K-d原子の理論計算の現状と今後の課題Shota Ohnishi

(Tokyo Inst. Tech. / RIKEN)in collaboration with

Yoichi Ikeda (RIKEN)Tetsuo Hyodo (YITP, Kyoto Univ. )

Emiko Hiyama (RIKEN)Wolfram Weise (ECT*)

2013/8/5 1

KbarN interaction

K-p cross section: above KbarN threshold energy (w/ large error)

Branching ratio kaonic atom

L(1405) : below KbarN threshold energy (one pole or two pole <-> L(1405) or L(1420))

Experimental data used to determine model parameters

: at/just below KbarN threshold energy

2013/8/5 2

Energy dependence of KbarN interaction

WT LagrangianDerivative coupling E-dependent E-independent

Ikeda, Sato, PRC76, 035203(2007); Ikeda, Kamano, Sato, PTP124, 533(2010)

2013/8/5 3

Signature of the KbarNN resonance

E-dep.

Ohnishi, Ikeda, Kamano, Sato arXiv:1302.2301[nucl-th]

Significant difference on production spectracan be used to obtain KbarN interaction information

E-indep.

to appear in PRC

2013/8/5 4

Kaonic hydrogenCoulomb

0-8.6keV

Only Coulomb Coulomb + strong int.

1s

L(1405)

1s kaonic hydrogen

Improved Deser formula

Important constraint on K-p scattering length from the energy shift and width

Meissner, Raha, Rusetsky, Eur. Phys. J. C41 (2005) 213.

2013/8/5 5

Kaonic hydrogenSIDDHARTA Collaboration Phys. Lett. B 704 (2011) 113.

SIDDHARTA measurement of the energy shift and width of the 1s state :

Improved Deser formula

Ikeda, Hyodo, Weise Nucl. Phys. A 881 (2012) 98.2013/8/5 6

Kaonic deuterium

K-p and K-d scattering lengths scattering lengths in I=0 and I=1 channels

2013/8/5 7

Deser formulaK--nuclear optical potential of the tr form :

neglect finite size effects

2013/8/5 8

Importance of multiple scattering• large cancelation of impulse approx. does NOT work• strong charge exchange interaction

between and worse convergence of scattering series

Impulse approx. Double scattering

+

+ …

2013/8/5 9

Rusetsky formulaimpulse approximation

double scattering

Rusetsky formula (all orders of the multiple scattering)

daK-d : three-body LECs neglect2013/8/5 10

Improved Deser formulaimproved Deser formula

Coulomb correction

QED relativistic correction necessary

electronic vacuum polarization is amplified by powers of

2013/8/5 11

full optical potential

Here, multiple scattering, NN-pair correlations, finite nuclear size effect and so on are taken into account except for deuteron excitations.

2013/8/5 12

Uehling potentialFor kaonic atom, electron vacuum polarization effect is so large, that if we try to solve Schrödinger equation for K-pn three-body system to study deuteron excitations effect, we also need to consider about correction of Coulomb force.

for non-relativistic limit

2013/8/5 13

modification of Coulomb potential

• As a first step to study K-d atom,– K-p atom

Deser formula

imp. Deser formula

2013/8/5 14

K-p interaction• We employ the Gaussian local potential based on chiral

effective field theory

Parameters are fitted to reproduce the amplitude of Ikeda, Hyodo, Weise Nucl. Phys. A 881 (2012) 98.

2013/8/5 15

We study the 1s energy shift by solving the Schrodinger equation with only Coulomb potential and with Coulomb and strong interaction using the variational method.

We obtain the value between Deser formula and improved Deser formula.

2013/8/5 16

electron vacuum polarization

Coulomb vs Coulomb + strong -> Coulomb + Uehling vs Coulomb + Uehling + strong

2013/8/5 17

Future work• How to handle the effect of electron vacuum polarization

effect.– Lamb shift, K-d

• Three-body caluculation of the K-pn• Faddeev calculation of AK-d

Summary• Deser formula and improved Deser formula– Effect of electron vacuum polarization

• K-p– Uehling potential

2013/8/5 18