Quarkonium Hybrids. Joan Soto. Universitat de Barcelona ) Departament de Física Quàntica i Astrofísica Institut de Ciències del Cosmos

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1 Quarkonium Hybrids Joan Soto Universitat de Barcelona ) Departament de Física Quàntica i Astrofísica Institut de Ciències del Cosmos INT-18-1b, Seattle, 05/29/18 Rubén Oncala, JS, Phys. Rev. D 96, (2017) (arxiv: ); JS, arxiv:

2 Heavy Quarkonium Hybrids Heavy Quarkonium: contain a Q Q pair, Q = b, c Hybrids: have a non-trivial gluon content May have exotic J PC : 0, 0 +, 1 +, 2 +,... If not, difficult to quantify for light hadrons, but easier for heavy ones Pioneering works: Exotics: MIT bag model (Jaffe, Johnson, 76) Heavy Hybrids: String model (Giles, Tye, 77; Horn, Mandula, 78) Born-Oppenheimer approximation (Hasenfratz, Horgan, Kuti, Richard, 80) Lattice potentials (Griffiths, Rakow, Michael, 83) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 2 / 43

3 Outline 1 Motivation 2 Heavy Quarkonium 3 Heavy Hybrids Spectrum Mixing Decay Hyperfine splittings 4 Conclusions Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 3 / 43

4 Motivation Undestanding the XYZ states from QCD: Hidden charm (hidden bottom) Above open charm (bottom) threshold Do not fit usual potential model expectations Tools: Effective Field Theories Lattice QCD inputs Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 4 / 43

5 Heavy Quarkonium Q Q bound state, m Q >> Λ QCD, α s (m Q ) << 1 Heavy quarks move slowly v << 1 Non-relativistic system multiscale problem m Q >> m Q v (Relative momentum) m Q v >> m Q v 2 m Q >> Λ QCD (Binding energy) EFTs are useful (N. Brambilla, A. Pineda, JS and A. Vairo, Rev. Mod. Phys. 77, 1423 (2005)) NRQCD: mq m Q v, m Q v 2, Λ QCD (W.E. Caswell and G.P. Lepage, Phys. Lett. 167B, 437 (1986)) pnrqcd (weak coupling): m Q v m Q v 2, Λ QCD (A. Pineda, JS, Nucl.Phys.Proc.Suppl.64: ,1998) pnrqcd (strong coupling): mq v, Λ QCD m Q v 2 (N. Brambilla, A. Pineda, JS, A. Vairo, Nucl.Phys.B566:275,2000) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 5 / 43

6 NRQCD W.E. Caswell and G.P. Lepage, Phys. Lett. 167B, 437 (1986) G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51 (1995) 1125 m Q >> m Q v, m Q v 2, Λ QCD { L ψ = ψ id D m Q 8mQ 3 D 4 + c F σ.gb + 2m Q + c D 8mQ 2 (D.gE ge.d) + i c S 8m 2 Q σ. (D ge ge D) c F, c D and c S are short distance matching coefficients calculable from QCD in powers of α s. They depend on m Q and µ (factorization scale) but not on the lower energy scales. } ψ Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 6 / 43

7 pnrqcd weak coupling regime Λ QCD m Q v 2 { L pnrqcd = d 3 r Tr S (i 0 h s (r, p, P R, S 1, S 2, µ)) S + +O (id 0 h o (r, p, P R, S 1, S 2, µ)) O +V A (r, µ)tr { O r ge S + S r ge O } + + V B(r, µ) Tr { O r ge O + O Or ge } + O(r 2 1, ) 2 m Q } h s, h o = quantum mechanical hamiltonians with scale dependent potentials calculable in pertubation theory in α s (m Q v) and 1/m Q S=S(r, R, t) is the color singlet wave function field O=O(r, R, t) is the color octet wave function field E=E(R, t) is the chromoelectric field Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 7 / 43

8 pnrqcd weak coupling regime Λ QCD m Q v 2 Leading non-perturbative ( Λ QCD ) contributions to the spectrum g 2 [ ] vac Ej a 1 (0) n, l r 6N c E n h o (0) id adj 0 ab r n, l E b j (0) vac. n is the principal quantum number, l the orbital angular momenta Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 8 / 43

9 pnrqcd weak coupling regime Λ QCD m Q v 2 Leading non-perturbative ( Λ QCD ) contributions to the spectrum g 2 [ ] vac Ej a 1 (0) n, l r 6N c E n h o (0) id adj 0 ab r n, l E b j (0) vac. n is the principal quantum number, l the orbital angular momenta If Λ QCD m Q α 2 s n4 Λ 2 QCD m Q If Λ QCD m Q α 2 s n6 Λ 4 QCD m 3 Q α3 s (Voloshin, 78; Leutwyler 80) oan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 8 / 43

10 pnrqcd weak coupling regime Λ QCD m Q v 2 Leading non-perturbative ( Λ QCD ) contributions to the spectrum g 2 [ ] vac Ej a 1 (0) n, l r 6N c E n h o (0) id adj 0 ab r n, l E b j (0) vac. n is the principal quantum number, l the orbital angular momenta If Λ QCD m Q α 2 s n4 Λ 2 QCD m Q If Λ QCD m Q α 2 s n6 Λ 4 QCD m 3 Q α3 s (Voloshin, 78; Leutwyler 80) The weak coupling regime is unlikely to hold beyond the ground state oan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 8 / 43

11 pnrqcd strong coupling regime Λ QCD mv L pnrqcd = d 3 x 1 d 3 x 2 S ( i 0 h s (x 1, x 2, p 1, p 2, S 1, S 2 ) ) S, h s (x 1, x 2, p 1, p 2, S 1, S 2 ) = p2 1 2m Q + p2 2 2m Q + V s (x 1, x 2, p 1, p 2, S 1, S 2 ), V s = V s (0) + V s (1) + V s (2) m Q m 2 Q +, All V s s can be, and most of them have been, calculated on the lattice V s (0) and V s (1) are central V (2) s contains spin and velocity dependent terms Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica Institut INT-18-1b, de Ciències Seattle, del 05/29/18 Cosmos ) 9 / 43

12 pnrqcd strong coupling regime at LO Matching to NRQCD in the static limit V s (0) is the ground state energy of two static color sources separated at a distance r Can be extracted from lattice calculations of the Wilson loop Figure: Meyer, Swanson, 2015 Well fitted by the Cornell potential V (0) s = V Σ + g (r) k g r + κr + E Q Q g, k g = 0.489, κ = 0.187GeV 2 Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 10 / 43

13 pnrqcd strong coupling regime at LO Charmonium spin averages m c = 1.47GeV, E c c g = 0.242GeV nl M c c M c c EXP S = 0 S = 1 1S 3068 (0) P 3494 (-31) (0, 1, 2) ++ 2S 3678 (4) D 3793 (20) (1, 2, 3) 2P 3968 (41) (0, 1, 2) ++ 3S 4130 (91) D 4210 (57) (1, 2, 3) 4S 4517 (96) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 11 / 43

14 pnrqcd strong coupling regime at LO Bottomonium spin averages m b = 4.88GeV, E b b g = 0.228GeV nl M b b M b bexp S = 0 S = 1 1S 9442 (-3) P 9908 (8) D (-9) (1, 2, 3) 2P (5) (0, 1, 2) ++ 3S (1) S (59) S (9) S (91) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 12 / 43

15 pnrqcd strong coupling regime beyond LO An example at O(1/m 2 Q): the V (1,1) L 2 S 1 V (1,1) L 2 S 1 (r) = c F ir lim r 2 T T 0 spin-orbit potential dt t gb(t, r/2) ge(0, r/2) V 2 (r) [1/r 0 2 ] β=5.85 β=6.0 β=6.2 β=6.3 fit curve (β=6.0) r / r 0 V 2 = V (1,1) L 2 S 1 /c F, Koma, Koma, 09 Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 13 / 43

16 pnrqcd strong coupling regime beyond LO An example at O(1/m 2 Q): the V (1,1) L 2 S 1 spin-orbit potential Short distance constraint: it must coincide with the perturbative evaluation, V (1,1) L 2 S 1 (r) c F C F α s r 3, r 0 (Gupta, Radford, 81) Long distance constraint: it must coincide with the QCD effective string theory result (Perez-Nadal, JS, 08) V (1,1) L 2 S 1 (r) = c F g 2 Λ 2 Λ κ r 2, r Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 14 / 43

17 The Static Limit 4 3 m ps + m s Π u 2 2 m ps [V(r)-V(r 0 )]r Σ g + -2 quenched κ = r/r 0 G.S. Bali at al. (TXL Collaboration), Phys. Rev. D62,(2000): Heavy Quarkonium: states built on the Σ + g potential (color singlet) Heavy Hybrids: states built on the Π u,... potentials (color octet) Heavy Tetraquarks, Pentaquarks,... : analogous to Hybrids but using operators that involve light quarks Molecular states: states built on D D or B B... Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 15 / 43

18 The Static Limit a t E Γ β=2.5 a s ~0.2 fm Gluon excitations string ordering N=4 N=3 N=2 N= u Π u Σ + u Π Σ g ḡ Π g g Σ + g crossover N=0 a s /a t = z*5 z=0.976(21) 0.4 Σ ū Π u short distance degeneracies Σ + g 0.3 R/a s Juge, Kuti, Morningstar (2002) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 16 / 43

19 D h The symmetry group of a diatomic molecule (two equal atoms separated at a distance r) The generators are Rotations around the z-axis, labeled by L = 0, 1, 2, Σ, Π,,... Reflections about the xz plain, labeled by ± (only important for Σ states) Parity, labeled by g (positive) and u (negative). In the case of a Q Q pair is replaced by CP. When r 0 reduces to O(3) (plus C in the case of Q Q), which implies short distance degeneracies (Σ u, Π u ), (Σ g, Π g, g ), (Σ + g, Π g ), (Σ + u, Π u, u ),.. When r the degeneracies of the QCD string must be reproduced (Π u ), (Σ + g, Πg, g ), (Σ + u, Σ u, Π u, Π u, u, Φ u ),... Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 17 / 43

20 Heavy Hybrids The Hybrid potentials have a minimum at r 1/Λ QCD The energy fluctuations about the minimum E Λ 3 QCD /m Q Λ QCD The energy scale Λ QCD can be integrated out An EFT can be built for the short distance multiplets, in a way analogous to the strong coupling regime of pnrqcd We focus on the lowest lying doublet At short distances it is described by tr(ob) in weak coupling pnrqcd We introduce a wave function field H with the same symmetry properties as tr(ob) [tr(ob) QBQ in QCD] The potentials for H are obtained from fitting the static energies of Juge, Kuti, Morningstar (2002), and imposing: Weak coupling pnrqcd constraints at short distances QCD string constraints at long distances Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 18 / 43

21 Spectrum [ ( (J 1)J 1 2 m Q r 2 + ( L = H i ( ) δij i 0 h H ij H j ) h H ij = ( 2 m Q +V Σ u (r) δ ij +(δ ij ˆr iˆr j )V q (r) m Q r 2 +V q(r) J+1 (J+1)J V q(r) 2J+1 V q (r) = V Πu (r) V Σ u (r) (J+1)J V 2J+1 q(r) 2J+1 (J+1)(J+2) m Q r 2 J +V q(r) 2J+1 ) 1 2 J(J + 1) + m Q r 2 m Q r 2 + V Πu (r) ) +V Σ u (r) P 0 J (r) = EP 0 J (r) ] ( ) ( ) P J (r) P P + J (r) =E J (r) P + J (r) J = L + J g L= orbital angular momentum of the heavy quarks J g = total angular momentum of the gluons, J g = 1 Heavy quark spin independence Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 19 / 43

22 Results for charm NL J w-f c c Hybrid J PC (S = 0) J PC (S = 1) Λ ɛ η 1s S Σ + g 2s S Σ + g 3s S Σ + g 1p 0, (H 3) P Σ u 4s S Σ + g 2p 0 P Σ u 3p 0 P Σ u 4p 0 P Σ u 1p S (0, 1, 2) ++ Σ + g 2p S (0, 1, 2) ++ Σ + g 1(s/d) 1, (H 1) P ± (0, 1, 2) + Π u Σ u 1p 1, (H 2) P (0, 1, 2) + Π u 2(s/d) 1 P ± (0, 1, 2) + Π u Σ u 3p S (0, 1, 2) ++ Σ + g 2p 1 P (0, 1, 2) + Π u 3(s/d) 1 P ± (0, 1, 2) + Π u Σ u 4(s/d) 1 P ± (0, 1, 2) + Π u Σ u 4p S (0, 1, 2) ++ Σ + g 3p 1 P (0, 1, 2) + Π u 5(s/d) 1 P ± (0, 1, 2) + Π u Σ u 5p S (0, 1, 2) ++ Σ + g 1d S (1, 2, 3) Σ + g 2d S (1, 2, 3) Σ + g 1(p/f ) 2, (H 4) P ± (1, 2, 3) + Π u Σ u 1d 2, (H 5) P (1, 2, 3) + Π u 2(p/f ) 2 P ± (1, 2, 3) + Π u Σ u 3d S (1, 2, 3) Σ + g 2d 2 P (1, 2, 3) + Π u 3(p/f ) 2 P ± (1, 2, 3) + Π u Σ u 4d S (1, 2, 3) Σ + g 4(p/f ) 2 P ± (1, 2, 3) + Π u Σ u 3d 2 P (1, 2, 3) + Π u Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 20 / 43

23 Results for bottom NL J w-f b b Hybrid J PC (S = 0) J PC (S = 1) Λ ɛ η 1s S Σ + g 2s S Σ + g 3s S Σ + g 4s S Σ + g 1p 0, (H 3) P Σ u 2p 0 P Σ u 3p 0 P Σ u 4p 0 P Σ u 1p S (0, 1, 2) ++ Σ + g 2p S (0, 1, 2) ++ Σ + g 3p S (0, 1, 2) ++ Σ + g 1(s/d) 1, (H 1) P ± (0, 1, 2) + Π u Σ u 1p 1, (H 2) P (0, 1, 2) + Π u 4p S (0, 1, 2) ++ Σ + g 2(s/d) 1 P ± (0, 1, 2) + Π u Σ u 2p 1 P (0, 1, 2) + Π u 5p S (0, 1, 2) ++ Σ + g 3(s/d) 1 P ± (0, 1, 2) + Π u Σ u 4(s/d) 1 P ± (0, 1, 2) + Π u Σ u 3p 1 P (0, 1, 2) + Π u 6p S (0, 1, 2) ++ Σ + g 5(s/d) 1 P ± (0, 1, 2) + Π u Σ u 1d S (1, 2, 3) Σ + g 2d S (1, 2, 3) Σ + g 3d S (1, 2, 3) Σ + g 1(p/f ) 2, (H 4) P ± (1, 2, 3) + Π u Σ u 1d 2, (H 5) P (1, 2, 3) + Π u 4d S (1, 2, 3) Σ + g 2(p/f ) 2 P ± (1, 2, 3) + Π u Σ u 2d 2 P (1, 2, 3) + Π u 5d S (1, 2, 3) Σ + g 3(p/f ) 2 P ± (1, 2, 3) + Π u Σ u 3d 2 P (1, 2, 3) + Π u 4(p/f ) 2 P ± (1, 2, 3) + Π u Σ u Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 21 / 43

24 Comments Only inputs: Lattice potential Heavy Quarkonium spectrum mc = 1.47 GeV, m b = 4.88 GeV Braaten, Langmack, Hudson Smith, 2014 Neglect Π u Σ u coupled channel Fix the lowest lying state for each potential to the Hadron Spectrum Collaboration, 2012 (HSC) Berwin, Brambilla, Tarrús Castellà, Vairo, 2015 Based on the weak coupling regime of pnrqcd Equivalent equations, different potentials and normalization Our results are consistent with the lower end of their error bars The hierarchy of the lower lying hybrid multiplets agrees with the lattice HSC 2016 but our numbers are about MeV lower Marginal agreement with the QCD sum rule results of Chen, Kleiv, Steele, Bulthuis, Harnett, Ho, Richards, Zhu, 2013 Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 22 / 43

25 Hybrids in XYZ? State M J PC XYZ M exp Γ exp Jexp PC 1(s/d) ,(0, 1, 2) + Y(4008) ± p ,(0, 1, 2) + Y(4140) 4144, 5 ± 2, X(4160) ??+ X(4320) 4320±17 101±30 1 X(4350) 4351± ??+ 2(s/d) ,(0, 1, 2) + Y(4360) 4361 ± ± 18 1 Y(4390) 4391±6 139±16 1 1p ,1 + X(4500) (s/d) ,(0, 1, 2) + Y(4660) 4664 ± ± 15 1 X(4630) (s/d) ,(0, 1, 2) + Y b (10890) 10888, 4 ± 3 30, 7 +8,9 7,7 1 C-parity implies that only spin zero hybrids would have been observed, except for X(4350). Decays to vector heavy quarkonium states have been observed for all spin zero 1 states above, except for X(4630) and Y (4390), which disfavors the hybrid interpretation due to spin symmetry. Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 23 / 43

26 Mixing with Heavy Quarkonium States with the same quantum numbers may mix Mixing is a 1/m Q suppressed effect If the energy gap E Λ 2 QCD /m Q it becomes next to leading order For ΛQCD = 400 MeV: E c 100 MeV, E b 30 MeV NL J w-f c c Hybrid J PC (S = 0) J PC (S = 1) Λ ɛ η 3s S Σ + g 1p 0 P Σ u 2p S (0, 1, 2) ++ Σ + g 1(s/d) 1 P ± (0, 1, 2) + Π uσ u 1p 1 H (0, 1, 2) + Π u 2(s/d) 1 P ± (0, 1, 2) + Π uσ u 3p S (0, 1, 2) ++ Σ + g 2d S (1, 2, 3) Σ + g 1(p/f ) 2 P ± (1, 2, 3) + Π uσ u NL J w-f b b Hybrid J PC (S = 0) J PC (S = 1) Λ ɛ η 2(s/d) 1 P ± (0, 1, 2) + Π uσ u 4d S (1, 2, 3) Σ + g Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 24 / 43

27 Mixing with Heavy Quarkonium Symmetries imply L mixing = tr [ { S V ij S σ i, H j} ] + h.c. Matching to NRQCD at O(1/m Q ) implies V ij S (r) 1 m Q O i B i This term mixes S = 0 Hybrids with S = 1 Quarkonium, and may explain spin symmetry violating decays of the 1 Y states Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 25 / 43

28 Mixing with Heavy Quarkonium V ij S = (δij ˆr iˆr j )V Πu S + ˆr iˆr j V Σ u S No lattice evaluation of V Πu S, V Σ u S, so far Short distance constraints: pnrqcd at weak coupling implies for r 0 V Πu S (r) V Σ u S (r) ± λ2 = const. m Q Long distance constraints: QCD string (EST) implies for r V Σ u S (r) 2π2 Λ m Q κr 3, π V Πu S (r) 3 Λ κ m Q r 2 κ, Λ and Λ also appear in the spin dependent potentials (Perez-Nadal, JS, 2011; Brambilla, Groher, Martinez, Vairo, 2014) Can be extracted from available lattice results of the long distance potentials (Koma, Koma, 2007; 2010) κ 0.187GeV 2, Λ 59MeV, Λ ±230MeV Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 26 / 43

29 Modeling the mixing potential V Π S [± ](r) = λ2 m Q V Σ S [±±](r) = λ2 m Q ( ±1 ( r r Π ) ( r r Π ) 4 ( ±1 ± ( r r Σ ) ( r r Σ ) 5 ), r Π = ( gλ π 3 2 ) 1 2λ 2 κ ), r Σ = ( gλ π 2 λ 2 κ ) 1 3 Simple interpolation that allows for a sign flip between short and long distance behavior We focus on charm and scan λ = 100, 300, 600 MeV VS Π[+ ] with V S Σ [++] and λ = 600 MeV produce the maximum mixing The spin symmetry violating decays of Y (4008) (29% S=1), Y (4360) (35% S=1) and Y (4660) (17% S=1) are qualitatively explained It would be important that lattice calculations confirm the signs and size of the mixing potentials Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 27 / 43

30 Hybrid-Quarkonium coupled equations The S = 0 case: P L 0 J M (r), J = J, L = J ± 1 (±), J (0) S1 L J M (r), L = J ± 1 (±), J (0) 2 coupled equations for S1 0 J M (r), P0 0 J M (r) 4 coupled equations for S + 1 J M (r), S 1 J M (r), P+ 0 J M (r), P 0 J M (r) The S = 1 case: P1 L J J M (r), J = J ± 1 (±), J (0), L = J ± 1(±), J (0) S 0 J M (r), L = J 2 coupled equations P +0 1 J M (r), P 0 1 J M (r) 6 coupled equations S 0 J M (r), P ++ 1 J M (r), P + (r), P+ (r), P (r), P00 1 J M (r) 1 J M 1 J M 1 J M Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 28 / 43

31 Results Resonance J PC Assignement Mass (MeV) Observations X(3823) 2 1d 3792 X(3860) 0 or p 3968 X(3872) p 3967 X(3915) 0 or p 3968 X(3940)??? 2p 3968 Y(4008) 1 1(s/d) mixing X(4140) 1 ++???? 1p 1 does not decay to quarkonium X(4160)??? 1p Y(4220) 1 2d 4180 Y (4260) Y (4220), mixing X(4230) 1 2d 4180 X(4230) = Y (4220), mixing X(4350)??+ 2(s/d) 1 or 3p 4355 or 4369 Y(4320) 1 2(s/d) mixing Y(4360) 1 2(s/d) Y (4360) = Y (4320)? X(4390) 1 2(s/d) Y (4390) = Y (4360)? X(4500) p not enough mixing Y(4630) 1 3d 4559 Y(4660) 1 3(s/d) mixing X(4700) p 4703 Υ(10860) 1 5s mixing Y b (10890) 1 2(s/d) mixing Υ(11020) 1 4d Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 29 / 43

32 A recent combined fit to e + e ωχ c 0, π + π h c, π + π J/ψ, π + π ψ(3686) only needs Y (4220), Y (4390) and Y (4660) in order to describe data Implies Y (4220) = X(4230) and Y (4390) = Y (4360) = Y (4320), consistent with our spectrum Zhang, Yuan, Wang, 18 Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 30 / 43

33 1 charmonium spectrum Y (4008) has not been confirmed by LHCb and BESIII. If it is not there: NL J λ = 0.6 Hybrid % PDG 1s J/ψ 2s ψ(2s) 1d ψ(3773) 1(s/d) ψ(4040) 3s ψ(4160) 2d X(4230) = X(4260) = Y (4220) 2(s/d) X(4360) = Y (4390) 4s ψ(4415) 3d Y (4630) 3(s/d) X(4660) Decays to h c should be observed for ψ(4040), X(4230)/X(4260), X(4360) and X(4660) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 31 / 43

34 1 bottomonium spectrum NL J λ = 0.6 Hybrid % PDG 1s Υ(1S) 2s Υ(2S) 1d Υ(1D) 3s Υ(3S) 2d ?? 4s Υ(4S) 1(s/d) ?? 3d ?? 5s Υ(10860) 2(s/d) Y b (10890) 4d Υ(11020) The 17% hybrid component of Υ(10860) may explain the observed spin symmetry violating decays to h b Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 32 / 43

35 Decay to lowest lying Heavy Quarkonium 4 m ps + m s 3 Π u 2 2 m ps [V(r)-V(r 0 )]r Σ g + -2 quenched κ = r/r 0 If the energy gap E to lowest lying heavy quarkonium is E 1GeV a perturbative estimate makes sense. If E H r Q Q 1 weak coupling pnrqcd can be used Γ(H m S n )= 4 α s T F Hm r i S n Sn r i H m ( En ) 3 3 N c Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 33 / 43

36 Results Hybrids with L = J do not decay to Heavy Quarkonium Charm NL J nl E (MeV) r nm (GeV 1 ) E r nm Γ (MeV) 1p 0 2s (s/d) 1 1p Bottom NL J nl E (MeV) r nm (GeV 1 ) E r nm Γ (MeV) 1p 0 1s p 0 2s p 0 1s p 0 2s p 0 3s (s/d) 1 1p Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 34 / 43

37 Hyperfine Splittings Pere Solé, JS They appear at O(1/m Q ) (O(1/mQ 2 )) in hybrids (quarkonium) They are controlled by a single operator iɛ ijk V S (r)tr (H [ i σ k, H j]) It leads to the following mass formulae M 1 J+1 M 0 J M 1 J M 0 J = J M 1 J 1 M 0 J M 1 J M 0 J = J + 1 (s/d) 1 : M M 0 + = M M 1 p 1 : M M 0 + = M M 1 ++ (p/f ) 2 : M M 1 + = M M 2 ++ d 2 : M M 1 + = M M 2 Consistent with the values of the lattice HSC Induces mixing between different hybrid states Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 35 / 43

38 Leads to zero ultrafine splitting (Lebed, Swanson, 17) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 36 / 43

39 Conclusions Heavy Hybrids containing c c or b b have been studied from QCD in a largely model independent way (EFT+lattice inputs) The lower lying states have been calculated at LO in the 1/m Q expansion of the potentials, including the Σ u Π u mixing. The mixing with Heavy Quarkonium states has been addressed It is an important source of spin symmetry violations that explains the decays of certain spin zero Hybrids to spin one Quarkonia. The decay width to lower lying Heavy Quarkonium states has been estimated The decays of J = L states are forbidden Spin and velocity dependent terms in the hybrid potentials enter at O(1/m Q ) We have produced model independent formulas for the hyperfine splittings A number of them can be identified with XYZ states (Y (4008), X(4160), X(4350), Y (4320)/Y (4360)/Y (4390), Y (4660), Y b (10890)) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 37 / 43

40 D h The symmetry group of a diatomic molecule (two equal atoms separated at a distance r) The generators are Rotations around the z-axis, labeled by L = 0, 1, 2, Σ, Π,,... Reflections about the xz plain, labeled by ± (only important for Σ states) Parity, labeled by g (positive) and u (negative). In the case of a Q Q pair is replaced by CP. When r 0 reduces to O(3) (plus C in the case of Q Q) Implies short distance degeneracies (Σ u, Π u ), (Σ g, Π g, g ), (Σ + g, Π g ), (Σ + u, Π u, u ),... (Brambilla, Pineda, JS, Vairo, 99) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 38 / 43

41 String breaking [E(r) - 2 m B ]a state 1> state 2> r/a Bali, Neff, Duessel, Lippert, Schilling, 2005 Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 39 / 43

42 XYZ with c c (Olsen, 15) State M (MeV) Γ (MeV) J PC Process (decay mode) X(3872) ±0.17 < B K + (J/ψ π + π ) p p (J/ψ π + π ) +... B K + (J/ψ π + π π 0 ) B K + (D 0 D 0 π 0 ) B K + (J/ψ γ) B K + (ψ γ) pp (J/ψ π + π ) +... X(3915) ± B K + (J/ψ ω) e + e e + e + (J/ψ ω) 0(?) (?)+ e + e J/ψ + (D D) e + e J/ψ + (...) G(3900) 3943 ± 21 52±11 1 e + e γ + (D D) X(3940) Y (4008) ±97 1 e + e γ + (J/ψ π + π ) Y (4140) 4144 ± 3 17 ± 9??+ B K + (J/ψ φ) X(4160) (?) (?)+ e + e J/ψ + (D D) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 40 / 43

43 State M (MeV) Γ (MeV) J PC Process (decay mode) Y (4260) ±14 1 e + e γ + (J/ψ π + π ) e + e (J/ψ π + π ) e + e (J/ψ π 0 π 0 ) Y (4360) 4361 ± 13 74±18 1 e + e γ + (ψ π + π ) X(4630) e + e γ (Λ + c Λ c ) Y (4660) 4664±12 48±15 1 e + e γ + (ψ π + π ) Z c + (3900) 3890 ± 3 33 ± Y (4260) π + (J/ψ π + ) Y (4260) π + (D D ) + Z c + (4020) 4024 ± 2 10 ± 3 1(?) +(?) Y (4260) π + (h c π + ) Y (4260) π + (D D ) + Zc 0 (4020) 4024 ± 4 10 ± 3 1(?) +(?) Y (4260) π 0 + (h c π 0 ) Z 1 + (4050) ??+ B K + (χ c1 π + ) Z + (4200) B K + (J/ψ π + ) Z 2 + (4250) ??+ B K + (χ c1 π + ) Z + (4430) 4477 ± ± B K + (ψ π + ) B K + (Jψ π + ) Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 41 / 43

44 XYZ with b b (Olsen, 15) State M (MeV) Γ (MeV) J PC Process (decay mode) Y b (10890) ± e + e (Υ(nS) π + π ) Z b + (10610) ± ± Υ(5S) π + (Υ(1, 2, 3S) π + ) Υ(5S) π + (h b (1, 2P) π + ) Υ(5S) π + (B B ) + Zb 0(10610) 10609± 6 1+ Υ(5S) π 0 + (Υ(1, 2, 3S) π 0 ) Z b + (10650) ± ± Υ(5S) π + (Υ(1, 2, 3S) π + ) Υ(5S) π + (h b (1, 2P) π + ) Υ(5S) π + (B B ) + Joan Soto ( Universitat de Barcelona ) Departament Quarkonium de Física Quàntica Hybrids i Astrofísica INT-18-1b, Institut de Ciències Seattle, del 05/29/18 Cosmos ) 42 / 43