Name: CMS_2014_I1305624
Year: 2014
Summary: Study of hadronic event-shape variables in multijet final states in $pp$ collisions at $\sqrt{s} = 7$ TeV
Experiment: CMS
Collider: LHC
InspireID: 1305624
Status: VALIDATED
Reentrant: true
Authors:
 - Sunanda Banerjee <Sunanda.Banerjee@cern.ch>
 - Sandeep Bhowmik <Sandeep.Bhowmik@cern.ch>
 - Monoranjan Guchait <Monoranjan.Guchait@cern.ch>
 - Gobinda Majumder <Gobinda.Majumder@cern.ch>
 - Manas Maity < Manas.Maity@cern.ch>
 - Debarati Roy <Debarati.Roy@cern.ch>
References:
 - 10.1007/JHEP10(2014)087
 - arXiv:1407.2856
 - CMS-PAS-SMP-12-022
 - CERN-PH-EP-2014-146
RunInfo:
  $pp$ QCD interactions at $\sqrt{s} = 7$ TeV. Data collected by CMS during the year 2011.
NumEvents: 2234304
Beams: [p+, p+]
Energies: [7000]
PtCuts: [30.0]
Description:
  'Event-shape variables, which are sensitive to perturbative and nonperturbative
   aspects of quantum chromodynamic (QCD) interactions, are studied in multijet
   events recorded in proton-proton collisions at $\sqrt{s}=7$ TeV. Events are
   selected with at least one jet with transverse momentum $p_T > 110$ GeV and
   pseudorapidity $\mid\eta\mid < 2.4$, in a data sample corresponding to
   integrated luminosities of up to $5 fb^{-1}$. The distributions of five
   event-shape variables in various leading jet $p_T$ ranges are compared to
   predictions from different QCD Monte Carlo event generators.

   Five event-shape variables are analyzed in this paper: the transverse thrust
   $\tau_{\perp}$, the total jet broadening $B_{tot}$, the total jet mass
   $\rho_{tot}$, the total transverse jet mass $\rho^T_{tot}$ and the third-jet
   resolution parameter $Y_{23}$. In the formulae below, $p_{T,i}$, $\eta_i$, and
   $\phi_i$ represent the transverse momentum, pseudorapidity, and azimuthal angle
   of the $i$th jet, and $\hat{n}_{T}$ is the unit vector that maximizes the sum of
   the projections of $\vec{p}_{T,i}$. The transverse thrust axis $\hat{n}_{T}$ and
   the beam form the so-called event plane. Based on the direction of
   $\hat{n}_{T}$, the transverse region is separated into an upper side
   $\cal{C}_U$, consisting of all jets with $\vec{p}_{T}\cdot\hat{n}_{T}$ $>$ 0,
   and a lower side $\cal{C}_L$, with $\vec{p}_{T}\cdot\hat{n}_{T}$ $<$ 0. The jet
   broadening and third-jet resolution variables require at least three jets,
   whereas the calculation of other variables requires at least two jets. The
   $\hat{n}_{T}$ vector is defined only up to a global sign - choosing one sign or
   the other has no consequence since it simply exchanges the upper and lower
   events regions.

   Transverse Thrust : The event thrust observable in the transverse plane is
   defined as \begin{eqnarray} \tau_{\perp} & \equiv & 1 - \max_{\hat{n}_{T}}
   \frac{\sum_i |\vec{p}_{T,i} \cdot \hat{n}_{T} |}{\sum_i p_{T,i}}
   \end{eqnarray} This variable probes the hadronization process and is sensitive
   to the modeling of two-jet and multijet topologies. In this paper ``multijet''
   refers to ``more-than-two-jet''. In the limit of a perfectly balanced two-jet
   event, $\tau_{\perp}$ is zero, while in isotropic multijet events it amounts
   to $(1-2/\pi)$.

   Jet Broadenings : The pseudorapidities and the azimuthal angles of the axes for
   the upper and lower event regions are defined by \begin{eqnarray} \eta_X &
   \equiv & \frac{\sum_{i\in{\cal{C}}_X} p_{T,i}\eta_i}{\sum_{i\in{\cal{C}}_X}
   p_{T,i}} ~, \\ \phi_X & \equiv & \frac{\sum_{i\in{\cal{C}}_X}
   p_{T,i}\phi_i}{\sum_{i\in{\cal{C}}_X} p_{T,i}} ~, \end{eqnarray} where $X$
   refers to upper ($U$) or lower ($L$) side. From these, the jet broadening
   variable in each region is defined as \begin{eqnarray} B_{X} & \equiv &
   \frac{1}{2P_{T}} \sum_{i\in{\cal{C}}_X}p_{T,i}\sqrt{(\eta_i -\eta_X)^2 +
   (\phi_i - \phi_X)^2} ~, \end{eqnarray} where $P_{T}$ is the scalar sum of
   the transverse momenta of all the jets. The total jet broadening is then
   defined as \begin{eqnarray} B_{tot} & \equiv & B_{U} + B_{L}.
   \end{eqnarray} Jet Masses : The normalized squared invariant mass of the
   jets in the upper and lower regions of the event is defined by
   \begin{eqnarray} \rho_X & \equiv & \frac{M^2_X}{P^2}, \end{eqnarray} where
   $M_X$ is the invariant mass of the constituents of the jets in the region
   $X$, and $P$ is the scalar sum of the momenta of all constituents in both
   sides.  The jet mass variable is defined as the sum of the masses in the
   upper and lower regions, \begin{eqnarray} \rho_{tot} & \equiv & \rho_U +
   \rho_L ~.  \end{eqnarray} The corresponding jet mass in the transverse
   plane, $\rho^T_{tot}$, is also similarly calculated in transverse plane.

   Third-jet resolution parameter : The third-jet resolution parameter is defined
   as \begin{eqnarray} Y_{23} \equiv
   \frac{\mathrm{min}(p_{T,3}^2,[\mathrm{min}(p_{T,i}, p_{T,j})^2 \times (\Delta
   R_{ij})^2/R^2])}{P_{12}^2} ~, \end{eqnarray} where i, j run over all three
   jets, $(\Delta R_{ij})^2 = (\eta_i - \eta_j)^2 + (\phi_i - \phi_j)^2$, and
   $p_{T,3}$ is the transverse momentum of the third jet in the event. If there
   are more than three jets in the event, they are iteratively merged using the
   $k_T$ algorithm with a distance parameter $R = 0.6$. To compute $P_{12}$,
   three jets are merged into two using the procedure described above and
   $P_{12}$ is then defined as the scalar sum of the transverse momenta of the
   two remaining jets.  The $Y_{23}$ variable estimates the relative strength of
   the $p_T$ of the third jet with respect to the other two jets. It vanishes for
   two-jet events, and a nonzero value of $Y_{23}$ indicates the presence of hard
   parton emission, which tests the parton showering model of QCD event
   generators. A test like this is less sensitive to the details of the
   underlying event (UE) and parton hadronization models than the other
   event-shape variables.'

BibKey: 'Khachatryan:2014ika'
BibTeX: '@article{Khachatryan:2014ika,
      author         = "Khachatryan, Vardan and others",
      title          = "{Study of hadronic event-shape variables in multijet
                        final states in $pp$ collisions at $\sqrt{s} = 7$~TeV}",
      collaboration  = "CMS Collaboration",
      journal        = "JHEP",
      volume         = "1410",
      pages          = "87",
      doi            = "10.1007/JHEP10(2014)087",
      year           = "2014",
      eprint         = "1407.2856",
      archivePrefix  = "arXiv",
      primaryClass   = "hep-ex",
      reportNumber   = "CMS-SMP-12-022, CERN-PH-EP-2014-146",
      SLACcitation   = "%%CITATION = ARXIV:1407.2856;%%",
}'

ReleaseTests:
 - $A LHC-7-Jets-4
 - $A-2 LHC-7-Jets-5
 - $A-3 LHC-7-Jets-6
 - $A-4 LHC-7-Jets-7

