How to turn a hep-ph paper into a simulation: Introduction M. E. Peskin May 2007
in memory of Maurice Jacob
If you have a model that makes sense and should be tested in detail, experimenters will ask, Is there a simulation? In any HEP experiment, tests of a model require detailed evaluation of its signatures, including estimation of the detector acceptance and response. This is especially true at a hadron collider, where signatures with quark jets resemble QCD background and signatures with leptons depend strongly on the detector geometry. It is even more true at the LHC, for which we are proposing complex models with many new particles. For an analysis at this level, experimenters need explicit events that can be passed through a simulated detector geometry. So, how do you make them?
needs and responsibilities accords with higher authority quantum interference gluon accompaniment
The complete simulation of an LHC event in a theory of physics beyond the Standard Model requires many ingredients. In principle, all of these should be included for appropriate realism. It is necessary to decide which of these ingredients will be included in the simulation and, for each that is included, who will take responsibility.
model level: detailed spectrum of the model production processes from quark and gluon initial states decay chains partial widths production cross sections and dynamics decay distributions and dynamics polarization dependence and spin correlations
perturbative QCD level: QCD showers for final quarks and gluons QCD showers for intermediate colored states initial state radiation nonperturbative level: underlying event (possibly with extra jet production) hadronization of all radiated quarks and gluons decays of hadrons and tau leptons
I will discuss perturbative QCD radiation later. The underlying event is not for the faint of heart. Its multiplicity affects the pt of jets constructed, for example, by cone algorithms. This multiplicity is highly uncertain and must eventually be determined from data. New physics simulations should include this and other tunings to LHC data. Hinchliffe - UCSD meeting
PYTHIA and HERWIG include all of these effects - but probably not for your favorite model. So it would be interesting if there is a simple way to put the model-level information for your model into these programs and let them do the rest.
The simplest idea would be the following: Generate 4-vectors for pair-production of your favorite particle from a standard (CTEQ or MRST) parton distribution. Decay each particle to a random two-body final state. Put the resulting vectors into PYTHIA to generate the other features of the event. If PYTHIA recognizes the final particles, it will know how to decay them.
There is now a simple technology that implements this program, called the Les Houches Accord. The basic Les Houches Accord allows insertion of events from a parton level event generator into a parton shower generator such as PYTHIA or HERWIG. Originally, the Accord was a common block transferring information between FORTRAN subroutines. But now, a stand-alone generator can write a text file that can then be read by one of these programs. The file type is lhe (actually an XML file), documented in J. Alwall et al., hep-ph/0609017 So, generate the initial and final 4-vectors in the diagram on the previous page, write them (with essential metadata) in an lhe file, and PYTHIA or HERWIG will read it and carry out the rest of the process.
For example, here is the specification of a Drell-Yan event. global event information -- no of particles factorization scale alpha and alphas <LesHouchesEvents version="1.0">... <event> 5 661 0.2119363E-01 0.7758777E+02 0.7818608E-02 0.1203148E+00 # 1-1 0 0 501 0 0.0000E+00 0.0000E+00 0.35806E+01 0.3580E+01 0.0E+00 0. -1. -2-1 0 0 0 501 0.000E+00 0.00000E+00-0.42030E+03 0.4203E+03 0.0E+00 0. 1. -24 2 1 2 0 0 0.000E+00 0.00000E+00-0.41672E+03 0.4238E+03 0.775E+02 0. 0. 11 1 3 3 0 0 0.3765E+02 0.45351E+01-0.16391E+03 0.1682E+03 0.000E+00 0. -1. -12 1 3 3 0 0-0.3765E+02-0.45351E+01-0.25283E+03 0.2556E+03 0.000E+00 0. 1. </event> PDG codes status parents color flow 4-vector mass spin
The PDG codes are standardized codes identifying the particle. The status is -1 for an initial particle, 1 for a final particle, 2 for an intermediate resonance. Parent-daughter relations will be written into the final record generated by PYTHIA. PYTHIA or HERWIG physics events can be passed to a detector simulation. This whole chain is available in MADGRAPH, using John Conway s PGS to generate simulated detector output. The LHC Olympics distrbution of PGS now allows the input to be an lhe file (thanks to Tommer Wizansky and Jesse Thaler).
Color is treated by color flow, in which all color variables are considered as 3 or 3bar lines carried by particles. For example, Gluons are treated as 3 x 3bar. This corresponds to the leading order in 1/N. For a detailed treatment of color, one should generate cross sections for each color structure (ignoring interference terms that are of higher order in 1/N.
The color flow will eventually become the strings used in hadronization. This is an approximation that one should think about carefully. Subleading terms in 1/N with singlet intermediate lines will generate characteristic hadronization with rapidity gaps. This will generate background to rapidity gap signatures (e.g. of WW -> h). In evaluating results from simulations for backgrounds to such processes, you need to ask, are the subleading color structures included?
If the first decay leads to final-state particles known to PYTHIA, you can stop here. If not, you should generate the subsequent decays. PYTHIA will decay known particles isotropically. You might think that this is not adequate, that you would like to include decay matrix elements and spin correlations. If so, you need to simulation more stages of the decay on your side before writing the lhe file. That is, you have to take more of the responsibility onto your side. I ll say more about spin correlations in a moment. It is possible in the Les Houches accord to define new particles not known to PYTHIA, specific their decay modes and branching fractions, and let PYTHIA generate the decay chains with isotropic decays at each stage.
The lhe file contain the spins of final quarks and leptons. PYTHIA does not use this information, but, still, you should think about whether it might be useful. New physics models typically produce highly polarized taus, and tau polarization effects in decay can be large. Trigger bias can favor the mode τ R τ π ν τ preferentially for (Godbole, Guchait, Roy). There is a special-purpose program, TAUOLA, that is sometimes interfaced to PYTHIA to give polarized tau decays. The LHC experiments should actually implement this by default (though they not yet). New physics models also typically generate large b quark polarization. This is very hard to use, but maybe it is possible with the hadronization process b Λ b in which the baryon can be built from b + (ud)(s = 0)
tau decay energy distributions at the Z events/0.05 2000 ALEPH 4000 ALEPH _ 3000 1000 2000 1000 0 0 0.25 0.5 0.75 1 x 0 0 0.25 0.5 0.75 1 x L R
Now it time to discuss inclusion of spin correlations. To generate spin correlations and other polarization effects, it is necessary to generate the whole decay chain on your side before transferrring to PYTHIA or HERWIG. In principle, by decaying all the way down to quarks and leptons (ie, including W, Z, and t decays on your side), the full spin information is included. There are three methods to include spin effects in decay chains: Feynman diagram computation (MADGRAPH, COMPHEP) Spin density matrices (HERWIG treatment of SUSY) Helicity amplitudes
Feynman diagram computation is the method that is most systematic and easiest to automate. However, you must supply the widths for particles that are almost on shell in order for to be correctly normalized. 1 p 2 M 2 + imγ It is much easier to get this right if intermediate particles are generated exactly on shell (zero width). This is the method used by MADGRAPH. BRIDGE, by Meade and Reese, supplies MADGRAPH with BR s computed by MADGRAPH.
The most beautiful and physical method is that of helicity amplitudes - amplitudes with initial and final helicities specified. These are invariant under rotations and under boosts along the direction of motion. They are often simple expressions, e.g. M(t L W + L b L) = 2gmt cos θ/2 m W The polarization average is accomplished by integrating over φ. (Detectors typically do not perform this average completely, so even if experimenters ignore polarization, you properly should not.)
The square of a helicity amplitude gives a spin density matrix: D(h, h ) M ( A(h) BC(h) ) M( ( A(h) BC(h ) ) This is easy to normalize: tr[d] = 1 and then we can generate decay products step by step. This is the method used to implement SUSY in HERWIG.
Here is an example of a spin correlation effect, generated by the implementation of SUSY in MADGRAPH at the benchmark point SPS1a Alves, Eboli, and Plehn have shown that the spin correlations generate distinctly different mass distributions for m(bl + ) vs. m(bl ) The large effect comes from the far b in gluino decay paired with the near l from N decay. At this spectrum point, these are the most energetic products.
Alves, Eboli, Plehn
The effect comes from a spin correlation in the sbottom decay noted by Barr and Kawagoe, Nojiri, Polesello: This is very tricky: The effect comes from the fact that the and partner specific helicity states of b and l. b l b But it is important also that is a scalar. This leads to 100% spin correlation in its decay.
Finally, we should think about how and where QCD showers are generated. QCD radiation comes from all parts of a particle production reaction, and from both the production and decay stages.
If you are happy with the parton showers generated by PYTHIA, the Les Houches accord specification will place these showers correctly, including both initial and final state radiation. The status +2 creates parton radiation in such a way that the mass specified for that intermediate state is preserved. This is a nice prescription. It generates radiation both before and after the creation of this intermediate state.
However, you might want to do better than PYTHIA showers. For example, you might be interested in a hard-to-see particle triggered by the initial state radiation from the quarks or gluons that produce it. It this case, you should supply the matrix element yourself (or generate gluon 4-vectors consistent with this matrix element). You should also worry about double-counting between the matrix element generation and the parton shower generation. The Les Houches accord allows event-by-event specification of a fragmentation scale - the hardest scale for generation of parton showers. A simple way to avoid double-counting is to set this scale to the pt of the gluon. Better ways exist; this is the subject of another seminar.
Here are some estimates of the rates for radiating 1, 2 hard gluons in tt production, comparing to the gluons radiated by PYTHIA showers. PYTHIA has several prescriptions for showers, from wimpy showers to power showers. A range of tunings is indicated. 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 GeV Plehn, Rainwater, Skands
Here are estimates by Plehn, Rainwater, and Skands of extra gluon radiation in supersymmetry events. The effect is much smaller than that for top quarks events at the LHC. 600 GeV gluino pair production: 600 GeV squark pair production: Plehn, Rainwater, Skands
I hope that this put forward the major issues for simulation of new particle production at the LHC. The tools are usable, at least if you have simple goals, but there is much room for improvement. Hopefully, we can make these tools more useful before we see the LHC data.