Charmonium Transitions

Transcription

1 Hans Kuipers & Maikel de Vries Student Seminar on Subatomic Physics October 14, 2009

2 Outline

3 n 2S+1 L J J PC

4 Aspects of charmonium Charmonium is a mesonic bound state of c c. Charmonium produced in e e + -collisions via intermediate photon, so J PC = 1. Examples of transitions ψ γη c (radiative) ψ J/ψ + π + π (hadronic) Open-charm threshold

5 Open-charm threshold The open charm threshold ( 3.73 GeV) is the energy above which the c c have enough energy to separate, creating both an q q pair to form two charmed mesons. The lightest charmed meson D 0 has a mass of 1865 MeV/c 2. A pair D 0 D 0 gives the open charm threshold.

6 Why charmonium physics? Heavy quarkonia are the simplest objects for studying the physics of hadrons due to their nonrelativistic nature. From virial theorem: T 1 2 V M(2c) GeV/c 2 = 3.0 GeV/c 2 M(ψ ) 3.7 GeV/c 2 V 700 MeV/c 2 So T 350 MeV/c 2 which is much smaller than the quark masses. c c is the lightest meson which is heavy. Energy scale reachable with BES-accelerator (2-5 GeV).

7 What are possible transitions? Weak decay, e.g. c c q c Annihilation, c c γγ h Hadronic, c c hc c Radiative c c γc c

8 Hadronic branching ratio are important decay mode of heavy quarkonia. Branching ratio for ψ hj/ψ is approximately 60%.

9

10 Potential models Solve Lattice QCD or Hψ = (E V )ψ Different potential models possible: Cornell potential Buchmüller-Grunberg-Tye (BGT) Model Godfrey-Isgur model

11 Cornell potential Short distance one-gluon exchange: Coulomb-like potential V (r) = 4 α s (r) 3 r Linear term from quark confinement (from QCD) Cornell potential V (r) = σr V (r) = 4 α s (r) + σr 3 r

12 Charmonium potential Cornell potential plus corrections give total charmonium potential: V (r) = 4 3 α s (r) +σr+v LS +V SS +V T r

13 Simple harmonic oscillator The σr-term causes an upward energy shift for the P-levels.

14 Fine structure splitting V LS = ( L S) 2m 2 cr [ 3 dv V dr dv ] S dr

15 Hyperfine splitting Spin Spin interaction (colour contact) m(j/ψ, η c ) V SS = 2( S 1 S 2 ) 3m 2 c 2 V V (r)

16 Tensor correction (colour tensor interaction) Splits L 0 multiplets. 2 [3( S 1 r)( ] S 2 r) S 2 [ 1 dv V V T = 12mc 2 d 2 ] V V r dr dr 2

17 Other models BGT-model Starts from momentum Fourier transform of potential more accurate on confining term Godfrey-Isgur model is a relativized extension of the nonrelativistic model.

18 Measurements

19 Model testing hyperfine splitting of 2S-states V SS = 2( S 1 S 2 ) 3m 2 c 2 V V (r) NR model prediction: m(ψ ) m(η c) = 42 MeV Measurement: m(ψ ) m(η c) = 48.3 ± 4.4 MeV spin-spin corrections hyperfine splitting of the P-states predict the measured mass splitting

20 Transition scheme: Φ I Φ F + h Typical momentum of emitted gluons is low, so perturbative QCD is not valid. QCD Multipole Expansion (QCDME) Works to predict hadronic c c transition rates.

21 QCD Multipole Expansion Gluon field vector potential, so colour magnetic and colour electric fields in low energy regime. Wave functions from potential models.

22 QCD Multipole Expansion M E1E1 = i g 2 E 6 KL Φ F x k KL KL x l Φ I h Ek a E I E E l a 0 KL

23 EM decays are like strong decays, but with photons as interaction bosons. EM transitions rates are a factor 100 less than strong transition rates. α S /α EM 100

24 Applying QCDME to ππ transitions Transition ni 3S 1 nf 3 S 1 + π + π is dominated by electric dipole transition (E1E1). Transition rate: Γ(nI 3S 1 nf 3 S 1ππ) = C 1 2 G f n I 0n F 0 G is the phase space factor. Its influence on Γ is known. f LP I P F n I l I n F l F is the QCDME vertex and can be calculated. C1 is the hadronization vertex and needs to be determined from experiment. Look at ψ J/ψ + π + π to determine C1. Γtot (ψ ) = 277 ± 22keV. B(ψ J/ψπ π + ) = (31.8 ± 0.6)%. B(ψ J/ψπ 0 π 0 ) = (16.46 ± 0.35)%.

25 Applying QCDME to ππ transitions QCDME is used to predict bottonium transition rates. Predictions of both potential models agree quite well. QCDME is a feasible approach to study heavy quarkonia. Relativistic corrections are needed near open-charm threshold. equivalent decay η c η c + π + π yet to be measured at BES-III.

26 G-parity G-parity is a multiplicative quantum number that results from the generalization of C-parity to multiplets of particles. π + π + G π 0 = η G π 0 where η G = ±1 are the eigenvalues of π π G-parity. G-parity is a combination of charge conjugation and an isospin rotation. G = C e (iπi2), where C is the C-parity operator and I 2 is an isospin operator. Charge conjugation and isospin are preserved by the strong interaction, and so is G-parity. Weak and EM interactions violate G-parity.

27 Selection rules strong interaction does not violate G-parity Gπ 0,± = π 0,± & Gη = η. η G = ( 1) S+L+I for f f. Only strong interaction for transitions with: S + L = odd, odd number of pions; S + L = even, even number of pions. EM-transitions violate G-parity

28 Examples of transitions ψ π + π J/ψ G-parity conserved, strong decay. ψ π + π π 0 η c G-parity conserved, strong decay. ψ π 0 h c G-parity violating, EM-decay.

29 Branching ratios of ψ hj/ψ: Clear difference between EM and strong transitions, c.f. π 0 π 0 J/ψ with π 0 J/ψ. are important decay modes (59.5 %).

30 Φ I Φ F + γ. Equivalent to the hydrogen atom.

31 Selection rules E1-transitions Parity violating S = 0 & L = ±1 M1-transitions Parity conserving S = ±1 & L = 0 J > 1 transitions P conserving: M1, E2, M3,... P violating: E1, M2, E3,...

32 Examples of transitions ψ γχ cj, J = 0, 1, 2 E1, E1/M2, E1/M2/E3 for J=0,1,2. No M1, E2 or M3 due to parity conservation. ψ γη c M1 transition, S = 1, parity conserved. ψ γh c why not?

33 Experimental data

34 Measurements at BES-III Below the open-charm threshold there are still a lot of transitions that need to be measured. BES-III has the highest production rate of ψ, thus it is well equipped for measuring these transitions. For example the the states η c and h c, of which is very little known at this moment. Also states above the open-charm threshold are of interest.

35 Charmonium has a high branching ratio for hadronic decays, which makes it useful for QCD research. BES-III is the best detector in the field of charmonium transitions. QCDME and the potential models can be tested to a higher accuracy with BES-III.

36 References 1. IHEP-Physics-Report-BES-III v1, Editors: Kuang-Ta Chao and Yifang Wang, pp CERN report on Heavy Quarkonium Physics, Editors: N. Brambilla et al., pp Yu-Ping Quang, QCD Multipole Expansion and Hadronic Transitions in Heavy Quarkonium Systems, arxiv.org/abs/hep-ph/ v2