# Branching fractions for the 125 GeV Higgs boson

Calculating the branching fractions of a Higgs boson $$m_h=125\,\text{GeV}$$ into a muon and an anti-muon, and a $$b$$-quark and an anti-$$b$$-quark from the decay formula
$$\Gamma=\frac{\alpha_{w}}{8 \hbar} m_{h} c^{2}\left(\frac{m}{M_{W}}\right)^{2}\left[1-\left(\frac{2 m}{m_{h}}\right)^{2}\right]^{3 / 2}$$

gives a different ratio in comparison with the ratio from this table SM Higgs Branching Ratios.

So basically why the ratio Γ(h→bb¯)/Γ(h→μμ¯) using the formula is not as the ratio BR(h→bb¯)/BR(h→μμ¯) found from the table? I'm getting 4633 while the table gives about 2630

what is special about $$m_h=125\,\text{GeV}$$? maybe something related to the experiment?

• Is the difference a factor of 3? You are missing a color factor of 3 for the bb final state. On top of that, the book contains QCD corrections which could be moderate to the bb state – innisfree Apr 29 '19 at 2:36
• I'm aware of the color factor. Thanks – hiery Apr 29 '19 at 3:37
• Perhaps the masses at the 125 GeV energy scales should be used? – ohwilleke Apr 29 '19 at 4:08
• No, it's not wrong, there is a reason behind this difference which I'm trying to find. – hiery Apr 29 '19 at 4:09
• @ohwilleke is probably right; going beyond tree-level, you should be using $m_b(m_h)$ which differs considerably from $m_b(m_b)$. You can find further discussion about the calculation in cds.cern.ch/record/340786/files/9712334.pdf $m_b(100\,\text{GeV}) \simeq 3\,\text{GeV}$. If these details more or less fix it, please write it up and answer your own question here. – innisfree Apr 29 '19 at 4:20