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RK and RK* in an Aligned 2HDM with Right-Handed Neutrinos

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RK and RK* in an Aligned 2HDM with Right-Handed Neutrinos PHYSICAL REVIEW D 101, 115009 (2020) RK and RKÃ in an aligned 2HDM with right-handed neutrinos † ‡ Luigi Delle Rose,1,2,* Shaaban Khalil,3, Simon J. D. King ,2,4, and Stefano Moretti2,5,§ 1INFN, Sezione di Firenze, and Dipartimento di Fisica ed Astronomia, Universit`a di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy 2School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, United Kingdom 3Center for Fundamental Physics, Zewail City of Science and Technology, 6 October City, Giza 12588, Egypt 4INFN, Sezione di Padova, and Dipartimento di Fisica ed Astronomia G. Galilei, Universit`a di Padova, Via Marzolo 8, 35131 Padova, Italy 5Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom (Received 3 September 2019; accepted 21 May 2020; published 4 June 2020) We consider the possibility of explaining the recent RK and RKÃ anomalies in a two-Higgs doublet model, known as aligned, combined with a low-scale seesaw mechanism generating light neutrino masses and mixings. In this class of models, a large Yukawa coupling allows for significant nonuniversal leptonic contributions, through box diagrams mediated by charged Higgs bosons and right-handed neutrinos, to the þ − b → sl l transition that can then account for both RK and RKÃ anomalies. DOI: 10.1103/PhysRevD.101.115009 I. INTRODUCTION Therefore, the RK and RKÃ anomalies attracted the attention of theoretical particle physicists, and several new physics Recently, the LHCb Collaboration announced intriguing þ → þμþμ− scenarios have been proposed to accommodate these results [1,2] for the ratios RK ¼ BRðB K Þ= – þ þ þ − 0 Ã0 þ − results; see Refs. [4 120]. B → K e e R Ã B → K μ μ = BRð Þ and K ¼ BRð Þ A nontrivial flavor structure in the lepton sector is 0 → Ã0 þ − BRðB K e e Þ. In fact, it was reported that for two already required, beyond the SM, in order to explain the dilepton invariant mass-squared bins, RK and RKÃ , are observation of neutrino oscillations. Therefore, it is plau- given by sible and very attractive if the mechanism behind the B anomalies can be related to the same physics responsible 0 846þ0.060þ0.016 1 1 2 ≤ 2 ≤ 6 2 RK ¼ . −0.054−0.014 for . GeV q GeV ; for the nonzero neutrino masses and oscillations. In view of 0 66þ0.11 0 03 0 045 2 ≤ 2 ≤ 1 1 2 this, one then ought to explore extensions of the SM able to . −0.07 Æ . for . GeV q . GeV R Ã ¼ address both phenomena. K 0 69þ0.11 0 05 1 1 2 ≤ 2 ≤ 6 2 . −0.07 Æ . for . GeV q GeV : One of the possible scenarios for generating the observed ð1Þ lepton nonuniversality is to allow for large Yukawa couplings of the right-handed neutrinos with Higgs fields These measurements contradict the standard model (SM) and charged leptons, as in a low-scale seesaw mechanism, SM ≃ SM ≃ 1 ≈2 5σ with the inverse seesaw being one of the most notorious expectations, RK RKÃ [3],bya . deviation. Hence, they are considered as important hints of new examples, for generating light neutrino masses. In this case, a nontrivial neutrino Yukawa matrix may lead to different physics that violates lepton universality. − − Any signal of possible lepton nonuniversality would be results for BRðB → Keþe Þ and BRðB → Kμþμ Þ. This striking evidence for physics beyond the SM (BSM). framework has been recently considered in the super- symmetric (SUSY) B − L extension of the SM, where it was shown that the box diagram mediated by a right- *[email protected] † [email protected] handed sneutrino, Higgsino-like chargino, and light stop ‡ [email protected] can account simultaneously for both RK and RKÃ [121].In §[email protected] non-SUSY models, a similar box diagram can be obtained through a charged Higgs, instead of a chargino, and a right- Published by the American Physical Society under the terms of handed neutrino, instead of a right-handed sneutrino. the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to Therefore, a rather minimal model that can account for the author(s) and the published article’s title, journal citation, these discrepancies is an extension of the SM with two- and DOI. Funded by SCOAP3. Higgs doublets (so that we can have a physical charged 2470-0010=2020=101(11)=115009(14) 115009-1 Published by the American Physical Society ROSE, KHALIL, KING, and MORETTI PHYS. REV. D 101, 115009 (2020) Higgs boson) and right-handed neutrinos along with a low- II. A2HDM scale seesaw mechanism (to guarantee large neutrino The 2HDM is characterized by two Higgs doublets with Yukawa couplings). For earlier works in the context of hypercharge Y ¼ 1=2, which, in the Higgs basis, can be two-Higgs doublet models with or without extra neutral parametrized as leptons, see, for instance, Refs. [101,122–125]. Note that there have been several attempts at explaining the above Gþ Hþ results through the penguin diagram as well, with a Φ1 ¼ 1 0 0 ; Φ2 ¼ 1 0 0 ; ð2Þ pffiffi ϕ pffiffi ϕ ϕ nonuniversal Z0 (see the previous list for examples, 2ðvþ 1 þiG Þ 2ð 2 þi 3Þ Refs. [4–120]) and also through tree-level mediation of a flavor-violating Z0 or leptoquark that induces a nonuniver- where v is the electroweak (EW) vacuum expectation value 0 sal b → slþl− transition. and Gþ and G denote the Goldstone bosons. The two The two-Higgs doublet model (2HDM), which is moti- doublets describe five physical scalar degrees of freedom vated by SUSY and grand unified theories, is the simplest which are given by the two components of the charged Æ φ0 model that includes charged Higgs bosons. According to Higgs H and three neutral states i ¼fh; H; Ag, the latter ϕ0 the types of couplings of the two-Higgs doublets to the SM obtained from the rotation of the i fields into the mass fermions doublets and singlets, we may have a different M2 eigenstate basis. The scalar squared mass matrix S is type of 2HDMs. For example, if only one Higgs doublet determined by the structure of the 2HDM scalar potential, couples to the SM fermions, one obtains the type I 2HDM, see, for instance, Refs. [126–128], and diagonalized by the while in the case of one Higgs doublet coupling to the up orthogonal matrix R, where quarks and the second Higgs doublet coupling to the down quarks and charged leptons, one obtains the type II 2HDM. RM2RT 2 2 2 φ0 R ϕ0 S ¼ diagðMh;MH;MAÞ; i ¼ ij i : ð3Þ Also, we may have a type III or IV 2HDM if both Higgs doublets couple to both up and down quarks as well as φ0 In general, the three mass eigenstates i do not have charged leptons. However, severe constraints are imposed definite CP transformation properties, but in the CP- on 2HDMs due to their large contributions to flavor 0 conserving scenario, ϕ3 does not mix with the other two changing neutral currents (FCNCs) that contradict the neutral states, and the scalar spectrum consists of a CP-odd current experimental limits. Therefore, assumptions on 0 field A ¼ ϕ3 and two CP-even fields h and H that are the Yukawa couplings generated by different Higgs dou- defined from the interaction eigenstates through the two- blets are usually imposed. One of these assumptions is the dimensional orthogonal matrix alignment between the Yukawa couplings generated by Φ1 and Φ2, the two Higgs doublet fields. This class of models 0 h cos α sin α ϕ1 is called the aligned 2HDM (A2HDM). It is worth ¼ : ð4Þ − α α ϕ0 mentioning that, as discussed below, other 2HDMs cannot H sin cos 2 account for the LHCb results of lepton nonuniversality. In this paper, we emphasize that in the A2HDM, The most general Yukawa Lagrangian of the 2HDM can extended by (heavy) right-handed neutrinos in order to be written in the Higgs basis as generate the (light) neutrino masses through a seesaw −L ¯ 0 0 Φ 0 Φ 0 ¯ 0 0 Φ˜ 0 Φ˜ 0 mechanism, interesting results can be obtained for several Y ¼ QL ðY1d 1 þ Y2d 2ÞdR þ QL ðY1u 1 þ Y2u 2ÞuR flavor observables, such as μ → eγ; B → μμ; and, indeed, ¯ 0 0 Φ 0 Φ l0 ¯ 0 0 Φ˜ 0 Φ˜ ν0 s þ LLðY1l 1 þ Y2l 2Þ R þ LLðY1ν 1 þ Y2ν 2Þ R R ðÞ . In particular, one can account simultaneously for K þ H:c:; ð5Þ both aforementioned results on RK and RKÃ , through a box diagram mediated by a right-handed neutrino, top quark, 0 0 0 0 l0 ν0 and charged Higgs boson. where the quark QL;uR;dR and lepton LR; R; R fields are The paper is organized as follows. In Sec. II,we defined in the weak interaction basis and we also included the couplings of the left-handed lepton doublets with introduce the main features of our A2HDM focusing on Φ the neutrino sector and its interplay with the Higgs the right-handed neutrinos. The 1;2 fields are the two structures. (Here, we also briefly review some particular Higgs doublets in the Higgs basis, and, as customary, Φ˜ σ2ΦÃ 0 0 realizations of low-scale seesaw models for generating light i ¼ i i . The Yukawa couplings Y1j and Y2j, with 0 0 neutrino masses.) In Sec. III, we discuss the most relevant j ¼ u; d; l, are 3 × 3 complex matrices, while Y1ν and Y2ν constraints from flavor physics that affect our A2HDM are 3 × nR matrices, with nR being the number of right- 0 0 parameter space.
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