# Search for $A' \to \mu^+ \mu^-$ decays

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## Abstract

Searches are performed for both prompt-like and long-lived dark photons, $A'$, produced in proton-proton collisions at a center-of-mass energy of 13 TeV. These searches look for $A' \to \mu^+\mu^-$ decays using a data sample corresponding to an integrated luminosity of 5.5/fb collected with the LHCb detector. Neither search finds evidence for a signal, and 90 confidence-level exclusion limits are placed on the $\gamma$-$A'$ kinetic-mixing strength. The prompt-like $A'$ search explores the mass region from near the dimuon threshold up to 70 GeV, and places the most stringent constraints to date on dark photons with $214 < m(A') \lesssim 740$ MeV and $10.6 < m(A') \lesssim 30$ GeV. The search for long-lived $A' \to \mu^+\mu^-$ decays places world-leading constraints on low-mass dark photons with lifetimes $\mathcal{O}(1)$ ps.

## Figures and captions

 Prompt-like 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 ${\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})]$ fits described in the text (examples of these fits are provided in the Supplemental Material). The anti-$k_{\rm T}$-based isolation requirement is applied for $m( A^{\prime} ) > 1.1\mathrm{ Ge V}$. Fig1.pdf [450 KiB] HiDef png [174 KiB] Thumbnail [117 KiB] *.C file Regions of the $[ m( A^{\prime} ) ,\varepsilon^2]$ parameter space excluded at 90% CL by the prompt-like $A^{\prime}$ search compared to the best published [35,38,83] and preliminary [104] limits. Fig2.pdf [172 KiB] HiDef png [391 KiB] Thumbnail [169 KiB] *.C file Expected reconstructed and selected long-lived $A^{\prime} \to \mu^+\mu^-$ yield. Fig3.pdf [128 KiB] HiDef png [1 MiB] Thumbnail [405 KiB] *.C file Ratio of the observed upper limit on $n_{\rm ob}^{ A^{\prime} }[ m( A^{\prime} ) ,\varepsilon^2]$ at 90% CL to the expected dark-photon yield, $n_{\rm ex}^{ A^{\prime} }[ m( A^{\prime} ) ,\varepsilon^2]$ , where regions less than unity are excluded. The only constraints in this region are from (hashed) the previous LHCb search [83]. Fig4.pdf [141 KiB] HiDef png [884 KiB] Thumbnail [375 KiB] *.C file Validation of the data-driven approach used to predict the long-lived $A^{\prime}$ properties from prompt $\gamma^* \to \mu^+\mu^-$ candidates in data is shown using two simulated $A^{\prime} \to \mu^+\mu^-$ samples, each generated with the same production kinematics, for (black points) $\tau( A^{\prime} ) =2 ps$ reconstructed and satisfying the long-lived selection criteria except the photon-conversion criterion, and (red line) the prediction for $\tau( A^{\prime} ) =2 ps$ based only on the prompt $A^{\prime} \to \mu^+\mu^-$ sample. { N.b.}, there is no free normalization factor, the red yield is predicted entirely from the prompt sample. FigS1.pdf [17 KiB] HiDef png [141 KiB] Thumbnail [127 KiB] *.C file Expected reconstructed and selected prompt-like $A^{\prime} \to \mu^+\mu^-$ yield divided by $\varepsilon^2$, where the displayed uncertainties include the systematic contributions. The gray boxes cover the regions with large SM resonance contributions, where no search for dark photons is performed. The anti-$k_{\rm T}$-based isolation requirement is applied for $m( A^{\prime} ) > 1.1\mathrm{ Ge V}$. FigS2.pdf [95 KiB] HiDef png [112 KiB] Thumbnail [84 KiB] *.C file Example ${\rm min}[\chi^2_{\mathrm{IP}}(\mu^{\pm})] ^{1/2}$ distributions with fit results overlaid for prompt-like 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. The background categories, as described in the Letter, are as follows: ($hh$) two prompt hadrons misidentified as muons; ($h\mu_Q$) a misidentified prompt hadron combined with a muon produced in the decay of a heavy-flavor quark, $Q$, that is misidentified as prompt; and ($\mu_Q\mu_Q$) two muons produced in $Q$-hadron decays that are both misidentified as prompt. FigS3a.pdf [14 KiB] HiDef png [129 KiB] Thumbnail [126 KiB] *.C file FigS3b.pdf [14 KiB] HiDef png [119 KiB] Thumbnail [118 KiB] *.C file FigS3c.pdf [15 KiB] HiDef png [144 KiB] Thumbnail [144 KiB] *.C file Signed local significances at each scan mass from (black points) all fits and (red) the expected distribution; if the best-fit signal-yield estimator is negative, the signed significance is negative and { vice versa}. The error bars account for the correlation between nearest-neighbor fit results, which often produces outliers in pairs due to the $\sigma[ m(\mu^+\mu^-) ] /2$ step size. FigS4.pdf [14 KiB] HiDef png [85 KiB] Thumbnail [82 KiB] *.C file Three-dimensional distribution of $\chi^2_{\rm DF}$ versus $t$ versus $m(\mu^+\mu^-)$ , which is fit to determine the long-lived 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 remaining few candidates at large $t$ and small $m(\mu^+\mu^-)$ are likely photon conversions. FigS5.pdf [183 KiB] HiDef png [606 KiB] Thumbnail [283 KiB] *.C file Long-lived $A^{\prime} \to \mu^+\mu^-$ 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. FigS6a.pdf [49 KiB] HiDef png [398 KiB] Thumbnail [271 KiB] *.C file FigS6b.pdf [59 KiB] HiDef png [464 KiB] Thumbnail [300 KiB] *.C file FigS6c.pdf [62 KiB] HiDef png [473 KiB] Thumbnail [304 KiB] *.C file FigS6d.pdf [63 KiB] HiDef png [474 KiB] Thumbnail [298 KiB] *.C file Comparison of the results presented in this Letter to existing constraints from previous experiments in the few-loop $\varepsilon$ region (see Ref. [102] for details about previous experiments). FigS7.pdf [143 KiB] HiDef png [497 KiB] Thumbnail [208 KiB] *.C file Comparison of the results presented in this Letter to existing constraints from previous experiments in the few-loop $\varepsilon$ region (see Ref. [102] for details about previous experiments), restricted to the mass region motivated by self-interacting dark matter [4]. FigS8.pdf [114 KiB] HiDef png [232 KiB] Thumbnail [161 KiB] *.C file Animated gif made out of all figures. PAPER-2019-031.gif Thumbnail

Created on 06 March 2021.