---
title: Prompt vs Non-Prompt D0 Mesons
url: https://www.emergentmind.com/topics/prompt-and-non-prompt-d-0-mesons
type: topic
---

# Prompt vs Non-Prompt D0 Mesons

Prompt and non-prompt $D^0$ mesons are distinct sub-populations of neutral open-charm mesons produced in high-energy hadronic collisions. Prompt $D^0$ mesons originate either via hadronization of directly produced charm quarks or feed-down from higher excited charm resonances and decay extremely close to the collision vertex. In contrast, non-prompt $D^0$ mesons arise from the weak decay of beauty hadrons ($B\to D^0+X$) and exhibit a significantly displaced decay vertex due to the longer $B$-hadron lifetime. The separation and precise measurement of these components provide critical probes for quantum chromodynamics (QCD), heavy-quark production dynamics, multi-partonic interactions, hadronization, and in-medium transport properties in both proton-proton and heavy-ion environments.

## 1. Production Mechanisms and Theoretical Framework

Prompt $D^0$ mesons are produced at the primary interaction vertex predominantly through leading-order QCD hard scatterings such as gluon-gluon fusion ($g + g \rightarrow c + \bar{c}$) and quark-antiquark annihilation ($q + \bar{q} \rightarrow c + \bar{c}$), with subsequent fragmentation of the charm quark to a $D^0$ meson or via feed-down from higher-mass open-charm hadrons. In collinear factorization:

\[
\frac{d\sigma_{\mathrm{prompt}}}{dp_T} = \sum_{i,j} \int dx_1 dx_2 f_i(x_1, \mu_F) f_j(x_2, \mu_F) \frac{d\hat{\sigma}_{ij\rightarrow c\bar{c}}}{dp_{T,c}} \otimes D_{c\rightarrow D}(z)\,\delta(p_T - z p_{T,c})
\]

Non-prompt $D^0$ mesons are produced from weak decays of beauty hadrons, which themselves originate from $b$-quark production via analogous hard-scattering processes ($g+g \rightarrow b+\bar{b}$, $q+\bar{q} \rightarrow b+\bar{b}$) and subsequent fragmentation:

\[
\frac{d\sigma_{\text{non-prompt}}}{dp_T} = \sum_{i,j} \int dx_1 dx_2 f_i(x_1)f_j(x_2) \frac{d\hat{\sigma}_{ij\rightarrow b\bar{b}}}{dp_{T,b}} \otimes D_{b\rightarrow B}(z_1) \otimes F_{B\rightarrow D}(z_2)\,\delta(p_T - z_1 z_2 p_{T,b})
\]

where $D_{c\to D}(z)$ and $D_{b\to B}(z_1)$ are fragmentation functions, and $F_{B\to D}(z_2)$ encodes the $B \to D^0$ decay kinematics [2601.06856].

## 2. Experimental Separation and Analysis Methodologies

The separation of prompt and non-prompt $D^0$ mesons exploits the distinct decay topologies arising from the disparate lifetimes of charm and beauty hadrons. The ALICE, CMS, and other LHC detectors utilize high-resolution silicon vertexing and tracking to reconstruct the $D^0\to K^-\pi^+$ decay. Key observables include:

- **(a) Vertex Displacement and Impact Parameter:** Prompt $D^0$ mesons have mean decay lengths of $c\tau\approx 123$ μm, while non-prompt candidates from $B$ decays have typical $B$-hadron $c\tau\approx 500$ μm [2302.07783, 2102.13601, 2404.09839]. Multi-variate classifiers, such as Boosted Decision Trees (BDT), are trained on simulated data to discriminate prompt and non-prompt using input variables including track impact parameters, decay-vertex displacement, pointing angle, and PID information.

- **(b) Pseudoproper Time and Decay Lengths:** Variables such as $t_z = (z_{D^0}-z_{\text{PV}}) m_{D^0}/p_z$ and transverse pseudoproper decay length $c\tau = c\,m_{D^0}(\vec{L}\cdot\vec{p}_T)/|\vec{p}_T|^2$ provide further discrimination [2404.09839].

- **(c) Yield Extraction:** By applying multiple classifier cuts, the raw candidate yields $Y_i$ are decomposed into prompt and non-prompt components using efficiency matrices. The final non-prompt fraction is given by 
\[
f_{\text{np}}(p_T,N_{\text{ch}}) = \frac{N_{\text{non-prompt}}(p_T,N_{\text{ch}})}{N_{\text{prompt}}(p_T,N_{\text{ch}}) + N_{\text{non-prompt}}(p_T,N_{\text{ch}})}
\] 
[2302.07783, 2102.13601].

- **(d) Machine Learning Approaches:** XGBoost, CatBoost, and Random Forest classifiers trained on topological and kinematic inputs achieve $\gtrsim 99\%$ purity/efficiency for prompt/non-prompt tagging on simulated data, with high fidelity in physical observables across $p_T$, $\eta$, and multiplicity bins [2404.09839].

## 3. Transverse Momentum, Multiplicity, and Event Shape Dependence

Prompt and non-prompt $D^0$ yields and fractions exhibit characteristic dependencies on transverse momentum ($p_T$), charged-particle multiplicity, and event topology.

- **$p_T$ Dependence:** The non-prompt fraction $f_{\text{np}}(p_T)$ rises monotonically with $p_T$, from $5$–$7\%$ at $1$–$2$ GeV/$c$ to $\sim 10\%$ above $8$ GeV/$c$ in inclusive (INEL$>$0) $pp$ samples at 13 TeV [2302.07783]. The $R_{\text{np/p}}(p_T)$ ratio is $\sim0.05$ at $p_T\approx1$ GeV/$c$ and grows to $\sim0.3$ at $p_T\approx12$ GeV/$c$ [2404.09839], with similar behaviors predicted by PYTHIA 8 and observed in ALICE data at various energies [2102.13601].

- **Multiplicity Dependence:** $f_{\text{np}}(p_T)$ shows no significant change with multiplicity, remaining constant within $|R-1|\lesssim10\%$ (with $R$ the double ratio of non-prompt fractions between multiplicity classes) [2302.07783]. However, self-normalized non-prompt $D^0$ yields $Y_{\text{norm}}(N_{\text{ch}})$ rise faster than linearly with normalized charged-particle multiplicity $N_{\text{ch}}/\langle N_{\text{ch}}\rangle$, especially at high $p_T$ and collision energy, due to the strong sensitivity of beauty production to multiple partonic interactions (MPI) [2404.09839, 2601.06856].

- **Event-Shape Engineering:** Non-prompt $D^0$ mesons demonstrate strong correlation with the hardest partonic scatter (high $\hat{p}_T$) and little dependence on late-stage color reconnection or event spherocity, reflecting their origin fixed by the primary hard process. In contrast, prompt $D^0$ mesons receive feed-down from semi-hard processes and are more sensitive to color reconnection effects and event isotropy [2601.06856].

## 4. Nuclear Modification and Collectivity in Heavy-Ion Collisions

In heavy-ion collisions, prompt and non-prompt $D^0$ mesons serve as mass-differentiated probes of parton energy loss and quark-gluon plasma (QGP) transport properties.

- **Suppression Patterns ($R_{AA}$):** Non-prompt $D^0$ $R_{AA}$ is consistently higher than that for prompt $D^0$ and charged hadrons for $p_T \sim 5$–$15$ GeV/$c$, expressing the dead-cone effect and reduced in-medium coupling for bottom quarks. For example, $R_{AA}$(non-prompt $D^0$) $\sim$ 0.25 (2–4 GeV/$c$), rising to $\sim$ 0.80 (14–30 GeV/$c$) in central PbPb collisions, while prompt $D^0$ and charged hadron $R_{AA}$ remain lower [1810.11102, 2404.12601]. The $R_{B/D}$ yield ratio increases with $p_T$, with differences between $pp$ and PbPb most pronounced at low $p_T$ due to stronger beauty suppression [1810.11102].

- **Elliptic and Triangular Flow ($v_2$, $v_3$):** Non-prompt $D^0$ mesons display significant but smaller $v_2$ and $v_3$ than their prompt counterparts, confirming reduced thermalization and weaker collective coupling for beauty quarks. Typical values for $v_2$(non-prompt $D^0$) are 0.02–0.07 across $p_T$ and centrality, with prompt $D^0$ $v_2$ reaching up to $\sim0.15$. The mass ordering $v_2^{D^0} > v_2^{\text{non-prompt}\; D^0}$ is observed in both ALICE and CMS, aligning with mechanistic expectations from Langevin transport and Boltzmann models [2307.14084, 2212.01636, 2404.12601].

- **Theoretical Models:** Heavy-quark energy loss calculations including mass-dependent drag and diffusion coefficients (TAMU, LBT, PHSD, CUJET, EPOS) describe the overall features of $R_{AA}$ and $v_n$ for prompt and non-prompt $D^0$, although in the low-$p_T$ range non-prompt suppression can be stronger than standard models predict, possibly implying enhanced collisional drag or altered $B$-hadron chemistry owing to coalescence [1810.11102, 2212.01636, 2404.12601].

## 5. Cross Sections, Yield Ratios, and Model Comparisons

Precise differential and total cross sections for prompt and non-prompt $D^0$ mesons have been extracted at multiple energies.

| $p_T$ (GeV/$c$) | $\frac{d^2\sigma}{dp_T dy}$ Prompt ($\mu$b/(GeV/$c$)) | $\frac{d^2\sigma}{dp_T dy}$ Non-prompt ($\mu$b/(GeV/$c$)) |
|:---------------:|:-----------------------------------------------------:|:----------------------------------------------------------:|
| 1–2             | $80\pm4\pm7$                                          | $0.16\pm0.02\pm0.02$                                       |
| 4–6             | $8.5\pm0.3\pm0.8$                                     | $0.070\pm0.010\pm0.007$                                    |
| 8–12            | $1.1\pm0.1\pm0.1$                                     | $0.018\pm0.003\pm0.002$                                    |
| 16–24           | $0.050\pm0.010\pm0.006$                               | $0.0025\pm0.0008\pm0.0005$                                 |

In $|y|<0.5$ for $pp$ at 5.02 TeV, the $p_T$-integrated visible non-prompt $D^0$ cross section is $14.5\pm1.2\pm1.3$ μb [2102.13601]. The $b\bar{b}$ production cross section per rapidity unit at midrapidity, extracted via non-prompt $D^0$ yields, is $34.5 \pm 2.4\, (\text{stat})^{+4.7}_{-2.9}\, (\text{syst})\ \mu$b, consistent with FONLL pQCD predictions [2102.13601]. The non-prompt/prompt $D^0$ yield ratio increases from $f_{\text{np}}/f_{\text{p}}\approx0.2$ at $p_T\sim1.5$ GeV/$c$ to $\sim0.8$ at $p_T\sim20$ GeV/$c$.

Model comparisons:

- PYTHIA 8, especially with Colour Reconnection beyond Leading Colour (CR-BLC) or Colour Ropes, reproduces qualitative $f_{\text{np}}(p_T)$ trends but overestimates absolute yields by $\sim20$–$30\%$, and predicts a slight multiplicity dependence disfavored by data [2302.07783, 2601.06856].
- EPOS 3/4 underpredict $f_{\text{np}}$ and predict stronger multiplicity dependence than observed [2302.07783].
- CGC calculations with three-pomeron fusion are compatible with the observed double ratios [2302.07783].

## 6. Implications for QCD and Heavy-Flavor Dynamics

Simultaneous measurements of prompt and non-prompt $D^0$ mesons constrain heavy-quark fragmentation functions, hadronization mechanisms, and the mass-dependence of parton diffusion and energy loss. The weak multiplicity dependence of $f_{\text{np}}$ at midrapidity indicates similar multi-parton and hadronization dynamics for charm and beauty in $pp$ collisions, disfavoring scenarios of strong enhancement in beauty-baryon over beauty-meson yields at high multiplicity [2302.07783, 2601.06856]. The observed hierarchy $R_{AA}$(charged)$<$ $R_{AA}$(prompt $D^0$)$<$ $R_{AA}$(non-prompt $D^0$) and $v_2$(prompt)$>$ $v_2$(non-prompt) in heavy-ion collisions quantitatively embody color coherence and the dead-cone effect, providing direct experimental access to the bottom-quark transport coefficient $D_s$ [2212.01636, 2404.12601].

These measurements, enabled by advances in experimental reconstruction and machine learning, underpin precision tests of QCD production and non-perturbative dynamics in both elementary and nuclear systems. They also provide benchmarks for future, more differential extractions of heavy-quark transport parameters and heavy-flavor hadronization in the high-luminosity era.

Source: https://www.emergentmind.com/topics/prompt-and-non-prompt-d-0-mesons