If there were compelling theoretical reasons, I might suppose that it existed. For example,
if every particle had a charge that was an element of a particular group, which could be factored into the Cartesian product of four groups, one for each force, and
a particle which has its charge being the identity element in any one of those groups doesn’t feel that force, and
this theory uses the group structure in some significant way, not just as a glorified table, and
every element of the overall group has exactly one kind of particle with that exact combination of charges,
except we couldn’t tell whether there was a particle in the ‘no interactions’ slot because it didn’t interact with anything...
I’d hazard that they exist, not that it would matter.
If there were compelling theoretical reasons, I might suppose that it existed. For example,
if every particle had a charge that was an element of a particular group, which could be factored into the Cartesian product of four groups, one for each force, and
a particle which has its charge being the identity element in any one of those groups doesn’t feel that force, and
this theory uses the group structure in some significant way, not just as a glorified table, and
every element of the overall group has exactly one kind of particle with that exact combination of charges,
except we couldn’t tell whether there was a particle in the ‘no interactions’ slot because it didn’t interact with anything...
I’d hazard that they exist, not that it would matter.
In that case I’d figure that they probably exist. Otherwise, I’d figure that they probably don’t. In either case, they might exist.