Chapter VI

--Barison 14:38, 12 Oct 2005 (MET DST)

Chapter 6  Analysis

• single top channels are little affected by combinatorics
• however ttbar and wjj backgrounds are dominant
• need to find good trade-off between selection efficiency and background rejection

6.1  AOD Definitions

Insert work on: electron selection, bjet tagging

6.2  Selection cuts

Cut efficiency studies in the past have been performed with old montecarlo generator. As first check, the efficiency is now lower (50%). Need a better study of cut efficiecies.

• isolated lepton cut: trigger efficiency, cut efficiency
• b-tagging: why do we use single instead of double b-tag (collinear b)
• forward light jet: discriminant against Wjj backgrounds
• no cut on missing Et. Need to insert one?

Here put a graph of the selection cuts with the efficiencies.

• Isolated lepton distributions
• Jet distribution
• Total invariant mass
• Other?

6.3  Kinematic fit to the W mass

• W mass measured with good resolution
• W mass can be used for calibration purposes (ttbar, usually)
• Quadratic function: two results. Good need handle on missing Et

6.4  Combinatorics and Top selection

There are almost no combinatorics, however there is a double ambiguity. A few methods to solve it:

6.4.1  Target mass

Retain the solution with mass closest to 175. It biases the event.

6.4.2  Reverse boost

Boost all the decay particles back to the top frame and select the couple close to the back-to-back configuration. It does not work very well (jet scale might be a problem).

6.4.3  Highest Pt

Select the top with the highest pt. Works well, but the physics of it escapes me.

6.5  Systematics

6.5.1  Minimum bias

Minimum bias events are events where the colliding protons undergo a soft elastic collisions or a soft parton collision (diffractive events). Occasionally, a soft parton collision might "fluctuate" to result in an event with high enough p_T to be measured by the detector.

Underlying events are defined as the sum of all types of events (beam remnants, ISR, secondary parton collisions) which happen at the same time of hard inelastic parton scattering. In the first approssimation, underlying events and minimum bias events are assumed to be governed by the same physical model. However, there can be significant differences, since color interactions between the hard scattering and the underlying events might occur, modifying the spectra of the two classes of events. At the detector level, underlying events generate extra tracks in the detector and deposit energy in the calorimeter, thus degrading the measurement of the hard scattering. Several studies have been performed to evaluate the effect of underlying events by modelling minimum bias in Montecarlo generators and using the same model to generate underlying events.

In PYTHIA, the model of minimum bias is the following: the number of underlying events is given by the ration between the cross section for "hard" minimum bias events divided by the cross-section of total, inelastic non-diffractive soft events: s_hard(p_{^ min})/s_nd(s). While p_{^ min} in principle should be zero, in practise a cut off must be included to prevent the aforementioned ratio to diverge. The minimum momentum applicable is calculated at run-time by PYHTIA with the following formula:

p^ min(s)=p82

/ | | \

Ecm p89

\ | | /

p90

,

where the parameters p_i are defined in pythia by PARP(I). The physical meaning of this formula is that when the exchanged momentum between the scattering parton is low, the exchanged gluon cannot resolve the individual colour of the partons, reducing the coupling constant. This screening effect limits the cross-section at low momenta.

The effect of the impact parameter on the minimum bias collision is parametrized by a double-gaussian parton density:

r(r)μ

1-b a13

exp

/ | | \

-

r2 a12

\ | | /

+

b a23

exp

/ | | \

-

r2 a22

\ | | /

,

which describes a parton model when a fraction b of the hadronic matter is contained inside a "core" the radius of which is a₂/a₁ of the proton radius. This model correctly describes the multiplicity of minimum bias events: harder collisions result in smaller impact parameter, which probes high density regions where minimum bias events are more likely to happen.

Minum bias was studied at CDF by Rick Field et al. to obtain a PYTHIA tuning capable do describe data. The method utilised at CDF is the following: minimum bias data is generated by PYTHIA by selecting MSEL=1 (QCD high- and low-pt events). For each event, jets are reconstructed with a cone of radius 0.7; the phi space is divided into four regions, using the jet with the highest pt in the event as a reference axis. Two of the zones are labelled as "transverse", and cover a region from 60 to 120 away from the jet axis. All charged particles included in these two regions are examined, event by event: the scalar pt sum of particles surviving the cut |h|<1, p_T>0.5 GeV is computed, and plotted against the pt of the leading jet. A similar technique can be used by examining jets instead of individual particle, but CDF used charged tracks because of the better resolution of the tracker w.r.t. the calorimeter.

If we separate the two transverse zones in a region of low energy deposition and a region of high energy deposition and we plot separately the scalar pt sum, we obtain two separate diagrams, where the amount of high energy deposition is correlated with the "hard" fraction of minimum bias, while the low energy plot is correlatedwith the "soft" and collinear scatterings. The PYTHIA parameters were tuned to make these two plots reproduce the same plot drawn for CDF minimum bias data.

The parametrisation obtained by Field is the following:

• PARP(82)=2.0 regularization scale of the minimum pt in the hard scattering (D=2.1);
• PARP(83)=0.5 fraction of hadronic matter inside the "core" (D=0.5);
• PARP(84)=0.4 ratio between the "core" radius and the proton radius (D=0.2);
• PARP(85)=0.9 probability of having an extra interaction giving two gluons (D=0.33);
• PARP(86)=0.95 probabilty of having an extra interaction giving two gluons or a closed gluon loop (D=0.66);
• PARP(89)=1800 regularization energy of the minimum pt --- 1.8 TeV (D=1000.);
• PARP(90)=0.25 exponent of the regularization function (D=0.16);
• PARP(67)=4.0 maximum virtuality (4× Q²) for spacelike parton showers (D=1.);

The main effect of the above tuning is to increase the core size, thus reducing the parton density and thus decrease the multiplicity, and to increase initial state showers. No plot this time, I screwed up badly.

The parametrization used at DC2, instead, is very simple:

• MSTJ(11)=3 fragmentation scheme: use Peterson fragmentation function

  f(z)=

  1 z / | | \ 1- 1 z - (-c) 1-z \ | | / 2

  for b- and c-quarks;
• MSTJ(22)=2 decay cutoff: decay particles only if ct>10 mm;
• PARJ(54)=-0.07 c factor in the Peterson function for c-quarks (D=-0.05);
• PARJ(55)=-0.006 c factor in the Peterson function for b-quarks (D=-0.005);
• PARP(82)=1.8 regularization scale of the minimum pt in the hard scattering (D=2.1);
• PARP(84)=0.5 ratio between the "core" radius and the proton radius (D=0.2);

UPDATE: the Field parametrization is now default in PYTHIA. DOH!

6.5.2  Multiple interactions

Using the Pileup sample instead of the normal one.