Flavour symmetries in the dark sector are a theoretically motivated and
phenomenologically appealing concept. The dark matter particle can be
stabilised with the help of flavour symmetries, without the need to introduce
an additional discrete symmetry by hand. Apart from the usual searches in
direct and indirect detection experiments and high energy colliders, flavoured
dark matter generally also gives rise to new flavour violating interactions
leading to interesting signatures in rare meson decays. This proceedings
article reviews a simplified model of flavoured dark matter in which the dark
matter coupling to quarks constitutes a new source of flavour violation, so
that the model goes beyond Minimal Flavour Violation. Particular emphasis is
put on the discussion of its phenomenological implications in flavour, collider
and direct detection experiments.Comment: 7 pages, proceedings of The European Physical Society Conference on
  High Energy Physics, 22-29 July 2015, Vienna, Austri

Blanke, Monika

English

arXiv

Flavour symmetries in the dark sector are a theoretically motivated and phenomenologically appealing concept. The dark matter particle can be stabilised with the help of flavour symmetries, without the need to introduce an additional discrete symmetry by hand. Apart from the usual searches in direct and indirect detection experiments and high energy colliders, flavoured dark matter generally also gives rise to new flavour violating interactions leading to interesting signatures in rare meson decays. This proceedings article reviews a simplified model of flavoured dark matter in which the dark matter coupling to quarks constitutes a new source of flavour violation, so that the model goes beyond Minimal Flavour Violation. Particular emphasis is put on the discussion of its phenomenological implications in flavour, collider and direct detection experiments

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Phenomenological aspects of flavoured dark matter

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PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matterMonika Blanke∗CERN Theory Division, CH-1211 Geneva 23, SwitzerlandInstitut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology, Engesserstraße 7,D-76128 Karlsruhe, GermanyInstitut für Kernphysik, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1,76344 Eggenstein-Leopoldshafen, GermanyE-mail: monika.blanke@kit.eduFlavour symmetries in the dark sector are a theoretically motivated and phenomenologically ap-pealing concept. The dark matter particle can be stabilised with the help of flavour symmetries,without the need to introduce an additional discrete symmetry by hand. Apart from the usualsearches in direct and indirect detection experiments and high energy colliders, flavoured darkmatter generally also gives rise to new flavour violating interactions leading to interesting sig-natures in rare meson decays. This proceedings article reviews a simplified model of flavoureddark matter in which the dark matter coupling to quarks constitutes a new source of flavour vi-olation, so that the model goes beyond Minimal Flavour Violation. Particular emphasis is puton the discussion of its phenomenological implications in flavour, collider and direct detectionexperiments.The European Physical Society Conference on High Energy Physics22-29 July 2015Vienna, Austria∗Speaker.© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika Blanke1. IntroductionAstrophysical and cosmological data tell us that the visible baryonic matter constitutes only asmall fraction of the total energy density in the universe. About five times more dark matter (DM)exists which manifests itself through its gravitational interactions with ordinary Standard Model(SM) matter.Yet we have very little information on the particle nature of DM. Motivated by the conceptof Grand Unification, DM, similarly to the visible matter, could come in multiple generationsdiffering only in their masses. This idea of flavoured DM has become quite popular in recentyears (see [1] for a review). However most studies so far adopted the Minimal Flavour Violation(MFV) assumption [2, 3] for the dark sector, i. e. that no new sources of flavour violation arepresent beyond the SM Yukawa couplings, thus saving well-measured flavour changing neutralcurrent (FCNC) observables from dangerously large new contributions. At the same time howeverit prevents us from observing DM effects in precision flavour experiments.Our analysis [4] therefore abandoned the MFV principle and instead presented a simplifiedmodel of flavoured DM, in which the coupling of DM to SM quarks constitutes a new source offlavour and CP violation. In addition to the usual DM discovery channels in direct and indirectdetection experiments and collider searches, c. f. left diagram in figure 1, sizeable contributions toFCNC observables are then also expected, as depicted in the right diagram in figure 1.DMDMSMSM DMDMSMSMSMSMFigure 1: Schematic diagrams contributing to experimental constraints on flavoured DM.2. Dark Minimal Flavour ViolationIn the simplified model of [4] the gauge singlet Dirac-fermionic DM χ transforms under thetriplet representation of a new global flavour symmetry U(3)χ . Its coupling to the right-handeddown type quarks of the SM is mediated by a coloured scalar field φ . The Lagrangian of thissimplified model readsL = LSM + iχ̄ /∂ χ−mχ χ̄χ− (λi jd̄Riχ jφ +h.c.)+(Dµφ)†(Dµφ)−m2φ φ †φ +λHφ φ †φ H†H +λφφ φ †φ φ †φ , (2.1)whith i, j = 1,2,3 being flavour indices.The new Yukawa coupling λ is assumed to be the only new source of flavour symmetry break-ing, in addition to the SM Yukawa couplings Yu,d . Conceptually this ansatz extends the MFVprinciple to the dark sector flavour group, and is therefore named Dark Minimal Flavour Violation2PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika Blanke(DMFV). Despite its conceptual analogy to the MFV hypothesis, the phenomenology is very dif-ferent, as the new flavour violating coupling λ is unrelated to the SM Yukawas. Therefore DMFVcan lead to large new physics contributions to FCNC observables.The DMFV hypothesis has a number of interesting implications. First, the mass splittingsamong the dark flavours are generated by non-universalities in the coupling matrix λ :mχi = mχ(1+η λ†λ + . . .)ii . (2.2)Second, the DMFV assumption significantly reduces the number of free parameters. A conve-nient parametrisation is given byλ =Uλ Dλ , (2.3)where Uλ is a unitary matrix containing three mixing angles θ λi j and three complex phases δλi j(i j = 12,13,23) parametrised as in [6]. Dλ is a real and diagonal matrix, for which we use theparametrisationsDλ ≡ diag(Dλ ,11,Dλ ,22,Dλ ,33) = λ0 ·1+diag(λ1,λ2,−(λ1 +λ2)) . (2.4)Last but not least the DMFV hypothesis ensures DM stability, in complete analogy to thestability of DM in the MFV case [5]. The flavour symmetry U(3)Q×U(3)u×U(3)d ×U(3)χbroken only by the Yukawa couplings Yu, Yd and λ , together with SU(3)QCD implies an unbrokenZ3 symmetry, under which only the new particles χi and φ are charged.3. Precision flavour constraintsNew flavour violating interactions at the weak scale are strongly constrained by meson mixingobservables. In DMFV new contributions to K0− K̄0 mixing are generated by the box diagram infigure 2. Analogous diagrams contribute to Bd,s− B̄d,s mixing.χiφ φχjs dd sFigure 2: New contribution to K0− K̄0 mixing in DMFV.The DMFV contributions to the K− K̄, Bd− B̄d and Bs− B̄s mixing amplitudes are schemati-cally given byMK,new12 ∼((λλ †)sd)2F(x) , Md,new12 ∼((λλ †)bd)2F(x) , Ms,new12 ∼((λλ †)bs)2F(x) ,(3.1)where F(x) is the relevant loop function that is flavour independent. We see that the size of newcontributions to FCNCs is determined by the off-diagonal entries of (λλ †) which, in order not tospoil the good agreement with the data, have to be small.3PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika BlankeSuch a structure can be achieved in various ways, as discussed in detail and checked numer-ically in [4]. In short, if a sizeable mixing angle θ λi j is present, then the entries Dλ ,ii and Dλ , j j ofthe diagonal component of λ have to be quasi degenerate. Consequently we end up with the fivescenarios for the structure of λ pointed out in [4] and depicted in figure 3:1. Universality scenario – The diagonal coupling matrix Dλ is nearly universal and large mixingangles in Uλ are allowed.2. Small mixing scenario – The mixing matrix Uλ is close to the unit matrix, while Dλ isarbitrary.3. i j-degeneracy scenarios (i j = 12,13,23) – Two elements of Dλ are almost equal, Dλ ,ii 'Dλ , j j, and only the corresponding mixing angle sλi j is allowed to be large.Figure 3: Allowed ranges for the mixing angle sλ12 = sinθλ12 as a function of the non-universality parametersλ1 and λ2. The five scenarios are: universality (black), small mixing (yellow), 12-degeneracy (blue), 13-degeneracy (red), 23-degeneracy (green).The new contributions to rare K and B decays, to electroweak precision observables, and toelectric dipole moments on the other hand are small and do not constrain DMFV further.4. Dark matter phenomenologyFlavour physics gives us valuable information on the structure of the coupling matrix λ , butit cannot constrain the mass spectrum mχi of the three dark generations. However there are goodreasons to assume that the lightest state is b-flavoured, i. e. it couples dominantly to the bottomquark. In this case the agreement with direct detection experiments and LHC searches can beimproved. Additionally, b flavoured DM produces interesting b-jet signatures at the LHC and canexplain the excess γ-rays observed at the galactic centre [7].We also require the DM to be a thermal relic and assume that the mass splitting between theDM and the heavier flavours is sizeable, ∼> 10%. Then the heavier states decay before the timeof freeze-out so that the observed relic abundance translates into a relation between the couplingDλ ,33, the DM and the mediator mass. The quasi-degenerate case has also been considered in [4].4PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika BlankeSeveral diagrams yield relevant contributions to direct DM detection, see figure 4. Note thatwith the precision achieved by present experiments, mainly LUX [8], we have become sensitiveto DM quark scattering at the one loop level. Thus even if the tree level diagram is suppressed bya small mixing angle θ λ13, large contributions stemming from box and penguin diagrams are stillpresent and need to be controlled.φχbχbddqiφφχjχbχbddφqiγχbχbppFigure 4: Diagrams contributing to WIMP-nucleon scattering in the mDMFV model.In fact the one loop box and photon penguin diagrams shown in figure 4 can not be suppressedby small flavour mixing angles. Luckily however these two contributions have opposite signs,so that for a certain range of the coupling Dλ ,11, their cancellation becomes effective. DMFV istherefore a natural realisation of xenophobic DM [9].In figure 5 one can see that for large DM masses mχb ∼> 100GeV only the thermal relic con-straint restricts the allowed range for Dλ ,11. However for smaller DM masses a non-trivial interplaybetween the LUX and flavour constraints can be observed which restricts Dλ ,11 to lie in a certainrange.Figure 5: First generation coupling Dλ ,11 as functions of the DM mass mχb . The red points satisfy the boundfrom LUX, while the blue points satisfy the flavour constraints. For the yellow points both LUX and flavourconstraints are imposed.5. LHC signaturesThe new particles introduced in DMFV are expected to be accessible to the LHC. Due to theconserved Z3 symmetry they have to be pair produced, and the lightest state (assumed to be χb)escapes detection and leads to missing energy signatures. The heavier χi states, due to the smallmass splitting, give rise to soft jets or photons when decaying into the lightest state.5PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika BlankeThe signatures of DMFV are very similar to the ones from popular SUSY models with R-parity conservation. The production of φ pairs is constrained by sbottom and light squark searches,leading to the same final state signatures. Therefore the DMFV exclusion contours in the mχ -mφ plane ,shown in figure 6, can be obtained by adapting the CMS 19.5 fb−1 sbottom [10] andsquark [11] searches, by taking into account both the changes in production cross section andbranching ratios. For light DM masses these bounds reach up to mediator masses of mφ ' 850GeV,however they become significantly weaker for increasing mχ mass.Figure 6: Limits on DMFV from the CMS 19.5 fb−1 sbottom [10] and squark [11] search. The DM couplingto b-quark, Dλ ,33 is fixed everywhere by the corresponding relic abundance constraint, and all mixing anglesare set to zero for simplicity.Monojet searches instead are sensitive to direct DM pair production, as well as to pair produc-tion of the heavier χ flavours. They provide constraints on the mediator mass mφ as function of thecouplings Dλ ,ii, shown in figure 7. Contrary to the dijet constraints, in this case the obtained resultis rather insensitive to the value of the DM mass mχ .Figure 7: Limits on DMFV in terms of mass of φ (in GeV) from the CMS monojet search [13].DMFV also gives rise to some interesting signatures accessible to future searches. Similarly tothe case of flavour violating squark decays [14], φ pair production and decay can lead to one b-jet6PoS(EPS-HEP2015)390Phenomenological aspects of flavoured dark matter Monika Blankeand one light jet in the final state, accompanied by missing energy. Due to the stringent flavourphysics constraints, such a signature is unlikely to emerge in SUSY models.6. SummaryMotivated by grand unification scenarios it is theoretically well-motivated to consider that DM,in analogy to the SM fermions, carries flavour quantum number and comes in multiple copies. Suchsetups lead to interesting phenomenological implications, in particular when new flavour violatinginteractions with the SM quarks are present. Flavour precision data provide useful constraints onthe structure of the DM coupling matrix, while the mass spectrum can be constrained mostly fromdirect DM and LHC searches. A non-trivial interplay of the various sectors is identified, provingthe importance of studying the various sectors in a correlated manner.I would like to thank Prateek Agrawal and Katrin Gemmler for a very enjoyable and fruitfulcollaboration on the topic presented here.References[1] J. Kile, Mod. Phys. Lett. A 28 (2013) 1330031 [arXiv:1308.0584 [hep-ph]].[2] A. J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Phys. Lett. B 500 (2001) 161[hep-ph/0007085].[3] G. D’Ambrosio, G. F. Giudice, G. Isidori and A. Strumia, Nucl. Phys. B 645 (2002) 155[hep-ph/0207036].[4] P. Agrawal, M. Blanke and K. Gemmler, JHEP 1410 (2014) 72 [arXiv:1405.6709 [hep-ph]].[5] B. Batell, J. Pradler and M. Spannowsky, JHEP 1108 (2011) 038 [arXiv:1105.1781 [hep-ph]].[6] M. Blanke, A. J. Buras, A. Poschenrieder, S. Recksiegel, C. Tarantino, S. Uhlig and A. Weiler, Phys.Lett. B 646 (2007) 253 [hep-ph/0609284].[7] P. Agrawal, B. Batell, D. Hooper and T. Lin, Phys. Rev. D 90 (2014) 063512 [arXiv:1404.1373[hep-ph]].[8] D. S. Akerib et al. [LUX Collaboration], Phys. Rev. Lett. 112 (2014) 9, 091303 [arXiv:1310.8214[astro-ph.CO]].[9] J. L. Feng, J. Kumar and D. Sanford, Phys. Rev. D 88, no. 1, 015021 (2013) [arXiv:1306.2315[hep-ph]].[10] CMS Collaboration [CMS Collaboration], CMS-PAS-SUS-13-018.[11] S. Chatrchyan et al. [CMS Collaboration], JHEP 1406 (2014) 055 [arXiv:1402.4770 [hep-ex]].[12] CMS Collaboration [CMS Collaboration], CMS-PAS-SUS-13-009.[13] [CMS Collaboration], CMS-PAS-EXO-12-048.[14] M. Blanke, G. F. Giudice, P. Paradisi, G. Perez and J. Zupan, JHEP 1306 (2013) 022[arXiv:1302.7232 [hep-ph]].7

Phenomenological aspects of flavoured dark matter

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