# Dimension of a partial decay width

1. Dec 23, 2015

### Safinaz

Hi all,

I know that the dimension of a partial decay width or a cross section should be GeV or pb respectively. But what if i have a decay width probational to

$\Gamma = 10^{-3} GeV^3 G_\mu$

where I calculated all the masses and constants in $\Gamma$, $G_\mu$ is the Fermi coupling constant equals $10^{-5} GeV^{-2}$, then

$\Gamma = 10^{-8} GeV$, not GeV, so should I multiply $\Gamma$ by 10^8 to have the right dimension ?

Regards,
S.

2. Dec 23, 2015

### ChrisVer

I am confused... you wrote Γ in GeV, and then you say "not GeV"...
why would you multiply it with 10^8 to get the right dimensions? the right dimension for what?

3. Dec 23, 2015

### Safinaz

Well, the problem that i calculate this decay width, namely:

Gamma(Sbb) = ((Ybb^2 * mS )/(128* Pi)) * beta^3,

where S is a coloured scalar, mS ~ 700 GeV , it's coupling to b b~ of order 10^-2, and beta =Sqrt[1-4mb^2/mS^2].

This formula is similar to Eq. 2.6 in ( http://arxiv.org/pdf/hep-ph/0503172v2.pdf ), but i adjusted the colour factors for the coloured scalars and used 1/v^2= G, mf^2/v^2 ~ Ybb^2.

I think now the dimension is aright => GeV, but while calculating this width by Mathematica gives ~ 10^-3 GeV, Matrix element calculators as Madgraph and Calchep gives it ~ 10^3 GeV !!, so what is missed in the analytic expression (some factor of 10^6) to make this discrepancy ..

Bests,
S.

4. Dec 24, 2015

### Staff: Mentor

The dimensions are right (GeV), just the numerical value disagrees.
106 could indicate some factor of 1000 applied in the wrong way, but it's hard to tell if you don't show all input values and results.

5. Jan 3, 2016

### RGevo

You should get something the same as the Higgs.

Your scalar mass is like 4 times larger, and a 10^-2 coupling for the yukawa is half that of the b roughly. Therefore your answer should be similar to the partial width of that of b quarks. Which is order 10^-3 GeV. So the calchep calculation has been done incorrectly, or its not in GeV