The ratios of the
B
c
(
2
S
)
+
to
B
+
c
,
B
∗
c
(
2
S
)
+
to
B
+
c
, and
B
∗
c
(
2
S
)
+
to
B
c
(
2
S
)
+
production cross sections are measured in proton-proton collisions at
√
s
=
13
 
 
TeV
, using a data sample collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of
143
 
 
fb
−
1
. The three measurements are made in the
B
+
c
meson phase space region defined by the transverse momentum
p
T
>
15
 
 
GeV
and absolute rapidity
|
y
|
<
2.4
, with the excited
B
(
*
)
c
(
2
S
)
+
states reconstructed through the
B
(
*
)
+
c
π
+
π
−
, followed by the
B
+
c
→
J
/
ψ
π
+
and
J
/
ψ
→
μ
+
μ
−
decays. The
B
c
(
2
S
)
+
to
B
+
c
,
B
∗
c
(
2
S
)
+
to
B
+
c
, and
B
∗
c
(
2
S
)
+
to
B
c
(
2
S
)
+
cross section ratios, including the unknown
B
(
*
)
c
(
2
S
)
+
→
B
(
*
)
+
c
π
+
π
−
branching fractions, are
(
3.47
±
0.63
(
stat
)
±
0.33
(
syst
)
)
%
,
(
4.69
±
0.71
(
stat
)
±
0.56
(
syst
)
)
%
, and
1.35
±
0.32
(
stat
)
±
0.09
(
syst
)
, respectively. None of these ratios shows a significant dependence on the
p
T
or
|
y
|
of the
B
+
c
meson. The normalized dipion invariant mass distributions from the decays
B
(
*
)
c
(
2
S
)
+
→
B
(
*
)
+
c
π
+
π
−
are also reported.