[222-130] INT Nov, 2015 Cusps, Resonances, and Exotic States Eric Swanson
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, 219 238 (1946). Hylleraas, E. A. & Ore, A. Binding energy of the positronium molecule. Phys. Rev.71, 493 496 (1947). 2007: Ps2 is observed Cassidy, D.B.; Mills, A.P. (Jr.) (2007). "The production of molecular positronium". Nature 449 (7159): 195 197
Multi-quark States L QED
Thresholds
X(4630)
not a threshold enhancement (?) J/
e + e J/ D ( ) D( ) [Belle] PRL100, 202001 (08)
A Quark Model Example S-wave P-wave
A Quark Model Example p =1/2+L CD min p = 1/2+L CD min endothermic exothermic max (0.2 0.5) QCD scale
Cusps E.P. Wigner, Phys. Rev. 73 (1948) 1002 D. V. Bugg, Europhys. Lett. 96, 11002 (2011) D. V. Bugg, Int. J. Mod. Phys. A 24, 394 (2009)
f0(980) example with effective range parameterization of the amplitude range [Bugg] Other examples K d ( p) pp J/ pp
Example = 2 / 2 d 3 q e q (2 ) 3 E m B m B q 2 /2µ + i =0.5 GeV
Exotic Experiment
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)
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 = 4248 +185 45 = 177 +113 J PC =? 72 X(4160) X(3940) c2 c h c R. Mizuk et al. [Belle], PRD76, 072004 (08)
Z 1 (4050) from Y(4360) [Belle] 1410.7641
Z 1 (4050) Y(4360) Y(4660) [Belle] 1410.7641
Z + (4430) B K + Z c (3900) M = 4443 +24 18 = 107 +113 71 X(4630) Y (4660).manifestly exotic.not confirmed by BaBar J PC =? 30 X(4160) Events/0.01 GeV 20 10 X(3940) c2 c h c 0 3.8 4.05 4.3 4.55 4.8 M(! + " # ) (GeV) S.-K Choi et al. [Belle] 0708.1790 F. Rubbo, Torino thesis Mokhtar, 0810.1073
Z + (4430).confirmed by LHCb J P =1 +
Z(4240) [?]
Z c (4200) B K J/ dotted: without Zc(4200) K. Chilikin et al. [Belle] 1408.6457
+ + Z b (10610) Z b (10650) Adachi et al. [Belle] 1105.4583 I G J P =1 + 1 + (2S) h b (1P ) h b (2P )
+ + Z b (10610) Z b (10650) [Belle] preliminary [C.-Z. Yuan, INT Nov 2015]
Shuangshi Feng [BESIII] H13
Zc(3900) e + e D D s =4.26 M = 3883.9 ± 1.5 ± 4.2 = 24.8 ± 3.3 ± 11.0 BESIII PRL112 022001 (14)
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.
Z c (4025) e + e (D D ) ± M = 4026.3 ± 2.6 ± 3.7 = 24.8 ± 5.6 ± 7.7 BESIII Phys. Rev. Lett. 112, 132001 (2014)
Zc(3900) Theory Zc(4025)
Exotic Phenomenology
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
Z c (3900) Z c (4025) 3870 3875 D 0 D 0 X( J/ ) D 0 D + D + D 0 4010 4015 D 0 D 0 D + D 0 3880 D + D 4020 D + D 3885 Z c (DD ) 4025 Z c ( h c ) Z c (D D ) 3890 4030 3895 3900 Z c ( J/ )
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) < 7.8 10 3 B*
Cusp Model E.S. Swanson, arxiv:1409.3291 0.2 0.15 B 0.1 0.05 0 (5S) B* (1S) -0.05-0.1 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 m(bb * ) (GeV) [NB: this exhibits phase motion!]
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
Cusp Model (5S) (ns) Zb(10610), Zb(10650) arb. units 90 80 70 60 50 40 30 i =0.7 GeV 20 10 0 10.6 10.62 10.64 10.66 10.68 10.7 10.72 10.74 m(y(3s) ) max (GeV) g 2 (ns)bb =0.9 g2 (ns)b B Adachi et al. [Belle Collaboration], arxiv:1105.4583 [hep-ex]; Garmash et al. [Belle Collaboration], arxiv:1403.0992 [hep-ex].
Cusp Model (5S) (ns) Zb(10610), Zb(10650) arb. units 90 80 70 60 50 40 30 20 10 0 10.4 10.45 10.5 10.55 10.6 10.65 10.7 10.75 10.8 m(y(2s) ) max (GeV) same couplings used! Adachi et al. [Belle Collaboration], arxiv:1105.4583 [hep-ex]; Garmash et al. [Belle Collaboration], arxiv:1403.0992 [hep-ex].
Cusp Model (5S) (ns) Zb(10610), Zb(10650) 60 50 arb. units 40 30 20 10 0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 m(y(1s) ) max (GeV) 30% smaller coupling required Adachi et al. [Belle Collaboration], arxiv:1105.4583 [hep-ex]; Garmash et al. [Belle Collaboration], arxiv:1403.0992 [hep-ex
Cusp Model (5S) h b (np ) Zb(10610), Zb(10650) 14000 12000 10000 h b (1P ) solid line: same as above arb. units 8000 6000 4000 2000 0-2000 dashed line: BB = 0.7 GeV, B B = 0.4 GeV gbb 2 =0.5gB 2 B 10.4 10.45 10.5 10.55 10.6 10.65 10.7 10.75 MM( ) (GeV)
Cusp Model (5S) h b (np ) Zb(10610), Zb(10650) 20000 15000 h b (2P ) solid line: same as above arb. units 10000 5000 0 dashed line: BB = 0.7 GeV, B B = 0.4 GeV gbb 2 =0.5gB 2 B -5000 10.5 10.55 10.6 10.65 10.7 10.75 MM( ) (GeV)
Cusp Model-II E.S. Swanson, arxiv:1504.07952 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 )
Cusp Model-II effect of the bubble sum 0.04 0.035 0.dat u 1:4 m100.dat u 1:4 m200.dat u 1:4 m400.dat u 1:4 200.dat u 1:4 0 0.03 0.025 0.02 0.015 0.01 0.005 0 3.6 3.7 3.8 3.9 4 4.1 4.2
Cusp Model-II 3875 MeV 0-0.2-0.4 Im(E) -0.6-0.8 3886 MeV -1-0.6-0.4-0.2 0 0.2 0.4 0.6 Re(E)
Cusp Model-II fit the pi Y: D*D* vertex attractive bubble 70 60 50 D D D D D D = 0.2 GeV = 0.3 GeV 90 80 = 0.4 GeV 70 60 D D = 0.3 GeV repulsive bubble events 40 30 events 50 40 20 30 20 10 10 0 4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 m(dd * ) (GeV) 0 4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 m(dd * ) (GeV) no evidence for π D* dynamics, background, or bubble
Cusp Model-II fit the pi Y: DD* vertex 100 80 DD = 0.25 GeV events 60 40 DD =0.2 GeV 20 0 3.85 3.9 3.95 4 4.05 4.1 4.15 m(dd * ) (GeV) no evidence for bubble evidence for incoherent background
Cusp Model-II fit the pi Y: DD* vertex 35 30 25 events 20 15 10 5 0 3.85 3.9 3.95 4 4.05 4.1 4.15 m(dd * ) (GeV) Wolfgang Gradl, Bound States in QCD, St Goar, Mar 24-27, 2015
Cusp Model-II continue to Y: pi pi J/psi Now pi pi dynamics is important 1.4 1.2 1 m 2 ( ) (GeV 2 ) 0.8 0.6 0.4 0.2 0 10 11 12 13 14 15 16 17 m 2 ( J/ ) (GeV 2 )
Cusp Model-II Y: pi pi J/psi
Cusp Model-II Y: pi pi J/psi 120 100 cusp reflection DD* cusp 80 events 60 40 20 0 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 m( J/ ) (GeV) BESIII
Cusp Model-II M. Ablikim et al. [BESIII Collaboration], Phys. Rev. Lett. 111, 242001 (2013). e + e + h c sums 13 different ee energy values no significant Zc(3900) observed 140 120 D*D* reflection DD* cusp [incoherent background only] D*D* cusp 100 events 80 60 40 20 0 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 m( h c ) (GeV)
Cusp Model-II e + e + h c
Cusp Model-III F.-K. Guo et al. arxiv: 1411.5584 two loop one loop tree Hanhart et al. claim that the strength of the vertex requires bubble summation, which generates a pole.
Cusp Model-IV Z.Y. Zhou and Z. Xiao, ``Distinguishing cusp effects and near-threshold-pole effects, ' arxiv:1505.05761 [hep-ph].
Exotic Phenomenology Additional Aspects
other cusp channels (5S) K K (ns) B B s + B B s B B s 10695 10745 e + e K KJ/ D D D D s + D D s s 3980 4120 will now argue for B 0 J/ B ± J/ 0 0 ± 0
Cusp Model missing exotics Y (4260) + J/ B 0 + J/ 2 Events / 0.02 GeV/c 100 80 60 40 20 Data MC Z c (3900) MC Sideband Events / (40 MeV) 1000 800 600 400 200 (a) LHCb Events / (20 MeV) 0 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 2 M( + J/ ) (GeV/c ) 0 3.5 4 4.5 5 m(j/ψπ + ) [GeV] BESIII LHCb R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 90, 012003 (2014).
Cusp Model missing exotics Y (4260) + J/ B 0 + J/
Cusp Model missing exotics B 0 s K + K J/
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:1407.6186v1
Cusp Model missing exotics
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
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
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%
Cusp Model missing exotics the wavefunction penalty is confirmed in the data B X Bf D D 8 10 4 DD 4 10 4 DD 4 10 4 4 10 5 5 10 5 4 10 5
Cusp Model missing exotics no penalty for extra light quarks B X Bf D + 2.7 10 3 D 0 + 8 10 4 D + + 6 10 3 K 8.2 10 4 K 1.2 10 3 0 1.7 10 5 + 4 10 5
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 0 0 0 J/ B ± ± 0 J/ B s J/
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
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
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 7 +17 4.6 Now: 0.82 +- 0.22 +- 0.05 arxiv:0809.1224
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.
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
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 c1 0.1 14.4 93% 94 5% 0.5 6.4 83% 120 10% χ c1 0.1 14.4 93% 60 100% 0.5 6.4 83% 80 > 100%
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 = +
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 10695 ( ) and 10745 ( ) e + e K KJ/ B 0 J/ B ± J/ 0 0 ± 0 (if the wavefunction enhanced rescattering diagram contributes)