Talk:Weak hypercharge

Dauto's edit

Specifically [1]. I'm not saying it's wrong, but I'm saying its different from what was there before. No citation is provided for this (either way), so a) which is right? b) anyone got a citation?Headbomb {^ταλκ_{κοντριβς} – WP Physics} 22:24, 23 February 2009 (UTC)

They are both right since the pion then decays into photons. I thought the photon version was conceptually simpler, since it was easier to show B-L conservation. --Michael C. Price ^talk 00:44, 24 February 2009 (UTC)

How about showing the two-step process then? And of course, refs to back this up would be nice.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:55, 24 February 2009 (UTC)

Well it looks like you've already included the complete decay chain.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 00:56, 24 February 2009 (UTC)

Yeah, refs would be nice, but I doubt anyone's going to actually challenge it. --Michael C. Price ^talk 01:12, 24 February 2009 (UTC)

On a more general note, this article is completely unreferenced. Nothing strikes me as false, but we should find something, at the very least an external link.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 01:27, 24 February 2009 (UTC)

Is there an on-line QFT book? --Michael C. Price ^talk 07:00, 24 February 2009 (UTC)

May be we should also point out that decays such as

p⁺
→
ν
+
π⁺

are also possible? Dauto (talk) 08:30, 24 February 2009 (UTC)

Good point. Does the proton decay article say that as well?

I take it that the pion also decays?:

p⁺
→
ν
+
π⁺
→
ν
+
ν
+
e⁺

--Michael C. Price ^talk 10:22, 24 February 2009 (UTC)

Relation with B−L

Relation $Y_{W}=B-L\,$ was changed to $X+2Y_{W}=5(B-L)\,$ where X is some undescribed "GUT-associated conserved quantum number".

Since weak hypercharge is $Y_{W}=2(Q-T_{z})\,$, first relation holds for all known particles:

• Quarks have B−L = 1⁄3
  • u, c and t quarks have Q = 2⁄3 and T_z = 1⁄2, so their weak hypercharge is Y_w = 1⁄3, which is also their B−L,
  • d, s and b quarks have Q = −1⁄3 and T_z = −1⁄2, so their weak hypercharge is Y_w = 1⁄3, which is also their B−L.
• Leptons have B−L = −1
  • charged leptons have Q = −1 and T_z = −1⁄2, so their weak hypercharge is Y_w = −1, which is also their B−L,
  • neutrinos have Q = 0 and T_z = 1⁄2, so their weak hypercharge is Y_w = −1, which is also their B−L.
• Other elementary particles (all of which are force carriers) have B−L = 0
  • W and Z bosons have weak isospin T_z equal to their charge Q, so their weak hypercharge is Y_w = 0, which is also their B−L,
  • other force carriers have zero Q and T_z, so their weak hypercharge is Y_w = 0, which is also their B−L.

From this it follows that $Y_{W}=B-L\,$ holds for all known particles and that X from the second relation is indeed an conserved quantum number — it is always equal to 3(B−L), so it's addition seems unnecessary. --93.138.216.166 (talk) 11:59, 3 October 2009 (UTC)

$Y_{W}=B-L\,$ is true for all left-handed fermions and right-handed anti-fermions but breaks down for (you guessed it!) right-handed fermions and left-handed anti-fermions. The right-handed down quark has zero T_z , for example. The more general formula, $X+2Y_{W}=5(B-L)\,$, is required to cover everything.

You have my sympathies -- I made the same mistake last year :-) --Michael C. Price ^talk 15:50, 3 October 2009 (UTC)

93.138.216.166 has a point though, that without specifying the meaning of the 'X' quantum number the equation is completely meaningless (or rather completely trivial since X can be interpreted to mean whatever is required in order to make the relation true). Instead of X I would rather define X' = [X - 3(B-L)]/2 which leads to the equation X' + Yw = (B-L) which is much more pleasing, in my opinion. Dauto (talk) 19:54, 3 October 2009 (UTC)

Agreed, 93.138.216.166 does have a point, but "X" is what is it called in the literature. Unfortunately I don't have a name for X; does anyone know it? Without a name it's hard to create an article for it. As for describing its meaning, I not sure how to do that. We could list the values that various particles possess, I guess..? --Michael C. Price ^talk 20:57, 3 October 2009 (UTC)

How about X (charge)? Headbomb {^ταλκ_{κοντριβς} – WP Physics} 03:57, 4 October 2009 (UTC)

Are there any right-handed fermions (and left-handed anti-fermions) discovered or at least predicted? Also, it would be nice to mention how relation simplifies in their absence. --78.0.226.2 (talk) 22:38, 3 October 2009 (UTC)

There are left and right handed electrons, for example, but only left handed neutrinos (that we know of).--Michael C. Price ^talk 23:14, 3 October 2009 (UTC)

That's the case for the Standard model. The discovery of neutrino oscilations requires neutrinos to have mass. In most models that is achieved by including a right handed neutrino in the model. Dauto (talk) 17:04, 14 October 2009 (UTC)

If you decide to write the article you should probabily mention SO(10) GUT models that follow the symmetry breaking pathway given by SO(10) -> SU(5) times U(1)_X -> Standard model, since that's when the X-charge is most relevant. The SU(5) times U(1)_X symmetry group is often refered to as a 'fliped'-SU(5) model in the literature. Dauto (talk) 17:10, 14 October 2009 (UTC)

I would like to see an X article, but I need to find out more about the Pati-Salam before I can contribute much. As I understand it both X and the righthanded neutrino emerge from SO(10). --Michael C. Price ^talk 22:51, 14 October 2009 (UTC)

I uploaded one of my weight diagrams for the 16 representation of the SO(10) group to the wikicommons. My experience is that these diagrams are quite helpful to understand the relationship between all these different charges. Dauto (talk)

It sure does look pretty. Is there an article (or link) that will decode it for us? --Michael C. Price ^talk 23:22, 25 October 2009 (UTC)

(Undent) We don't have an article about Weight diagram but we do have an article about root system. A root system is nothing more than the set of (non-vanishing) weights of the adjoint representation of a group.

Root system A₂

The picture to the left (from the root system article) will likely look familiar. That's the SU(3) octet that can also be seen at the articles Eightfold Way (physics), Baryon, and Meson. A₂ is another name for SU(3). Those diagrams are not too hard to visualise because SU(3) space is bidimensional (yes, bidimensional - the quark article needs to be fixed because it claims incorrectly that the color space is three-dimensional). SO(10) space is 5-dimensional which makes it a little harder to visualise the weight diagram structure (5-dimensional screans are not an standard feature of most modern laptops). That's why I labeled the conections between the vertices of diagrams with numbers from 1 to 5 and also color-coded them to make easy to identify the respective eigenvalues (listed inside of the boxes on the vertices). For the SU(3) group those eigenvalues would be Hypercharge and Isospin, for instance. For the SO(10) group, five eigenvalues are necessary to completely label the vertices (By convetion we use twice the values of the five different isospin components to avoid fractions). To see the relationship of that to the Standard Model simply remove the conections labeled 2 (yellow) and 5 (green). These are the generators associated with the part of the symmetry that must be broken in order to reduce SO(10) to the Standard Model. The remaining generators are associated with color SU(3) (blue and purple) and weak isospin (red). Weak hypercharge is given by $Y=-2I_{1}-4I_{2}-{\frac {8}{3}}I_{3}-{\frac {4}{3}}I_{4}\,$ which also gives us $Q=-2I_{2}-{\frac {4}{3}}I_{3}-{\frac {2}{3}}I_{4}\,$, $(B-L)={\frac {4}{3}}I_{3}+{\frac {2}{3}}I_{4}+2I_{5}\,$, and $X=4I_{1}+8I_{2}+12I_{3}+6I_{4}+10I_{5}\,$. Dauto (talk) 18:19, 27 October 2009 (UTC)

Hi Dauto, thanks for the explanation. I followed most of it, and am relieved to see that we end up with $X+2Y_{W}=5(B-L)\,$. A couple of things are still unclear to me. The subscripts M and C; are they anti-colours or what? And do we need to specify the chirality of these quarks and neutrinos? (Are they all left handed?)--Michael C. Price ^talk 11:29, 28 October 2009 (UTC)

Yes. M,C,Y stand for the anti-colors magenta, cyan, and yellow, while R,G,B stand for the colors red, green and blue. Some people don't like those lables and simply call them 1,2,3. And yes. All these particles are left-handed. All the right-handed particles belong to the 16* representation which is identical to the 16 but up-side-down and will have the oposite eigenvalues for all five generators. Dauto (talk) 02:32, 31 October 2009 (UTC)

Table is inadequate

The table has no apparent connection to the article. I actually came to this article because I am trying to understand the relationship between weak charge, weak isospin, parity, and handedness. So, while I have a vague understanding of what e_R means, most people will not. I also question whether the values of T₃ for the quarks are correct? Perhaps I've confused T3 with T (weak isospin, total) but I'm pretty sure I've run across several references in WIKIPEDIA which state T3 is +/- ½ for the quarks?? So, the table should either be removed or preferably discussed/explained in the article (as well as corrected, if wrong). A reference SHOULD really be provided, also. I'd also suggest expanding it to include both T and T3, as well as noting that isospin and weak isospin are unrelated (?!) in the text.Abitslow (talk) 17:28, 6 March 2015 (UTC)

I just checked. The article Weak Interaction clearly claims that T₃ is NOT zero for the quarks and states that T₃ IS weak isospin. I understand that various authors consider the T₃ component as weak isospin, but the difference between T and T₃ is important, imho. Important enough to be made clear in each article using it (or at least those which give a value for it)!Abitslow (talk) 17:36, 6 March 2015 (UTC)

T specifies the weak isomultiplet. T₃ specifies a component of the isomultiplet. So the T=1/2 doublet may have T₃ =±1/2 isocomponents. Informal language, but crystal-clear from context. Unless one is familiar with SU(2) from sophomore QM , or the original isospin, this is not the place to come to brush up on them. Cuzkatzimhut (talk) 15:22, 10 February 2018 (UTC)