An air carrier flight crew reported they descended in response to a TCAS/RA warning for parallel runway traffic and received a Low Altitude Alert from Tower.

Narrative

SFO weather was CAVOK and they were using simultaneous visuals to 28L/28R. We were on the SERFR4 arrival and were advised to expect the Tipp Toe visual 28L; so per company guidance we loaded the RNV 28L-T approach. We were advised there would be traffic on the 28R visual. The autopilot was engaged to join the approach; our final vector to join was inside CHERA and was given a 310 heading to join. Upon established on 310; the vector was directly aimed at D9-28L; so I engaged NAV for course guidance. After passing D9-28L and on course to D6-28L; additional traffic (Aircraft Y) was joining 28R. There was hardly any spacing and it was evident that we would be parallel for the whole final. Just before passing D6-28L; we received a TCAS alert for the traffic followed almost immediately by a TCAS-RA. I disconnected the autopilot and followed the DESCENDING RA guidance (down 1700' per minute). The FO made the RA call to Tower and was trying to get visual contact with the traffic while monitoring me flying the RA. He was unable to get visual contact as the Aircraft Y flight was now slightly behind and above us. The RA continued for about 10-12 seconds (it felt like 5 minutes) and about the same time the RA went away; the Tower called a low altitude alert and to say intentions; the FO called the go-around and we executed a missed approach on Tower provided vectors. We were vectored back around for another visual to 28L and made a normal successful approach and landing.