Kd Shota Ohnishi Tokyo Inst Tech RIKEN in

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

Kbar. N interaction Experimental data used to determine model parameters K-p cross section: above Kbar. N threshold energy (w/ large error) Branching ratio bar. N threshold energy : at/just below K kaonic atom L(1405) 2013/8/5 : below Kbar. N threshold energy (one pole or two pole <-> L(1405) or L(1420)) 2

Energy dependence of Kbar. N interaction Ikeda, Sato, PRC 76, 035203(2007); Ikeda, Kamano, Sato, PTP 124, 533(2010) WT Lagrangian Derivative coupling E-dependent 2013/8/5 E-independent 3

Signature of the Kbar. NN resonance Ohnishi, Ikeda, Kamano, Sato ar. Xiv: 1302. 2301[nucl-th] to appear in PRC E-dep. E-indep. Significant difference on production spectra bar. N interaction information can be used to obtain K 2013/8/5 4

Kaonic hydrogen Only Coulomb + strong int. 1 s 1 s -8. 6 ke. V kaonic hydrogen L(1405) Improved Deser formula Meissner, Raha, Rusetsky, Eur. Phys. J. C 41 (2005) 213. Important constraint on K-p scattering length from the energy shift and width 2013/8/5 5

Kaonic hydrogen SIDDHARTA Collaboration Phys. Lett. B 704 (2011) 113. SIDDHARTA measurement of the energy shift and width of the 1 s state : Improved Deser formula 2013/8/5 Ikeda, Hyodo, Weise Nucl. Phys. A 881 (2012) 98. 6

Kaonic deuterium K-p and K-d scattering lengths in I=0 and I=1 channels 2013/8/5 7

Deser formula K--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 formula impulse approximation double scattering Rusetsky formula (all orders of the multiple scattering) da. K-d : three-body LECs neglect 2013/8/5 10

Improved Deser formula improved Deser formula Coulomb correction electronic vacuum polarization is amplified by powers of QED relativistic correction necessary 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 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 2013/8/5 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 1 s 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

Summary • Deser formula and improved Deser formula – Effect of electron vacuum polarization • K -p – Uehling potential 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 2013/8/5 18