Physics Letters B 757 (2016) 330–333
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
From
b
→
b
π to
c
→
c
π
Michael Gronau
a,∗
, Jonathan L. Rosner
b
a
Physics Department, Technion, Haifa 32000, Israel
b
Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
29 March 2016
Accepted
6 April 2016
Available
online 11 April 2016
Editor:
G.F. Giudice
Using a successful framework for describing S-wave hadronic decays of light hyperons induced by a
subprocess s → u(
¯
ud), we presented recently a model-independent calculation of the amplitude and
branching ratio for
−
b
→
b
π
−
in agreement with a LHCb measurement. The same quark process
contributes to
0
c
→
c
π
−
, while a second term from the subprocess cs → cd has been related by
Voloshin to differences among total decay rates of charmed baryons. We calculate this term and find
it to have a magnitude approximately equal to the s → u(
¯
ud) term. We argue for a negligible relative
phase between these two contributions, potentially due to final state interactions. However, we do not
know whether they interfere destructively or constructively. For constructive interference one predicts
B(
0
c
→
c
π
−
) = (1.94 ± 0.70) × 10
−3
and B(
+
c
→
c
π
0
) = (3.86 ± 1.35) × 10
−3
. For destructive
interference, the respective branching fractions are expected to be less than about 10
−4
and 2 ×10
−4
.
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Most decays of charmed and beauty baryons observed up to
now occur by c and b quark decays. In strange heavy flavor baryons
an s quark may decay instead via the heavy flavor conserving sub-
process
s → u(
¯
ud) or su → ud, with the c or b quark acting as
a spectator. In strange charmed baryons an additional Cabibbo-
suppressed
subprocess cs →cd can contribute. Early investigations
of heavy flavor conserving two body hadronic decays of charmed
and beauty baryons involving a low energy pion have been per-
formed
in Ref. [1–6]. In these studies a soft pion limit, partial
conservation of the axial-vector current (PCAC) and current algebra
have implied expressions for decay amplitudes in terms of ma-
trix
elements of four-fermion operators between initial and heavy
baryon states. These matrix elements are difficult to estimate and
depend strongly on models for heavy baryon wave functions.
Recently
we proposed a model-independent approach for study-
ing
the decay
−
b
→
b
π
−
[7] which had just been observed by
the LHCb collaboration at CERN [8]. In the heavy b quark limit this
decay by s → u(
¯
ud) proceeds purely via an S-wave. Assuming that
properties of the light diquark in
−
b
are not greatly affected by
the heavy nature of the spectator b quark, the decay amplitude
for
−
b
→
b
π
−
may be related to amplitudes for S-wave nonlep-
tonic
decays of , , and which have been measured with high
*
Corresponding author.
E-mail
address: gronau@physics.technion.ac.il (M. Gronau).
precision [9]. We calculated a branching fraction for
−
b
→
b
π
−
consistent with the range allowed in the LHCb analysis. Our pur-
pose
now is to extend this calculation to charmed baryon decays
0
c
→
c
π
−
and
+
c
→
c
π
0
.
Sec. 2 summarizes
the result of Ref. [7] for the amplitude of
−
b
→
b
π
−
, in which the underlying quark transition is s →
u(
¯
ud). This result is then applied to a contribution of the same
quark subprocess to
0
c
→
c
π
−
. A second term in this amplitude
due to the subprocess cs → cd is studied in Sec. 3. The total am-
plitude
and the branching ratios for
0
c
→
c
π
−
and
+
c
→
c
π
0
are calculated in Sec. 4 while Section 5 concludes.
2. s → u(
¯
ud) term in
−
b
→
b
π
−
and
0
c
→
c
π
−
We will use notations which are common for describing
hadronic hyperon decays [9]. The effective Lagrangian for B
1
→
B
2
π given by
L
eff
= G
F
m
2
π
[
¯
ψ
2
(A + Bγ
5
)ψ
1
]φ
π
(1)
involves two dimensionless parameters A and B describing S-
wave
and P-wave amplitudes, respectively. Here G
F
= 1.16638 ×
10
−5
GeV
−2
is the Fermi decay constant. The partial width is
(B
1
→ B
2
π) =
(
G
F
m
2
π
)
2
8πm
2
1
q[(m
1
+m
2
)
2
−m
2
π
]|A|
2
+[(m
1
−m
2
)
2
−m
2
π
]|B|
2
, (2)
http://dx.doi.org/10.1016/j.physletb.2016.04.020
0370-2693/
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.