Exotic and excited-state radiative transitions in charmonium from lattice QCD

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1 Exotic and excited-state radiative transitions in charmonium from lattice QCD Christopher Thomas, Jefferson Lab Hadron Spectroscopy Workshop, INT, November 2009 In collaboration with: Jo Dudek, Robert Edwards, David Richards and the Hadron Spectrum Collaboration

2 Outline Introduction and motivation Method Result highlights and interpretations Conclusions 1

3 Charmonium radiative transitions BABAR, Belle, BES, CLEO-c Meson Photon coupling Exotic 1 -+? 2

4 Broader Picture Develop Lattice QCD Techniques Test in the charmonium system Apply to lighter mesons... Photoproduction at GlueX Exotic 1 -+? For progress on the light meson spectrum see Jo Dudek s talk from Tuesday 3

5 Spectroscopy on the lattice Calculate energies and matrix elements (Z) from correlation functions of meson interpolating fields 4

6 Variational Method Consider a large basis of operators matrix of correlators C ij (t) Generalised eigenvector problem: Eigenvalues energies (t >> t 0 ) Eigenvectors optimal linear combination of operators to overlap on to a state Z (n) related to eigenvectors 5

7 Photocouplings on the Lattice Calculate from 3-point correlators: Known from 2-point analysis What we want: parameterize in terms of multipoles ( form factors) and known factors 6

8 Multipoles Multipoles J i = J f k (k > 0) Experimentally measure multipoles at Q 2 = 0 Discrete momenta on the lattice 7

9 Charmonium radiative transitions Caveats: Quenched (no quark loops; no light quarks at all) One lattice spacing (a -1 t = 6.05 GeV) One volume (L s 1.2 fm) Only connected diagrams Only a selection; results and details in Dudek, Edwards & CT, PR D (2009) Also: Dudek et al PR D (2008); Dudek & Rrapaj PR D (2008) 8

10 Exotic 1 -+ Vector 1 -- Spectrum analysis: 1 -+ c1 state found at 4300(50) MeV Exotic quantum numbers can t be fermion-antifermion pair Can t be a molecular/multi-quark state in quenched lattice calc. Strongly suggests a hybrid What about radiative transitions? 9

11 Exotic 1 -+ Vector 1 -- M 1 multipole dominates Same scale as many measured conventional charmonium transitions BUT very large for an M 1 transition Usually M 1 spin flip (e.g. 3 S 1 1 S 0 ) 1/m c suppression Spin-triplet hybrid extra gluonic degrees of freedom M 1 transition without spin flip not suppressed 10

12 Exotic 1 -+ Vector 1 -- M 1 multipole dominates Same scale as many measured conventional charmonium transitions If heavy quark physics is any guide, expect GlueX to produce lots of exotic 1 -+ BUT very large for an M 1 transition Usually M 1 spin flip (e.g. 3 S 1 1 S 0 ) 1/m c suppression Spin-triplet hybrid extra gluonic degrees of freedom M 1 transition without spin flip not suppressed 11

13 Tensor 2 ++ Vector 1 -- E 1, M 2, E 3 Lattice: discrete set of allowed momenta Can t calculate E 1 (0) at > Q M 2 = 0 2 (0) and >> so Eextrapolate: 3 (0) 12

14 Tensor 2 ++ Vector 1 -- E 1, M 2, E 3 PDG08: 406(31) kev Quark models (1 3 P 2 ) kev a 2 = (7) a 2 =M 2 / (E 12 +M 22 +E 32 ) PDG08: -0.13(5) CLEO: (19) [CLEO arxiv: ] Same hierarchy as expected: E 1 (0) > M 2 (0) >> E 3 (0) Ratio M 2 /E 1 is considerably larger than experiment 13

15 Tensor 2 ++ Vector 1 -- E 1, M 2, E 3 Completely different hierarchy! E 3 (0) > M 2 (0), E 1 (0) 14

16 Tensor 2 ++ Vector 1 -- E 1, M 2, E 3 Quark models (2 3 P 2 ) kev Reverted to expected hierarchy: E 1 (0) > M 2 (0) >> E 3 (0) 15

17 Tensor 2 ++ Vector 1 -- Interpretation: single quark transition model In general: J i = J f k (k > 0) E 1, M 2, E 3 (k = 1,2,3) If only a single quark is involved ( 3 P 2 3 S 1 ): j = 3/2 j = 1/2 k = 1,2 only and E 3 = 0 E 1 (0) > M 2 (0) >> E 3 (0) If instead tensor is 3 F 2 ( 3 F 2 3 S 1 ): j = 5/2 j = 1/2 k = 2,3 only and E 1 = 0 E 3 (0) > M 2 (0) >> E 1 (0) 16

18 Tensor 2 ++ Vector 1 -- Interpretation: single quark transition model In general: J i = J f k (k > 0) E 1, M 2, E 3 (k = 1,2,3) Interpretation: If only a single quark is involved ( 3 P 2 3 S 1 ): c2 1 j = 3/2 j = 1/2 3 P 2 k = 1,2 only and c2 E 3 = 1 3 0F 2 E 1 (0) > M 2 (0) >> E 3 (0) c2 2 3 P 2 If instead tensor is 3 F 2 ( 3 F 2 3 S 1 ): j = 5/2 Supported j = 1/2 by spectrum analysis k = 2,3 only and E 1 = 0 E 3 (0) > M 2 (0) >> E 1 (0) 17

19 Tensor 2 ++ Vector 1 -- Belle χ c MeV Needs lattice calc of two-photon coupling Belle [PRL (2006)] 18

20 Vector 1 -- Pseudoscalar 0 -+ Spectrum results [PR D (2008), PR D (2008) ]: 19

21 Vector 1 -- Pseudoscalar 0 -+ Only M 1 [CLEO PRL (2009)] 20

22 Vector 1 -- Pseudoscalar 0 -+ Only M 1 Quark model: spin flip ( 1/m c ) gives suppression is 2 3 S S 0 further suppressed [CLEO PRL (2009)] 21

23 Vector 1 -- Pseudoscalar 0 -+ Loops Li & Zhao [PL B (2008)]: loop contributions in vector psuedoscalar transitions Large loop contrib ( 10 kev) to Interferes with 10 kev bare amp. 1 kev (in line with experiment) But no room for large loop contrib with 0.4(8) kev from quenched lattice Actually loops calc has uncertainties from couplings an phases E.g. use c.f. QM 30 kev Not incompatible with lattice results 22

24 Vector 1 -- Pseudoscalar 0 -+ Only M 1 Quark model: 1 3 D S 0 has same leading Q 2 behaviour as 2 3 S S 0 23

25 Vector 1 -- Pseudoscalar 0 -+ Only M 1 Much larger than other M 1 trans Spectrum analysis suggests a vector hybrid (spin-singlet) Analogous to 1 -+ hybrid to vector trans: M 1 with no spin flip c.f. flux tube model kev 24

26 Scalar 0 ++ Vector 1 -- Only E 1 25

27 Scalar 0 ++ Vector 1 -- Only E 1 26

28 Summary and Outlook Charmonium Summary Method successful: first calc. of excited meson rad. trans. on lattice Hybrid photocoupling is large: M 1 transitions: Non-exotic vector hybrid candidate E 1, M 2, E 3 multipoles; 2 3 P 2, 1 3 F 2 states in Comparison with quark models Outlook Systematically improvable Apply to lighter mesons (unquenched calc.) 27