Addendum to: Combined Constraints on First Generation Leptoquarks

In this addendum to arXiv:2101.07811 we discuss the implications of the recent CMS analysis of lepton flavour universality violation in non-resonant di-lepton pairs for first generation leptoquarks. As CMS finds more electron events than expected from background, this analysis prefers the LQ representations $\tilde{S}_1, S_2, S_3, \tilde{V}_1, V_2\,(\kappa_2^{RL}\ne 0)$ and $V_3$ which lead to constructive interference with the SM. In principle the excess could also be (partially) explained by the representations $\tilde{S}_2, V_1\,(\kappa_1^R\ne 0), V_2\,(\kappa_2^{LR}\ne 0), \tilde{V}_2$ which are interfering destructively, as this would still lead to the right effect in bins with high invariant mass where the new physics contribution dominates. However, in these cases large couplings would be required which are excluded by other observables. The representations $S_1, V_1\, (\kappa_1^{L} \ne 0)$ cannot improve the fit to the CMS data compared to the SM.

In Ref. [1] we studied the interplay of low and high energy constraints on first generation leptoquarks (LQs). In this addendum we update this analysis by including the recent CMS measurement of lepton flavour universality violation (LFUV) in non-resonant di-leptons [155]. The CMS data points towards constructively interfering new physics in the electron channel which can improve the fit compared to the SM by more than 3 σ [156]. * Electronic address: andreas.crivellin@cern.ch † Electronic address: luschnel@student.ethz.ch

II. SETUP
Let us briefly review our conventions. For details, the interested reader is referred to Ref. [1]. All 10 possible LQ representations under the SM gauge group are listed in Table I with the convention that the electric charge Q is given by Q = 1 2 Y +T 3 , where Y is the hypercharge and T 3 the third component of the weak isospin. These representations allow for couplings to SM quarks and leptons as given in Table II. In the following, we denote the LQ masses according to their representation and use small m for the scalar LQs and capital M for the vector LQs.

III. CMS ANALYSIS OF NON-RESONANT DI-LEPTON PAIRS
In Ref. [155] CMS presented an analysis of nonresonant high-mass di-lepton events at the LHC. Since in our framework of first generation LQs we only get effects in electrons, we can make use of the ratio arXiv:2104.06417v1 [hep-ph] 13 Apr 2021  Table I, where Q and L represent the left-handed quark and lepton SU (2)L doublets, e, d and u the right-handed SU (2)L singlets, the superscript c stands for charge conjugation and τi are the Pauli matrices.
of differential cross sections, measuring lepton flavour universality (which reduces the uncertainties [116]), to derive bounds on the LQ masses and couplings. Here, m ( = µ, e) is the invariant mass of the lepton pair. In Ref. [155] R µµ/ee was measured for nine bins in an invariant mass range between 200 and 3,500 GeV (R Data µµ/ee ) and normalized to the same ratio calculated via SM Monte-Carlo routines (R MC µµ/ee ). This ratio in turn was normalized to unity in the bin from 200 to 400 GeV in order to correct for differences in acceptance and efficiency between the di-electron and di-muon channels. The resulting data points are shown in Fig. 1 where gray (black) represents the cases where none (at least one) of the final state leptons were observed in the detector endcaps.
We calculated the ratio R LQ µµ/ee (m, λ)/R SM µµ/ee for the different LQ models (at leading order in perturbation theory) using the PDF set NNPDF23LO, also employed e.g. in the ATLAS analysis to generate the signal DY process [157], with the help of the Mathematica package ManeParse [158]. We then integrated this ratio over the invariant mass ranges of the corresponding bins and compared the resulting signal strength to the data. Here a complication arises if the LQ mass is not much higher than the energy of the lepton pair such that the 4-Fermi approximation is no longer appropriate. In this case we replaced the effective interaction by the LQ propagator as described in Sec. 4 in Ref. [159]. Therefore, R LQ µµ/ee is dependent both on the LQ mass m and the LQ coupling strength λ 1 . We also estimated the relative sensitivities of the CMS detector to the LR/RL vs LL/RR channels, resulting from their different angular distributions, based on the CI limits stated in Ref. [155]. We found a small enhancement of 10% for the LR/RL channels and therefore decided to neglect this effect, obtaining a conservative estimate of the LR/RL LQ contributions in our calculations.
Then we performed a χ 2 statistical analysis with two degrees of freedom, defining where i runs over the data points available from the nine bins with and without leptons detected in the CMS endcaps and σ i are the corresponding uncertainties reported in Ref. [155]. Minimizing the χ 2 function with respect to (m, λ) we find the best fit pointsm andλ given in Tab. III. The corresponding values of R SM+LQ µµ/ee /R SM µµ/ee for the different bins are shown in Fig. 1, together with the CMS measurement.

IV. PHENOMENOLOGICAL ANALYSIS
The regions allowed at the 1σ and 2σ level (with respect to the best fit points) from the CMS measurement are shown in Fig. 2 and 3 together with the other constraints on first generation LQs. For λ 1 , λ LR 2 , λ RL 2 ,λ 2 , λ 3 , κ R 1 ,κ 1 , κ LR 2 , κ RL 2 ,κ 2 and κ 3 , the model explains data better than the SM, with ∆χ 2 ≡ χ 2 (∞, 0) − χ 2 (m,λ) being ≈ −11 as they provide clear effects in the high m bins. The representations with λ L 1 , λ R 1 and κ L 1 feature a destructive LQ-SM interference term. While they can also yield R SM +LQ µµ/ee /R SM µµ/ee < 1 at large m values for sizable LQ contributions, the destructive interference then results in deviations R SM +LQ µµ/ee /R SM µµ/ee > 1 for intermediate invariant masses (m ≈ 500 GeV) leading to a fit that is worse than the one of the SM. The representations with couplings λ 2 , κ R 1 , κ LR 2 ,κ 2 also lead to destructive interference with the SM, but they feature smaller interference terms. In these cases, R SM +LQ µµ/ee /R SM µµ/ee is only slightly larger than 1 for intermediate m , allowing still for a good fit to the data.
Taking into account the other exclusion limits already presented in Ref. [1], we see from Fig. 2 and 3 that the representations with the couplingsλ 1 , λ LR 2 , λ RL 2 ,κ 1 , κ RL 2 and κ 3 can account for the CMS measurement without violating other bounds, since these representations interfere constructively with the SM such that small LQ contributions are sufficient to explain the excess in electron pairs. λ LR Barrel Data

Endcap Data
FIG. 1: The ratio R Data µµ/ee /R MC µµ/ee measured by CMS [155] in the various bins compared to the R SM+LQ µµ/ee /R SM µµ/ee values for the best fit of the various LQ models. The gray data points correspond to measurements where both leptons were detected in the CMS barrel while the black dots correspond to measurements where at least one of the leptons was detected in the CMS endcaps. The parameters of the fit to the different LQ representations are given in Tab. III. for the CMS data, but also explain the Cabbibo angle anomaly. Although the representations with the couplingsλ 2 , λ 3 , κ R 1 , κ LR 2 andκ 2 explain the CMS data, they are excluded by parity violation, K + → π + νν, or the ATLAS Drell-Yan measurement. Except for λ 3 , these representations all interfere destructively with the SM, requiring excluded lower values ofm/λ (corresponding to larger LQ contributions) to explain the electron excess at high m .

V. CONCLUSION
In this addendum we examined the impact of the CMS measurement on LFU violation in non-resonant di-lepton pairs. We found that the first generation LQs with the couplingsλ 1 , λ LR 2 , λ RL 2 ,λ 2 , λ 3 , κ R 1 ,κ 1 , κ LR 2 , κ RL 2 ,κ 2 and κ 3 provide better fits to the CMS data than the SM with ∆χ 2 ≈ −11. Among these,λ 1 , λ LR 2 , λ RL 2 ,κ 1 , κ RL 2 , κ 3 feature constructive interference with the SM and are consistent with all other available measurements. In case of alignment to the up sector and allowing for fine-tuning in D 0 −D 0 mixing, V 3 could not only account for the CMS data, but also explain the Cabbibo angle anomaly.
QWEAK & APV   While LHC limits and the bounds from parity violation are to a good approximation independent of β (for β = O(θc)) the bounds from kaon and D decays depend on it. We consider the two scenarios β = θc or β = 0. In the first case, the kaon limits arise for LQ representations with left-handed quark fields while in the second case these limits are absent but bounds from D 0 −D 0 arise.