'Capita Selecta', Antwerp 2008

Welcome! If you are looking for material related to the tutorial in the framework of the 'Capita Selecta', you are at the right place! Enjoy!

Michel & Rik

Exercises and (partial) solutions

handouts-2.pdf​: handout with exercises

Z+jets at the Tevatron

The biggest difficulty in generating events with multiple jets is to prevent double counting. For example, an event with three jets in the final state could have come from a three parton configuration of which all three showered into different jets, or a 2-parton event of which a third jet is generated by the parton shower (or even an 1 (or zero) parton event with two (or three) jets generated by the shower). The otherway around is also possible. A two jet final state could also have come from a three parton state, of which two parton are belonging to the same jet, and this could therefore lead to double counting with a two-parton sample of which both the partons are showered to a two jet final state.

There are basically several schemes to avoid this double counting. MadGraph uses a method based on the MLM scheme (also a version of the CKKW method is implemented for more details see this page). It works as follows.

Multi-parton events are produced by first generating all the diagrams belonging to the +0, 1, 2, 3, ... jet configurations. Any number of additional particles can be included, the more the 'better' the result will be. In practice, up to 3 jets is the maximum due to the large number of diagrams contributing to these high multiplicity states. For the $p\bar{p} \to Z/\gamma^{* \to \mu}+\mu^{- +0,1,2,3\textrm{ jets}$ sample, the proc_card can be found here​. Note that all the diagrams with multiplicities up to three jets will be generated (a couple of thousand diagrams) and this takes in general 1 or 2 hours or so.}

The second step is, as usual, to generate events by integrating the matrix elements over the phase space. Later-on we will remove events where the 'distance' between two partons is very small, so to improve the effficiency a cut has to be put on the 'kT'-distance between two particles that could form a jet togheter. This 'kT'-distance between particle i and j is defined as $k_T^{{ij}=\sqrt{2\textrm{ min}[p_T}i,p_T^j]2(\cosh(\eta^i-\etaj)-\cos(\phi^i-\phij))^{2}$. A cut on this variable can be set with the 'xqcut' parameter in the run_card. Altough this is a non-phyical cut, and the final result should be independent of its value, chosing it in an appropriate way improves the efficiency quite a lot. Note that for consistency it has to be smaller than other scales in the process, in particular it should be smaller than the jet measure cut-off (described later). At this stage also the minimum transverse momentum (and possibly invariant mass) of the jets has to be set equal to the xqcut to make sure that there are no gaps in the phase space and increase the efficiency. However, the dR-distance can be set (almost) to zero (e.g. 0.001), because the xqcut already takes care of this.}

The third step is to shower the events. Now we have to make sure that we remove events that 'change the number of jets' to avoid the couple counting. A showered event is clustered to jets using a k_T jet algorithm with a jet measure cut-off (generally speaking 1.5-2 as large as the xqcut). This cut-off makes sure that no new jets are generated from a given parton level multiplicity: if an event generates an extra jet, it is removed from the event sample (except for the highest multiplicity samples, so that also events with 4, 5, 6 or even more jets are generated from the 3 jet sample). Because no new jets are generated for the low multiplicity samples, all double counting is removed. And because the minimum transverse momentum of a jet was equal to the xqcut, the full phase space is covered, and we are not removing too many events.

For more technical details also have a look at this page about Matching. Also this page has a lot of information about matching/merging and testing your event samples.

$p\bar{p} \to Z/\gamma^{* \to \mu}+\mu^{- +$ (no matching)}

run_01_banner.txt​: Z banner

• at hadron level with jets above $p_t >10$ GeV event file​, plots​.
• at detector level with jets above $p_t >10$ GeV event file​, plots​.

$p\bar{p} \to Z/\gamma^{* \to \mu}+\mu^{- +0,1,2,3\textrm{ jets}$ matched}

run_01_1_banner.txt​: Z+0,1,2,3 jets banner

• at hadron level with jets above $p_t >10$ GeV event file​, plots​.
• at detector level with jets above $p_t >10$ GeV event file​, plots​.

Example difference with and without matching

Here is the (reconstructed) transverse momentum of the Z boson plotted for the two event samples. From this plot it is clear that the event sample generated without the matching clearly underestimates the number of event for the high pt region. This is exactly as expected, because the pt of the Z for the sample without matching is purely generated from the parton shower. As we know the shower only generates partons in the soft and collinear region, hence the high pt region is underestimated. Using the matching ensures that at the parton level higher multiplicities are already included, so the matrix elements itself can already generate a non-zero pt for the Z boson, therefore it is much larger.

Back-up Files

Events for p\bar{p}>Zh>bb~l+l- at parton level​ (plots​), hadron level​ (plots)

and detector level​ (plots). Generated with the standard set of cuts (i.e. pt(l)>10GeV,

eta(l)

<2.5 and dR(ll)>0.4, with no cuts on the b quarks (at parton level))

Here​ can the model for the "spin-1 Higgs" be found and some parton level events​ and the plots​.