuclei (e.g., K-pp )
K-p - pS amplitude is essential input
current status for K-pp : rather large model dependence
B.E. = 10 – 100 MeV, Width = 35 – 110 MeV
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Pole structure of (1405)L
• Two-pole
cloudy bag model Veit et al. PRD 31, 1033 (1985)
chiral unitary model Jido et al. NPA 725, 181 (2002)
• Single-pole
potential models Fink et al., PRC 41, 2720 (1990)
Akaishi-Yamazaki model PRC 65, 044005 (2002)
Still, pole structure has not been established
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Attempt to determine (1405) L pole from data
EpS K N
_
1330 1430(MeV)
(1405, -25)(1405) L
Ideal experiment p S p S Impossible !
N
K+
S
p
, g p
} Energy at (1405) L
Two-meson production experiment
difficulty in determining (1405) L pole structure
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How to extract (1405)L pole from two-meson production data
• Construct a model that consists of production mechanism + final state interaction (FSI)
• FSI contains MB p S amplitude
• Fit data with adjustable parameters in production mechanism and MB p S amplitude
• Extract poles from MB p S amplitude
But, good data had not been available until recently
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Photo-production of (1405)L
• LEPS/Spring-8 Ahn et al., NPA 721, 715 (2003)
• LEPS/Spring-8 Niiyama et al., PRC 78, 035202 (2008)
• CLAS/JLab Moriya et al., PRC 87, 035206 (2013) ( p S invariant mass distribution) PRC 88, 045201 (2013) (K+ angular distribution)
g p K+ L(1405) K+ p S
Experiments
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p S line-shape data from CLAS/JLab g p K+ L(1405) K+ p S
Moriya et al., PRC 87, 035206 (2013)
Cleanest data for L(1405) progress toward pole extraction
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What to do here ?
• Production mechanism + s-wave rescattering
• Gauge invariance at tree level
• Fit data
Develop cUM-based model for g p K+ p S
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MODEL
• Chiral unitary model
• Photo-production mechanism
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Chiral Unitary Model (cUM)
: Weinberg-Tomozawa interaction
Coupled-channel scattering equationOset & Ramos, NPA (1998)Oset et al., PLB (2002)
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Chiral Unitary Model (cUM)
On-shell factorization
(m : renormalization scale )
(W : total energy)
Dimensional regularization
_
Subtraction constant, fitted to data
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Chiral Unitary Model (cUM)
Good description of K-p K N, pS, pL data above and near K-p threshold_
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Chiral Unitary Model (cUM)
pole position 1390 - 66i 1426 - 16i
pS 2.9 1.5
KN 2.1 2.7-Coupling strength
Jido et al. NPA 725, 181 (2002)Two-pole structure
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Photo-production Model
Minimal substitution
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Photo-production Model
Minimal substitution
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Photo-production Model
Minimal substitution
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Photo-production Model
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Photo-production Model
Rescattering
cUM s-wave amplitude ( (1405) )L
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Fit data• Subtraction constants (10 parameters)
• contact production mechanism (30 parameters) (total energy (W) dependent complex couplings, gauge invariant)
• Form factors (1 parameters)
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* Good description of line-shape data
* Different peak position for different charge states
Two-pole structure plays a role ??
Results
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Resonant and non-resonant contributions
Non-resonant Resonant
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Resonant and non-resonant contributions
* Significant non-resonant contribution
Shifting peak positions
• Same resonance peak position
2nd pole (1426 – 16i) seems dominant
Single-pole model works as well ??
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Isospin decomposition
• I=0 ( (1405)) L dominance
• Small but nonnegligible effect of I=2 contribution
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Single Breit-Wigner model
Single Breit-Wigner model works !1 pole solution is still not excluded
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K+ angular distribution
Moriya et al, PRC 88, 045201 (2013)
New data from CLAS/JLab
for g p K+ p S
Fitting only lineshape very different angular distributions is still possible
K+ angle data are important to constrain production mechanism
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K+ angular distribution (not fitted)
Overall trend is captured in our model More fit will be done L(1405) pole structure will be extracted
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Summary
• Pole structure of L(1405) has not been well confirmed by data
• New CLAS data for g p K+ p S ; cleanest data in L(1405)
region
hope to extract L(1405) pole structure
• g p K+ p S model is developed with cUM amplitude
-- meson-exchange + contact production mechanism
(gauge invariant @ tree level)
-- Line-shape data are well fitted
-- Single Breit-Wigner model also can fit line-shape data
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Future work• Fit K+ angle data from CLAS
cUM amplitude (subtraction constant) is also varied
extraction of L(1405) pole structure
• Use different contact interactions, form factors
study model dependence of extracted poles
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Future work
One- or two-pole structure ?
Very new data from CLAS (yesterday) for electroproduction of L(1405) PRC 88, 045202 (2013)
1.6 (GeV/c)2 < Q2 < 3.0 (GeV/c)2
Fairly clear two peaks ! two-pole solution ?
Higher statistics data hoped !
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Possible ideas for (1405)L photoproduction experiments at ELPH, LEPS, LEPS2
Data wanted for less model-dependent determination of (1405) L properties
• Double-differential cross sections
• Polarization observable
• Multi-channel data
• K*, S*(1385) unsubtracted data (cf. CLAS data)
gp K+ p S K+ K N K+ p L …
-
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Backups
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• p- p K0 (1405) L K0 p S Thomas et al., NPB 56, 15 (1973)
• K- p p0 (1405) L p0 p0 S0 Crystall Ball, PRC 70, 034605 (2004)
• K- d n (1405) L n p S J-PARC proposal
Attempt to determine pole structure of (1405)L
Hadron beam experiments
Confront theory with data below KN threshold
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cUM-based calculation for p- p K0 p SHyodo et al., PRC 68, 065203 (2003)
…
p-
p
K0
Data: Thomas et al., NPB (1973)
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cUM-based calculation for K- p p0 p0 S0 Magas et al., PRL 95, 052301 (2005)
+
Data: Crystall Ball, PRC (2004) the peak is due to second pole
d /sd
MI (
arbi
trar
y sc
ale)
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K+ angular distribution
Moriya et al, arXiv:1305.6776
Very new data from CLAS/JLab
for g p K+ p S
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LEPS/SPring8 dataForward K+ kinematics of g p K+ Y*
• LEPS and CLAS data are consistent at low energies• No LEPS data for normalized line shape for g p K+ p S
We analyze only CLAS data
Comparison with CLAS data for g p K+ Y*
Niiyama et al., PRC (2008)
• CLAS• LEPS
(Moriya et al, arXiv:1305.6776)
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Lagrangians
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Hidden local symmetry model
fixed by V gM decay width; relative phase by SU(3)
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Tensor coupling
SU(3) relation for magnetic coupling
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Nacher et al., PLB 455, 55 (1999)
Niiyama et al., PRC (2008)Nacher et al., PLB (1999)
Calculated line shape is :
• Wrong in ordering p-S+ and p+S-
• Too small cross section ?
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P-wave scattering model (cUM)
+ (relativistic correction to WT term)
Jido et al., PRC 66, 055203 (2002)
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Is (1405) L exotic ?
Naïve 3-quark picture is not likely
Nucleon (1/2+)
940 MeVN(1535) (1/2- )
1535 MeV
L (1/2+)
1116 MeVL(1405) (1/2- )1405 MeV
Radial excitation to L=1 costs ~ 600 MeV
~ 300 MeV
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cUM-based calculation for g p K+ p S
Nacher et al., PLB 455, 55 (1999)
W=2.02 GeV
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(1405) L in Lattice QCD
Quench 3-quark ~ 1.7 GeV Nemoto et al., PRD (2003)
Quench 5-quark ~ 1.89 GeV Ishii et al., PTP (2007)
Full 3-quark ~ 1.6 GeV Takahashi et al., PRD (2010)
Full 3-quark ~ 1.45 GeV Menadue et al., PRL (2012) (variational analysis)
operator M (1405)L
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cUM-based calculation for g p K+ p S
Nacher et al., PLB 455, 55 (1999)
Contact photo-production (WT term) + s-wave cUM rescattering
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Nacher et al., PLB (1999)W=2.02 GeV
Comparison with CLAS data
K. Moriya et al. PRC (2013)
Calculated line-shape is :• wrong in ordering
p-S+ and p+S-
• Overestimate in magnitude
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Contributions from mechanisms
• Small contribution from WT
interference changed by subtraction const.• Large contribution from contact terms
short-range dynamics play important role