## Chapter 10 Implemented physics- 10.1 The hard interaction models
- 10.2 The SUSY Les Houches Accord (SLHA) interface
- 10.3 Lepton Collider Beam Spectra
## 10.1 The hard interaction modelsIn this section, we give a brief overview over the different incarnations of models for the description of the realm of subatomic particles and their interactions inside WHIZARD. In Sec. 10.1.1, the Standard Model (SM) itself and straightforward extensions and modifications thereof in the gauge, fermionic and Higgs sector are described. Then, Sec. 10.1.2 gives a list and short description of all genuine beyond the SM models (BSM) that are currently implemented in WHIZARD and its matrix element generator O’Mega. Additional models beyond that can be integrated and handled via the interfaces to external tools like SARAH and FeynRules, or the universal model format UFO, cf. Chap. 17. ## 10.1.1 The Standard Model and friends## 10.1.2 Beyond the Standard Model
## Strongly Interacting Models and Composite ModelsHiggsless models have been studied extensively before the Higgs boson
discovery at the LHC Run I in 2012 in order to detect possible
loopholes in the electroweak Higgs sector discovery potential of this
collider. The Threesite Higgsless Model is one of the simplest
incarnations of these models, and was one of the first BSM models
beyond SUSY and Little Higgs models that have been implemented in
WHIZARD [34]. It is also called the Minimal
Higgsless Model (MHM) [35] is a minimal
deconstructed Higgsless model which contains only the first resonance
in the tower of Kaluza-Klein modes of a Higgsless extra-dimensional
model. It is a non-renormalizable, effective theory whose
gauge group is an extension of the SM with an extra SU(2) gauge
group. The breaking of the extended electroweak gauge symmetry is
accomplished by a set of nonlinear sigma fields which represent the
effects of physics at a higher scale and make the theory
nonrenormalizable. The physical vector boson spectrum contains the
usual photon, W ## Supersymmetric ModelsWHIZARD/O’Mega was the first multi-leg matrix-element/event generator to include the full Minimal Supersymmetric Standard Model (MSSM), and also the NMSSM. The SUSY implementations in WHIZARD have been extensively tested [38, 39], and have been used for many theoretical and experimental studies (some prime examples being [40, 41, 51]. ## Little Higgs Models## Inofficial modelsThere have been several models that have been included within the WHIZARD/O’Mega framework but never found their way into the official release series. One famous example is the non-commutative extension of the SM, the NCSM. There have been several studies, e.g. simulations on the s-channel production of a Z boson at the photon collider option of the ILC [44]. Also, the production of electroweak gauge bosons at the LHC in the framework of the NCSM have been studied [45]. ## 10.2 The SUSY Les Houches Accord (SLHA) interfaceTo be filled in ... [47, 48, 49]. The neutralino sector deserves special attention. After diagonalization of the mass matrix expresssed in terms of the gaugino and higgsino eigenstates, the resulting mass eigenvalues may be either negative or positive. In this case, two procedures can be followed. Either the masses are rendered positive and the associated mixing matrix gets purely imaginary entries or the masses are kept signed, the mixing matrix in this case being real. According to the SLHA agreement, the second option is adopted. For a specific eigenvalue, the phase is absorbed into the definition of the relevant eigenvector, rendering the mass negative. However, WHIZARD has not yet officially tested for negative masses. For external SUSY models (cf. Chap. 17) this means, that one must be careful using a SLHA file with explicit factors of the complex unity in the mixing matrix, and on the other hand, real and positive masses for the neutralinos. For the hard-coded SUSY models, this is completely handled internally. Especially Ref. [51] discusses the details of the neutralino (and chargino) mixing matrix. ## 10.3 Lepton Collider Beam SpectraFor the simulation of lepton collider beam spectra there are two
dedicated tools, CIRCE1 and CIRCE2 that have been written as
in principle independent tools. Both attempt to describe the
details of electron (and positron) beams in a realistic lepton
collider environment. Due to the quest for achieving high peak
luminosities at e ## 10.3.1 CIRCE1While the bunches in a linear collider cross only once, due to their small size they experience a strong beam-beam effect. There is a code to simulate the impact of this effect on luminosity and background, called GuineaPig++ [10, 11, 12]. This takes into account the details of the accelerator, the final focus etc. on the structure of the beam and the main features of the resulting energy spectrum of the electrons and positrons. It offers the state-of-the-art simulation of lepton-collider beam spectra as close as possible to reality. However, for many high-luminosity simulations, event files produced with GuineaPig++ are usually too small, in the sense that not enough independent events are available for physics simulations. Lepton collider beam spectra do peak at the nominal beam energy (√s/2) of the collider, and feature very steeply falling tails. Such steeply falling distributions are very poorly mapped by histogrammed distributions with fixed bin widths. The main working assumption to handle such spectra are being followed within CIRCE1: -
The beam spectra for the two beams P
_{1}and P_{2}factorize (here x_{1}and x_{2}are the energy fractions of the two beams, respectively):D _{P1P2}(x_{1}, x_{2}) = D_{P1}(x_{1}) · D_{P2}(x_{2}) - The peak is described with a delta distribution, and the tail with a
power law:
D(x) = d · δ(1−x) + c · x ^{α}(1−x)^{β}
The two powers α and β are the main coefficients that can be tuned in order to describe the spectrum with CIRCE1 as close as possible as the original GuineaPig++ spectrum. More details about how CIRCE1 works and what it does can be found in its own write-up in circe1/share/doc. ## 10.3.2 CIRCE2The two conditions listed in 10.3.1 are too restrictive and hence insufficient to describe more complicated lepton-collider beam spectra, as they e.g. occur in the CLIC drive-beam design. Here, the two beams are highly correlated and also a power-law description does not give good enough precision for the tails. To deal with these problems, CIRCE2 starts with a two-dimensional histogram featuring factorized, but variable bin widths in order to simulate the steep parts of the distributions. The limited statistics from too small GuineaPig++ event output files leads to correlated fluctuations that would leave strange artifacts in the distributions. To abandon them, Gaussian filters are applied to smooth out the correlated fluctuations. Here care has to be taken when going from the continuum in x momentum fraction space to the corresponding
boundaries: separate smoothing procedures are being applied to the
bins in the continuum region and those in the boundary in order to
avoid artificial unphysical beam energy
spreads. Fig. ?? shows the smoothing of the
distribution for the bin at the x WHIZARD ships (inside its subpackage CIRCE2) with prepared beam spectra ready to be used within CIRCE2 for the ILC beam spectra used in the ILC TDR [13, 14, 15, 16, 17]. These comprise the designed staging energies of 200 GeV, 230 GeV, 250 GeV, 350 GeV, and 500 GeV. Note that all of these spectra up to now do not take polarization of the original beams on the beamstrahlung into account, but are polarization-averaged. For backwards compatibility, also the 500 GeV spectra for the TESLA design [27, 28], here both for polarized and polarization-averaged cases, are included. Correlated spectra for CLIC staging energies like 350 GeV, 1400 GeV and 3000 GeV are not yet (as of version 2.2.4) included in the WHIZARD distribution. In the following we describe how to obtain such files with the tools included in WHIZARD(resp. CIRCE2). The procedure is equivalent to the so-called lumi-linker construction used by Timothy Barklow (SLAC) together with the legacy version WHIZARD 1.95. The workflow to produce such files is to run GuineaPig++ with the following input parameters:
This demands from GuineaPig++ the generation of distributions
for the e The next step is to transfer these output files from GuineaPig++ into input files used with CIRCE2. This is done by means of the tool circe_tool.opt that is installed together with the WHIZARD main binary and libraries. The user should run this executable with the following input file:
The first line defines the output file, that later can be read in into the beamstrahlung’s description of WHIZARD (cf. below). Then, in the second line the design of the collider (here: ILC for 500 GeV center-of-mass energy, with the number of bins) is specified. The next line tells the tool to take the unpolarized case, then the GuineaPig++ parameters (event file and luminosity) are set. In the last three lines, details concerning the adaptation of the simulation as well as the smoothing procedure are being specified: the number of iterations in the adaptation procedure, and for the smoothing with the Gaussian filter first in the continuum and then at the two edges of the spectrum. For more details confer the documentation in the CIRCE2 subpackage. This produces the corresponding input files that can be used within WHIZARD to describe beamstrahlung for lepton colliders, using a SINDARIN input file like:
## 10.3.3 Photon Collider SpectraFor details confer the complete write-up of the CIRCE2 subpackage. |