Decay into hadrons Sample Clauses

Decay into hadrons. The scalar mass below 1 GeV If the mass of the scalar particle S is above the hadronic threshold, i.e. mS > 2mπ, then the decay into pions is possible. The best (known to us) description of this decay is given in the paper [207], which combines chiral perturbation theory next to leading order with the method of dispersion rela- tions. Using data on pion-pion scattering, the authors produced a prediction for the light Xxxxx decay width into 2 pions, see Fig. 2.5. 300 250 ΓS→ππ /ΓS→μμ 200 150 100 50 0 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 mS[GeV] Figure 2.5: The ratio of the decay widths of the Xxxxx boson into pions and muons as a function of the scalar mass. Adapted from work [207]. The scalar mass above 2 GeV For this mass region, the decay width into hadrons can be estimated as the decay width into gluons and quarks. The decay width into gluons (with QCD corrections) [182, 208] is, Γ(S → gg) = |5 | 2 4π 8πv2 1 + 8v2π2 α θ m s 2 3 S m2 t . (2.3.2) Σ Here mt is the mass of the top quark and 5 = q 5q is a sum of the loop contributions from quarks, which is defined as, q 5q = −2yq(1 + (1 − yq)x2), (2.3.3) with yq = 4m2/m2 and q S  Arctan√ 1 , for yq > 1, √ π + ilog 1 − √y xq =  1  yq − 1 ! 1 + yq − 1 q − 1 , for yq ≤ 1.