%about the article that should go on the front page should be
%placed here. General acknowledgments should be placed at the end of the article.
\thankstext{e1}{e-mail: raghav.k.e@cern.ch}
\thankstext{e2}{e-mail: korinna.zapp@cern.ch}
%\authorrunning{Short form of author list} % if too long for running head
\institute{Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA \label{addr1}
\and CENTRA, Instituto Superior T\'ecnico, Universidade de Lisboa, Av. Rovisco Pais, P-1049-001 Lisboa, Portugal \label{addr2}
\and Physics Department, Theory Unit, CERN, CH-1211 Gen\`eve 23, Switzerland \label{addr3}
}
\date{Received: date / Accepted: date}
% The correct dates will be entered by the editor
\maketitle
\begin{abstract}
- Hard scattered partons in JEWEL undergoes collisions with thermal partons from the medium, leading to both elastic and radiative energy loss. The recoiling medium scattering centers carry away energy and momentum from the jet. Since the thermal component of the recoils is part of the soft background activity, comparison with data on jet observables requires the implementation of a background subtraction procedure. We present two independent procedures through which background subtraction can be performed and discuss the impact of the medium recoil on jet shape observables and jet-background correlations. Keeping track of the medium recoil significantly improves the JEWEL description of jet shape measurements.
+ Hard scattered partons in \textsc{Jewel} undergoes collisions with thermal partons from the medium, leading to both elastic and radiative energy loss. The recoiling medium scattering centers carry away energy and momentum from the jet. Since the thermal component of the recoils is part of the soft background activity, comparison with data on jet observables requires the implementation of a background subtraction procedure. We present two independent procedures through which background subtraction can be performed and discuss the impact of the medium recoil on jet shape observables and jet-background correlations. Keeping track of the medium recoil significantly improves the \textsc{Jewel} description of jet shape measurements.
- The two main operational modes of JEWEL~\cite{jewel2.0.2} when producing events from collisions of heavy ions, involve the treatment of the so called ``recoil" partons. The user has the capability of run the event generation, with or without storing the recoil information. When run without recoils, the scattering centers (including the partons originating from them) are removed before hadronization and no background subtraction is necessary to describe inclusive jet observables such as $R_{AA}, A_{J},$ azimuthal correlation of dijets, boson-jets etc... This leads to a slight mismatch when comparing with data, since experimentally the soft underlying background due to the quark gluon plasma and its interactions are subtracted from the jets.
+ The two main operational modes of \textsc{Jewel}~\cite{Zapp:2013vla} when producing events from collisions of heavy ions, involve the treatment of the so called ``recoil" partons. The user has the capability of run the event generation, with or without storing the recoil information. When run without recoils, the scattering centers (including the partons originating from them) are removed before hadronization and no background subtraction is necessary to describe inclusive jet observables such as $R_{AA}, A_{J},$ azimuthal correlation of dijets, boson-jets etc... This leads to a slight mismatch when comparing with data, since experimentally the soft underlying background due to the quark gluon plasma and its interactions are subtracted from the jets.
- Scattering centers in JEWEL contain the 4-momentum of the thermal parton the jet interacts with. The partons which originate from these scattering centers are called as the recoil partons. Post production, recoiled partons do not further interact in the medium and free-stream towards hadronization and hence the final state particle collection. This represents an upper limit for the recoil behavior since it is possible to let these partons interact further with the medium as done in the calculations presented before~\cite{hybrid-model, XianNianLBT}.
- %We find this limit to be qualitatively comparable to what a real parton would experience as it propagates through the QGP.
- In order to compare our predictions for jet shape (differential and in-jet) observables with data from the LHC and RHIC, it is imperative we perform a background subtraction when JEWEL with run with the recoils. Along with the recoiled partons, we are storing the information of the thermal background from the scattering centers which constitute the background. In the following sections, we explain the physics of recoils in JEWEL and present two independent background subtraction methods which can be employed at the analysis level. This is followed by a systematic treatment of these methods and their effects on jets and finally we present predictions and comparisons to experiments for a variety of jet shape observables.
+ Scattering centers in \textsc{Jewel} contain the 4-momentum of the thermal parton the jet interacts with. The partons which originate from these scattering centers are called as the recoil partons. Post production, recoiled partons do not further interact in the medium and free-stream towards hadronization (which in the case of \textsc{Jewel} is provided by a tune of \textsc{Pythia} 6.4~\cite{Sjostrand:2006za}) and hence the final state particle collection. This represents an upper limit for the recoil behavior since it is possible to let these partons interact further with the medium as done in the calculations presented before~\cite{Casalderrey-Solana:2015vaa,He:2015pra,Mehtar-Tani:2016xwr}.
+ In order to compare our predictions for jet shape (differential and in-jet) observables with data from the LHC~\cite{Chatrchyan:2013kwa,Cunqueiro:2015dmx,CMS:2016jys}, it is imperative we perform a background subtraction when \textsc{Jewel} with run with the recoils. Along with the recoiled partons, we are storing the information of the thermal background from the scattering centers which constitute the background. In the following sections, we explain the physics of recoils in \textsc{Jewel} and present two independent background subtraction methods which can be employed at the analysis level. This is followed by a systematic treatment of these methods and their effects on jets and finally we present predictions and comparisons to experiments for a variety of jet shape observables.
\section{Treatment of recoils and background subtraction}
- Scattering centers in JEWEL are drawn from a combination of the temperature and centrality of the event given by a glauber model. The energy density at a certain position $(x,y)$ in the overlap region is given by
+ Scattering centers in \textsc{Jewel} are drawn from a combination of the temperature and centrality of the event given by a glauber model. The energy density at a certain position $(x,y)$ in the overlap region is given by
$$
\epsilon(x, y, b, \tau_i) \propto T^{4} \frac{n_{\rm{part}}(x, y, b)}{\langle n_{\rm{part}}\rangle (b=0)},
$$
where $\tau_i$ is the initial proper time of the hydro evolution, $b$ is the impart parameter of the collision and $n_{\rm{part}}$ is the participant number density derived from a simple glauber model.
- Further details of the scattering centers/recoils are available here~\cite{cite}. In order to remove this thermal contribution of the recoils, we utilize the scattering center information as mentioned below.
+ Further details \textsc{Jewel} and of the scattering centers/recoils are available here~\cite{Zapp:2012ak, Zapp:2013zya, Zapp:2011ya}. In order to remove this thermal contribution of the recoils, we utilize the scattering center information as mentioned below.
\subsection{Background subtraction}
- The event record in JEWEL is modified to include the location of the scattering centers with a separate index so as to not affect the final state particles during clustering. A separate list of particles with very small energy and momenta with location of the scattering centers are added to the final state particles list. These ``dummy" particles are effectively the same as ghosts that fastjet uses during its clustering to determine the jet area. Armed with these lists of scattering centers (noting their position and momenta), dummy particles (that are now jet constituents), we perform two different background subtraction methods event by event;
+ The event record in \textsc{Jewel} is modified to include the location of the scattering centers with a separate index so as to not affect the final state particles during clustering. A separate list of particles with very small energy and momenta with location of the scattering centers are added to the final state particles list. These ``dummy" particles are effectively the same as ghosts that fastjet uses during its clustering to determine the jet area. Armed with these lists of scattering centers (noting their position and momenta), dummy particles (that are now jet constituents), we perform two different background subtraction methods event by event;
\begin{itemize}
\item 4MomSub: This is a ``real" subtraction method in that we are exactly removing, from the jet, the thermal components that originate from the medium induced interactions. Scattering centers are first matched in position (in the $\phi$ azimuthal angle, $\eta$ pseudorapidity plane) to the jet constituents. Those that match are deemed as background and are then vectorially subtracted from the rest of the jet's constituents. The resulting four vector constitutes is the background subtracted jet.
- \item GridSub: This method is more akin to what is performed in experiments. We utilize the same information regarding matching the constituent to the scattering centers from the previous method as the initial step. Then a finite resolution grid (in the $\phi-\eta$ plane) is superimposed on the jet and its constituents. The four vector of each cell in the grid is the difference of the jet's constituent and the scattering centers. Finally, we cluster with a four vector for each cell as the input to the jet clustering algorithm. Due to the finite size of the grid, it is possible to have certain cells with only background objects hence coming out with a negative overall fourmomenta which in our case is set to zero before clustering. This effect, along with others, will be quantified in the following sections.
+ \item GridSub: This method is more akin to what is performed in experiments. We utilize the same information regarding matching the constituent to the scattering centers from the previous method as the initial step. Then a finite resolution grid (in the $\phi-\eta$ plane) is superimposed on the jet and its constituents. The four vector of each cell in the grid is the difference of the jet's constituent and the scattering centers. Finally, we cluster with a four vector for each cell as the input to the jet clustering algorithm. Due to the finite size of the grid, it is possible to have certain cells with only background objects hence coming out with a negative overall four momenta which in our case is set to zero before clustering. This effect, along with others, will be quantified in the following sections.
\end{itemize}
The use of the 4MomSub method is recommended when possible since it is an accurate subtraction and is useful for full jet observables such as the jet $p_{T}$ and. As one looks at the jet-backgorund correlations such as jet shapes etc..., this becomes complicated and we employ the GridSub method. This preference is due to ability to access background subtracted constituents of a jet as opposed a single four momenta for the subtracted jet.
\subsection{Systematic studies}
- \begin{figure}[h] % figure placement: here, top, bottom, or page
+ The background subtraction techniques (introduced in the previous section) and their effects on jets are studied henceforth in a systematic fashion. Since one of the running modes of \textsc{Jewel} involves removal of the recoils, any subtraction technique should produce reasonably small asymmetry in the jet $p_{T}$ when comparing w/o recoils and w/ recoils + background removal without any hadronization effects. This is shown in Fig:~\ref{fig:subAsym_partonLevel}, where we see the asymmetry for 4MomSub (solid lines) and the GridSub (dotted lines) with deviations at the few percent level. As expected, the 4MomSub is narrower compared to the GridSub due to additional jet smearing introduced by the discretization of the event into cells of a finite size. \begin{figure}[h] % figure placement: here, top, bottom, or page
\caption{Asymmetry in parton level jet $p_{T}$ with removal of the recoils by hand and background subtraction techniques without any hadronization effects. The GridSub is shown in dotted lines as opposed to the more narrower 4MomSub technique in solid lines.}
\label{fig:subAsym_partonLevel}
\end{figure}
-
+
\begin{figure*}[h] % figure placement: here, top, bottom, or page
- \caption{Smearing introduced by the grid on the particle level jet, quantized by the asymmetry in the jet $p_{T}$ on the left and the absolute shift in the $\eta-\phi$ plane, on the right, respectively shown as a function of the particle jet $p_{T}$. As expected, as the $p_{T}$ increases, effect of the grid becomes much smaller. Note: The log scales on the z axis span more than 4 orders of magnitude.}
- \label{fig:gridasymjetpT}
- \end{figure*}
-
- \begin{figure*}[h] % figure placement: here, top, bottom, or page
- \caption{Relative shifts in the grid jet $\eta$ (left) and $\phi$ (right) shown as a function of the respective particle jet $\eta$ and $\phi$. The shift is observed to be very small in the $p_{T}$ range studied with any of the large shifts being dominated by the low $p_{T}$ jets. Note: The log scales on the z axis span more than 4 orders of magnitude.}
+ \caption{Smearing introduced by the grid on the particle level jet, quantized by the asymmetry in the jet $p_{T}$ on the left and the absolute shift in the $\eta-\phi$ plane, on the right, respectively shown as a function of the particle jet $p_{T}$. As expected, as the $p_{T}$ increases, effect of the grid becomes much smaller. Bottom plots show the relative shifts in the grid jet $\eta$ (left) and $\phi$ (right) shown as a function of the respective particle jet $\eta$ and $\phi$. The shift is observed to be very small in the $p_{T}$ range studied with any of the large shifts being dominated by the low $p_{T}$ jets. Note: The log scales on the z axis span more than 4 orders of magnitude.}
\label{fig:gridjetsmearing}
\end{figure*}
\begin{figure}[h] % figure placement: here, top, bottom, or page
- \caption{Total negative energy per jet shown for different jet $p_{T}$ bins introduced by the GridSub technique for the central PbPb ($0-20\%$) JEWEL+PYTHIA events generated with recoils.}
+ \caption{Total negative energy per jet shown for different jet $p_{T}$ bins introduced by the GridSub technique for the central PbPb ($0-20\%$) \textsc{Jewel}+\textsc{Pythia} events generated with recoils.}
\label{fig:gridnegativeenergy}
\end{figure}
- \begin{figure*}[h] % figure placement: here, top, bottom, or page
+ \begin{figure}[h] % figure placement: here, top, bottom, or page
\caption{Shift in the jet energy scale in the jet $p_{T},\eta$, represented as the mean of the grid jet $p_{T},\eta$ over particle jet $p_{T},\eta$ as a function of the particle jet $p_{T},\eta$ (left, right) respectively.}
\label{fig:jes}
- \end{figure*}
+ \end{figure}
- The background subtraction techniques (introduced in the previous section) and their effects on jets are studied henceforth in a systematic fashion. Since one of the running modes of JEWEL involves removal of the recoils, any subtraction technique should produce reasonably small asymmetry in the jet $p_{T}$ when comparing w/o recoils and w/ recoils + background removal without any hadronization effects. This is shown in Fig:~\ref{fig:subAsym_partonLevel}, where we see the asymmetry for 4MomSub (solid lines) and the GridSub (dotted lines) with deviations at the few percent level. As expected, the 4MomSub is narrower compared to the GridSub due to additional jet smearing introduced by the discretization of the event into cells of a finite size.
-
-
- The primary effect of the grid, before any background subtraction is introduced, is to smear both the jet $p_{T}$ and the position of the jet in the $\eta-\phi$ plane. This effect is studied in JEWEL with events generated without any recoils to highlight the inherent behavior. Fig:~\ref{fig:gridasymjetpT} shows the asymmetry in the jet $p_{T}$ (on the left) and the $\Delta R$ (on the right, characterizing the displacement of the jet cone) between the particle jet and the grid jet as a function of the particle jet pT. The respective relative shifts in $\eta$ and $\phi$ are shown in Fig:~\ref{fig:gridjetsmearing} All our studies of the grid are shown for a nominal grid size of $0.05$ in $\eta-\phi$. As one would expect, increasing the jet $p_{T}$ reduces the smearing introduced by the grid.
+ The primary effect of the grid, before any background subtraction is introduced, is to smear both the jet $p_{T}$ and the position of the jet in the $\eta-\phi$ plane. This effect is studied in \textsc{Jewel} with events generated without any recoils to highlight the inherent behavior. Fig:~\ref{fig:gridasymjetpT} shows the asymmetry in the jet $p_{T}$ (on the left) and the $\Delta R$ (on the right, characterizing the displacement of the jet cone) between the particle jet and the grid jet as a function of the particle jet pT. The respective relative shifts in $\eta$ and $\phi$ are shown in Fig:~\ref{fig:gridjetsmearing} All our studies of the grid are shown for a nominal grid size of $0.05$ in $\eta-\phi$. As one would expect, increasing the jet $p_{T}$ reduces the smearing introduced by the grid.
As previously mentioned, the GridSub technique sets the cell's four momenta to zero if it only contains background objects so this is one of the contributions to the grid smearing effect. The sum of the negative energy per grid jet is shown in Fig:~\ref{fig:gridnegativeenergy} for different jet $p_{T}$ ranges in the dotted (low $p_{T}$) to dotdashed (high $p_{T}$) lines. The contribution of the negative energy, i.e the amount of background that remains un-subtracted from the jet, is small compared to the full jet $p_{T}$.
-
- All of these aforementioned effects, introduce a shift in the jet energy scale and resolution, for GridSub jets which for 4MomSub are not an issue due to the nature of the subtraction. These shifts are corrected in experiments by introducing detector level correction factors as a function of the jet $p_{T}$ and $\eta$. In our case, due to the imposition of the grid, we see these corrections are of the order $3\%$ or less and is flat as a function of both $p_{T}$ and $\eta$ as shown in Fig:~\ref{fig:jes}. In the following results for observables, GridSub jets are not corrected for this shift in their energy scale and it especially cancels when looking at ratios of PbPb with pp due to their flat nature.
+ All of these aforementioned effects, introduce a shift in the jet energy scale and resolution, for GridSub jets which for 4MomSub are not an issue due to the nature of the subtraction. These shifts are corrected in experiments~\cite{Chatrchyan:2011ds,Berta:2016ukt} by introducing detector level correction factors as a function of the jet $p_{T}$ and $\eta$. In our case, due to the imposition of the grid, we see these corrections are of the order $3\%$ or less and is flat as a function of both $p_{T}$ and $\eta$ as shown in Fig:~\ref{fig:jes}. In the following results for observables, GridSub jets are not corrected for this shift in their energy scale and it especially cancels when looking at ratios of PbPb with pp due to their flat nature.
\section{Predictions and comparisons with data}
- \begin{figure*}[h] % figure placement: here, top, bottom, or page
+ The comparisons of \textsc{Jewel} with data for several observables without any of the background subtraction techniques are available in past publications. Since the latest high luminosity heavy ion runs at the LHC, the focus heavy ion jet physics has shifted to detailed characterization of jet shapes and in-jet observables such as jet track correlations, radial moments and subjet splitting fractions etc... to mention a few. In this paper, we focus on the predictions from \textsc{Jewel} for these observables and the physics inference we conclude. We generate events in the standard setup~\cite{Zapp:2013vla} at $\sqrt{s_\text{NN}} = \unit[2.76]{TeV}$ and $\sqrt{s_\text{NN}} = \unit[5.02]{TeV}$ with the simple parametrisation of the background discussed in detail in~\cite{Zapp:2013zya}. The initial conditions for the background model are initial time $\tau_\text{i}=\unit[0.6]{fm}$ and temperature $T_\text{i}=\unit[485]{MeV}$ for $\sqrt{s_\text{NN}} = \unit[2.76]{TeV}$~\cite{Shen:2012vn} and $\tau_\text{i}=\unit[0.4]{fm}$ and $T_\text{i}=\unit[590]{MeV}$ for $\sqrt{s_\text{NN}} = \unit[5.02]{TeV}$~\cite{Shen:2014vra}. The proton PDF set is \textsc{Cteq6LL}~\cite{Pumplin:2002vw} and for the Pb+Pb sample the \textsc{Eps09}~\cite{Eskola:2009uj} nuclear PDF set is used in addition, both are provided by \textsc{Lhapdf}~\cite{Whalley:2005nh}. We use the \textsc{Rivet} analysis framework~\cite{Buckley:2010ar} for all our studies. Jets are reconstructed using the same jet algorithm as the experiments (anti-$k_{t}$~\cite{Cacciari:2008gp}) from the \textsc{FastJet} package~\cite{Cacciari:2011ma}.
+
+ \subsection{Inter-Jet observables/distributions with 4MomSub}
+
+ \begin{figure}[h] % figure placement: here, top, bottom, or page
\caption{Effect of background subtraction to the jet $p_{T}$ (left) and mass (right) with different methods (colored lines) and compared with un-subtracted pp (in black). The bottom panel on the left shows the ratio with pp, i.e. the nuclear modification factor $R_{AA}$.}
\label{fig:effect_bkgsub}
- \end{figure*}
+ \end{figure}
+
+ Fig:~\ref{effect_bkgsub} shows the individual jet spectra (top-left), the $R_{\rm{AA}}$ i.e. the ratio of yield in PbPb over binary collisions scaled pp (bottom-left) and predictions for the inclusive jet mass distributions for anti k$_{t}$ jets with distance parameter $R = 0.4$, with jet $p_{T} > 100$ GeV/c and in the mid rapidity region for several \textsc{Jewel}+\textsc{Pythia} curves. The legends for the all the following plots show pp in black solid lines, PbPb without recoils in dotted green lines, PbPb with recoils 4MomSub and Grid Sub in dashed blue and dotdashed red lines. Both 4MomSub and GridSub curves show similar jet $R_{\rm{AA}}$ and jet mass distributions. The inclusive jet mass in \textsc{Jewel}+\textsc{Pythia}, for central events ($0-10\%$) show a shift to the right towards larger masses with run with recoils and background subtraction whilst without recoils, as expected we predict a smaller jet mass for jets of the same kinematic range. The increase in the jet mass points to a more broader jet and towards a possible cancellation between the reduced mother parton's virtuality (due to multiple scatterings in the medium) and an enhancement of particle multiplicity in the jet cone.
+
\begin{figure}[h] % figure placement: here, top, bottom, or page
- \caption{Differential Jet shapes measurement from CMS (black points) compared with JEWEL+PYTHIA predictions (blue lines). The Data systematic uncertainties are shown in the yellow boxes around unity.}
+ \caption{Differential Jet shapes measurement from CMS (black points) compared with \textsc{Jewel}+\textsc{Pythia} predictions (blue lines). The Data systematic uncertainties are shown in the yellow boxes around unity.}
\label{fig:cmsJetShape}
\end{figure}
+ Fig:~\ref{fig:cmsJetShape} shows our \textsc{Jewel}+\textsc{Pythia} result compared with CMS data points for the differential jet shape $\rho^{\text{PbPb}}/\rho^{\text{pp}}$, ratio between pp and PbPb as a function of distance $r$ from the jet axis, in the $\eta-\phi$ plane. After performing 4MomSub, we are able to reproduce the general trend of the data points. \textsc{Jewel}+\textsc{Pythia} with the recoils also describe the enlargement of the jet shape at large radii mostly due to soft particles ($p_{T} < 3$ GeV/c).
- The comparisons of JEWEL with data for several observables without any of the background subtraction techniques are available in past publications. Fig:~\ref{effect_bkgsub} shows the individual jet spectra (top-left), the $R_{\rm{AA}}$ i.e. the ratio of yield in PbPb over binary collisions scaled pp (bottom-left) and predictions for the inclusive jet mass distributions for anti k$_{t}$ jets with distance parameter $R = 0.4$, with jet $p_{T} > 100$ GeV/c and in the mid rapidity region for several JEWEL+PYTHIA curves. The legends for the all the following plots show pp in black solid lines, PbPb without recoils in dotted green lines, PbPb with recoils 4MomSub and Grid Sub in dashed blue and dotdashed red lines. Both 4MomSub and GridSub curves show similar jet $R_{\rm{AA}}$ and jet mass distributions. The inclusive jet mass in JEWEL+PYTHIA, for central events ($0-10\%$) show a shift to the right towards larger masses with run with recoils and background subtraction whilst without recoils, as expected we predict a smaller jet mass for jets of the same kinematic range. The increase in the jet mass points to a more broader jet and towards a possible cancellation between the reduced mother parton's virtuality (due to multiple scatterings in the medium) and an enhancement of particle multiplicity in the jet cone.
+ \subsection{Intra-Jet observables with GridSub}
+ With our GridSub technique, \textsc{Jewel}+\textsc{Pythia} with recoils is now able to provide predictions and comparisons to new data and extract meaningful physics insights from these comparisons. The first radial moment of the jet (girth)~\cite{Giele:1997hd} is defined as
+ $$
+ g = \frac{\Sigma_{k\in j} p_{T, k} \Delta R_{k,j}}{p_{T,j}}
+ $$
+ where the numerator sums the distance (with the jet axis in $\phi-\eta$ plane) weighted $p_{T,k}$ of each constituent k of the jet. The distribution of g, normalized to the number of jets are shown on the left of Fig:~\ref{injetObser} with the ratio of PbPb to pp shown in the bottom panel for without recoils in dotted green curves and with recoils GridSub in the red dotdashed curve. We predict a shift to smaller values of g for high $p_{T}$ (greater than 100 GeV/c) anti-k$_{t}, \ R=0.4$ fully reconstructed jets for central PbPb collisions at 2.76 TeV at the LHC. This shift is a result of interplay between two complimentary phenomenon that effects jets propagating through the QGP such as narrowing of the jet core (consisting of high $p_{T}$ constituents) and enhancement of soft particles (low $p_{T}$) at the edges of the jet cone. The dominating effect is however not easy to pickout from this observable alone.
- \begin{figure*}[h] % figure placement: here, top, bottom, or page
+ \begin{figure}[h] % figure placement: here, top, bottom, or page
\caption{Predictions for the radial moment (left) and the subjet shared momentum fraction for anti k$_{t}$ jets in central PbPb events with different methods (colored lines) and compared with un-subtracted pp (in black).}
\label{fig:injetObser}
- \end{figure*}
-
+ \end{figure}
- \begin{figure*}[h] % figure placement: here, top, bottom, or page
+ \begin{figure}[h] % figure placement: here, top, bottom, or page
- \caption{Comparison of JEWEL+PYTHIA predictions for the ratio of the subjet shared momentum fraction distributions in central PbPb events to pp events for low and high $p_{T}$ ranges on the left and right respectively.}
+ \caption{Comparison of \textsc{Jewel}+\textsc{Pythia} predictions for the ratio of the subjet shared momentum fraction distributions in central PbPb events to pp events for low and high $p_{T}$ ranges on the left and right respectively.}
\label{fig:cmsSplitting}
- \end{figure*}
-
-
- Fig:~\ref{fig:cmsJetShape} shows our JEWEL+PYTHIA result compared with CMS data points for the differential jet shape $\rho^{\text{PbPb}}/\rho^{\text{pp}}$, ratio between pp and PbPb as a function of distance $r$ from the jet axis, in the $\eta-\phi$ plane. After performing 4MomSub, we are able to reproduce the general trend of the data points. JEWEL+PYTHIA with the recoils also describe the enlargement of the jet shape at large radii mostly due to soft particles ($p_{T} < 3$ GeV/c).
-
- Since the latest high luminosity heavy ion runs at the LHC, the focus heavy ion jet physics has shifted to detailed characterization of jet shapes and in-jet observables such as jet track correlations, radial moments and subjet splitting fractions etc... to mention a few. With our GridSub technique, JEWEL+PYTHIA with recoils is now able to provide predictions and comparisons to new data and extract meaningful physics insights from these comparisons. The first radial moment of the jet (``girth") is defined as
- $$
- g = \frac{\Sigma_{k\in j} p_{T, k} \Delta R_{k,j}}{p_{T,j}}
- $$
- where the numerator sums the distance (with the jet axis in $\phi-\eta$ plane) weighted $p_{T,k}$ of each constituent k of the jet. The distribution of g, normalized to the number of jets are shown on the left of Fig:~\ref{injetObser} with the ratio of PbPb to pp shown in the bottom panel for without recoils in dotted green curves and with recoils GridSub in the red dotdashed curve. We predict a shift to smaller values of g for high $p_{T}$ (greater than 100 GeV/c) anti-k$_{t}, \ R=0.4$ fully reconstructed jets for central PbPb collisions at 2.76 TeV at the LHC. This shift is a result of interplay between two complimentary phenomenon that effects jets propagating through the QGP such as narrowing of the jet core (consisting of high $p_{T}$ constituents) and enhancement of soft particles (low $p_{T}$) at the edges of the jet cone. The dominating effect is however not easy to pickout from this observable alone.
-
- In the same kinematic range, we show the prediction for the subjet shared momentum fraction, first studied in $e^{+}e^{-}$ collisions to investigate the first splitting in the fragmentation of the parton which forms the jet. The soft drop tagger available in the fastjet contrib toolkit is used to extract the momentum fraction of the first hardest splitting (or subjet) above a certain cut off as follows
+ \end{figure}
+
+ In the same kinematic range, we show the prediction for the subjet shared momentum fraction, first studied in $e^{+}e^{-}$ collisions to investigate the first splitting in the fragmentation of the parton which forms the jet. The soft drop tagger~\cite{Larkoski:2015lea} available in the fastjet~\cite{} contrib toolkit is used to extract the momentum fraction of the first hardest splitting (or subjet) above a certain cut off as follows
- where $z_{cut}$ and $\beta$ are tunable parameters. The angular ordering is envisaged in the $\beta$ parameter, whereas moving $z_{cut}$ up or down, varies how far back in time (of the parton's fragmentation) we probe the splitting. For this study $z_{cut} = 0.1$ and $\beta = 0$ to probe the momentum ordering of the first hardest splitting. We see a very interesting effect, as shown in the right of Fig:~\ref{fig:injetObser}, that points to a increase in asymmetrical splittings in the jet cone for PbPb jets as opposed to pp jets which is also the same trend observed in recent preliminary CMS results with Run2 data at 5.02 TeV. The ratio between PbPb and pp for central collisions at two different $p_{T}$ ranges are shown in Fig:~\ref{fig:cmsSplitting} and the corresponding JEWEL+PYTHIA predictions for a nominal grid cell size of 0.05 and systematic bounds shown by varying the cell size by a factor of two. The general trend in data is well reproduced quite well as evident in the bottom panels which show the ratio of JEWEL with data. The secondary feature observed in this result is an apparent reduction of the asymmetric behavior for higher $p_{T}$ jets. JEWEL reproduces this behavior qualitatively as well with very high $p_{T}$ jets showing very little difference in the momentum fraction of the first splitting.
+ where $z_{cut}$ and $\beta$ are tunable parameters. The angular ordering is envisaged in the $\beta$ parameter, whereas moving $z_{cut}$ up or down, varies how far back in time (of the parton's fragmentation) we probe the splitting. For this study $z_{cut} = 0.1$ and $\beta = 0$ to probe the momentum ordering of the first hardest splitting. We see a very interesting effect, as shown in the right of Fig:~\ref{fig:injetObser}, that points to a increase in asymmetrical splittings in the jet cone for PbPb jets as opposed to pp jets which is also the same trend observed in recent preliminary CMS results with Run2 data at 5.02 TeV. The ratio between PbPb and pp for central collisions at two different $p_{T}$ ranges are shown in Fig:~\ref{fig:cmsSplitting} and the corresponding \textsc{Jewel}+\textsc{Pythia} predictions for a nominal grid cell size of 0.05 and systematic bounds shown by varying the cell size by a factor of two. The general trend in data is well reproduced quite well as evident in the bottom panels which show the ratio of \textsc{Jewel} with data. The secondary feature observed in this result is an apparent reduction of the asymmetric behavior for higher $p_{T}$ jets. \textsc{Jewel} reproduces this behavior qualitatively as well with very high $p_{T}$ jets showing very little difference in the momentum fraction of the first splitting.
% \begin{figure*}[h] % figure placement: here, top, bottom, or page
- We description the behavior of recoil partons in JEWEL and realize their importance in predicting differential and in-jet observables. Upon adding the recoils and performing background subtraction, similar to what is done in experiments, we are able to reproduce the general trend of several jet shape observables and qualitatively describe the physics of jet structure modification as it propagates through the QGP. A new class of jet observables probing deeper and further back in time in jet fragmentation are discussed. The same picture provides very good predictions for the subjet shared momentum fraction and the radial moment which match experimental data from experiments at the LHC.
+ We description the behavior of recoil partons in \textsc{Jewel} and realize their importance in predicting differential and in-jet observables. Upon adding the recoils and performing background subtraction, similar to what is done in experiments, we are able to reproduce the general trend of several jet shape observables and qualitatively describe the physics of jet structure modification as it propagates through the QGP. A new class of jet observables probing deeper and further back in time in jet fragmentation are discussed. The same picture provides very good predictions for the subjet shared momentum fraction and the radial moment which match experimental data from experiments at the LHC.
\begin{acknowledgements}
This work was supported by Funda\c{c}\~{a}o para a Ci\^{e}ncia e a Tecnologia (Portugal) under postdoctoral fellowship SFRH/BPD/102844/2014 (KCZ) and by the European Union as part of the FP7 Marie Curie Initial Training Network MCnetITN (PITN-GA-2012-315877) (RKE). RKE also acknowledges support from the National Science Foundation under Grant No.1067907 \& 1352081.
We also like to thank Dr. Chun Shen for providing the initial hydrodynamics parameters for our event generation at 5 TeV.