Universal physics of two neutrons with one flavored meson

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1 Uiversal physics of two eutros with oe flavored meso U. Raha a, Y. Kamiya b, S.-I. Ado c, T. Hyodo b a IIT Guwahati, Idia, b YITP, Kyoto Uiv. c Sumoo Uiv., Korea 2017, Mar 13th 1

2 Cotets Cotets Itroductio - Mesos i few-body uclei - Uiversal physics i few-body system Two-body meso-eutro iteractio - Experimetal costraits - Idealizatio Three-body system K - - Effective field theory - RG limit cycle i the asymptotic regio Summary 2

3 Itroductio K (su, sd ) uclei Mesos i uclei Y. Akaishi, T. Yamazaki, Phys. Rev. C 65, (2002), - attractio i K (I=0): Λ(1405) - quasiboud states up to 7-body systems K S. Ohishi, W. Horiuchi, T. Hoshio, K. Miyahara, T. Hyodo, arxiv: [ucl-th] D (cu, cd ) uclei A. Hosaka, T. Hyodo, K. Sudoh, Y. Yamaguchi, S. Yasui, arxiv: [hep-ph] - hadroic molecules i XYZ > D ca be a costituet - Λc(2595) ~ D(I=0) molecule? as Λ(1405) T. Mizutai, A. Ramos, Phys. Rev. C 74, (2006) - D quasiboud state D M. Bayar, C.W. Xiao, T. Hyodo, A. Dote, M. Oka, E. Oset, Phys. Rev. C86, (2012) 3

Itroductio Study of few-body systems Properties of few-body systems < > two-body iteractio - c.f. hyperuclei Λ Λ I some cases, differet iteractios give the same physics.

4 Itroductio Study of few-body systems Properties of few-body systems < > two-body iteractio - c.f. hyperuclei Λ Λ I some cases, differet iteractios give the same physics. same! uiversal physics Λ 4

5 Itroductio Two-body uiversal physics Uiversal two-body physics E. Braate, H.-W. Hammer, Phys. Rept. 428, 259 (2006) 1) s-wave short rage iteractio 2) scatterig legth : a rs : iteractio rage - system is scale ivariat - a shallow boud state exists if a > 0 B 2 = 1 h rs i ma 2 1+O a Examples: ucleos ad 4 He atoms [MeV] B /ma He [mk] strog vdw 4 He 5

6 Itroductio Three-body uiversal physics Three-body system i hyperspherical coordiates (r 12, r 3,12 ) $ (R, 3, ˆr 12, ˆr 3,12 ) hyperradius hyperagular variables Ω (dimesioless) 2 r 12 1 r 3,12 3 If a >, system is scale ivariat. V (R, ) / 1 R 2 E 1/2 -~1 ~ Efimov effect: attractive 1/R 2 V. Efimov, Phys. Lett. B 33, (1970) g<g. g>g, 1/a B 3 /B ifiitely may boud states - discrete scale ivariace: RG limit cycle P.F. Bedaque, H.-W. Hammer, U. va Kolck, Phys. Rev. Lett. 82, (1999) 6

7 Itroductio Uiversal physics of three pios Uiversal physics < large scatterig legth a T. Hyodo, T. Hatsuda, Y. ishida, Phys. Rev. C89, (R) (2014) π π π - I=0 ππ scatterig legth ca be icreased by chagig mq isospi sym. (π 0 π 0 π 0 -π 0 π - π + ) isospi breakig (π 0 π 0 π 0 ) E Three-body boud states! 1/a -B 2 -B 3 E' /a' -B 2 -B 3 - Efimov effect of π 0 π 0 π uphysical mq - Coupled-chael effect reduces the attractio. 7

8 Itroductio Two eutros ad oe flavored meso K - /D 0 system with J=0, I=3/2, I3=-3/2 - differet from J=0, I=1/2 (so-called K - pp-k 0 p) - all iteractios: isospi I=1 (o Λ(1405)) Desirable features for Efimov effect - o coupled chaels - o Coulomb iteractio - a ~ -20 fm rs ~ O(1) fm I=1 I=1 I=1 K - Two-body K - : uitary? > yes, with suitable idealizatio. Three-body K - : Efimov? > yes, if two-body K - is uitary. 8

9 Two-body meso-eutro iteractio Kao-eutro iteractio Experimetal database i K sector - cross sectios of K - p scatterig (elastic, ielastic) - threshold brachig ratios - kaoic hydroge by SIDDHARTA > ak-p M. Bazzi, et al., Phys. Lett. B704, 113 (2011); ucl. Phys. A881, 88 (2012), U.G. Meisser, U. Raha, A. Rusetsuky, Eur. Phys. J. C35, 349 (2004). Aalysis i LO chiral SU(3) dyamics Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B (2012); ucl. Phys. A881, 98 (2012) - data fitted as χ 2 /d.o.f. ~ 1 a 0,K = i fm Re f(k! K ) [fm] TW TWB LO Im f(k! K ) [fm] TW TWB LO p s [MeV] p s [MeV] K - p scatterig legth is attractive (o quasi-boud state). 9

10 Two-body meso-eutro iteractio D-eutro iteractio o experimetal iformatio of scatterig legth - SU(4) cotact iteractio model (Λc(2595) fixed) T. Mizutai, A. Ramos, Phys. Rev. C 74, (2006), M. Bayar, C.W. Xiao, T. Hyodo, A. Dote, M. Oka, E. Oset, Phys. Rev. C86, (2012) πσc t (I) [MeV -1 ] I=1 Re t Im t 2700 W [MeV] 2800 (b) a I=1 resoace aroud 2760 MeV D - Σc(2800) as a quasi-boud state (D threshold ~ 2804 MeV) C. Patrigai et al., (Particle Data Group) Chi. Phys. C40, (2016) M 0 c (2800) = MeV, 0 c (2800) = MeV D 0 scatterig legth is repulsive (with quasi-boud state). 10

11 Two-body meso-eutro iteractio Idealizatio Whe decay chaels (πσ-πλ, πσc-πλc) are eglected: - ak- < 0 (attractive), ad0 > 0 (repulsive, with boud state) Extrapolatio i quark mass strage, uboud charm, boud V P (r) r a > uitary limit Uitary limit: eglectig decay chaels ad tuig ms/c 11

12 Two-body meso-eutro iteractio Model for K /D scatterig Cotact iteractio model T. Mizutai, A. Ramos, Phys. Rev. C 74, (2006), Y. Ikeda, T. Hyodo, W. Weise, Phys. Lett. B (2012); ucl. Phys. A881, 98 (2012) T (W )=[V 1 (W ) G(W )] 1 - four chaels: K - -π - Λ-π 0 Σ - -π - Σ 0, D 0 -π - Λc-π 0 Σc 0 -π - Σc + - V(W): flavor symmetric cotact iteractio V ij (W )= C r ij Mi + E i (2W M i M j ) f i f j 2M i - cutoff i G(W) < Experimets (K ), Σc(2800) (D) Extrapolatio parameter x m(x) =m K (1 x)+m D x, etc. s M j + E j 2M j - x=0 (x=1) correspods to the K (D) scatterig. 12

13 Two-body meso-eutro iteractio Extrapolatio Model extrapolatio - elimiate coupligs to decay chaels C 1i = C i1 =0 fori =2, 3, 4 - vary extrapolatio parameter x to calculate 1/aK- 1/a 0 [fm -1 ] ak- < 0 (attractive) x [dimesioless] ad0 > 0 (repulsive, with boud state) Uitary limit at mk = 1337 MeV (x=0.62) 13

14 Three-body system Effective field theory Effective field theory with dihadro fields P.F. Bedaque, H.-W. Hammer, U. va Kolck, Phys. Rev. Lett. 82, (1999) S.-I. Ado, U. Raha, Y. Oh, Phys. Rev. C 92, (2015) L = L + L K + L s() + L d(k) + L 3-body - hadro fields K - dihadro fields s () d (K) - iteractios Reormalizatio i two-body sector (dressig s(), d(k)) - system is determied by mk, M, as(), ad(k). 14

15 Three-body system Three-body equatio Three-body equatio for K - system - coupled itegral equatios (quasi two-body) - dressed dihadro propagators d (K) a d (K) = + a + b d (K) b s () K = + a If Efimov effect occurs, we eed three body cotact term. 15

16 Three-body system Asymptotic expressios a > limit: check whether Efimov effect occurs - trascedetal equatio for three idetical bosos P.F. Bedaque, H.-W. Hammer, U. va Kolck, Phys. Rev. Lett. 82, (1999) 1= 8 p 3s si( s/6) cos( s/2) ) s = ±is 0, s 0 = imagiary s: RG limit cycle with factor exp[π/s0] ~ 22.7 For K - /D 0 system at x=0.62: - as() > ad ad(k) > 1=C 1 2 s si[s arcsi(a/2)] cos( s/2) + C s 2 - as() fixed ad ad(k) > si 2 p [s arccot( 4b 1)] cos 2 ( s/2) ) s 0 = =C 1 2 s si[s arcsi(a/2)] cos( s/2) ) s 0 = RG limit cycle i the asymptotic expressios: Efimov effect 16

17 Summary Summary Uiversal physics of the K - /D 0 system. Two-body sector: meso-eutro scatterig legth ca be ifiitely large with suitable idealizatio (tue mq, eglect decay chaels). Three-body sector: Efimov effect occurs whe two-body iteractio is uitary. Implicatio at physical poit: three-body resoace? K - U. Raha, Y. Kamiya, S.-I. Ado, T. Hyodo, i preparatio 17

Construction of K N potential and structure of Λ(1405) based on chiral unitary approach

Construction of K N potential and structure of Λ(1405) based on chiral unitary approach Kenta Miyahara Kyoto Univ. Tetsuo Hyodo YITP NSTAR 2015, May Contents 1. Motivation 2. Previous work (construction