Semi-relativistic study of K pp with a fully coupled ... · Y. Suzuki and K. Varga, “Stochastic...
Transcript of Semi-relativistic study of K pp with a fully coupled ... · Y. Suzuki and K. Varga, “Stochastic...
Semi-relativistic study of K-pp with a fully
coupled-channel complex scaling method
1. Introduction (Motivation)
2. Formalism
• Semi-relativistic treatment
• Chiral SU(3)-based potential
3. Result• Check: Complex eigenvalue distribution in Semi-rela. case
• Result w/ Martin constraint
• Result w/ SIDDHARTA constraint
4. A concern ...
5. Summary and future plan
Akinobu Doté (KEK Theory Center, IPNS / J-PARC branch)
Takashi Inoue (Nihon university)
Takayuki Myo (Osaka Institute of Technology)
ELPH 研究会 C023
「原子核中におけるハドロンの性質とカイラル対称性の役割」,
11. Sept. ’18
@ Research center for
ELectron Photon science (ELPH),
Tohoku University of Science, Sendai, Japan
1. Introduction
Why semi-relativistic?→ Of course, pion is light.
It should be treated in a relativistic way.
In addition, ...
P PK-
“K-pp” = KbarNN – πΣN – πΛN
K-
Proton
Excited hyperon Λ(1405) ... KbarN quasi-bound state
= KbarN two-body system
Kaonic nuclei = Nuclear many-body system
with antikaons
P PK-
K- pp = the simplest kaonic nucleus
... bridge from Λ(1405) to general kaonic nuclei
Doorway to dense matter?→ Chiral symmetry restoration in dense matter??
→ Strong KbarN attractionT. Hyodo, D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012)
Experimental search for K-pp• Deeply bound region (near πΣN threshold = 103 MeV below KbarNN threshold)
FINUDA (2005), DISTO (2010), J-PARC E27 (2013)
• Shallowly bound region (near KbarNN threshold)
J-PARC E15 1st run (2013)
• No signal in bound region
LEPS/SPring8 (2015) and more ...
Clear evidence of K-pp bound state
J-PARC E15 (2nd run):
Exclusive exp. 3He(K-, Λp)nmissing
⇒ “Fully coupled-channel
Complex Scaling Method”A. Dote, T. Inoue, T. Myo, PRC 95, 062201(R) (2017)
According to early theoretical studies of “K-pp” ...
Resonant state of
KbarNN-πΣN-πΛN coupled channel
three-body system
“K-pp” (Jπ=0-, T=1/2) • Doté, Hyodo, Weise, PRC79, 014003(2009).
• Akaishi, Yamazaki, PRC76, 045201(2007)
• Ikeda, Sato, PRC76, 035203(2007).
• Shevchenko, Gal, Mares, PRC76, 044004(2007)
• Barnea, Gal, Liverts, PLB712, 132(2012)
→ Summarized in
A. Gal, E. V. Hungerford, D. J. Millener,
Rev. Mod. Phys. 88, 035004 (2016).
Resonance & Channel coupling
Results of “K-pp”
J-PARC E15-1st
J-PARC E27
DISTO
FINUDA
Faddeev-AGS
Pheno. pot. (E-indep.)
Variational (Gauss)
Pheno. pot. (E-indep.)
Variational (Gauss)
Chial. pot. (E-dep.)
Faddeev-AGS
Chiral pot. (E-dep.)
K-pp binding energy BK-pp [MeV]KbarNN threshold πΣN threshold
SGM
AYDHW
BGL
IKS
Full ccCSM
w/ Chiral SU(3) pot. (SIDDHARTA)PLB 704, 405 (2018)
J-PARC E15 2nd
arXiv: 1805.12275 FINUDA
DISTO
J-PARC E27
Results of “K-pp”
Full ccCSM
w/ AY pot. (Coupled)PRC 95, 062201(R) (2017)
SGM
AYDHW
BGL
IKS
Full ccCSM
w/ Chiral SU(3) pot. (SIDDHARTA)PLB 704, 405 (2018)
J-PARC E15 2nd
arXiv: 1805.12275 FINUDA
DISTO
J-PARC E27
Results of “K-pp”
Full ccCSM
w/ AY pot. (Coupled)PRC 95, 062201(R) (2017)
Too small decay width obtained with Full ccCSM???
2. Relativistic effect??
... Phase volume for decay is underestimated
in non-relativistic kinematics.
Suggested by Prof. S. Shinmura
1. Contribution of non-mesonic decay (ΓNM)?
• Width calculated in theory = Mesonic decay width (ΓM)
• Width measured in exp’t = Total decay width (ΓM+ ΓNM)
2. Formalism
• Semi-relativistic treatment
• Chiral SU(3)-based KbarN potential
Summary of methodology
Employ Chiral SU(3)-based KbarN potential
in relativistic kinematicsNo non-rela. approximation
A. Dote, T. Inoue, T. Myo,
NPA 912, 66 (2013)
Use Semi-Relativistic Hamiltonian
... Kinetic energy is given in relativistic form.
3
1
22
NN MB
i
iiH Vm V
p1 2 3 p p p 0 (CM sys.)
Y. Suzuki and K. Varga, “Stochastic Variational
Approach to Quantum-Mechanical Few-Body
Problems” (Springer, Berlin, 1998).
, where
Investigate “K-pp” with Full ccCSM as our previous studies
• “K-pp” = KbarNN-πΣN-πΛN (Jπ=0-, T=1/2)
• Search for resonance pole on complex-energy plane
• Correlated Gaussian basis function
• Self-consistent calculation for energy-dependent potential
A. Dote, T. Inoue, T. Myo,
PRC 95, 062201(R) (2017);
PLB 704, 405 (2018)
Complex Scaling Method… Powerful tool for resonance study of many-body system
S. Aoyama, T. Myo, K. Kato, K. Ikeda, PTP116, 1 (2006)
T. Myo, Y. Kikuchi, H. Masui, K. Kato, PPNP79, 1 (2014)
!!! Caution !!!
This is Non-rela. case.
Chiral SU(3)-based KbarN potential
Coupled-channel chiral dynamics
(Chiral Unitary model)N. Kaiser, P.B. Siegel, W. Weise, NPA 594 (1995) 325
E. Oset, A. Ramos, NPA 635 (1998) 99
Weinberg-Tomozawa term
of effective chiral Lagrangian
Based on Chiral SU(3) theory
→ Energy dependence
• Anti-kaon, Pion = Nambu-Goldstone boson
... governed by chiral dynamics
Constrained by KbarN scattering length
• Old data: aKN(I=0) = -1.70 + i0.67 fm, aKN(I=1) = 0.37 + i0.60 fm A. D. Martin, NPB179, 33(1979)
• SIDDHARTA K-p data with a coupled-channel chiral dynamics:
aK-p = -0.70 + i0.89 fm, aK-n = 0.57 + i0.72 fm M. Bazzi et al., NPA 881, 88 (2012)
Y. Ikeda, T. Hyodo, W. Weise, NPA 881, 98 (2012)
( 0,1)
( 0,1)
28
I
ij i jI
ij ijji
i j
C M MV r g r
f s
3
2
/ 2 3ex
1p
ijij
ij
g rd
r d
Potential in relativistic kinematics
: Gaussian form
ωi: meson energy
A. Dote, T. Inoue, T. Myo, NPA 912, 66 (2013)
Chiral SU(3)-based KbarN potential
Two types of the potentials...
Λ* resonance pole
Broad Narrow
Martin constraint
fπ=110 MeV
A. Dote, T. Inoue, T. Myo, NPA 912, 66 (2013)
3. Result
• Check: Complex eigenvalue distribution
in Semi-rela. case
• Result w/ Martin constraint
• Result w/ SIDDHARTA constraint
Check: Complex eigenvalue distribution in Semi-rela. case
22 2
22
2
i ii i
i
i
i
pp e m m
e
m
In low energy region, eigenvalues of three-body continuum
states are on 2θ lines, similarly to Non-rela. case.
πΛN πΣN KbarNNComplex energy plane
(Units are MeV.)
Case:
• SIDDHARTA / Field
• fπ=110 MeV
• θ=24°, 6400 dim.
“K-pp” “Λ*”
Check: Complex eigenvalue distribution in Semi-rela. case
In high energy region, eigenvalues of three-body continuum
states are on 1θ lines, differently from Non-rela. case.
Complex energy plane
(Units are MeV.)
Case:
• SIDDHARTA / Field
• fπ=110 MeV
• θ=24°, 6400 dim.
πΛN
2 2 2 2 2 2i i
i i i
i
ip m p e p ee
Start at –(mπ+MΛ+MN),
since the origin is taken
to be the πΛN threshold.
Result w/ Martin constraint
• Field
• Particle
-62.6 - i16.8
-50.5 - i22.2
-20.4 - i11.3
-21.7 - i11.7
“K-pp”- BK-pp - i Γ/2 [MeV]
SR-A SR-B
Λ* 1419.5 - i 25.0 1420.0 - i 12.7
M - i Γ/2 [MeV]
( fπ=110 )
An interacting MB pair carries
100% of B(M) = “Field picture”
50% of B(M) = “Particle picture”
* B(M) ... “Meson’s binding energy”
NN potential = Av18 potential (R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, PRC 51, 38 (1995))
Result w/ Martin constraint
• Field
• Particle
-62.6 - i16.8
-50.5 - i22.2
-20.4 - i11.3
-21.7 - i11.7
“K-pp”- BK-pp - i Γ/2 [MeV]
SR-A SR-B
Λ* 1419.5 - i 25.0 1420.0 - i 12.7
M - i Γ/2 [MeV]
( fπ=110 )
SR-A: Large binding energy as well as large decay width
Very attractive in bound region!
Result w/ Martin constraint
• fπ and ansatz dependence
SR-A SR-B
fπ=100
120
120
100fπ=90
120X
• No self-consistent solution at fπ=100 MeV
• Large binding energy and decay width
• Strongly depends on fπ and ansatz
• Small binding energy and decay width
• Small fπ dependence
• Similar solutions obtained by both ansatzes
(BK-pp, Γ/2)
• Field: (55,17) ~ (63,17)
• Particle: (43,20) ~ (62,26)
(BK-pp, Γ/2)
• Field: (19,10) ~ (28,16)
• Particle: (21,11) ~ (29,16)
Result w/ SIDDHARTA constraint
a(I=0) [fm] -1.974 + i1.058
a(I=1) [fm] 0.570 + i0.731
KbarN scat. leng. SIDDHARTA+IHW
-1.97 + i1.05
0.57 + i0.73
• Field
• Particle
-46.4 - i 23.9
-33.8 - i 23.7
1.62 - i0.19
1.66 - i0.06
“K-pp”- BK-pp - i Γ/2 [MeV] RNN [fm]
fπ=110 MeV
Λ*1429.1 - i 16.2
M - i Γ/2 [MeV]
SR-A ( fπ=110 MeV)
Result w/ SIDDHARTA constraint
• fπ and ansatz dependence
fπ=100
120120
100SR-A
Binding energy (BKpp)
and half decay width (ΓπYN/2)
• Field picture
BKpp = 39 ~ 59 MeV
ΓπYN/2 = 21 ~ 26 MeV
• Particle picture
BKpp = 29 ~ 41 MeV
ΓπYN/2 = 19 ~ 33 MeVNN potential = Av18 potential
Result w/ SIDDHARTA constraint
• Comparison with Martin case
SR-A
• Weaker binding (10~20 MeV)
• Larger decay width
... as expected from the scattering length
Matin case
• Comparison with Non-rela. case
Non-rela.
A. Dote, T. Inoue, T. Myo,
PLB 704, 405 (2018)
• Larger decay width, as expected
• Larger binding energy
4. A concern ...
Consistency between
NN potential and kinematics?
Av18 NN potential was constructed under non-relativistic kinematics.
Can it be used in semi-rela. kinematics? (By Shinmura, Harada, Akaishi)
← NN kinematics might not give an influence to the result,
because nucleon mass is much larger, compared with its momentum. (Dote)
NN phase shift(1E)
Av18 potential
Phase shift calculated in SR is slightly more attractive
than that calculated in NR.
A test calculation:
Baryons are again treated non-relativisitcally.
• Meson ... Semi-relativistic kinematics• Baryon ... Non-relativistic kinematics
22
( )
( )
1 ( )
22
2
Baryon i
Baryon i
i Bary
NN MBMesonMe
o
so
i
n
n
H m V Vmm
p
p
NN kinematics modifies the result more than my expectation...
Result
• Binding energy decreases
by 5~16 MeV.
• Decay width increases.
• Case: SIDDHARTA/ Field picture
SR+NR SRfπ -B.E. (K-pp) -Γ /2 -B.E. (K-pp) -Γ /2
100 -52.3 -32.8 -58.5 -25.8
110 -30.2 -29.3 -46.4 -23.9120 -23.4 -22.3 -39.4 -21.4
5. Summary
and Future plan
Future plan• NN potential for semi-relativistic kinematics
• More conditions to constrain the KbarN potential
• Non-mesonic decay mode (KbarNN→YN)
• Spectrum calculation using Green function method in ccCSM
Focusing on the decay width of K-pp, we examine the semi-relativistic kinematics (SR)
in a fully coupled-channel complex scaling method.
It is confirmed that the decay width of K-pp can be larger in SR kinematics
than in non-relativistic kinematics (NR). (ΓπYN/2 is less than 20 MeV in NR.)
However, there is a concern on consistency between NN potential and kinematics.
Since Av18 NN potential is constructed under the NR kinematics, it might be inconsistent
to use it in SR kinematics ...
SIDDHARTA constraint case,
• (BK-pp, ΓπYN/2) = (39,21) ~ (59,26) w/ Field picture
• (BK-pp, ΓπYN/2) = (29,19) ~ (41,33) w/ Particle picture
* Av18 potential is used as a realistic NN potential.
Summary
In addition, it is found that in SR kinematics K-pp could be deeply bound with
a chiral SU(3)-based KbarN potential, although it is obtained to be shallowly bound
in NR kinematics. (BK-pp is up to 40 MeV with Field picture in NR.)
References:
• A. Dote, T. Inoue, T. Myo, PLB 784, 405 (2018)• A. Dote, T. Inoue, T. Myo, PRC 95, 062201(R) (2017)
Thank you very much!