Charming Nuclear Physics

Transcription

1 Charming Nuclear Physics Masaoki Kusunoki Univ. of Arizona (with Sean Fleming, Tom Mehen, Bira van Kolck)

2 Outline Charming Nuclear Physics Introduction (Nuclear EFT) X(3872) as shallow DD* bound state Pionful EFT for shallow DD* bound state Conclusion

3 Introduction Study of low-energy NN scattering Effective field theory (EFT) with symmetries of QCD Separation of scales: e.g. Q << Λχ Systematic expansion Unnatural scales in NN sector Large scattering length: a np ( 1 S 0 ) = 23.8 fm a np ( 3 1/m S 1 ) = 5.4 fm π Shallow bound state: E D = 2.22 MeV Q << mπ Pionless EFT: pions are integreated out Q mπ Pionful EFT: nucleons and pions as EFT fields More complicated EFTs: include Δ s, etc

4 Introduction NN scattering amplitude from EFT with pions Weinberg scheme Weinberg power counting applied to NN potential Solve Schrödinger or LS eq. V0 = + T = V + V T

5 Introduction NN scattering amplitude from EFT with pions KSW scheme Kaplan, Savage, Wise power counting applied to NN scattering amplitude LO contact int. resumed to all orders NLO Pions are perturbative T0 = T1 = + T0 +

6 Introduction Convergence of KSW expansion (perturbative pions): (Q m π ) Naively, estimate OPE and TPE from dim. analysis g 2 A Q2 2f 2 π (Q2 + m 2 π ) ga 4 Q4 M N Q 4fπ 4(Q2 + m 2 π )2 4π Expansion parameter R N = g2 A M Nm π 8πf 2 π m π Λ NN 0.5 Cannot tell its convergence due to O(1) numerical factor need explicit calculations NNLO analysis by FMS Fleming, Mehen, Stewart

7 Properties of X(3872) Recent charm spectroscopy Discovery of XYZ state! Narrow charmonium-like state near 3872 MeV X(3872) Exclusive production in B decays Inclusive production in p-pbar collisions Γx 2.3 MeV (90% C.L.) B X(3872)K p p X(3872) + anything Belle %&' &( )*)*+!"#$%!"#$%&'!! PRL (2003), PRL (2003) PRL (2004), PRD (2005)

8 Properties of X(3872) Various interpretations include: charmonium (c c) charm meson molecule threshold cusp at DD* (c ū) + ( c u) Barns,Godfrey; Eichten et al, Meng et al Tornqvist;Voloshin Wong;Swanson; Braaten et al AlFiky et al Bugg hybrid (c c g) tetraquark (c c q q) diquark-diquark (c q) + ( c q) Li Vijande, et al Buccella et al Ebert et al Stancu; Cui et.al. Bigi, Maiani et al Karliner et al. glueball (g g g) Seth X(3872) as a shallow S-wave D 0 D 0 bound state

9 Properties of X(3872) More about X(3872): Narrow width: < 2.3 MeV (90 % C.L) Experiments favor its quantum numbers Observed decay modes: J P C = 1 ++ Belle, CDF, CLEO X J/ψ π + π X J/ψ π + π π 0 X J/ψ γ Recent observation by Belle near MeV X D 0 D0 π 0 Br[X D 0 D 0 π 0 ] Br[X J/ψ π + π ] = Belle

10 Properties of X(3872) Mass of X(3872): combined averaged mass m X = ± 0.5 MeV

11 X(3872) as DD* bound state Mass of X(3872) is extremely close to DD* threshold: m X = ± 0.5MeV m D 0 + m D 0 = ± 1.0MeV m X (m D 0 + m D 0) = +0.6 ± 1.1MeV Binding energy is unnaturally small: E X = (m D 0 + m D 0) m X = 0.6 ± 1.1 MeV < 0.8 MeV (90% C.L.) E X m2 π 2M DD 10 MeV Small Ex indicates a large S-wave DD* scattering length: a = (2M DD E X ) 1/2 > 5 fm Universality for production and decays of X(3872) Voloshin Braaten, Kusunoki

12 X(3872) as DD* bound state Potential models support existence of DD* molecules one-pion-exchange potential Isospin-0 combinations of D D and DD could be bound Tornqvist one-pion-exchange potential + quark exchange potential Swanson C=+ superposition of D 0 D 0 and D 0 D 0 could be bound m D 0 m D 0 m π 0 7 MeV OPE is not Yukawa-type Suzuki

13 EFT for D D* π system EFT for S-wave DD* scattering near threshold take into account existence of shallow bound state C = + DD* channel: DD = 1 2 ( D 0 D 0 + D 0 D 0 ) EFT for only DD* pionless EFT S-wave contact interaction (LO) L int = C 0 2 ( DD + D D) ( DD + D D) scattering amplitude by summing all bubbles shallow bound state

14 EFT for D D* π system Recent Belle s Report dominant decay mode X D 0 D0 π 0 EFT with pions ( pionful EFT) Estimate relevant scales Binding energy: D mesons are highly nonrelativistic: Typical D meson momentum: E X 1 MeV v D (E X /M DD ) 1/ p D m D v D 60 MeV Energy of emitted pion: E π m2 X 4m2 D + m2 π = 142 MeV 2m X Emitted pions are slow: Typical momentum for emitted pion: v π 0.32 p π m π v π 43 MeV

15 EFT for D D* π system Estimate scales for exchanged pions D 0 D 0 hyperfine splitting: = m D m D = ± 0.07 MeV Pion propagator in OPE: D D π 0 1 q 2 m 2 π + iɛ q 2 m 2 π = q 2 0 m 2 π q 2 µ 2 q 2 µ 2 = 2 m 2 π (44 MeV) 2 μ is comparable to other low-energy scale: Pionful EFT NR D mesons and NR pions µ p D p π v D 0.03 v π 0.3

16 EFT for D D* π system Power counting for pionful EFT Weinberg or KSW? Estimate convergence of KSW expansion: v.s. R D = g2 DD π M DD µ 4πf 2 π µ Λ DD 0.1 ( R N = m ) π 0.5 Λ NN Expect good convergence of KSW expansion Perturbative pions for DD* bound state

17 EFT for D D* π system Effective Lagrangian for DD*π system in KSW scheme from HHχPT: H = 1 + v/ 2 [P µ a γ µ P a γ 5 ] Σ = ξ 2 = e 2iΠ/f π ( π Π ab = 0 / ) 2 π + π π 0 / 2 L H = itr[ H(v D)H] + gtr[ HHγ µ γ 5 A µ ] 8 Tr[ Hσ µν Hσ µν ] + L π = f 2 π 8 Tr[ µ Σ µ Σ] + f 2 πω 4 Tr[m qσ + m q Σ ] + Also 4 D meson interaction terms: L = L D + L D + L π + L 4D

18 EFT for D D* π system Field redifinitions to eliminate large scale Δ δ = m π 7 MeV Pions are nonrelativistic NLO effective lagrangian ( L D = D i 0 + ) ( 2 D + D i 0 + ) 2 D 2m D 2m D ( ) g 1 (DD π ) + h.c. +, 2fπ 2mπ ( L π = π i 0 + ) 2 + δ π + 2m π L 4D = C 0 2 C 2 16 ( DD + D D ) ( DD + D D ) ( DD + D D ) ( D( ) 2 D + D( ) D) 2 D 2 µ 2 2 ( DD + D D ) ( DD + D D ) +,

19 EFT for D D* π system S-wave DD* scattering amplitude A(p) = [A 1 (p) + A 0 (p) + ] (ɛ 1 ɛ 2) LO amplitude is same as pionless EFT s: Summing C0 term to all orders = Dim. reg. + power divergence subtraction (PDS) scheme A 1 (p) = 2π M DD 1 γ + ip

20 EFT for D D* π system S-wave DD* scattering amplitude NLO amplitude includes perturbative pions and derivative contact interactions = A 0 (p) = (A 1 (p)) 2 [ ζ 1 p 2 + ζ 2 µ 2 ig2 M 2 DD µ2 γ 48π 2 f 2 π p ln µ + 2p ]. µ 2p

21 EFT for D D* π system DD*π coupling is fixed by tree-level extraction: D D + π g = 0.6 ± 0.1 syst ± 0.1 stat CLEO NLO amplitude has 3 parameters: γ, ζ 1, ζ 2 Eliminate spurious douple pole by imposing A 0 (A 1 ) 2 = 0 p=iγ ζ 2 = ζ 1 γ 2 µ 2 + g2 M 2 DD 48π 2 f 2 π ln µ + 2iγ µ 2iγ

22 EFT for D D* π system Match to effective range expansion parameters p cot δ(p) = 1 a + r 0 2 p2 +. matching condition: p cot δ(p) = ip + 2π [ (A 1 ) 1 (A 1 ) 2 A 0 + ] M DD S-wave scattering length and effective range: 1 a = ( 1 2iR ) 3 γ + 2πµ2 M DD ζ 2 r 0 = 16iγ 9µ 2 R 4π M DD ζ 1

23 Conclusion X(3872) provides an interesting opportunity to apply Nuclear-type EFT with pions EFT with nonrelativistic pions EFT with perturbative pions in KSW scheme more in progress...