Comments on: Dark Matter and Fifth Forces

By: Dark Forces Revisited | Cosmic Variance | Discover Magazine

Dark Forces Revisited | Cosmic Variance | Discover Magazine — Fri, 27 Feb 2009 17:24:13 +0000

[...] have a new paper out with Sonny Mantry and Michael Ramsey-Musolf, following up on our earlier paper with Chris Stubbs. The original idea was to imagine a new long-range force that couples directly to [...]

By: Dark Photons | Cosmic Variance

Dark Photons | Cosmic Variance — Thu, 30 Oct 2008 01:20:20 +0000

[...] idea of new forces acting on dark matter is by no means new; I’ve worked on it recently myself, and so have certain co-bloggers. (Strong, silent types who are too proud to blog about their own [...]

By: Mark

Mark — Thu, 21 Aug 2008 02:58:56 +0000

OneForce, you might try searching our archive for “cosmic acceleration”. Here are a couple of other posts from our earlier blogs that might help further:

http://orangequark.blogspot.com/2005/04/theories-of-cosmic-acceleration.html

http://preposterousuniverse.blogspot.com/2004/09/dark-energy-equation-of-state.html

By: OneForce

OneForce — Thu, 21 Aug 2008 02:43:04 +0000

Say, I don’t know if this is the proper venue for a fellow to just drop in and pop a question or not but I have one so I’ll ask it and let the chips fall where they may.

Question: Is it fair to say in our mysteriously accelerating and occasionally preposterous Universe that Gravitation as a strictly Attractive force fails to sufficiently explain what’s going on? That there must be a corresponding Repulsion force at play or the whole interpretation goes up in flames? Based on the relatively new evidence we’ve accumulated about not just our expanding universe but a rapidly expanding one, in that it expands at ever greater rates as our conception of Time passes?

Feel free to shoo me away if this is an annoying question.

By: Tim Tait

Tim Tait — Wed, 20 Aug 2008 18:07:52 +0000

Sean: You’re right… Equations ARE easy…!

By: Tim Tait

Tim Tait — Wed, 20 Aug 2008 18:07:28 +0000

That’s right. What I mean is that one can just think of the four-component fermion $latex \psi$ which contains both $latex \psi_L$ and $latex \psi_R$. In that language there is no fermion propagator and no Higgs insertion – the effect of the Higgs has been summed into our definition of the massive fermion.

And you’re right, the denominator of that propagator looks like it is zero otherwise, which is from various points of view: why we redefine the two massless fermions into a single massive one as above, why we amputate diagrams with self-energy corrections to external legs (but that is the same thing I just said in a more general language), and (I think implicitly) what Sean and collaborators were worrying about in the original (three loop) version of the diagram.

By: TimG

TimG — Wed, 20 Aug 2008 01:28:54 +0000

Tim Tait wrote:

Going back to the Higgs insertion, it doesn

By: Tim Tait

Tim Tait — Tue, 19 Aug 2008 19:58:40 +0000

You can also make reasonably pretty Feynman diagrams using root-

http://root.cern.ch/

(the documentation is not great, but search for ‘Feynman’) though of course root itself is a much more sophisticated and general tool. I use it for all of my other plotting needs as well, so it works well for me.

Going back to the Higgs insertion, it doesn’t carry any momentum, and in fact you shouldn’t think of it as a real interaction at all… Think of any number of such insertions as having been already resummed into our definition of the fermion. That language is very useful in order to keep track of fermion chiralities (which in this example is what tells you the whole graph is proprtional to the fermion mass), but it is not really intended for serious calculations.

Oh, and Furry’s theorem works well for QED, but it has loopholes that apply to non-Abelian gauge theories, or a theory with chiral interactions (such as the electroweak theory of the Standard Model).

Tim

By: Mark

Mark — Tue, 19 Aug 2008 16:08:19 +0000

The jaxodraw disk image for OS X just seems to work for me – it is a pretty nice program!

By: Sean

Sean — Tue, 19 Aug 2008 15:57:53 +0000

There is a free program, specifically for making Feynman diagrams: Jaxodraw. I've never been able to get it to work, although I've admittedly not tried to hard, as I like Illustrator.

By: Alex F

Alex F — Tue, 19 Aug 2008 15:47:51 +0000

Shoot. I was worried it was Illustrator. I had a trial version of it once and it was great… but it’s a $600 program. I’d been hoping you could point me to an awesome free program, since I’d only ever use about $2 of the $600 worth… (And no, Inkscape is no substitute).

By: Lawrence B. Crowell

Lawrence B. Crowell — Tue, 19 Aug 2008 15:39:59 +0000

I managed to convince myself this would indeed vanish. It appears that this is the case for SU(2). I’d have to check to see if this is the case for SU(3).

L. C.

By: Count Iblis

Count Iblis — Tue, 19 Aug 2008 15:34:06 +0000

Furry’s theorem says that an odd number of vertices will yield zero.

By: Lawrence B. Crowell

Lawrence B. Crowell — Tue, 19 Aug 2008 14:16:07 +0000

It seems possible to have an odd number of vertices, we just can’t have one. The action S = log det(iD + m), for D = gam^a(&_a + W_a), an expansion gives a second order Tr[(1/i& + m)W(1/i& + m)W] and higher. The first order term in W is tadpole —> 0 and the zeroth order is subtracted. The vertices will contain traceless terms gam*(tW) which will contribute to a quadratic term in t which has a trace. Yet a third order term may not be zero as it appears there might be a Levi-Civita Tr(gam^a gam^b gam^c) = eps^{abc}. Might this then contribute to a a nonvanishing cubic term in the group elements t?

Is suppose that if the mass of the chi-field or WIMP is large enough then chi-loop divergence can be handled by introducing mass counter terms as the loop contracts to zero or large momentum. I am not sure how this would be done.

Lawrence B. Crowell

By: TimG

TimG — Tue, 19 Aug 2008 13:54:38 +0000

Thanks again to everyone for the very informative answers. Is there any more that can be said about why we didn’t have to worry about the coupling to the Higgs being amputated after all? (See the second half of my post #35 for more detail on why I’m confused.)

By: Count Iblis

Count Iblis — Tue, 19 Aug 2008 13:50:51 +0000

TimG, the sneutrino is an example of a bosonic DM candidate that has been investigated, see e.g. here.

By: Sean

Sean — Tue, 19 Aug 2008 05:54:18 +0000

TimG– dark matter certainly could be bosonic, although many of the most popular candidates for WIMP’s are fermions.

Alex F– Two crucial ingredients: (1) Adobe Illustrator, (2) Long, boring plane flights.

By: Alex F

Alex F — Tue, 19 Aug 2008 04:41:59 +0000

Sean — a little off-topic, but can I ask how you make those pretty pictures with the circles and the wavy lines? (This might be a little too technical to answer via blog comments, I know you like to keep the discussion here light).

By: TimG

TimG — Tue, 19 Aug 2008 04:14:19 +0000

And of course, even in the fermion case I don’t need to worry about how we get an even number of gammas, since we already knew we needed an even number of $latex W\chi^2$vertices to get an even number of $latex t^a$’s.

Sorry for the repeated comments — I wish there was a way to edit (or, for that matter, to preview).

By: TimG

TimG — Tue, 19 Aug 2008 04:10:55 +0000

I guess you can forget that question about whether the diagram cancels for a boson loop. First, I’m pretty sure there wouldn’t even be a gamma on the vertex in that case, so my concern about that was groundless. But more importantly I forgot that the diagram we’re looking at has two W’s, so everything in the vertex factor appears twice.