Flavoured Dark Matter moving left

Journal of High Energy Physics, Feb 2018

Monika Blanke, Satrajit Das, Simon Kast

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Flavoured Dark Matter moving left

HJE Dark Matter moving left Monika Blanke 0 1 2 3 5 Satrajit Das 0 1 2 4 Simon Kast 0 1 2 3 Quark Physics, Kaon Physics 0 Powai , Mumbai, Maharashtra 400076 , India 1 Engesserstra e 7 , D-76128 Karlsruhe , Germany 2 Hermann-von-Helmholtz-Platz 1 , D-76344 Eggenstein-Leopoldshafen , Germany 3 Institut fur Theoretische Teilchenphysik, Karlsruhe Institute of Technology 4 Physics Department, Indian Institute of Technology Bombay 5 Institut fur Kernphysik, Karlsruhe Institute of Technology We investigate the phenomenology of a simpli ed model of avoured Dark Matter (DM), with a dark fermionic avour triplet coupling to the left-handed SU(2)L quark doublets via a scalar mediator. The DM-quark coupling matrix is assumed to constitute the only new source of avour and CP violation, following the hypothesis of Dark Minimal Flavour Violation. We analyse the constraints from LHC searches, from meson mixing data in the K, D, and Bd;s meson systems, from thermal DM freeze-out, and from direct detection experiments. Our combined analysis shows that while the experimental constraints are similar to the DMFV models with DM coupling to right-handed quarks, the multitude of couplings between DM and the SM quark sector resulting from the SU(2)L structure implies a richer phenomenology and signi cantly alters the resulting impact on the viable parameter space. Beyond Standard Model; Cosmology of Theories beyond the SM; Heavy - Flavoured 1 Introduction 2 3 4 5 6 7 8 LHC constraints Flavour constraints Relic abundance constraint Direct detection constraints Combined analysis Summary and outlook A Technical details 1 Introduction avour precision experiments, more recently also models with a non-minimal avour structure have been investigated [3, 22{24]. In [3] the concept of Dark Minimal Flavour Violation (DMFV) has been put forward, which assumes the coupling of the DM avour triplet with the SM avour triplets to constitute the only new source of avour and CP violation. DMFV models coupling the dark sector to the right-handed down quarks, the right-handed up quarks and the right-handed charged leptons have been studied, with the outcome that the introduction of a new avour structure signi cantly enriches the phenomenology of the respective models. In the present paper we continue our expedition into the DMFV model space and investigate the possibility of a new avour violating coupling of the DM to left-handed fermions for the rst time. We introduce a simpli ed DMFV model in which the DM avour triplet couples to the left-handed quark doublets of the SM in a non-MFV manner. The study naturally follows our previous analyses of DMFV models with couplings to the right-handed down [3] and up [22] quarks, respectively. It turns out that the present model combines the phenomenological implications of the scenarios studied previously in a non-trivial manner, yielding interesting results for the allowed parameter space of the model. Our paper is organised as follows. In section 2 we introduce the structure of the simpli ed model that we study and discuss its basic features. The most important LHC constraints on the parameter space of the model are analysed in section 3. Then in section 4, section 5, and section 6 we study in turn the constraints from precision avour observables, from the observed relic abundance, and from direct detection experiments. In section 7 we present the results of a combined analysis of all constraints. We conclude in section 8 with a summary of our results and a brief outlook. 2 basis, and 0ij denotes the NP coupling between the DM avour j , the mediator and the quark-doublet qi0 in the avour basis. Just as in the previously studied DMFV models, we choose the DM avour triplet to be a gauge singlet. For convenience we label its components the same way as in the up quark DMFV model [22]: j = ( u; c; t)> : { 2 { (2.1) (2.2) D U = U23U13U12 = B0 0 as weak doublet, quark doublet. Throughout our analysis we assume the top avoured state t to be the lightest of the three avours, so that t forms the entire observed DM. We will see in section 6 that this case is indeed phenomenologically preferred. Finally, the scalar mediator transforms = ( u; d)>, and carries the QCD colour and hypercharge of the SM Following the hypothesis of Dark Minimal Flavour Violation (DMFV) proposed in [3], the DM coupling 0 constitutes the only new source of avour and CP violation. This assumption limits the number of free parameters and guarantees a stable DM candidate, in analogy to the MFV scenario in [2]. Transforming (2.1) to the mass eigenstate basis, without loss of generality we can decompose the coupling as (uLi ij j u + h:c) (dLi ~ij j d + h:c:); with uLi and dLi denoting the quarks in the mass eigenstate basis. In analogy to [3, 22], we parametrise by = U D with a diagonal matrix D with real and positive entries, and U consisting of three unitary matrices carrying a mixing angle ij and a phase ij (ij = 12; 13; 23) each [28]: s23e i 23 C B 0 c23 Here cij = cos ij and sij = sin ij . The CKM misalignment between the left-handed up and down quarks then leads to ~ = VCyKM ; and ~ are related to each other by the (small) CKM mixing. Throughout this paper, for the numerical values of the CKM parameters we use the latest new physics t results of the UT t Collaboration [29]. The new physics t provides the best determination of the CKM matrix in the presence of NP contributions to FCNC processes. We can see from the interaction Lagrangian (2.3) that, barring the di erent chirality of the coupling, the quark doublet DMFV model in some sense combines the previously studied right-handed DMFV models [3, 22]. Yet its phenomenology is not a mere superposition of the e ects previously identi ed, since the couplings in the up and down sectors are connected by (2.7). We hence can expect an interesting and non-trivial interplay of the constraints found on those models. The mass terms for the new particles are again realized following the principles of DMFV: Lmass = m m2 y : { 3 { (2.3) (2.4) (2.5) (2.6) (2.7) (2.8) i. e. at this level the di erent avours of are degenerate. Note that electroweak symmetry breaking will create a small mass splitting between m v, we can safely neglect this splitting in what follows. u and d of the order of v2=m . As The di erent avours of receive a sizable mass splitting which can be parametrised in terms of the usual DMFV expansion [3, 22]: m ;ij = m 1 + 1 y + 2 ~y ~ + O( 4) ij = m 1 + (D ;ii)2 + O( 4) ij : (2.9) Note that due to its unitarity VCKM drops out of the above formula. In our simpli ed model we incorporate = 1 + 2 as a free parameter. In summary this leaves our model with twelve free parameters, which are the bare mass parameters m and m , the nine parameters of the coupling matrix (three diagonal \couplings" D ;ii, three mixing angles ij , and three phases ij ) as well as the parameter , governing the mass splitting of the DM avours. If not mentioned otherwise in the text or gures, all these parameters are scanned over in our analysis. One exception is the parameter , which is set to a xed benchmark value depending on the studied freezeout scenario. 3 LHC constraints In this section we investigate the constraints that NP searches at the LHC place on the parameter space of our model. As discussed in [30] and con rmed in [3] for the DMFV model with coupling to down quarks, the strongest bounds on DM models with coloured tchannel mediator typically originate from mediator pair production and subsequent decay. This holds true for the quark doublet DMFV model as well. Due to the SU(2)L charge of the mediator, in the present case both u and d production contribute to the total cross-section. Recall that u couples DM to the left-handed up quarks, while d couples DM to the left-handed down quarks. We identify the following new features compared to the LHC phenomenology of the up quark [22] and down quark [3] DMFV model, respectively: Production: both yu u and yd d pairs are produced via QCD interactions, and via tree level exchange of the DM triplet in the t-channel. In addition, exchange generates the mixed states yu d and yd u, see gure 1. Thus, pair production of the scalar mediator is signi cantly enhancend with respect to the previously studied DMFV models. Decay : the interaction Lagrangian (2.3) implies that u decays into a DM avour plus a member of the up quark avour triplet, while d decays into plus a member of the down quark avour triplet. Hence, we need to consider the following possible nal states for which dedicated ATLAS and CMS searches exist: tt + E T emerges from yu u production and subsequent decay into the third generation quarks. The resulting limits on the parameter space are the same as found for the up quark DMFV model [22]. Furthermore, bb + E T is realised from the yd d intermediate state and { 4 { dk j y u d yu u and yd d intermediate states, but also from the mixed states of u and d | each time with both mediators decaying to quarks of the rst two generations. HJEP02(18)5 While the production cross section for the jets+ E T nal state is signi cantly increased with respect to our previous DMFV studies [3, 22], the contributions to the bb + E T and tt+E T nal states remain unchanged and the results from [3, 22] hold. It hence comes as no surprise that in the quark doublet DMFV model we obtain by far the strongest constraints from the jets+E T bounds, as the latter have already been found to be dominant in the righthanded DMFV models, respectively. In order to allow for a straightforward comparison with the bounds on the right-handed DMFV models, in what follows we restrict ourselves to the constraints obtained from run 1 of the LHC. We note that with the rapidly increasing integrated luminosity at LHC run 2, the lower bound on the mediator mass will become more stringent. For the phenomenological analysis we employ the same assumptions, simpli cations and strategies as discussed in detail in [3]. For the sake of brevity we only show the exclusion bounds from the jets + E T nal state, see gure 2. We observe that the constraints for equivalent coupling strengths exclude a signi cantly larger region of the m - m t plane than in the up quark DMFV model. We do not show the exclusion bounds for mediator masses larger than 1 TeV, since in this range numerical uncertainties from extrapolation of the exclusion data given in [31] dominate. From the results shown in gure 2 we learn that for mediator masses as low as the DM couplings have to be restricted to in order to satisfy the LHC constraints. Note that the upper bound on the couplings for a given mediator mass is signi cantly lower in the quark doublet model than in the righthanded DMFV models [3, 22]. In what follows we restrict the parameter space of the model to the \collider-safe" region de ned by (3.1) and (3.2). Before moving on let us point out that the quark doublet DMFV model predicts various avour violating signatures at the LHC. As in the right-handed DMFV model coupling m { 5 { (3.1) (3.2) Dλ,11=Dλ,22=1.5, Dλ,33=1.0 Dλ,11=Dλ,22=1.5, Dλ,33=1.5 Dλ,11=Dλ,22=1.5, Dλ,33=2.0 Dλ,11=Dλ,22=2.0, Dλ,33=0.5 Dλ,11=Dλ,22=2.0, Dλ,33=1.0 Dλ,11=Dλ,22=2.0, Dλ,33=1.5 Dλ,11=Dλ,22=2.0, Dλ,33=2.0 800 1000 discussed in detail in [22], the latter do not a ect the identi ed safe parameter space. to up quarks [22], the nal state tj + E T is produced with signi cant rate, even in the limit of no avour mixing, ij = 0.1 Additionally, the present model gives rise to the smoking gun signature tb + E T which becomes relevant for sizable DM couplings D ;ii. This signature arises from the mixed u d production with both mediators decaying to the third quark generation and is hence present only if DM couples to the SM quark doublets. A measurement of the tb + E T cross section would therefore provide a direct measure of the DM coupling strength, as the QCD production channels do not contribute in this case. Note that such nal state is not generated in supersymmetric models with signi cant rate. While these signatures in principle have some impact on single-top studies already preformed at the LHC, we expect that a dedicated search including a cut on E T would have a signi cantly improved reach, due to the much reduced SM background. 4 Flavour constraints Having restricted the parameter space of our model to a region that complies with present LHC searches, we now move on to the study of precision avour observables. In analogy to the right-handed DMFV models [3, 22], the most stringent constraints on the quark doublet model stem from meson antimeson mixing observables, while the e ects on rare decays are negligible. 1This is to be contrasted with the case of supersymmetric models, where such signatures are generated only in the presence of large avour mixing [32{37]. { 6 { i u s d u u d d j i Since, due to the SU(2)L structure in the DM-quark coupling, the NP particles in this model couple to all six quark mixing as well as from K0 avours, we have to consider constraints from D0 D0 K0 mixing and Bd0;s Bd0;s mixing. The relevant one loop box diagrams for D0 D0 and K0 K0 mixing are shown in gure 3, the contributions to Bd0;s Bd0;s mixing are analogous. Calculating the contributions to the dispersive part of the o -diagonal mixing amplitude, we nd in analogy to the results of [3, 22] M1D2;new = M1K2;new = M1B2q;new = 1 1 1 384 2m2 D mD f D2 BD ( 384 2m2 2 mK f K2 B^K (~~y)sd 384 2m2 B mBq fB2 q B^Bq (~~y)bq 2 2 2 y)cu L(xi; xj ) ; L(xi; xj ) ; L(xi; xj ) (q = d; s) : The loop function L(xi; xj ), with xi = m2 i =m2 , has been calculated in [3], and can be found together with the QCD input parameters in the appendix. The mass splitting between the DM avours constitutes a small correction, and we neglect it in what follows. Note that while (4.1) includes the coupling , (4.2) and (4.3) include the coupling ~ and hence are sensitive to the CKM mixing of the SM. Using the parametrisation of in (2.4), we observe that the unitary matrices VCKM and U cancel in the expressions (4.1){ (4.3) in the degeneracy limit for the couplings D ;ii. The size of the NP contributions to the neutral meson mixing observables is hence suppressed by the splittings ij = jD ;ii D ;jj j. and ~ De ning as well as M1B2q = CBq e2i Bq M1B2q;SM (q = d; s) ReM1K2 = C MK ReM1K2;SM ; ImM1K2 = C K ImM1K2;SM ; we can compare our predictions for C MK , C K , CBd , Bd , CBs and Bs to the allowed ranges collected in table 1. In the case of D0 D0 mixing, we make the conservative { 7 { d s (4.1) (4.2) (4.3) (4.4) (4.5) (4.6) HJEP02(18)5 C MK C K x1D2 D 12 0:44 K0, D0 in the standard phase conventions, the bounds in table 1 can be directly applied to our model. The necessary input parameters are collected in the appendix. Imposing the constraints from meson antimeson mixing in this way, we obtain the viable ranges for the avour mixing angles ij as function of the respective splitting jD ;ii D ;jj j = ij , see gure 4. We observe that the structure of the coupling matrix is signi cantly more constrained than in the case of the up quark DMFV model [22], due to the additional strong constraints from K0 K0 and Bd0;s Bd0;s mixing data. In particular we nd signi cant e ects on 13 and 23 as well. The constraints on 12 remain the most severe, and in fact the combination of K0 K0 and D0 D0 mixing constraints rejects any splitting 12 larger than approximately 0.3. This is a direct consequence of the CKM misalignment between the left-handed up and down quarks with a rather large jVusj 0:225 | a su cient alignment of the NP sector with both the up and down sectors cannot be achieved for large splittings. { 8 { dependence of the splittings between couplings D ;ii and D ;jj, for mediator mass m = 250 GeV. Di erent colours correspond to the di erent mixing angles ij and ij, with each colour representing one pair of indices: ij = 12 in yellow, assumption that the long distance dominated SM contribution to is at most 3%. With x1D2 = 2jM1D2j = 2jM1D2j D0 D 1D2 = arg M1D2 (4.7) (4.8) HJEP02(18)5 Comparing the allowed ranges in gure 4 with those obtained in appears as if our upper bounds on the avour mixing angles are less severe | apart from the cut for a too large 12. This seems unexpected, since the quark doublet model is constrained by the same bounds as the down quark DMFV model plus the limits from D0 D0 mixing. The reason for this di erence is the di erent approaches in scanning the couplings D ;ii. While in [3] in the avour analysis only the avour violating parameters were varied and the trace of D was xed to Tr D = 3, in the present study we vary all couplings D ;ii independently between 0 and 1.5, thereby allowing for 0 Tr D 4:5. It is hence not surprising that larger viable parameter ranges are found in gure 4. 5 Relic abundance constraint In this section we investigate the constraints on the quark doublet DMFV model imposed by the observed relic abundance, assuming the DM to be the relic of a thermal freezeout. In this model the DM avours can annihilate to all six quark avours of the SM. The number of possible nal states is thus larger than in the right-handed DMFV models [3, 22]. The e ective annihilation cross section is then given as the sum of the annihilation cross sections into up and down nal states: HJEP02(18)5 h vie = h vieu + h vied : h vie ' 2:0 10 26 cm3=s : In order to reproduce the observed relic abundance, the e ective annihilation cross section has to satisfy [41, 42] As discussed in detail in [3, 22], di erent freeze-out scenarios are possible depending on the mass splitting between the DM avours. If the mass splitting between the DM and the heavier avours u; c is small, < 1%, then the lifetime of the heavier states is long enough that they fully contribute to the freeze-out process. This scenario is called quasi-degenerate freeze-out (QDF). hilation cross section reads [22] In the QDF scenario the contribution from up quark nal states to the e ective annih vieu = 1 where an averaging factor 1=9 for the 3 3 di erent initial states has been included. For DM masses below mt the tt nal state becomes kinematically inacessible and has to be excluded. Similarly for m < mt=2 all nal states containing a top quark become inaccessible. In the down quark contribution the quark masses can be neglected and the expression simpli es to [3] h vied = 1 { 9 { (5.1) (5.2) t ; (5.3) (5.4) 0:01) compatible with the relic abundance constraint, at di erent DM masses. If on the other hand the splitting of the heavier states with respect to the light stable avour t is large, then their decay is su ciently rapid that these states are no longer present at the time of freeze-out. This scenario is referred to as single avour freeze-out (SFF). In this case only the t t initial state contributes to the e ective annihilation cross section and the avour averaging factor 1=9 is absent. The phenomenological implications of the thermal freeze-out condition (5.2) are quite similar to the ones observed for the up quark DMFV model in [22]. We therefore refer the interested reader to section 5 of that paper for a detailed discussion. Here we restrict ourselves to pointing out the di erences with respect to the up quark model: Due to the larger number of nal states, at a xed mediator mass m and xed coupling matrix , the relic abundance constraint (5.2) demands a smaller DM mass in this model, relative to the up quark DMFV model. We can observe this in gure 5, when compared to gure 5.2 of [22]. Therefore, the obtained lower DM mass bound is similar to the one obtained in [22], although the LHC constraints studied in section 3 force us to impose a more stringent upper bound on the DM coupling strength. Since more nal states exist for the DM annihilation process, the impact of passing the threshold for the tt nal state is less signi cant. 6 Direct detection constraints Last but not least, in this section we consider the constraints from direct detection experiments that search for the scattering of DM particles o the nuclei of the target material. The current best limits on the WIMP nucleon scattering cross section are set by experiments using xenon as target material, in particular XENON1T [43], and major improvements are expected over the coming years. The WIMP nucleon scattering is dominated by spin-independent contributions, due to coherence e ects. In the quark doublet DMFV model, in analogy to the right-handed DMFV models [3, 22], the total spin-independent cross section reads n;nat-Xe = X SI i 9 i=1 2 An2 Zfp + (Ai i Z)fn 2 ; (6.1) where n is the reduced mass of the WIMP nucleon system. In writing (6.1) we sum over all stable and quasi-stable xenon isotopes. Their atomic mass numbers Ai and natural abundance i can be found in table 2 of [22]. The scattering amplitudes o protons and neutrons, fp and fn, receive contributions from the DM couplings to both up and down quarks. These contributions turn out to be the same as in the right-handed DMFV models [3, 22]. For completeness, their analytic expressions are listed in the appendix. The relevant contributions are: Tree level exchange of the mediator u;d. These contributions are positive and proportional to the avour mixing between the rst and third generation, sin2 13. Box diagrams yield contributions to both fp and fn. These are always positive. The photon penguin only contributes to fp and is positive for virtual up quarks in the loop, but negative for virtual down quarks. This additional negative contribution, relative to the up quark DMFV model, opens up the possibility for more diverse cancellation patterns of the various contributions. The Z penguin contribution with the top quark in the loop. As this contribution is proportional to the squared quark mass in the loop, the e ects of the light quarks are negligible. Note that the Z penguin provides the only negative contribution to fn. Figure 6 shows the allowed values of the avour mixing angle 13 in dependence of the coupling D ;33 of the DM t to the visible SM matter. We show the allowed regions for various strength of the direct detection bounds. The current XENON1T bounds [44], as well as the projected bounds from XENON1T [45], XENONnT [45], LUX-ZEPLIN (LZ) [46] and DARWIN [47] have been imposed respectively. For small coupling D ;33 we observe all 13 values to be allowed. This is due to the overall suppression of the scattering cross section by (D ;33)4, as discussed in detail for the up quark DMFV model in [22]. Also similar to the up quark DMFV model, for larger D ;33, an upper bound on the avour mixing angle 13 can be observed. The reason is the suppression of the tree level contributions that is required in order to allow for a su cient interference between the positive and negative contributions discussed above. For the same mediator mass and DM mass, we nd the upper bound at a slightly lower value than in the up quark DMFV model. This shift originates in the additional tree level contributions from down quark scattering. Since an average xenon isotope contains more neutrons than protons, the tree level contribution to DM-xenon scattering from down quark scattering is larger than the one from up quark scattering. At the same time, the additional negative contribution from the photon penguin with down quark avours in the loop are smaller in magnitude than the negative Z penguin with the top quark in the loop. Hence, the WIMP nucleon scattering cross section limits, for DM mass m = 250 GeV and mediator mass m = 850 GeV. The current exclusion bounds of XENON1T [43], as well as the projected bounds of XENON1T [45], XENONnT [45], LUX-ZEPLIN (LZ) [46] and DARWIN [47] have been imposed respectively. Note that in this scan we did not impose any of the other constraints discussed before, as we focus on the bare in uence of the direct detection bounds. tree level contributions need to be more strongly suppressed compared to the up quark DMFV model. This shifted balance between positive and negative contributions is also the reason why, in contrast to the up quark DMFV model, we do not nd a lower bound on 13 for any value of D ;33. Even if the tree level contributions are absent, the increased number of positive contributions can still be large enough to su ciently cancel the large (in magnitude) negative Z penguin and the smaller (in magnitude) negative photon penguin contribution. In addition, we observe that this changed cancellation pattern allows for larger (compared to the up quark DMFV model) D ;33 values for the more stringent projected bounds from future xenon experiments. This is due to the fact that in this model there is both a negative contribution to the proton coupling and to the neutron coupling, suppressing both fn and fp independently. Hence a su cient suppression of the scattering cross section is easier to achieve for the multiple xenon isotopes. Nevertheless, we still observe that more stringent bounds signi cantly constrain the allowed D ;33 values. For completeness we need to mention that, as in the up quark DMFV model [22], the top avoured DM case is still the preferred scenario in this model. The large negative Z penguin contribution to fn is the most e cient way to cancel the multitude of positive contributions and hence allows for the largest viable parameter space. 7 Combined analysis Having studied the implications of the experimental constraints from avour data, the observed relic density, and direct detection experiments, what remains to be done is to conduct a combined analysis, which is the subject of this section. Note that the LHC (a) QDF, m = 150 GeV (b) QDF, m = 450 GeV avour, relic abundance and direct detection constraints applied, for QDF scenario and di erent DM masses, with m mixing angles ij and splittings jD ;ii constraints are taken into account by restricting the parameter space of our model as discussed in section 3. For the QDF scenario, gure 7 shows the viable parameter ranges for the coupling matrix that remain after imposing the avour, relic abundance and direct detection constraints simultaneously. We observe that the allowed splittings jD ;ii D ;jj j are very restricted due to the combination of the strong avour constraints and the freeze-out scenario splitting conditions. The avour mixing angle 13 is bounded from above, which is the consequence of the combination of relic abundance and direct detection constraints. Interestingly, for the largest allowed splittings 13 the mixing angle 13 is required to take values close to the upper bound. The reason can be found in the direct detection constraint. A larger splitting 13 in QDF with a top- avoured DM candidate means a smaller D ;11 compared to D ;33. Hence, the positive box diagram contributions are smaller compared to the absolute size of the negative Z penguin. To still allow for a su cient cancellation, the mixing angle 13 must not be too small, allowing for a relevant tree level and not too large (in magnitude) Z penguin contribution. In gure 8 we show the allowed regions in the m - m t plane in the QDF scenario for di erent strengths of the direct detection exclusion limits. We observe that the current lower DM mass bound is similar to the one found in the up quark DMFV model. The reason is that the changed relic abundance phenomenology, requiring smaller couplings, counterbalances the more stringend LHC constraints. Details can be found in section 5 and section 3, respectively. Furthermore we nd that the changed cancellation pattern in the various contributions to the WIMP nucleon scattering cross section allows for larger (compared to the up quark DMFV model) D ;33 when the projected limits from future direct detection experiments are imposed. This (in addition to the previously explained relic abundance e ect) explains why the lower DM mass bound from the combined analysis is less stringent (compared avour, relic abundance and direct detection constraints applied in the QDF scenario, for = 0:01. We show the viable ranges for di erent strengths of direct detection bounds. The current exclusion bounds of XENON1T [43] as well as the projected bounds of XENON1T [45], XENONnT [45], LUXZEPLIN (LZ) [46] and DARWIN [47] are applied respectively. The interference of relic abundance and direct detection e ects results in a lower bound on the DM mass, increasing with more stringent direct detection bounds. to the up quark DMFV model) for the future direct detection bounds. For the current XENON1T limit however the weaker direct detection constraints are compensated by the stronger LHC bounds, which led us to impose a lower upper limit on the couplings D ;ii than in the up quark model. We show no results for the SFF scenario, since the combined bounds disfavour this scenario for the quark doublet model. The reason are the more stringent avour constraints in combination with the direct detection constraints on 13. To realise the SFF scenario, a su ciently large splitting between the coupling D ;33 and the other couplings is necessary. For a signi cant splitting between the couplings, the avour constraints require small avour mixing angles 13 and 23. At the same time a large splitting between D ;33 and the other couplings results in a relatively small size of the direct detection box diagram contributions compared to the absolute size of the negative Z penguin contribution. As discussed before, this requires 13 to be su ciently large, which then is in con ict with the avour constraints. Only for large values 0:3 it is possible to generate a su cient mass splitting from small splittings D ;33 D ;ii (i = 1; 2). 8 Summary and outlook To conclude our analysis of the quark doublet DMFV model, we now give a summary of all observed constraints from the multitude of data. We focus mainly on the di erences compared to the right-handed DMFV models [3, 22]. The following crucial di erences have been identi ed: The limits from LHC searches result in considerably stronger constraints, due to both additional production channels as well as the additional decay modes. To avoid constraints for the phenomenologically interesting parameter region, the couplings have to be more strictly constrained than in the right-handed DMFV models. Since the dark sector in the quark doublet model couples to all quark avours of both up- and down-type, the model is a ected by the constraints from meson mixing data in the K0 K0, D0 D0, and Bd0;s Bd0;s systems. This results in signi cantly stronger bounds on the avour mixing angles of the coupling matrix than in the up quark model which only contributed to D meson phenomenology. In case of 12, the constraints are also more stringent than in the down quark model. Since now D0 D0 and K0 K0 mixing bounds have to be satis ed simultaneously, the splitting between D ;11 and D ;22 is bounded from above, as due to the CKM misalignment small values of 12 are not enough to obtain a su cient suppression of the NP contributions. Due to the larger number of possible nal states in DM annihilation, the required coupling strength for xed DM and mediator masses is lower than in the up quark DMFV model. This e ect roughly compensates the more stringent upper bound on the couplings D ;ii from the LHC searches, so that the lower bound on the DM mass remains similar. The number of relevant contributions to the WIMP-nucleon scattering cross section is larger, resulting in a more diverse cancellation pattern in order to suppress the model prediction below the exclusion limits from direct detection experiments. In contrast to the right-handed models, we now have two negative contributions which allow to suppress both the scattering amplitudes with protons and neutrons. This not only changes the viable parameter ranges with respect to the right-handed DMFV models, but it also softens the constraints from future xenon experiments for which the isotope composition of natural xenon becomes more relevant. The full power of the constraints described above can only be appreciated in a combined analysis. We have found the following main implications for the viable parameter space of the model: The stronger avour bounds in combination with the relic abundance and direct detection constraints require small splittings between the couplings D ;ii. The QDF scenario is hence favoured over the SFF scenario. For the same reason, two avour freeze-out scenarios requiring a signi cant splitting between D ;11 and D ;22 are ruled out. The combination of LHC, relic abundance and direct detection constraints result in a lower bound on the DM mass, becoming stronger with future improved direct detection cross section limits. The bound is however more relaxed than in the up quark DMFV model, thanks to the smaller couplings required by the thermal freezeout condition. Keeping in mind that the lowest valid DM masses demand the largest allowed couplings, we have to conclude that the bounds from LHC searches result in the most HJEP02(18)5 stringent limits for a large part of the phenomenologically interesting parameter space. LHC run 2 data will hence push the exclusion limits even further. In contrast to the right-handed DMFV models, collider constraints prove to be the most e cient way to test a signi cant part of the parameter space of the quark doublet DMFV model, in particular reaching to increased mediator masses m and signi cant couplings. Nevertheless, it is the combination of relic abundance and direct detection constraints that enables us to exclude low DM masses for all mediator masses, which remains an advantage over the pure collider bounds. Finally a brief comment is in order concerning possible signals in indirect detection experiments from DM annihilation. Annihilation in the early universe can a ect reionisation, constrained by the PLANCK experiment. With the lower bound on the DM mass of at least 100 GeV, the current data are however not sensitive enough to probe the annihilation cross-section required for thermal freeze-out [48]. Annihilation of b- avoured DM has also been shown to provide a possible explanation for the galactic center gamma-ray excess [15]. However, also in this case the lower bound on the DM mass is in con ict with the required mass scale of about 50 GeV. The analysis presented in this paper completes our exploratory study of quark avoured DM beyond MFV, having investigated in turn the phenomenology of coupling to the righthanded down quarks [3], right-handed up quarks [22], and the left-handed quark doublets. Throughout this journey, Dark Minimal Flavour Violation has proven to serve as a simple yet e cient concept to allow for new avour and CP violating e ects in the coupling to the dark sector, thereby signi cantly altering the predicted phenomenology. While restricting ourselves to the study of simpli ed models is phenomenologically justi ed, it would certainly also be interesting to investigate possible embeddings of the analysed setups We are grateful to the Karlsruhe House of Young Scientists (KHYS) for supporting S. D.'s internship at the KIT. S. D. acknowledges the hospitality of the KIT Institute of Theoretical Particle Physics during his stay. The work of S. K. is supported by the DFG-funded into more complete theories. Acknowledgments Doctoral School KSETA. A Technical details relevant for our analysis. In this appendix we provide some analytic expressions and numerical input parameters The loop function L(xx; xj ) is given by L(xi; xj ) = (xi xi2 log(xi) xj )(1 xi)2 + xj2 log(xj ) (xj xi)(1 xj )2 + (1 1 xi)(1 xj ) ! : (A.1) BK = 0:7625 fD = 209:2 MeV BD(3 GeV) = 0:75 fBd fBs q ^ q ^ BBd = 228 MeV BBs = 275 MeV The DM scattering amplitudes o protons, fp, and neutrons, fn, receive various contributions discussed in section 6. Denoting the contributions from the DM-up (down) quark coupling by a superscript u (d), we have: Z penguin contributions: tree level contributions box diagram contributions f tree;u = 2fntree;u = j4 mut2j2 ; p 2fptree;d = fntree;d = j4~mdb2j2 ; f box;u = 2fnbox;u = p 2fpbox;d = fnbox;d = i;j i;j X j 3u2ij22jmj2tj2 L X j~3d2ij22j~mjb2j2 L mq2i m2 mq2i m2 ; ; m2 j ! m2 m2 j ! m2 ; ; with the loop function L given in equation (A.1); photon penguin contributions f photon;u = p f photon;d = + X j~ibj2e2 " p W being the weak mixing angle. 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Monika Blanke, Satrajit Das, Simon Kast. Flavoured Dark Matter moving left, Journal of High Energy Physics, 2018, 105, DOI: 10.1007/JHEP02(2018)105