  A peak structure of $J/\psi$ pair production around $6.9~{\rm GeV}$ was
observed and analyzed by the LHCb collaboration using the Run I and II data of
LHC. How to understand this peak arouses enthusiastic discussions among both
theorists and experimentalists of high energy physics, because this discovery
might hint something new. Overwhelming works on this topic tend to attribute
the peak as a four-quark state: tetraquark or molecule. Instead, we suggest
that this peak is corresponding to a fundamental Higgs-like boson with mass
about $6.9~{\rm GeV}$ which is advocated by a BSM effective theory. We present
a detailed analysis on both signal and SM background, including integrated
cross sections and invariant mass distributions of the final-state $J/\psi$
pair. Our numerical results are well in coincidence with the experimental data,
as postulating the resonance observed by LHCb to be a BSM $0^{++}$ scalar.
Therefore, the peak at $M_{\text{di-}J/\psi} \sim 6.9~{\rm GeV}$ might be a
hint of new physics beyond the SM whose scale is not as large as mostly
expected by high energy physicists. More further works are urgently needed in
both experimental and theoretical aspects to validate or negate this
assumption.
