100 101 χ 2 /N df ˜p
quadratic interpolation(s), Nruns=194
cubic interpolation(s), Nruns=393
scan MC data min(χ2/N df) =4.6 Best tune 10 40 ∆ N ∆˜p
Figure 77:Line scan validation of the tuning result obtained with Professor. The scan-line is done along
the direction of smallest uncertainty as calculated from the minimization result’s covariance matrix, showing a perfect agreement of the minima for both, the predictions from the parameterizations and the true generator response. The histogram on top shows the distribution of the minimization results obtained with these parameterizations if projected on the scan-line. The scan-line is parameterised by ˜p, its values are scaled: ˜p∈ [0· · ·1].
successful.
By looking at the goodness of fit values it has to be taken into consideration that the statistical treatment of the true data is not perfect, since bin-bin correlations are not considered and in many cases not quantified by the analyses.
6.5
Parameter-parameter correlations
The great advantage of the Professor tuning system over any other tuning attempts so far is that it can handle a comparably big number of parameters simultaneously and that is respects lowest order parameter-parameter correlations in the case of the quadratic parameterization (see equation (1), terms with γ(ijb) p0ip0j) and an even higher degree of correlations in the case of approximations using third order polynomials. It is the nature of the phenomenological models in question that the existing parameter- parameter correlations are a priori unknown. However, in Professor it is possible to
6 TUNING THE UNDERLYING EVENT 6.5 Parameter-parameter correlations
Parameter Best tune – tune S0 Largest uncertainty Smallest uncertainty
PARP(64) -0.10 -0.24 0.79 PARP(71) 0.67 -0.33 -0.58 PARP(78) 0.01 -0.44 0.16 PARP(79) 0.28 -0.68 -0.10 PARP(82) 0.00 0.22 0.08 PARP(83) -0.07 -0.06 0.05 PARP(90) -0.02 0.33 -0.05 PARP(91) 0.00 -0.07 -0.02 PARP(93) -0.67 0.09 -0.01
Table 10: Vectors used for the definition of the scan-lines in the nine-dimensional parameter hypercube.
Weighted observables Unweighted observables
Tuning χ2 χ2/N df Ndf χ2 χ2/Ndf Ndf Professor 15664 8.3 1897 8655 6.9 1251 S0 63556 33.5 1897 32354 25.9 1251 AW 97688 51.5 1897 49528 40.0 1251 Atlas ’08 149488 78.8 1897 76027 61.0 1251
Table 11: Global χ2-comparison for different tunings of Pythia 6. Shown are the goodness of fit of all the
6.5 Parameter-parameter correlations 6 TUNING THE UNDERLYING EVENT
quantify linear correlation coefficients with the help of the covariance matrix, C (see
equation (11)).
The calculated parameter-parameter correlations for the best tune can be found in Table 12. The correlations cannot be neglected, further showing the need of systematic tunings approaches that are able to tune several parameters at the same time.
The largest correlation (ρ=0.51) is found for PARP(82) and PARP(90), not surprising
since they are connected by equation (19).
The anti-correlation of PARP(82) and PARP(83) (ρ = −0.45) is interesting since it
indicates a dependence of the hadronic matter distribution with the underlying event cut-off. This is backed since also PARP(90) is anti-correlated with PARP(83). A higher underlying event cut-off means that there will be less multiple parton interactions, the anti-correlation might reflect this since PARP(83) eventually steers the amount of multiple parton interactions.
Another large correlation (ρ =0.33) is found for PARP(78) and PARP(83) which could
be interpreted as follows. A larger value of PARP(83) means a less spiked hadronic matter distribution which leads to a smaller probability of multiple parton interaction and therefore a smaller number of particles that are being produced. Thus, the amount of colour-reconnection (steered by PARP(78)) needed to describe the data must be larger since more colour-reconnection means shorter colour strings and therefore less final state particles.
6 TUNING THE UNDERLYING EVENT 6.5 Parameter-parameter correlations
PARP(64) PARP(71) PARP(78) PARP(79) PARP(82)
PARP(64) 1.00 0.05 −0.18 −0.06 −0.34
PARP(71) 1.00 0.23 0.03 −0.12
PARP(78) 1.00 −0.25 −0.09
PARP(79) 1.00 0.07
PARP(82) 1.00
PARP(83) PARP(90) PARP(91) PARP(93)
PARP(64) 0.16 −0.10 −0.06 −0.02 PARP(71) 0.19 −0.07 −0.02 −0.14 PARP(78) 0.33 −0.12 −0.19 0.14 PARP(79) −0.08 0.10 0.04 −0.04 PARP(82) −0.45 0.51 0.00 0.04 PARP(83) 1.00 −0.23 −0.05 0.13 PARP(90) 1.00 −0.06 −0.02 PARP(91) 1.00 0.08 PARP(93) 1.00
7 CONCLUSIONS
7
Conclusions
In this thesis, the Professor framework for the systematic and automatised tuning of Monte Carlo event generators to data was described.
The key feature of Professor is the bin-wise parameterisation of the generator’s response to shifts in parameter space using polynomials of second or third order. This parameter- isation, together with measured observables, can be used to define a goodness-of-fit measure in the high-dimensional parameter space. A numerical minimisation of this measure leads to an estimate of the parameter settings that describe the data best, which can be validated with the Professor system in many ways. The minimisation only takes seconds or minutes, while the most time-consuming part of a tuning with Professor is the generation of Monte Carlo "data", which, however, has to be done only once and so far did not take longer than two days on a batch farm. Furthermore, the definition of the goodness-of-fit is very flexible and even allows for a subjective weighting of individual observables. The parameterisations can further be used to identify the parameters an observable is most sensitive to and thereby help to improve the fit.
After the Professor system was used to systematically tune fragmentation and, for the first time, also flavour parameters in Pythia 6 to data of the LEP experiments (ALEPH, DELPHI, OPAL), the main task for the work described in this thesis was the tuning of underlying event parameters in Pythia 6. The underlying event is an unavoidable background in every hadron-collider experiment. It is especially relevant for the LHC, where the number of events per beam-crossing will be up to 25 and the number of multiple parton interactions is expected to be between four and five in a single proton-proton collision.
The presented tuning has found its way into Pythia 6 (version 420) as a choice of standard
parameter settings (preset 329). With this new tuning not less than 24 parameters of
Pythia 6 have been tuned to data by the Professor system, allowing for a simulation of high energy physics processes from those present at the LEP experiments up to those found at the Tevatron experiments using one single tuning.
The underlying event model was tuned to 44 observables measured by the CDF and DØ detectors in p-p collisions at the Tevatron at center of momentum energies of 630, 1800 and 1960 GeV. This tuning is significantly better in the description of these observables than the standard parameter settings available so far (tune S0, tune AW, Atlas ’08 tune). The tuning is systematically kept under control. It shows a generally good description of the generator response using a quadratic parameterisation with some improvement if cubic parameterisations are used but no clear preference could be drawn for the use
7 CONCLUSIONS of the latter.
The following Pythia 6 parameters were tightly constrained by the tuning:
• PARP(64), scale of αsin initial state radiation
• PARP(78), colour-reconnection
• PARP(82), underlying event cut-off
• PARP(83), hadronic matter distribution
• PARP(90), energy scaling of the underlying event cut-off scale
The following parameters could be constrained only slightly:
• PARP(71), merging of matrix elements and FSR parton showers
• PARP(79), beam-remnant x-enhancement
• PARP(91), width of primordial k⊥
• PARP(93), upper cut-off of primordial k⊥
The next step in the tuning of the underlying event will include more experimental data, preferentially from experiments like RHIC (p-p) and UA5 (p-p) where data is taken at center of momentum energies of 200 and 900 GeV, respectively. As soon as the first LHC data are available this data will be included as well. This will help to improve the energy scaling of the underlying event and to perform reasonable extrapolations to LHC energies (8, 10 and 14 TeV). Given the ability of the Professor tuning system to include and thereby to respond to new data in an easy way makes Professor an ideal tool for this task.
Tunings of the widely-used generators Pythia 8, Herwig++ and Sherpa are in prepara- tion.
A PROFESSOR-USAGE
A
Professor-usage
The following passages are a mini manual for the Professor package. The main scripts for tuning and validation are briefly described. In general, a quick help is available for
each script, if the switch-his supplied as command line option.