Template talk:Flavour quantum numbers

B−L

The anomalies that break B and L individually cancel exactly to conserve B−L. See, for example, the end of the SM section of Phenomenological guide to physics beyond the Standard Model. In fact, you can (in Beyond-the-SM models) gauge the B−L symmetry. Of course, you can also break the symmetry in some SuSy models, but that's decidedly beyond-the-SM. -- Xerxes 18:25, 19 December 2005 (UTC)

Oops, that's my bad. I'mm a jerk. -lethe ^talk 18:43, 19 December 2005 (UTC)

More than Flavour

This is more than just the flavour associated quantum numbers. Perhaps we should rename it just "quantum numbers"? --Michael C. Price ^talk 23:27, 11 November 2008 (UTC)

I split up the (baryonic) flavour quantum numbers from the others. This should solve your question. --Dogbert66 (talk) 09:30, 24 January 2011 (UTC)

Up and Down

Why do we not call Up and Down flavour quantum numbers? They are conserved by the strong force, are they not? --Michael C. Price ^talk 23:29, 11 November 2008 (UTC)

I think this has historical (and some practical) reason. Let's use the following ad-hoc definitions for some 'Upness' U and and 'Downness' D as follows:

$U=(n_{u}-n_{\overline {u}})$

where $n_{\overline {u}}$ represents the number of up antiquarks (
u
) and $n_{u}\$ represents the number of up quarks (
u
).

$D=-(n_{d}-n_{\overline {d}})$

where $n_{\overline {d}}$ represents the number of down antiquarks (
d
) and $n_{d}\$ represents the number of down quarks (
d
).

Please keep in mind, that we have a minus sign for all down-like quarks as defined in Strangeness and Bottomness but not for the up-like quarks as defined in Charm and Topness.

By this we have

$I_{z}={\frac {1}{2}}(U+D)$

(per definition of I_z )

$B={\frac {1}{3}}(U-D+C-S+T-B')$

(per definitions of B, U, D, C, S, T, and B': Count 'em all)

Solved for U, D we yield:

$U=I_{z}+{\frac {3}{2}}B-{\frac {1}{2}}(C-S+T-B')$

 

$D=I_{z}-{\frac {3}{2}}B+{\frac {1}{2}}(C-S+T-B')$

This shows that we could use U and D as a substitute for B and I_z as well. Examples:

(1) For the hypercharge Y as given by

$Y{\frac {}{}}=B+S+C+T+B'$

we yield

$Y={\frac {1}{3}}(U-D+4C+2S+4T+2B')$

(2) For the electric charge Q as given by Gell-Mann–Nishijima formula

$Q=I_{z}+{\frac {1}{2}}Y$

wie yield finally

$Q={\frac {2}{3}}(U+C+T)+{\frac {1}{3}}(D+S+B')$

which resembles the corresponding Q term as given in article Gell-Mann–Nishijima formula. Keeping in mind the definitions for U, C, T, and D, S, B' (minus sign for D, S, and B !) we can verify the broken electric charge numbers of the quarks:
u
,
c
and
t
have Q=+2/3, whilst
d
,
s
and
b
have Q=-1/3. The corresponding antiquarks have the opposite sign. --ErnstS ^talk 12:30, 31 January 2009 (CET)

Topness and Weak Isospin

Topness and weak isospin both are denoted by T. This is an ambiguosity like denoting bottomness and baryon number both by B. The latter was resolved in denoting bottomness by B' (sometimes B^* used). Shouldn't we do the same for topness, i. e. using a T' as symbol? We could leave T_z aka T₃ as it is. --ErnstS ^talk 12:55, 31 January 2009 (CET)

A better proposal might be to leave T as the sign for topness. Instead, we might use I_W for weak isospin (just like Y_W for weak hypercharge) instead of the ambiguous T, and I_W3 or I_Wz for its 3rd component (instead of T₃ or T_z).--ErnstS ^talk 10:20, 19 February 2009 (CET)

Yes I_W for weak isospin make sense to me. The dashes are too easy to miss. --Michael C. Price ^talk 13:58, 19 February 2009 (UTC)

Third component of isospin and weak isospin

This template uses I_z as a denotation for the 3rd component of isospin rather than I₃ (same for weak isospin, currently T_z instead of T₃). When I changed some articles in english and german WP I messed up with several Z-s (also used as index). These are:

1) z (lowercase) as denotation for the 3rd component instead of 3

2) Z (uppercase) for the Z Boson

3) z (lowercase) for dimensionless charge number, i.e. the charge measured in units of the elementary charge e. This is used if there is a need for disambiguation with the Charge Q = z • e . For atoms this is identical with the atomic number Z (uppercase).

Especially for discussion of the electroweak interaction couplings, all three z's mess up, terrible :-( ! German example: de:schwache Ladung

What do you think about using 3 instead of z for the 3rd component, i.e. I₃ for 3rd component of isospin, T₃ (or maybe I_W3) as 3rd component of weak isospin?

Thanks in advance for any comments --Ernsts (talk) 20:35, 10 March 2009 (UTC)

I like the idea of 3 instead of z. Plus it seems more common in the literature. Updated.--Michael C. Price ^talk 22:37, 1 November 2009 (UTC)

PS I looked in the literature and it seems to be choice between I₃ & T₃; I can't see z used as a subscript anywhere. All my QFT books (Cheng & Li, Kaku, Itzykson & Zuber, Leite Lopes, Sterman) use either T₃ or I₃, not T_z or I_z. Nishijima's original paper uses I₃. --Michael C. Price ^talk 00:39, 7 November 2009 (UTC)

Removed typesetting problem

The title was overlaid with text. This was caused by the {{Tnavbar-header}} so I removed it. I suggest not replacing the {{Tnavbar-header}} unless you can solve the typesetting problem using it causes.Puzl bustr (talk) 14:11, 30 November 2009 (UTC)

Different formulas for Hypercharge??

On the wiki site for "Hypercharge" it says Y = B + S - (C - B' + T)/3 while the template says Y = (B + S + C + B′ + T) below "Combinations / Hypercharge: Y" 46.142.91.204 (talk) 14:20, 14 February 2024 (UTC)