Juan-Luis%20Domenech-Garret%20a%20%20

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Leptonic decays, the nature of heavy
quarkonia and velocity counting rules

• 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
email mas_at_ific.uv.es
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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
• ?QCD lt mv2 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
• ?QCD gt mv2 in
  the strong or non-perturbative regime

It is important to know the nature of heavy
quarkonia, for example to calculate rates of
hindered transitions between ?(nS) and ?b(nS)
states Brambilla, Vairo and Jia hep-ph/0512369
relevant for hunting ?b states
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
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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-ph0208019
• Beneke hep-ph/9703429, Fleming, Rothstein
  and Leibovich hep-ph/0012062
• Test of lepton universality (talk at BSM session)
  arXiv0709.3647
• BF??ee BF??µµ
  BF??tt K(x) 1
• Therefore, a good knowledge of the ? system
  is a basic ingredient
• for seeking new physics if lepton
  universality were (slightly) broken

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Partial decay width accoording to pNRQCD
Let us start with the general expression for the
leptonic decay width of a vector resonance (in
the strong-coupling regime)
N. Brambilla et al hep-ph/0208019
m heavy (bottom) quark mass
?i , Bi 6 universal (flavor and state
independent) non-perturbative gluonic parameters
N. Brambilla et al hep-ph/0208019
Notably those not depending on n
Exp
Theory
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Radial wave functions at the origin Rn(0)
(0)2
Experimental values of partial
In units of keV
?ee?(1S) ?ee ?(2S)
?ee?(3S) 1.340 0.018
0.612 0.011 0.443 0.008
Error in the ratios few
Units of GeV3
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
Static potential
PDG (1) Eichten and Quigg, hep-ph/9503356 (2)
P. Gonzalez et al, hep-ph/0307310
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Velocity counting rules
perturbative regime
non-perturbative regime
Suggested by latice studies Koma et al.
hep-ph/0607009
Spin-independent
conservative
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Comparing theory versus experiment
?
INPUT
OUTPUT
Exp
O (v q)
Theory
Collects all uncertainties from the radial wave
functions and dnr exp error
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Extraction of non-perturbative parameters
3.6
3.6 5.3
2.6 5.3
2.9
?(1GeV)
?3(5 GeV)
3.5
2.2
hep-ph/0109130 hep-ph/0007003

• The value of ?3 at µ5 MeV can be extracted from
• Experimental data from ? leptonic decays,
  wavefunctions from
• potential models and our evaluation of dnr
  suggest small ?3 values

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Results
?(1S,2S,3S), ?3 (mb) 3.6
Potential Cornell (1) Cornell (2)
Screened (2) Buchmüller-Tye(1) ?13()
33 37
37 17 ?12()
28 31
31 12 ?23()
8 10
10 8
Note that ?nr is systematically positive ? the
leptonic width ratio is overestimated by the
theory
Rn(0) (0) 2 ? using the VLO in potential
model calculations
We conclude q 2 is favored unless
cancellations between different sectors happen
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)
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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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