Secondary Hadron--Nucleus Collisions of Short-Lived Hadrons in Ultra-Relativistic Fixed-Target Heavy-Ion Interactions

Ultra-relativistic heavy nuclei traversing a solid target undergo successive nuclear encounters separated by atomic lattice spacings. At sufficiently high beam energies, Lorentz contraction reduces the proper time between collisions to $\mathcal{O}(10^4)$~fm$/c$ in the center-of-mass frame of the first interaction. We then consider the fragmentation region of this first collision, and show that short-lived hadrons produced in this region, with additional Lorentz boost, can reach the next nucleus before decaying. We show that this geometry enables secondary hadron--nucleus collisions involving species that cannot be realized as conventional secondary beams or in subsequent hadron--nucleus interactions in cosmic-ray cascades. For a $2.76$ TeV-per-nucleon Pb beam incident on a solid Pb lattice, we determine which forward-produced hadrons can survive to a second interaction, estimate their collision probabilities, and analyze potential observable consequences. In particular, we identify some representative hadrons whose proper lifetimes are of order $10^3$ fm/c, e.g. specific mesons ($\eta^\prime$) and heavy-flavor resonances ($J/\psi, D^*(2010)$), as projectile species that become accessible through this collision space-time geometry. At substantially higher beam energies (for example, with 10 TeV per-nucleon Pb beam), the survival probabilities are significantly enhanced. This can make even very short lived hadrons with life times of few tens fm ( $\Xi(1530)$, $\omega(782)$, $\phi(1020)$) available for this secondary hadron-nucleus collision, providing an additional motivation for future ultra-relativistic fixed-target heavy-ion experiments.