Top quark mass measurement in the dilepton channel

A study focusing on the measurement of $m_{top}$ using dilepton final states produced with pp collisions at $\sqrt{s}=10~GeV/c^2$.

Tasks

Samples

MC samples

The reference page for the cross sections and samples to be used is located in this link.

Signal samples

The $t\bar{t}$ dilepton samples were generated with PYTHIA6 and FastSim (version 2_2_6).

More  Less  The base configuration file was generated using the recipe provided in the following link and can be retrieved from here. The samples were generated by scanning the top mass according to the values specified in the following table:

Signal samples used
located @ ==/lustre/lip.pt/data/cms/store/user/pedros/==
$M_{top}~(GeV/c^{2})$ Cross section (pb) N$_{evts}$ Size(Gb) !DBS link
arXiv:0804.2800 Pythia
150 776 $^{+73}_{-73}$ (scale)$^{+34}_{-30}$ (pdf) 760 $\pm$ 6 20000 7.8 link
160 571 $^{+52}_{-53}$ (scale)$^{+26}_{-23}$ (pdf) 554 $\pm$ 8 20000 7.9 link
165 492 $^{+44}_{-45}$ (scale) $^{+23}_{-21}$ (pdf) 475 $\pm$ 5 20000 7.9 link
170 426 $^{+37}_{-39}$ (scale)$^{+20}_{-18}$ (pdf) 411 $\pm$ 6 20000 8.0 link
175 370 $^{+31}_{-34}$ (scale)$^{+18}_{-16}$ (pdf) 359 $\pm$ 2 20000 8.0 link
180 323 $^{+27}_{-30}$ (scale)$^{+15}_{-14}$ (pdf) 309 $\pm$ 3 20000 8.1 link
190 247 $^{+19}_{-22}$ (scale)$^{+12}_{-12}$ (pdf) 237 $\pm$ 2 20000 8.2 link

Note: To run on these samples you need to add dbs_url=https://cmsdbsprod.cern.ch:8443/cms_dbs_prod_local_09_writer/servlet/DBSServlet to the [CMSSW] section of your CRAB configuration file.

The inclusive $t\bar{t}$ samples are taken from the official CMS production ( Fall08 / Winter09).

Official signal samples used
$M_{top}~(GeV/c^{2})$ Dataset path N$_{evts}$
167 /TTJets_MTop167-madgraph/Winter09_IDEAL_V12_FastSim_v11/GEN-SIM-DIGI-RECO 1000000
174 /TTbar-madgraph/Winter09_IDEAL_V11_FastSim_v1/GEN-SIM-DIGI-RECO 10000000
/TTJets-madgraph/Fall08_IDEAL_V9_v2/GEN-SIM-RECO 1000000
180 /TTJets_MTop180-madgraph/Winter09_IDEAL_V12_FastSim_v11/GEN-SIM-DIGI-RECO 1000000

Background samples

Background samples are taken from the official CMS production ( Fall08 / Winter09).

Studies list

Event selection

Total number of events selected events ($t\bar{t}$ dilepton channel) (pb)
Selection step $m_{top}~(GeV/c^2)$
150 160 170 180 190
generated 50.4 37.1 27.7 21.0 16.0
triggered 45.9 33.8 25.2 19.3 14.9
${\mit \geq 2}$ leptons 14.9 11.0 8.6 6.7 5.3
${\mit e~+~\mu}$ 7.2 5.5 4.2 3.4 2.6
${\mit \geq 2}$ jets 4.5 3.7 3.0 2.4 2.0
MET 3.8 3.2 2.6 2.1 1.8
opposite sign 3.7 $\pm$ 0.4 3.1 $\pm$ 0.3 2.5 $\pm$ 0.3 2.1 $\pm$ 0.2 1.8 $\pm$ 0.2
Acceptance ($\%$) 0.48 $\pm$ 0.05 0.54 $\pm$ 0.06 0.59 $\pm$ 0.06 0.64 $\pm$ 0.07 0.71 $\pm$ 0.07

Measuring top mass

Method A: leptonic $p_{T}$ spectrum

The lepton $p_{T}$ spectrum can be modelled by a $\Gamma$-like function:

$f(p_T)=\frac{1}{a\[\Gamma(1+b)\]} \cdot  (\frac{p_T}{a})^b \cdot e^{-\frac{p_T}{a} }$ Lepton $p_T$ fitting fuction

According to Ref the depedence of the parameters $a$ and $b$ on the mass of the top quark are linear. By measuring the charged leptons $p_T$ spectrum and fitting $a$ and $b$ one can derive the top mass.

The following plots show some kinematical variables of interest for the selected events.

Selected charged leptons $p_T$ spectrum Correct lepton-jet assignments in the selected events

Method B: scan neutrinos $\vec{p}$

This method consists in determining the two neutrinos momentum for a given input value of the top mass. The distribution of the number of events with solutions found as function of the top mass allows to extract to extract this value.

Determination of the neutrinos momentum

If the top-quark and the W-boson are produced on-shell, we can relate their masses to the 4-momentum of their daugther particles as follows:

$m_W^2 = (P^l+P^{\nu})^2$

$m_t^2 = (P^l+P^{\nu}+P^b)^2$

where $P^{i}=(E,\vec{p})$ is the 4-momentum of the particle i (l-lepton; v - neutrino; b-b-jet) with energy E and 3-momentum p.

More  Less  Squaring and expanding these equations we can eliminate the neutrino's energy variable to find the following parameterization of the neutrino's longitudinal momentum as a function of it's transverse momentum:

$p^{\nu}_{z}(\vec{p}_{T}^{\nu}) = \frac{ E^{b}(m_{W}^{2}-m_{l}^{2})-E^{l}(m_{t}^{2}-m_{W}^{2}-m_{b}^{2}-2P^{e} \cdot P^{b})+2(E^{b}\vec{p}_{T}^{e}-E^{l}\vec{p}_{T}^{b})\cdot\vec{p}_{T}^{\nu} } {2(E^{l}p^{b}_{z}-E^{b}p^{l}_{z})}$

In the former we have made use of of the transverse momentum of a particle defined as: $\vec{p}_{T}=(p_{x},p_{y})$. Using this definition together with the fact that $E^{\nu}=\sqrt{\vec{p}^{\nu}\cdot \vec{p}^{\nu}}$ and substituting in the equation for the W-boson mass we obtain:

$4E^{e}^{2}[ \vec{p}_{T}^{\nu} \cdot \vec{p}_{T}^{\nu} + p_{z}^{\nu}(\vec{p}_{T}^{\nu})^{2} ] -{ \{m_{W}^{2}-m_{l}^{2}+2[\vec{p}_{T}^{l}\cdot \vec{p}_{T}^{\nu}+ p_{z}^{l} p_{z}^{\nu}(\vec{p}_{T}^{\nu}) ] \} }^{2} =0$

For simplicity we do not expand all the terms in this equation. This equation describes a conic intersection in the $(p_x,p_y)$ plane.

The momentum of the neutrino in the transverse plane $\vec{p}_{T}^{\nu}$ is thus constrained by a conics equation of the type:

$\vec{p}_{T}^{\nu}\cdot A \cdot \vec{p}_{T}^{\nu} + B\cdot \vec{p}_{T}^{\nu} + C = 0$ Conics equation

The B-vector and the C-constant are functions of the top mass and the A-matrix is independent of the top mass in the conics equation. The two figures below show the conics of the (anti-)neutrino for a $t\bar{t}$ event in the $(p_x,p_y)$ plane. The MC truth value of the neutrinos' $\vec{p}_{T}$ is superimposed for comparison.

$t\bar{t}$ event Particle 3-momentum (GeV/c)
NeutrinoConics.png Decay 1 Decay 2
b-quark (95.8; -33.3; 396.6) (-105.4; 98.6; 248.9)
charged lepton (44.5;-36.9; 119.0) (-9.8; 57.2; 86.1)
neutrino (-32.3; -75.4; 179.5) (10.2; -1.3;-14.7)

The 2 conics leaves 2 free parameters: for instance the x-component of each neutrinos' 3-momentum. In order to relate the two conics (because they describe 2 decays happening in the same event) a further constraint can be used taking into account the kinematics of the event. Some constraint examples are the following:

  1. MET constraint (missing transverse energy) : $\vec{p}_{T}^{\nu_1}+\vec{p}_{T}^{\nu_2}=\vec{{\not}E}_{T}$
  2. $p_{T}$ balance :$\sum_{i=1}^{2} (\vec{p}_{T}^{\nu_i}+\vec{p}_{T}^{l_i}+\vec{p}_{T}^{b_i})=0$

If one of these constraints is used we are able to remap one neutrino momentum as a function of the other neutrino momentum. This will remap one of the conics and by definition it must intersect the other one. It is the intersection of the conics (after using the event kinematical constraint) that yields the solution for the momentum of the neutrinos generated by the $t\bar{t}$ system decay cascade. The figure below shows the result of remapping the second conics using the MET constraint. The pairs of solutions found are superimposed for comparison.

$t\bar{t}$ event solutions MET Constraints
NeutrinoConicsConstrained.png $p_{x}^{\nu_2}=-22.1-p_{x}^{\nu_1}$ $p_{y}^{\nu_2}=76.7-p_{y}^{\nu_1}$
Solution 1 (triangles) $\vec{p}^{\nu_1}=$(-32.3; -75.4; 179.5)
$\vec{p}^{\nu_2}=$(10.2; -1.3;-14.7)
Solution 2 (boxes) $\vec{p}^{\nu_1}=$(70,-225,811)
$\vec{p}^{\nu_2}=$(-92,148,252)

Presentations

Documentation

-- GiulianoMini - 15 May 2009

Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng CorrectAssignments.png r1 manage 30.9 K 2009-06-04 - 15:56 PedroSilva  
PNGpng CorrectAssignments_ratio.png r1 manage 21.2 K 2009-06-04 - 15:56 PedroSilva  
PNGpng NeutrinoConics.png r1 manage 27.0 K 2009-06-02 - 14:36 PedroSilva  
PNGpng NeutrinoConicsConstrained.png r1 manage 23.9 K 2009-06-02 - 14:59 PedroSilva  
PDFpdf Pedro_TopMassDileptons_24.11.09.pdf r1 manage 667.0 K 2009-12-15 - 12:45 MicheleGallinaro  
PNGpng RecoChargedLeptonsPt.png r1 manage 30.9 K 2009-06-04 - 15:57 PedroSilva  
PNGpng RecoChargedLeptonsPt_ratio.png r1 manage 23.5 K 2009-06-04 - 15:57 PedroSilva  
Texttxt TTjets_10TeV_cfg.py.txt r2 r1 manage 14.9 K 2009-06-03 - 14:56 PedroSilva  
PDFpdf TopMassDileptons_24.11.09.pdf r1 manage 596.7 K 2009-11-23 - 20:50 PedroSilva  
PDFpdf Top_Quark_mass_7.pdf r1 manage 218.0 K 2009-12-15 - 12:45 MicheleGallinaro  
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