for my $file ( qw/path_n path_p/ ) {
   open PATH, $file or die "$file: $!";
   while (<PATH>)
   {
      # use a regex match with parens to capture path string in $1
      # and test to see if the path string was in dif_file:

      if ( /^(\S+)/ and exists( $diff_hash{$1} )) {
          print;
          # or whatever else you need to do with this record
      }
   }
   close PATH;
}