SoftSusy-4.0 was the first version of many including the decay calculator program and therefore contained only the modes deemed crucial to collider applications. Since then, minor additions and changes have been made in updating the package to the latest SoftSusy-4.1.4 version; these include the introduction of the chargino to neutralino pion modes described in Chapter 4.2.5 and the addition of a limit to improve the accuracy of predictions for extremely compressed gluino spectra as outlined in Chapter 3.3.5 and elucidated further in Appendix A.4.1, amongst others. We hope the decay calculator aspect will prove of tremendous use for collider search applications, representing a major upgrade of the SoftSusy package capabilities. To this end, we plan a program of future developments and improvements to the decay calculator program, building on the foundations we have laid in its first versions. The exact changes, additions and augmentations made and the order of these improvements will be guided by the needs of users, and by data from ATLAS and CMS, nonetheless the following are a selection of those we currently intend to prioritise:
7
For example, running on my personal laptop with the lesHouchesInput file provided with the SoftSusy code, I find the mass spectrum generator takes 0.75s, the decay calculator with 3-body modes included takes 0.04s and without 3-body modes included takes 0.01s.
• 3-body sfermion ˜f decays - The current version of SoftSusy includes the most phenomeno- logically relevant 3-body decay modes of the gluinos, charginos and neutralinos; however currently no sfermion 3-body decays are included. These may be particularly relevant for searching compressed spectra regions, for example these are pertinent to spectra with light stop masses8 such that m˜ti < mt+mZ˜1, mb +mW˜1±, but m˜ti > mb +mW +mZ˜1. These points can arise for light stops due to the larger top mass preventing 2-body decays including tops in the final state. There are also ˜ti → bl˜ldecays (where l˜lare a lepton sneu-
trino or slepton neutrino pair): these 3-body decays arise where again no 2-body modes are available and sleptons are lighter than squarks, the latter condition often occurring for common GUT scale scalar masses, such as those imposed in mSUGRA. Meanwhile ˜
ti → ˜bif ¯f0 decays mediated viaW bosons or charged Higgses, may be relevant for larger
tanβ in regions where ˜ti − ˜bi < mW. More information on the 3-body decays of third
generation squarks is given in [189].
• Further chargino, neutralino and gluino 3-body decays - Whilst the most likely 3-body decays relevant to colliders are included for charginos and neutralinos, there are some rarer candidate decays remaining which may be apposite. These include the chargino or neutralino 3-body modes to gluinos and quark-antiquark pairs, which can easily be incorpo- rated into the program, being the crossing of 3-body gluino modes already included. Also, as of yet, 3-body heaviest chargino to lightest chargino modes plus a fermion-antifermion pair via Higgs, Z or sfermion intermediates are not included, although these are of sub- stantially reduced importance as spectra with the two charginos quasi-degenerate are rare phenomenologically. Concurrently, gluino 3-body decays to stops, a bottom quark and a W boson (or charged Higgs) could also be of relevance in some regions of parameter space, whilst neutralino to neutralino pion modes could also be added, reflecting regions where two neutralinos (particularly the lightest two) are quasi-degenerate
• Loop decay modes - These early versions of the SoftSusy decay calculator included only the crucial 1-loop decay modes of Higgs particles, albeit in both the MSSM and NMSSM. However, given we explained briefly in Chapter 3.1 that 1-loop and 3-body modes are ordinarily similarly suppressed, there are radiative decay modes relevant to the compressed spectra regions for which we have included 3-body modes to target. Key examples are the ˜
g → g ˜Zi and the ˜Zj → ˜Ziγ decays, the latter of which can be especially relevant for ˜Z2
decays [190]. In addition, the mode ˜ti→ c ˜Z1 may be needed for some regions of parameter
space, even though it is CKM and loop-suppressed, if no tree-level 2-body modes are available and the phase space for the 3-body modes is small due to the compressed nature of the spectra.
• Further QCD Corrections - To date, the SoftSusy decay calculator has only included QCD corrections in the neutral Higgs decays to quarks (at 1-loop) and to gluons (at 2- 8The lightest stop is often light as the mixing between the stop eigenstates is proportional to the large top
loop), although already in both the MSSM and NMSSM, as these are essential to correctly reproducing the branching ratios of the Standard Model-like Higgs. Nonetheless, QCD corrections can have significant impacts on the decays of other supersymmetric particles, in particular the branching ratios of squark and gluino decays. Modes for which QCD corrections will be added include ˜g → ˜q¯q, ˜q → ˜gq, ˜q → ˜Ziq, ˜q → ˜Wi±q0, ˜q2 → ˜q1V and
˜
q2 → ˜q1φ. More minutiae are given in [134, 191–196], in some regions of parameter space
the effects of such SUSY-QCD corrections can be of order 10%.
• Very Compressed Regions - In very compressed regions spectrum generators and decay calculators can lose precision due to two main factors: first of all, decays in such regions are very phase space dominated, and so any small differences in the particle masses de- termined by the spectrum generator can alter the partial widths significantly by altering the phase space available. Secondly, decay calculators can lose accuracy due to numerical precision in such regions as very fine cancellations frequently arise at the ends of phase space integrals. Whilst the former issue can only be resolved with greater precision in the spectrum generation, the latter can be aided by taking appropriate limits for very compressed regions. This has been performed for the gluino 3-body decays, as described in Chapter 3.3.5 and Appendix A.4.1. This approach could be extended to other very compressed decays.
• NMSSM 3-body decays - Longer term, as we enhance the program with further MSSM 3-body decays, we may also decide to extend this work into incorporating NMSSM 3-body decays. Currently these are less important due to the enlarged parameter space and limited constraints on the NMSSM, nevertheless they may become relevant with time and collider results. A selection of these modes are available in NMSSMTools.
• R-parity violation - SoftSusy is in limited company as a spectrum generator able to in- corporate RPV effects for the MSSM, with only sPHENO able to do the same amongst the main programs publicly available (see Table 3.1). Extending this to the decay calculator may therefore offer significant benefits to the community in searching for RPV signatures at colliders, particularly as R-parity conserving models become further restricted by ex- perimental exclusions. Again this would be a longer term development of the program and so is dependent upon the nature of collider results in the interim.
As can be seen, this represents a significant program of development and many opportunities for improvement. We therefore hope and expect this program of research continues considerably into the longer term future.
Differential Spectra and Resumma-
tion
We now take a breath and move onto a different track, describing in this chapter and the next two (Chapters 5-7) the research we have undertaken in the development of the reSolve program [2] for transverse momentum resummations and the general production of differential spectra for hadron-hadron processes.
5.1
Precision Physics at the LHC
In our previous discussions of the research performed for the SoftSusy decay program in Chapters 2-4, we focused on the search for new physics states via specific model-dependent direct and indirect searches for new particles; through resonances, in loops or via their signatures at the LHC. However, with no clear new discoveries forthcoming from such searches since that of the Higgs boson in 2012 [12, 13], and increasing exclusions on the most minimal Beyond Standard Model parameter spaces, there is a growing endeavour at the LHC and elsewhere to develop efforts in precision physics measurements and searches. In particular, such a lack of observations suggests that new physics may be largely decoupled from the Standard Model at LHC scales and so may only produce small deviations in measured results. In such precision physics analyses, we aim to measure known Standard Model processes to high precision with the objectives being twofold; firstly to further our knowledge and understanding of Standard Model physics, and secondly to look for tiny model-independent deviations of experimental results from precise theoretical predictions as an alternative sign of new physics states. In this vein, differential cross- sections for a variety of processes are being measured at unprecedented precisions during Run II of the LHC and beyond. In order to take advantage of these precise measurements however we need equally precise theoretical predictions. In fact, unlike direct searches which may proceed to a degree without precise theoretical predictions - requiring theoretical predictions largely for the interpretation of new physics results (or lack thereof) in terms of the various model parameter spaces, for precision physics measurements the strategy is fundamentally dependent upon precise theoretical predictions. The calculation of such theoretical predictions for a particularly vital and difficult class of spectra, transverse momentum (pT) spectra at lowpT, is the target of our
work in this area. Transverse momentum spectra are of great importance for the testing of the Standard Model and for the precise measurement of its parameters, including the W mass
and PDFs. The resulting precise determinations of Standard Model parameters allow smaller theoretical uncertainties in many other calculations. In addition, these precise measurements are also able to serve as new physics searches, with any small deviations from the precise Standard Model predictions indicating the potential presence of Beyond Standard Model particles.
Nonetheless, before we embark upon an explanation of the underlying technicalities involved and the functionalities and results of the reSolve program we have written to augment efforts in this area through Chapters 6 and 7, we first begin outlining in this chapter some of the basic concepts in collider kinematics, differential spectra and resummation that are required to attain an understanding of this work.