Vector-boson-fusion timing references for four-dimensional displaced-vertex searches

Abstract

Long-lived particles that decay inside the tracker are searched for via the spatial displacement of their decay vertices. However, the same decays also arrive late, providing a handle made available by a precision timing layer at the HL-LHC that displaced-vertex searches do not exploit. We study the exotic decay of a Higgs boson produced through vector-boson fusion (VBF), $pp\to hjj$ with $h\to ss$, in which the long-lived scalar decays as $s\to b\bar b$, and use the VBF tag jets to identify the hard-scatter vertex. Its prompt central tracks, timed by a CMS-MTD-like barrel layer that also times the central tracks of the displaced vertex, define a per-event start time, turning each displaced vertex into a four-dimensional object. Because a fast simulation cannot determine the absolute normalization of the heavy-flavour and instrumental displaced-vertex backgrounds, we take as the primary result a normalization-free figure of merit: the ratio of the timing-enhanced sensitivity to the spatial-only sensitivity. Adding the timing layer improves this ratio by a factor of $\simeq2.8$ at a nominal working point and by up to an order of magnitude for a tighter delayed-vertex requirement, because the heavy-flavour background that survives the spatial selection is prompt in collision time. The improvement increases with decay length, extending sensitivity into the long-lifetime regime in which purely spatial searches lose tracker acceptance. The gain is essentially mass-independent at a decay length of $\ctau\simeq100\mm$, where the trend with scalar mass reverses: lighter scalars benefit more at short lifetimes because of their larger boost, whereas heavier scalars benefit more at long lifetimes as the lighter states leak out of the tracker.