Study of Jet Shapes at CMS

Study of Jet Shapes at CMS in pp Collisions at √s = 14 TeV

Analysis note	link to AN details:
Physics analysis summary
Reconstruction software	CMSSW1612
Simulated data	HERWIG++ 2.2 and PYTHIA6.4 CSA07data

Introduction

The CMS (Compact Muon Solenoid) detector will detect high transverse momentum jets produced in the final state of proton-proton collisions at the center of mass energy of 14 TeV . These data will allow us to measure jet shapes, defined as the fractional transverse momentum distribution as a function of the distance from the jet axis. Since jet shapes are sensitive to parton showering process they provide a good test of Monte Carlo event simulation programs. In this study we present a study of jet shapes reconstructed using calorimeter energies based on an integrated luminosity of 10 pb^-1. We compare the predictions of the Monte Carlo generators PYTHIA and HERWIG.

Jet Shapes

The jet shape is defined as the average fraction of the jet transverse momentum within a cone of a given size r around the jet axis, δR²= δφ ² + δy². Jet shapes can be studied by using an integrated or a differential quantity, and both have been used to define the energy flow in a jet. In the present study only two leading jets within |y|<1 cut are used. All particles and calotowers within distance δR=0.7 are used . This large cone size ensures that most of the parent parton energy is included.

The physical observables used for jet shape are differential jet shape $\rho(r)$ and integrated jet shape $\psi(r)$. $\rho(r)$, is defined as the fraction of the jet transverse momentum contained inside an annulus of inner radius $r-\delta r/2$ and outer radius $r+\delta r/2$ around the jet in the case of $0\leq r\leq R$:

\begin{equation} \rho(r)=\frac{1}{\delta r}\frac{1}{N_{jet}}\sum_{jets}\frac{P_T(r-\delta r/2,r+\delta r/2)}{P_T(0,R)} \end{equation}

where $N_{jet}$ denotes the total number of jets, and the sum is over all the jets,$P_{T}$ is the sum of all particles or towers in the range $(r-\delta r/2,r+\delta r/2)$ in the numerator where $r= \sqrt{(y_{i}-y_{j})^2 + (\phi_{i}-\phi_{j})^2}$ with $(y_{i},\phi_{i})$ and $(y_{j},\phi_{j})$ being the position of the jet and the particle or tower. The denominator $P_T (0,R)$ is the scalar sum of transverse momenta of all the particles within cone $R$.

Calorimeter towers and particles are used to reconstruct the differential jet shape. For each jet, the scalar sum of the transverse momentum of the calorimeter towers or particles within $(r-\delta r/2,r+\delta r/2)$, is determined and divided by $P_T(0,R)$. The differential jet shape, $\rho^{CAL}(r)$ and $\rho^{HAD}(r)$ (see Figure~\ref{quantityDiff}) are then determined by using equation 5.

Similarly, the integrated jet shapes (see Figure~\ref{quantityInt}) , $\psi^{CAL}$ and $\psi^{HAD}$ corresponding to calorimeter tower and particle energies, respectively, are defined as:

This study used the same definitions and variables as CDF experiment and it repeats the CDF analysis for CMS experiment.

Systematic Uncertainities

The systematic uncertainty arise mainly from the calorimeter response to the particles in the jet. The main sources of uncertainties include:

• Jet energy scale
• Transverse shape of calorimeter showers
• Non-linearity of calorimeter response
• Jet fragmentation

As the calorimeter response depends on the $p_T$ fo the particles in the jets, the jet fragmentation enters indirectly. Uncertainties due to the fragmentation model can be estimated by comparing results using PYTHIA and HERWIG.

The uncertainties arising from jet energy and position resolution, and event selection cuts are expected to be negligible compared to the sources listed above and are not considered.

References

• S.D.Ellis, Z.Kunszt and D.E. Soper, Phys.Rev.Lett. 69, 3615 (1992)
• J.Pumplin, Phys.Rev. D 44, 7(1991)
• Other experiments:
  • CDF Collaboration, Phys.Rev. D71, 112002 (2005)
  • ZEUS Collaboration, J.Breitweg et al., The Eur.Phys.Journal C 2, 1 61-75 (1998)
  • OPAL Collaboration, R.Akers et al., Zeit.f.Phys. C 63, 197 (1994)

Plan

We have a method to measure jet shapes in pp collisions at 14 TeV . By taking pp as a reference I am planning to look at jet shapes in Pb-Pb collisions at CMS. The work is going on in the Heavy Ion High-pT group.

Contributors

My Links

• ATasteOfTWiki - view a short introductory presentation on TWiki for beginners
• WelcomeGuest - starting points on TWiki
• TWikiUsersGuide - complete TWiki documentation, Quick Start to Reference
• Sandbox - try out TWiki on your own
• PelinKurtSandbox - just for me

My Personal Preferences

• Show tool-tip topic info on mouse-over of WikiWord links, on or off:
  • Set LINKTOOLTIPINFO = off

Note: TWiki has system wide preferences settings defined in TWikiPreferences. You can customize preferences settings to your needs: To overload a system setting, (1) do a "raw view" on TWikiPreferences, (2) copy a Set VARIABLE = value bullet, (3) do a "raw edit" of your user homepage, (4) add the bullet to the bullet list above, and (5) customize the value as needed. Make sure the settings render as real bullets (in "raw edit", a bullet requires 3 or 6 spaces before the asterisk).

Related Topics

• ChangePassword for changing your password
• ChangeEmailAddress for changing your email address
• TWikiUsers has a list of other TWiki users
• UserDocumentationCategory is a list of TWiki user documentation
• UserToolsCategory lists all TWiki user tools