Dimension of a partial decay width

[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.

 

[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?

 

[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.

 

[mfb]

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.

 

[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