NMSSM scan

One advantage that programs such as SoftSusy have is that they can calculate the particles masses and couplings for a variety of input parameters, this enables scanning of the parameter spaces of supersymmetric models. With the addition of MSSM and NMSSM supersymmetric and Higgs decays, this scanning may be extended to examining how decay widths (and hence signatures) vary across the parameter spaces of the various supersymmetric models included. Given the inclusion of the NMSSM is rare, and the NMSSM parameter space is enriched via the additional singlet coupling parameters, here we present such a scan for the extended neutralino sector decays of the NMSSM in Figure 4.14. The neutralino singlino components are solid lines in the figure read on the left-hand y-axis and the corresponding neutralino total widths are dashed lines read on the right-hand y-axis . This scan is demonstrative of the analyses which may be performed with SoftSusy’s spectrum generator and decay calculator linked together, indicating the improved model examination power of such an all-in-one program package.

As the scan is only for display purposes, we simply take the nmssmSLHAnoZ3Input file pro- vided with the SoftSusy program and scan λ from 0.001 to 0.25. The data however stop at λ_{≈ 0.2295 as at this point the lightest Higgs becomes tachyonic (has negative mass squared)} - this is a problem for correct electroweak symmetry breaking so these model points are not valid and the spectrum and decays are not calculated. Referring back to our introduction to the

NMSSM in Chapter 2.4, in equation 2.45 we see that theλ parameter in the extended neutralino sector dictates the coupling of the two Higgsino neutralino gauge eigenstates to the singlino, this ultimately originates in theλSHuHd NMSSM superpotential coupling. Therefore we can con-

sider λ as the mixing of the singlino component into the Higgsino like neutralinos. For our setup here the third and fourth heaviest neutralinos are the dominantly Higgsino neutralinos; therefore as we increaseλ in Figure 4.14 we observe that their singlino components (N (3, 5) and N (4, 5)) rise most (although those of all the four MSSM neutralino all rise slightly), meanwhile the singlino component of the heaviest neutralino (N (5, 5)) correspondingly drops as it mixes more with the other neutralinos. As the singlino only interacts with non-Higgs like particles via mixing, we can observe the same effects in the total widths of the neutralinos. At small λ the heaviest neutralino (which is the dominantly singlino one at this stage) has very small total decay width and asλ increases its singlino component reduces and its decay width accord- ingly increases rapidly as it gains Higgsino neutralino decays. Meanwhile the total width of the fourth heaviest neutralino drops concurrently as it cedes its Higgsino component gradually to the heaviest neutralino. There is also an interesting feature in the singlino components, and in the same manner in the decay widths, atλ_{≈ 0.1347; as the Higgsino like neutralinos mix with} the singlino, initially it is the fourth heaviest neutralino which mixes most, however as it does so its mass reduces whilst the absolute mass of the third heaviest neutralino increases. Eventually atλ_{≈ 0.1347 the third and fourth heaviest neutralinos are relabelled as the absolute values of} their masses cross; as a result in our plot we see theN (3, 5) and N (4, 5) singlino components, and the Γ3 and Γ4 total decay width values each interchange.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0 0.5 1 1.5 2 2.5 3

|Singlino component|, |N(i,5)|

Total width,

Γ

i

(GeV)

λ

Figure 4.14: A scan of the λ parameter in the NMSSM using SoftSusy-4.1.4 and the base point nmssmSLHAnoZ3Input. The singlino components of each of the 5 physical mass-ordered neutralinos are shown on the left-handy-axis and are given by the solid lines. This shows that the 3rd _{and 4}th _heaviest

neutralinos, being the dominantly Higgsino neutralinos, mix increasingly with the singlino asλ increases as expected. The dashed lines and right-handy-axis indicates how the total decay width of each neutralino varies withλ. Increasing/decreasing singlino fraction reduces/increases the total width as expected.

4.3.1 Decay Calculator Processing Performance

In performing such scans the issue is often the program speed; many different parameter points must be evaluated for both their mass spectrum and couplings, and their decay widths. As such, the speed of evaluation of one parameter point is important for allowing such analyses to be easily manageable. Of course, spectrum generator and decay calculator programs are far from the bottleneck in the overall analysis chain (given previously in Figure 3.2), this is in the Monte Carlo event generation for particle production cross-section evaluation. Nonetheless, if investigations include only the spectrum generation and decay calculation we should ensure the decay calculation does not significantly slow the program and thereby make such scans more cumbersome than necessary. Fortunately the decay calculations are not computationally intensive, and our approach to include as many formulae as possible hand-coded and evaluated analytically ensures the decay calculations require minimal time to evaluate. The only modes which may take more significant computational power are the 3-body modes, requiring numerical integration; however even in these cases we have first analytically reduced the integral to one- dimension lessening the computer time required. As a consequence, the decay calculation step adds minimal additional burden to the SoftSusy package, typically increasing the evaluation time by only 5% when 3-body modes are included and by only 2% if these are excluded7. Although this evaluation time of the decay calculator will increase as further modes, particularly 3-body modes, are added; we still anticipate it taking no more than a fraction of the spectrum calculator computation time, as the spectrum calculator requires an iterative process to be completed until convergence is reached.