Associated Z ′ production in the flavorful U ( 1 ) scenario for R K ( ∗ )

The flavorful Z ′ model with its couplings restricted to the left-handed second generation leptons and third generation quarks can potentially resolve the observed anomalies in RK and RK∗ . After examining the current limits on this model from various low-energy processes, we probe this scenario at 14 TeV high-luminosity run of the LHC using two complementary channels: one governed by the coupling of Z ′ to b-quarks and the other to muons. We also discuss the implications of the latest LHC high mass resonance searches in the dimuon channel on the model parameter space of our interest. ∗tpsd5@iacs.res.in †adam.falkowski@th.u-psud.fr ‡tpdkg@iacs.res.in §tpng@iacs.res.in 1 ar X iv :1 90 8. 03 03 1v 1 [ he pph ] 8 A ug 2 01 9


Introduction
In the last few years, the LHCb collaboration has reported a number of deviations from µ-e universality in B-meson processes. In particular, the ratios of µ + µ − to e + e − final states in B → K ( * ) + − decays: R K [1] and R K * [2] are observed to be smaller than one, each displaying a ∼ 2.5σ deviation from lepton-flavor universality predicted by the Standard Model (SM). Recent global analyses [3][4][5][6][7], which also take into account other b → s + − mediated processes, conclude that the SM is disfavored by the current experimental data with a confidence level exceeding 5σ.
The global fit can be significantly improved if the effective Lagrangian below the weak scale contains new contributions to the 4-fermion operator (b L γ ρ s L )(μ L γ ρ µ L ), in addition to the ones generated by the exchange of SM particles in loops. One option to arrange for these contributions is to assume that the high-energy theory contains a new electrically neutral vector particle Z coupled to muons and, in a flavor-violating way, to bottom and strange quarks. In this scenario, the 4-fermion operator in question can arise from tree-level Z exchange. There is already a vast literature discussing Z models explaining the b → s anomalies, see e.g. . A generic feature of these model is that the Z is within the kinematic reach of the LHC and thus can be searched for directly. In particular, these models always predict a non-zero cross section for the quarklevel process b(b)s(s) → Z → µµ, which leads to the dimuon resonance signature at the LHC. Furthermore, in some models the Z coupling to bs is correlated with couplings to other quarks, which opens further production channels at the LHC [27,32].
The goal of this paper is to study new LHC signatures of the Z boson responsible for the b → s anomalies. We consider the model described in Ref. [37] where Z , in addition to the coupling to muons, also possesses a sizable coupling to bb. This model predicts several new signatures where Z is produced in association with some SM particles. We focus on two such signatures, which we find especially promising: • pp → Z + 1b(2b) → µ + µ − + 1b(2b), • pp → Z µ ± + E T → 3µ + E T .
For these two processes we study the discovery prospects at the LHC run 3 and the subsequent high-luminosity phase (HL-LHC). We show that the above signature can be observed with the significance exceeding 5σ in the parameter space of the Z model favored by the b → s anomalies and consistent with all other experimental constraints. The information obtained by studying these two processes is complementary to that conveyed by generic dimuon resonance searches, and will be crucial for the identification of the microscopic model responsible for the b → s anomalies.
In what follows, in Section 2 we discuss the model and list the range of couplings of the Z to muons and b-quarks allowed by low-energy precision measurements. In Section 3 we present a detailed analysis of LHC prospects of discovering the Z in two complementary channels where the Z is produced in association with SM particles. The production rate of Z in the two channels is governed by its coupling either to b-quarks or to muons and thus they can potentially probe different regions of the allowed parameter space dominated by either of the two couplings. In Section 4 we compare the sensitivity of these associated Z production searches with that of the generic dimuon resonance searches.. Finally, we summarise and conclude in Section 5.

The model
We consider a massive spin-1 boson Z with coupling to quarks and leptons that can address the R K and R * K anomalies. We work with the setup described in Ref. [37], however in this paper we assume that only the Z boson can be produced at the energy scale available at the LHC. The relevant BSM interactions pertaining to our collider analysis are encoded in the following Lagrangian: The Z couplings g µµ , g bb , and g bs to muons, s-and b-quarks are in principle free parameters. However, in the setup of [37] in the absence of fine-tuning one expects |g bs | ∼ |V ts g bb |, where |V ts | ≈ 0.04 is the 3-2 entry of the CKM matrix. In the following for simplicity we assume g bs = V ts g bb , and that g bb and g µµ have the same sign. Thus, the parameter space in our analysis is 3-dimensional, and consists of the 2 couplings g bb , g µµ and the Z mass M Z . Integrating out the Z boson generates four-fermion contact interactions in the effective theory below the scale M Z . In particular, a new contribution to the effective interaction (b L γ ρ s L )(μ L γ ρ µ L ) is generated, adding to the SM contribution induced at the loop level. This is the scenario with C NP 9µ = −C NP 10µ , using the standard notation of flavor physics. Such a pattern of new physics corrections provides a very good fit to the measured R K , R * K , and other b → sµµ observables [3][4][5][6][7]. The best fit of Ref. [5], C NP 9µ = −C NP 10µ = −0.53 ± 0.09, translates into the following constraint on our parameters: g bb g µµ M 2 Z = 1.00 ± 0.17 (6.9 TeV) 2 @ 68% CL. (2.2) In the following of this analysis we will assume that the values of the parameters correspond to this best fit within 1σ uncertainty. There are further low-energy constraints on these parameters. One is due to four-lepton interactions generated by integrating out Z , which are constrained by the trident muon production in neutrino scattering [44][45][46]. Using the global fit of Ref. [47] one finds Another combination of the model parameters is probed thanks to the Z contribution to the ∆F = 2 operator (b L γ µ s L ) 2 , which affects the B s meson mass difference. The analysis in Ref. [48] translates into the constraint  Figure 1: The parameter space in the (g µµ , g bs ) plane for M Z = 200 GeV preferred at 68% CL by the b → s + − anomalies (parabolic green band), compared to the regions excluded at 99% CL. by trident neutrino production (vertical orange band), and B → D * ν (horizontal blue band).
An example of the parameter space is shown in Figure 1 for M Z = 200 GeV. Clearly, fitting the b → sµµ anomalies together with the low-energy constraints discussed above leaves a finite interval for the Z coupling g µµ and g bb . The intervals g min µµ g µµ g max µµ and g min bb g bb g max bb allowed at 99% CL for the particular values of M Z used in our collider analysis are shown in Table 1.  Table 1: Intervals for the couplings g µµ and g bb consistent with explaining the b → s anomalies, and not excluded at 99% CL by the B → D * ν and trident constraints. We also show the 1σ confidence interval for the coupling g µµ obtained from the likelihood combining the above mentioned constraints.

Collider Analysis
In this section we discuss LHC signatures of a Z boson with a pattern of couplings to matter motivated by the b → sµµ anomalies, as given in Eq. (2.1). One signature, already discussed in several previous works [32,37], is the resonant dimuon production, pp → Z → µ + µ − . In this scenario, the Z is predominantly produced at the LHC via the bb fusion, with a subleading contribution from the bs andbs fusion, and it decays to a pair of muons with a branching fraction that is strongly dependent on the couplings g bb and g µµ . Another signature is pp → Z → 4µ [10,46,49], where the Z boson first decays to two muons, and then a Z (off-shell or on-shell, depending on its mass) is radiated off one of the muons. The goal of this paper is to explore alternative signatures of the Z boson at the LHC. We focus on the following two processes: The leading Feynman diagrams for these processes are shown in Figure 2 and 3. In the first process the Z boson is radiated off a b-quark, while in the second it is radiated off a muon or a neutrino. In both cases we study the situation where the Z decays to a muon pair. Consequently, the rate of the first process depends on both g bb and g µµ couplings, while in the second case it Figure 3: depends only on g µµ . Note that, following Eq. (2.2), the magnitude of g bb and g µµ is anti-correlated in our scenario. For this reason, the two processes target complementary regions of the parameter We implemented the interactions in Eq. (2.1) in FeynRules [50] so as to generate a Mad-Graph5 model file. We then generated both the signal as well as SM backgrounds events using MadGraph5 aMC@NLO [51] at the leading order (LO) and at the parton level. For the parton distribution function (PDF) we used the NN23LO1 implementation [52]. The parton level events are passed to PYTHIA 8 [53] for showering and hadronization. Finally, the showered events are passed through the detector level simulation using Delphes3 [54], with the jets reconstructed using the anti-k T jet algorithm [55]. In our analysis we ignore Z production proceeding via the Z -b-s coupling, which is suppressed due to the smallness of that coupling in our model, g bs /g bb ∼ |V ts | = O(10 −2 ).

pp
In this channel we consider the production of the Z boson in √ s = 14 TeV LHC in association with either one or two b-quarks, followed by the Z decay into a muon pair. The dominant background contributions for this signal arise from the SM processes pp → µ + µ − + jj, pp → tt → bbW + W − → bbµ + µ − ν µνµ and pp → µ + µ − + 1b(2b). Here j denote the light quark partons which can contribute to the background via being mistagged as b-jets. For the µ + µ − jj background the events are matched up to three jets using kt-MLM matching scheme [56,57]. To generate our signal and background events, we employ the following preselection cuts: After implementing these cuts, the dependence of the signal cross section on the coupling g µµ is shown in Figure 4 for M Z = 200, 500 and 1000 GeV. In our simulations, for a given g µµ and M Z , the value of g bb is fixed to the central value determined from Eq. (2.2). The upper and lower ends of each signal cross-section curve are due to the finite allowed range of the couplings g bb and g µµ as shown in Table 1.
We require the final state to be comprised of two oppositely charged muons and one or two b-tagged jets with p T (b) > 20 GeV. We also impose an electron veto in the final state. The We show the results for M Z =200, 500 and 1000 GeV at √ s =14 TeV. Each curve is plotted for the corresponding g µµ range taken from Table 1, which is determined by flavor and trident constraints.  [58]. To further optimize the signal selection cuts, we study the distributions of selected kinematic variables. First, we study the transverse momentum distributions of the two muons. In the signal events these two muons originate from the decay of a heavy Z , while for the standard model background, they originate from the Drell-Yan process, from the decay of t(t) in top pair production process. For the signal, we show the distributions for two representative mass points M Z = 200 GeV and 500 GeV. Since the muons in the signal come from the decay of a heavy Z , thus they are expected to have high transverse momentum. In comparison, the p T spectrum of muons for the SM background processes are expected to peak at relatively lower values. In Figure  5, the p T distributions of the leading (µ 1 ) and sub-leading (µ 2 ) muons are contrasted between the signal and the background. We find that cutting on p T (µ 1 ) > 90 GeV, and p T (µ 2 ) > 50 GeV allows us to efficiently discriminate the signal over the SM background.
We now construct the kinematic variable R defined as a ratio of the missing transverse energy For the signal, E T can come only from p T mismeasurement of muons and b-jets, whereas for the tt background, E T comes from the neutrinos in the leptonic decay of W ± . In Figure 6 we show the normalized distribution of R. For this reason, for the signal, R peaks at a lower value while for the tt background the distribution tends to peak at a higher value of R. We find that the cut R < 0.2 allows one to significantly reduce the tt background. Finally we require the invariant mass of the muon pair to be in the window around the Z peak as dictated by, where Γ Z is the width of the Z resonance. This cut is instrumental in further reducing the µ + µ − + 1b(2b) and µ + µ − + jj backgrounds as for these process the invariant mass of the muon pair peaks around the Z boson mass. The invariant mass distributions are depicted in Figure 7.
where S(B) are the number of signal (background) events after all the cuts. For calculating the significance, the signal and the backgrounds have been multiplied by respective k-factors to account for the next-to-leading-order (NLO) corrections. For the signal and µ + µ − + 1b(2b) backgrounds we use the k-factor of 1.38 [60], while for tt and µ + µ − jj backgrounds we use the k-factors of 1.40 [61] and 1.15 [62], respectively. Based on the results in Table 2, we can calculate the signal significance for two particular benchmark points, assuming the integrated luminosity of 300(3000) fb These benchmarks highlight the good prospect of observing the Z in this final state in the coming LHC runs. A broader set of results is shown in Figure 8, where the signal significance for several

Cross-section after cut (fb) Process
Preselection   representative values of M Z is plotted as a function of the coupling g µµ . One can see that the discovery potential in this final state is more more pronounced for lower g µµ (which correspons to higher g bb ). As expected, the discovery potential quickly diminishes with the increasing M Z . Nevertheless, a 5σ discovery is possible in this channel for M Z 500 GeV with 300 fb −1 luminosity at √ s = 14 TeV LHC, assuming the values of g µµ and g bb preferred by the b → sµµ anomalies and allowed by low-energy constraints. In the same conditions, a 3σ discovery is possible for M Z 1 TeV.

pp
We move to discussing another possible signature of the Z' particle: tri-muon plus missing energy final state. This final state in arises when the Z is radiated from µ ± or ν µ (ν µ ) leg in pp → W ± * → Z µ ± ν µ (ν µ ), followed by Z → µ + µ − decay. As stated earlier, in this case both production and decay of the Z is controlled by its coupling g µµ to the lepton sector. Thus this channel is best suited for probing the parameter space region with relatively higher values of g µµ . Similarly to the µ + µ − + 1b(2b) analysis in the previous subsection, we generate signal events in MadGraph with the following preselection cuts: ∆R jj,bb,b ,j > 0.4, R > 0.2, p T (j, b, ) > 10 GeV, |η j,b, | < 2.5. (3.5) In Figure 9 we show the dependence of the leading order signal cross section of the coupling g µµ after imposing the preselection cuts, for three representative values of M Z = 200, 300 and 500 GeV. For the final state in question we can have the following SM processes that contribute to the background: W Z + jets, ZZ + jets, W W +jets, tt, Z +jets. Out of these, W Z + jets and ZZ + jets are the irreducible backgrounds. tt can contribute to the background when each top quark decays leptonically: t → bν µ µ, and the third muon arises from the semileptonic decay of one of the b-quarks. Other sub-dominant contributions arise from ttV (V = W ± , Z) or W W Z, W ZZ channels [63].
To optimize our signal versus background discrimination, we demand our final state to be comprised of exactly three muons with two muons of the same sign and the third muon of the opposite sign along with missing energy ( E T ). We also impose a b-veto on the final state which This helps to exclude the background contribution where the opposite sign muon pair(s) arise from Z resonance. We also impose M 1,2 OSD > 12 GeV to suppress the Drell-Yan background [63]. With the above criteria, the dominantly surviving background contribution comes from W Z+jets.
In our analysis we assume that the Z mass is greater than the Z and W ± boson masses. Thus, the muons in the signal are expected to have higher p T than those coming from the decay of the Z or W ± bosons in the SM backgrounds. The comparative distributions of the transverse momenta of the the leading (µ 1 ), sub-leading (µ 2 ) and sub-sub-leading muons (µ 3 ) in the final state for the signal and backgrounds are shown in Figure 10. To enhance the signal over background ratio we impose the following cuts Finally, in Figure 11 we compare the E T distributions of signal and the W Z+jets background. The missing energy for the background comes from the leptonic decay of the W ± boson in W Z +jets or from mismeasurement of leptons or jets in the Drell-Yan process. As a result, the distribution of E T peaks at around half of the W ± mass for the background, whereas for the signal it is shifted towards higher values. In our analysis we impose the cut E T > 60 GeV which provides an optimal cut capturing the relatively long tail in the signal and avoiding the peak in the W Z+jets background.  Figure 10: Normalized transverse momentum (p T ) distributions of the leading (10a), sub-leading (10b) and sub-sub-leading (10c) muons for the 3µ + E T final state. Signal distributions are for M Z = 200 GeV, g µµ = 0.20, g bb = 4.2 × 10 −3 , and for M Z = 500 GeV, g µµ = 0.48, g bb = 1.10 × 10 −2 ). We also show the analogous distributions for the W Z background.
We summarize the above discussed cut flow in Table 3 for our two representative benchmark points. Given these results, we can calculate the signal significance for our 2 benchmark points, assuming the integrated luminosity of 300(3000) fb −1 : The projected significance for our analysis in the 3µ + E T channel as a function of the coupling g µµ is portrayed for M Z = 200(12a), 300(12b) and 500(12c) GeV in Figure 12. For the significance calculation signal and background have been scaled by k-factors of 1.25 [64] and 1.83 [65] respectively. Note that in this case, and unlike in the previously discussed µ + µ − + 1b(2b) channel,  Table 3: Effective cross-section at √ s =14 TeV for both signal and background for (3µ + E T / ) channel after each cut described in the next . The signal benchmarks correspond to the couplings g µµ = 0.20, g bb = 4.2×10 −3 for M Z = 200 GeV, and g µµ = 0.48, g bb = (1.10×10 −2 ) for M Z = 500 GeV.
the significance increases with increasing g µµ . This demonstrates the complementarity of the two final states discussed in this paper.

Comparison with dimuon searches
Our Z model leads to additional LHC signatures besides those studied in Sections 3.1 and 3.2. One is the 4 muon final state produced in the process pp → Z → 4µ where the Z boson decays to a muon pair and an on-shell or virtual Z is radiated off a muon and subsequently decays into pair of muons. This is however relevant only for fairly low Z' masses, 5 M Z 70 GeV [10,46,49], which are outside of our direct interest in this paper. For a heavier Z , the strongest constraints comes from dimuon resonance searches, pp → Z → µ − µ + [32,41]. In our scenario, Z is dominantly produced through its couplings to bottom quarks. Its branching fraction into muons depends on g µµ , g bb and M Z , and it is typically significant in the interesting parameter space of the model. Other than to muons, Z may also decay into top and bottom quarks and into neutrinos, however these channels are less competitive. In particular, we have verified that the constraints from dijet resonance searches at the LHC [66,67] are much weaker than those we obtain from the dimuon resonance searches. Figure 13 illustrates constraints on the parameter space of the model from dimuon reasonance searches. The blue band shows the range of g µµ excluded at 95% CL by the ATLAS analysis at 13 TeV with 139 fb −1 of data [68,69]. We show the exclusion region for M Z = 300 GeV and 500 GeV, assuming the coupling g bb is determined by the central value of the best fit to the b → s anomalies in Eq. (2.2). We can see that the regions with smaller g µµ (hence larger g bb ) are disfavored; in particular the region preferred by the global fit to low-energy data is excluded by the LHC. Nevertheless, an important chunk of the parameter space remains allowed at 2σ by all existing LHC and low-energy analyses. Those region will be probed in the future LHC runs.
Furthermore, from Figure 13 we learn that the dimuon and 2µ+b searches probe similar regions of the parameter space, and they exhibit a similar sensitivity. This is not an accident, as the two signals are closely related, and there is an overlap between the dimuon resonance and the 2µ + b signal regions. We note however that dimuon resonances are predicted by multiple new physics scenarios. Conversely, observing a signal in the 2µ + b channel would be a spectacular confirmation that the newly found resonance could explain the b → s anomalies.
On the other hand, in Figure 13 we observe that the 3µ + E T / process probes a complementary region of the parameter space compared to the 2µ+b channel or generic dimuon resonance searches. Combining information from all of these channels will allow one to completely exclude the parameter space of our model with M Z 500 GeV. Heavier Z resonances may escape discovery at the LHC in the parameter space preferred by the b → s anomalies. Significance (S) g µµ Figure 13: The parameter range of our model excluded at 95% CL by the ATLAS dimuon resonance search [68,69] at √ s =13 TeV with 139 fb −1 (light blue band) for M Z = 300 GeV (13a) and M Z = 500 GeV (13b). This is compared with the signal significance expected in the 2µ + 1b(2b) (red) and 3µ + E T / (blue) channels for the same collision energy and luminosity. The brown region is preferred at 1σ CL by combining the constraints from b → s anomalies, the neutrino trident production, and B → D ( * ) ν processes.

Summary and Conclusions
In this work we have analyzed the LHC discovery prospects of a new massive spin-1 particle (Z ) in a model explaining the b → s + − anomalies. We focused on the model proposed in Ref. [37] where tree-level exchange of the Z contributes to b → sµ + µ − processes, and can explain in particular the apparent violation of lepton flavor universality encoded in the R K ( * ) observables. In this model the Z has sizable couplings to left-handed bottom quarks and muons, as well as their SU (2) W partners. Therefore it can be produced on its own via bb fusion and decay into a muon pair, showing up at the LHC as a dimuon resonance. In addition, the Z can be produced in association with another SM particle when it is radiated off a bottom, top, muon, and neutrino legs. While the dimuon resonance signature has been previously studied in this context, the associated production is less explored. In this paper we identified two promising signatures of the associated Z production: pp → Z + 1(2)b with Z radiated of a bottom quark, and pp → Z µ ± + E T with Z radiated of a muon or a neutrino. In both cases we focused on Z decays to µ + µ − .
The interesting parameter space of our model can be succinctly characterized by two variables: the Z mass M Z , and its coupling to muons g µµ . The coupling to b-quarks g bb is approximately fixed by the previous two via Eq. (2.2) as a result of fitting the b → s + − anomalies. From Eq. (2.2) g bb and g µµ are anti-correlated. We find that the pp → Z + b channel is sensitive to lower values of g µµ ), as the Z production cross section is proportional g 2 bb . This feature is the same as for Z produced alone, and we find that these two production mechanisms offer a comparable sensitivity to the parameter space of the model. Conversely, pp → Z µ ± + E T is sensitive to larger g µµ ) as the Z production cross section is proportional g 2 µµ . Taken together, the two associated production channels offer a good and complementary sensitivity to a wide range of the parameter space explaining the b → s + − anomalies for 200 M Z 500 GeV.