R({K^{(*)}}) from dark matter exchange

$R({K^{(*)}})$ from dark matter exchange


Hints of lepton flavor violation have been observed by LHCb in the rate of the decay relative to that of . This can be explained by new scalars and fermions which couple to standard model particles and contribute to these processes at loop level. We explore a simple model of this kind, in which one of the new fermions is a dark matter candidate, while the other is a heavy vector-like quark and the scalar is an inert Higgs doublet. We explore the constraints on this model from flavor observables, dark matter direct detection, and LHC run II searches, and find that, while currently viable, this scenario will be directly tested by future experiments.

Figure 1: Diagrams leading to (a) , (b) , (c) - mixing and (d) dark matter scattering on quarks. Arrows on the scalars show the flow of SU(2) quantum number, presumed to not be carried by or .

Introduction. The LHCb experiment has observed intriguing deficits in and , defined as the ratio of branching ratios Aaij et al. (2014, 2017). These “hadronically clean” ratios are free from theoretical uncertainties in hadronic matrix elements, which cancel out Hiller and Kruger (2004). In the standard model (SM) it is expected that Bordone et al. (2016), while experimentally deficits of approximately 20% are observed. Although the significance in either observation or is not high, model-independent fits to both data, and possibly including quantities more sensitive to hadronic physics, including , and the angular observable , indicate a higher significance of Capdevila et al. (2017); Geng et al. (2017); Ciuchini et al. (2017); Hiller and Nisandzic (2017); Altmannshofer et al. (2017) Ref. D’Amico et al. (2017) shows that the best fits and significance do not change appreciably whether one includes the hadronically sensitive observables or not, and that it is possible to find a good fit to the data by including a single dimension-6 operator in the effective Hamiltonian,


with , which is approximately times the SM contribution at one loop.

The new physics contribution (1) can be obtained from tree-level exchange of a heavy vector boson Di Chiara et al. (2017); Chiang et al. (2017a); Dalchenko et al. (2017); Agrawal et al. (2018); Romao et al. (2017); Faisel and Tandean (2018); Falkowski et al. (2018); Kohda et al. (2018) or leptoquark Chen et al. (2017); Crivellin et al. (2017); Cai et al. (2017); Chauhan et al. (2017); Diaz et al. (2017); Doršner et al. (2017); Crivellin et al. (2018); Aloni et al. (2017); Assad et al. (2018); Di Luzio et al. (2017); Calibbi et al. (2017); Dey et al. (2017); Chauhan and Kindra (2017); Müller (2018); Doršner and Greljo (2018); Hiller et al. (2018); Fajfer et al. (2018); Monteux and Rajaraman (2018), or through loop effects of new particles. In ref. Arnan et al. (2017), an exhaustive classification and study of the simplest loop models was carried out, where it was shown that one needs either two new scalars and one new fermion, or two new fermions and one new scalar, to explain the decay anomalies. Many possible quantum numbers of the new particles are possible. Here we note that these include cases where one of them can be neutral under the SM gauge interactions, opening the possibility that it could be dark matter (DM), and thus allowing the model to explain two observed phenomena requiring new physics.

We prefer to minimize the number of new scalars so there is just one, thereby allowing the DM candidate to be one of the new fermions.1 Fermionic dark matter is free from relevant Higgs portal couplings, making for a more predictive theory in which the dark matter properties are determined by the same couplings that explain the flavor anomaly. It will be shown that considerations of the dark matter relic density and direct detection give interesting additional restrictions on the model, and that it is also constrained by existing LHC searches as well as flavor-changing neutral current processes. The model therefore has high potential for discovery by a variety of complementary experimental searches.

SU(3) SU(2) U(1) U(1)
Table 1: Quantum numbers of new physics particles, including accidental discrete symmetry that insures stability of the dark matter , baryon () and lepton () number. SM particles do not transform under the .

Model and low-energy effective theory. We introduce a Majorana fermionic DM particle , a vectorlike heavy quark that carries SM color and hypercharge, and a scalar that is an inert SU(2) doublet. The quantum numbers are shown in table 1. The only couplings of the new fields to SM particles allowed by gauge and global symmetries (see table 1) are


where are the SM quark and lepton doublets, is the SU(2) index and is the flavor index. The relevant interactions at low energy are generated at one loop and thus require sizable couplings. Since there is no flavor symmetry, we will see that this model lives in a corner of parameter space where meson mixing constraints are nearly saturated. In a more complete model, the global symmetries could be an accidental consequence of a spontaneously broken gauge symmetry under which the new physics particles are charged.

The Higgs portal couplings play no important role in the following; gives an overall shift to after electroweak symmetry breaking, while splits the charged and neutral components of by a small amount (relative to as constrained by LHC searches). A coupling of the form


violates lepton number conservation, as can be seen from the charge assignments in table 1. (Notice that cannot be assigned lepton number since it is Majorana.) Of course one expects that is only an approximate symmetry, if neutrinos have Majorana masses, which constrains the size of . In fact this operator could be the origin of one of the neutrino masses through the loop diagram shown in fig. 2, with mass matrix (where GeV), which has a single nonvanishing eigenvalue given by the trace.2 If eV for example, .

Figure 2: Loop-induced contribution to light neutrino Majorana mass.

To make definite predictions from (2), we must specify which field bases are referred to. We will assume that for the leptons and down-type quarks, it is the mass eigenbasis. This implies that up-type quarks have couplings that are rotated by the CKM matrix:

operator coefficient operator coefficient
Table 2: Effective Hamiltonian dimension 6 operators and coefficients; denotes (with the exception of , which corresponds to ) and coefficients are in units of with and loop functions given in text. .

The box diagrams relevant for , , neutral meson mixing and DM scattering on nucleons are shown in fig. 1.3 Evaluating them we find the effective dimension-6 operators of the same form as (1) but different external states. The operator coefficients are shown in table 2, where for simplicity we take . Below we will see that  TeV to meet LHC constraints, but can be light since it is dark matter. The loop functions are given by and , normalized such that and and .

Flavor constraints. To match the observed anomalies, we require that D’Amico et al. (2017). Therefore the couplings must be of order unity, since LHC searches discussed below require TeV. On the other hand, strong mixing constraints, as determined by the mass splitting between and , limit the coefficient of in table 2 to be less than at 95% confidence level (c.l.) Arnan et al. (2017), giving the bound . Combined with the previous determination, this demands large ,


Analogous bounds arise from , and Bona et al. (2008); Bona (2016) mixing: , . .

As an example, suppose that TeV and the bound on mixing is saturated. We can satisfy all other constraints with hierarchical quark couplings


If all of the couplings are positive and real, , right at the mixing 95% c.l. limit. If has the opposite sign to , is smaller, .

The hierarchical nature of the quark couplings is preserved under renormalization group running, since they are multiplicatively renormalized. The one-loop beta functions take the form Luo and Xiao (2003); Machacek and Vaughn (1983)


For the choice of couplings in (6), this leads to a Landau pole in at a scale of around , indicating the need for further new physics at such scales. For example a spontaneously broken nonabelian gauge symmetry, such as we already suggested for explaining the global symmetries of the model, could avert the Landau pole.

It is technically natural to assume the other leptonic couplings are negligible, since they are generated radiatively only through neutrino mass insertions. However aesthetically it may seem peculiar to have . If , the box diagrams leads to lepton flavor-violating decays such as and . However because of the Majorana nature of , there are crossed box diagrams, shown in fig. 1, that exactly cancel the uncrossed ones in the limit where external momenta are neglected in the loop. Their amplitudes then scale as and respectively. After comparing them to those of leptonic decays in the SM, , and imposing the experimental limits on the forbidden decay modes Patrignani et al. (2016) we find no significant constraints on or .

Figure 3: Diagrams leading to (a) , (b) , or , and (c) anapole moment.

Radiative transitions are another flavor-sensitive observable, as shown in fig. 3. For , fig. 3(a) generates the dipole operator


where , , is the photon momentum and . The electric charges of and are as in table 1. Due to operator mixing, the chromomagnetic moment also contributes. Using the results of ref. Arnan et al. (2017), the Wilson coefficients for our benchmark model with TeV give , a factor of 10 below the current limit on this combination from measurements of the branching ratio of .

Fig. 3(b) gives a contribution to the anomalous magnetic moment of the muon of , by saturating (5) and taking TeV. Ultimately this model increases the tension between the measured and predicted values of , but the effect is minimal, 20 times smaller than the SM discrepancy Patrignani et al. (2016). A similar diagram with the photon replaced by the leads to a correction of the coupling of the to left-handed muons of the form Arnan et al. (2017). This is significantly smaller than the uncertainty on the most accurate measurements of this coupling by LEP, Schael et al. (2006), which has a 0.4% error at the level.

If the couplings , are nonzero, there are contributions to , , and , with partial width Giunti and Studenikin (2015) where . Using and TeV, the requirement that the partial width of induced by the new physics contributions not exceed the measured value requires , while leads to the strong limit .

Figure 4: Excluded regions in the plane of versus from an ATLAS slepton search collaboration (2017) (green), and the requirement that is the lightest particle so that it can be the DM (grey). The blue lines correspond to values of and that give the correct relic density for different values of the ratio . is set everywhere to the minimum value that allows for explanation of the flavor anomalies while avoiding mixing constraints.

Figure 5: The current limit on the anapole moment from LUX at 90% c.l. Kopp et al. (2014); Akerib et al. (2017) and the estimated eventual sensitivity of the DARWIN experiment Aalbers et al. (2016). The prediction of our model for this quantity, based on the need to achieve the correct relic density and explain the anomalies, is shown by the red curve.

Dark matter constraints. The dark matter candidate in our model has tree-level annihilation to and . The -wave contribution to the cross section is helicity suppressed, so the term dominates Chang et al. (2014). The total thermally averaged annihilation cross section, counting both final states, either muons or neutrinos, is


where . To get the observed relic density Ade et al. (2016), at the freeze-out temperature this should be roughly equal to the standard value /s Steigman et al. (2012) appropriate for -wave annihilating Majorana dark matter in the mass range GeV, that we will see is required by collider constraints. By assuming that saturates the inequality (5) so that it is no larger than needed to satisfy the flavor constraints, the relation requires


This is valid if ; one can show that (10) is further reduced by the factor if .

We verified the previous estimate by numerically solving the Boltzmann equation with micrOMEGAs 4.3.5 Belanger et al. (2007); contours corresponding to the cosmologically preferred value Ade et al. (2016) are displayed in fig. 4. annihilations can lead to indirect signals in gamma rays and charged cosmic rays, but the -wave suppression of the cross section makes the limits from such searches very weak. Collider limits are far more constraining, notably ATLAS searches for 2 leptons and missing transverse energy collaboration (2017), which exclude the green region in fig. 4.

Because is a Majorana particle, the box diagram for scattering of off quarks leads only to spin-dependent or velocity-suppressed scattering off nucleons. The spin-dependent cross section for DM scattering off a single nucleon is given by where for low-energy scattering (e.g. Belanger et al. (2009)). The determination of the parameters is reviewed in Bringmann et al. (2017). For our benchmark model with TeV this leads to cm for scattering off neutrons, far below current experimental limits on spin-dependent scattering from the PICO-60 direct detection experiment Amole et al. (2017).

Had the dark matter been Dirac, diagram (c) of fig. 3 would give both a magnetic moment for the dark matter , [approximating consistently with eq. (10)], and a charge-radius interaction that lead to scattering on protons. Although the former is below current direct detection limits, the latter is far too large, which obliges us to take to be Majorana.4  Then there is only an anapole moment , which has been computed and constrained (using 2013 LUX results) for our class of models in ref. Kopp et al. (2014). We rescale their limit on to reflect more recent results from LUX Akerib et al. (2017), as well as the projected eventual sensitivity of DARWIN Aalbers et al. (2016), in fig. 5. The predicted value is also shown, using (5) and (10) with to eliminate and in favor of . For the lowest allowed value of GeV (considering that GeV from LHC constraints), the limit is a factor of weaker than the prediction, corresponding to a factor of 500 in the cross section. This is below the reach of the LZ experiment Szydagis (2016), but slightly above the expected sensitivity of DARWIN, leaving open the possibility of direct detection.

Figure 6: Processes for production of quark jets, leptons, and missing energy.

Figure 7: Shaded regions in the - plane are excluded at 95% c.l. by ATLAS run 2 searches for one (blue) or two (red) leptons, jets, and missing energy collaboration (2016a, b). For each point, and the couplings are set as described in text to satisfy flavor and DM relic density constraints.

Collider constraints. The new states and carry SM quantum numbers, and can therefore be pair-produced in particle collisions. Fig. 6 shows the main production modes at a hadron collider and their decays. The final states necessarily include hard lepton pairs, since the splitting between and must be large, eq. (10). This also produces missing energy as the decay products inevitably include dark matter pairs. Moreover hadronic jets appear if is produced, since decays into plus quarks.

For Drell-Yan production of - pairs, the signal is lepton pairs and missing energy, with no jets. (One of the leptons is a neutrino if occurs). This is the same final state as in production of slepton pairs, so SUSY searches collaboration (2017) may be applied.5 The excluded region is shown in fig. 4, constraining GeV for all for which the relic density can be accommodated.

In diagrams 6(b,c,d), is produced, which subsequently decays to or . Such final states have been searched for by ATLAS in 13.3 fb of TeV data, including events with one or two leptons, jets and missing transverse momentum collaboration (2016a, b). These analyses has been implemented in CheckMATE 2.0.14 Drees et al. (2015), which we used to constrain our model, in conjunction with FeynRules 2.3 Alloul et al. (2014) and MadGraph 2.6.0 Alwall et al. (2014). 20,000 events per model point were generated for the process ( is suppressed by the small couplings of and to first generation quarks, or the parton distribution function of or ). The subsequent showering and hadronisation of the final state partons was modelled with Pythia 8.230 Sjöstrand et al. (2015) and detector simulation was done with Delphes 3.4.1 de Favereau et al. (2014).

Fig. 7 shows the resulting 95% c.l. limits on versus for models which both explain the flavor anomalies and give the correct DM relic density. Here is set by eq. 10 with and the couplings are scaled relative to (6) by the factor , where ; this choice keeps all the box diagrams approximately constant. At values of GeV, the lowest values that allow for the correct relic density while avoiding slepton search constraints, the one-lepton search limits GeV, except for a narrow window with just below . The two-lepton search does not constrain as strongly but is more sensitive to larger DM masses.

Conclusions. The indications from LHCb of lepton flavor universality breaking down are currently our best hint of physics beyond the standard model from colliders. These anomalies should be verified within a few years by further data from LHCb and Belle II Albrecht et al. (2017). If confirmed, it is not unreasonable to expect that the relevant new physics could also shed light on other shortcomings of the standard model. We have shown how a very economical model, in which dark matter plays an essential role, could be the source of anomalies, while predicting imminent tensions in other flavor observables, notably mixing. The model may be tested by the next generation of direct detection searches and can be discovered at the LHC via searches for leptons, jets and missing energy.

Acknowledgment. We thank J. Martin Camalich and D. London for helpful discussions, and S. Okawa for alerting us to a problem with the first version of this paper. Our work is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.


  1. Ref. Gripaios et al. (2016) focuses on the opposite choice, and observes that the possible scalar dark matter candidate cannot satisfy direct detection constraints because of its coupling to . Previous attempts to connect to dark matter can be found in refs. Aristizabal Sierra et al. (2015); Bélanger et al. (2015); Celis et al. (2017); Altmannshofer et al. (2016); Cline et al. (2017); Baek (2017); Cline (2017); Sala and Straub (2017). In addition, refs. Kawamura et al. (2017); Chiang et al. (2017b) recently studied models similar to ours, but in which the DM is chosen to be a new scalar. These studies do not fully consider the impact of the Higgs portal coupling on the DM relic density and direct detection. In ref. Bhattacharya et al. (2015) it was shown that tends to dominate over any other new physics effects. Even if it vanishes at tree level, the one-loop correction tends to be too large to ignore without fine tuning.
  2. A more complicated model with two or more flavors of dark matter would allow for nonsingular mass matrices.
  3. The charges of the fields in this theory do not allow it to contribute to at one loop.
  4. We thank S. Okawa for pointing out the importance of the charge radius contribution.
  5. These limits assume annihilation to all flavors of both right and left handed sleptons, taken to be degenerate. Comparing production cross sections of all sleptons to that of a pair using MadGraph Alwall et al. (2014) indicates that they may be overly stringent for our model; at 13 TeV, the slepton production cross section is fb for  GeV, whereas  fb for production with  GeV.


  1. Roel Aaij et al. (LHCb), “Test of lepton universality using decays,” Phys. Rev. Lett. 113, 151601 (2014)arXiv:1406.6482 [hep-ex] .
  2. R. Aaij et al. (LHCb), “Test of lepton universality with decays,” JHEP 08, 055 (2017)arXiv:1705.05802 [hep-ex] .
  3. Gudrun Hiller and Frank Kruger, “More model-independent analysis of processes,” Phys. Rev. D69, 074020 (2004)arXiv:hep-ph/0310219 [hep-ph] .
  4. Marzia Bordone, Gino Isidori,  and Andrea Pattori, “On the Standard Model predictions for and ,” Eur. Phys. J. C76, 440 (2016)arXiv:1605.07633 [hep-ph] .
  5. Bernat Capdevila, Andreas Crivellin, Sébastien Descotes-Genon, Joaquim Matias,  and Javier Virto, “Patterns of New Physics in transitions in the light of recent data,”  (2017), arXiv:1704.05340 [hep-ph] .
  6. Li-Sheng Geng, Benjamín Grinstein, Sebastian Jäger, Jorge Martin Camalich, Xiu-Lei Ren,  and Rui-Xiang Shi, “Towards the discovery of new physics with lepton-universality ratios of decays,” Phys. Rev. D96, 093006 (2017)arXiv:1704.05446 [hep-ph] .
  7. Marco Ciuchini, Antonio M. Coutinho, Marco Fedele, Enrico Franco, Ayan Paul, Luca Silvestrini,  and Mauro Valli, “On Flavourful Easter eggs for New Physics hunger and Lepton Flavour Universality violation,” Eur. Phys. J. C77, 688 (2017)arXiv:1704.05447 [hep-ph] .
  8. Gudrun Hiller and Ivan Nisandzic, “ and beyond the standard model,” Phys. Rev. D96, 035003 (2017)arXiv:1704.05444 [hep-ph] .
  9. Wolfgang Altmannshofer, Peter Stangl,  and David M. Straub, “Interpreting Hints for Lepton Flavor Universality Violation,” Phys. Rev. D96, 055008 (2017)arXiv:1704.05435 [hep-ph] .
  10. Guido D’Amico, Marco Nardecchia, Paolo Panci, Francesco Sannino, Alessandro Strumia, Riccardo Torre,  and Alfredo Urbano, “Flavour anomalies after the measurement,” JHEP 09, 010 (2017)arXiv:1704.05438 [hep-ph] .
  11. Stefano Di Chiara, Andrew Fowlie, Sean Fraser, Carlo Marzo, Luca Marzola, Martti Raidal,  and Christian Spethmann, “Minimal flavor-changing models and muon after the measurement,” Nucl. Phys. B923, 245–257 (2017)arXiv:1704.06200 [hep-ph] .
  12. Cheng-Wei Chiang, Xiao-Gang He, Jusak Tandean,  and Xing-Bo Yuan, “ and related anomalies in minimal flavor violation framework with boson,” Phys. Rev. D96, 115022 (2017a)arXiv:1706.02696 [hep-ph] .
  13. Mykhailo Dalchenko, Bhaskar Dutta, Ricardo Eusebi, Peisi Huang, Teruki Kamon,  and Denis Rathjens, “Bottom-quark Fusion Processes at the LHC for Probing Models and B-meson Decay Anomalies,”  (2017), arXiv:1707.07016 [hep-ph] .
  14. Pankaj Agrawal, Debashis Saha,  and Ambresh Shivaji, “Production of and at the hadron colliders,” Phys. Rev. D97, 036006 (2018)arXiv:1708.03580 [hep-ph] .
  15. Miguel Crispim Romao, Stephen F. King,  and George K. Leontaris, “Non-universal from Fluxed GUTs,”  (2017), arXiv:1710.02349 [hep-ph] .
  16. Gaber Faisel and Jusak Tandean, “Connecting anomalies to enhanced rare nonleptonic decays in model,” JHEP 02, 074 (2018)arXiv:1710.11102 [hep-ph] .
  17. Adam Falkowski, Stephen F. King, Elena Perdomo,  and Mathias Pierre, “Flavourful portal for vector-like neutrino Dark Matter and ,”  (2018), arXiv:1803.04430 [hep-ph] .
  18. Masaya Kohda, Tanmoy Modak,  and Abner Soffer, “Identifying a behind anomalies at the LHC,”  (2018), arXiv:1803.07492 [hep-ph] .
  19. Chuan-Hung Chen, Takaaki Nomura,  and Hiroshi Okada, “Excesses of muon , , and in a leptoquark model,” Phys. Lett. B774, 456–464 (2017)arXiv:1703.03251 [hep-ph] .
  20. Andreas Crivellin, Dario Müller,  and Toshihiko Ota, “Simultaneous explanation of R(D) and : the last scalar leptoquarks standing,” JHEP 09, 040 (2017)arXiv:1703.09226 [hep-ph] .
  21. Yi Cai, John Gargalionis, Michael A. Schmidt,  and Raymond R. Volkas, “Reconsidering the One Leptoquark solution: flavor anomalies and neutrino mass,” JHEP 10, 047 (2017)arXiv:1704.05849 [hep-ph] .
  22. Bhavesh Chauhan, Bharti Kindra,  and Ashish Narang, “A Leptoquark explanation for , , and, IceCube PeV events,”  (2017), arXiv:1706.04598 [hep-ph] .
  23. Bastian Diaz, Martin Schmaltz,  and Yi-Ming Zhong, “The leptoquark Hunter’s guide: Pair production,” JHEP 10, 097 (2017)arXiv:1706.05033 [hep-ph] .
  24. Ilja Doršner, Svjetlana Fajfer, Darius A. Faroughy,  and Nejc Košnik, “The role of the GUT leptoquark in flavor universality and collider searches,”  (2017), 10.1007/JHEP10(2017)188, [JHEP10,188(2017)], arXiv:1706.07779 [hep-ph] .
  25. Andreas Crivellin, Dario Müller, Adrian Signer,  and Yannick Ulrich, “Correlating lepton flavor universality violation in decays with using leptoquarks,” Phys. Rev. D97, 015019 (2018)arXiv:1706.08511 [hep-ph] .
  26. Daniel Aloni, Avital Dery, Claudia Frugiuele,  and Yosef Nir, “Testing minimal flavor violation in leptoquark models of the anomaly,” JHEP 11, 109 (2017)arXiv:1708.06161 [hep-ph] .
  27. Nima Assad, Bartosz Fornal,  and Benjamin Grinstein, “Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models,” Phys. Lett. B777, 324–331 (2018)arXiv:1708.06350 [hep-ph] .
  28. Luca Di Luzio, Admir Greljo,  and Marco Nardecchia, “Gauge leptoquark as the origin of B-physics anomalies,” Phys. Rev. D96, 115011 (2017)arXiv:1708.08450 [hep-ph] .
  29. Lorenzo Calibbi, Andreas Crivellin,  and Tianjun Li, “A model of vector leptoquarks in view of the -physics anomalies,”  (2017), arXiv:1709.00692 [hep-ph] .
  30. Ujjal Kumar Dey, Deepak Kar, Manimala Mitra, Michael Spannowsky,  and Aaron C. Vincent, “Searching for Leptoquarks at IceCube and the LHC,”  (2017), arXiv:1709.02009 [hep-ph] .
  31. Bhavesh Chauhan and Bharti Kindra, “Invoking Chiral Vector Leptoquark to explain LFU violation in B Decays,”  (2017), arXiv:1709.09989 [hep-ph] .
  32. Dario Müller, “Leptoquarks in Flavour Physics,” in Workshop on Flavour changing and conserving processes (FCCP2017) Anacapri, Capri Island, Italy, September 7-9, 2017 (2018) arXiv:1801.03380 [hep-ph] .
  33. Ilja Doršner and Admir Greljo, “Leptoquark toolbox for precision collider studies,”  (2018), arXiv:1801.07641 [hep-ph] .
  34. Gudrun Hiller, Dennis Loose,  and Ivan Nišandžić, “Flavorful leptoquarks at hadron colliders,” Phys. Rev. D97, 075004 (2018)arXiv:1801.09399 [hep-ph] .
  35. S. Fajfer, N. Košnik,  and L. Vale Silva, “Footprints of leptoquarks: from to ,” Eur. Phys. J. C78, 275 (2018)arXiv:1802.00786 [hep-ph] .
  36. Angelo Monteux and Arvind Rajaraman, “B Anomalies and Leptoquarks at the LHC: Beyond the Lepton-Quark Final State,”  (2018), arXiv:1803.05962 [hep-ph] .
  37. Pere Arnan, Lars Hofer, Federico Mescia,  and Andreas Crivellin, “Loop effects of heavy new scalars and fermions in ,” JHEP 04, 043 (2017)arXiv:1608.07832 [hep-ph] .
  38. Ben Gripaios, M. Nardecchia,  and S. A. Renner, “Linear flavour violation and anomalies in B physics,” JHEP 06, 083 (2016)arXiv:1509.05020 [hep-ph] .
  39. D. Aristizabal Sierra, Florian Staub,  and Avelino Vicente, “Shedding light on the anomalies with a dark sector,” Phys. Rev. D92, 015001 (2015)arXiv:1503.06077 [hep-ph] .
  40. Geneviève Bélanger, Cédric Delaunay,  and Susanne Westhoff, “A Dark Matter Relic From Muon Anomalies,” Phys. Rev. D92, 055021 (2015)arXiv:1507.06660 [hep-ph] .
  41. Alejandro Celis, Wan-Zhe Feng,  and Martin Vollmann, “Dirac dark matter and with gauge symmetry,” Phys. Rev. D95, 035018 (2017)arXiv:1608.03894 [hep-ph] .
  42. Wolfgang Altmannshofer, Stefania Gori, Stefano Profumo,  and Farinaldo S. Queiroz, “Explaining dark matter and B decay anomalies with an model,” JHEP 12, 106 (2016)arXiv:1609.04026 [hep-ph] .
  43. James M. Cline, Jonathan M. Cornell, David London,  and Ryoutaro Watanabe, “Hidden sector explanation of -decay and cosmic ray anomalies,” Phys. Rev. D95, 095015 (2017)arXiv:1702.00395 [hep-ph] .
  44. Seungwon Baek, “Dark matter contribution to anomaly in local model,”  (2017), arXiv:1707.04573 [hep-ph] .
  45. James M. Cline, “ decay anomalies and dark matter from vectorlike confinement,”  (2017), arXiv:1710.02140 [hep-ph] .
  46. Filippo Sala and David M. Straub, “A New Light Particle in B Decays?” Phys. Lett. B774, 205–209 (2017)arXiv:1704.06188 [hep-ph] .
  47. Junichiro Kawamura, Shohei Okawa,  and Yuji Omura, “Interplay between the b anomalies and dark matter physics,” Phys. Rev. D96, 075041 (2017)arXiv:1706.04344 [hep-ph] .
  48. Cheng-Wei Chiang, Guan-Jie Huang,  and Hiroshi Okada, “A simple model for explaining muon-related anomalies and dark matter,”  (2017b), arXiv:1711.07365 [hep-ph] .
  49. Bhubanjyoti Bhattacharya, David London, James M. Cline, Alakabha Datta,  and Grace Dupuis, “Quark-flavored scalar dark matter,” Phys. Rev. D92, 115012 (2015)arXiv:1509.04271 [hep-ph] .
  50. M. Bona et al. (UTfit), “Model-independent constraints on operators and the scale of new physics,” JHEP 03, 049 (2008)arXiv:0707.0636 [hep-ph] .
  51. Marcella Bona (UTfit), “Unitarity Triangle analysis beyond the Standard Model from UTfit,” Proceedings, 38th International Conference on High Energy Physics (ICHEP 2016): Chicago, IL, USA, August 3-10, 2016, PoS ICHEP2016, 149 (2016).
  52. Ming-xing Luo and Yong Xiao, “Two loop renormalization group equations in the standard model,” Phys. Rev. Lett. 90, 011601 (2003)arXiv:hep-ph/0207271 [hep-ph] .
  53. Marie E. Machacek and Michael T. Vaughn, “Two Loop Renormalization Group Equations in a General Quantum Field Theory. 1. Wave Function Renormalization,” Nucl. Phys. B222, 83–103 (1983).
  54. C. Patrignani et al. (Particle Data Group), “Review of Particle Physics,” Chin. Phys. C40, 100001 (2016).
  55. S. Schael et al. (SLD Electroweak Group, DELPHI, ALEPH, SLD, SLD Heavy Flavour Group, OPAL, LEP Electroweak Working Group, L3), “Precision electroweak measurements on the resonance,” Phys. Rept. 427, 257–454 (2006)arXiv:hep-ex/0509008 [hep-ex] .
  56. Carlo Giunti and Alexander Studenikin, “Neutrino electromagnetic interactions: a window to new physics,” Rev. Mod. Phys. 87, 531 (2015)arXiv:1403.6344 [hep-ph] .
  57. The ATLAS collaboration (ATLAS), “Search for electroweak production of supersymmetric particles in the two and three lepton final state at TeV with the ATLAS detector,” ATLAS-CONF-2017-039  (2017).
  58. Joachim Kopp, Lisa Michaels,  and Juri Smirnov, “Loopy Constraints on Leptophilic Dark Matter and Internal Bremsstrahlung,” JCAP 1404, 022 (2014)arXiv:1401.6457 [hep-ph] .
  59. D. S. Akerib et al. (LUX), “Results from a search for dark matter in the complete LUX exposure,” Phys. Rev. Lett. 118, 021303 (2017)arXiv:1608.07648 [astro-ph.CO] .
  60. J. Aalbers et al. (DARWIN), “DARWIN: towards the ultimate dark matter detector,” JCAP 1611, 017 (2016)arXiv:1606.07001 [astro-ph.IM] .
  61. Spencer Chang, Ralph Edezhath, Jeffrey Hutchinson,  and Markus Luty, “Leptophilic Effective WIMPs,” Phys. Rev. D90, 015011 (2014)arXiv:1402.7358 [hep-ph] .
  62. P. A. R. Ade et al. (Planck), “Planck 2015 results. XIII. Cosmological parameters,” Astron. Astrophys. 594, A13 (2016)arXiv:1502.01589 [astro-ph.CO] .
  63. Gary Steigman, Basudeb Dasgupta,  and John F. Beacom, “Precise Relic WIMP Abundance and its Impact on Searches for Dark Matter Annihilation,” Phys. Rev. D86, 023506 (2012)arXiv:1204.3622 [hep-ph] .
  64. G. Belanger, F. Boudjema, A. Pukhov,  and A. Semenov, “MicrOMEGAs 2.0: A Program to calculate the relic density of dark matter in a generic model,” Comput. Phys. Commun. 176, 367–382 (2007)arXiv:hep-ph/0607059 [hep-ph] .
  65. G. Belanger, F. Boudjema, A. Pukhov,  and A. Semenov, “Dark matter direct detection rate in a generic model with micrOMEGAs 2.2,” Comput. Phys. Commun. 180, 747–767 (2009)arXiv:0803.2360 [hep-ph] .
  66. Torsten Bringmann et al., “DarkBit: A GAMBIT module for computing dark matter observables and likelihoods,” Eur. Phys. J. C77, 831 (2017)arXiv:1705.07920 [hep-ph] .
  67. C. Amole et al. (PICO), “Dark Matter Search Results from the PICO-60 CF Bubble Chamber,” Phys. Rev. Lett. 118, 251301 (2017)arXiv:1702.07666 [astro-ph.CO] .
  68. M. Szydagis (LUX, LZ), “The Present and Future of Searching for Dark Matter with LUX and LZ,” Proceedings, 38th International Conference on High Energy Physics (ICHEP 2016): Chicago, IL, USA, August 3-10, 2016, PoS ICHEP2016, 220 (2016), arXiv:1611.05525 [astro-ph.CO] .
  69. The ATLAS collaboration (ATLAS), “Search for top squarks in final states with one isolated lepton, jets, and missing transverse momentum in = 13 TeV pp collisions with the ATLAS detector,” ATLAS-CONF-2016-050  (2016a).
  70. The ATLAS collaboration (ATLAS), “Search for direct top squark pair production and dark matter production in final states with two leptons in TeV collisions using 13.3 fb of ATLAS data,” ATLAS-CONF-2016-076  (2016b).
  71. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli,  and M. Zaro, “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,” JHEP 07, 079 (2014)arXiv:1405.0301 [hep-ph] .
  72. Manuel Drees, Herbi Dreiner, Daniel Schmeier, Jamie Tattersall,  and Jong Soo Kim, “CheckMATE: Confronting your Favourite New Physics Model with LHC Data,” Comput. Phys. Commun. 187, 227–265 (2015)arXiv:1312.2591 [hep-ph] .
  73. Adam Alloul, Neil D. Christensen, Céline Degrande, Claude Duhr,  and Benjamin Fuks, “FeynRules 2.0 - A complete toolbox for tree-level phenomenology,” Comput. Phys. Commun. 185, 2250–2300 (2014)arXiv:1310.1921 [hep-ph] .
  74. Torbjörn Sjöstrand, Stefan Ask, Jesper R. Christiansen, Richard Corke, Nishita Desai, Philip Ilten, Stephen Mrenna, Stefan Prestel, Christine O. Rasmussen,  and Peter Z. Skands, “An Introduction to PYTHIA 8.2,” Comput. Phys. Commun. 191, 159–177 (2015)arXiv:1410.3012 [hep-ph] .
  75. J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaître, A. Mertens,  and M. Selvaggi (DELPHES 3), “DELPHES 3, A modular framework for fast simulation of a generic collider experiment,” JHEP 02, 057 (2014)arXiv:1307.6346 [hep-ex] .
  76. Johannes Albrecht, Florian Bernlochner, Matthew Kenzie, Stefanie Reichert, David Straub,  and Alison Tully, “Future prospects for exploring present day anomalies in flavour physics measurements with Belle II and LHCb,”  (2017), arXiv:1709.10308 [hep-ph] .
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