arXiv subjects

Ben-Wei Zhang

Publications and source records attributed to Ben-Wei Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

The Fox-Wolfram Moment of Jet Production in Relativistic Heavy Ion Collisions

We present the first theoretical investigation of Fox-Wolfram moments (FWMs) for multi-jet production in relativistic heavy ion collisions. In this work, jet productions in p+p collisions are computed with a Monte Carlo event generator SHERPA, while the Linear Boltzmann Transport model is utilized to simulate the multiple scattering of energetic partons in the hot and dense QCD matter. The event-normalized distributions of the lower-order FWM, $H_1^T$ in p+p and Pb+Pb collisions are calculated. It is found that for events with jet number $n_\text{jet} = 2$ the $H_1^T$ distribution in Pb+Pb is suppressed at small $H_1^T$ while enhanced at large $H_1^T$ region as compared to p+p. For events with $n_\text{jet}>2$, the jet number reduction effect due to jet quenching in the QGP decreases the $H_1^T$ distribution at large $H_1^T$ in Pb+Pb relative to p+p. The medium modification of the Fox-Wolfram moment $H_1^T$ for events with $n_\text{jet}\ge 2$ are also presented, which resemble those of events with $n_\text{jet} = 2$. Its reason is revealed through the relative contribution fractions of events with different final-state jet numbers to $H_1^T$.

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arXiv2025

Phenomenological study of the angle between jet axes in heavy-ion collisions

This paper presents a phenomenological study on the angle between the Standard and the Winner-Take-All (WTA) jet axes ($ΔR_{\rm axis}^{\rm WTA-Std}$) in high-energy nuclear collisions. The $p$+$p$ baseline is provided by the Pythia8 event generator. The in-medium jet propagation is simulated by the linear Boltzmann transport (LBT) model, which considers both the elastic and inelastic jet-medium interactions. Our theoretical results calculated by the LBT model show that the $ΔR_{\rm axis}^{\rm WTA-Std}$ distribution in Pb+Pb at $\sqrt{s}=5.02$ TeV is narrower than that in $p$+$p$, which agrees well with the recent ALICE measurements. The narrowing of $ΔR_{\rm axis}^{\rm WTA-Std}$ seems to violate the $p_T$-broadening nature of the jet quenching effect, usually explained by the influence of "selection bias". However, the physical details still need to be fully understood. Utilizing a matching-jet method to track the jet evolution in the QGP to remove the selection bias in the Monte Carlo simulations, we observe that the $ΔR_{\rm axis}^{\rm WTA-Std}$ distribution becomes broader due to the jet-medium interactions. At the same time, by rescaling the quark/gluon-jet fractions in Pb+Pb collisions to be the same as that in $p$+$p$, we find that the fraction change may not significantly influence the modification pattern of jet $ΔR_{\rm axis}^{\rm WTA-Std}$. On the other hand, the selected jet sample in A+A collisions has a significantly narrower initial $ΔR_{\rm axis}^{\rm WTA-Std}$ distribution than the $p$+$p$ baseline, and such a biased comparison between $p$+$p$ and A+A conceals the actual jet-broadening effect in the experimental measurements. The investigations presented in this paper will deepen our understanding of the relationship between the actual intra-jet modifications in the QGP and the experimental observations.

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arXiv2025

Production of leptons from decay of heavy-flavor hadrons in high-energy nuclear collisions

This paper presents a theoretical study on the production of the heavy-flavour decay lepton (HFL) in high-energy nuclear collisions at the LHC. The pp-baseline is calculated by the FONLL program, which matches the next-to-leading order pQCD calculation with the next-to-leading-log large-$p_T$ resummation. The in-medium propagation of heavy quarks is driven by the modified Langevin equations, which consider both the elastic and inelastic partonic interactions. We propose a method to separate the respective influence of the six factors, such as pp-spectra, the cold nuclear matter (CNM) effects, in-medium energy loss (E-loss), fragmentation functions (FFs), coalescence (Coal), and decay channels, which may contribute to the larger $R_{AA}$ of HFL $\leftarrow b$ compared to that of HFL $\leftarrow c$ in nucleus-nucleus collisions. Based on quantitative analysis, we demonstrate that both coalescence hadronization, decay channels and the mass-dependent E-loss play an essential role at $p_T<5$ GeV, while the latter dominates the higher $p_T$ region. It is also found that the influences of the CNM effects and FFs are insignificant. At the same time, different initial pp-spectra of charm and bottom quarks have a considerable impact at $p_T>5$ GeV. Furthermore, we explore the path-length dependence of jet quenching by comparing the HFL $R_{AA}$ in two different collision systems. Our investigations show smaller HFL $R_{AA}$ in Pb+Pb than in Xe+Xe within the same centrality bin, consistent with the ALICE data. The longer propagation time and more effective energy loss of heavy quarks in Pb+Pb collisions play critical roles in the stronger yield suppression of the HFL compared to that in Xe+Xe. In addition, we observe a scaling behavior of the HFL $R_{AA}$ in Xe+Xe and Pb+Pb collisions.

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arXiv2025

Probing the mass effect of heavy quark jets in high-energy nuclear collisions

The production of heavy quark (HQ) jets provides a new arena to address the mass effect of jet quenching in heavy-ion physics. This paper presents a theoretical study of HQ jet yield suppression in Pb+Pb collisions at the LHC and focuses on the energy loss of HQ jets produced by different mechanisms. The p+p baseline is carried out by the SHERPA generator, and the jet-medium interactions are described by the SHELL transport model, which considers the elastic and inelastic partonic energy loss in the quark-gluon plasma (QGP). In p+p collisions, our numerical results indicate that the HQ jets from gluon splitting ($g \rightarrow Q$-jet) give the dominant contribution at high $p_T$, and it shows more dispersive structures than the HQ-initiated one ($Q \rightarrow Q$-jet). In nucleus-nucleus collisions, our calculations are consistent with the inclusive and b-jet $R_{AA}$ recently measured by the ATLAS collaboration, which suggests a remarkable manifestation of the mass effect of jet energy loss. As a result of the dispersive substructure, the $g \rightarrow Q$-jet will lose more energy than the $Q \rightarrow Q$-jet in the QGP. Due to the significant contribution of $g \rightarrow c$-jet, the $R_{AA}$ of c-jet will be comparable or even smaller than that of inclusive jet. To experimentally distinguish the $g \rightarrow Q$-jet and $Q \rightarrow Q$-jet, we propose the event selection strategies based on their topological features and test the performances. By isolating the $c \rightarrow c$-jet and $b \rightarrow b$-jet, the jets initiated by heavy quarks, we predict that the order of their $R_{AA}$ are in line with the mass hierarchy of energy loss. Future measurements on the $R_{AA}$ of $Q \rightarrow Q$-jet and $g \rightarrow Q$-jet will provide a unique chance to test the flavor/mass dependence of energy loss at the jet level.

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arXiv2025

Exposing the dead-cone effect of jet quenching in QCD medium

When an energetic parton traverses the hot QCD medium it may suffer multiple scattering and lose its energy. The medium-induced gluon radiation for a massive quark will be suppressed relative to that of a light quark due to the dead-cone effect. The development of new declustering techniques of jet evolution makes a direct study of the dead-cone effect in the QCD medium possible for the first time. In this work, we compute the emission angle distribution of the charm-quark initiated splittings in $\rm D^0$ meson tagged jet and that of the light parton initiated splittings in an inclusive jet in p+p and Pb+Pb at $\rm 5.02$~TeV by utilizing the declustering techniques of jet evolution. The heavy quark propagation and indued energy loss in the QCD medium are simulated with the SHELL model based on the Langevin equation. By directly comparing the emission angle distributions of charm-quark-initiated splittings with those of light parton-initiated splittings at the same energy intervals of the initial parton, we provide insights into the fundamental splitting structure in A+A collisions, thereby exploring the possible observation of the dead-cone effect in medium-induced radiation. We further investigate the case of the emission angle distributions normalized to the number of splittings and find the dead-cone effect will broaden the emission angle of the splitting and reduce the possibility to occur such splitting, therefore leading the massive parton to lose less energy. We also find the collisional energy loss mechanism has a negligible impact on the medium modification to the emission angle distribution of the charm-quark initiated splittings for $\rm D^0$-meson tagged jets.

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arXiv2024

Medium modifications of heavy-flavor jet angularities in high-energy nuclear collisions

We present the first theoretical study of heavy-flavor jet angularities ($λ^κ_α$) in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=$ 5.02 TeV. The initial production of heavy-flavor jets is carried out using the POWHEG+PYTHIA8 prescription, while the jet evolution in the quark-gluon plasma (QGP) is described by the SHELL transport model. In p+p collisions, we observe narrower angularity distributions for D$^0$-tagged jets compared to inclusive jets, consistent with the ALICE preliminary results. We then demonstrate that jet quenching in the QGP slightly widens the angularity distribution of D$^0$-tagged jets in Pb+Pb collisions relative to that in p+p collisions for jet transverse momentum of $10 < p_{\rm T,jet} < 20$ GeV/c, while the angularity distributions of inclusive and D$^0$-tagged jets become narrower in Pb+Pb collisions relative to p+p at $p_{\rm T,jet} > 20$ GeV/c due to the strong influence of the selection bias. Additionally, by comparing the average angularities $\langle λ^κ_α \rangle$ of inclusive, D$^0$-tagged and B$^0$-tagged jets with varying $α$ and $κ$, we show that the larger the quark mass is, the lower the jet's $\langle λ^κ_α \rangle$ values are. As a result of the slenderer initial distribution, we predict that as compared to inclusive jets, the heavy-flavor jets, especially the B$^0$-tagged ones, will suffer stronger modifications of $\langle λ^κ_α \rangle$ in Pb+Pb relative to p+p at $10 < p_{\rm T,jet} < 20$ GeV/c. For a larger jet radius, a more significant broadening of jet angularities is predicted because of the enhanced contributions of the wide-angle particles.

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arXiv2024

$\mathcal{R}^2$ curvature-squared corrections on Langevin diffusion coefficients

The effect of finite coupling corrections to the Langevin diffusion coefficients on a moving heavy quark in the Super Yang-Mills plasma is investigated. These corrections are related to curvature squared corrections in the corresponding gravity sector. We compare the results of both longitudinal and perpendicular Langevin diffusion coefficients with those in $\mathcal{N}$=4 Super Yang-Mills plasma. It is observed that the curvature-squared corrections influence the Langevin diffusion coefficients, and the corrections for both Langevin diffusion coefficients demonstrate the dependence on the velocity of the moving heavy quark and the specifics of the higher derivative correction. In addition, we conduct calculations for the Langevin diffusion coefficients of a moving heavy quark within the Gauss-Bonnet background.

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arXiv2024

Unraveling the Energy-Energy Correlators for Heavy Flavor Tagged Jets in pp, p+Pb and Pb+Pb Collisions

In this study, energy-energy correlator (EEC) distributions for the $\rm D^0$, $\rm B^0$-tagged, inclusive, and the PYTHIA generated pure quark jets are computed in pp, p+Pb, and Pb+Pb collisions at \sqrts =5.02 TeV for a same jet transverse momentum interval 15-30 GeV. We find the number of particles per jet determines the height of the EEC distribution in pp baseline. The averaged energy weight distribution resulted in a shift of the originally larger angular distributed particle distribution to a smaller RL, thereby obtaining an EEC distribution. The EEC distributions for all quark-tagged jets in A+A exhibit a noticeable shift towards larger RL region, suggesting that the jets will be more widely distributed compared to those in pp collisions. The jet quenching effect will cause the pair angular distribution to shift towards larger values and increase the number of particles per jet. This redistribution of energy within the jets suggests that the already reduced jet energy is redistributed among a larger number of particles, leading to a reduced energy weight per pair. The enhancement of the number of particles per jet and the reduced averaged energy weight interplay with each other to form the medium modification of EEC.

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arXiv2024

The medium-temperature dependence of jet transport coefficient in high-energy heavy-ion collisions

The medium-temperature $T$ dependence of the jet transport coefficient $\hat q$ was studied via the nuclear modification factor $R_{AA}(p_{\rm T})$ and elliptical flow parameter $v_2(p_{\rm T})$ for large transverse momentum $p_{\rm T}$ hadrons in high-energy nucleus-nucleus collisions. Within a next-to-leading-order perturbative QCD parton model for hard scatterings with modified fragmentation functions due to jet quenching controlled by $\hat q$, we check the suppression and azimuthal anisotropy for large $p_{\rm T}$ hadrons, and extract $\hat q$ by global fits to $R_{AA}(p_{\rm T})$ and $v_2(p_{\rm T})$ data in A + A collisions at RHIC and LHC, respectively. The numerical results from the best fits show that $\hat q/T^3$ goes down with local medium temperature $T$ in the parton jet trajectory. Compared with the case of a constant $\hat{q}/T^3$, the going-down $T$ dependence of $\hat{q}/T^3$ makes a hard parton jet to lose more energy near $T_{\rm c}$ and therefore strengthens the azimuthal anisotropy for large $p_{\rm T}$ hadrons. As a result, $v_2(p_{\rm T})$ for large $p_{\rm T}$ hadrons was enhanced by approximately 10% to better fit the data at RHIC/LHC. Considering the first-order phase transition from QGP to the hadron phase and the additional energy loss in the hadron phase, $v_2(p_{\rm T})$ is again enhanced by 5%-10% at RHIC/LHC.

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arXiv2024

Modified Trento initial condition and its impact on collective flows and global polarization in Cu+Au collisions

Collective flow coefficients and spin polarization are valuable probes of the geometry and flow velocity field of the quark-gluon plasma (QGP) produced in relativistic heavy-ion collisions. Using a modified TRENTo initial condition coupled to a (3+1)-dimensional (D) viscous hydrodynamic model CLVisc, we study the directed flow and elliptic flow coefficients of hadrons, together with the global polarization of $Λ$ and $\barΛ$ hyperons in asymmetric Cu+Au collisions. We extend the 2D TRENTo model to the 3D space, and find that the initial tilted geometry of the QGP fireball with respect to the longitudinal direction leads to a decrease of directed flow from positive to negative values with increasing pseudorapidity, an enhancement of elliptic flow at forward and backward pseudorapidities, and a non-monotonic dependence of global polarization on the transverse momentum of hyperons. The initial longitudinal flow velocity gradient further enhances the values of directed flow and global polarization. Our model calculation provides a satisfactory description of the rapidity, transverse momentum, and centrality dependences of the directed flow of charged hadrons in Cu+Au collisions for the first time, and proposes that such asymmetric heavy-ion collisions create a better environment for studying the initial tilted geometry and longitudinal flow field of the QGP than symmetric Au+Au collisions do.

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arXiv2024

Impact of (magneto-)thermoelectric effect on diffusion of conserved charges in hot and dense hadronic matter

We investigate the thermoelectric effect, which describes the generation of an electric field induced by temperature and conserved charge chemical potential gradients, in the hot and dense hadronic matter created in heavy-ion collisions. Utilizing the Boltzmann kinetic theory within the repulsive mean-field hadron resonance gas model, we evaluate both the diffusion thermopower matrix and diffusion coefficient matrix for the baryon number ($B$), electric charge ($Q$), and strangeness ($S$). The Landau-Lifshitz choice for the rest frame of the fluid is enforced in the derivation. We find that the thermoelectric effect hinders the diffusion processes of multiple conserved charges, particularly reducing the coupling between electric charge and baryon number (strangeness) in baryon (strangeness) diffusion. Given that the repulsive mean-field interactions between hadrons have a significant effect on the diffusion thermopower matrix and diffusion coefficient matrix in the baryon-rich region, we extend the investigation to include the impact of magnetic fields, analyzing the magneto-thermoelectric effect on both the diffusion coefficient matrix and the Hall-like diffusion coefficient matrix. The sensitivities of the magnetic field-dependent diffusion thermopower matrix and magneto-thermoelectric modified diffusion coefficient matrix to the choices of various transverse conditions are also studied.

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arXiv2024

Transverse momentum balance of dijets in Xe+Xe collisions at the LHC

We present a theoretical study of the medium modifications of the $p_T$ balance ($x_J$) of dijets in Xe+Xe collisions at $\sqrt{s_{NN}}=5.44$ TeV. The initial production of dijets was carried out using the POWHEG+PYTHIA8 prescription, which matches the next-to-leading-order (NLO) QCD matrix elements with the parton shower (PS) effect. The SHELL model described the in-medium evolution of nucleus-nucleus collisions using a transport approach. The theoretical results of the dijet $x_J$ in the Xe+Xe collisions exhibit more imbalanced distributions than those in the p+p collisions, consistent with recently reported ATLAS data. By utilizing the Interleaved Flavor Neutralisation, an infrared-and-collinear-safe jet flavor algorithm, to identify the flavor of the reconstructed jets, we classify dijets processes into three categories: gluon-gluon ($gg$), quark-gluon ($qg$), and quark-quark ($qq$), and investigated the respective medium modification patterns and fraction changes of the $gg$, $qg$, and $qq$ components of the dijet sample in Xe+Xe collisions. It is shown that the increased fraction of $qg$ component at a small $x_J$ contributes to the imbalance of the dijet; in particular, the $q_1g_2$ (quark-jet-leading) dijets experience more significant asymmetric energy loss than the $g_1q_2$ (gluon-jet-leading) dijets traversing the QGP. By comparing the $Δ\langle x_J\rangle = \langle x_J \rangle_{pp} - \langle x_J \rangle_{AA}$ of inclusive, $c\bar{c}$ and $b\bar{b}$ dijets in Xe+Xe collisions, we observe $Δ\langle x_J \rangle_{incl.}>Δ\langle x_J \rangle_{c\bar{c}}>Δ\langle x_J \rangle_{b\bar{b}}$. Moreover, $ρ_{Xe, Pb}$, the ratios of the nuclear modification factors of dijets in Xe+Xe to those in Pb+Pb, were calculated, which indicates that the yield suppression of dijets in Pb+Pb is more pronounced than that in Xe+Xe owing to the larger radius of the lead nucleus.

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arXiv2024

External magnetic field induced paramagnetic squeezing effect in heavy-ion collisions at the LHC

In non-central heavy-ion collisions, the quark-gluon plasma (QGP) encounters the most intense magnetic field ever produced in nature, with a strength of approximately 10$^{19 - 20}$ Gauss. Recent lattice-QCD calculations reveal that the QGP exhibits paramagnetic properties at high temperatures. When an external strong magnetic field is applied, it generates an anisotropic squeezing force density that competes with pressure gradients resulting from the purely QGP geometric expansion. In this study, we employ (3+1)-dimensional ideal hydrodynamics simulations to estimate the paramagnetic squeezing effect of this force density on the anisotropic expansion of QGP in non-central Pb+Pb collisions at the Large Hadron Collider (LHC). We consider both up-to-date magnetic susceptibility and various magnetic field profiles in this work. We find that the impact of rapidly decaying magnetic fields is insignificant, while enduring magnetic fields produce a strong force density that diminishes the momentum anisotropy of the QGP by up to 10% at the intial stage, leaving a visible imprint on the elliptic flow $v_{2}$ of final charged particles. Our results provide insights into the interplay between magnetic fields and the dynamics of QGP expansion in non-central heavy-ion collisions.

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arXiv2024

Hadron productions and jet substructures associated with $Z^0/γ$ in Pb+Pb collisions at the LHC

We carry out a detailed study of medium modifications on $Z^0$/$γ$+hadron correlations as well as jet substructures in association with $Z^0/γ$ in Pb+Pb collisions with $\sqrt{s_{NN}}=5.02$ TeV at the LHC. We utilize the Linear Boltzmann transport (LBT) model to simulate the jet-medium interactions and medium response, and an extended cluster hadronization model to investigate the non-perturbative transition of quarks and gluons into final hadrons in heavy-ion collisions. Including hadronization effect, we can well describe $Z^0/γ$+hadrons correlations and $Z^0/γ$-tagged jet substructures in both p+p and Pb+Pb collisions simultaneously. Medium modification on jet profile and jet fragmentation functions indicate that particles carrying a large fraction of the jet momentum are generally closely aligned with the jet axis, whereas low-momentum particles are observed to have a much broader angular distribution relative to jet axis in Pb+Pb collisions due to jet-medium interactions. In particular, we find that $Z^0/γ$-tagged hadron correlations are sensitive to the soft particles from the dense medium and medium response, while jet-substructures show weak dependence on those soft hadrons with only a fraction of them falling inside the jet area

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arXiv2024

Flavor dependence of jet quenching in heavy-ion collisions from a Bayesian analysis

We investigate the flavor dependence of jet quenching, by performing a systematic analysis of medium modifications on the inclusive jet, $γ$+jet, and $b$-jet in Pb+Pb collisions at the LHC. Our results from MadGraph+PYTHIA exhibit excellent agreement with experimental measurements of the inclusive jet, $γ$+jet and $b$-jet simultaneously in p+p collisions. We then utilize a Bayesian data-driven method to extract systematically the flavor-dependent jet energy loss distributions from experimental data, where the gluon, light quark and $b$-quark initiated energy loss distributions are well constrained and satisfy the predicted flavor hierarchy of jet quenching, i.e. $\langle ΔE_g \rangle > \langleΔE_q\rangle > \langleΔE_b\rangle$. It is shown that the quark-initiated jet energy loss distribution shows weaker centrality and $p_\text{T}$ dependence than the gluon-initiated one. We demonstrate the impacts of the slope of initial spectra, color-charge as well as parton mass dependent jet energy attenuation on the $γ/b$-jet suppression observed in heavy-ion collisions.

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arXiv2023

Hydrodynamic simulations of directed flow for light hadrons in Au+Au and isobar collisions $\sqrt{s_{\textrm{NN}}}=$ 200 GeV

Using a (3+1)-D hydrodynamic model CLVisc, we study the directed flow ($v_{1}$) of light hadrons produced in Au+Au, Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\textrm{NN}}}=$ 200 GeV. The evolution of tilted energy density, pressure gradient and radial flow along the $x$-direction are systematically investigated. Counter-clockwise tilt of initial fireball is shown to be a vital source of the directed flow for final light hadrons. A good description of directed flow is provided for light hadrons in central and mid-central Au+Au and isobar collisions at RHIC. Our numerical results show a clear system size dependence for light hadron $v_{1}$ across different collision systems. We further study the effect of nuclear structure on the directed flow and find that the $v_{1}$ for light hadrons is insensitive to the nuclei with quadrupole deformation.

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arXiv2023

Hyperon polarization and its relation with directed flow in high-energy nuclear collisions

We investigate the hyperon polarization and its relation with the directed flow of the quark-gluon plasma (QGP) in non-central Au+Au collisions at $\sqrt{s_{\textrm{NN}}} = 27$ GeV. A modified 3-dimensional (3D) Glauber model is developed and coupled to a (3+1)-D viscous hydrodynamic evolution of the QGP. Within this framework, we obtain a satisfactory simultaneous description of the directed flow of identified particles and $Λ$ polarization, and show sensitivity of polarization to both the tilted geometry and the longitudinal flow profile of the QGP. A non-monotonic transverse momentum dependence of the $Λ$ polarization is found in our calculation, which is absent from hydrodynamic simulation using other initialization methods and can be tested by future experimental data with higher precision. The relation between the global polarization and directed flow of $Λ$ is explored as the longitudinal flow field or the medium deformation varies. Due to the common origin of these two observables, their combination may provide a more stringent constraint on the initial condition of the QGP.

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arXiv2023

Longitudinal momentum fraction of heavy-flavor mesons in jets in high-energy nuclear collisions

Heavy-flavor jets are powerful tools to gain insight into the in-medium partonic energy-loss mechanisms and the quark-gluon plasma's (QGP) transport properties in high-energy nuclear collisions. In this work we present the first theoretical study of the longitudinal momentum fraction $z_{||}$ carried by heavy-flavor mesons in jets in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. The p+p baseline is provided by POWHEG+PYTHIA8, which matches the next-to-leading-order hard processes with the parton shower. We employ a Monte Carlo transport model, which considers the collisional and radiative partonic energy loss, to simulate the evolution of heavy-flavor jets in the expanding QGP medium. We observe steeper $z_{||}$ distributions of $\rm{B^0}$ jets compared to those of $\rm{D^0}$ jets at the same kinematics region in p+p collisions, which may be a hint of the harder jet fragmentation function of b jets compared to c jets in vacuum. In A+A collisions, it is shown that the jet quenching effect would generally decrease the values of $z_{||}$. We have made a systematical study on how several factors, including jet $p_{\rm{T}}$, jet radius $R$, and collision centrality, would influence the medium modification of $z_{||}$ distributions of a $\rm{D^0}$ jet. In addition, we predict visibly stronger nuclear modifications of $\rm{B^0}$-jet $z_{||}$ distributions compared to a $\rm{D^0}$ jet within the same $p_{\rm T}$ windows as a result of the much steeper initial $z_{||}$ distribution of the $\rm{B^0}$ jet in vacuum.

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