Searches are performed for both promptlike and longlived dark photons, $A^{\prime}$, produced in protonproton collisions at a centerofmass energy of 13 TeV, using $A^{\prime}\to\mu^+\mu^$ decays and a data sample corresponding to an integrated luminosity of 1.6 fb$^{1}$ collected with the LHCb detector. The promptlike $A^{\prime}$ search covers the mass range from near the dimuon threshold up to 70 GeV, while the longlived $A^{\prime}$ search is restricted to the lowmass region $214<m(A^{\prime})<350$ MeV. No evidence for a signal is found, and 90 confidence level exclusion limits are placed on the $\gamma$$A^{\prime}$ kineticmixing strength. The constraints placed on promptlike dark photons are the most stringent to date for the mass range $10.6 < m(A^{\prime}) < 70$ GeV, and are comparable to the best existing limits for $m(A^{\prime}) < 0.5$ GeV. The search for longlived dark photons is the first to achieve sensitivity using a displacedvertex signature.
Promptlike mass spectrum, where the categorization of the data as prompt $\mu^+\mu^$, $\mu_Q\mu_Q$, and $hh+h\mu_Q$ is determined using the fits described in the text. 
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Regions of the $ [ m( A^{\prime} ) ,\varepsilon^2]$ parameter space excluded at 90% CL by the promptlike $ A^{\prime}$ search compared to the best existing limits [27,38]. 
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Ratio of the observed upper limit on $ n_{\rm ob}^{ A^{\prime} }[ m( A^{\prime} ) ,\varepsilon^2]$ at 90% CL to its expected value, where regions less than unity are excluded. There are no constraints from previous experiments in this region. 
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Threedimensional distribution of $\chi^2_{\rm DF}$ versus $t$ versus $ m(\mu^+\mu^)$ , which is fit to determine the longlived signal yields. The data are consistent with being predominantly due to $b$hadron decays at small $t$, and due to $ K^0_{\mathrm{ \scriptscriptstyle S}}$ decays for large $t$ and $ m(\mu^+\mu^) \gtrsim 280\mathrm{ Me V} $. The largest signallike excess occurs at $ m( A^{\prime} ) = 239\mathrm{ Me V} $ and $\tau( A^{\prime} ) = 0.86 ps $. 
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Efficiency ratio $\epsilon_{{}^{\gamma^*}}^{{}_{ A^{\prime} }}[ m( A^{\prime} ) ,\tau( A^{\prime} ) ]$ for longlived dark photons, integrated over decay time. The sharp decrease at larger values of $\varepsilon^2$ is due to the stringent $ {\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})]$ criterion applied in the 2016 trigger. 
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Longlived $ A^{\prime} \to \mu^+\mu^$ candidates (black points) showing $t$ versus $ m(\mu^+\mu^)$ in bins of $\chi^2_{\rm DF}$, compared to the pulls from binned fits performed without a signal contribution (color axis). Positive pulls denote an excess of data candidates. 
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Mass spectrum selected by the promptlike $ A^{\prime} \to \mu^+\mu^$ trigger. 
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Example $ {\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})] ^{1/2}$ distributions with fit results overlaid for promptlike candidates near (left) $ m( A^{\prime} ) =0.5$, (middle) 5, and (right) 50 $\mathrm{ Ge V}$ . The square root of $ {\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})]$ is used in the fits to increase the bin occupancies at large $ {\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})]$ values. 
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Comparison of the results presented in this Letter to existing constraints from previous experiments (see Ref. [1] for details about previous experiments). 
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Animated gif made out of all figures. 
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Summary of mass regions with special treatment in the promptlike $ A^{\prime}$ search. In all other mass regions from 214 $\mathrm{ Me V}$ to 70 $\mathrm{ Ge V}$ , limits are set and the $p$values are considered as possible evidence for $ A^{\prime} \to \mu^+\mu^$ decays. 
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Created on 06 March 2021.