The dominant decay mode of the Higgs boson is to "bottom" quark-anti-quark pairs. The bottom quark is the second-heaviest of the quarks with a mass of 4.2 GeV. The quark and anti-quark have the same mass. For simplicity, we will consider Higgs bosons created at the LHC with zero momentum transverse to the beam direction. In fact, the Higgs bosons are always created with some non-zero transverse momentum, but including that in the kinematics just adds un-instructive complications. Assume that beam direction is along the x axis and the outgoing bottom quark and anti-quark have momenta that lie in the x- z plane. Evaluate the kinematics of the two quarks as observed in the laboratory when the Higgs has a rapidity, y, as seen in the laboratory, and the decay products are emitted at an angle * with respect to the x axis as seen in the rest frame of the Higgs boson (See Figure 11.4 in the course notes) Take the Higgs mass to be 125 GeV. What is the maximum momentum of the bottom quark transverse to the beam?

The dominant decay mode of the Higgs boson is to "bottom" quark-anti-quark pairs. The bottom quark is the second-heaviest of the quarks with a mass of 4.2 GeV. The quark and anti-quark have the same mass. For simplicity, we will consider Higgs bosons created at the LHC with zero momentum transverse to the beam direction. In fact, the Higgs bosons are always created with some non-zero transverse momentum, but including that in the kinematics just adds un-instructive complications. Assume that beam direction is along the x axis and the outgoing bottom quark and anti-quark have momenta that lie in the x- z plane. Evaluate the kinematics of the two quarks as observed in the laboratory when the Higgs has a rapidity, y, as seen in the laboratory, and the decay products are emitted at an angle * with respect to the x axis as seen in the rest frame of the Higgs boson (See Figure 11.4 in the course notes) Take the Higgs mass to be 125 GeV. What is the maximum momentum of the bottom quark transverse to the beam?