red-giant branch

The term red-giant branch (RGB) is a grouping of stars (RGB stars) on the H-R diagram (HRD) that form a line on the diagram, leading away from the main sequence, consisting of stars in a phase of their evolution (RGB phase) that follows its main-sequence phase, i.e., during its post-main-sequence evolution. The grouping constitutes some of the red giants, i.e., very bright, reddish stars.

RGB stars are stars with a helium core that is not burning, surrounded by hydrogen undergoing fusion (a hydrogen-burning shell). (Only stars with a mass of about a half solar mass minimum undergo this stage: smaller stars, red dwarfs, keep mixing their helium and hydrogen by convection.) Spectrally, the RGB stars have become K-type stars or M-type stars, but are much more luminous than main sequence stars in those classes, having larger radii, i.e., giant stars or subgiants. Their higher luminosity is due to their greater energy production, more than during their main-sequence phase, due to the region of hydrogen fusion being larger. Their energy production is within the main-sequence B-class range, but red giants grow much larger than B-class main-sequence stars, I assume due to the less massive star having less gravity counteracting the same outward radiation pressure due to the "B-class luminosity". Given this larger size, the energy spreads out to a larger surface than that of a B-class main-sequence star, giving them a cooler photosphere and a redder color.

After the RGB phase, a helium burning phase begins, forming a horizontal grouping on the HRD termed the horizontal branch (HB). Among some of these helium-burning stars (specifically, those with substantial metallicity and which were of certain spectral classes during their main sequence) there is little variation in color during their helium-burning phase, and their grouping on the HRD is termed the red clump.