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I need to calculate the lifetime of the W boson given its decay width. From what I know the lifetime of a particle is calculated by dividing $\hbar$ with the decay width $\Gamma$. From my textbook $\Gamma=2.141 $ GeV, and $\hbar=6.852 \times10^{-15} $Gev$\cdot$s, doing the lifetime calculation with these values gives me:

$$\tau=\hbar/\Gamma\approx3.2\times10^{-15}s$$

I know the correct solution is $3.2\times10^{-25}s$, but I can't for the life of me figure out how to get that number. What am I missing here?

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  • $\begingroup$ Which unit has $\hbar=6.852 \times10^{-15}$? eVs, or GeVs, or something else? $\endgroup$ – Thomas Fritsch Jun 13 '19 at 17:23
  • $\begingroup$ @ThomasFritsch I apologize, the units are Gev$\cdot$s. I have edited my post. $\endgroup$ – matryoshka Jun 13 '19 at 17:26
  • $\begingroup$ Look at Wikipedia:Planck constant. They have $\hbar = 6.582 \cdot 10^{-16}$ eVs. (i.e. without G) $\endgroup$ – Thomas Fritsch Jun 13 '19 at 17:31
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    $\begingroup$ You seem to have done an incorrect conversion from $eV$ to $GeV$ as $\hbar = 6.582\times 10^{-16}eV \cdot s$, and $1 \; eV = 10^{-9}\; GeV$ $\endgroup$ – Triatticus Jun 13 '19 at 17:31
  • $\begingroup$ The Google calculator says hbar/(2.141 GeV) is $3.07432018\times 10^{-25}$ seconds. $\endgroup$ – PM 2Ring Jun 13 '19 at 17:34
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You might want to check that value for $\hbar$ carefully.

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