exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

Analysis of the Kl3K
form factors
l3
IPNO Participation: Véronique Bernard, Jan Stern (malheureusement décédé au cours du travail)
Collaboration : Bern (Suisse), LUTH, Valence (Espagne)
Une paramétrisation dispersive du facteur de forme scalaire changeant l’étrangeté a été introduite, guidée
par le théorème de Callan-Treiman, permettant de tester le Modèle Standard (MS). Elle a été étendue au
facteur de forme vecteur. Sa robustesse a été étudiée en détail. En particulier, la dépendance en cut-off,
les effets de brisure d’isospin et la présence possible de zéro ont été discutés. Les résultats publiés de
KTeV ont été réanalysés à l’aide de cette paramétrisation et un bon accord avec le MS a été obtenu. La
connaissance de la valeur du facteur de forme vecteur à zéro moment transféré permet de déterminer l’élément
de matrice CKM, V us et conduit donc à un test supplémentaire du MS. Cette valeur a été obtenue
en QCD sur réseau. Toutefois une extrapolation chirale est nécessaire pour passer des valeurs des
masses de quarks atteintes aujourd’hui sur réseau aux valeurs physiques. Une première étude exploratoire
a été faite dans le cadre de la théorie chirale des perturbations (théorie effective du MS) à deux boucles.
Experimental information on the shape of the
strangeness changing vector and scalar form factors
f 0 and f + can be obtained from the study of K l3
decays. These quantities indeed enter the differential
decay rates of these semi-leptonic processes.
One of the main aim of these experiments is the
extraction of the CKM matrix element V us providing
a test of the Standard Model (SM). A dispersive
parameterization of f 0 [1] allows for another
test by the measurement of its only parameter, the
the two collaborations of 2.1σ. We have, in collaboration
with KTeV [3], reanalyzed their data
confirming the KLOE result with a value of lnC=
0.195 ± 0.0122 in good agreement with the SM.
At the same time that these efforts are put in testing
the SM, lots of progress has been made in
QCD lattice calculations. One important progress
in the light quark sector concerns the values of the
quark masses that can now be reached. These are
very close to the physical ones making a controlled,
i.e. trustable, chiral extrapolation of the lattice
results to the physical points possible. A very
powerful model-independent framework to perform
this extrapolation is Chiral Perturbation Theory
(ChPT), the Effective Field Theory of QCD at low
energies. Indeed it allows to calculate low-energy
QCD processes in terms of the light pseudoscalar
meson masses. The scalar form factor has been
studied on the lattice [4]. Some parameterization of
its momentum-dependence plus the knowledge of
the one-loop ChPT result at zero momentum trans-
Fig.1: Dispersive representation of the scalar
form factor. The blue lines delimits the physical
region of K l3 decays. For comparison two different
values of lnC have been used. The black/red
band take care of all the uncertainties discussed.
value of the form factor at the so-called Callan-
Treiman point, f 0 (Δ Kπ )≡C where Δ Kπ ≡ m 2 K -m 2 π with
m π and m K the pion and kaon mass respectively.
This value is indeed known from a soft pion theorem
derived in the sixtees by Callan and Treiman.
Due to the importance of such a measurement it is
mandatory to make a detailed study of the robustness
of the dispersive parameterization [2]. Fig.1
shows the result of such an analysis. Experimentally
a reanalysis of the data by the NA48 and
KLOE collaboration with the dispersive parameterization
was done with a difference in the result of
Fig.2 Momentum dependence of the scalar
form factor. The result of the fit is shown
(solid line) as well as the convergence of the
chiral expansion. The dash dotted line is the
result at leading order, the dashed line displays
the one up to next to leading order.
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