Higgs Decay

Let us consider the decay modes of an on-shell Higgs boson. The properties of a particle’s decay are captured by the differential decay width $d\Gamma$. For a decay of one particle with momentum P into n particles,

$d\Gamma =\frac{(2\pi {)}^4}{2M}|\mathcal{M}{|}^{2}d{\Phi }_n(P;p_1,\dots ,p_n)$.

$\mathcal{M}$ is the off-diagonal S-matrix element for the decay process,

$i(2\pi {)}^4{\delta }^{(4)}(P-p_1-\cdots -p_n)\mathcal{M}(P;p_1,\dots ,p_n)=⟨p_1,\dots ,p_n|S-1|P⟩$,

and $d{\Phi }_n$ is the phase space element for the decay of a particle with mass M into n particles with momenta $p_1,\dots ,p_n$ and masses $m_1,\dots ,m_n$.

$d{\Phi }_n(P;p_1,\dots ,p_n)={\delta }^{(4)}\left(P-{\sum }_{i=1}^n{p}_i\right){\prod }_{i=1}^n\frac{d^3{p}_i}{(2\pi {)}^{3}2E_i}$.

Since we require only the $1\to 2$,

$d{\Phi }_2(P;p_1,p_2)=\frac{1}{2}\frac{1}{(2\pi {)}^6}\frac{|{\vec{p}}_1|}{2M}d\Omega ,|{\vec{p}}_1|=\frac{{\lambda }^{1/2}(M^2,m_1^2,m_2^2)}{2M}$.

Here, $\lambda (x,y,z)=x^2+y^2+z^2-2xy-2xz-2yz$ is the Källén function and $d\Omega =d\cos \theta d\varphi$ is the solid angle element of the first decay product in the center-of-mass frame of the initial particle. Since the Higgs boson is a scalar particle, the decay width is isotropic, i.e., the matrix element does not depend on the solid angle. Hence,

$\Gamma =\frac{1}{16\pi M^3}|\mathcal{M}{|}^2{\lambda }^{1/2}(M^2,m_1^2,m_2^2)$.

• Tree-level Decay Modes
• Loop-induced Decay Modes
• Higgs Decay Branching Ratios
• Status of Higgs Decay Measurements