$B\overline{B}$ angular correlations at the LHC in the parton Reggeization approach merged with higher-order matrix elements

We calculate the angular distribution spectra between beauty ($B$) and antibeauty ($\overline{B}$) mesons in proton-proton collisions in the leading order approximation of the parton Reggeization approach consistently merged with the next-to-leading order corrections from the emission of an additional hard gluon. To describe b-quark hadronization we use the universal scale-dependent parton-to-meson fragmentation functions extracted from the world $e^{+}{e}^{-}$ annihilation data. We have obtained good agreement between our predictions and data from the CMS Collaboration at the energy $\sqrt{S}=7\mathrm{TeV}$ for $B\overline{B}$ angular correlations within uncertainties and without free parameters. Predictions for analogous correlation observables at $\sqrt{S}=13\mathrm{TeV}$ are provided.

Figure 1

Feynman rules of the EFT [19]. The propagator of the Reggeized gluon (top left panel) and Reggeon-gluon induced vertices up to the $O(g_s^2)$ are shown. The usual Feynman rules of QCD hold for interactions of ordinary quarks and gluons.

Figure 2

Structure of the effective vertices $R_{\pm }gg$ (top left), $R_{\pm }q\overline{q}$ (top right), $R_{+}{R}_{-}g$ (bottom left), and the $R_{+}{R}_{-}gg$ combined vertex (bottom right). These vertices appear in the diagrams of Figs. 3, 5, and 7.

Figure 3

Diagrammatic representation of the MRK asymptotics for the squared amplitude of the subprocess (1).

Figure 4

Distribution in the rapidity of gluon jets with $|{\mathbf{k}}_T|>\mu /2$ from the last stage of the parton cascade, as given by the KMR model (18). The solid line represents ${\mu }^2={10}^3{\mathrm{GeV}}^2$; the dashed line represents ${\mu }^2={10}^5{\mathrm{GeV}}^2$. Both plots are normalized to the common integral; the scale of the $G$-axis is arbitrary. For both distributions, $x=\mu /\sqrt{S}$; i.e., the rapidity of the hard process is zero.

Figure 5

The Feynman diagrams of Lipatov’s EFT for the Reggeized amplitude of subprocess $R_{+}+R_{-}\to b+\overline{b}$.

Figure 6

The kinematic cuts for the $2\to 2$ contribution (20) and $2\to 3$ contribution (21) in the space of transverse momentum of the leading $b$-jet in the event ($p_T^{\mathrm{b}\text{-jet}}$) vs transverse momentum of the leading light-quark/gluon jet in the same event ($p_T^{\text{non}\text{-b}\text{jet}}$).

Figure 7

The Feynman diagrams of Lipatov’s EFT for the Reggeized amplitude of subprocess $R_{+}+R_{-}\to b+\overline{b}+g$.

Figure 8

Comparison of the predictions for $\mathrm{\Delta }\varphi$-spectra of $B\overline{B}$-pairs with the CMS data [3]. The dashed, dashed-dotted, and solid lines represent the contribution of the LO subprocess (20), contribution of the NLO subprocess (21), and sum of the LO and NLO contributions, respectively.

Figure 9

Comparison of the predictions for $\mathrm{\Delta }R$-spectra of $B\overline{B}$-pairs with the CMS data [3]. Notation for the histograms is the same as in Fig. 8.

Figure 10

Predictions for the $d\sigma /d\mathrm{\Delta }\varphi$-spectra $\sqrt{S}=13\mathrm{TeV}$ for the same kinematic cuts as in Ref. [3]. Notation for the histograms is the same as in Fig. 8.

Figure 11

Predictions for the $d\sigma /d\mathrm{\Delta }R$-spectra $\sqrt{S}=13\mathrm{TeV}$ for the same kinematic cuts as in Ref. [3]. Notation for the histograms is the same as in Fig. 8.

Figure 12

Predictions for the ratio of $d\sigma /d\mathrm{\Delta }\varphi$-spectra at $\sqrt{S}=13\mathrm{TeV}$ and $\sqrt{S}=7\mathrm{TeV}$ for the same kinematic cuts as in Ref. [3].

Figure 13

Predictions for the ratio of $d\sigma /d\mathrm{\Delta }R$-spectra at $\sqrt{S}=13\mathrm{TeV}$ and $\sqrt{S}=7\mathrm{TeV}$ for the same kinematic cuts as in Ref. [3].