Abstract
A measurement of four branching-fraction ratios for three-body decays of B mesons involving two open-charm hadrons in the final state is presented. Run 1 and Run 2 pp collision data are used, recorded by the LHCb experiment at centre-of-mass energies 7, 8, and 13 TeV and corresponding to an integrated luminosity of 9 fb−1. The measured branching-fraction ratios are$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast +}{D}^{-}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {\overline{D}}^0{D}^0{K}^{+}\right)}=0.517\pm 0.015\pm 0.013\pm 0.011,\\ {}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast -}{D}^{+}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {\overline{D}}^0{D}^0{K}^{+}\right)}=0.577\pm 0.016\pm 0.013\pm 0.013,\\ {}\begin{array}{c}\frac{\mathcal{B}\left({B}^0\to {D}^{\ast -}{D}^0{K}^{+}\right)}{\mathcal{B}\left({B}^0\to {D}^{-}{D}^0{K}^{+}\right)}=1.754\pm 0.028\pm 0.016\pm 0.035,\\ {}\frac{\mathcal{B}\left({B}^{+}\to {D}^{\ast +}{D}^{-}{K}^{+}\right)}{\mathcal{B}\left({B}^{+}\to {D}^{\ast -}{D}^{+}{K}^{+}\right)}=0.907\pm 0.033\pm 0.014,\end{array}\end{array}} $$
B
B
+
→
D
∗
+
D
−
K
+
B
B
+
→
D
¯
0
D
0
K
+
=
0.517
±
0.015
±
0.013
±
0.011
,
B
B
+
→
D
∗
−
D
+
K
+
B
B
+
→
D
¯
0
D
0
K
+
=
0.577
±
0.016
±
0.013
±
0.013
,
B
B
0
→
D
∗
−
D
0
K
+
B
B
0
→
D
−
D
0
K
+
=
1.754
±
0.028
±
0.016
±
0.035
,
B
B
+
→
D
∗
+
D
−
K
+
B
B
+
→
D
∗
−
D
+
K
+
=
0.907
±
0.033
±
0.014
,
where the first of the uncertainties is statistical, the second systematic, and the third is due to the uncertainties on the D-meson branching fractions. These are the most accurate measurements of these ratios to date.
Global CP asymmetries in charmless three-body B decays with final state interactions
