Cusps, Resonances, and Exotic States. Eric Swanson

Transcription

1 [ ] INT Nov, 2015 Cusps, Resonances, and Exotic States Eric Swanson

2 Multi-electron States 1946: Wheeler suggests that Ps2 might be bound 1946: Ore proves it is unbound 1947: Hylleraas & Ore prove it is bound Wheeler, J. A. Polyelectrons. Ann. NY Acad. Sci. 48, (1946). Hylleraas, E. A. & Ore, A. Binding energy of the positronium molecule. Phys. Rev.71, (1947). 2007: Ps2 is observed Cassidy, D.B.; Mills, A.P. (Jr.) (2007). "The production of molecular positronium". Nature 449 (7159):

3 Multi-quark States L QED

4 Thresholds

5

6 X(4630)

7 not a threshold enhancement (?) J/

8 e + e J/ D ( ) D( ) [Belle] PRL100, (08)

9 A Quark Model Example S-wave P-wave

10 A Quark Model Example p =1/2+L CD min p = 1/2+L CD min endothermic exothermic max ( ) QCD scale

11 Cusps E.P. Wigner, Phys. Rev. 73 (1948) 1002 D. V. Bugg, Europhys. Lett. 96, (2011) D. V. Bugg, Int. J. Mod. Phys. A 24, 394 (2009)

12 f0(980) example with effective range parameterization of the amplitude range [Bugg] Other examples K d ( p) pp J/ pp

13 Example = 2 / 2 d 3 q e q (2 ) 3 E m B m B q 2 /2µ + i =0.5 GeV

14 Exotic Experiment

15 four-quark states(?) J/ h c D D D D K cj K J/ (2S) Z 1 (4050) Z c (3900) Z c (4025) Z c (4200) Z 2 (4250) K Z c (4240) Z c (4475) (ns) h b (np ) B B Z b (10610) Z b (10650)

16 Z 1 (4050) Z 2 (4250) B ZK c1 K Z c (3900) Y (4660).manifestly exotic X(4630).dubious M = 4051(30) = 82(51) M = = J PC =? 72 X(4160) X(3940) c2 c h c R. Mizuk et al. [Belle], PRD76, (08)

17 Z 1 (4050) from Y(4360) [Belle]

18 Z 1 (4050) Y(4360) Y(4660) [Belle]

19 Z + (4430) B K + Z c (3900) M = = X(4630) Y (4660).manifestly exotic.not confirmed by BaBar J PC =? 30 X(4160) Events/0.01 GeV X(3940) c2 c h c M(! + " # ) (GeV) S.-K Choi et al. [Belle] F. Rubbo, Torino thesis Mokhtar,

20 Z + (4430).confirmed by LHCb J P =1 +

21 Z(4240) [?]

22 Z c (4200) B K J/ dotted: without Zc(4200) K. Chilikin et al. [Belle]

23 + + Z b (10610) Z b (10650) Adachi et al. [Belle] I G J P = (2S) h b (1P ) h b (2P )

24 + + Z b (10610) Z b (10650) [Belle] preliminary [C.-Z. Yuan, INT Nov 2015]

25 Shuangshi Feng [BESIII] H13

26 Zc(3900) e + e D D s =4.26 M = ± 1.5 ± 4.2 = 24.8 ± 3.3 ± 11.0 BESIII PRL (14)

27 Zc(3900) Wolfgang Gradl, Bound States in QCD, St Goar, Mar 24-27, 2015 New BESIII result with all three particles identified. Much smaller background.

28 Z c (4025) e + e (D D ) ± M = ± 2.6 ± 3.7 = 24.8 ± 5.6 ± 7.7 BESIII Phys. Rev. Lett. 112, (2014)

29 Zc(3900) Theory Zc(4025)

30 Exotic Phenomenology

31 Charged Exotics as Threshold Cusps It seems foolish to ignore that many of these states are just above open charm/bottom thresholds. B B B B

32 Z c (3900) Z c (4025) D 0 D 0 X( J/ ) D 0 D + D + D D 0 D 0 D + D D + D 4020 D + D 3885 Z c (DD ) 4025 Z c ( h c ) Z c (D D ) Z c ( J/ )

33 Cusp Model Q: how does Y(5S) couple to Yππ? (5S) hidden bottom = 3.8% (5S) B ( ) B( ) = 57.3% (5S) B ( ) B( ) =8.3% B (5S) (ns) < B*

34 Cusp Model E.S. Swanson, arxiv: B (5S) B* (1S) m(bb * ) (GeV) [NB: this exhibits phase motion!]

35 Cusp Model Im (s) = i k 1+ i+ i i F i = g i exp( s/2 2 i) F i (s)f i (s) k 2 i = (s (m 1i + m 2i ) 2 )(s (m 1i m 2i ) 2 ) 4s B B* (s) = 1 s th ds Im (s ) s s i

36 Cusp Model (5S) (ns) Zb(10610), Zb(10650) arb. units i =0.7 GeV m(y(3s) ) max (GeV) g 2 (ns)bb =0.9 g2 (ns)b B Adachi et al. [Belle Collaboration], arxiv: [hep-ex]; Garmash et al. [Belle Collaboration], arxiv: [hep-ex].

37 Cusp Model (5S) (ns) Zb(10610), Zb(10650) arb. units m(y(2s) ) max (GeV) same couplings used! Adachi et al. [Belle Collaboration], arxiv: [hep-ex]; Garmash et al. [Belle Collaboration], arxiv: [hep-ex].

38 Cusp Model (5S) (ns) Zb(10610), Zb(10650) arb. units m(y(1s) ) max (GeV) 30% smaller coupling required Adachi et al. [Belle Collaboration], arxiv: [hep-ex]; Garmash et al. [Belle Collaboration], arxiv: [hep-ex

39 Cusp Model (5S) h b (np ) Zb(10610), Zb(10650) h b (1P ) solid line: same as above arb. units dashed line: BB = 0.7 GeV, B B = 0.4 GeV gbb 2 =0.5gB 2 B MM( ) (GeV)

40 Cusp Model (5S) h b (np ) Zb(10610), Zb(10650) h b (2P ) solid line: same as above arb. units dashed line: BB = 0.7 GeV, B B = 0.4 GeV gbb 2 =0.5gB 2 B MM( ) (GeV)

41 Cusp Model-II E.S. Swanson, arxiv: Attempt a microscopic cusp model [separable nonrelativistic model; solve exactly] [iterate all bubbles] Y (4260) D D Y (4260) J/ g DD exp( (s Y )/ 2 Y ) exp( (s DD )/ 2 DD )

42 Cusp Model-II effect of the bubble sum dat u 1:4 m100.dat u 1:4 m200.dat u 1:4 m400.dat u 1:4 200.dat u 1:

43 Cusp Model-II 3875 MeV Im(E) MeV Re(E)

44 Cusp Model-II fit the pi Y: D*D* vertex attractive bubble D D D D D D = 0.2 GeV = 0.3 GeV = 0.4 GeV D D = 0.3 GeV repulsive bubble events events m(dd * ) (GeV) m(dd * ) (GeV) no evidence for π D* dynamics, background, or bubble

45 Cusp Model-II fit the pi Y: DD* vertex DD = 0.25 GeV events DD =0.2 GeV m(dd * ) (GeV) no evidence for bubble evidence for incoherent background

46 Cusp Model-II fit the pi Y: DD* vertex events m(dd * ) (GeV) Wolfgang Gradl, Bound States in QCD, St Goar, Mar 24-27, 2015

47 Cusp Model-II continue to Y: pi pi J/psi Now pi pi dynamics is important m 2 ( ) (GeV 2 ) m 2 ( J/ ) (GeV 2 )

48 Cusp Model-II Y: pi pi J/psi

49 Cusp Model-II Y: pi pi J/psi cusp reflection DD* cusp 80 events m( J/ ) (GeV) BESIII

50 Cusp Model-II M. Ablikim et al. [BESIII Collaboration], Phys. Rev. Lett. 111, (2013). e + e + h c sums 13 different ee energy values no significant Zc(3900) observed D*D* reflection DD* cusp [incoherent background only] D*D* cusp 100 events m( h c ) (GeV)

51 Cusp Model-II e + e + h c

52 Cusp Model-III F.-K. Guo et al. arxiv: two loop one loop tree Hanhart et al. claim that the strength of the vertex requires bubble summation, which generates a pole.

53 Cusp Model-IV Z.Y. Zhou and Z. Xiao, ``Distinguishing cusp effects and near-threshold-pole effects, ' arxiv: [hep-ph].

54 Exotic Phenomenology Additional Aspects

55 other cusp channels (5S) K K (ns) B B s + B B s B B s e + e K KJ/ D D D D s + D D s s will now argue for B 0 J/ B ± J/ 0 0 ± 0

56 Cusp Model missing exotics Y (4260) + J/ B 0 + J/ 2 Events / 0.02 GeV/c Data MC Z c (3900) MC Sideband Events / (40 MeV) (a) LHCb Events / (20 MeV) M( + J/ ) (GeV/c ) m(j/ψπ + ) [GeV] BESIII LHCb R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 90, (2014).

57 Cusp Model missing exotics Y (4260) + J/ B 0 + J/

58 Cusp Model missing exotics B 0 s K + K J/

59 Cusp Model missing exotics COMPASS s N = 7 GeV exp( (s N,m 2,m 2 )/(4s N 2 ) exp( (s N m 2 ) 2 /(4s N 2 ) exp( 88) C. Adolph et al. [COMPASS] arxiv: v1

60 Cusp Model missing exotics

61 Cusp Model missing exotics B 0 b direct d c c d J/ colour enhanced, indirect I b B 0 d d c c D D colour enhanced, indirect II b B 0 d c d c D D + colour suppressed, wavefunction enhanced, indirect D b d B 0 0 d c c D

62 Cusp Model missing exotics the direct process is suppressed due to the small odds of back to back charm quarks making a J/psi b c c

63 Cusp Model missing exotics W d c in more detail b c (m c c )= M 2 (m c c,m d c ) dm 2 d c p = m 2 b /4 m2 c (p)p dp 0 m 2 b /4 m2 c (p) dp 0. P(p) = p d 3 q (q) 2 P(0.92) = 25%

64 Cusp Model missing exotics the wavefunction penalty is confirmed in the data B X Bf D D DD DD

65 Cusp Model missing exotics no penalty for extra light quarks B X Bf D D D K K

66 Cusp Model missing exotics direct => wavefunction suppressed colour enhanced, indirect I, II => rescattering suppressed colour suppressed, wavefunction enhanced => < rescattering suppressed The first three must be weak since the Zc is not seen by LHCb in B -> psi pi+ pi-. The same happens in Bs -> psi K+ K-, which should see a 3980 (DsD* + DDs*) and a 4215 (DsDs*). We conclude that either the direct diagram or the rescattering wavefunction enhanced diagram dominates. If the latter dominates then cusp states should be visible in B J/ B ± ± 0 J/ B s J/

67 Cusp Model Application to X(3872) u/d u/d b c c s ū/ d b c s c ū/ d colour enhanced, II rescattering suppressed B + K + D 0 D0 B + K 0 D + D 0 B 0 K 0 D D + B 0 K + D D 0 colour suppressed rescattering enhanced B + K + D 0 D0 B + K + D + D B 0 K 0 D + D B 0 K 0 D 0 D0

68 Cusp Model Application to X(3872) colour enhanced rescattering suppressed B + K + D 0 D0 B + K 0 D + D 0 B 0 K 0 D D + B 0 K + D D 0 colour suppressed rescattering enhanced B + K + D 0 D0 B + K + D + D B 0 K 0 D + D B 0 K 0 D 0 D0 Br(B 0 K 0 X) Br(B + K + X) = N cz + + Z 00 + Z + N c Z 00 + Z 00 + Z + 2 N c + 2

69 Cusp Model Application to X(3872) Br(B 0 K 0 X) Br(B + K + X) = N cz + + Z 00 + Z + N c Z 00 + Z 00 + Z + 2 N c + 2 Br(B 0 K 0 X) Br(B + K + X) = 0.50 ± 0.30 ± 0.05 Thus Now: arxiv:

70 Cusp Model Application to X(3872) colour enhanced rescattering suppressed B + K + D 0 D0 B + K 0 D + D 0 B 0 K 0 D D + B 0 K + D D 0 colour suppressed rescattering enhanced B + K + D 0 D0 B + K + D + D B 0 K 0 D + D B 0 K 0 D 0 D0 An X + or X should be made with approximately the same strength as the X. These modes are not seen X has no charge-partners, and X is not a cusp effect.

71 Cusp Model Application to X(3872) u/d u/d b c c s ū/ d b c s c ū/ d Note that the rescattering enhanced diagram goes through a explaining the large production seen, if this state has a large overlap with the X. c1

72 Cusp Model Application to X(3872) X-χ mixing Table 1: X χ c1 Mixing. state E B (MeV) a (fm) Z 00 a χ (MeV) prob χ c % 94 5% % % χ c % % % 80 > 100%

73 Cusp Model to do examine the X(3872): interplay of cusp, possible bound state dynamics, and mixing with cc states K DB B* B J/ D 1 = 1 = +

74 Cusp Diagnostics lie just above thresholds S-wave quantum numbers asymmetric lineshapes partner states of similar width widths will depend on channel the reaction (5S) K K (ns) should reveal B B s + B B s B B s states at ( ) and ( ) e + e K KJ/ B 0 J/ B ± J/ 0 0 ± 0 (if the wavefunction enhanced rescattering diagram contributes)