OPEN CHARM and CHARMONIUM STATES

Transcription

1 1 OPEN CHARM and CHARMONIUM STATES from EFFECTIVE FIELD THEORIES Ulf-G. Meißner, Univ. Bonn & FZ Jülich Supported by DFG, SFB/TR-16 and by EU, QCDnet and by BMBF 06BN9006 and by HGF VIQCD VH-VI-231

2 2 CONTENTS Intro: Salient features of QCD Goldstone boson scattering off D ( ) -mesons Symmetry tests in charmonium transitions Summary & outlook

3 3 Introduction

4 LIMITS of QCD 4 light quarks: L QCD = q L id/ q L + q R id/ q R + O(m q /Λ QCD ) L- and R-handed quarks decouple chiral symmetry spontaneous chiral symmetry breaking pseudo-goldstone bosons pertinent EFT chiral perturbation theory (CHPT) heavy quarks: L QCD = Q f iv D Q f + O(Λ QCD /m Q ) independent of quark spin and flavor SU(2) spin and SU(2) flavor symmetries pertinent EFT heavy quark effective field theory heavy-light systems: heavy hadrons act as matter fields coupled to light pions combine CHPT and HQEFT Donoghue, Wise, Yan,...

5 5 Goldstone boson scattering off D ( ) -mesons Guo, Krewald, M., Phys. Lett. B 665 (2008) 157 Guo, Hanhart, Krewald, M., Phys. Lett. B 666 (2008) 251 Guo, Hanhart, M., Eur. Phys. J. A 40 (2009) 171 Cleven, Guo, Hanhart, M., arxiv: [hep-ph]

6 EFFECTIVE LAGRANGIAN for φd φd 6 Goldstone boson octet (π, K, η) scatters off D-meson triplet (D 0, D +, D + s ) multi-scale/multi-faceted problem: light particles, chiral symmetry chiral expansion in (p, m q ) heavy particles, heavy quark symmetry expansion in 1/m c isospin-violation strong = quark mass difference m d m u electromagnetic = quark charge difference q u q d 16 channels with different total strangeness and isospin some are perturbative some are non-perturbative, require resummation possible molecules

7 EFFECTIVE LAGRANGIAN for φd φd 7 Effective Lagrangian at NLO: L = L (1) + L (2) L (1) = D µ DD µ D M 2 D DD L (2) str. = D ( h 0 χ + h 1 χ + + h 2 u µ u µ h 3 u µ u µ) D + D µ D ( h 4 u µ u ν h 5 {u µ, u ν } h 6 [u µ, u ν ] ) D ν D drop terms with flavor traces (large N C suppressed) fix h 1 from D-meson mass differences (incl. em effects) fix h 3 from Ds0 (2317) mass (as DK molecule) h 5 varied within natural range, h 5 [ 1, +1]/M 2 D

8 SCATTERING AMPLITUDE 8 Chiral expansion T (s, t, u) = T (1) (s, t, u) + T (2) (s, t, u) = C 0 4F 2 (s u) + 2C 1 3F 2 h 1 + 2C 35 F 2 H 35(s, t, u) C 0, C 1, C 35 : channel-dependent Clebsch-Gordan coeffs Unitarization: iteration of the fundamental bubble T (s) = V (s) [1 G(s) V (s)] 1 once-subtracted dispersive representation Oller, M. (2001) G(s) = φ D subtraction constant to fit mass of the Ds0 (2317) at LO

9 9 RESULTS for φd φd etc Width of the Ds0 (2317) in the molecular picture Γ(D s0 (2317)+ D + s π0 ) = (180 ± 110) kev testable prediction uncertainty from exp. input and variation of h 5 note: much smaller in quark models (a few kev) expectation for the scattering length for DK(I = 0) in the molecular picture: DK = g2 eff 1 DK = 2 µ DK ε 1 fm a I=0 no data, but first lattice investigations at varying quark masses Liu, Lin, Orginos, PoS LATTICE2008:112,2008

10 QUARK MASS DEPENDENCE 10 predictions: channels with no poles a (-1,0) [fm] DK DK M [MeV] 0.0 a (-1,1) [fm] DK DK M [MeV] 0.0 a (0,3/2) [fm] D D M [MeV] a (2,1/2) [fm] D s K D s K M [MeV]

11 QUARK MASS DEPENDENCE cont d 11 predictions: channels with poles resonances or molecular states a (0,1/2) [fm] D D Dπ Dπ (0, 1/2) DK DK (1, 0) M [MeV] a (1,0) [fm] DK DK 1,0 0,5 0,0-0,5-1, M [MeV] a pair of poles above thr. a bound states below thr. D s0 (2317) a (0,1/2) Dπ = 0.35(1) fm a (1,0) DK = 0.93(5) fm lattice test of the molecular nature

12 NATURE of the D s1 (2460) 12 Nature of the D s1 (2460): M Ds1 (2460) M D s0 (2317) M D M D most likely a D K molecule (if the Ds0 (2317) is DK) study Goldstone boson scattering off D- and D -mesons Use heavy meson chiral perturbation theory Wise, Falk et al., Caslabuoni et al.,... H v = 1 + v/ 2 P = (D 0, D +, D s + ), [V/ v + ip v γ 5 ] V µ = (D 0 µ, D + µ, D + s,µ ) T-matrix: φ φ D D* D* Unitarization (as before) find poles in the complex plane φ D

13 KAON MASS DEPENDENCE 13 Mass and binding energy: M mol = M K + M H ɛ MDs MeV ΕDs MeV M K MeV M K MeV MDs MeV ΕDs MeV M K MeV M K MeV typical for a molecule test in LQCD

14 14 Symmetry tests in charmonium transitions Guo, Hanhart, M., Phys. Rev. Lett. 103 (2009) Guo, Hanhart, Li, M., Zhao, Phys. Rev. D 82 (2010) Guo, Hanhart, Li, M., Zhao, arxiv: [hep-ph] Guo, Hanhart, M., Phys. Rev. Lett. 105 (2010)

15 CHARMONIUM TRANSITIONS 15 consider charmonium transitions with emission of one neutral pion or one η between S and P -wave states: SS, SP, P P 4000 c (3637) h c c0 c1 c2 (3929) D * D * DD * DD Mass (MeV) 3500 h c (3526) c0 (3415) c1 (3510) c2 (3556) 3000 c (2981) J PC = analysis combining HQEFT and CHPT for most transitions possible B(ψ J/ψπ 0 )/B(ψ J/ψη) long believed a fine probe for m u /m d Ioffe, Voloshin, Donoghue,...

16 BASIC INGREDIENTS 16 QCD multipole expansion: soft gluon dominance/hadronization q q π 0 λ glue r quarkonium Q Gottfried (1978), Voloshin (1979),... Q Non-multipole (coupled-channel) effects: intermediate meson loops Q q q π 0 two-step OZI-violating process Lipkin (1987), Lipkin, Tuan (1989),... Q

17 EFFECTIVE LAGRANGIAN Leading order effective Lagrangian: Casalbuoni et al., Mehen, Yan et al., L eff = L SS + L SP + L P P L SS = A 4 [ J σ i J J σ i J ] i (χ ) aa L SP = i 4 C [ χ σj + J σ χ ] (χ ) aa L P P = i γ 2 ɛijk χ i χ j k (χ ) aa Building blocks: J = ψ σ + η c ( ) χ i = σ j χ ij c2 1 2 ɛ ijk χ k c δ ij χ c0 + h i c } heavy fields U = exp(i 2φ/F π ), U = u 2, χ = uχ u u χu light fields

18 LEADING ORDER TRANSITIONS 18 all transitions break SU(2) or SU(3) flavor sensitive to quark mass differences virtual photons can be shown to be absent at leading order transitions at leading order (LO): ψ J/ψπ 0 ψ J/ψη ψ h c π 0 η c χ c0π 0 χ c0 χ c1π 0 χ c1 χ c1π 0 χ c1 χ c2π 0 χ c2 χ c2π 0 h c h cπ 0 i6aɛ ijk ε i (ψ )ε j (J/ψ)q k B du i(8/ 3)Aɛ ijk ε i (ψ )ε j (J/ψ)q k B sl 6C ε(ψ ) ε(h c )B du 6 3CB du 2 6iγ ε(χ c1 ) qb du i3γɛ ijk ε i (χ c1 )εj (χ c1 )q k B du 3 2iγε i (χ c1 )εij (χ c2 )q j B du i6γɛ ijk ε il (χ c2 )εjl (χ c2 )q k B du i6γɛ ijk ε i (h c )εj (h c )q k B du B du (m d m u ), B sl (m s m l ) [m l = (m d + m u )/2]

19 INCLUSION of CHARMED MESON LOOPS 19 consider intermediate charmed mesons power counting scheme: 3 parameters q momentum of the soft pion/eta δ strength of SU(2)/SU(3) breaking v heavy quark velocity, v 0.5 ψ ψ D D D D D π 0 (η) J/ψ (a) π 0 (η) D J/ψ (d) ψ ψ D D D D D π 0 (η) D J/ψ (b) π 0 (η) D J/ψ (e) ψ ψ D D D D D π 0 (η) J/ψ (c) π 0 (η) D J/ψ (f) SS SP P P tree level qδ δ qδ loops q 1 v δ q 2 v 3 M 2 D δ q 1 v 3 δ

20 GOOD NEWS and BAD NEWS I 20 bad news first: v = charmed meson loops dominate ψ J/ψπ 0 (η) transitions (2M D M ψ)/m D 0.53 results (coupling g from D Dπ): Γ(ψ J/ψπ 0 ) = (4.8 ± 2.5) 10 2 g 2 2 (g 2 )2 kev Γ(ψ J/ψη) = (4.3 ± 2.3) 10 1 g 2 2 (g 2 )2 kev R loop π 0 /η = 0.11 ± 0.06 [0.04 ± 0.003] Ψ g 2 D D g g 2 D* φ J/ Ψ need higher order calculation in v (1/m c ) to achieve the necessary precision for the extraction of m u /m d

21 GOOD NEWS and BAD NEWS II 21 and now the good news: charmed meson loops suppressed in ψ h c π 0 and η c χ c0π 0 1 v 3 predictions: q 2 π m 2 D 0.02 [0.1] for ψ h c π 0 [η c χ c0π 0 ] relative prediction from the tree graphs [accuracy O(m π /Λ χ, Λ QCD /m c )]: Γ ( η c χ c0π 0) Γ (ψ h c π 0 ) = 5.86±0.94 Γ ( η c χ c0π 0) = 1.5 ± 0.3 exp ± 0.2 th kev testable prediction (PANDA at FAIR) absolute prediction using m u /m d = 0.47 ± 0.08 Leutwyler 2010 Γ ( ψ h c π 0) = (0.9 ± 0.6) C 2 kev cf Γ(ψ h c π 0 ) = 0.26 ± 0.05 kev BES-III, PRL 105 (2010)

22 TESTING the LOOPS in PP TRANSITIONS 22 consider χ c2, χ c1 P-wave transitions R 2112 = Γ(χ c2 χ c1π 0 ) Γ(χ c1 χ c2π 0 ) R 2212 = Γ(χ c2 χ c2π 0 ) Γ(χ c1 χ c2π 0 ) Χ c2 Π 0 Χ cj Π 0 Χ c1 Χ c loop R 2212 loop R 2112 tree R 2212 tree R M Χ c1 GeV Note: χ c2 identified with Z(3930) Belle (2006) mass of χ c1 from quark model predictions more testable predictions

23 ... and EVEN BETTER NEWS 23 Consider bottomonium transitions: Υ(4S) h b π 0 (η) Loops are suppressed for two reasons: q 2 /(v 3 MB 2 ) 0.6 (0.2) M B 0 M B + = 0.33 ± 0.06 MeV m d m u due to strong & em interference Guo, Hanhart, M., JHEP 0809 (2008) 136 r = m d m u m s + ˆm m d + m u m s ˆm can be extracted with an accuracy of about 23 % by-product: Υ(4S) h b η is a nice channel to search for the h b (sizeable bf 10 3 ) possible to measure at LHCb

24 24 SUMMARY & OUTLOOK Charm-strange mesons as DK resp. D K molecules unitarized CHPT at next-to-leading order various tests proposed for this scenario (exp., lattice) Charmonium transitions with emission of a neutral pion or eta charmed meson loops must be considered many tests of the loop scenario see talk by Qiang Zhao on Saturday m u /m d best from Υ(4S) h b π 0 (η) Need to improve theoretical framework, more connection to latttice QCD golden times with BEPCII & FAIR ahead

25 25 SPARES etc.

26 26 RESULTS for the SCATTERING LENGTHS (S, I) Channel LO NLO UChPT CUChPT Lattice ( 1, 0) D K D K (2) 0.96(20) ( 1, 1) D K D K (2) 0.22(2) 0.23(4) 1 `0, Dπ Dπ (0) 0.36(1) 0.35(1) 2 Dη Dη (1) 0.08(1) 0.19(9) + i0.02(2) D s K Ds K (6) 1.10(57) 0.60(53) + i0.77(15) 3 `0, Dπ Dπ (0) 0.10(1) 0.16(4) 2 (1, 0) DK DK (4) 1.47(20) 0.93(5) D s η D s η (10) 0.02(10) 0.33(4) + i0.05(1) (1, 1) D s π D s π (4) 0.00(1) DK DK (6) + i0.29(11) (2, 1 2 ) D sk D s K (6) 0.23(5) 0.31(2) parameter-free predictions agreement wit LQCD (where available) in most channels, sizeable unitarization effects

27 27 EFFECTIVE LAGRANGIAN for φd φd Effective Lagrangian at NLO: L = L (1) + L (2) L (1) = itr[ H a v µ D µ H b ] + g π Tr[ H a H b γ ν γ 5 ]u ν ba + λ m Q Tr[ H a σ µν H a σ µν ] g π from D Dπ decay, g π = 0.30 ± 0.08 spin-splitting = m V m P = 8 λ m Q from phys. masses L (2) [H v, U] with LECs h 1,..., h 5 as before

28 PION MASS DEPENDENCE 28 Mass and binding energy MDs MeV ΕDs MeV M Π MeV M Π MeV MDs MeV ΕDs MeV M Π MeV M Π MeV different in strength from a quark-antiquark state

29