Comments on: Matter v Antimatter III: Leptogenesis http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/ Random samplings from a universe of ideas. Mon, 09 Nov 2009 05:46:49 -0600 http://wordpress.org/?v=2.8.4 hourly 1 By: Shantanu http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42118 Shantanu Fri, 22 Aug 2008 02:18:43 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42118 Mark, thanks for the nice post. On a different note I haven't seen any blog on this year's SLAC summer school (where from the agenda I see you gave a talk). Do you (or Joanne) know if the videos of the talks are going to be put up? Thanks Mark, thanks for the nice post. On a different note I haven’t seen any
blog on this year’s SLAC summer school (where from the agenda I see
you gave a talk). Do you (or Joanne) know if the videos of the talks are
going to be put up?
Thanks

]]> By: Mark http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42117 Mark Wed, 20 Aug 2008 19:05:25 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42117 Hi Mike. In practice this is true, just because such processes are mediated by instantons of high Euclidean action, and therefore will be fantastically rare at today's temperatures. In principle though, one <i>could</i> happen today (there's always a tiny chance). Hi Mike. In practice this is true, just because such processes are mediated by instantons of high Euclidean action, and therefore will be fantastically rare at today’s temperatures. In principle though, one could happen today (there’s always a tiny chance).

]]> By: Mike http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42104 Mike Wed, 20 Aug 2008 18:56:36 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42104 "Another way to say this is that whenever there is an anomalous process that produces more baryons than antibaryons, it is guaranteed to be accompanied by the production of more leptons than antileptons" The anomalous process should occur above the electroweak scale, right? Not that this is a problem here. “Another way to say this is that whenever there is an anomalous process that produces more baryons than antibaryons, it is guaranteed to be accompanied by the production of more leptons than antileptons”

The anomalous process should occur above the electroweak scale, right? Not that this is a problem here.

]]> By: Matter v Antimatter III: Leptogenesis : Sophoblog http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42116 Matter v Antimatter III: Leptogenesis : Sophoblog Tue, 19 Aug 2008 18:00:22 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42116 [...] Matter v Antimatter III: Leptogenesis [...] [...] Matter v Antimatter III: Leptogenesis [...]

]]> By: Jacques Distler http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42101 Jacques Distler Tue, 19 Aug 2008 14:16:15 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42101 Ah, yes, Dirac versus Majorana masses. Another pointlessly confusing bit of nomenclature. If you have two left-handed Weyl fermions, $latex \psi,\tilde{\psi}$, transforming in <em>complex conjugate representations</em> of the gauge group, you can write down a mass term $latex m \psi \tilde{\psi}$ That's called a "Dirac mass" (because this pair of Weyl fermions can be assembled into a Dirac fermion). On the other hand, if $latex \psi$ is in a real representation of the gauge group, you can write down a mass term for it, all by its lonesome $latex m \psi \psi$ That's called a "Majorana mass." And, just to confuse you, if $latex \psi$ is in a <em>pseudoreal</em> representation of the gauge group, then you <em>still</em> need a pair of such fermions to write down a mass term, $latex m \psi_1 \psi_2$ even though both fermions transform in the <em>same</em> representation of the gauge group. Ah, yes, Dirac versus Majorana masses. Another pointlessly confusing bit of nomenclature.

If you have two left-handed Weyl fermions, \psi,\tilde{\psi}, transforming in complex conjugate representations of the gauge group, you can write down a mass term

m \psi \tilde{\psi}

That’s called a “Dirac mass” (because this pair of Weyl fermions can be assembled into a Dirac fermion). On the other hand, if \psi is in a real representation of the gauge group, you can write down a mass term for it, all by its lonesome

m \psi \psi

That’s called a “Majorana mass.”

And, just to confuse you, if \psi is in a pseudoreal representation of the gauge group, then you still need a pair of such fermions to write down a mass term,

m \psi_1 \psi_2

even though both fermions transform in the same representation of the gauge group.

]]> By: TimG http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42102 TimG Tue, 19 Aug 2008 13:50:15 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42102 <strong>Ralph</strong>, if I'm understanding the discussion correctly the difference is that the right-handed neutrino $latex \Psi$ can have a mass term that couples it to itself (a Majorana mass, if I'm remembering the terminology) whereas the right-handed electron only has a mass term that couples it to the left-handed electron (a Dirac mass, again if remember the terminology.) So the electron mass matrix looks like: 0 m m 0 which when you diagonalize to find the mass eigenstates gives you two equal masses. Whereas, the neutrino mass matrix looks like: 0 m m M with M >> m, which gives you one large mass eigenstate (~ M) and one small one ($latex ~ m^2/M$) So in terms of the difference between electron masses and neutrino masses, I think the question is not just "Why does the neutrino have such a large Majorana mass?" but "Why does it have any Majorana mass at all?" I think you're right in thinking the Majorana mass is allowed because of its lack of charges, but I could be wrong. I'm sure if any of the above isn't right that Jacques, Mark or someone else will be along soon to correct it. :) Ralph, if I’m understanding the discussion correctly the difference is that the right-handed neutrino \Psi can have a mass term that couples it to itself (a Majorana mass, if I’m remembering the terminology) whereas the right-handed electron only has a mass term that couples it to the left-handed electron (a Dirac mass, again if remember the terminology.)

So the electron mass matrix looks like:
0 m
m 0

which when you diagonalize to find the mass eigenstates gives you two equal masses. Whereas, the neutrino mass matrix looks like:
0 m
m M

with M >> m, which gives you one large mass eigenstate (~ M) and one small one (~ m^2/M)

So in terms of the difference between electron masses and neutrino masses, I think the question is not just “Why does the neutrino have such a large Majorana mass?” but “Why does it have any Majorana mass at all?” I think you’re right in thinking the Majorana mass is allowed because of its lack of charges, but I could be wrong.

I’m sure if any of the above isn’t right that Jacques, Mark or someone else will be along soon to correct it. :)

]]> By: Ralph http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42103 Ralph Tue, 19 Aug 2008 08:53:01 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42103 Still one more question about electrons v. neutrino masses: The neutrino singlet Phi has a large mass, but the electron singlet e~ does not. Is there any reason for that? Hmmm... IIUC the neutrino singlet has no weak isospin, zero electric charge and so zero weak hypercharge ... is it this lack of charges that allows the neutrino singlets to have large masses? Still one more question about electrons v. neutrino masses: The neutrino singlet Phi has a large mass, but the electron singlet e~ does not. Is there any reason for that?

Hmmm… IIUC the neutrino singlet has no weak isospin, zero electric charge and so zero weak hypercharge … is it this lack of charges that allows the neutrino singlets to have large masses?

]]> By: TimG http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42115 TimG Tue, 19 Aug 2008 04:40:06 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42115 Ah, I get it now. Thanks for the explanation. Ah, I get it now. Thanks for the explanation.

]]> By: Jacques Distler http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42114 Jacques Distler Tue, 19 Aug 2008 02:15:11 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42114 <blockquote>In particular, why is it that the left-handed electron, which is in the same SU(2) doublet, is allowed to have a mass, but the neutrino is not? What’s the difference?</blockquote> Because there's another left-handed Weyl fermion, $latex \tilde{e}$, which is an SU(2) singlet, and has hypercharge +1. When the Higgs gets a VEV, the Yukawa coupling $latex \tilde{e} L \cdot \overline{h}$ gives a mass to $latex \tilde{e}$ and one component of the lepton doublet. For the other component of the lepton doublet, $latex \Psi$ plays the same role that $latex \tilde{e}$ did. <strong>Except</strong> that $latex \Psi$ ican have a large gauge-invariant mass term all by itself. That leads to the "seesaw" mechanism discussed above.

In particular, why is it that the left-handed electron, which is in the same SU(2) doublet, is allowed to have a mass, but the neutrino is not? What’s the difference?

Because there’s another left-handed Weyl fermion, \tilde{e}, which is an SU(2) singlet, and has hypercharge +1. When the Higgs gets a VEV, the Yukawa coupling \tilde{e} L \cdot \overline{h} gives a mass to \tilde{e} and one component of the lepton doublet. For the other component of the lepton doublet, \Psi plays the same role that \tilde{e} did. Except that \Psi ican have a large gauge-invariant mass term all by itself. That leads to the “seesaw” mechanism discussed above.

]]> By: TimG http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/comment-page-1/#comment-42113 TimG Tue, 19 Aug 2008 01:50:33 +0000 http://blogs.discovermagazine.com/cosmicvariance/2008/08/18/matter-v-antimatter-iii-leptogenesis/#comment-42113 This business of left-handed and right-handed has always confused me. Am I correct in understanding that there are <em>two</em> meanings of "left-handed", and that being left-handed in terms of belonging to the left-handed doublet doesn't necessarily mean you have left-handed helicity? What is the connection (if any) between these two definitions of "left-handed"? Also, could someone expand on this statement: <blockquote>The neutrino (the guy who is usually called "left-handed") is part of an SU(2) doublet, L, with hypercharge -1/2. SU(2)×U(1) gauge invariance forbids a mass term for him.</blockquote>In particular, why is it that the left-handed electron, which is in the same SU(2) doublet, <em>is</em> allowed to have a mass, but the neutrino is not? What's the difference? This business of left-handed and right-handed has always confused me. Am I correct in understanding that there are two meanings of “left-handed”, and that being left-handed in terms of belonging to the left-handed doublet doesn’t necessarily mean you have left-handed helicity? What is the connection (if any) between these two definitions of “left-handed”?

Also, could someone expand on this statement:

The neutrino (the guy who is usually called “left-handed”) is part of an SU(2) doublet, L, with hypercharge -1/2. SU(2)×U(1) gauge invariance forbids a mass term for him.

In particular, why is it that the left-handed electron, which is in the same SU(2) doublet, is allowed to have a mass, but the neutrino is not? What’s the difference?

]]>