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Gauge/gravity duality is used to study properties of the doubly heavy baryon$(\mathrm{QQq})$ at finite rapidity and finite temperature in the heavy-ioncollision. We investigated the impact of rapidity on the string breaking andthe melting into free quarks. Computations reveal that when $\mathrm{QQq}$ isconfined, the larger the rapidity, the larger the distance of string breaking,but the impact is not significant, which aligns with our conjecture abouthadrons. $\mathrm{QQq}$ transitions to a deconfined state when the temperatureand rapidity reach critical values. In this case, a higher rapidity makes itmore prone to melt into free quarks. We attempt to optimize the model fordistinguishing confined and deconfined states of hadrons based on theirbehavior of string breaking or melting into free quarks at long distances.Additionally, unlike heavy quarkonium $\mathrm{(Q\bar{Q})}$, $\mathrm{QQq}$ hasa distinct property in that its temperature or rapidity cannot increaseindefinitely. Beyond that, $\mathrm{QQq}$ theoretically cannot exist in ahigher temperature or rapidity medium. Other qualitative properties remainconsistent with heavy quarkonium, but overall, $\mathrm{Q\bar{Q}}$ is morestable. This discrepancy arises due to the light quark in $\mathrm{QQq}$. Wealso plot a state diagram on the $T- \eta$ plane by examining whether stringbreaking or melting occurs and comparing it with $\mathrm{Q\bar{Q}}$.$\mathrm{QQq}$ is more prone to enter the deconfined state.

Moving doubly heavy baryon in a strongly coupled plasma from holography