Questions in Quarkonium Spectroscopy

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1 Questions in Quarkonium Spectroscopy International Workshop on Heavy Quarkonium Steve Godfrey Carleton University/DESY A very brief introduction to potential models Questions in Quarkonium Spectroscopy Summary S. Godfrey, Carleton University/DESY

2 Nora s assignment: have someone review in an exhaustive way which class of predictions/results follow from which class of potential models. * *in 20 minutes S. Godfrey, Carleton University/DESY 2

3 I don t think this is the right question. We must think what we can learn from potential models vs what we can learn from Lattice QCD, NRQCD etc Lattice QCD and NRQCD are more fundamental so ultimately they are the truer test of QCD But at present they are very limited in what they can do Absolutely necessary to test theory against experiment Use the (venerable) Quark Model to point the way: Potential models are an important complement to what we can learn from other approaches to acquire intuition to the physics to give direction to physics studies S. Godfrey, Carleton University/DESY 3

4 In the spirit of HQWG I will highlight where I feel we can make the most progress Questions in Quarkonium Spectroscopy:. P vs 3 P cog mass distinguish models 2. 3 D J masses test spin dependent splittings 3. E transitions 4. M transitions 5. Coupled Channel effects 6. 2γ widths (not covered) S. Godfrey, Carleton University/DESY 4

5 Introduction to potential models Meson quantum numbers characterized by given J PC : S L S 2 S = S + S 2 J = L + S P = (-) L + C = (-) L + S For given spin and orbital angular momentum configurations & radial excitations generate our known spectrum of light quark mesons S. Godfrey, Carleton University/DESY 5

6 Spin-dependent potentials: Lorentz structure of confining potential: scalar? vector? pseudoscalar? Lorentz vector -gluon exchange + scalar confinement Spin-dependent interactions are (v/c) 2 corrections Spin-spin interactions: 3 S S y Spin-orbit interactions: P S 0 h c c 2 ( 3 P 2 ) c ( 3 P ) c 0 ( 3 P 0 ) S. Godfrey, Carleton University/DESY 6

7 . P vs 3 P cog mass distinguish models In QM triplet-singlet splittings test the Lorentz nature of the confining potential Relativistic effects important validation of lattice QCD calculations NRQCD calculations Observation of P states is an important test of theory S. Godfrey, Carleton University/DESY 7

8 Wide variation of theoretical predictions: QM QM QM PQCD lattice EFG S. Godfrey, Carleton University/DESY 8

9 Quark Potential Models with -gluon exchange: H hyp qq 32π αs = m m S r S 3 q r qδ ( r ) 9 q q δ function is short range but smeared by relativistic effects modeled by a Gaussian. gives M( 3 P cog ) > M( P ) Godfrey & Isgur, PR D32, 89 (985) but with spin-independent relativistic corrections McClary & Byers find M( 3 P cog ) < M( P ) McLary & Byers, PR D28, 692 (983) Introducing long range Lorentz Vector Franzini finds: M( 3 P cog ) < M( P ) Franzini, PL B296, 99 (992) S. Godfrey, Carleton University/DESY 9

10 Perturbative QCD: M( 3 P cog ) < M( P ) Pantaleone and Tye, PR D37, 3337 (988) -ve for N f > 0 but other possible contributions; long-range, relativistic, coupled channel.. Lattice QCD: M( 3 P cog ) > M( P ) Ultimately the definitive answer Need more precise results. NRQCD people: Please calculate this! wide variation in predictions indicates need for experimental data S. Godfrey, Carleton University/DESY 0

11 Production of the singlet P-wave states Most promising approach: Υ(3S) h b + π η b + γ + π ψ(2s) h c + π η c + γ + π BR[Υ(3S) π P ] = 0.% S.G + J. Rosner, PR D66,0402 (2002) Γ[ hb ( P ) ηb ( S0) + γ ] = αeq S0 r P ω = 37 kev Γ[ hb ( P ) ggg] = Γ[ χb ( P ) qqg] = kev 2n f BR[Υ(3S) π P S 0 γ]=4 x events/0 6 Υ(3S) s BR[ ψ(2s) π P S 0 γ ] = 3.8 x event /0 6 ψ(2s) s S. Godfrey, Carleton University/DESY

12 2. 3 D J masses test spin dependent splittings CESR/CLEO has just completed high statistics run at Υ(3S) Expect very rich spectroscopy S. Godfrey, Carleton University/DESY 2

13 There is still some question about the Lorentz structure of the qq potential vector -gluon exchange + scalar confinement vector -gluon exchange + colour electric confinement + more complicated structures because the D-waves are larger they will feel the long range spin-dependent potential more than the P-waves observation of 3 D J would be important in understanding the Lorentz structure of the confining potential see Eichten & Feinberg PRL 43, 205 (979) Pantaleone Tye & Ng PR D33, 777 (986); Buchmuller Ng & Tye PR D24, 3003 (98) Gupta Radford & Repko PR D26, 3305 (982); Gromes, Z. Phys C22, 265 (984).. S. Godfrey, Carleton University/DESY 3

14 3. E transitions McClary and Byers, PR D28, 692 (983) E decays sensitive to nodes in wavefunction radiative transitions tests internal structure Γ = 4 eqαc( Ji Li J f Lf S) P r S 3 ω 2 3 S. Godfrey, Carleton University/DESY 4

15 Including relativistic corrections corresponds to using eigenfunctions and eigenvalues of the Breit-Fermi Hamiltonian (Siegert s theorem) S. Godfrey, Carleton University/DESY 5

16 Relativistic effects gives differences between E matrix elements: 2P r 3S = 2. 7 ± 0. 2 GeV P r 3 S P r 3 S P r 3 S GeV GeV GeV P r 2S ± 9. ± 0. 2 GeV P r 2 S P r 2 S P r 2 S 3. 0 GeV GeV GeV see also McClary and Byers, PR D28, 692 (983) S. Godfrey, Carleton University/DESY 6

17 Node in 3S wavefunction near maximum in P wavefunction so large cancellation very sensitive to details of the wavefunctions 3 3 P r 3 S GeV S. Godfrey, Carleton University/DESY P r 3 S GeV P r 3 S GeV - -

18 Matrix elements sensitive to relativistic corrections via shifts in nodes in wavefunctions there can big difference in matrix elements (not clear what exactly CLEO did) More useful to compare individual matrix elements to test relativistic corrections transitions involving D-waves would be interesting tests Angular distributions also provide additional information S. Godfrey, Carleton University/DESY 8

19 Can use angular distributions in E transitions to probe internal structure eg 3 3 S D mixing in charmonium ψ ' γ + χ and χ γ + ψ J SG, G. Karl, P.O Donnell, Z. Phys. C3, 77 (986) Parametrize the contribution with the parameter ζ: Where θ is the J 3 D 3 ς = tanθ 2 S 3 D 3 3 D S r r P P mixing angle 3 3 J J S. Godfrey, Carleton University/DESY 9

20 For θ and θ the angles between the photon and either lepton in the ψ or ψ rest frame the angular distributions are of the form: β β β 0 2 = = = J 2 W ( θ, θ ) + β cos ( θ, θ ) ζ ζ ε ζ + ζ 2 + ζ ζ ε ζ + ζ To first order in ε = ξkγ / 4m c ξ=+ for χ γψ ξ= for ψ γχ One could make a quantitative determination of the Mixing angle with new, more precise, measurements. S. Godfrey, Carleton University/DESY 20

21 4. M transitions: production of η b (ns)) states Proceeds via magnetic dipole (M) transitions: Υ(nS) η(n S) ) + γ S.G + J. Rosner, Phys Rev D64, 0740 (200) Γ e Q 2 3 ( S S0 + γ ) = α f j 2 0( kr/ 2) i ω 3 mq Hindered transitions have large phase space Relativistic corrections resulting in differences in 3 S and S 0 wavefunctions due to hyperfine interaction S. Godfrey, Carleton University/DESY 2

22 Υ(3S) (Γ tot =52.5 kev) Υ(2S) (Γ tot =44 kev) Υ(S) (Γ tot =26.3 kev) Transition 3 S0 2 S0 S0 2 S0 S0 S0 BR (0-4 ) Expect substantial rate to produce η b s Also Υ(3S) h b ( P ) ππ η b + γ + ππ BR=0.-% BR = 50% [Kuang & Yan PRD24, 2874 (98); Voloshin Yad Fiz 43, 57 (986)] S. Godfrey, Carleton University/DESY 22

23 But no signal found! Ebert Faustov Galkin Is there a problem? S. Godfrey, Carleton University/DESY 23

24 Does not appear due to wavefunction effects like in E transitions: BR=2.3 x 0-3 BR=2.4 x 0-3 Not much difference Most likely due to poorly understood relativistic effects: I 2 2 r2 r2 k r 2 p p V = m 6 m m the last term is due to pair creation in the binding potential see Sucher, Rep. Prog. Phys 4, 78 (978), Kang & Sucher PR D8, 2698 (978), Feinberg & Sucher, PRL 35, 740 (975); Grotch Owen & Sebastian PR D30, 924 (984), Zabetakis & Byers PR D28, 2908 (983) S. Godfrey, Carleton University/DESY 24 Q Q S Q

25 5. Coupled Channel effects See talk by Eichten Interaction Hamiltonian: Eichten et al, Phys Rev D7, 3090 (978); D2, 203 (980). Pair produced in pseudoscalar static potential produces S state S. Godfrey, Carleton University/DESY 25

26 Expected to be most important for states near threshold Induces splittings of states of different J with same L Mechanism induces strong 2 3 S - 3 D mixing in charmonium: Shifts M( 2 3 S )=mass 8 MeV vs M( 3 S )=-48 MeV explains large 3 D leptonic width predicts 3 3 S -2 3 D mixing in bottomonium and possibly also 4 3 S -3 3 D No work on this important subject since! S. Godfrey, Carleton University/DESY 26

27 Summary In the last decade there has been much theoretical progress especially in lattice QCD and NRQCD. Need comparable experimental results to compare to theoretical results and to understand the nature of confinement in QCD. Theory and experiment go hand in hand First narrow bb state observed in 9 years! Only long lived L=2 meson This result has created considerable interest in the theory community I strongly urge Cornell to continue gathering data on the upsilon system S. Godfrey, Carleton University/DESY 27