# Higgs boson lifetime and decay length?

1. Jan 13, 2012

### MarekS

I am trying to figure out how fast the Higgs decays and how far it travels in a detector at the LHC. Figure 2.5 in http://www.hep.lu.se/atlas/thesis/egede/thesis-node14.html gives decay widths of the Higgs as a function of its mass.

For a Higgs of 125 GeV, it is 0.002 GeV. Using the Heisenberg Uncertainty eq. lifetime*decay width = h-bar/2, I find lifetime = 1 zeptosecond. Is this correct? What kind of assumptions can I make about its speed so that I could calculate distance travelled?

2. Jan 13, 2012

### Bill_K

An easy way is to use the value of Planck's constant in the form ħc ≈ 200 MeV-f. This says that a particle with a width of 200 MeV will travel about a fermi before it decays. More generally the distance traveled is ħc/Γ. So if the width of the Higgs boson is, as this guy claims, 2 MeV, the distance it travels will be about 100 fermis. A highly energetic Higgs will travel somewhat farther than this due to time dilation.

3. Jan 13, 2012

### MarekS

Dear Bill_K,

thanks for the input. By using c in the equation, you are assuming that the Higgs travels at (close to) c, are you not? If this is the case, then time dilation will be a significant effect.

Marek

4. Jan 13, 2012

If the resonance peak is centred on the Higgs rest mass, and Γ << mH, then it will be slow.

Its momentum will be of the order

pH ≈ Γ / c

so, by the uncertainty principle, this implies an uncertainty in its position of

Δx > ħ / pH = ħc / Γ

which gives an indication of how far it will travel.

5. Jan 13, 2012