Pointer arithmetic and integral promotion

In the expression p + a where p is a pointer type and a is an integer, will integer promotion rules apply? For example, if a is a char, on a 64-bit machine it will surely be extended to 64 bit before being added to the pointer value (in the compiled assembly), but is it specified by the standards? What will it be promoted to? int, intptr_t or ptrdiff_t? What will unsigned char or size_t be converted to?