Full jet evolution in quark-gluon plasma and nuclear modification of jet production and jet shape in $\text{Pb}+\text{Pb}$ collisions at $2.76A\mathrm{TeV}$ at the CERN Large Hadron Collider

We study the evolution of the full jet shower in quark-gluon plasma by solving a set of coupled differential transport equations for the three-dimensional momentum distributions of quarks and gluons contained in full jets. In our jet evolution equations, we include all partonic splitting processes as well as the collisional energy loss and transverse momentum broadening for both the leading and radiated partons of the full jets. Combining with a realistic ($2+1$)-dimensional viscous hydrodynamic simulation for the spacetime profiles of the hot and dense nuclear medium produced in heavy-ion collisions, we apply our formalism to calculate the nuclear modification of single inclusive full jet spectra, the momentum imbalance of photon-jet and dijet pairs, and the jet shape function (at partonic level) in $\text{Pb}+\text{Pb}$ collisions at $2.76A$ TeV. The roles of various jet-medium interaction mechanisms on the full jet modification are studied. We find that the nuclear modification of jet shape is sensitive to the interplay of different interaction mechanisms as well as the energies of the full jets.

Figure 1

The geometry for a parton $i$ (inside a jet) radiating a parton $j$, where ${\theta }_i$ and ${\theta }_j$ are the angles of the parton $i$ and the parton $j$ with respect to the direction of jet axis ($z$ axis in the figure), and ${\theta }_{ij}$ is the relative angle of parton $j$ with respect to the propagation direction of parton $i$.

Figure 2

The jet shape function for $p+p$ collisions at 2.76 TeV with $p_T>100$ GeV, compared with CMS data [23].

Figure 3

The nuclear modification factor $R_{AA}$ for single inclusive full jet production in (a) most-central 0%–10% and (b) mid-central 30%–40% $\text{Pb}+\text{Pb}$ collisions at $2.76A$ TeV, compared to the full jet $R_{CP}$ measured by the ATLAS and ALICE collaborations [68, 69].

Figure 4

The event distribution of dijet momentum imbalance $A_J$ for (a) most-central 0%–10% and (b) mid-central 30%–40% $\text{Pb}+\text{Pb}$ collisions at $2.76A\mathrm{TeV}$, compared with data from the CMS Collaboration [70].

Figure 5

The event distribution of photon-jet momentum imbalance variable $x_{J\gamma }$ in (a) most-central 0%–10% and (b) mid-central 30%–40% $\text{Pb}+\text{Pb}$ collisions at $2.76A\mathrm{TeV}$, compared with data from the CMS Collaboration [20].

Figure 6

The nuclear modification factor $R_{AA}^{\rho }\left(r\right)={\rho }_{AA}\left(r\right)/{\rho }_{pp}\left(r\right)$ for the differential jet shape function in (a) most-central 0%–10% and (b) mid-central 30%–40% $\text{Pb}+\text{Pb}$ collisions at $2.76A\mathrm{TeV}$. The experimental data are taken from the CMS Collaboration [23].

Figure 7

The nuclear modification factor $R_{AA}^{\rho }\left(r\right)={\rho }_{AA}\left(r\right)/{\rho }_{pp}\left(r\right)$ for the differential jet shape function of quark, gluon, and inclusive jets in most-central 0%–10% $\text{Pb}+\text{Pb}$ collisions at $2.76A\mathrm{TeV}$: the upper panel (a) is for $p_T>100\mathrm{GeV}$ and the lower panel (b) is for $p_T>50\mathrm{GeV}$.

Figure 8

The relative contributions from different jet-medium interaction mechanisms to the total full quark (a) and gluon (b) jet energy loss. The jets are produced at the center of the medium created in most-central 0%–10% $\text{Pb}+\text{Pb}$ collisions and propagate along the $\varphi =0$ direction.

Figure 9

The relative contributions from different jet-medium interaction mechanisms to the nuclear modification of the differential jet shape function. The jets are produced at the center of the medium created in the most-central 0%–10% $\text{Pb}+\text{Pb}$ collisions and propagate along $\varphi =0$ direction. The upper panel (a) is for inclusive jets with $p_T>100$ GeV, and the lower panel (b) is for $p_T>50$ GeV.

Figure 10

The sensitivity of the nuclear modification of the differential jet shape function to the jet transport coefficient. The jets are produced at the center of the medium created in the most-central 0%–10% $\text{Pb}+\text{Pb}$ collisions and propagate along the $\varphi =0$ direction. The results for different jet-medium interaction mechanisms and their combination are compared.