A new purpose for the $W$-boson mass measurement: searching for New Physics in lepton+$MET$

We show that the $m_W$ measurement is a direct probe of New Physics (NP) contributing to lepton and missing transverse momentum ($\ell+MET$), independently from indirect tests via the electroweak fit. Such NP modifies the kinematic distributions used to extract $m_W$, necessitating a simultaneous fit to $m_W$ and NP. This effect can in principle bias the $m_W$ measurement, but only to a limited extent for our considered models. Given that, we demonstrate that the agreement at high-precision with SM-predicted shapes results in bounds competitive to, if not exceeding, existing ones for two examples: anomalous $W$ decay involving a $L_{\mu} - L_{\tau}$ gauge boson and $\tilde{\nu}_{l} \tilde{l}$ production in the MSSM.


I. INTRODUCTION
The mass of the W boson plays a crucial role in our understanding of nature.The discrepancy between the recent and most precise measurement by CDF [1] and the SM prediction might already be a hint of new physics (NP) beyond the Standard Model (BSM).Theoretical explanations commonly invoke new contributions to the electroweak (EW) fit [2] in order to shift the value of the SM prediction (see for instance [3,4]) and explain the anomaly.Yet, the more recent re-measurement by ATLAS [5,6] adds to the puzzle, confirming the SM-predicted value and the previous measurements by LHCb, D∅ and LEP [7][8][9].Whether in the future the CDF anomaly will be confirmed cannot be foreseen.The only fact that we have today is the striking precision of 10 −4 of these measurements and of the corresponding theory SM predictions.This precision might even improve in the near future due to an ongoing intense experimental [5,10] and theoretical effort (see e.g.Refs.[11][12][13][14][15][16][17] for recent works).
The m W experimental value is extracted from the simultaneous fit of different measured kinematic distributions (see below) in leptonic decays of singly-produced W -bosons to the SM predictions.Both ATLAS and CDF find perfect agreement with their best-fit SM distributions.
We show in this letter that the data used for the m W measurement can simultaneously be a powerful direct probe for any NP that contributes to the same final state.
The key observation is that NP produces kinematic distributions that are sufficiently different with respect to those in the SM.Hence, the same analysis can be used for the extraction of both m W and NP parameters.The correct procedure thus requires a global fit, which might in principle shift the measurement of m W , with NP providing new nuisance parameters.
This paradigm is general, having already been attempted in [18][19][20][21][22][23][24] for the top quark, in the context of NP copiously produced via strong interactions.Fainter signals of NP charged only under the electroweak interaction are more challenging.Yet we will show how the extraordinary precision of the m W measurement can put competitive bounds on motivated new physics scenarios, and in some cases to exceed present bounds, e.g.those for long-sought SUSY sleptons.This strategy is in addition to the classic test based on EW fit of the SM to which we are accustomed since LEP [25].In this letter, we focus solely on the m W measurement.We classify the possible NP that can contaminate the measured sample and quantify the sensitivity to two concrete, well-known BSM scenarios (see Fig. 1).All the lines include detector simulations.Pileup (⟨µ⟩ = 50), simulated through the dedicated Delphes ATLAS card, is included unless indicated otherwise.In the SUSY projections, we include the no pileup (⟨µ⟩ = 0) lines only for the competitive run-2 projections.Present bounds are obtained from [26] and [27] respectively for the left and right figure.

II. INVISIBLE NEW PHYSICS BEHIND THE SEMI-INVISIBLE W-BOSON
The W -boson mass measurement is special.The remarkable precision, reached by hadron colliders, relies only on the partially visible leptonic decays.The masses of other heavy SM bosons are instead extracted from fully visible and clean final states (e.g., h → γγ, Z → ℓ + ℓ − ), hence resonance reconstruction is possible in a narrow region.For hadronic W -boson decays, resonance reconstruction is plagued by the challenges of QCD observables.The semi-invisible final state of leptonic W -decays, namely ℓ + MET, is cleaner, but it presents a good hideout for invisible NP.
Given that the W -boson decay cannot be fully reconstructed, the measurement of the m W is a result of the fit to the lepton p ℓ T and the transverse mass m T distributions. 1 Hence, any BSM that contributes to the same final state, modifying these kinematic distributions, can affect the m W measurement.Such NP can be classified in three possibilities:  The first (second) possibility includes all BSM models that modify the W -boson decay (production), yet resulting in ℓ + MET.Option (C) collects all BSM models that can produce an ℓ + MET final state, without the involvement of any on-shell W -boson.This category includes the production of new particles, decaying into ℓ + MET, and new interactions among quark/gluons and leptons. 2ere we explore two simple, yet relevant, case studies that cover options (A) and (C).In Sec.III, we focus on anomalous W -boson decay in the invisibly-decaying L µ − L τ gauge boson scenario (Fig. 1 left).This represents a proof-of-principle of our idea, highlighting the relevant points with rather simple phenomenology.Nevertheless, we find that the m W measurement represents a competitive probe for this model (see Fig. 2a).In Sec.IV we focus on category (C), using ν l production in SUSY as an example.This production mechanism is not currently investigated at the LHC.Remarkably, our results in Fig. 2b show that the m W measurement can cover an unexplored parameter space of slepton searches.
In a follow-up paper [31], we will study additional examples of category (A) and an illustration of category (B): a Z ′ -boson gauging baryon number (see [32] and references therein).Overall, our two papers thus represent a comprehensive study of probing NP giving ℓ + MET using m W analysis.Ref. [33] studied a specific example of category (B) only.Moreover, in the following, we describe a more general approach than Ref. [33] for the associated analyses.

III. A PROOF-OF-PRINCIPLE: Lµ − Lτ GAUGE BOSON
The first model that we consider is the L µ −L τ Z ′ [34]: where g Z ′ and g D are the couplings of Z ′ -boson to SM and dark-sector states, respectively.The U (1) Lµ−Lτ current reads The term Z ′ ρ J ρ D describes the interaction of the Z ′ -boson with some invisible, unspecified dark-sector states.The key assumptions, that g D ≫ g Z ′ and the dark sector contains states sufficiently lighter than m Z ′ , guarantee that the Z ′ -boson decays predominantly invisibly.
The 3-body decay (versus 2-body) softens the p T and m T distributions, as seen in Fig. 3 for a benchmark value of (m Z ′ , g Z ′ ) = (10 GeV, 0.12). 5s shown in Fig. 3, for g Z ′ ∼ O(0.1), the expected S/B ratio is O(10 −3 ).Sensitivity to these effects strongly relies on the various sources of uncertainties, which is exactly the main target for the experimental collaborations that reached percent [1] and even sub-percent uncertainties [5,6], aimed at measuring m W . Also backgrounds are extensively studied and they are only a few% in the region of interest.In this letter we will not attempt a complete study of the various sources of uncertainties in the presence of NP.We just comment on the possible effect of our NP hypothesis on the sample of Z → ℓℓ events which are heavily used for detector calibration [1,6] and for tuning the boson production model on data [15].Thus a contamination of NP in the Z → ℓℓ sample might affect the calibration of the MCs, "calibrating away" signs of NP [42].However, by isolating pure Z-boson events with appropriate kinematic cuts, such as those imposed by ATLAS [6]: 80 < m ℓℓ /GeV < 100, the possible contamination of NP in the calibration sample is limited to O(10 −4 ), still for g Z ′ ∼ O(0.1).
We estimate the sensitivity and the impact of our NP hypothesis on the m W measurement through a binned χ 2 analysis for the p ℓ T and m T distributions.Our analysis is aligned as much as possible with the ATLAS measurement [5,6], only slightly extending the fit range aiming at maximal sensitivity (see Tab. I).We then construct the following χ 2 : where N i ev (∆ m W , ∆ NP ) is the expected number of events in the the bin i as function of m W (∆ m W = m W − m W ) and the NP parameters.We centered our χ 2 at ∆ NP = 0 and ∆ m W = 0 because we are assuming data to realize the SM expectation for the W-boson mass m W .We stress that we are testing the New Physics hypothesis with no prior on m W , as both ∆ NP and m W are floated.
On the contrary, the authors of [33] fixed m W in the hypothesis to the EW fit prediction.The simultaneous fit to m W and NP that we perform here is thus a more general test of NP and has the added value to be independent of the EW fit results and the assumptions therein.
The qualitatively new aspect of ∆ m W being a floated parameter in Eq. ( 3) implies that with the same analysis we extract m W and test NP.The 2-dimensional fit in the (∆ m W , ∆ NP ) is reported in Fig. 4 for m Z ′ = 10 GeV.By assuming 0.5% per-bin uncorrelated systematics and including the effect of pileup through Delphes, the ATLAS measured uncertainty is roughly reproduced. 6 Pileup has an impact on the m T distribution and on the resulting m W sensitivity.The p ℓ T distribution, on the contrary, is largely insensitive to pileup, hence we use it to draw more firm conclusions on features of our 2D-fit.
The systematics on the kinematic distributions shown in [5] are below 0.5%.Therefore, we also consider per-bin systematics of 0.1%.The expected sensitivity to m W (at zero g Z ′ ) is slightly stronger than the current ATLAS 7 TeV L = 4.6 fb −1 measurement [5].This is mainly because we are not including any source of correlated systematics, and we are assuming much larger statistics from a 13 TeV run with L = 300 fb −1 .
The distortion of the p ℓ T exclusion line (blue) at large values of g Z ′ implies a preference towards positive ∆ m W .This suggests that NP might in principle impact the sensitivity to m W , possibly producing a shift in the extracted value and/or affecting the estimate of the associated uncertainty on m W . Yet, the effect shown in Fig. 4 is limited to only ∼ 10 MeV.However, a quantitative assessment of this effect requires the inclusion of the proper experimental setup and is beyond the scope of this letter.The sensitivity to g Z ′ at ∆ m W = 0 is only marginally affected by pileup, showing the robustness of the sensitivity to NP.
For completeness, we report in Fig. 5a in the supplemental material an analogous study for CDF [1].In this case, the effect of the NP in the m W determination is less pronounced, due to a sharper Jacobian peak related to the better control of the hadronic activity at CDF which anchors the m W fit more robustly.
We now turn to the test of the NP hypothesis.Assuming no prior knowledge on m W , the correct procedure to put bounds on NP is to marginalize on ∆m W for each value of the NP parameters.This is shown in Fig. 2a for LHC (L = 300 fb −1 ) sensitivity projection.Prior knowledge on m W (either from other measurements or from theory predictions) might impact the sensitivity to NP, as shown in Fig. 4.
For this analysis, positively and negatively chargedmuon events are added together, and χ 2 for p ℓ T and m T are combined without correlation.Here, the sensitivity projections for CDF are also reported.The reach for m Z ′ ≃ 10 GeV is competitive with the best probe for this model from a dedicated experiment (CCFR) [26,43].Yet, it is remarkable that for a 10 GeV Z ′ -boson, the 6 The average number of pileup events per bunch crossing is ⟨µ⟩ = 50.m W measurement has the power to probe couplings ∼ f ew × 0.01, provided sufficient control of the systematics.Interestingly, less constrained models such as the "neutrinophilic scalar" of [44] or the "Dirac neutrino portal" [45] fall in category (A).For the neutrinophilic scalar, we expect the m W measurement to be the best probe [31].

IV. MSSM: SLEPTON-SNEUTRINO PRODUCTION
We now turn to the minimal supersymmetric standard model (MSSM) [46], which offers a simple irreducible "background" for the m W measurement: "left-handed" SU (2) L doublet slepton-sneutrino production, with subsequent decay into lepton plus only invisible particles (see Fig. 1 In this scenario, both the sneutrino and neutralino are invisible, and either one could be the lightest stable particle (LSP). 7For simplicity, we assume that the other superpartners, including SU (2) L singlet -or right-handed sleptons -are heavy, thus having negligible cross-sections at the LHC.Sleptons lighter than 100 GeV are excluded by LEP [47][48][49][50][51]. Sleptons heavier than the LEP bound have negligible cross-section at the Tevatron so we do not consider 7 When the lightest neutralino χ0 1 is the LSP, l → ℓ χ0 1 , and ν → ν χ0 1 , as illustrated in Fig. 1, produces the ℓ + MET final state.If the sneutrino is the LSP (not shown), then χ0 1 → ν ν also maintains the ℓ + MET final state.
CDF in this section.LHC searches for di-sleptons [27,52] are sensitive to sleptons above the LEP bounds but suffer when the sleptons and χ0 are close by in mass.In particular, when the mass gap m l−m χ0 ∼ m W , the lepton p T resembles that of the lepton from SM W -boson decay.This compressed region of parameter space is dominated by SM events and requires a dedicated analysis.In [53,54] it has been proposed to use precision measurements to disentangle W W events from di-slepton production.Yet, there is still some uncovered gap in the parameter space in the experimental results (see our summary of present constraints in Fig. 2b).Addressing this shortcoming of the present searches by filling this gap is a main result of this letter.
The phenomenology of the process in eq. ( 4) belongs to category (C), since no on-shell W -boson is produced (see Fig. 1).As shown in Fig. 3, NP produces a rather flat and extended m T distribution with a rising S/B ratio at "high-m T ", since the process is not initiated by the decay of a resonance.The contamination in the Z-boson sample due to pp → ll → lℓ χ0 χ0 is limited to O(10 −5 ).
For this model, we follow the same procedure as in Sec.III of marginalizing on ∆ m W for varying NP parameters.For each point on the m l − m χ0 1 plane, m W is varied as an input in the template, and the minimum χ 2 is obtained from the fit.The m W determination is largely governed by the peak positions of p ℓ T and m T spectra.Therefore, the rather flat kinematic distributions of NP contributions make a milder impact on the m W measurement than what is shown in Fig. 4. Sensitivity projections are reported in Fig. 2b as functions of (m l, m χ0 ).The sneutrino mass is fixed at the lowest allowed value in the MSSM, assuming the large tan β limit [46].
Two sets of expected sensitivities are reported in Fig. 2b, corresponding to the inclusion or not of pileup.In both cases, the fitting range (see Tab. I) is chosen to cover part of the unexplored parameter space.Extending the range to "high-m T ", still keeping sufficient control of the systematics, might improve the sensitivity, as shown in Fig. 3.However, far from the "m W " region, systematics becomes more challenging.This is caused, for instance, by the limited Z-boson sample available for calibrations, or by the increasing backgrounds.The study of systematics outside of the range presently used for each kinematic distribution employed in the m W measurement can only be carried out by the experimental collaborations.Here we are pointing out the huge gain in sensitivity to NP that can be obtained by enlarging the fitting range.Ideally ATLAS and CMS experiments will find the best range of each kinematic variable for which the experiment can keep systematics under control so as to maximize the sensitivity to NP.
A major result of ours is that the same analysis used for the m W measurement, with only a slightly extended fitting range, can put new bounds and potentially discover new physics in an unexplored parameter space of MSSM.
ATLAS [5,6]  Table I: Kinematic range considered for our fit.⃗ u T is the hadronic recoil vector.The range with * is considered when we include no pileup effects.We construct bins of 2 GeV for m T and 1 GeV for p ℓ T [5].

V. CONCLUSION
New physics resulting in ℓ + MET is an irreducible "background" for the m W measurement.The kinematic distributions arising from NP do not match those of the SM W -boson.Consequently, a simultaneous fit to NP parameters and m W is required to capture this contamination of NP.This more general procedure also tests the robustness of the extraction of m W .
Concerning the sensitivity to NP, the inclusion of possible NP worsens the goodness of the fit of the data to (pure) SM template.This results in strong bounds on the NP hypothesis.Yet, given the underlying uncertainties, the distributions contaminated by NP can also modify the extracted value of m W (Fig. 4).
In this letter, we followed this path through two examples: anomalous W -boson decay via an invisible L µ − L τ Z ′ -boson and slepton-sneutrino production in the MSSM.We find that the LHC, provided sufficient control of the systematics, is potentially sensitive to an uncovered parameter space of the MSSM and provides a competitive probe for the L µ − L τ Z ′ -boson, as shown in Fig. 2. A faithful assessment of this effect requires precise simulations of the experimental environment.
The paradigm that we follow in this letter is general and applies to all NP scenarios producing ℓ + MET, pinpointed in Sec.II.This is postponed to a future publication [31].

Figure 2 :
Figure2: LHC 95% CL projected sensitivity to (a) L µ − L τ and (b) MSSM slepton-sneutrino production.All the lines include detector simulations.Pileup (⟨µ⟩ = 50), simulated through the dedicated Delphes ATLAS card, is included unless indicated otherwise.In the SUSY projections, we include the no pileup (⟨µ⟩ = 0) lines only for the competitive run-2 projections.Present bounds are obtained from[26] and[27] respectively for the left and right figure.

1
CDF also fits the missing transverse momentum p miss T distribution.

Figure 3 :
Figure 3: Normalized transverse mass distributions for µ + MET at the LHC.Blue line: m Z ′ = 10 GeV, g Z ′ = 0.12).Red line: m μ = 115 GeV, m ν = 83 GeV, m χ0 1 = 70 GeV.The dashed lines in the lower panel are obtained from selected Z events.The dashed gray lines indicate the ATLAS fitting range.

DOEFigure 5 :
Figure 5: (a) 2D fit with 68% CL projected sensitivity to L µ − L τ for m Z ′ = 10 GeV and (b) 95% CL projected sensitivity to L µ − L τ combining p ℓ T , p miss T , and m T at CDF.The solid lines and dashed lines represent the results when detector effects are included and when they are not included, respectively.