Interplaying mechanisms behind single inclusive jet suppression in heavy-ion collisions

The suppression factor for single inclusive jets in $\text{Pb}+\text{Pb}$ collisions at the Large Hadron Collider (LHC) has a weak dependence on the transverse momentum $p_T$ and remains almost the same at two colliding energies, $\sqrt{s}=2.76$ and 5.02 TeV, though the central rapidity density of bulk hadrons increases by about 20%. This phenomenon is investigated within the linear Boltzmann transport (LBT) model, which includes elastic and inelastic processes based on perturbative QCD for both jet shower and recoil medium partons as they propagate through a quark-gluon plasma (QGP). With the dynamic evolution of the QGP given by the $3+1\mathrm{D}$ CLVisc hydrodynamic model with event-by-event fully fluctuating initial conditions, single inclusive jet suppression in $\text{Pb}+\text{Pb}$ collisions from LBT agrees well with experimental data. The weak $\sqrt{s}$ and $p_T$ dependence of the jet suppression factor at LHC are found to result directly from the $\sqrt{s}$ dependence of the initial jet $p_T$ spectra and slow $p_T$ dependence of the jet energy loss. Contributions from jet-induced medium response, influence of radial expansion, both of which depend on jet-cone size, and jet flavor composition all conjoin to give a slow $p_T$ dependence of jet energy loss and the single jet suppression factor $R_{\mathrm{AA}}$, their dependence on $\sqrt{s}$, and jet-cone size. Single inclusive jet suppression at $\sqrt{s}=200\mathrm{GeV}$ is also predicted that actually decreases slightly with $p_T$ in the $p_T<50\mathrm{GeV}/c$ range because of the steeper initial jet spectra though the $p_T$ dependence of the jet energy loss is weaker than that at LHC.

Figure 1

The single inclusive jet double differential cross section as a function of $p_T$ in different rapidity bins in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ using anti-$k_t$ algorithm with jet-cone radius $R=0.4$. The closed symbols are ATLAS experimental data [42] while the curves are from pythia8 simulations. The results for different rapidities are scaled by successive powers of ${10}^2$ for clear presentation.

Figure 2

The inclusive jet double differential cross section as a function of $p_T$ in different rapidity bins in $p+p$ collisons at $\sqrt{s}=5.02\mathrm{TeV}$ (solid) using anti-$k_t$ algorithm with jet-cone radius $R=0.4$ from pythia8 as compared to ATLAS experimental data [43]. pythia8 results at $\sqrt{s}=2.76$ (dashed) are also shown as a comparison. Results for different rapidities are scaled by successive powers of ${10}^2$.

Figure 3

The suppression factor $R_{\mathrm{AA}}$ of single inclusive jet spectra in the central rapidity $\left|y\right|<2.1$ region of 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ from LBT simulations with different values of ${\alpha }_{\mathrm{s}}$ as compared to the ATLAS data at the LHC [42]. UES and “negative” partons are both included in the jet reconstruction with $R=0.4$ and anti-$k_t$ jet-finding algorithm.

Figure 4

${\chi }^2$/d.o.f. of LBT fits to ATLAS data [42] on $R_{\mathrm{AA}}\left(p_T\right)$ as a function of ${\alpha }_s$ in 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ with anti-$k_t$ algorithm and jet-cone size $R=0.4$ in jet rapidity range $\left|y\right|<2.1$, (black line with circle) with “negative” partons and UES, (red line with square) with negative partons but without UES, (blue line with uptriangle) with UES but without negative partons, and (purple line with down triangle) without “negative” partons and UES.

Figure 5

The suppression factor $R_{\mathrm{AA}}$ of single inclusive jet spectra in the central rapidity $\left|y\right|<2.1$ region of 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ from LBT simulations with fixed ${\alpha }_{\mathrm{s}}=0.15$ as compared to the ATLAS data at the LHC [42]. The jet reconstruction with $R=0.4$ and anti-$k_t$ algorithm includes four different options on negative partons and UES: (a) with both negative partons and UES, (b) with negative partons but without UES, (c) with UES but without “negative” partons, and (d) without negative partons and UES.

Figure 6

LBT results on $R_{\mathrm{AA}}\left(p_T\right)$ in the central rapidity $\left|y\right|<2.1$ region of $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ for different centralities as compared to ATLAS data [42].

Figure 7

LBT results on $R_{\mathrm{AA}}$ in $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ as a function of the number of nucleon participants $\langle N_{\mathrm{part}}\rangle$ in each centrality bin in two $p_T$ ranges, $p_T=80–100$ (solid), $180–200\mathrm{GeV}/c$ (dashed), as compared to experimental data from ATLAS [42].

Figure 8

LBT results on $R_{\mathrm{AA}}\left(p_T\right)$ in four different jet rapidities of (red solid) 0–10% and (blue dashed) 30–40% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.67\mathrm{TeV}$ as compared to ATLAS data [42].

Figure 9

Experimental data on $R_{\mathrm{AA}}\left(p_T\right)$ from ATLAS [42] (red circle) and CMS [44] (blue square) for 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ are compared to LBT calculations.

Figure 10

LBT results on $R_{\mathrm{AA}}\left(p_T\right)$ in central rapidity $\left|y\right|<2.1$ for single inclusive jet spectra in 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76$ (red dashed line) and 5.02 TeV (blue solid line) as compared to ATLAS data [42, 43].

Figure 11

Average jet transverse energy loss as a function of vacuum jet $p_T$ with anti-$k_t$ and $R=0.4$ in $\left|y\right|<2.1$ of central 0–10% $\text{Pb}+\text{Pb}$ collisions at (solid) $\sqrt{s}=5.02\mathrm{GeV}$ and (dash) 2.76 TeV. Black lines with circles are the LBT results without recoil and negative partons, while red lines with squares are with recoil and negative partons and blue lines with diamonds are with recoil but without negative partons.

Figure 12

LBT results on jet energy loss distribution $W_{\mathrm{AA}}\left(x\right)$ as a function of the scaled jet energy loss $x=\mathrm{\Delta }{p}_T/\langle \mathrm{\Delta }{p}_T\rangle$ in $\text{Pb}+\text{Pb}$ collisions (a) for three different vacuum jet energies, (b) three different centralities, and (c) two different colliding energies at LHC.

Figure 13

Experimental data on $R_{\mathrm{AA}}$ for 0–10% central $\text{Pb}+\text{Pb}$ collisions at (red solid squares) $\sqrt{s}=2.76\mathrm{TeV}$ and (blue solid circles) 5.02 TeV [42, 43] as compared to (solid lines) LBT calculations and (dashed) the suppression factor obtained by shifting the jet spectra in $p+p$ collisions by the average jet energy loss from Fig. 11 according to Eq. (21).

Figure 14

LBT results on average $p_T$ loss $\langle \mathrm{\Delta }{p}_T\rangle$ for jets in $\left|y\right|<2.1$ as a function of the vacuum jet $p_T$ with anti-$k_t$ algorithm and $R=0.3,0.4,0.5$ for (a), (c), (e) hydrodynamic background in central 0–10% $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ and (b), (d), (f) static medium at $T=0.28\mathrm{GeV}$ with fixed length $L=4$ fm. Black lines with circles are results without recoil and negative partons, while red lines with squares are with recoil and negative partons and blue lines with diamonds are with recoil but without negative partons.

Figure 15

The same as Fig. 14 except for $\sqrt{s}=5.02\mathrm{TeV}$.

Figure 16

The same as Fig. 14 but for (solid lines) gluon and (dashed lines) quark jets.

Figure 17

The same as Fig. 14 except for gluon (solid lines) and quark jets (dashed lines) at $\sqrt{s}=5.02\mathrm{TeV}$.

Figure 18

LBT results on ratios of energy loss of gluon jets over quark jets in $\left|y\right|<2.1$ as a function of the vacuum jet $p_T$ with anti-$k_t$ algorithm and $R=0.3,0.4,0.5$ for (a), (c), (e) hydrodynamic background in central 0–10% $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ and (b), (d), (f) static medium at $T=0.28\mathrm{GeV}$ with fixed length $L=4$ fm. Black lines with circles are results without recoil and negative partons, while red lines with squares are with recoil and negative partons and blue lines with diamonds are with recoil but without negative partons.

Figure 19

The same as Fig. 18 except for $\sqrt{s}=5.02\mathrm{TeV}$.

Figure 20

Transverse momentum dependence of the fraction of (solid lines) gluon jet and (dashed lines) quark jet within $\left|y\right|<2.1$ in $p+p$ collisions at (red squares) $\sqrt{s}=2.76$ and (blue circles) 5.02 TeV from pythia8 simulations with anti-$k_t$ and $R=0.3,0.4,0.5$.

Figure 21

Transverse momentum dependence of the fraction of gluon jet (red solid lines) and quark jet (blue dashed lines) for different jet rapidity $y$ in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ from pythia8 simulations with anti-$k_t$ and $R=0.4$.

Figure 22

Rapidity dependence of the initial gluon jet fraction ${\gamma }_g$ (blue solid line) and jet suppression factor $R_{AA}$ for $80<p_T<100$ (red dashed line) in 0–10% central $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ from LBT simulations with anti-$k_t$ and $R=0.4$. Solid squares are ATLAS data [42] on $R_{AA}$. Note that two different observables, gluon fraction ${\gamma }_g$ and single jet suppression factor $R_{AA}$, are plotted in this figure.

Figure 23

Ratios of single inclusive jet spectra with different jet-cone size, $\sigma (R=0.2)/\sigma (R=0.4)$ (lines with squares) and $\sigma (R=0.3)/\sigma (R=0.4)$ (lines with circles), as a function of $p_T$ in (solid) 0–10% central $\text{Pb}+\text{Pb}$ and (dashed) $p+p$ collisions at $\sqrt{s}=5.02\mathrm{TeV}$ from LBT and pythia8 simulations, respectively.

Figure 24

Suppression factor of single inclusive jet spectra $R_{\mathrm{AA}}$ as a function of $p_T$ in central rapidity region of 0–10% $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=5.02\mathrm{TeV}$ from LBT with (solid) and without medium recoil (including negative partons) (dashed) for different jet-cone sizes, $R=0.5$, 0.4, 0.3, and 0.2 as compared to CMS data [44] in 0–5% $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$.

Figure 25

pythia8 result of the inclusive jet differential cross section as a function of $p_T$ in the central rapidity of $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ with anti-$k_t$ algorithm and jet-cone radius $R=0.4$ as compared to STAR data [86].

Figure 26

Transverse momentum dependence of the number fraction of (solid) gluon and (dashed) quark jets in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ from pythia8 with anti-$k_t$ and jet-cone sizes $R=0.3,0.4,$ and 0.5.

Figure 27

LBT results on the average jet transverse energy loss of (solid) gluon and (dashed) quark jets within $\left|y\right|<2.1$ with anti-$k_t$ algorithm and jet-cone sizes $R=0.3,0.4,0.5$ as a function of the vacuum jet $p_T$ in $0–10\%$ central $\text{Au}+\text{Au}$ collisions at $\sqrt{s}=200\mathrm{GeV}$. Black lines with circles are without recoil and negative partons, while red lines with squares are with recoil and negative partons and blue lines with diamonds are with recoil but without negative partons.

Figure 28

The same as Fig. 27 except for flavor-averaged jet transverse energy loss.

Figure 29

LBT predictions for $R_{\mathrm{AA}}$ of single inclusive jet spectra in $\text{Au}+\text{Au}$ collisions at $\sqrt{s}=200\mathrm{GeV}$ with three different centralities.