I'm reading about CPU caches and I read that typically, cache line sizes start from 32 bytes. Since memory is slower than CPU caches therefore data is frequently loaded from the RAM into the cache and the size of the data loaded depends on the cache line size.
Now I wanted to know what are the typical sizes of the data bus in between CPU caches and RAM in modern CPUs. Does this depend on the register size of CPU architecture or is it independent of that? Will a 32 bit CPU have a 32 bit data bus connecting the cache and RAM and a 64 bit CPU will have a 64 bit data bus? If it's true than am I right to conclude that if cache line size and RAM is similar then a 64 bit CPU should be about twice as fast as the 32 bit CPU? Because the data loading in cache will be faster.