1. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 1 Juan-Luis Domenech-Garret a & Miguel-Angel Sanchis-Lozano b, * a) Departament MACS, Física Aplicada, Universitat de LLeida, Spain b) Departament de Física Teòrica & IFIC, Universitat de València – CSIC, Spain Leptonic decays, the nature of heavy quarkonia and velocity counting rules *email: mas@ific.uv.es

2. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 2 Weak and strong coupling regime of heavy quarkonium states Weak coupling regime: the binding is essentially due to a Coulombic-like potential. States below QQ threshold and not too deep Λ QCD < mv 2 are expected in the weak or perturbative regime Strong coupling regime: the binding is essentially due to the confining potential. States deep in the potential are expected Λ QCD > mv 2 in the strong or non-perturbative regime ~ ~ In hep-ph/0511167 X. Garcia i Tormo and J. Soto employed radiative decays to obtain important information on the nature of  resonances. We present here a related idea using leptonic decays It is important to know the nature of heavy quarkonia, for example to calculate rates of hindered transitions between  (nS) and η b (n’S) states Brambilla, Vairo and Jia [hep-ph/0512369] relevant for hunting η b states

3. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 3 Leptonic partial widths in  decays Leptonic partial widths are a probe of the compactness of the quarkonium system providing important information complementary to spectroscopy. NRQCD matrix (color-singlet and –octet) elements can be related to wave functions at the origin. Potential models can provide the latter though they can also be obtained without resorting to data fitting (e.g. lattice). Still open questions about the accuracy (e.g. power counting in the non-perturbative situation) and consistency within NRQCD! There are different possible countings e.g., Brambilla et al hep-ph:0208019 Beneke hep-ph/9703429, Fleming, Rothstein and Leibovich hep-ph/0012062 Test of lepton universality (talk at BSM session) [arXiv:0709.3647] BF[  ee] = BF[  μμ] = BF[  ττ] K(x) ≈ 1 Therefore, a good knowledge of the  system is a basic ingredient for seeking new physics if lepton universality were (slightly) broken

4. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 4 Partial decay width accoording to pNRQCD N. Brambilla et al [hep-ph/0208019] Let us start with the general expression for the leptonic decay width of a vector resonance (in the strong-coupling regime) :  i, B i : 6 universal (flavor and state independent) non-perturbative gluonic parameters m: heavy (bottom) quark mass ExpTheory Notably those not depending on “n” N. Brambilla et al hep-ph/0208019

5. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 5 Radial wave functions at the origin: |R n (0) (0)| 2 Potential : Cornell (1) Cornell (2) Screened (2) Buchmüller-Tye (1)  (1S) 14.05 12.23 12.22 6.477  (2S) 5.665 4.797 4.795 3.234  (3S) 4.271 3.581 3.579 2.474 Units of GeV 3 Static potential: * PDG (1) Eichten and Quigg, hep-ph/9503356 (2) P. Gonzalez et al, hep-ph/0307310 Experimental values of partial*  ee [  (1S)]  ee [  (2S)]  ee [  (3S)] 1.340 ± 0.018 0.612 ± 0.011 0.443 ± 0.008 In units of keV Error in the ratios ≈ few %

6. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 6 Velocity counting rules Suggested by latice studies Koma et al. hep-ph/0607009 Spin-independent perturbative regimenon-perturbative regime conservative

7. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 7 Comparing theory versus experiment Collects all uncertainties from the radial wave functions and δ nr + exp error Exp Theory INPUT: O ( v q ) OUTPUT: ?

8. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 8 Extraction of non-perturbative parameters The value of  3 at μ=5 MeV can be extracted from Experimental data from  leptonic decays, wavefunctions from potential models and our evaluation of δ nr suggest small  3 values  (1GeV) = 3.6 ± 5.3 ± 3.6 2.9 3.5 2.2  3 (5 GeV) = 2.6 5.3 hep-ph/0109130 hep-ph/0007003

9. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 9 Results Potential : Cornell (1) Cornell (2) Screened (2) Buchmüller-Tye (1) Δ 13 (%) 33 37 37 17 Δ 12 (%) 28 31 31 12 Δ 23 (%) 8 10 10 8 | R n (0) (0) | 2 ? using the V LO in potential model calculations We conclude: q = 2 is favored unless cancellations between different sectors happen Note that Δ nr is systematically positive  the leptonic width ratio is overestimated by the theory  (1S,2S,3S),  3 (m b ) =3.6 Spectrocopy effects of V (1) /m in the lattice potential: good (better) agreement between predicted and experimental mass levels ( ≈ several tens of MeV) for the bottomonium family (on-going analysis)

10. QWG5 DESY October 2007 Miguel A. Sanchis-Lozano IFIC-Valencia 10 Conclusions In the leptonic decays of heavy quarkonium several parameters cancel out in the ratios of partial widths Still the ratio is sensitive to the gluonic universal parameter  3 Experimental data on  (nS) leptonic decays together with the values of the wave functions at the origin obtained from potential models favor:  (2S) and  (3S) belonging to the strong regime, while  (1S) to the weak regime A not so conservative power counting, as naively expected from dimensional counting in the non-perturbative regime. Low values for  3 More precise experimental measurements of leptonic decays should shed light on the nature of  resonances, to be of great help in the search for new physics effects, e.g., at high-luminosity (Super) B factories

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