$T \sf{(K)} \ \equiv \ \mathit{T} \sf{(ºC)} + \mathrm{273.15}$
where $\, T \sf{(ºC)} \,$ is the Celsius temperature. In the following discussion, the symbol $T$ refers to the thermodynamic temperature, in units called kelvins, noted by (K).
Quarks are indestructible but compound quarks may decay. Their stability is characterized by a number called the mean-life. Let particle P be described by its thermodynamic temperature $T$. Definition: The mean life of P is
$\tau \equiv k_{\tau} e^{ -T}$
where $e$ is the exponential function and the constant $k_{\tau} = \sf{ 2.6 x 10 }^{\sf{56}}$ seconds. Customarily, if $\sf{P}$ is an atom of hydrogen in its ground-state, then $T=0 \ \sf{(K)}$ and $e^{ 0} = 1$, so this constant $k_{\tau}$ is called the mean-life of hydrogen.1 A particle with a negative temperature supposedly has a longer mean-life than hydrogen. But for WikiMechanics, the only particles like this are some quarks and field quanta that are not assigned positions. All models of observed nuclear particles have a positive thermodynamic temperature. Particle stability is also characterized by a number called the full width which is noted by $\varGamma$ and defined as$\begin{align} \varGamma \equiv \frac{h}{2 \pi \tau} \end{align}$
The total number of any specific type of quark does not vary if ordinary-quarks are swapped with anti-quarks of the same type. And with the assumption of conjugate symmetry, ordinary-quarks and anti-quarks both have the same temperature. So
$\tau ( \sf{P} ) = \tau ( \overline{\sf{P}} ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sf{\text{and}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \varGamma ( \sf{P} ) = \varGamma ( \overline{\sf{P}} )$
Particles and their associated anti-particles have the same mean-life and full-width.
Here is a link to the most recent version of this content, including the full text.
Lifetime |
Summary |
Adjective | Definition | |
Thermodynamic Temperature | $T \sf{(K)} \ \equiv \ \mathit{T} \sf{(ºC)} + \mathrm{273.15}$ | 8-4 |
Adjective | Definition | |
Mean Life | $\tau \equiv k_{\tau} e^{ -T}$ | 8-5 |
Adjective | Definition | |
Full Width | $\begin{align} \varGamma \equiv \frac{h}{2 \pi \tau} \end{align}$ | 8-6 |