Search for B c ⁺ \!→ π ⁺ μ ⁺μ ⁻ decays and measurement of the branching fraction ratio B (B c ⁺ \!→ ψ (2S) π ⁺ )/B (B c ⁺ \!→ J -1.66656pt/-1.111ptψ π ⁺ )

The first search for nonresonant B c ⁺ \!→ π ⁺ μ ⁺μ ⁻ B c + → π + μ + μ - decays is reported. The analysis uses proton–proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 \,fb ⁻¹ fb - 1 . No evidence for an excess of signal events over background is observed and an upper limit is set on the branching fraction ratio B (B c ⁺ \!→ π ⁺ μ ⁺μ ⁻ )/B (B c ⁺ \!→ J -1.66656pt/-1.111ptψ π ⁺ ) < 2.1× 10⁻⁴ B ( B c + → π + μ + μ - ) / B ( B c + → J / ψ π + ) < 2.1 × 10 - 4 at $$90%$$ 90 % confidence level. Additionally, an updated measurement of the ratio of the B c ⁺ \!→ ψ (2S) π ⁺ B c + → ψ ( 2 S ) π + and B c ⁺ \!→ J -1.66656pt/-1.111ptψ π ⁺ B c + → J / ψ π + branching fractions is reported. The ratio B (B c ⁺ \!→ ψ (2S) π ⁺ )/B (B c ⁺ \!→ J -1.66656pt/-1.111ptψ π ⁺ ) B ( B c + → ψ ( 2 S ) π + ) / B ( B c + → J / ψ π + ) is measured to be 0.254± 0.018 ± 0.003 ± 0.005 0.254 ± 0.018 ± 0.003 ± 0.005 , where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the leptonic J -1.66656pt/-1.111ptψ J / ψ and ψ (2S) ψ ( 2 S ) decays. This measurement is the most precise to date and is consistent with previous LHCb results.