Confronting the vector leptoquark hypothesis with new low- and high-energy data

Abstract

In light of new data we present an updated phenomenological analysis of the simplified $U_1$ -leptoquark model addressing charged-current B-meson anomalies. The analysis shows a good compatibility of low-energy data (dominated by the lepton flavor universality ratios $R_D$ and $R_{D^{\ast }}$ ) with the high-energy constraints posed by $pp\to \tau \overline{\tau }$ Drell-Yan data. We also show that present data are well compatible with a framework where the leptoquark couples with similar strength to both left- and right-handed third-generation fermions, a scenario that is well-motivated from a model building perspective. We find that the high-energy implications of this setup will be probed at the 95% confidence level in the high-luminosity phase of the LHC.

Fig. 1

Determination of ${\mathcal{C}}_{\mathit{LL}}^c$ and ${\mathcal{C}}_{\mathit{LR}}^c$ from a ${\chi }^2$-fit to low-energy observables. The Wilson coefficients, assumed to be real, are renormalized at the reference scale ${\mathrm{\Lambda }}_{\text{UV}}=1$ TeV. The blue ellipses denote the 1, 2, and 3$\sigma$ contours fitting only $b\to c$ observables. The black dot indicates the best fit point of $(0.05,-0.02)$. The dotted lines are obtained including also $\mathcal{B}\left(B_u^{-},\to ,\tau ,\overline{\nu }\right)$ in the limit of up alignment. The $\mathrm{\Delta }{\chi }^2=1$ regions preferred by each observable are also indicated, except in the case of $R_{{\mathrm{\Lambda }}_c}$ where we give the 90% CL region (due to the large error)

Fig. 2

High-$p_T$ constraints on the $U_1$ model parameters ${\beta }_R$ and ${\mathrm{\Lambda }}_U$ derived from the $pp\to \tau \overline{\tau }$ searches by CMS [36] (gray) and ATLAS [39] (green) in the b-tag and b-veto channels. The functional dependence is extracted using the HighPT package [63, 77] and rescaled to the results presented in Ref. [34]. The shaded regions correspond to the excluded parameter space at $95\%$ CL. The solid lines correspond to the constraints obtained using LHC run-II $(\sim 140{\text{fb}}^{-1})$ data, whereas the dashed line displays the projections for LHC’s high luminosity phase $(\sim 3{\text{ab}}^{-1})$ for the ATLAS b-tag search

Fig. 3

High-$p_T$ constraints superimposed on the low-energy fit. The red and blue bands represent the $\mathrm{\Delta }{\chi }^2=1$ regions preferred by $R_D$ and $R_{D^{\ast }}$. The blue lines correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ contours of the combined low-energy fit including all $b\to c$ observables (dot = best fit point). The high-$p_T$ exclusion limits derived from the b-tag channel of the CMS [36] (ATLAS [39]) search are given by regions outside of the gray (green) lines. On the other hand, the region inside the innermost dotted curve is our projection for the allowed parameter space from high-$p_T$ searches (in absence of a signal) with a luminosity of $3{\text{ab}}^{-1}$. Finally, the region to the right of the red line is excluded by $\tau$-LFU tests assuming leading log running of $C_{\mathit{LL}}^{33\tau \tau }$. See text for more details

Fig. 4

Preferred region at 90% CL from low-energy charged-current data for mass ($M_U$) and leading fermion coupling ($g_U$) of the $U_1$ LQ. Top: Purely left-handed case (${\beta }_R=0$). Bottom: Pati-Salam-like case ($|{\beta }_R|=1$). The gray region and solid lines indicate constraints of present high-energy searches at 95% CL, while the dotted line gives the projected sensitivity at the HL-LHC with a luminosity of $3{\text{ab}}^{-1}$

Fig. 5

Predicted range for $\mathcal{B}(B_s\to {\tau }^{+}{\tau }^{-})$ as a function of $\delta R_{D^{\ast }}=R_{D^{\ast }}/R_{D^{\ast }}^{\text{SM}}-1$. The filled orange and purple colored regions correspond to the 90% CL preferred regions from the low-energy charged-current fit. The blue vertical bands denote the present $1\sigma$ and $2\sigma$ experimental ranges for $\delta R_{D^{\ast }}$