Sigma Baryons

We describe sigma baryons using chains of events that represent the particles in their ground-states

\mbox{\fontsize{14}{18}\selectfont $ \Psi ^{\sf{\Sigma}} = \left( \sf{\Omega}_{0} , \sf{\Omega}_{1} , \sf{\Omega}_{2} \ \ldots \ \sf{\Omega}_{\it{j}} \ \ldots \ \right) $}

where each repeated event Ω is composed of the following quarks

Quark Coefficients
Sigma u d e g m a t b s c u d e g m a t b s c
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{+} $} 12 20 128 11 129 2 4 130 2 12 130 18 8 13 13
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{+}} $} 4 130 2 12 130 18 8 13 13 12 20 128 11 129 2
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{\circ} $} 4 49 12 51 1 4 2 2 4 4 49 10 49 1 4
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}} ^{\circ} $} 4 4 49 10 49 1 4 4 49 12 51 1 4 2 2
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{-}} $} 4 26 16 27 3 2 4 8 26 18 29 1 4
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{-}} $} 8 26 18 29 1 4 4 26 16 27 3 2 4

We visualize theses baryons as cores of rotating and baryonic quarks that are surrounded by swarms of leptonic quarks that make up the particle's electromagnetic field. Here is a schematic picture of the rotating quarks in the core of a neutral sigma anti-baryon.

u u
d d u u
d d d d
d d

The quark coefficients determine quantum numbers as

Sigma σ L B q S
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{+} $} 0.5 1 1 -1
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{+}} $} 0.5 -1 -1 1
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{\circ} $} 0.5 1 -1
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}}^{\circ} $} 0.5 -1 1
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{-} $} 0.5 1 -1 -1
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{-}} $} 0.5 -1 1 1

The masses are calculated and compared with laboratory observations

Sigma calculated
mass (MeV)		 observed
mass (MeV)		 observed
uncertainty		 ok? ∆ m%
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{+} $} 1,189.429 1,189.37 ±0.07 \definecolor{green}{rgb}{0.2,0.5,0.2} \color{green} \large{\pmb{\surd}} +0.005
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{+}} $} 1,189.429
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{\circ} $} 1,192.683 2 1,192.642 ±0.024 \color{red} \LARGE{\pmb{\times}} +0.003
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}} ^{\circ} $} 1,192.683 2
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{-}} $} 1,197.410 5 1,197.449 ±0.030 \color{red} \LARGE{\pmb{\times}} -0.003
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{-}} $} 1,197.410 5

The lifetimes are found as

Sigma calculated
lifetime		 observed
lifetime		 observed
uncertainty		 units
(s)		 ok? ∆ τ%
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{+} $} 7.993 8.02 ±0.03 x10-11 \definecolor{green}{rgb}{0.2,0.5,0.2} \color{green} \large{\pmb{\surd}} -0.3
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{+}} $} 7.993 x10-11
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{\circ} $} 7.69 7.4 ±0.7 x10-20 \definecolor{green}{rgb}{0.2,0.5,0.2} \color{green} \large{\pmb{\surd}} +4
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}} ^{\circ} $} 7.69 x10-20
\mbox{\fontsize{14}{18}\selectfont $ \sf{\Sigma}^{-}} $} 1.480 1.48 ±0.01 x10-10 \definecolor{green}{rgb}{0.2,0.5,0.2} \color{green} \large{\pmb{\surd}} +0.04
\mbox{\fontsize{14}{18}\selectfont $ \overline{\sf{\Sigma}^{-}} $} 1.480 x10-10

For spreadsheets that detail how these calculations are done, click here.

Page tags: sigma-baryon
page_revision: 23, last_edited: 1277758198|%e %b %Y, %H:%M %Z (%O ago)
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