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White Dwarfs as Dark Matter Detectors
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Is $chi_{led}$ independent of density? #3

Closed rjanish closed 7 years ago

rjanish commented 7 years ago

[first paragraph of DM Transit section]

over the range of WD densities we consider it is reasonable that the only variation in $\partial E /\partial x$ for different stars is a linear scaling in $n$, so $\chi_{led}$ is independent of stellar variations.

RJ: does this need more justification? PR: definitely, especially since we have processes turning on or off in different density regimes. perhaps this is true because were almost always dominated by showers?

rjanish commented 7 years ago

It is definitely not true that $\chi{led}$ is independent of density in general. But I didn't intend this to involve showers, or anything that happens after the DM-SM interaction produces outgoing particles. I am thinking just about the $\chi{led}$ of DM-SM scattering - i.e., is the total energy per length that initially appears in the form of kinetic energy of SM products released by the DM-SM process a linear function of density? I think it is. (But note that $L$ is definitely not, except perhaps if $L$ is always dominated by a hadronic shower length).

The reason that (\partial E/\partial x)_{deposit} might not be linear in $n$ is if the DM-SM interaction depended significantly on the kinematics of the targets, if the phase space available to the products varied with $n$, or if multi-particle interactions mattered (like charge-screening or LPM-like effects). There are probably more effects here, but these are what I can think of at the moment. We've seen all of these (except the kinematics?) in the deviation of our stopping power calculations from PDG values.

For a heavy DM, I think the DM-SM interaction must be short range, with an $E_{COM}$ much larger than energy scales of the inter-medium physics and the DM acting as a brick-wall in the COM-frame. I don't see how any of the above effect should be significant in that picture.

I didn't want to spend a lot of text on this in the paper, but maybe it is worth more discussion since our constraints are much more direct if we can view $\chi_{led}$ as a function of DM model parameters only.

vijayoct27 commented 7 years ago

ok, I think I see what you are trying to accomplish, RJ. Basically, you want $\chi_\text{led}$ to be purely a DM quantity independent of the detector it is transiting (i.e. WD vs. LUX). Is this right?

rjanish commented 7 years ago

Basically, you want $\chi_\text{led}$ to be purely a DM quantity independent of the detector it is transiting (i.e. WD vs. LUX). Is this right?

Mostly, but not quite as strong. I want $\chi{led}$ to be independent of any WD detector. So for a given DM model that permits WD transit events, there is one number $\chi{led}$ that applies for transits of any (carbon-oxygen) WD regardless of WD density. This same DM model may well have a $\chi_{led}$ for interacting with LUX that is very different, but I don't think we care about that.