The first search for nonresonant  $${{B} _{c} ^+} \!\rightarrow {{\pi } ^+} {\mu ^+\mu ^-} $$  <math> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mrow> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </mrow> </math>   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 $$\,\text {fb} ^{-1}$$  <math> <mrow> <mspace width="0.166667em"></mspace> <msup> <mtext>fb</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math>  . No evidence for an excess of signal events over background is observed and an upper limit is set on the branching fraction ratio  $${\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {{\pi } ^+} {\mu ^+\mu ^-} )/{\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\pi } ^+} ) &lt; 2.1\times 10^{-4}$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mrow> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>J</mi> <mspace width="-1.66656pt"></mspace> <mo>/</mo> <mspace width="-1.111pt"></mspace> <mi>ψ</mi> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>&lt;</mo> <mn>2.1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </mrow> </math>   at  $$90\%$$  <math> <mrow> <mn>90</mn> <mo>%</mo> </mrow> </math>   confidence level. Additionally, an updated measurement of the ratio of the  $${{B} _{c} ^+} \!\rightarrow {\psi {(2S)}} {{\pi } ^+} $$  <math> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> </mrow> </math>   and  $${{B} _{c} ^+} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\pi } ^+} $$  <math> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>J</mi> <mspace width="-1.66656pt"></mspace> <mo>/</mo> <mspace width="-1.111pt"></mspace> <mi>ψ</mi> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> </mrow> </math>   branching fractions is reported. The ratio  $${\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {\psi {(2S)}} {{\pi } ^+} )/{\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\pi } ^+} )$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>/</mo> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>J</mi> <mspace width="-1.66656pt"></mspace> <mo>/</mo> <mspace width="-1.111pt"></mspace> <mi>ψ</mi> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>   is measured to be  $$0.254\pm 0.018 \pm 0.003 \pm 0.005$$  <math> <mrow> <mn>0.254</mn> <mo>±</mo> <mn>0.018</mn> <mo>±</mo> <mn>0.003</mn> <mo>±</mo> <mn>0.005</mn> </mrow> </math>  , where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the leptonic  $${J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }$$  <math> <mrow> <mi>J</mi> <mspace width="-1.66656pt"></mspace> <mo>/</mo> <mspace width="-1.111pt"></mspace> <mi>ψ</mi> </mrow> </math>   and  $$\psi {(2S)}$$  <math> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </math>   decays. This measurement is the most precise to date and is consistent with previous LHCb results.

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Search for  $${{B} _{c} ^+} \!\rightarrow {{\pi } ^+} {\mu ^+\mu ^-} $$  <math> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mrow> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </mrow> </math>   decays and measurement of the branching fraction ratio  $${\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {\psi {(2S)}} {{\pi } ^+} )/{\mathcal {B}} ({{B} _{c} ^+} \!\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\pi } ^+} )$$  <math> <mrow> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> <mo>/</mo> <mi>B</mi> <mrow> <mo>(</mo> <msubsup> <mi>B</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mspace width="-0.166667em"></mspace> <mo>→</mo> <mrow> <mi>J</mi> <mspace width="-1.66656pt"></mspace> <mo>/</mo> <mspace width="-1.111pt"></mspace> <mi>ψ</mi> </mrow> <msup> <mrow> <mi>π</mi> </mrow> <mo>+</mo> </msup> <mo>)</mo> </mrow> </mrow> </math>