This is happening because the arrow tips don't count in the computation of the bounding box by Tikz
As one of the comments (by Gonzola) mentionned, you can specify a border in the standalone document class options. Personally, I prefer specifying an all-around border with border = 4pt, but with Gonzalo's suggestion, only the bottom border is drawn, which is what you want.
Another way is to specify, within the picture code, what the bounding box should be. For example
\path[use as bounding box] <some code here>
tells tikz what to use.
In addition to including everything you want from your picture, this approach has another use. It can help in aligning a picture within a document according to your preferences: Say you want a part of a picture to be aligned with the center of the page but some annotation always makes the picture shift left with respect to the page, manually selecting the bounding box can fix this. Of course, using the bounding box to align a picture is only useful in a complete document, it is of no use for a standalone picture.
\documentclass[border={0 4pt 0 0}]{standalone}– Gonzalo Medina Jun 05 '13 at 16:58According to the feature request https://sourceforge.net/p/pgf/feature-requests/77/, it is not yet documented but available.
– LaRiFaRi Sep 19 '13 at 08:04