The Θ + Photoproduction in a Regge Model

Transcript

1 The Θ + Photoproduction in a Regge Model Herry Kwee College of illiam and Mary Cascade 5 Jefferson Lab December 3, 5 1

2 1. Introduction. Photoproduction γn Θ + K for spin-1/ Θ + γp Θ + K for spin-1/ Θ + γn Θ + K for spin-3/ Θ + 3. Results Total cross sections (σ) Differential cross sections ( dσ dt ) Photon asymmetries (Σ) Decay angular distributions 4. Conclusions

3 Pentaquarks (q 4 q) QCD does not prohibit pentaquarks Known: Baryon (qqq) and Meson (q q) Other possibility: (qqq)(qqq), (q q)(q q), glueball, and Pentaquark (q 4 q) Questions: here should we look? How can we distinguish pentaquark from (qqq) resonance? and How stable? (width) Theoretical prediction: Diakanov et. al. (hep-ph/973373) lightest pentaquark: antidecuplet no ordinary baryon (qqq) has s = +1 mass around 153 MeV width 15 MeV 3

4 Hidden Strangeness: uudd s Θ + (153) P 5 = 3 uuds s uudd d Σ + 5 = 3 uuds d uuss s Ξ 5 Ξ + (186?) 5 ddssū uuss d Figure 1: SU(3) F Antidecuplet for Pentaquark naively, m(ξ + 5 ) m(θ+ ) = m s 15 MeV. Mixing: effect only on N 5 and Σ 5. 4

5 Experimental Evidence First experimental sign: Nakano et. al. (LEP collaboration, hep-ex/31) mass 154 ± 1 MeV width less than 5 MeV Other experiment: V.V. Barmin et al. (hep-ex/344) very narrow width ( 9 MeV) Current experimental status: positive signal: 1 published experiments non-observing experiment: 11 published results LEP still see signal (see talk by Nakano at International Conference on QCD and Hadronic Physiscs, Beijing). 5

6 Quantum Numbers SU(3) F : many possibilities (multiplets). Θ + (s = +1) can be member of 35plet, 7plet or antidecuplet. Antidecuplet?? isospin = (searches for θ ++ no result, J. Barth et al., hep-ex/3783) result has been ruled out by new CLAS g11 experiment also STAR see signal for Θ ++ (see talk by Huang at International Conference on QCD and Hadronic Physics, Beijing). The spin and parity of the Θ + is currently unknown 6

7 Θ + Photoproduction γ(q) + N(p N ) K(p K ) + Θ + (p Θ ) s (p N + q), t (q p K ), and u (q p Θ ) (M. Guidal, HJK, M.V. Polyakov, M. Vanderhaeghen, hep-ph/5718) 7

8 γn K Θ + : J P Θ = 1 ( ) + 1 8

9 M K = ( i) e g KNΘ P K Regge(s, t) ε µ (q, λ) [ F K (t) (p K q) µ Θ γ 5 N F Θ (u) (t m K) Θ γ µ (γ p u + M Θ ) u MΘ γ 5 N + p µ K ( ˆF (s, t, u) F K (t)) Θ γ 5 N ( ) ] t m K u m p µ Θ { ˆF (s, t, u) F Θ (u)} Θ γ 5 N Θ difference between (+) and (-) parity: only in γ 5 and (±, i) t- and u-channel reggeized the same way (required by gauge invariance) the last terms: required contact terms 9

10 Θ Decay and KNΘ Vertex J P = 1 l =, S-wave J P = 1 + l = 1, P-wave J P = 3 + l = 1, P-wave J P = 3 l =, D-wave 1

11 J P = 1 + KNΘ + vertex and Θ + idth L KNΘ = i g KNΘ K Θγ5 N + Nγ 5 ΘK Γ Θ KN = g KNΘ π p K M Θ q p K + M N M N «p K.67 GeV with Γ Θ KN = 1 MeV g KNΘ 1.56 J P = 1 L KNΘ = g KNΘ K ΘN + NΘK Γ Θ KN = g KNΘ π p K M Θ q «p K + M N + M N Γ Θ KN = 1 MeV g KNΘ

12 K Regge Exchange 4 α K 3 (.3) K 4 (.5) K (1.77) K 1 (1.7) K (.49) - m 4 6 K t (GeV ) - imagine K as a tube (rod) with quarks at the end rotate higher angular momentum higher-spin excitation of Kaons lie on K Regge trajectory K Regge trajectory for t-channel: α K (t) = α K + α K t trajectories can be either non-degenerate or degenerate 1

13 Non-degenerate Regge Trajectory 1 t m K = P K Regge(s, t) = s s «αk (t) S K + e iπα K (t) πα K sin(πα K (t)) 1 Γ(1 + α K (t)) s 1 GeV standard linear trajectory for K is: α K (t) =.7 (t m K) as t m K, α K and P K Regge(s, t) 1 t m K Γ(1 + α(t)) suppresses propagator poles in the unphysical region J P =,, 4,... correspond with S = +1 J P = 1 +, 3 +, 5 +,... correspond with S = 1 13

14 Degenerate Regge Trajectory Degenerate trajectory: obtained by adding or subtracting the two non-degenerate trajectories with the two opposite signatures 1. a constant (1) phase. a rotating (e iπα(t) ) phase: strong degeneracy assumption 1 t m K «αk (t) = PRegge(s, K s πα K t) = s sin(πα K (t)) e iπα K (t) 1 Γ(1 + α K (t)) 14

15 Regge vertex functions (Regge residues) away from the pole position, need form factors F K (t), F Θ (u), and ˆF. e choose monopole forms for F K and F u : ( F K (t) = 1 + t + ) 1 m K, F Θ (u) = Λ ( 1 + u + M Θ Λ where cut-off Λ is chosen to be 1 GeV, ) 1, and ˆF = F K (t) + F Θ (u) F K (t) F Θ (u) to cancel the poles in the contact terms. 15

16 γp K Θ + : J P Θ = 1 ( ) + 1 M K = (i) e f K K γ f K NΘ PRegge(s, K t) ε µ (q, λ)» i σ ε µνλα q ν (q p K ) λ Θ αβ (q p K ) β γ 5 N (1) M N + M Θ f K K γ is determined from radiative K decay experiment similar term contributes to γn Θ + K if K is considered 16

17 J P = 1 L K NΘ + 1 = i f K NΘ Θ K NΘ + vertex» i σµν p ν K M N + M Θ γ 5 N V µ (p K ) + h.c. Using SU(3) symmetry for the vector meson couplings within the baryon octet and SU(6) symmetry between the baryon octet and antidecuplet g ρ pp + f ρ pp = 7 1 g φpp + f φpp = 1 1 f K Θ + p = V + 1 «V V = 18.7(input) V + 1 «V V = (input) 3 3 V V 1 1 V «17

18 g V NN (f V NN ): vector (tensor) coupling constants f K pθ + = (g ρ pp + f ρ pp) /5 r r + where r V 1 /V.35 is obtained in the chiral quark soliton model f K NΘ f K pθ rescaling r, corresponding to Θ + width of 1 MeV yields: f K NΘ f K pθ

19 K Regge Exchange 1 t m K = P K Regge = s s «αk (t) 1 S K + e iπα K (t) πα K sin(πα K (t)) 1 Γ(α K (t)) Regge trajectory: α K (t) = α K + α K t standard linear trajectory for the K (89) is : α K (t) =.5 + α K t where α K =.83 GeV strong degeneracy assumption 19

20 γn K Θ + : J P Θ = 3 ( ) + 3 additional contact term: to preserve gauge invariance Θ Θ α (spin-3/): change the vertex and propagator structure

21 M K = ( ) (i) e g KNΘ m K P K Regge(s, t) ε µ (q, λ) ˆF K (t) (p K q) µ (p K q) α Θ α γ 5 N F Θ (u) (t m K) Θ α γ αβµ (γ p u + M Θ ) u M Θ S βν γ νσρ (p K ) σ (p u ) ρ M Θ γ 5 N with + (t m K) Θ α γ αµν (F Θ (u) p K + F K (t) p Θ ) ν M Θ γ 5 N + p µ K ( ˆF (s, t, u) F K (t)) p α K Θ γ 5 N «t m K p µ u m Θ { ˆF (s, t, u) F Θ (u)} p α K Θ γ 5 N Θ S βν = g βν γ β γ ν 3 (γ β (p u ) ν γ ν (p u ) β ) 3M Θ ((p u) β (p u ) ν ) 3M Θ again difference between (+) and (-) parity: only in γ 5 and (±, i) 1

22 KNΘ + vertex J P = 3 + L KNΘ = g KNΘ m K Γ Θ KN = g KNΘ π n Θα g αβ N β K + NΘ α g αβ β K o q «p K p K p M Θ 3m K + M N + M N K with Γ Θ KN = 1 MeV g KNΘ.4741 J P = 3 L KNΘ = g KNΘ m K n Θα γ 5 Ng αβ Γ Θ KN = g KNΘ π p K p K M Θ 3m K Γ Θ KN = 1 MeV g KNΘ β K q p K + M N M N + Nγ 5 Θ α g αβ β K o «

23 Cross Section for γn Θ + K σ tot (nb) / / + K Regge K * Regge K + K * Regge K - K * Regge.5 σ tot (nb) 1.5 1/ / s (GeV ) s (GeV ) Note the uncertainty in the sign of the coupling f K pθ + 3

24 Cross section for γp Θ + K.1.9 1/ - σ tot (nb).6.3 K * Regge σ tot (nb) / s (GeV ) 4

25 Differential Cross section for γn Θ + K, s= 8.4 GeV.5 dσ/dt (nb/gev ) / / + K Regge K * Regge K + K * Regge K - K * Regge.8 1/ + 4 3/ - dσ/dt (nb/gev ) t (GeV ) t (GeV ) spin-1/ has peak around t. GeV 5

26 Differential Cross section γp Θ + K, s = 8.4 GeV.4 dσ/dt (nb/gev ).3..1 K * Regge 1/ - dσ/dt (nb/gev ) / t (GeV ) γp has peak(from K )around t.4.5gev 6

27 Photon Asymmetries for γn Θ + K, s= 8.4 GeV 1.5 1/ / + Σ K Regge K * Regge K + K * Regge K - K * Regge / +.8 3/ - Σ t (GeV ) t (GeV ) Σ = σ σ σ +σ K(K ) exchange dominant, Σ go to -1(1) 7

28 Photon Asymmetries for γp Θ + K, s = 8.4 GeV 1 Σ / - K * Regge / + Σ t (GeV ) 8

29 Decay Angular Distribution 9

30 angular distribution of Θ + K + n (θ, φ) = ˆR sf,s θ ρ sθ,s (Θ+ ) ˆR θ s f,s θ s f,s f ;s θ,s θ = s θ,s θ { ˆR 1,s θ ρ s θ,s θ + ˆR 1,s θ ρ s θ,s θ ˆR 1,s θ ˆR 1,s θ + ˆR 1,s θ ρ s θ,s θ + ˆR 1,s θ ρ s θ,s θ ˆR 1,s θ ˆR 1,s θ } The transition operator ˆR sf,s θ n, s f, P θ p ˆt Θ +, s θ, P θ = ρ sθ,s : the photon density matrix elements in the Θ+ θ production 3

31 1. in φ = 1/ - 1/ + 3/ + 3/ - φ = π/4 φ = π/ Figure : γn Θ + K, α =, s= 8.4 GeV, t =.1 GeV 31

32 in φ = 1/ - φ = π/4 φ = π/ 1/ + 3/ + 3/ Figure 3: γn Θ + K, α = 1, s= 8.4 GeV, t =.1 GeV 3

33 in φ = 1/ - φ = π/4 φ = π/ 1/ + 3/ + 3/ Figure 4: γn Θ + K, α =, s= 8.4 GeV, t =.1 GeV 33

34 in φ = 1/ - φ = π/4 φ = π/ 1/ + 3/ + 3/ Figure 5: γn Θ + K, α = 3, pol γ = 1, s= 8.4 GeV, t =.1 GeV 34

35 in φ = 1/ - φ = π/4 φ = π/ 1/ + 3/ + 3/ Figure 6: γn Θ + K, α = 3, pol γ = 1, s= 8.4 GeV, t =.1 GeV 35

36 1. in.15.1 φ = 1/ - φ = π/4 φ = π/.5.1 1/ Figure 7: γp Θ + K, α = 3, pol γ = 1, s = 8.4 GeV, t =.1 GeV 36

37 1. in.15 φ = 1/ - φ = π/4 φ = π/.1.5 1/ Figure 8: γp Θ + K, α = 3, pol γ = 1, s = 8.4 GeV, t =.1 GeV 37

38 Some observable of the (decay angular distribution): more variation in: γn K Θ + circular polarization hard to miss spin-3/ characteristic φ = π/ mostly not interesting 38

39 Conclusion theoretically both parity assignment of the Θ + are allowed the spin of the Θ + can be 1/ or 3/ photoproduction experiments: good place to determine the spin and parity of the Θ + if statistics allow, decay angular distribution is even better to determine the spin and parity of the Θ + 39