Asteroseismology allows us to probe stellar interiors. Mixed modes can be used to probe the physical conditions in red giant cores. However, we still need to identify the physical mechanisms that transport angular momentum inside red giants, leading to the slow-down observed for the red giant core rotation. Thus large-scale measurements of the red giant core rotation are of prime importance to obtain tighter constraints on the efficiency of the internal angular momentum transport, and to study how this efficiency changes with stellar parameters. This work aims at identifying the components of the rotational multiplets for dipole mixed modes in a large number of red giant oscillation spectra observed by Kepler. Such identification provides us with a direct measurement of the red giant mean core rotation. We compute stretched spectra that mimic the regular pattern of pure dipole gravity modes. Mixed modes with same azimuthal order are expected to be almost equally spaced in stretched period. The departure from this regular pattern allows us to disentangle the various rotational components and therefore to determine the mean core rotation rates of red giants. We obtained mean core rotation measurements for 875 red giant branch stars. This large sample includes stars with a mass as large as 2.5 $M_{odot}$, allowing us to test the dependence of the core slow-down rate on the stellar mass. This work on a large sample allows us to refine previous measurements of the evolution of the mean core rotation on the red giant branch. Rather than a slight slow down, our results suggest rotation to be constant along the red giant branch, with values independent on the mass.
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