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Lifetime

The lifetime of a particle is suggested by this ancient network of threads and spectral figures.
Textile fragment, Chancay people. Pre-Columbian Peru, 50 x 30 cm. Photograph by D Dunlop.
The temperature of a bottom quark is represented by this snowflace icon.

Recall that the reference sensation of touching ice is used to calibrate the measurement of temperature. So to make good measurements we are getting more precise about what we mean by ice. Accordingly, here is a definition of temperature that is tied to the triple point of water. The thermodynamic temperature is defined by

T \mathsf{(K)} \; \equiv \;  T ( ^{\circ} \mathsf{C} ) + \mathrm{273.15}

where  T ( ^{\circ} \mathsf{C} ) 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 conserved 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. The mean life of P is defined as

  \tau \equiv k_{\tau} e^{-T}

where  e is the exponential function and the constant  k_{\tau} = \mathsf{ 2.6 x 10 }^{\mathsf{56}} seconds. Customarily, if P is an atom of hydrogen in its ground-state, then  T=0 \; \mathsf{ (K) } and  e^{ 0} = 1, so this constant  k_{\tau} is called the mean-life of hydrogen1For more detail, see the discussion of stability in the article about atomic hydrogen.. A particle with a negative temperature supposedly has a longer mean-life than hydrogen. But for EthnoPhysics, the only particles like this are some quarks and field quanta which are not given space-time descriptions. 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

  \varGamma \equiv \dfrac{h}{2 \pi \tau}

The total number of any specific type of thermodynamic quark does not vary if ordinary-quarks are swapped with anti-quarks of the same type. And with the assumption of conjugate symmetry both kinds of quarks have the same temperature. So

\tau ( \mathsf{P} ) =  \tau ( \overline{\mathsf{P}} )

and

\varGamma ( \mathsf{P} ) = \varGamma ( \overline{\mathsf{P}} )

Particles and their associated anti-particles have the same mean-life and full-width. Next we consider a special nuclear particle, the proton.

References
1For more detail, see the discussion of stability in the article about atomic hydrogen.