Physics Letters B 730 (2014) 336–341
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Physics Letters B
www.elsevier.com/locate/physletb
Generalized heavy-to-light form factors in light-cone sum rules
Ulf-G. Meißner
a,b
,Wei Wang
a,∗
a
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany
b
Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany
article i nfo abstract
Article history:
Received 16 December 2013
Received in revised form 3 February 2014
Accepted 5 February 2014
Availableonline13February2014
Editor: A. Ringwald
We study the form factors for a heavy meson into the S-wave K π/ππ system with an invariant mass
below 1 GeV. The mesonic final state interactions are described in terms of the scalar form factors,
which are obtained from unitarized chiral perturbation theory. Employing generalized light-cone distri-
bution amplitudes, we compute the heavy-to-light transition using light-cone sum rules. Our approach
simultaneously respects constraints from analyticity and unitarity, and also takes advantage of the power
expansion in the 1
/m
b
and the strong coupling constant.
© 2014 Elsevier B.V. Open access under CC BY license.
Funded by SCOAP
3
.
1. Introduction
B decays into a light vector meson are of particular interest
as they can provide valuable information to extract the Standard
Model (SM) parameters and therefore test the SM. In the case that
large deviations from the SM calculations are found, these will
shed light on new physics scenarios. Examples for such type of de-
cays include e.g. the process B
→ ρ(→ ππ)l
¯
ν for the extraction of
the CKM matrix element |V
ub
|, the reaction B → K
∗
(→ Kπ)l
+
l
−
to test the chirality structure in weak interaction, and the decay
B
s
→ J/ψφ(→ K
¯
K ) to determine the B
s
–
¯
B
s
mixing phase. Recent
experimental data on these channels can be found in Refs. [1–4].
Due to the short lifetime, the light vector meson cannot be di-
r
ectly detected by experiments and must be reconstructed from
the two or three pseudo-scalars
π/K final state. Thus these de-
cay modes are at least four-body processes and the semi-leptonic
ones are refereed to as B
l4
decays in the literature [5] (for a recent
dispersion theoretical approach to this reaction, see Ref. [6]). To se-
lect candidate events and suppress the combinatorial background,
experimentalists often implement kinematic cuts on the invariant
mass. During this procedure various partial waves of the K
π/ππ
system may get entangled and bring dilutions to physical observ-
ables. Particularly it is very likely the S-wave contributions are of
great importance [7–29]. Therefore it is mandatory to have reliable
and accurate predictions considering the high precision achieved
or to be achieved by experiments.
Decay amplitudes for semi-leptonic B deca
ys into two light-
pseudo-scalar mesons show two distinctive features. On the one
hand, the final state interaction of the two pseudo-scalars should
*
Corresponding author.
E-mail address: weiwang@hiskp.uni-bonn.de (W. Wang).
satisfy unitarity and analyticity. On the other hand, the b mass
scale is much higher than the hadronic scale, which allows an
expansion of the hard-scattering kernels in terms of the strong
coupling constant and the dimensionless power-scaling parameter
Λ
QCD
/m
b
. In this Letter, we aim to develop a formalism that makes
use of both these advantages. It simultaneously combines the per-
turbation theory at the m
b
scale based on the operator product
expansion and the low-energy effective theory inspired by the chi-
ral symmetry to describe the S-wave
ππ and K π scattering. For
concreteness, we will choose the B → K π matrix elements with
the K π invariant mass below 1 GeV as an example in the follow-
ing, while other processes including the charm meson decay can
be treated in an analogous way. If the factorization can be proved,
these form factors will also play an important role in the study of
charmless three-body B decays [30–33].
2. Generalized form factor
The matrix elements
(K π)
0
(p
Kπ
)
¯
s γ
μ
γ
5
b
¯
B(p
B
)
=−
i
1
m
Kπ
P
μ
−
m
2
B
− m
2
K
π
q
2
q
μ
F
B→K π
1
m
2
K
π
,q
2
+
m
2
B
− m
2
K
π
q
2
q
μ
F
B→K π
0
m
2
K
π
,q
2
,
(
K π)
0
(p
Kπ
)
¯
s σ
μν
q
ν
γ
5
b
¯
B(p
B
)
=−
F
B→K π
T
(m
2
K
π
,q
2
)
m
Kπ
(m
B
+ m
Kπ
)
q
2
P
μ
−
m
2
B
− m
2
K
π
q
μ
(1)
define the S-wave generalized form factors F
i
[16]. Here, P =
p
B
+ p
Kπ
and q = p
B
− p
Kπ
.
http://dx.doi.org/10.1016/j.physletb.2014.02.009
0370-2693 © 2014 Elsevier B.V. Open access under CC BY license. Funded by SCOAP
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