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1 25, Nov. 24th

2 - - T. Hyodo, Int. J. Mod. Phys. A 28, 3345 (23) T. Hyodo, Phys. ev. Lett., 322 (23) Λ(45) Y. Kamiya, T. Hyodo, arxiv:59.46 [hep-ph] K or N 2

3 イントロダクション ハドロンの構造とエキゾチック状態 ハドロンの分類 観測されているハドロン PDG25 JP JP π ω cc π φ π π φ π ω ω π sj ψ cb ub ψ sj χ χ sj /ψ χ χ χ ψ ψ φ π π ω φ π ψ χ χ χ χ χ χ χ バリオン~5種類 メソン~2種類 ~ 35種類全てが単一のQCDラグランジアンから出てくる qqq/qq で記述される量子数のみ 自明ではない 3

4 gions are shown in Figs. (a) and (b), respechere M½ðnSÞŠ max is the maximum invariant the two ðnsþ combinations. This is used to ðnsþ þ and ðnsþ events for visualization o (Belle) horizontal bands are evident in the ð2sþ ear 2:6 GeV2=c 4 and 3:3 GeV 2 =c 4, where rtion Zb(6), from straightzb(65) lines is due to interference with termediate Υ(5S) > states, π + as demonstrated below. Onenal invariant mass projections for events in Zb the 4 (LHCb) Pc(445), Pc(438) 2 Λb > K- + Pc qqq/qq Υ(nS)(bb ) + π (ud /dū) 6 A. Bondar, et al., Phys. ev. Lett. 8, 22 (22) (a) (b) LHCb. Aaij, et al., Phys. ev. Lett. 5, 72 (25) (a) J/ψ(cc ) + p(uud) data total fit background P c (445) P c (438) Λ(45) Λ(52) Λ(6) Λ(67) Λ(69) Λ(8) Λ(8) Λ(82) Λ(83) Λ(89) Λ(2) Λ(2) Events/(5 MeV) (b) LHCb m J/ψp [GeV] FIG. 3 (color online). Fit projections for (a) m Kp and (b) m J=ψp for the reduced Λ model with two P þ c states (see Table I). The shown as solid (black) squares, while the solid (red) points show the perimental results of the fit. The data solid (points (red) histogram with showserror the back distribution. The (blue) open squares with the shaded histogram represent the P c ð445þ þ state, and the shaded histogram topp 4 Dalitz plots for ð2sþ þ events in the (a) ð2sþ (c) π FIG. 2. (e) π π Comparison of fit resul

5 qq B M QCD qqq - qqq > 5

6 イントロダクション ハドロン物理における共鳴状態 強い相互作用で不安定な状態 励起ハドロンの性質 PDG25 JP JP π ω cc π φ π π φ π ω ω π sj ψ cb ub ψ sj χ χ sj /ψ χ χ χ ψ ψ φ π π ω φ π ψ χ χ χ χ χ χ χ - 強い相互作用で安定 不安定 - 励起状態のほとんどが不安定 ハドロン散乱の共鳴状態 6

7 ) - (P) - E> - - (P ) K N V P r 2) - (P+Q) V Q - Q EQ<, EP> - - (P ) P r 7

8 - G. Gamow, Z. Phys. 5, 24 (928) Zur Quantentheorie des Atomkernes. Von G. Gamow~ z. Zt. in GSttingen. Mit 5 Abbildungen. (Eingegangen am 2. August 928.) Um diese Schwierigkeit zu ilberwinden, miissen wir annehmen, dal] die Schwingungen ged~mpft sin(t, und E komplex setzen: we E o die gewshnliche Energie ist und 9[ das D~mpfungsdekrement (Zer~allskonstante). ])ann sehen wir aber aus den elationen (2 a) und (2 b), - h i = Z dr (r) 2! bi-orthogonal basis Gamow vector N. Hokkyo, Prog. Theor. Phys. 33, 6 (965) T. Berggren, Nucl. Phys. A 9, 265 (968) Z i = i, h i = dr[ (r)] 2 < hz - <r 2 > > 8

9 X S. Weinberg, Phys. ev. 37, B672 (965) or Z 9

10 s ( typ) <X< S. Weinberg, Phys. ev. 37, B672 (965); T. Hyodo, Int. J. Mod. Phys. A 28, 3345 (23) 2X a = +X + O typ X, r e = X a, re = (2μB) -/2 typ : + O typ - NN a~ re < X ~ -

11 - QFT D.B. Kaplan, Nucl. Phys. B494, 47 (997) E. Braaten, M. Kusunoki, D. Zhang, Annals Phys. 323, 77 (28) Z apple H free = dr 2M r r + 2m r r + rb 2M rb + B B, Z i H int = dr hg B + B + v B B g + g B + v - Λ ~ /typ - p Λ

12 H free B i = B i, (H free + H int ) B i = B B i - B> + Z h B B i =, = B ih B + - H free p i = p2 2µ p i =Z + X, Z h B B i 2, X dp (2 ) 3 p ih p Z dp h p B i 2 (2 ) 3 Z, X: > 2

13 ΨΦ f(e) = µ 2 [v(e)] G(E) v(e) =v + g2 E, G(E) = 2 2 Z = v + p 2 dp E p 2 /(2µ)+i + X v(e) G(E) T. Sekihara, T. Hyodo, D. Jido, PTEP25, 63D4 (25) T. Hyodo, arxiv:5.87 [hep-ph] g g + v + g g X = {+G 2 ( B)v ( B)[G ( B)] } / X a = f(e = ) = 2X +X + O typ X < (B, a) typ 3

14 H free = H int = Z Z apple dr 2M r r + 2m r r, apple dr g B + B + v + v( t + ), H = H free + H free + H int + H int H QB i = E QB QB i, E QB 2 C a = ( 2X +X + O typ + s µ 3 µ 3 O l ν 3 ), = B p 2µEQB, l μ μ p 2µ X < (EQB, a) (typ, l) 4

15 > Z X Z + X =, Z,X 2 C Z X Z X Z X + Z 2 - Z + X =, Z, X 2 [, ] Z + X, X, U Z + X 2 - U= c.f. V. Baru, et al., Phys. Lett. B 586, 53 (24) F. Aceti, et al., Eur. Phys. J. A 5, 57 (24) Z.H. Guo, J.A. Oller, arxiv:58.64 [hep-ph] 5

16 Λ(45) X < (EQB, a) a = ( 2X +X + O typ + s µ 3 µ 3 O l 3 ), = p 2µEQB, l p 2µ - Λ(45) K N Y. Ikeda, T. Hyodo, W. Weise, PLB 76, 63 (2); NPA (22), - EQB = - -26i MeV > ~ 2 fm > typ..2, l 3..6 πσ ef. E QB (MeV) a (fm) X KN X KN U r e /a [43] i26.39 i.85.2+i [44] 4 i 8.8 i.92.6+i [45] 3 i2.3 i.85.9 i [46] 2 i.2 i.47.6+i [46] 3 i2.52 i.85.+i Λ(45) K N < 6

17 a = S. Weinberg, Phys. ev. 37, B672 (965) ( 2X +X + O typ + s µ 3 µ 3 O Λ(45) l 3 ), = p 2µEQB, l p 2µ K N Y. Kamiya, T. Hyodo, arxiv:59.46 [hep-ph] K N 7

Y. Nambu and G. Jona-Lasinio, A Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity I, Phys. Rev. 122, 345 (1961). http://prola.aps.org/pdf/pr/v122/i1/p345_1 Y. Nambu and

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