aa r X i v : . [ h e p - ph ] D ec November 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools
Computational Tools for Supersymmetry Calculations
Howard Baer
Homer L. Dodge Department of Physics and Astronomy,University of Oklahoma, Norman, OK 73019 [email protected]
I present a brief overview of a variety of computational tools for su-persymmetry calculations, including: spectrum generators, cross sectionand branching fraction calculators, low energy constraints, general pur-pose event generators, matrix element event generators, SUSY dark mat-ter codes, parameter extraction codes and Les Houches interface tools.
The Standard Model (SM) of particle physics provides an excellent descrip-tion of almost all physical processes as measured in terrestrial experiments,and is rightly regarded as the crowning achievement of many decades ofexperimental and theoretical work in elementary particle physics. As exciting as this is, it is also apparent that the SM cannot accountfor a wide assortment of astrophysical data, including neutrino oscillations,the matter-anti-matter content of the universe, the presence of dark energyand the presence of dark matter in the universe, and it doesn’t includegravitation. Even before these astrophysical anomalies became evident,it was apparent on theoretical grounds, mainly associated with quadraticdivergences in the scalar (Higgs) sector, that the SM was to be regarded asan effective theory valid only at the energy scale of ∼
100 GeV and below.At higher energies, it seemed likely that some new physics must arise, whichwould be associated with the mechanism for electroweak symmetry breakingWhile a vast array of physics theories beyond the SM have been pro-posed, the general class of theories including weak scale supersymmetry seem to most naturally solve the theoretical ills of the SM, while at thesame time they receive support from a variety of precision experimental ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer measurements. Most impressive is the measured values of three SM gaugecouplings at the weak scale: when extrapolated to high energies using therenormalization group group equations, the gauge couplings very nearlymeet at a point under supersymmetric standard model evolution, whilethey miss badly under SM evolution. Gauge coupling unification suggeststhat physics at scales M GUT ∼ × GeV is described by a supersym-metric grand unified theory, and that below M GUT , the correct effectivefield theory is the Minimal Supersymmetric Standard Model (MSSM), orthe MSSM plus gauge singlets (since gauge singlets don’t affect the runningof gauge couplings at one loop).Supersymmetric models predict the existence of a whole new class ofmatter states at or around the weak scale: the so-called super-partners.Gluinos, charginos, neutralinos, squarks, sleptons plus additional Higgsscalars ( H , A and H ± ) should all be present in addition to the usual statesof matter present in the SM. In order to fully test the hypothesis of weakscale supersymmetry, it seems necessary to actually produce at least someof the superpartners at high energy collider experiments, and to measuremany of their properties (mass, spin, coupling strengths and mixing), inorder to verify that any new physics signal indeed comes from superpartnerproduction. In addition, the properties of the superpartners will be key tounderstanding the next level of understanding in the laws of physics, per-haps opening windows to the physics of grand unification and even stringtheory.The key link between theoretical musings about various theories ofSUSY or other new physics, and the experimental observation of particletracks and calorimeter depositions in collider detectors is the event gener-ator program . Given some theory of new physics, which usually predictsthe existence of new matter states or new interactions, the event generatorprogram allows us to compute how such a theory would manifest itself athigh energy colliding beam experiments. Thus, event generator programsfunction as a sort of beacon, showing the way to finding new physics in avast assortment of collider data.Searches for new matter states at the CERN LEP2 collider have foundno firm new physics signals. We thus conclude that the SM Higgs bosonmust have mass m H SM > ∼
114 GeV, while the charginos of supersymmetrymust have mass m ˜ χ > ∼ . pp collider which is just now beginning to explore the energy regime ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools where the SM breaks down, and where new physics ought to lie. LHC isexpected to operate at energy scales √ s = 7 −
14 TeV; this ought to besufficient to either produce some superpartners, or rule out most particlephysics models which include weak scale supersymmetry.As we enter the LHC era, it is important to review the available calcula-tional tools which are available, that aid in connecting theory to experiment.In this chapter, I present a brief overview of some of the publicly availabletools. In Section 1.2, I examine the various • sparticle mass spectrum calculators,and the Les Houche Accord files which provide a handy interface betweenthese and event generator programs. Sec. 1.3 lists some • codes which calculate sparticle production rates, decay widths andbranching fractions.Sec. 1.4 reviews • event generators for SUSY processes, including – multi-purpose generators, complete with parton showers,hadronization and underlying events, and – more specialized matrix element generators, which tend tofocus on specific reactions.The Les Houche Event files allow parton level collider events to be easilypassed into general purpose event generators so that showering, hadroniza-tion and underlying events can be included. Sec. 1.5 lists • codes relevant to supersymmetric dark matter calculations,while Sec. 1.6 examines • codes designed to extract fundamental theory parameters from setsof experimental measurements.The supersymmetry parameter analysis (SPA) project seeks to develop auniform set of conventions which would allow unambiguous extraction ofhigh energy model parameters from various collider measurements of su-persymmetric production and decay reactions.I note here that this Chapter is an updated version of the 1997 versionby H. Baer and S. Mrenna which appeared in the volume Perspectives onSupersymmetry , edited by G. Kane (World Scientific). ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer
The first step in connecting supersymmetric theory to experiment is tobegin with a supersymmetric model, and calculate the expected spectrumof superpartner and Higgs boson masses and couplings. The models we willbe focusing on are 4-d supersymmetric quantum field theories with softlybroken supersymmetry at the TeV scale. These models might be the lowenergy effective theory resulting from some even more encompassing theory,such as superstring theory, or a particular SUSY GUT model, or which mayinvoke some specific mechanism for supersymmetry breaking.The effective field theory is specified by adopting 1. the gauge sym-metry, 2. the (super-) field content and 3. the Lagrangian. In the caseof supersymmetric theories, the Lagrangian is derived from the more fun-damental superpotential and K¨ahler potential, and for non-renormalizablemodels, the gauge kinetic function. The effects of SUSY breaking are en-coded in the Lagrangian soft SUSY breaking (SSB) terms. One must alsospecify the energy scale at which the effective theory and Lagrangian pa-rameters are valid. Since collider experiments will be testing physics atthe weak scale Q ∼ e.g. M GUT or M P ), the renormalizationgroup equations (RGEs) must be used to connect the disparate scales in themodel.Once the Lagrangian parameters are known at the weak scale, then thephysical (s)particle masses must be identified, often by diagonalizing therelevant mass matrices . Higher order perturbative corrections to the masseigenstates– at least at 1-loop– are nowadays necessary to gain sufficientaccuracy in the predictions. Numerous researchers have developed private codes to calculate sparti-cle masses given high scale model inputs. Here, we will focus only on pub-licly available codes , since these are available to the general user, and arefrequently kept up-to-date and user friendly. The first of the publicly avail-able spectrum calculator codes to appear was the
Isasugra subprogramof the event generator Isajet , in 1994. This was followed by SuSpect (1997), Softsusy (2002) and Spheno (2003). Isasusy, Isasugra and Isajet
Isasusy is a subprogram of the
Isajet event generator which calculatessparticle mass spectra given a set of 24 SSB input parameters at the weak ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools scale. The program includes full 1-loop corrections to all sparticle masses.For Higgs masses and couplings, the full 1-loop effective potential is min-imized at an optimized scale choice which accounts for leading 2-loop ef-fects. Yukawa couplings which are necessary for the loop calculations areevaluated using simple SM running mass expressions.The
Isasugra program starts with models defined at a much highermass scale ( e.g. Q = M GUT ), and calculates the weak scale SUSY param-eters via the full set of 2-loop RGEs. An iterative approach to solvingthe RGEs is employed, since weak scale threshold corrections which de-pend on the entire SUSY mass spectrum are included. Once convergenceis achieved, then the complete set of 1-loop corrected sparticle and Higgsmasses are computed as in
Isasusy . Since
Isasugra employs full 2-looprunning of gauge and Yukawa couplings including threshold corrections–while
Isasusy does not– the sparticle masses will differ between
Isasusy and
Isasugra even for the same weak scale parameter inputs.A listing of pre-programmed
Isasugra models include the following: • mSUGRA (or CMSSM) model: 4 parameters plus a sign( m , m / , A , tan β, sign ( µ )), • minimal gauge-mediated SUSY breaking (mGMSB, 4 param’s plussign plus C grav ) and non-minimal GMSB, • non-universal supergravity (19 param’s plus sign) – SSB terms can be assigned at any intermediate scale M weak SuSpect runs the 2-loop MSSM RGEs to determine weak scaleSUSY parameters in the mSUGRA, GMSB and AMSB models,and in the pMSSM (a more general MSSM model). One-loop ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer sparticle mass corrections are included. Some two loop correc-tions to Higgs masses are included. The webpage is located at . SoftSUSY Softsusy is a C + + code that calculates 2-loop MSSM RGEs to deter-mine weak scale SUSY parameters in the mSUGRA, mGMSB and mAMSBmodels, and in the general MSSM. R -parity violating effects are possible.One-loop sparticle mass corrections are included. Some two loop correctionsto Higgs masses are included. Softsusy calculates the complete flavor ma-trix structure of the MSSM soft terms and Yukawa couplings. The webpageis located at http://projects.hepforge.org/softsusy/ . Spheno Spheno is a Fortran 90 code that calculates 2-loop MSSMRGEs to determine weak scale SUSY parameters in the mSUGRA,mGMSB and mAMSB models, and in the general MSSM. One-loop sparticle mass corrections are included. Some two loop cor-rections to Higgs masses are included. The webpage is located at . Les Houches Accord (LHA) files A standard input/output file under the name of Les Houches Accord (LHA)files has been created. All of the above codes can create LHA output files.The advantage of LHA output files is that various event generator and darkmatter codes (see below) can use these as inputs for generating colliderevents or dark matter observables. The specific form of the LHA files ispresented in Ref. In addition, the Isasugra and Isasusy codes output to a special IsaWIG file, which is created expressly for input of sparticle mass spectraand decay branching fractions to the event generator Herwig . Comparison of spectra generator codes Several papers have been written comparing the SUSY spectra codes, although these tend to be all dated material, as the codes are continu-ally being updated and debugged. While many features of these codes ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools are similar, and so agreement between spectra tends to be good in genericparameter space regions, there are some differences as well. In particu-lar, the codes SuSpect , Softsusy and Spheno all adopt a sharp cut-offscale between the MSSM and SM effective theories. Allowance for thesharp cut-off is compensated for by log terms in the 1-loop sparticle andHiggs boson mass corrections. The Isasugra code instead adopts a “towerof effective theories” approach, and incorporates threshold corrections inthe 1-loop RGEs. Here, the beta-functions changes each time a sparticlemass threshold is passed over. One loop corrections to non-mixing sparticlemasses are implemented at each sparticle’s mass scale, so all logs are min-imized. Sparticles that mix have all their SUSY parameters evaluated atthe M SUSY ≡ √ m ˜ t L m ˜ t R scale due to a need for consistency amongst thevarious soft terms that enter the mass matrices. In this way, better accu-racy is expected in cases where the sparticle mass spectra is spread across alarge energy range, as happens– for instance– in focus point or split SUSY,where scalars are at multi-TeV values or beyond, whereas gauginos can bequite light. Production cross sections The multi-purpose event generators Isajet , Pythia , Herwig , SUSYGeN and Sherpa all have a complete set of tree-level SUSY particle productionreactions encoded, and can be used to calculate tree-level sparticle pro-duction cross sections. In the case of Pythia or Herwig , the LHA filesfrom spectra generators can be used as input to calculate these, or generalSUSY parameter inputs are allowed. Isajet does not allow LHA inputsince it has its own spectra generator. The Isajet code also calculates allsparticle and Higgs boson production reactions for e + e − colliders includingvariable beam polarization, and bremsstrahlung and beamstrahlung. The Spheno code also calculates lowest order e + e − → SU SY cross sections.The code Prospino has been created to calculate all 2 → Prospino takes LHA files as its input format. ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer Decay widths and branching fractions The programs Isasusy and Isasugra also calculate all sparticle and Higgsboson 1 → → Isajet standard output files,and are used internally for event generation. The chargino and neutralinobranching fractions are sensitive to the parameter tan β in that at largetan β , decays to third generation quarks and leptons are enhanced relativeto decays to first/second generation fermions.The program SusyHIT is a relatively new release that combines SuS-pect with the branching fraction codes SDecay and HDecay to also gen-erate a table of sparticle and Higgs boson decay widths and branchingfractions. Some of the decay modes in SusyHIT are calculated at NLO inQCD.The program Spheno also computes sparticle decay widths and branch-ing fractions.The branching fractions from Isajet , SusyHIT and Spheno all seemto enjoy excellent agreement with each other. The branching fractions ofall these codes can be input to event generators via the LHA input/outputfiles. Early versions of Herwig took branching fraction inputs from the IsaWIG output files.Care must be taken in extracting branching fractions for neutralinosand charginos computed internally from Pythia in that they may not bevalid at large tan β values > ∼ 10, since Yukawa couplings, mixing effects,and decays through intermediate Higgs bosons are neglected.Some specialized codes are available for calculating decays modes of theSUSY Higgs bosons. These include FeynHiggs , which calculates MSSMHiggs boson masses at two-loop level, along with branching fractions, CP-superH which calculates Higgs boson branching fractions including CP-violating parameters, and NHMDecay , which calculates Higgs bosonmasses and branching fractions in the next-to-minimal supersymmetricStandard Model (NMSSM). Supersymmetric models can be used to calculate sparticle masses and mix-ings, which in turn allow for a prediction of various sparticle productionrates and decay widths into final states containing quarks, leptons, pho-tons, gluons (and LSPs in R -parity conserving models). However, quarks ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools and gluons are never directly measured in any collider detector. Instead,detectors measure tracks of (quasi-)stable charged particles and their mo-menta as they bend in a magnetic field. They also measure energy depositedin calorimeter cells by hadrons, charged leptons and photons. There is thusa gap between the predictions of supersymmetric models in terms of finalstates involving quarks, gluons, leptons and photons, with what is actuallydetected in the experimental apparatus. This gap is bridged by event gen-erator computer programs. Once a collider type and supersymmetric modelis specified, the event generator program can produce a complete simulationof the sorts of scattering events that are to be expected. The final state ofany simulated scattering event is composed of a listing of electrons, muons,photons and the long-lived hadrons (pions, kaons, nucleons etc.) and theirassociated 4-vectors that may be measured in a collider experiment.The underlying idea of SUSY event generator programs is that for aspecified collider type ( e + e − , pp , p ¯ p , · · · ) and center of mass energy, theevent generator will, for any set of model parameters, generate various spar-ticle pair production events in the ratio of their production cross sections,and with distributions as given by their differential cross sections. More-over, the produced sparticles will undergo a (possibly multi-step cascade)decay into a partonic final state, according to branching ratios as fixedby the model. Finally, this partonic final state is converted to one that iscomprised of particles that are detected in an experimental apparatus. Bygenerating a large number of “SUSY events” using these computer codes,the user can statistically simulate the various final states that are expectedto be produced within the framework of any particular model.Several general purpose event generator programs that incorporateSUSY are currently available, including Isajet , Pythia , Herwig , SUSYGeN and Sherpa . These include usually just the leading order2 → → n ( n ≤ 6) SUSY reactions may be generated bysuch programs as CompHEP , CalcHEP , MadGraph , SUSY-Grace , Amegic++ and O’Mega . The output of these latter programs can beinterfaced with the Pythia or Herwig programs to yield complete scat-tering event simulations by generating output in the Les Houches Event file (LHE) format. (Isajet generates LHE output, but does not accept LHE filesas input, since it includes its own mass and branching fraction generator).Ideally, event generator programs should be flexible enough to enable simu-lation of SUSY events from a variety of models such as mSUGRA, GMSB,AMSB etc. . This is usually accomplished nowadays by reading in the LHA ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer model files into the event generators Pythia or Herwig . Since Isajet does its own spectra calculation, it only outputs LHA files, but does notaccept them as input.The simulation of hadron collider scattering events may be broken upinto several steps, as illustrated in Fig. 1.1. The steps include: • the perturbative calculation of the hard scattering subprocess in theparton model, and convolution with parton distribution functions(PDFs), • inclusion of sparticle cascade decays, • implementation of perturbative parton showers for initial and finalstate colored particles, and for other colored particles which maybe produced as decay products of heavier objects, • implementation of a hadronization model which describes the for-mation of mesons and baryons from quarks and gluons. Also, un-stable particles must be decayed to the (quasi-)stable daughtersthat are ultimately detected in the apparatus, with rates and dis-tributions in accord with their measured or predicted values. • Finally, the debris from the colored remnants of the initial beamsmust be modeled to obtain a valid description of physics in theforward regions of the collider detector.For e + e − collider simulations, in addition we have to allow for the possibilityof polarized initial beams, and beam-strahlung effects. Hard scattering The hard scattering and convolution with PDFs forms the central calcula-tion of event generator programs. The calculations are usually performedat lowest order in perturbation theory, so that the hard scattering is eithera 2 → → → n processes, with n ≥ Q -dependent PDFs commonly used are constructed tobe solutions of the Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP)QCD evolution equations, which account for multiple collinear emissions ofquarks and gluons from the initial state in the leading log approximation. ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools As Q increases, more gluons are radiated, so that the distributions softenfor large values of x , and correspondingly increase at small x values. Useof a running QCD coupling constant makes the entire calculation valid atleading log level.Once the total cross sections are evaluated for all the allowed subpro-cesses, then reactions may be selected probabilistically (with an assignedweight) using a random number generator. This will yield sparticle eventsin the ratio predicted by the particular model being simulated.For sparticle production at e + e − colliders, it may also be necessary to ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer convolute with electron and positron PDFs to incorporate bremsstrahlungand beamstrahlung effects. In addition, if beam polarization is used, theneach subprocess cross section will depend on beam polarization parametersas well. Parton showers For reactions occurring at both hadron and lepton colliders, to obtain arealistic portrait of supersymmetric (or Standard Model) events, it is nec-essary to account for multiple non-collinear QCD radiation effects. Theevaluation of the cross section using matrix elements for multi-parton fi-nal states is prohibitively difficult. Instead, these multiple emissions areapproximately included in an event simulation via a parton shower (PS)algorithm. They give rise to effects such as jet broadening, radiation in theforward regions and energy flow into detector regions that are not describedby calculations with only a limited number of final state partons.In leading log approximation (LLA), the cross section for single gluonemission from a quark line is given by dσ = σ α s π dtt P qq ( z ) dz, (1.1)where σ is the overall hard scattering cross section, t is the intermedi-ate state virtual quark mass, and P qq ( z ) = (cid:16) z − z (cid:17) coincides with theAltarelli-Parisi splitting function for q ′ → qg for the fractional momentumof the final quark z ≡ | ~p q || ~p q ′ | < 1. Interference between various multiple gluon emission Feynman graphs, where the gluons are ordered differently,is a subleading effect. Thus, Eq. (1.1) can be applied successively, and givesa factorized probability for each gluon emission. The idea behind the PSalgorithm is then to use these approximate emission probabilities (whichare exact in the collinear limit), along with exact (non-collinear) kinemat-ics to construct a program which describes multiple non-collinear partonemissions. Notice, however, that the cross section (1.1) is singular as t → z → i.e. in the regime of collinear and also soft gluon emission.These singularities can be regulated by introducing physically appropriatecut-offs. A cutoff on the value of | t | of order | t c | ∼ z is also necessary, and physically corresponds to the limit beyond whichthe gluon is too soft to be resolved.The PS algorithms available vary in their degree of sophistication. Thesimplest algorithm was created by Fox and Wolfram in 1979. Their ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools method was improved to account for interference effects in the angle-orderedalgorithm of Marchesini and Webber. In addition, parton emission fromheavy particles results in a dead-cone effect, where emissions in the direc-tion of the heavy particle are suppressed. Furthermore, it is possible toinclude spin correlations in the PS algorithm.PS algorithms are also applied to the initial state partons. In thiscase, a backwards shower algorithm is most efficient, which develops theemissions from the hard scattering backwards in time towards the initialstate. The backward shower algorithm developed by Sj¨ostrand makes useof the PDFs evaluated at different energy scales to calculate the initial stateparton emission probabilities. Cascade decays Not only are there many reactions available via which SUSY particles maybe produced at colliders, but once produced, there exist many ways in whichsuperparticles may decay. For the next-to-lightest SUSY particle (NLSP),there may be only one or at most a few ways to decay to the LSP. Thus,for a collider such as LEP or even the Fermilab Tevatron, where only thelightest sparticles will have significant production rates, we might expectthat their associated decay patterns will be relatively simple. However, thenumber of possible final states increases rapidly if squarks and gluinos thatcan decay into the heavier charginos and neutralinos are accessible, andthe book-keeping becomes correspondingly more complicated. Indeed, atthe CERN LHC, where the massive strongly interacting sparticles such asgluinos and squarks are expected to be produced at large rates, sparticlecascade decay patterns can be very complex. As a rough estimate, of order10 subprocess cross sections may be active at LHC energies, with of order10 decay modes for each sparticle. Naively, this would give of order 10 → n -body subprocesses that would need to be calculated.Monte Carlo event generators immensely facilitate the analysis of signalsfrom such complex cascade decays, especially in the case where no singledecay chain dominates. An event generator can select different cascadedecay branches by generating a random number which picks out a particulardecay choice, with a weight proportional to the corresponding branchingfraction, at each step of the cascade decay. Quarks and gluons producedas the end products of cascade decays will shower off still more quarks andgluons, with probabilities determined by the PS algorithm.The procedure that we have just described is exact for cascade decays ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer of spinless particles into two other spinless particles at each step in thecascade. This is because the squared matrix element is just a constant,and there are no spin correlations possible. This is not true in generaland in many cases, it can be very important to include the decay matrixelement and/or spin correlations in the calculation of cascade decays ofsparticles. A general method for incorporating spin correlations based ondensity matrices has been put forth by Richardson, and incorporated into Herwig .Spin correlation effects are especially important for precision measure-ments at e + e − linear colliders. While retaining spin correlations may beless crucial in many situations at a hadron collider, this is not always thecase. For instance, relativistic τ − leptons produced from W decay are al-ways left-handed, while those produced from a charged Higgs decay arealways right-handed. Likewise, the polarization of the taus from ˜ τ decaysdepends on the stau mixing angle. Since the undetectable energy carriedoff by ν τ from tau decay depends sensitively on the parent tau helicity,it is necessary to include effects of tau polarization in any considerationinvolving the energy of “tau jets”. By evaluating the mean polarization oftaus in any particular process, these effects can be incorporated, at leaston average, into event generator programs such as Isajet . Of course, sucha procedure would not include correlations between decay products of twotaus produced in the same reaction.Another aspect is to include appropriately the complete 3-body decaymatrix elements. While some programs merely use a flat phase space distri-bution, Isajet and Herwig include pre-programmed exact decay matrixelements. Models of hadronization Once sparticles have been produced and have decayed through their cas-cades, and parton showers have been evolved up to the point where the par-tons have virtuality smaller than ∼ , the partons must be convertedto hadrons. This is a non-perturbative process, and one must appeal to phe-nomenological models for its description. The independent hadronization(IH) model of Field and Feynman is the simplest such model to imple-ment. In this picture, a new quark anti-quark pair q ¯ q can be created inthe color field of the parent quark q . Then the q ¯ q pair can turn into ameson with a longitudinal momentum fraction described by a phenomeno-logical function, with the remainder of the longitudinal momentum carried ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools by the quark q . This process is repeated by the creation of a q ¯ q pair inthe color field of q , and so on down the line to q n ¯ q n . A host of mesonsare thus produced, and decayed to the quasi-stable π , K, · · · mesons ac-cording to their experimental properties. The final residual quark q n willhave very little energy, and can be discarded without significantly affectingjet physics. Finally, a small transverse momentum can be added accordingto a pre-assigned Gaussian probability distribution to obtain a better de-scription of the data. Quark fragmentation into baryons is also possible bycreation of diquark pairs in its color field, and can be incorporated. TheIH scheme, with many parameters tuned to fit the data, will thus describethe bulk features of hadronization needed for event simulation programs.The string model of hadronization developed at Lund is a more so-phisticated model than IH, which treats hadron production as a universalprocess independent of the environment of the fragmenting quark. In thestring model, a produced quark-antiquark pair is assumed to be connectedby a color flux tube or string. As the quark-antiquark pair moves apart,more and more energy is stored in the string until it is energetically favor-able for the string to break, creating a new quark-antiquark pair. Gluonsare regarded as kinks in the string. The string model correctly accountsfor color flow in the hadronization process, as opposed to the IH model.In e + e − → q ¯ qg (3-jet) events, the string model predicts fewer producedhadrons in the regions between jets than the IH model, in accord withobservation.A third scheme for hadronization is known as the cluster hadronizationmodel. In this case, color flow is still accounted for, but quarks and anti-quarks that are nearby in phase space will form a cluster, and will hadronizeaccording to preassigned probabilities. This model avoids non-locality prob-lems associated with the string hadronization model, where quarks andantiquarks separated by spacelike distances can affect the hadronizationprocess. Beam remnants Finally, at a hadron collider the colored remnants of the nucleon that didnot participate in the hard scattering must be accounted for. These beamremnant effects produce additional energy flow, especially in the far forwardregions of the detector. A variety of approaches are available to describethese non-perturbative processes, including models involving Pomeron ex-change and multiple scatterings. In addition, the beam remnants must ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer be hadronized as well, and appear to require a different parametrizationfrom “minimum bias” events where there are only beam jets but no hardscattering. Multi-purpose event generators Publicly available event generators for SUSY processes include, • ISAJET: (H. Baer, F. Paige, S. Protopopescu and X. Tata), • PYTHIA: (T. Sj¨ostrand, L. L¨onnblad and S. Mrenna), • HERWIG: (G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti,K. Odagiri, P. Richardson, M. Seymour and B. R. Webber), • SUSYGEN: (N. Ghodbane, S. Katsanevas, P. Morawitz and E.Perez), http://lyoinfo.in2p3.fr/susygen/susygen3.html • SHERPA: (T. Gleisberg, S. H¨oche, F.Krauss, M. Sch¨onherr, S. Schumann, F. Siegert and j. Winter) http://projects.hepforge.org/sherpa/dokuwiki/doku.php The event generator program Isajet was originally developed in the late1970’s to describe scattering events at the ill-fated ISABELLE pp colliderat Brookhaven National Laboratory. It was developed by F. Paige andS. Protopopescu to generate SM and beyond scattering events at hadronand e + e − colliders. H. Baer and X. Tata, in collaboration with Paigeand Protopopescu, developed Isajet to give a realistic portrayal of SUSYscattering events. Isajet uses the IH model for hadronization, and theoriginal Fox-Wolfram (Sj¨ostrand) PS shower algorithm for final state (initialstate) parton showers. It includes an n -cut Pomeron model to describebeam-jet evolution.The event generator Pythia was developed mainly by T. Sj¨ostrand inthe early 1980s to implement the Lund string model for event generation. Pythia uses the FW virtuality-ordered shower model, but with an angle-ordered veto. S. Mrenna contributed the inclusion of SUSY processes in Pythia .The event generator Herwig was developed in the mid-1980s to describescattering events with angle-ordered parton showers, which accounted forinterference effects neglected in the FW shower approach. Herwig imple- ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools ments a cluster hadronization model. Herwig is notable in that it includessparticle production and decay spin correlations using density matrix tech-niques. The program SUSYGeN was developed by S. Katsanevas and P.Morawitz to generate e + e − → SU SY events for the LEP experiments. SUSYGeN interfaces with Pythia for hadronization and showering. SUSYGeN has since been upgraded to also generate events for hadroncolliders.The program Sherpa was developed as a new generation event gen-erator in the C + + language. It calculates subprocess reactions using Amegic++ . It includes its own shower and cluster hadronization rou-tines. Matrix element generators For generating various 2 → n scattering reactions using complete matrixelements, a number of automated tree-level codes are available.The code CompHEP by E. Boos et al. is designed to take one di-rectly from a Lagrangian to distributions. Feynman rules can be calculatedusing the LanHEP code, and then CompHEP will generate the squaredmatrix element by constructing the squared amplitude, taking traces, andstoring the output as subroutines. CompHEP also includes code for doingthe phase space integration, convolution with PDFs, and after integration,numerical output, or output in terms of histograms.The code CalcHEP by Pukhov, Belyaev and Christensen is verysimilar to CompHEP , and was in fact created as a spin-off by some of theoriginal authors of CompHEP .The code MadGraph / MadEvent was developed by Stelzer and Longand others. It allows the user to input initial and final state particles,and then generates all Feynman diagrams along with a subroutine whichevaluates the scattering amplitude as a complex number using the Helas helicity amplitude subroutines developed by Hagiwara and Murayama. Since MadGraph directly evaluates the amplitude, and not amplitudesquared, computational sampling of the squared matrix element should befaster than programs which evaluate traces over gamma matrices. Thelatest versions of MadGraph , updated to MadEvent , will convolutewith PDFs and perform phase space integration and evaluate distributionsas well. A number of models for BSM physics, including the MSSM , areavailable in MadGraph / MadEvent . ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer The program O’Mega by Ohl, Reuter and Schwinn, also generatestree-level SM and MSSM amplitudes, and can work in concert with the Whizard program for event generation. The program SUSY-Grace by Tanaka, Kuroda, Kaneko, Jimbo andKon also generates SM and MSSM amplitudes, and generates scatteringevents in association with the Grappa program. Les Houches Event (LHE) files A Les Houches Event (LHE) file format has been proposed which allowsfor a simple communication between parton level event generators and allpurpose generators such as Pythia and Herwig . This is particularlyuseful when matrix element generators like CalcHEP or MadGraph areused, but the user needs a complete event output including parton showers,hadronization and underlying event simulation.The LHE file is an ascii file which includes lines pertaining to thegenerator initialization. It then follows with a listing of partons (particle IDcode), their associated 4-vectors and color flow information. The generators Pythia and Herwig then can read in these files, to add on showering,hadronization and underlying event. A sample SUSY event in LHE formatis listed below. It lists a reaction with sg → ˜ s ˜ g , with ˜ s → s ˜ χ and ˜ g → ˜ d ¯ d and then ˜ d → d ˜ χ . After listing a line of event characteristics, theevent listing follows. The first column corresponds to particle ID, 2ndcolumn to stability of particle, 3rd and 4th columns list the source of theparticle, 5th and 6th columns relate to color flow, and 7th column is the x -component of the energy-momentum four-vector. The four-vector listinghas been truncated to fit on the page. DarkSUSY The DarkSUSY code, developed by Gondolo et al. , evaluates the relicdensity of neutralino dark matter in SUSY models. DarkSUSY computes allrelevant neutralino annihilation and co-annihilation processes, and solvesthe Boltzmann equation to output the current density of neutralino CDM. Itaccepts input files from Isajet/Isasugra or from LHA input files. DarkSUSYalso calculates: spin-independent and spin-dependent neutralino-nucleonscattering rates (direct WIMP detection), and indirect neutralino detectionrates, such as: muon flux from neutralino annihilation in the core of earthor sun, flux of γ rays, ¯ p s, e + s and ¯ d s from neutralino annihilation in thegalactic core or halo. The halo annihilation rates all depend on an assumedform for the galactic dark matter density profile. Micromegas MicrOMEGAS was developed by Belanger et al. , and also evaluates theneutralino relic density due to all annihilation and co-annihilation processes.It also computes the WIMP relic density for a variety of other non-SUSYmodels. It also outputs neutralino direct and indirect detection rates, b → sγ branching fraction and ( g − µ . Isatools Isatools is part of the Isajet package. It includes a subroutine IsaReD to evaluate the neutralino relic density, the direct neutralino detection ratesvia spin-independent and spin-dependent scattering, the b → sγ branchingfraction, ( g − SUSYµ , BF ( B s → µ + µ − ) and the thermally averaged neu-tralino annihilation cross section, which is key input to neutralino haloannihilation calculations. ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools H. Baer If supersymmetry is indeed discovered at the Tevatron, LHC and/or a linear e + e − collider, then an exciting task will be to make precision measurementsof all sparticle masses, spins, couplings and mixings. Once these are known,then, if the MSSM is indeed the correct effective theory all the way from M weak to M GUT , it is possible to map out the GUT scale values of the softSUSY breaking parameters. Once these are known, important informationwill be gained which will allow for the construction of SUSY models at orbeyond the GUT scale. Two such codes are available which accomplish thistask: Sfitter and Fittino . The supersymmetry parameter analysis (SPA) project is an attempt toachieve co-ordination between the various sparticle mass generation codes,event generators, relic density codes, and parameter fitting codes, with agoal in mind to determine the fundamental SUSY Lagrangian. In the SPAconvention, all programs should input/ouput SUSY parameters in the DR scheme at the Q = 1 TeV scale. Once this benchmark is set, then allremaining calculations may proceed from this common agreed upon point. In the past decade, there has been an explosion of interest in supersymmetryphenomenology. This is exhibited in part by the corresponding developmentof numerous computational tools to aid in supersymmetry calculations forexpected collider events and for dark matter observables. Supersymmetryhas certainly been an enduring theme in high energy physics. Hopefully,at the dawn of the LHC era, we are on the verge of actual discovery ofsupersymmetry. In this case, many of these tools for SUSY will be put togood hard use, as the community analyzes the upcoming collider data.We expect that new tools for SUSY will emerge, which will be more fo-cused on the new matter states that might appear. As an example, if SUSYis discovered, then the MSSM (or perhaps NMSSM) may become the newSM, and radiative corrections will have to be calculated for any remainingproduction and decay reactions, and in a form suitable for embedding inevent generator programs. The clues we find pertaining to dark matterwill impact on all astrophysical codes. In addition, new tools should also ovember 4, 2018 2:24 World Scientific Review Volume - 9in x 6in tools emerge that facilitate model building, as the clues we expect to emerge fromthe data point the way to a new paradigm in physics beyond the StandardModel. 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