Phenomenology of nonperturbative charm in the nucleon

TL;DR

This work reassesses intrinsic charm in the nucleon by contrasting simple five-quark (BHPS) pictures with dynamical meson–baryon fluctuations (MBM). It derives meson–baryon splitting functions, constrains couplings and cutoffs from hadronic data, and computes charm and anticharm distributions inside charmed hadrons to form nucleon PDFs via convolution. A robust finding is that the vector-meson–baryon channel $\bar{D}^{*0} \Lambda_c^+$ dominates intrinsic charm, producing a harder $\bar{c}$ distribution and a measurable $c$–$\bar{c}$ asymmetry, with the total intrinsic charm momentum fraction $P_c$ typically near $1$–$4\%$, depending on the regulator. When combined with perturbative charm, the MBM predictions for $F_2^c$ can overshoot large-$x$ EMC data unless the cutoff is tuned, highlighting ongoing tension and the need for new measurements (e.g., at an Electron–Ion Collider) to sharpen constraints on nonperturbative charm in the nucleon.

Abstract

We perform a comprehensive analysis of the role of nonperturbative (or intrinsic) charm in the nucleon, generated through Fock state expansions of the nucleon wave function involving five-quark virtual states represented by charmed mesons and baryons. We consider contributions from a variety of charmed meson-baryon states and find surprisingly dominant effects from the (Dbar^{*0} Lambda_c+) configuration. Particular attention is paid to the existence and persistence of high-x structure for intrinsic charm, and the x dependence of the c-cbar asymmetry predicted in meson-baryon models. We discuss how studies of charmed baryons and mesons in hadronic reactions can be used to constrain models, and outline future measurements that could further illuminate the intrinsic charm component of the nucleon.

Figures (12)

• Figure 1: (color online) Spin configurations ($J=$ meson + baryon spin) and masses for the spectrum of charmed hadron configurations included in the present MBM calculation.
• Figure 2: (color online) (a) Differential cross section $d\sigma/d\bar{y}$ for the inclusive charm production reaction $pp \to \Lambda_c^+ X$ as a function of the momentum fraction $\bar{y}$ carried by the $\Lambda_c^+$. The MBM cross section (solid) is computed using the central value for the $Dp$ cross section $\sigma^{Dp}_{\rm tot} = 20$ mb, and the resulting error band (shaded) represents the purely statistical uncertainty. The data (red circles) are from the R608 collaboration at the ISR Chauvat:1987kb. (b) Charge asymmetry $A^{\Lambda_c}$ for $\Lambda_c^+/\bar{\Lambda}_c^-$ production in the MBM (solid), using the ${x_{{ F}}}$ dependence of the $\bar{\Lambda}_c$ cross section in Eq. (\ref{['eq:SELEX-iii']}), compared with data from the SELEX Collaboration Garcia:2001xj.
• Figure 3: (color online) Splitting functions for the four basic dissociations of a proton into charmed meson--baryon states, for the spin-1 meson + spin-1/2 baryon state $\bar{D}^{*0} \Lambda_c^+$ (red solid), spin-0 meson + spin-1/2 baryon state $\bar{D}^0 \Lambda_c^+$ (scaled $\times 10$, blue dotted), spin-1 meson + spin-3/2 baryon state $\bar{D}^{*0} \Sigma_c^{*+}$ (scaled $\times 10$, green dashed), and spin-0 meson + spin-3/2 baryon state $\bar{D}^0 \Sigma_c^{*+}$ (scaled $\times 100$, black dot-dashed). A universal exponential cutoff mass $\Lambda = 3$ GeV is used with the couplings from Table \ref{['table:couplings']}.
• Figure 4: (color online) Contributions to the $p \to \bar{D}^{*0} \Lambda_c^+$ splitting function from the vector (dashed), tensor (solid) and vector-tensor interference (dotted) terms in Eq. (\ref{['eq:spin1-fMB']}). The curves are computed for a cutoff mass $\Lambda = 3$ GeV with charm coupling constants from SU(4) symmetry (red) and using the corresponding SU(2) values for $\rho NN$ (blue).
• Figure 5: (color online) (a) Normalizations $\langle n \rangle_{MB}$ of the charmed meson--baryon splitting functions as a function of the form factor cutoff $\Lambda$, for the states $\bar{D}^{*0} \Lambda_c^+$ (red solid), $\bar{D}^0 \Lambda_c^+$ (scaled $\times 10$, blue dotted), $\bar{D}^{*0} \Sigma_c^{*+}$ (scaled $\times 10$, green dashed), and $\bar{D}^0 \Sigma_c^{*+}$ (scaled $\times 100$, black dot-dashed), as well as the sum of all contributions (black dashed). The (yellow) shaded band represents the uncertainty on the cutoff obtained from fits to inclusive $\Lambda_c^+$ production data. (b) Normalizations of the splitting functions to pseudoscalar (solid) and vector (dashed) mesons computed with SU(2) sector ($\pi N$ and $\rho N$) masses (black), SU(3) masses, denoted by "$K \Lambda$" and "$K^* \Lambda$" (blue), and SU(4) masses, denoted by "$D \Lambda_c$" and "$D^* \Lambda_c$" (scaled $\times 100$, red), all for the same SU(2) couplings.