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We report the time-resolved spectral analysis of a bright near-infrared andmoderate X-ray flare of Sgr A*. We obtained light curves in the $M$-, $K$-, and$H$-bands in the mid- and near-infrared and in the $2-8~\mathrm{keV}$ and$2-70~\mathrm{keV}$ bands in the X-ray. The observed spectral slope in thenear-infrared band is $\nu L_\nu\propto \nu^{0.5\pm0.2}$; the spectral slopeobserved in the X-ray band is $\nu L_\nu \propto \nu^{-0.7\pm0.5}$. We testedsynchrotron and synchrotron self-Compton (SSC) scenarios. The observednear-infrared brightness and X-ray faintness, together with the observedspectral slopes, pose challenges for all models explored. We rule out ascenario in which the near-infrared emission is synchrotron emission and theX-ray emission is SSC. A one-zone model in which both the near-infrared andX-ray luminosity are produced by SSC and a model in which the luminosity stemsfrom a cooled synchrotron spectrum can explain the flare. In order to describethe mean SED, both models require specific values of the maximum Lorentz factor$\gamma_{max}$, which however differ by roughly two orders of magnitude: theSSC model suggests that electrons are accelerated to $\gamma_{max}\sim 500$,while cooled synchrotron model requires acceleration up to$\gamma_{max}\sim5\times 10^{4}$. The SSC scenario requires electron densitiesof $10^{10}~\mathrm{cm^{-3}}$ much larger than typical ambient densities in theaccretion flow, and thus require in an extraordinary accretion event. Incontrast, assuming a source size of $1R_s$, the cooled synchrotron scenario canbe realized with densities and magnetic fields comparable with the ambientaccretion flow. For both models, the temporal evolution is regulated throughthe maximum acceleration factor $\gamma_{max}$, implying that sustainedparticle acceleration is required to explain at least a part of the temporalevolution of the flare.

Constraining particle acceleration in Sgr A* with simultaneous GRAVITY, Spitzer, NuSTAR and Chandra observations