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*) 2013/8/51

K bar N interaction K - p cross section: above K bar N threshold energy (w/ large error) Branching ratio kaonic atom  (1405) : below K bar N threshold energy (one pole or two pole  (1405) or  (1420)) Experimental data used to determine model parameters : at/just below K bar N threshold energy 2013/8/52

Energy dependence of K bar N interaction WT Lagrangian Derivative coupling  E-dependent E-independent Ikeda, Sato, PRC76, (2007); Ikeda, Kamano, Sato, PTP124, 533(2010) 2013/8/53

Signature of the K bar NN resonance E-dep. Ohnishi, Ikeda, Kamano, Sato arXiv: [nucl-th] Significant difference on production spectra can be used to obtain K bar N interaction information E-indep. to appear in PRC 2013/8/54

Kaonic hydrogen Coulomb -8.6keV Only Coulomb Coulomb + strong int. 1s1s  (1405) 1s1s 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) /8/55

Kaonic hydrogen SIDDHARTA 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) /8/56

Kaonic deuterium K - p and K - d scattering lengths  scattering lengths in I=0 and I=1 channels 2013/8/57

Deser formula K - -nuclear optical potential of the t  form : neglect finite size effects 2013/8/58

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 + + … 2013/8/59

Rusetsky formula impulse approximation double scattering Rusetsky formula (all orders of the multiple scattering)  a K-d : three-body LECs neglect 2013/8/510

Improved Deser formula improved Deser formula Coulomb correction QED relativistic correction necessary electronic vacuum polarization is amplified by powers of 2013/8/511

full optical potential Here, multiple scattering, NN-pair correlations, finite nuclear size effect and so on are taken into account except for deuteron excitations. 2013/8/512

Uehling potential For 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 2013/8/513

modification of Coulomb potential As a first step to study K - d atom, – K - p atom Deser formula imp. Deser formula 2013/8/514

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) /8/515

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. 2013/8/516

electron vacuum polarization Coulomb vs Coulomb + strong -> Coulomb + Uehling vs Coulomb + Uehling + strong 2013/8/517

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 A K-d Summary Deser formula and improved Deser formula – Effect of electron vacuum polarization K - p – Uehling potential 2013/8/518