It is hard to adhere to a single standard as software performance testing has to be tailored to their contextual environments.
Software performance testing has relatively vague requirements, as performance testing does NOT target functional quality, instead, it targets software's structural quality. For example, we use performance testing measure efficiency, execution time, response time, loading time and etc. It is not possible to come up with a universal standard that applies to all software products; you will need to coordinate with your BA, BO and devs on specifics.
Depends on what exactly you are looking for from a standard, without specifics, I can not provide detailed info. If you want, you can tell us more about your project and we may be able to help you with more on performance testing.
This article is worth reading. Performance testing