Apollo generator
Introduction
In particle physics we translate theories to experimental observables with the use of "event generators". The current event generators are not efficient in generating new-physics events. The user has to supply them with
fixed model parameters, run them, change the parameters and repeat. Imagine you have 5 parameters and you would like to investigate the expected signal sampling 10 values per parameter. Right now, you need to generate 10
^{5} Monte Carlo samples! Because this is impossible, you end up fixing some parameters to
arbitrary values, limiting your understanding of the new-physics signal. Also, in the process, you generate "blindly" without knowing in advance in which areas of the parameter space you should concentrate (e.g., where the production cross-section is higher, or where the background is lower). For some models the relation between the multidimensional parameter space and physical observables is more obvious. But, generally speaking, it is not!
Apollo generator
First of all, let me explain why I chose the name "Apollo". Ancient Greeks visited the oracle of Delphi to learn about their future. Pythia was the priestess that communicated with god Apollo and gave the prophecies. The problem is that you could not talk directly to Pythia, some elders helped as liaisons, in order to make the prophecy realistic (based on knowledge of detailed information about the inquirers). Well, the situation is the same in high energy physics. Pythia is a generator that makes predictions, but you need a detector simulator (elder) to really know what to expect to see in your particle detector. Now, to really study any random theory, you need a lower-order matrix-element generator, that has the full knowledge of the new-physics Lagrangian. On top of that -- and this is my contribution -- you need to be able to vary the model parameters real time (i.e., during generation) and use importance sampling to concentrate in the multi-parameter space where the new-physics cross section is higher. Sounds like a divine quality, to really know how physics looks like in a multi-parameter new-physics parameter space. And given that this generator has to talk to Pythia for fragmentation, the ideal name for this generator is Apollo! By the way, notice that the user above is holding an ancient ....Feynman diagram.
Description of idea
The usual matrix-element event generators integrate the differential partonic cross section using importance Monte Carlo sampling (this is for a hadron collider like the Tevatron or LHC):
where f
_{i} are the Parton Distribution Functions, x
_{i} is the fraction of the hadron's momentum carried by the parton i, M is the matrix element, P
_{i}(E
_{i}) is the momentum(energy) of the incoming parton i (and P
_{out,k}(E
_{k}) the respective quantities for the outgoing particles). My modification is to include the model parameters Q
_{i} in the picture and make the Monte Carlo simulation sample the parameter space as well (and not just the kinematic space):
In other words
in the same generation process I generate not only 4-momenta for the outgoing particles, but I also generate model parameters. It is like browsing multiple universes (in a "landscape" fashion), which makes sense, since we don't know what the true parameters of the theory are! This practically means that 1 MC file will have all the theory-parameter space of interest and we can set cuts on parameters to study the effect on kinematics and vice-versa.
Advantages
- The MC generator will concentrate in regions of the parameter
space were the cross-section is higher and our limit-setting or
discovery potential much better (assuming known backgrounds)
- efﬁcient and physics-based generation
- We can have all signiﬁcant regions of parameter-space in one ﬁle
- efﬁcient use of resources
- We can study all possible correlations between observables and
kinematic variables
- understand our theory and phenomenology
- Possibility of model-independent studies
- We will be more efﬁcient in optimizing our analyses and
understanding our sensitivity to new physics
- same ﬁle can be used by different analyses and different
parameter-space regions
- We can set multi-dimensional limits
- limits on different combinations of parameters as well
- And, if we make a discovery, we can easier determine the region
of the parameter space that is allowed, given the observation
- we will have the full range of parameters to investigate
- All the above with only 1 (one!) MC sample per theory and
parameter range
It works!
The natural question is: "can the integral converge"? Especially in a multi-dimensional kinematics space
and multi-dimensional theory-parameter space. I demonstrated that it can. I tried Apollo on a 2→2 Drell-Yan
generation (4 kinematic variables) with variable couplings, Z mass and lepton masses (4 theory parameters, total dimension of integration:8) and a 2→6 chargino production (16 kinematic and 6 theory parameters, total dimension of integral:22). Both cases converged after few iterations and gave results similar to expectation (as compared with Madevent). The two plots below show convergence for the Drell-Yan and chargino-neutralino production (click on images for a better version):
For more details about the technical issues related to these two examples, please check slides 15 and 20 of my
pheno08 talk. In this talk you will see some nice plots of playing with (literary) thousands of
theory parameter values. A short description can be found in the Apollo phenomenology page