Towards ruling out the charged Higgs interpretation of the RD∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{D^{\left(\ast \right)}} $$\end{document} anomaly

Motivated by the notorious anomaly in the lepton flavor universality ratios RD∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{D^{\left(\ast \right)}} $$\end{document}, we study the sensitivity of the Large Hadron Collider (LHC) to a low-mass charged Higgs boson H− lighter than 400 GeV in a generic two Higgs doublet model. A combination of current constraints from the Bc→ τν decay, Bs meson mixing data, tau sleptons and di-jet searches at the LHC allows to explain the RD∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{D^{\left(\ast \right)}} $$\end{document} anomaly at the 1σ level by a low-mass charged Higgs. In this context, we estimate the reach of an LHC search for resonant H− production, where the final state contains an energetic τ lepton decaying hadronically, a neutrino with large transverse momentum, and an additional b-jet (pp → b + τh + ν). Requiring the additional b-tagged jet in the τν resonance search profits from the suppression of the Standard Model background, and therefore it allows us to judge the low-mass H− interpretation of the RD∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_{D^{\left(\ast \right)}} $$\end{document} anomaly. To demonstrate this, we perform a fast collider simulation for the τν resonance search with an additional b-tagged jet, and find that most of the interesting parameter region of the whole mass range can already be probed with the current integrated luminosity of 139 fb−1.


Introduction
It has been almost a decade since the BaBar collaboration released the astonishing 4 σ discrepancy in the lepton universality ratios [1] R D ( * ) = BR(B → D ( * ) τ ν) BR(B → D ( * ) ν) , (1.1) where = e, µ. Since then tremendous progress has been made to reduce the theoretical and experimental uncertainties [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. On the experimental side, Belle and LHCb have joined the game and the R D ( * ) HFLAV world average [15] has moved towards the SM prediction and the uncertainties have been reduced considerably. In the meantime, on the theory side, the simple CLN parametrization [18] of the B → D ( * ) transition form factor has been shown to be insufficient [16,19] and the more general parametrization based on heavy-quark effective theory has been proposed up to O(Λ 2 QCD /m 2 c ) [16,17]. As a result, the current significance of the anomaly is about 4σ [16]. Furthermore, more modest but interesting deviations have been observed in the D * polarization data in B → D * τ ν, F D * L [20], and in B c → J/ψτν [21]. On the other hand, the LHCb collaboration recently reported R Λc =BR(Λ b → Λ c τ ν)/BR(Λ b → Λ c µν) that is below, albeit consistent with the SM prediction [22]. While a suppression of R Λc below its SM value would rule out a new physics (NP) origin of the R D ( * ) anomaly based on a model-independent sum rule [23,24], the experimental uncertainty in R Λc is still too large to draw a clear-cut conclusion.
In this paper we investigate the LHC sensitivity to the low-mass charged Higgs H − interpretation of the anomaly focusing on a specific channel: final states with an energetic JHEP06(2022)043 τ lepton that decays hadronically, large missing transverse momentum from an energetic neutrino, and an additional b-jet (pp → b+τ h +E miss T ). The model has widely been discussed in the literature [25][26][27][28][29][30][31][32][33][34][35], and recently been revisited in ref. [36] since the constraint from B c → τ ν is significantly relaxed [23,24,37]. The revision [36] found that a charged scalar can still explain the R D ( * ) anomaly within the 1 σ region when m H − ≤ 400 GeV holds. It is noted that the charged-Higgs scenario with larger mass is excluded by the τ ν resonance search at the LHC [38,39], 1 and the low-mass bottom flavored di-jet search [40,41] and a conventional search for tau sleptons [42] constrain the available parameter region. The result clearly shows the importance of the improvement in τ ν resonance searches [36], which is the main subject of this paper. From the results obtained in refs. [30,[43][44][45][46][47], one can infer that requiring an additional b-tagged jet is also effective in probing the low mass window. The reason is that the additional b-jet reduces the number of SM-originated background (SM BG) events and thereby improves the signal to BG ratio. However this technique has not yet been used in the experimental analyses. In this paper, we will thus employ this technique and quantify its impact on the LHC sensitivity to a low-mass charged Higgs boson.
The rest of the paper is structured as follows. A simplified H − model and its relevant parameters are introduced in section 2. We propose an LHC search strategy for the bτ ν signature in section 3 including the relevant kinematic cuts, and describe our method in generating signal and background events. The resulting collider prospects and their impact on the H − interpretation of the R D ( * ) anomaly are discussed in section 4. Finally section 5 is devoted to the conclusions.

Model and parameters
We now introduce the simplified model for a charged scalar boson H − solving the R D ( * ) anomaly. Such a charged Higgs emerges from the second SU(2) doublet of a generic two Higgs doublet model (G2HDM), along with CP even and odd neutral scalars. In the model under consideration the additional Higgs doublet couples to all fermions, a setup which appears in many UV models, such as the left-right model [48][49][50][51][52][53][54][55][56][57][58] and even in the TeV scale Pati-Salam model to break the symmetry with a bi-doublet field [59,60]. In general such a coupling structure is dangerous since the additional neutral scalars possess flavor violating interactions at tree level. [61]. A detailed analysis of the model's flavor phenomenology can be found in refs. [26,30].
Following ref. [36], we introduce the simplified interaction Lagrangian for a charged scalar H − entering R D ( * ) as and we focus on the low-mass window

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which is currently not constrained by direct searches at colliders. By integrating out the heavy degrees of freedom, the low-energy effective Hamiltonian describing b → cτ ν transitions is given as with P L/R = (1∓γ 5 )/2 being the chirality projection operators. The first term corresponds to the SM contribution, stemming from a tree-level W − exchange. With the normalization fixed in eq. (2.3), we have and use V cb = 0.042 hereafter. In addition, we employ the numerical description of R D , R D * and BR(B c → τ ν) given in [23], 2 In this work we restrict ourselves to the scenario in which only the couplings y Q and y τ are nonzero. The Yukawa term y Q d H + (cP R b) is severely constrained by B s mixing mediated by the neutral scalars, thus it is difficult to significantly enhance R D ( * ) with this coupling. Other Yukawa-originated contributions to b → cτ ν receive a CKM suppression in the WC defined in eq. (2.3), and hence their impact on R D ( * ) is small. Phenomenologically our choice is a good approximation since other couplings are constrained when y Q and y τ are sizable. For instance additional Yukawa couplings to light leptons are stringently constrained by B c → eν and B c → µν, due to the even larger chirality enhancement factor. An additional top Yukawa coupling is constrained by B s mixing data and the heavy neutral Higgs search in a tauonic decay [63], see figure 13 of ref. [30]. Furthermore the decay H − →tb induced by the top Yukawa coupling is kinematically suppressed when m H − 200 GeV. Other quark Yukawa couplings especially to the light quark generations are dangerous since they contribute to heavy Higgs production and therefore have to be suppressed. Therefore we conclude that allowing only the couplings y Q and y τ to be nonzero is sufficient for the purpose of our analysis, since the presence of other couplings cannot significantly affect the bτ ν event number and it does not worsen the sensitivity.

Strategy
Currently experimental constraints on resonant H − production decaying to τ ν are available from LHC Run 2 for m H − ≥ 400 GeV [39] and m H − ≥ 500 GeV [64], and from LHC Run 1 for m H − ≥ 300 GeV [65]. These analyses originally searched for a W boson in a sequential standard model, looking for a single hadronically decaying τ lepton in association with missing transverse energy. The key kinematic variable discriminating the signal from the SM BG is the transverse mass, where ∆φ is the relative angle between the two momenta (0 ≤ ∆φ ≤ π), and the missing transverse momentum is expressed by p miss T with magnitude E miss T . τ h stands for the hadronic objects from the τ decay. The low m T region suffers from the huge SM BG which stems from the tail of the W boson. The latter is dominantly produced through It is worth noting that since u and d quarks can be valence quarks, there is a charge asymmetry in the number of W + /W − bosons produced. However the W resonance is not heavy, so that the sea quark contribution can be sizable, diluting the asymmetry. For a charged Higgs resonance with the coupling structure defined in eq. (2.1), the initial state does not involve the u, d valence quarks, and hence H + and H − are produced at equal rates. On the other hand in the present paper we are interested in the low-mass region, m H − ≤ 400 GeV, for which the sea quark contribution is more relevant. Furthermore, since we require an additional b-tagged jet, as discussed below, the main SM background processes are single-top and tt, so that the charge asymmetry of the SM background is expected to be much less pronounced. Consequently, for the sake of simplicity, we will not impose a selection cut based on the charge of the τ lepton.
We next argue how the requirement of an additional b-tagged jet in the final state can further improve the sensitivity of the charged Higgs searches. The importance of such a b-jet requirement was first realized in ref. [43], using a reference NP scale of m NP = 1 TeV.
Ref. [30] demonstrated the impact of the additional b-jet in a parton-level comparison performed within the G2HDM but fixing m H − = 500 GeV for simplicity. Including a fast detector simulation, ref. [44] showed that an additional flavor tagging is useful to search for low-mass W scenarios.
An additional b-tagging is effective to further reduce the SM BG to our H − resonance search, since the process is suppressed by the mis-tagging rate j→b to meet the b-tagging requirement. The btag requirement also serves to efficiently suppress the "fake τ " BG from QCD jets. As a JHEP06(2022)043 The signal cross-section in our model can be parameterized in terms of (m H − , y Q , y τ ) as follows: where σ 0 (m H − ) is a function of the charged Higgs mass only, while the y Q dependence has been factorized. Note that flavor physics constraints, e.g. from B meson mixings, preclude large y Q values, and thus the narrow width approximation is viable.

Event generation
Both NP signal and SM BG processes are simulated with Monte Carlo (MC) event generators at √ s = 13 TeV. Event samples generated using MadGraph5_aMC@NLO v3.2.0 [66] are interfaced with PYTHIA v8.3 [67] for hadronization and decay of the partons. NNPDF2.3 [68] in the five-flavor scheme is adopted and the MLM merging is used [69]. Detector effects are simulated based on Delphes v3.4 [70]. Jets are reconstructed using the anti-k T algorithm [71] with a radius parameter of R = 0.5.

Background simulation
The SM BG events are generated following the method explored in ref. [47]. Motivated by the previous phenomenological studies and experimental analyses, we consider five BG categories: W jj, Zjj, tt, single top, and V V (= W W, ZZ, W Z). More explicitly different from ref. [47], we combined Zjj with Z or γ (Drell-Yan) categories and renamed them as Zjj for simplicity. We generated 5M, 15M, 8M, 10M, and 3M events, respectively, for the five BG categories. A detailed process description is available in section 3.1 of ref. [47].
To study the sensitivity of the bτ ν search the following set of kinematic cuts is considered. We require exactly one b-tagged jet with p b T ≥ 30 GeV and |η b | < 2.5, and exactly JHEP06(2022)043 selection criteria one τ -tagged jet with the transverse momentum of τ h satisfying p τ h T ≥ 70 GeV, and the pseudo-rapidity of τ h , |η τ h | ≤ 2.1. We also impose the large missing transverse momentum condition, E miss T ≥ 80 GeV, to suppress the large W resonance contribution, and we reject events with isolated light leptons with p e,µ T ≥ 20 GeV within |η e | ≤ 2.5 or |η µ | ≤ 2.4. Furthermore, we restrict the number of light-flavored jets, N j ≤ 2 , to suppress the toporiginated backgrounds, where the jets satisfy p j T ≥ 20 GeV and |η j | ≤ 2.5. Then, to select the back-to-back configuration in which the missing momentum is balanced with the τtagged jet, we require ∆φ( Note that in order to focus on the low-mass resonance the p τ h T and E miss T thresholds are lowered compared to the selection cuts in ref. [47]. The above cuts are summarized in table 1.
An energetic τ lepton can also stem from the decay of an energetic hadron, however, it is likely to be accompanied by nearby jets and hence vetoed by τ isolation criteria. Therefore we do not consider BG events with τ whose parent particle is a meson or baryon. For the τ -tagging efficiency, the "VLoose" working point is adopted for the hadronic decays: τ →τ = 0.7 [72]. For the mis-tagging rates, we apply p j T -dependent efficiency based on ref. [72]. As a reference the mis-tagging rate c,b→τ is assumed to be 7.2×10 −4 . As for the b-tagging efficiencies, the following working point is applied based on table 4 of ref. [73], b→b = 0.6 , c→b = 1/27 , j→b = 1/1300 . The resulting m T distribution of the SM BG after applying the kinematic cuts described above is shown in figure 2 in the range 150 GeV≤ m T ≤450 GeV. Here we have chosen an m T binning with 20 GeV steps. This m T bin width is moderate as seen in ref. [64]. As seen from figure 2, single top gives the largest BG contribution for the whole m T region. This is mainly due to the cut on the number of light-flavored jets N j ≤ 2, which is not introduced in ref. [44]. The next-to-leading contribution comes from tt. The event distribution of the Zjj category appears statistically unstable even with 15M of simulated events. However, our statistical method which we explain in the next section suppresses the possible bias.

Signal simulation
Within the simplified H − model of section 2, we generate 100K signal events for the following set of H − masses, and allowing for up to two additional jets. In the event generation we set y Q = y τ = 1 and rescale the signal cross section based on eq. (3.4). The width-to-mass ratio of this working point is about 8%. This choice leads to a small dilution of the m T distribution, which could result in too conservative sensitivity estimates. The NP-SM interference is expected to be negligible due to the resonance nature of the signal and the smallness of the SM pp → bτ ν amplitude.

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The representative normalized signal m T distribution after imposing the kinematic cuts is shown in figure 3 for the various masses, as detailed in the plot. It is noted that the m T distribution for m H − = 200 GeV is similar to that of m H − = 180 GeV and thus not shown. The expected signal event numbers after imposing the above kinematic cuts, in the range 150 GeV ≤ m T ≤ 450 GeV, assuming 139 fb −1 , and fixing y Q = y τ = 1 with m H − = 180, 200, 250, 300, 350, and 400 GeV are 8.2 × 10 4 , 1.1 × 10 5 , 1.3 × 10 5 , 8.5 × 10 4 , 6.6 × 10 4 , and 4.7 × 10 4 , respectively. Interestingly, the number of signal events after imposing the kinematic cuts varies only mildly with increasing mass m H − , despite the steeply decreasing function σ 0 (m H − ). This is a direct consequence of the broader m T distribution. As a result, the sensitivity of the bτ ν search in the (y Q , y τ ) coupling plane depends only mildly on m H − , as we will see below.

Results
We now turn to the discussion of the results for the bτ ν search proposed in this paper. We first quantify the sensitivity of the bτ ν signal to a low-mass charged-Higgs boson, using the currently available 139 fb −1 of LHC data. We then discuss the implications for the charged-Higgs solution of the R D ( * ) anomaly.

Sensitivity of bτ ν search
In order to determine the sensitivity of the bτ ν signature to a low-mass charged Higgs, we follow the procedure in ref. [47]. To account for statistical uncertainties, we employ Poissonian statistics.
Based on the CMS analysis with 36 fb −1 of data [74], 30% of systematic uncertainty is assigned to the BG as a conservative estimate. In addition, to be conservative, we also assign a 30% systematic uncertainty to the signal, in order to account for PDF and scale uncertainties.
Based on the background-only hypothesis, the upper limit on the event number N 95% is calculated at 95% C.L. using the sum of the expected number of events in at least three m T bins in a row, N BG . This procedure suppresses the effect of the statistical fluctuations in the distribution of the Zjj BG category. We then subtract the BG event number in those bins, multiplied by a factor of 0.7, and obtain the maximum number of NP events, N NPmax (= N 95% −N BG ×0.7). Finally we deduce the NP sensitivity by comparing N NPmax and 0.7 × N NP , where N NP means the number of signal H − events in our simulation.
The resulting sensitivity assuming 139 fb −1 of data is shown in figure 4 by the black dashed line. The dotted line denotes the HL-LHC sensitivity, assuming that the significance S scales as S ∝ √ L, here L denotes the integrated luminosity. For the HL-LHC projection we assumed 3 ab −1 of data. We also show the various complementary experimental constraints following the color scheme in a previous paper [36].
We find that the sensitivity of the bτ ν signal almost covers the entire parameter region favored by the R D ( * ) anomaly. We also observe that it is easier to cover the heavier charged Higgs scenario: while the sensitivity of the bτ ν search in the (y Q , y τ ) plane depends only JHEP06(2022)043
R D ( * ) y Q × y τ all 1 , green(1σ) and yellow(2σ) [15] B c → τ ν y Q × y τ all 2 , light pink [37] B meson mixings y Q all 3 , light green [75] stau search y τ (y Q ) all 4 , red [42] 2b y Q (y τ ) m H − ≥ 325 GeV 5 , cyan [40] 2j y Q (y τ ) m H − ≤ 300 GeV 6 , blue [76] 2b + γ y Q (y τ ) m H − ≥ 225 GeV 7 , purple [41] τ ν (Run 1) y Q × y τ m H − ≥ 300 GeV 8 , orange [65] τ ν (Run 2) y Q × y τ m H − ≥ 400 GeV 9 , grey [39] bτ ν (Run 2) y Q × y τ all 10 , black -  mildly on m H − , larger masses require larger couplings to solve the R D ( * ) anomaly. According to eq. (3.4), we see that the signal cross section is maximized at |y Q | = √ 3|y τ | when the product of couplings is fixed. On the other hand, the cross section is minimized in the limit |y Q | |y τ | thanks to the color factor in the normalization of the H − → τ ν branching ratio. As a result, the sensitivity is best around |y Q | ∼ √ 3|y τ | and gets worse for |y Q | |y τ |. In the m H − = 180 GeV case, the combination with the existing low-mass di-jet search with 36 fb −1 of data and the bτ ν prospect with 139 fb −1 , corresponding to the moon symbol, is less constraining than the conservative bound from the B c → τ ν decay. However, once combined with the di-jet prospect for 139 fb −1 , corresponding to the sun symbol, we can test a broader parameter space. The HL-LHC reach denoted by the star symbol shows the great sensitivity and promising future of the bτ ν channel.
For all cases with m H − ≥ 200 GeV we find an increased sensitivity, which grows with larger charged Higgs mass. It is worth mentioning that the sensitivity of the bτ ν signature is better than the τ ν reach even for m H − ≥ 400 GeV.
For later convenience we define benchmark points in each figure which maximize the possible enhancement in R D ( * ) . The numerical values of the Yukawa couplings (y Q , y τ ) are listed in table 3.

Impact on the H − solution to the R D ( * ) anomaly
In figure 5, we project the sensitivity of the bτ ν search to the R D ( * ) plane. To this end we show the R D ( * ) predictions of the benchmark points defined in figure 4 and table 3 that were chosen to maximize the enhancement in R D ( * ) . Note that, in contrast to the LHC searches discussed above, the predictions for R D ( * ) are sensitive to the complex phases of the Yukawa JHEP06(2022)043   couplings. Therefore, by varying the complex phase, the benchmark points result in the predictions shown by the blue lines in the R D ( * ) plane. The red solid, dashed and dotted contours show the world average of the R D ( * ) data at 1, 2 and 3 σ. The SM prediction shown as a yellow star is taken from HFLAV2021 [77], and the horizontal magenta solid and dashed lines correspond to BR(B c → τ ν) = 63 and 30 %. The area above the lines is exluded by the respective bound. Note that the grey shaded region cannot be accessed within our model. From figure 5 it is obvious that the bτ ν signature provides a very powerful tool to test the low-mass charged Higgs interpretation of the R D ( * ) anomaly. For the entire charged-Higgs mass range, 139 fb −1 of data provide an excellent sensitivity and can cover most of the 1 σ range of the anomaly even for the most challenging case of m H − = 180 GeV. For heavier charged-Higgs bosons, e.g. m H − = 300 GeV, the currently available data can even cover most of the 2 σ region.
In passing we note that selecting events with negatively charged τ leptons could further improve the sensitivity, as discussed in section 3.1. Furthermore, to suppress the dominant single top-originated BG, rejecting events with a large-p T b-jet could be a good option. Finally we caution the reader that our evaluation is based on fast detector simulation, and further dedicated studies by the experimental collaborations are necessary to draw definite conclusions.

Conclusions
The current experimental data for the lepton-flavor universality ratios R D ( * ) may imply the existence of new physics in b → cτ ν transitions. Recently it was shown that a charged Higgs from a generic two Higgs doublet model can still explain the anomaly within 1σ when its mass is lighter than 400 GeV. Because of this low mass, it is expected that direct LHC searches can play an important role in testing this possibility, and the HL-LHC prospects have been assessed in a previous paper [36]. There it was observed that it is difficult to test the whole range of the interesting parameter region based on extrapolations of the existing experimental results.
A τ ν resonance search has been known to be a powerful tool to test the new physics effect in b → cτ ν, however, it suffers from large SM background in the low m T region. An additional b-tagging can suppress this BG and improve the sensitivity, however it has not JHEP06(2022)043 yet been performed by the experimental collaborations. In this paper we studied the sensitivity of the pp → bH ± → bτ ν signature to the low-mass region of the charged Higgs boson.
Our results show that most of the parameter region solving the R D ( * ) anomaly can already be tested with the currently available LHC data. If in a dedicated experimental bτ ν search no excess is found, a major step towards ruling out the charged-scalar interpretation of the R D ( * ) anomaly will be taken, favoring other new physics scenarios such as leptoquarks.