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Chapter 10  Implemented physics

10.1  The hard interaction models

In 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, cf. Chap. 17.

10.1.1  The Standard Model and friends

10.1.2  Beyond the Standard Model

MODEL TYPEwith CKM matrixtrivial CKM
Yukawa test model---Test
QED with e,µ,τ,γ---QED
QCD with d,u,s,c,b,t,g---QCD
Standard ModelSM_CKMSM
SM with anomalous gauge couplingsSM_ac_CKM SM_ac
SM with Hgg, Hγγ, Hµµ--- SM_Higgs
SM with charge 4/3 top--- SM_top
SM with anomalous top couplings--- SM_top_anom
SM with anomalous Higgs couplings--- SM_rx/NoH_rx/SM_ul
SM extensions for VV scattering--- SSC/AltH/SSC_2/SSC_AltT
SM with Z---Zprime
Two-Higgs Doublet Model2HDM_CKM2HDM
MSSM with gravitinos---MSSM_Grav
extended SUSY models---PSSSM
Littlest Higgs---Littlest
Littlest Higgs with ungauged U(1)--- Littlest_Eta
Littlest Higgs with T parity--- Littlest_Tpar
Simplest Little Higgs (anomaly-free)--- Simplest
Simplest Little Higgs (universal)--- Simplest_univ
SM with graviton---Xdim
“SQED” with gravitino---GravTest
Augmentable SM template---Template
Table 10.1: List of models available in WHIZARD. There are pure test models or models implemented for theoretical investigations, a long list of SM variants as well as a large number of BSM models.

Strongly Interacting Models and Composite Models

Higgsless 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± and Z bosons as well as a W± and Z′ boson. Additionally, a new set of heavy fermions are introduced to accompany the new gauge group “site” which mix to form the physical eigenstates. This mixing is controlled by the small mixing parameter єL which is adjusted to satisfy constraints from precision observables, such as the S parameter [36]. Here, additional weak gauge boson production at the LHC was one of the focus of the studies with WHIZARD [37].

Supersymmetric Models

WHIZARD/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 models

There 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) interface

To 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 Spectra

For 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+e machines, the goal is to make the spatial extension of the beam as small as possible but keeping the area of the beam roughly constant. This is achieved by forcing the beams in the final focus into the shape of a quasi-2D bunch. Due to the high charge density in that bunch, the bunch electron distribution is modified by classical electromagnetic radiation, so called beamstrahlung. The two CIRCE packages are intended to perform a simulation of this beamstrahlung and its consequences on the electron beam spectrum as realistic as possible. More details about the two packages can be found in their stand-alone documentations. We will discuss the basic features of lepton-collider beam simulations in the next two sections, including the technicalities of passing simulations of the machine beam setup to WHIZARD. This will be followed by a section on the simulation of photon collider spectra, included for historical reasons.

10.3.1  CIRCE1

While 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:

  1. The beam spectra for the two beams P1 and P2 factorize (here x1 and x2 are the energy fractions of the two beams, respectively):
    DP1P2 (x1x2) = DP1 (x1) · DP2 (x2
  2. The peak is described with a delta distribution, and the tail with a power law:
    D(x) = d · δ(1−x)   +   c · xα  (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  CIRCE2

The 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

Figure 10.1: Smoothing the bin at the xe+ = 1 boundary with Gaussian filters of 3 and 10 bins width compared to no smoothing.

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 xe+ = 1 boundary. The blue dots show the direct GuineaPig++ output comprising the fluctuations due to the low statistics. Gaussian filters with widths of 3 and 10 bins, respectively, have been applied (orange and green dots, resp.). While there is still considerable fluctuation for 3 bin width Gaussian filtering, the distribution is perfectly smooth for 10 bin width. Hence, five bin widths seem a reasonable compromise for histograms with a total of 100 bins. Note that the bins are not equidistant, but shrink with a power law towards the xe = 1 boundary on the right hand side of Fig. ??.

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:

  do_lumi = 7;
  num_lumi = 100000000;
  num_lumi_eg = 100000000;
  num_lumi_gg = 100000000;

This demands from GuineaPig++ the generation of distributions for the ee+, eγ, and γγ components of the beamstrahlung’s spectrum, respectively. These are the files lumi.ee.out, lumi.eg.out, lumi.ge.out, and lumi.gg.out, respectively. These contain pairs (E1, E2) of beam energies, not fractions of the original beam energy. Huge event numbers are out in here, as GuineaPig++ will produce only a small fraction due to a very low generation efficiency.

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:

{ file="ilc500/ilc500.circe"                   # to be loaded by WHIZARD
  { design="ILC" roots=500 bins=100 scale=250 # E in [0,1]
    { pid/1=electron pid/2=positron pol=0     # unpolarized e-/e+
      events="ilc500/lumi.ee.out" columns=2   # <= Guinea-Pig
      lumi = 1564.763360                      # <= Guinea-Pig
      iterations = 10                         # adapting bins
      smooth = 5 [0,1) [0,1)                  # Gaussian filter 5 bins
      smooth = 5 [1] [0,1) smooth = 5 [0,1) [1] } } }  

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:

        beams = e1, E1 => circe2
        $circe2_file = "ilc500.circe"
        $circe2_design = "ILC"
        ?circe2_polarized = false  

10.3.3  Photon Collider Spectra

For details confer the complete write-up of the CIRCE2 subpackage.

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