Vector boson fusion

 The process of Higgs production through vector boson fusion shown in fig. 2.1b will only be important for high Higgs masses where the coupling to longitudinal polarised vector bosons is strong (see section 2.3.1).

At the high energies where a heavy Higgs particle is created the vector bosons act essentially as massless particles and can be treated as particles present inside the colliding protons. With this simplification the full process in fig. 2.1b can be separated into a calculation of the vector boson structure function in the proton and a calculation of Higgs production in colliding vector boson beams. The method is called the effective W approximation.

Following the derivation in [10] the cross section for production of a particle X in the fusion of two vector bosons can be written as

 

$$\sigma \rightarrow {\frac{16 \pi^2}{\hat{s}m_{X}}} \sum_{\lambda}^{} \int_{m_{X}^2/\hat{s}}^{1} {\frac{{d}x}{x}} \lambda \lambda {\frac{m_{X}^2}{\hat{s}x}} \Gamma_{\lambda}^{} \rightarrow$$ (24)

where F_$\lambda$ is the structure function for the vector boson V with partial width $\Gamma_{\lambda}^{}$ in the state with polarisation $\lambda$ , $\hat{s}$ = x₁x₂s the centre of mass energy squared of the two colliding quarks and q₁' , q₂' denoting the two outgoing quarks.

For the production of a Higgs, the decay width described in section 2.3.1 is dominated by the longitudinal polarised state. Ignoring the small contribution from the transverse polarised states the cross section for a heavy Higgs can be written as

 

$$\sigma \rightarrow {\frac{16 \pi^2}{\hat{s}m_{H}}} \sum_{V = W,Z}^{} \int_{m_{H}^2/\hat{s}}^{1} {\frac{{d}x}{x}} {\frac{m_{H}^2}{\hat{s}x}} \Gamma_{L}^{} \rightarrow$$ (25)

To get the full cross section for the Higgs from vector boson fusion the cross section above has to be convoluted with the structure functions of the incoming quarks. For all possible values of the Higgs mass the cross section is below the gluon fusion process, but with the additional signature of the two outgoing quarks participating in the process the identification will be easier in this production channel for a large Higgs mass. Chapter 8 details how a heavy Higgs can be identified with the use of the forward jets.