In-medium jet shape from energy collimation in parton showers: Comparison with CMS PbPb data at 2.76 TeV

We present the medium-modified energy collimation in the leading-logarithmic approximation (LLA) and next-to-leading-logarithmic approximation (NLLA) of QCD. As a consequence of more accurate kinematic considerations in the argument of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) fragmentation functions (FFs) we find a new NLLA correction $\mathcal{O}({\alpha }_s)$ which accounts for the scaling violation of DGLAP FFs at small $x$. The jet shape is derived from the energy collimation within the same approximations and we also compare our calculations for the energy collimation with the event generators pythia6 and YaJEM for the first time in this paper. The modification of jets by the medium in both cases is implemented by altering the infrared sector using the Borghini-Wiedemann model. The energy collimation and jet shapes qualitatively describe a clear broadening of showers in the medium, which is further supported by YaJEM in the final comparison of the jet shape with CMS PbPb data at center-of-mass energy 2.76 TeV. The comparison of the biased versus unbiased YaJEM jet shape with the CMS data shows a more accurate agreement for biased showers and illustrates the importance of an accurate simulation of the experimental jet-finding strategy.

Figure 1

Fragmentation of a jet $A$ of half opening angle ${\mathrm{\Theta }}_0$ into a sub-jet $B$ of half opening angle $\mathrm{\Theta }<{\mathrm{\Theta }}_0$.

Figure 2

Jet (${\mathrm{\Theta }}_0=R$) and sub-jet ($\mathrm{\Theta }=r$) cones sharing the bulk of the jet energy.

Figure 3

Energy collimation inside a gluon jet for $x=0.5$ (left) and $x=0.8$ (right) with $R=1.0$.

Figure 4

Collimation of energy inside a gluon jet for $x=0.5$ (left) and $x=0.8$ (right) with $R=0.3$.

Figure 5

Medium-modified and vacuum energy collimation ratios $r_{g,\text{med}}/r_{g,\text{vac}}$ for $x=0.5$ (left), $x=0.8$ (center) and $x=0.9$ (right) with $R=0.3$.

Figure 6

Collimation of energy inside a gluon jet for $x=0.5$ (left) and $x=0.8$ (right) with $R=1.0$.

Figure 7

Collimation of energy inside a quark jet for $x=0.4$ (left) and $x=0.8$ (right) with $R=0.3$.

Figure 8

Collimation of energy inside a gluon jet for $x=0.5$ (left) and $x=0.8$ (right) with $R=0.1$.

Figure 9

Medium-modified and vacuum energy collimation ratios $r_{\text{q, med}}/r_{\text{q, vac}}$ for $x=0.5$ (left), $x=0.8$ (center) and $x=0.9$ (right) with $R=0.3$.

Figure 10

Collimation of energy inside a gluon jet (left) and quark jet (right) for $x=0.8$ with $R=0.3$ in the vacuum ($N_s=1$).

Figure 11

Parton versus hadron energy collimation for $x=0.5$ and $x=0.8$ inside a gluon jet (left) and a quark jet (right) with $R=0.3$.

Figure 12

Jet shape for CMS $pp$ and PbPb data with $R=0.3$, compared with pythia6, YaJEM+BW, the LLA formula (left panel) and the NLLA formula (right panel).

Figure 13

Biased versus unbiased jet shape for CMS $pp$ data (left panel) and PbPb data (right panel) with $R=0.3$.

Figure 14

Parton versus hadron jet shape inside a gluon jet (left) and a quark jet (right) with $R=0.3$.