Non-Standard Physics in Leptonic and Semileptonic Decays of Charmed Mesons Page: 2 of 9
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1. Introduction
Recent years have witnessed significant improvements in charmed-meson leptonic and semilep-
tonic decays, both in experimental measurements and in calculations of the hadronic transition am-
plitudes with lattice QCD. A puzzle has arisen, namely a discrepancy of approximately 3.5- in the
rate of the leptonic decay DS -> fv, where f is a muon or 2 lepton [1]. If the measured counts have
not fluctuated high, and the lattice QCD calculations are confirmed (by further calculations with
2+1 flavors of sea quarks), then this may be a signal of physics beyond the Standard Model [2].
If non-Standard interactions mediate cs -> vi, then they also alter, at some level, the rate and
q2-distribution of D -> Kpv. (D -> Krv is kinematically forbidden.) In this paper, section 2 recalls
the origin of the leptonic discrepancy, incorporating new, preliminary results. Section 3 updates the
new-physics analysis of Ref. [2] and extends it to encompass semileptonic decays. Then section 4
discusses the phenomenology of semileptonic decays in the context of new physics. For lattice
QCD the main conclusion, discussed in section 5, is that precise calculations of the semileptonic
form factors, including a tensor form factor defined below, are vital.
2. Leptonic Decays
In the Standard Model the partial width for DS -> fvf is
F(DS -> fvf) = 87f IGFVsm 2 (1 - M2/ms , (2.1)
where the decay constant fDs is defined by (OsYP Y5cjD,(p)) = ifDspP, and is also computed via
(+ms) (0sycID,(p)) = -ifDsm ; PCAC ensures that the two definitions are the same. The par-
tial widths are small: for muonic decays owing to the helicity-suppression factor m2; for r-leptonic
decays owing to the phase-space factor (1 - m2/m2)2. Experiments measure the branching frac-
tion B = FZDs but usually quote fDs assuming that no non-Standard amplitude contributes to F.
In this sense, fDs has been measured recently by the BaBar [3], Belle [4], and CLEO [5, 6] Col-
laborations. The experiments measure B(DS -> fv) directly, without complicated modeling of the
events or background, and the experimental errors are principally statistical. Radiative corrections
are at most 1-2%, and the discrepancy cannot be explained with any value of IV,, consistent with
a unitary n x n CKM matrix [2]. In summary, it seems sound to take the experimental measure-
ments of fDs at face value, yielding Table 1. Treating both statistical and systematic uncertainties
in quadrature, the average of the measurements in Table 1 is
fDs expt avg = 272 8 MeV (2.2)
combining p v and rv and including new results reported by CLEO at conferences through Septem-
ber 2008 [7]. Separate averages for the two final states are in Table 1.
Now let us turn to lattice QCD calculations of fDs. There are two calculations with 2+1 flavors
of sea quarks, the first from the Fermilab Lattice and MILC Collaborations [8] and more recently
from the HPQCD Collaboration [9]. These are
fDs HPQCD = 241 3 MeV, fDs Fermilab-MILC = 249 11 MeV, (2.3)
where the Fermilab-MILC result is an update presented at this conference by Mackenzie [10]. Both
calculations use the improved staggered Asqtad action for the sea quarks, taking advantage of the2
Non-Standard sc -vf
Andreas S. Kronfeld
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Kronfeld, Andreas S. Non-Standard Physics in Leptonic and Semileptonic Decays of Charmed Mesons, article, December 1, 2008; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc899764/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.