  We investigate the mutual influence of tilt, disorder, and Coulomb
interaction in a type-I Dirac semimetal (DSM) with $x$-direction tilt by
performing a renormalization group analysis. The interplay between disorder and
ordinary tilt generates an effective tilt along the $x$-direction, which is the
physically observable one. There exist two types of disorder which increase the
effective tilt and drive a phase transition from the DSM phase to the diffusive
metal phase. The diffusive phase transition stops the increase of the effective
tilt and the surface of the original Dirac cone in the diffusive metal phase is
just slightly tilted. Surprisingly, the Dirac point is replaced by a bulk nodal
arc in the diffusive metal phase. The Coulomb interaction suppresses the
diffusive phase transition and therefore is harmful to the formation of bulk
nodal arc. In contrast, there also exists other two types of disorder which
reduce the effective tilt and induce no phase transition. For these two types
of disorder, the Coulomb interaction enhances their low-energy relevances.
Coexistence of Coulomb interaction with any of them leads to a stable infrared
fixed point where the coupling strengths for two kinds of interaction are
identical and the effective tilt vanishes. The original tilted Dirac semimetal
now reacts like an untilted and interaction-free Dirac semimetal. Our results
show that interplay between tilt, disorder, and Coulomb interaction results in
rich low-energy properties for the tilted Dirac fermions.
