Constraints on neutrino non-standard interactions from LHC data with large missing transverse momentum

The possible non-standard interactions (NSIs) of neutrinos with matter plays important role in the global determination of neutrino properties. In our study we select various data sets from LHC measurements at 13 TeV with integrated luminosities of 35 ∼ 139 fb−1, including production of a single jet, photon, W/Z boson, or charged lepton accompanied with large missing transverse momentum. We derive constraints on neutral-current NSIs with quarks imposed by different data sets in a framework of either effective operators or simplified Z′ models. We use theoretical predictions of productions induced by NSIs at next-to-leading order in QCD matched with parton showering which stabilize the theory predictions and result in more robust constraints. In a simplified Z′ model we obtain a 95% CLs upper limit on the conventional NSI strength ϵ of 0.042 and 0.0028 for a Z′ mass of 0.2 and 2 TeV respectively. We also discuss possible improvements from future runs of LHC with higher luminosities.


Introduction
Confirmation on neutrino oscillation in recent decades requires non-vanishing neutrino masses. The effective operator with lowest dimensions that respects Standard Model(SM) gauge symmetry is the dimension-five Weinberg operator. This operator can give rise to neutrino masses, and can be achieved by different UV-complete models depending on the portal particle [1][2][3][4]. Many extensions of the SM such as Supersymmetry also introduce dimension-six operators of the form known as Charged-Current Non-Standard neutrino Interaction(CC NSI) and known as Neutral-Current NSI (NC NSI), that was first proposed by Wolfenstein in 1977 to explain the neutrino oscillation [5]. f f ,Y αβ and f,Y αβ define the strength of NSIs respectively, α, β ∈ {e, µ, τ }, f denote charged leptons or quarks and P Y is chiral projection operator(P L or P R ). CC NSI modifies the neutrino production and detection through its effect on processes such as muon decay and inverse beta decay [6][7][8]. From those processes severe bound can be obtained [9]. NC NSI plays an important role in neutrino oscillation experiments due to modification to the effective Hamiltonian, especially the matter potential [5,[10][11][12][13][14][15][16]. This produced by NSI at the LHC would leave large unbalanced transverse energy or momentum in detectors. The major irreducible SM backgrounds are from the decay of W and Z bosons to neutrinos. Meanwhile, an underlying theory model, however, is generally needed since in this scenario the validity of effective field theory (EFT) approach is no longer guaranteed. Simplified Z models with possible UV-completions have been considered [79][80][81][82][83][84][85]. And given that the mass of Z boson is much larger than momentum transfer at LHC, one can come back to the EFT case. It is noted that similar signals can be produced for various models with dark matters at the LHC. To discriminate these two sources, one can add the shape of distribution of missing energy to the data analysis [86]. Also, given consideration that neutrinos are produced along with charged leptons due to the SU (2) L doublet nature, data from multi-lepton channel can be complemented to give further discrimination [57,86].
In this paper, we focus on the aforementioned Z model and study constraints on NC NSI parameters based on various measurements at LHC 13 TeV with large missing transverse momentums in the final states. We considered data sets on production of mono-jet, mono-W/Z boson, mono-lepton and mono-photon recorded by both ATLAS and CMS collaborations. We conclude the CMS mono-jet data imposes the strongest constraints, and a flavor-blind bound of a few per mille has been obtained for Z mass around 2 TeV.
The rest of this paper is organized as follows. In Section 2, we discuss the model assumptions and the resultant constraints. In Section 3, we discuss the theoretical uncertainties. The LHC combination and projections are presented in Section 4, and we conclude in Section 5.

Model assumptions and constraints
Phenomenologies of neutrino non-standard interactions can span an energy range from MeV in neutrino oscillations to TeV at high energy colliders, or even higher in reaction of cosmic neutrinos. Simplified models or descriptions of NSIs are always adopted in various analyses and for easy comparison of constraints from different experiments. We outline the simplified models used in our study and then the constraints obtained with LHC data.

Theoretical setup
It is justified to express the NSI in a model-independent manner using the effective field theory framework in neutrino study at low energies, for example in study of neutrino oscillations. NC NSI between neutrino and matters can be described by dimension-six four fermion operators in the EFT framework as [5,87,88] where G F is the Fermi constant, αβ is the strength of NSIs, α, β denotes the lepton flavors {e, µ, τ }, and f can be either charged leptons or quarks. P Y can be P L or P R which are chiral projectors of left-handed and right-handed. In our study we focus on NSI between neutrinos and quarks of both up and down-type f = {u, d}. In general the above operators can be embedded into a gauge invariant operator from integrating out heavy degree of freedoms of new physics, Λ is the typical scale of the new physics models and c is the Wilson coefficient. The conventional NSI strength can be related to Λ as αβ = c/(2 √ 2G F Λ 2 ). Stringent limits on NSI exist due to various measurements on charged leptons at colliders once the interaction also involves charged leptons as in Eq. (2.2), for example see Ref. [57] for recent discussions.
At high energies, for instance at the LHC, effects of neutrino NSI may not be simply described by EFT operators since the momentum transfers can be sufficiently high to resolve further dynamics of the new physics. In this study we focus on a simplified model with NSI between neutrinos and quarks induced by s-channel exchange of a Z boson. This simplified model is more appropriate than the aforementioned EFT description at high energy regions. The effective Lagrangian of the interactions can be written as [62] where Z µ represents the force mediator with mass M Z . We assume the interactions are independent of quark generations, and only contain vector current for simplicity, namely At low energies or for a Z boson with sufficiently large mass the s-channel Z model can be matched onto the EFT representation defined in Eq. (2.1) with where the superscript V indicates a vector-current form on the matter side in Eq. (2.1). There are many new physics models on ultraviolet completion of neutrino NSI such as Zee Model [89] and One-Loop LQ Model [90,91]. In this study we utilize experimental measurements on signature with large missing transverse momentum at the LHC to constrain neutrino NSI. We select recent ATLAS and CMS data sets on production of mono-jet, mono-photon, mono-W/Z and mono-lepton. The representative Feynman diagrams of these processes as induced by neutrino NSI are shown in Fig. 1 for the Z model at tree level. We include the interference with SM production as well. At the LHC one will not be able to identify the flavor of neutrinos in the final states. We introduce u(d) ≡ α,β | u(d),V αβ | 2 summed over all neutrino flavors. It is understood that in case of Z model above couplings are constructed out from the couplings with Z as in Eq. (2.4). The NSI contributions to cross sections at LHC thus are directly sensitive to u(d) with which we set the constraint 1 . The LHC measurements on NSI are complementary to 1 In the actual calculation we assume only u(d),V ee are non-zero and derive the constraint. However, since the interference effects between NSI and SM interactions are small, one can translate the same constraint to u(d) as a good approximation.
those from neutrino oscillations in the sense that they probe absolute values of the couplings rather than differences of couplings of different flavors. We present constraints on NSI in both frameworks of EFT and simplified Z model. It is understood that the former one equals the later constraint with sufficiently large M Z . For MC simulation of the NSI signals we use a model file generated with FeynRule [92] similar to that used for dark matters with spin-1 mediator [73]. We generate signal samples with MG5 aMC@NLO [93] followed by parton showering and hadronizations with PYTHIA8 [94], and analyse the events with MadAnalysis5 [95]. We use CTEQ6M [96] PDFs in the simulation and use the default renormalization and factorization scale choices in MadGraph5, which is the sum of transverse energy of all final states divided by two. In this section we report results using leading-order calculations matched with parton showering and hadronization. We will discuss the impact of next-to-leading order (NLO) QCD corrections and theoretical uncertainties due to scale variation and choice of parton distribution functions later.

Data selection
We summarize the LHC data sets used in our study. They include recent measurements of mono-jet [97,98], mono-V [98,99], mono-photon[100, 101], and mono-lepton[102, 103] production from both ATLAS and CMS collaborations at LHC 13 TeV. The experimental analyses unfold the raw data to particle level with minimal selection cuts. The final measurements are presented in a model-independent form of upper limit on total cross section in different fiducial regions. That ensures a direct comparison to various new physics beyond the standard model which generates large missing transverse momentums. We reproduce the major selection cuts used in all analyses as below for completeness. In the following jets are clustered with anti-k T jet algorithm [104] and a distance parameter of D = 0.4 unless specified.
We start with measurements on hadronic final states recoiling against large missing energies. The mono-jet production has the largest rate among all processes considered. In the ATLAS analysis it requires a lower threshold on the missing transverse momentum of p miss T > 250 GeV. For the visible objects it requires a leading jet with p T > 250 GeV and |η| < 2.4, and a maximum of four jets with p T > 30 GeV and |η| < 2.8. Furthermore, the separation of each jet and the missing transverse momentum in azimuthal plane should satisfy ∆φ(j, p miss T ) > 0.4. The CMS analysis imposes the same lower threshold of p miss T > 250 GeV, and requires a leading jet with p T > 100 GeV and |η| < 2.4. The separation in azimuthal plane are ∆φ(j, p miss T ) > 0.5 for each of the first four leading jets with p T > 30 GeV. Unlike the ATLAS case no jet veto are applied in the CMS analysis. For the production of large missing energies with a single W/Z boson, and subsequent hadronic decays, both ATLAS and CMS collaborations use sophisticated technique of jet substructures to isolate the hadronic decaying W/Z bosons from backgrounds of QCD jets production. However, efficiencies of those selections are derived for specific models, and can be applied to deduce limits on cross sections of production of W/Z boson without decays. In this sense the minimum requirements are a lower threshold of 250 GeV for both the missing transverse momentum and the transverse momentum of the W/Z boson. The ATLAS analysis presents results for final state with W and Z boson separately while CMS analysis only shows results with W and Z boson combined.
In case of production of large missing energies with a W boson, and subsequent leptonic decays, that leads to the mono-lepton signatures. Indeed such final states are indistinguishable from those induced by production of a heavy W boson followed with leptonic decays. The principal variable used in both ATLAS and CMS analyses concerning mono-lepton signature is the transverse mass of the charged lepton and the missing transverse momentum, m T . The ATLAS analysis requires electron (muon) candidates to have |η| < 1.37 or 1.52 < |η| < 2.47 (|η| < 2.5) and p T > 65(55) GeV. The lower threshold on missing transverse momentum p miss T and the transverse mass m T are 65 GeV and 130 GeV respectively for electron final state, and 55 GeV and 110 GeV for muon. The CMS analysis requires electron (muon) candidates to have |η| < 1.44 or 1.56 < |η| < 2.47 (|η| < 2.4) and p T > 130(53) GeV. A lower limit of 150 GeV on missing transverse momentum is imposed. In the ATLAS mono-photon analysis it requires a leading photon with |η| < 1.37 or 1.52 < |η| < 2.37 and p γ T > 150 GeV, and ∆φ(γ, p miss T ) > 0.4. The CMS analysis requires a leading photon with p γ T > 175 GeV and |η| < 1.44. In addition the missing transverse momentum should satisfy p miss T > 170 GeV and p γ T /p miss T < 1.4. In all above analyses the measured cross sections are binned in the principal variables, which are p miss T , p γ T , and m T for mono-jet and mono-V , mono-photon, and mono-lepton, respectively. Each bin in the principal variable is also called an exclusive region. Besides, ATLAS and CMS also measure the cumulated cross sections from a lower threshold of the principal variable to almost the largest value allowed. Each of those selected kinematic range is called an inclusive region. We use the cross sections measured in inclusive regions to constrain the non-standard interactions in our analysis by default, and compare results to those obtained from exclusive regions if the latter is available. In Table. 1 we summarize further information on the LHC data sets used in our analysis. That includes the total luminosity corresponds to each measurement, the largest sensible values of the principal variable probed in each measurement, and a ranking on different measurements according to the constraint derived. The CMS mono-jet measurement sets the strongest constraint on the non-standard interactions, followed by the CMS mono-W/Z measurement, ATLAS mono-jet and mono-Z measurements.  Table 1: Summary of various information on data sets used in this study, including the principal variable used in each data set, its highest value probed, the total luminosity, and a ranking of different data sets.
We explain briefly the statistical procedure used to derive exclusion limit on the nonstandard interactions. We use the CLs [105] method together with the log-likelihood χ 2 as a function of the model parameters and the signal strength µ, for each data set and with i runs from all regions considered. For each region, N obs,i and N bg,i are the total number of events observed and predicted by the SM, δ sys,i is the total systematic error, and σ i ( , M Z ) represents the cross section predicted by the model of nonstandard interactions. L is the integrated luminosity. The χ 2 is a quadratic function of µ with coefficients A, B and χ 2 0 depending on model parameters M Z and . CLs upper limit on the NSI strength for fixed M Z at a confidence level 1-α is determined bŷ Φ is the cumulative distribution function of normal distribution. In case of using exclusive region/bin we can include all regions of the data set into χ 2 to derive the limit on if bin-bin experimental correlations are known. For using inclusive region, we can only include one of them at a time since different inclusive regions are statistically correlated. For a single inclusive region/bin, the CLs limit on the cross section induced by non-standard interactions can be simplified as with the maximum likelihood estimator and the uncertainty of σ given bŷ σ = (N obs − N bg )/L, ∆ σ = N obs + δ 2 sys /L. (2.8) In our analysis for each data set we scan over all the inclusive regions for the exclusive limit on and take the strongest one among them. We have verified explicitly with the CMS mono-jet measurement that the exclusion limit as derived from a scan on the inclusive regions is similar to that obtained using a χ 2 with all exclusive regions.

Constraints for effective operator
We first present results for case of using effective operator. In Fig. 2 we show the contour of 95% CLs upper limit on the plane of the NSI u and d , from all LHC data sets discussed earlier. We only include one representative result for mono-lepton from CMS for simplicity. The effective parton-parton center-of-mass energy is approximately 5 TeV for 13 TeV run of LHC. It indicates the new physics scale Λ in the effective operator approach should be larger than that to ensure its validity. Meanwhile, the Wilson coefficient c in Eq.(2.2) can not exceed a perturbative bound of 4π assuming it is induced by tree-level amplitude in a weakly coupled theory. That sets a boundary value of about 0.015 for the NSIs as shown by  Fig. 2. Outside the bounded region the effective operator approach is not valid at the LHC if one does not apply any cut on the center-ofmass energy of the scattering. Furthermore, for NSIs with left-handed quarks, to maintain the gauge invariance of SM SU (2) L symmetry one should set u = d . Otherwise it may lead to apparently too strong constraints on the NSIs in the direction of u = − d due to violation of gauge invariance [79], as can be seen for mono-W and mono-lepton production in Fig. 2. In the following we will focus on constraints along diagonal direction u = d = .
The CMS mono-jet measurement sets the strongest constraint of 0.011, followed by CMS mono-W/Z with constraints of 0.015, both within the perturbative region, and ATLAS mono-jet with constraints of 0.020. Measurements on mono-photon and monolepton production lead to much weaker constraints. The constraints are almost symmetric in the positive and negative directions due to the relatively smallness of interference effects with SM for the NSI strength probed. It is interesting that CMS measurements in general impose stronger constraints than ATLAS for the same final states due to the smaller systematic uncertainties of CMS.

Constraints for simplified Z model
We turn to the constraints for NSIs from simplified Z model. The production cross sections at the LHC depend on couplings of the Z boson to quarks, neutrinos, as well as on mass and width of the boson, M Z and Γ Z . Similar as before we would like to translate the constraints to the conventional NSI parameter u = d = defined in Eq. (2.4). For a fixed value of , one can still vary M Z and Γ Z for changes of cross sections at the LHC. We fix Γ Z /M Z = 0.1 and study the constraints on as a function of the mass of Z boson for simplicity. In Fig. 3 we summarize the constraints imposed by mono-jet and mono-V measurements from both ATLAS and CMS. We show the 95% CLs upper limits on the positive axis of . The limits on negative side of the axis are quite similar since the interference effects are small in general. For a certain choice of M Z the NSI can not be arbitrarily large otherwise the partial widths of Z decaying into neutrinos and quarks can easily saturate the assumed total width. That leads to a theoretical upper bound on the NSI as [62] where N is the number of massless quarks plus possible contributions from heavy quarks with mass below M Z /2. The parameter space in Fig. 3 with colors are thus excluded. The CMS measurement on mono-jet production again gives the strongest constraints, with an upper limit ranging from about 0.6 for a Z mass of 50 GeV to 0.0028 for a Z mass of 2 TeV. The constraints become weaker when M Z goes beyond 2 TeV since then the Z boson can hardly be produced directly. The ATLAS mono-jet measurement sets a limit of about two times larger than CMS. Our results on constraints from ATLAS monojet production agree well with that shown in Ref. [62]. The constraints from CMS mono-V measurement are weaker than those from ATLAS mono-jet except for very large M Z . The constraints from ATLAS mono-Z/W measurements are weaker than the theoretical bounds. Results shown in Fig. 3 can also be translated into constraints for different choices of Γ Z /M Z easily. For instance, if instead assuming Γ Z /M Z = 5%, constraints from all data sets will scale down by 1/ √ 2 since the cross sections are approximately proportional to 2 /Γ Z for not too heavy Z . Meanwhile, the theoretical bounds will scale down by a factor of 2 and are more closer to the experimental constraints.

Theoretical uncertainties
In this section we extend our results by using theoretical predictions calculated at next-toleading order in QCD. The NLO QCD corrections can be potentially large in tail region of various distributions, that have the strongest sensitivity to NSIs. We further study impact of theoretical uncertainties on the constraints to NSIs, including the scale variations and uncertainties due to parton distribution functions.

Next-to-leading order QCD corrections
The NLO calculations for various processes mentioned earlier can be carried out straightforwardly by generating the model file of NSIs at NLO in QCD with FeynRules [92] followed by simulation with MG5 aMC@NLO [93] and PYTHIA8 [94]. The impact of corrections to various distributions can be described by a K-factor defined as  and increase to about 50 (25)% slowly with M Z =100 GeV (1 TeV). The peculiar shape of K-factor in mono-jet plot with M Z = 100 GeV is partly due to the MC errors. In all cases uncertainties due to scale variations are dominant over PDF uncertainties. We observe a reduction of scale uncertainties for NLO predictions except for mono-W/Z production with M Z = 100 GeV where the scale variations at LO underestimate the genuine perturbative uncertainties. The total uncertainties increase with p miss T at both LO and NLO. For NLO predictions the relative total uncertainties range between 7∼11% for mono-jet production with two choices of masses, and between 4∼10% for mono-W/Z production.

Constraints at NLO
We are now ready to study impact of the NLO corrections and theoretical uncertainties on the derived limit of NSIs. The results are presented in Fig. 6 as a function of the mass of Z for constraint with CMS mono-jet and mono-W/Z production respectively. We derive four groups of 95% CLs upper limit on . They include the two using our nominal LO and NLO predictions on the cross sections. In the other two we use the LO predictions scaled to the lower side of the uncertainty band and similar for NLO predictions, which corresponds to conservative constraints on NSIs than those using nominal theory predictions. We plot all four constraints normalized to the one with nominal LO predictions as a function of M Z in Fig. 6.
For the case of CMS mono-jet production, the theoretical uncertainties weaken the limit by 10 ∼ 15% at LO across the full range of M Z . The NLO corrections increase the cross sections and thus lead to an improvement of 5 ∼ 10% on the constraints of NSIs. The theoretical uncertainties have less impact at NLO than at LO due to the stabilization of theory predictions at higher orders. In combination with NLO corrections and theory uncertainties the constraints on NSIs improve slightly as comparing to the nominal LO ones that we show in Sect. 2. For CMS mono-W/Z production, the theoretical uncertainties change the limit by less than 10% at LO and even smaller at NLO. The constraints on NSIs are improved by 10% in the full range of M Z when considering the NLO corrections together with theoretical uncertainties.

LHC combination and projections
We have shown that for individual measurement the strongest constraints on NSIs arise from CMS mono-jet production in both the EFT framework and the simplified Z model. It is worth to study the improvement once we combine constraints from several data sets, specifically the CMS mono-jet, CMS mono-W/Z, and ATLAS mono-jet measurements. For each value of the Z mass, we first identify the most sensitive inclusive region for each of the three measurements. We construct the total χ 2 function in Eq. (2.5) as a sum of the three individual χ 2 . The 95% CLs upper limit is then determined following the prescription outlined earlier. We neglect correlations between systematic errors of different measurements which are not available. The results are presented in Fig. 7 using the NLO predictions with theoretical uncertainties. For M Z below 1 TeV the combined limits are almost identical to those from CMS mono-jet alone since the latter are stronger by more than a factor of two than other data sets. The constraints are improved by about 10% for M Z greater than 1 TeV.  The LHC is expected to accumulate a total integrated luminosity of 3000 fb −1 for the high luminosity run. The constraints on NSIs can benefit from the high statistics of various measurements. We calculate the projections for constraints on NSIs with mono-jet and mono-W/Z measurements at LHC with higher luminosities. We rescale the number of SM background events from current values with luminosities and set the number of observed events to be the same as the SM backgrounds. We assume the relative size of systematic uncertainties remain the same though one may expect certain improvements from both experimental and theoretical sides. In Fig. 8 we plot the expected upper limit on the NSIs as a function of M Z for an integrated luminosity of 300 fb −1 . The increase of statistics improves the constraints as from CMS mono-W/Z production while has less impact on mono-jet production since the measurements are already dominated by systematic uncertainties. It is interesting to find the constraints from CMS mono-W/Z measurement become as good as those from CMS mono-jet measurement for M Z > 2 TeV. We summarize the limits on in Table. 2 for several choices of the mass of Z and different measurements. It is understood that the case with M Z = 100 TeV is equivalent to that using the EFT approach. The current best limit is 0.0028 for M Z = 2 TeV with combination of the three measurements. We expect reducing the limit to 0.0025 with 300 fb −1 data at the LHC. We note that all limits presented so far are for the choice of Z width Γ Z /M Z ≡ r=0.1. As mentioned earlier the constraints on scale as √ r approximately. Thus for r = 0.05 the current best limit would be 0.0020. We also calculate the projections for HL-LHC with a luminosity of 3000 fb −1 , and only find improvements of a few percents for the limits on NSIs in the full range of M Z considered. However, in future measurements with high statistics, one can further extend the measured p miss T to even higher values. That requires a dedicated study on the SM backgrounds in that region, and we expect more improvements can be gained than those shown in Table. 2.  Table 2: Summary of current and projected 95% CLs upper limit on NSIs in a simplified Z model with Z mass of 0.2, 2, and 100 TeV respectively. We assume u = d = and Γ Z /M Z = 0.1, and use the NLO predictions with theoretical uncertainties.
LHC constraints on NC NSIs based on missing transverse energy have also been studied in previous works [61,62]. It is noted that the data set taken by both works are ATLAS mono-jet production with 36.1 fb −1 , and therefore partly overlapped with this paper. Our results concerning ATLAS mono-jet production are consistent with [62], however, less stringent than [61]. By utilizing the more precise data from CMS mono-jet production with 35.9 fb −1 data, we have set a limit stronger by a factor of two than [62], which can be read from Table. 2. Projections for future run of LHC with integrated luminosities of 300 fb −1 and 3000 fb −1 have also been given in previous studies. With consideration of reduced systematic uncertainties, they expect larger improvement than in our study of which rather conservative assumptions are taken. On the other hand, there exist indirect searches of NSIs at the LHC utilizing SM gauge symmetries. Under consideration of the common U (1) coupling shared by the SU (2) L doublet, process pp → Z → l + l − +X is taken into account, and measurements on dilepton final state are used to set limits on NC NSIs [57]. Due to the better sensitivities for final state with charged leptons, a stringent limit has been obtained on the common coupling g between Z and fermions, to be about 10 −2 for M Z ≈ 1TeV, based on ATLAS searches of dilepton resonances [106]. This limit can be converted into a limit on conventional coupling strength of NSIs, 10 −5 through Eq. (2.4). Finally, it is worth noting that LHC constraints are fairly loose for light mediators with mass smaller than electro-weak scale. For M Z ≈50 MeV, a limit of 0.1 has been reached with the COHERENT experiment [57,107].

Conclusion
The study on possible non-standard interactions of neutrinos with matter has a long history, and stringent limits have been imposed from various experiments. The NSIs can affect the production, propagation as well as detection of neutrinos, and have a direct consequence on global analysis of neutrino properties like mass ordering and CP phases. The successful operation of LHC opens new opportunities on searching for neutrino NSIs at high momentum transfers which are complementary to other experiments. Neutrinos appear as signal of missing transverse momentums in detectors same as those from dark matters. There have been several studies on constraining NC NSIs using measurements of mono-jet production at the LHC [60][61][62]. In our study we select various data sets from LHC measurements at 13 TeV with integrated luminosities of 35 ∼ 139 fb −1 , including production of a single jet, photon, W/Z boson, or charged lepton, accompanied with large missing transverse momentums. We derive constraints on neutral-current NSIs with quarks imposed by different data sets in a framework of either effective operators or simplified Z models. We found the CMS measurement on mono-jet production gives the strongest constraints on NSIs followed by the CMS measurement on mono-W/Z production. The ATLAS monojet measurement also leads to comparable constraints while the mono-photon and monolepton production show less sensitivities. We use theoretical predictions of various production induced by NSIs calculated at next-to-leading in QCD matched with parton showering and hadronizations. The inclusion of higher order QCD effects stabilize the theory predictions and result in more robust constraints. In the framework of effective operators we find a 95% CLs upper limit of 0.010 on the conventional NSI strength parameter . In a simplified Z model we obtain an upper limit on of 0.042 and 0.0028 for a Z mass of 0.2 and 2 TeV respectively, assuming Γ Z /M Z = 0.1. Moreover, we discuss possible improvements from future runs of LHC with higher luminosities. We find a moderate reduction of the limits if using the same experimental setups but expect further gains by extending current measured missing transverse momentums to higher values.