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New high-statistics total cross section data for $\gamma p\to J/\psi p$ fromthe GLUonic EXcitation (GlueX) experiment are fitted in a search for the exotic$P_c(4312)^+$ state observed by the Large Hadron Collider beauty (LHCb)collaboration. The integrated luminosity of this GlueX experiment was about$320~\mathrm{pb^{-1}}$. The fits show that destructive interference involvingan $S$-wave resonance and associated non-resonance background produces a sharpdip structure about $75~\mathrm{MeV}$ below the LHCb mass, in the same locationas a similar structure is seen in the data. Limitations of the employed modeland the need for improved statistics are discussed.

Is the LHCb $P_c(4312)^+$ plausible in the GlueX $\gamma p\to J/\psi p$ total cross sections ?