Exotic Hadrons: models applied to LHCb pentaquarks

Exotic Hadrons: models applied to LHCb pentaquarks Tim Burns Swansea University 6 September 017 [T.B., Eur.Phys.J. A51, 15 (015), 1509.0460] [T.B. & E.Swanson (ongoing)]

Conventional and exotic hadrons

Conventional and exotic hadrons Baryons Mesons

Conventional and exotic hadrons Hybrids

Conventional and exotic hadrons Hybrids Compact multiquarks

Conventional and exotic hadrons Hybrids Compact multiquarks Hadronic molecules

Conventional and exotic hadrons Hybrids Compact multiquarks Hadronic molecules Threshold eect

P c (4380) and P c (4450)

P c (4380) and P c (4450) LHCb amplitude analysis of the three-body decay Λ b J/ψpK. [LHCb,PRL115,07001,015] u d b u d u ū s c c p K J/ψ Two J/ψp states, the avour of the proton with hidden charm (uudc c).

P c (4380) and P c (4450) P c (4380) + P c (4450) + Mass 4380 ± 8±9 4449.8 ± 1.7 ±.5 Width 05 ± 18 ± 86 35 ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/

Compact pentaquark

Compact pentaquark The uudc c combination in S-wave gives: I (J P ) 1 3 4 5 6 7 8 9 10 ( ) 1 1 1 3 3 3 ( ( ( ( ( 1 3 5 1 3 5 ) ) ) ) )

Compact pentaquark

Threshold eect

Threshold eect P c (4380) + P c (4450) + Mass 4380 ± 8±9 4449.8 ± 1.7 ±.5 Width 05 ± 18 ± 86 35 ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/

Threshold eect P c (4380) + P c (4450) + Mass 4380 ± 8±9 4449.8 ± 1.7 ±.5 Width 05 ± 18 ± 86 35 ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) 438.3 ±.4 Σ + D c 0 (udc)(u c) 4459.9 ± 0.5 Λ + c (1P) D 0 (udc)(u c) 4457.09 ± 0.35 χ c1 p (udu)(c c) 4448.93 ± 0.07

Threshold eect u d b u d c s c

Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p

Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p c c b u d s u d

Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d c c s u d Λ b Λ J/ψ, χ c,... p K J/ψ p

Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d u b d c c s u d ū c s c d Λ b Λ J/ψ, χ c,... p K J/ψ p

Threshold eect u d b u d c s c Λ b D s Λ c D K J/ψ p b u d u b d c c s u d ū c s c d Λ b Λ b Λ Ξ c J/ψ, χ c,... p K D Λ c /Σ c K J/ψ p J/ψ p

Threshold eect Enhancements expected at Λ c D = 1/ Λ c D = 1/, 3/ not seen at LHCb Λ b D s Λ c D K J/ψ p J/ψ, χ c,... J/ψ Λ b Λ p K p D J/ψ Λ b Ξ c Λ c /Σ c K p

Threshold eect Λ c (1P) D P c (4450) mass, but S-wave = 1/ + Λ b P-wave = 1/, 3/ why no Λ c (1P) D states? D s Λ c D K J/ψ p J/ψ, χ c,... J/ψ Λ b Λ p K p D J/ψ Λ b Ξ c Λ c /Σ c K p

Threshold eect Λ c (1P) D P c (4450) mass, but S-wave = 1/ + Λ b P-wave = 1/, 3/ why no Λ c (1P) D states? D s Λ c D K J/ψ p χ c1 p = P c (4450) mass, but doubly suppressed S-wave = 1/ +, 3/ + P-wave = 1/, 3/, 5/ Λ b Λ J/ψ, χ c,... p K J/ψ p D J/ψ Λ b Ξ c Λ c /Σ c K p

Hadronic molecule

Hadronic molecule Consider the deuteron, a 0(1 ) state. MeV below pn threshold. vs.

Hadronic molecule P c (4380) + P c (4450) + Mass 4380 ± 8±9 4449.8 ± 1.7 ±.5 Width 05 ± 18 ± 86 35 ± 5 ± 19 Assignment 1 3/ 5/ + Assignment 3/ + 5/ Assignment 3 5/ + 3/ Σ + c D 0 (udc)(u c) 438.3 ±.4 Σ + D c 0 (udc)(u c) 4459.9 ± 0.5 Λ + c (1P) D 0 (udc)(u c) 4457.09 ± 0.35 χ c1 p (udu)(c c) 4448.93 ± 0.07

Hadronic molecule The (udc)(u c) combinations in S-wave are: I (J P ) Λ c D Λ c D Σ c D Σ D c Σ c D Σ D c ( ) 1 1 1 3 3 3 ( ( ( ( ( 1 3 5 1 3 5 ) ) ) ) )

Hadronic molecule Forbidden vertices: Λ c Λ c 0 0 + 1 (isospin) π D D 0 0 + 0 (spin-parity) π

Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π u c u c D, D V ( r) = ij [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j

Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π V ( r) = ij u c u c [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j D, D All I = 3/ potentials suppressed by 1/.

Hadronic molecule c u d c u d Λ c, Σ c, Σ c π π V ( r) = ij u c u c [ C(r) σi σ j + T (r)s ij (ˆr) ] τ i τ j D, D All I = 3/ potentials suppressed by 1/. Coecient of C(r) is important.

Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )

Hadronic molecule I (J P ) Λ c D Λ c D Σ c D Σ c D Σ c D Σ c D 1 ( 1 ) 1 ( 3 ) P c (4450)? 1 ( 5 ) 3 ( 1 ) 3 ( 3 ) 3 ( 5 )

Summary exotic-ness high! low medium d.o.f. quarks hadrons hadrons interactions g exchange rescattering π exchange colour (1 1) (8 8) (1 1) (1 1) size compact extended masses model dependent at thresholds at thresholds J PC all restricted restricted avours all restricted restricted(i -mix) channels most restricted HQ restricted falsiability low medium high

Backup slides

Ξ c D molecules Λ c = ((ud) 0 c) 1/ = Ξ c = ((us) 0 c) 1/ Σ c = ((ud) 1 c) 1/ = Ξ c = ((us) 1 c) 1/ Σ c = ((ud) 1 c) 3/ = Ξ c = ((us) 1 c) 3/ c u d c u s π = π u c u c The potential matrices (central + tensor) are directly related. Predict loosely bound 0(5/ ) Ξ c D state, observable in Λ b J/ψΛη.

Isospin mixing: P c (4380) and P c (4450) uudc c comes in two charge combinations { (udc)(u c) = Σ + c D 0 (uuc)(d c) = Σ ++ c D Isospin-conserving interactions would produce I, I 3 eigenstates, ( 1, 1 ) 3, 1 = ( ) 1 3 3 Σ + c D 0 Σ ++ c D but only if the masses Σ + c = Σ ++ c and D 0 = D. 3 1 3 Otherwise, isospin is not a good quantum number.

Isospin mixing: P c (4380) and P c (4450) Σ + c D 0 = 438.3 ±.4 Σ + c D 0 = 4459.9 ± 0.5 Σ ++ c D = 4387.5 ± 0.7 Σ ++ c D = 4464.4 ± 0.3

Isospin mixing: P c (4380) and P c (4450) P c (4380) = 4380 ± 8 ± 9 P c (4450) = 4449 ± 1.7 ±.5 D 0 = 438.3 ±.4 Σ + D c 0 = 4459.9 ± 0.5 Σ + c Σ ++ c D = 4387.5 ± 0.7 Σ ++ c D = 4464.4 ± 0.3

Isospin mixing: P c (4380) and P c (4450) P c (4380) = 4380 ± 8 ± 9 P c (4450) = 4449 ± 1.7 ±.5 D 0 = 438.3 ±.4 Σ + D c 0 = 4459.9 ± 0.5 Σ + c Σ ++ c D = 4387.5 ± 0.7 Σ ++ c D = 4464.4 ± 0.3 The P c states have mixed isospin: P c = cos φ 1, 1 + sin φ 3, 1 They should decay also into J/ψ + and η c +, with weights: J/ψp : J/ψ + : η c + = cos φ : 5 sin φ : 3 sin φ [P c (4380)] J/ψp : J/ψ + : η c + = cos φ : 10 sin φ : 6 sin φ [P c (4450)]

Isospin mixing: predicted 5/ states Σ c D 1/(5/ ) Σ + c D 0 = 454.4 ±.4 Σ ++ c D = 458. ± 0.7 Mixed isopsin: P = cos φ 1, 1 + sin φ 3, 1 Decays: J/ψp: D-wave, spin ip Reason for absence at LHCb? J/ψ : S-wave, spin cons. = I = 3/ decay enhanced.

Isospin mixing: predicted 5/ states Σ c D 1/(5/ ) Ξ c D 0(5/ ) Σ + c D 0 = 454.4 ±.4 Σ ++ c D = 458. ± 0.7 Ξ 0 c D 0 = 465.9 ± 0.6 Ξ + c D = 4656. ± 0.7 Mixed isopsin: P = cos φ 1, 1 + sin φ 3, 1 Mixed isopsin: P = cos φ 0, 0 + sin φ 1, 0 Decays: J/ψp: D-wave, spin ip Reason for absence at LHCb? Decays: J/ψΛ: D-wave, spin ip e.g. Λ 0 b J/ψΛη, J/ψΛφ J/ψ : S-wave, spin cons. = I = 3/ decay enhanced. J/ψΣ : S-wave, spin cons. = I = 1 decay enhanced.

Pion exchange: central potential C(r) r(gev 1 ) Yukawa

Pion exchange: central potential C(r) without delta term C(r) with delta term 1 GeV r(gev 1 ) GeV Yukawa

Pion exchange: central potential C(r) without delta term C(r) with delta term 1 GeV r(gev 1 ) GeV +C(r) Yukawa +C(r)