EPJ Web of Conferences 49, 18002 (2013) DOI: 10.1051/epjconf/ 20134918002 C Owned by the authors, published by EDP Sciences, 2013

Lepton number violation at the LHC with and diquarks⋆

Hiroaki Sugiyama1 1Department of Physics, University of Toyama, Toyama 930-8555, Japan

Abstract. We investigate a model in which tiny masses are generated at the two-loop level by using scalar and multiplets. The diquark can be singly produced at the LHC, and it can decay into a pair of leptoquarks through the number violating interaction. Subsequent decays of the two leptoquarks can provide a clear signature of the violation, namely two QCD jets and a pair of same-signed charged without missing energy. We show that the signal process is not suppressed while neutrino masses are appropriately suppressed.

1 Introduction Table 1. List of scalar added to the SM.

Although the lepton number is conserved in the standard SU(3)C SU(2)L U(1)Y L# B# model (SM) of physics, the addition of the Ma- S α 3 1 −1/3 1 1/3 jorana mass term of (ννc where c denotes the LQ αβ − / / charge conjugation) breaks the lepton number conserva- S DQ 6 1 2 3 0 2 3 tion by two units. The measurement of the lepton number violating (L#V) processes such as the neutrinoless dou- ble is extremely important because it gives ev- SU(2)L, and Y = −1/3. We also introduce a idence that neutrinos are Majorana particles. Such pro- scalar diquark multiplet S DQ whose number is 2/3. cesses are naively expected to be very rare because neu- We take S DQ as a 6 representation of SU(3)C, a singlet un- trino masses are very small. However, in models of radia- = − / αβ = βα der SU(2)L, and a Y 2 3 field. Note that S DQ S DQ, tively generated neutrino masses, a trilinear coupling con- where α and β (= r, g, b) denote the color indices. stant for light (e.g. TeV-scale) scalars can be more funda- The conservation is imposed to the mental than light neutrino masses as the L#V parameter at model such that the decay is forbidden. We intro- the accessible energy scale. Then, L#V processes via the duce the soft-breaking term (see the next paragraph) of the trilinear coupling constant can be significant at the TeV- lepton number conservation to the scalar potential in or- scale even if the neutrino masses are suppressed enough. der to generate Majorana neutrino masses. The Yukawa New particles related to the neutrino mass generation interactions with the leptoquark and diquark are given by are usually produced via the electroweak interaction, and { } therefore the production cross sections are not so signif- c α α α ∗ L = − L (Y )ℓ i σ Q + (ℓ )c (Y )ℓ u (S ) icant at the LHC. However, new particles in the loop Yukawa ℓ L i 2 i R R i iR LQ β αβ of the radiative seesaw models can be charged under the − α c ∗ + , (diR) (Ys)i j d jR (S DQ) H.c. (1) SU(3)C [2–4]. Such a colored particle can easily be pro- duced at . In this presentation, we inves- where σa (a = 1–3) are the Pauli matrices. We choose tigate a radiative seesaw model with a scalar leptoquark the diagonal bases of mass matrices for the charged lep- multiplet and a scalar diquark multiplet. tons and down-type . Then, the SU(2)L part- ′ = † ner of diL is described as uiL (VCKM)i j u jL, where 2 The Model VCKM is the Cabibbo-Kobayashi-Maskawa (CKM) ma- = , T trix and u j (u jR u jL) are mass eigenstates of up-type Scalar particles listed in Table 1 are introduced to the SM. ν quarks. Mass eigenstates iL of neutrinos are given by The model is briefly mentioned in Ref. [2]. The model † ν = (U ) ℓ νℓ , where UMNS is the Maki-Nakagawa- includes a scalar leptoquark multiplet S whose lepton iL MNS i L LQ Sakata (MNS) matrix. The Yukawa matrices (YL, YR, and number (L#) and baryon number (B#) are 1 and 1/3, re- Ys) are 3 × 3 matrices under the lepton flavor (ℓ = e, µ, τ) spectively. Under the SM gauge group, the S is as- LQ and the down-type flavor ( ij, = 1–3). While YL and signed to the same representation of right-handed down- YR are general complex matrices, Ys is a symmetric matrix type quarks; a 3 representation of SU(3)C, a singlet under T = (Ys Ys). Note that neutrinos interact with the leptoquark ⋆ This presentation is based on our work in Ref. [1]. only through YL.

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j 3α YLY /(256πG m ), where α = 1/137. EM L eµ F LQ EM For example, a benchmark point shown in Appendix A Figure 1. The two-loop diagram for the neutrino mass generation gives BR(µ → eγ) = 6.5 × 10−13 which satisfies the cur- in the model. rent upper bound (2.4 × 10−12 at 90 % confidence level) in the MEG experiment [11].

In the scalar potential of the model, we introduce the following three-point interaction: 3.2 Diquark

α ∗ β ∗ αβ µ + At the LHC, the diquark S DQ in the cZBM would be singly (S LQ) (S LQ) S DQ H.c. (2) produced by the annihilation of two down-type quarks The coupling constant µ softly breaks the lepton number via (Ys)11. The (Ys)11 in the cZBM is less constrained conservation by two units while the baryon number is con- by the data because its contribution 2/ 2 served. There is no other possible soft-breaking term of to neutrino masses is suppressed by md mDQ. If we as- / = . = the lepton number and or the baryon number. sume (Ys)11 0 1 and mDQ 4 TeV, the single pro- 1 ′ ν ν c σ → The neutrino mass term 2 (Mν)ℓℓ ℓL ( ℓ′ L) in the fla- duction cross√ section (dd S DQ) is about 5 fb at the vor basis is generated by a two-loop diagram in Fig. 1 in- LHC with√ s = 14 TeV [12]. Note that the CMS exper- cluding the leptoquark and the diquark. The diagram is iment at s = 7 TeV with 1 fb−1 integrated luminosity similar to the one in the Zee-Babu model (ZBM) [6] al- excludes diquark masses between 1 TeV and 3.52 TeV at though SU(3)C-singlet particles in the loop are replaced 95 % confidence level by assuming the diquark decay into with colored particles. Thus, we refer to this model as the two QCD jets for the E6 diquark which couples with an colored Zee-Babu model (cZBM). The neutrino mass ma- up-type quark and a down-type quark [13]. trix in the cZBM is calculated as The diquark induces flavor changing

∗ † processes in the down-type quark sector. Especially, it ′ = + µ , (Mν)ℓℓ 24 (YL)ℓi md (Ys)i j Ii j md (YL) jℓ′ (3) 0 0 0 0 0 0 i j gives tree-level contributions to K -K , Bd-Bd and Bs -Bs mixings, resulting in strong constraints on Ys. By using where Ii j is the two loop function (See Ref. [5] for the the notations in Ref. [14], the benchmark point in Eqs. (4) explicit form of Ii j). gives Ce1 = −(Y∗) (Y ) /(2m2 ) = 0. Similarly, we have Hereafter, we restrict ourselves to the simplest sce- K s 11 s 22 DQ Ce1 = +1.2 × 10−12 GeV−2 and Ce1 = 0. These values nario where YR (which does not contribute to (Mν)ℓℓ′ ) is Bd Bs small enough to be ignored. A benchmark point in the pa- satisfy the constraints obtained in Ref. [14]. rameter space of the cZBM is shown in Appendix A. The diquark in the cZBM decays into not only a pair of the down-type quarks but also a pair of leptoquarks. Sub- sequently, 50 % of each leptoquark decays into an up-type 3 New colored scalars at the LHC quark (a down-type quark) and a charged lepton (a neu- trino). Then, the model provides a characteristic signature 3.1 Leptoquark in Fig. 2, whose final state consists of two QCD jets and the same-signed charged lepton pair without missing en- The leptoquarks have been searched at the and ergy. The decay chain of the diquark can be fully recon- the LHC. The most stringent lower bound on m at 95 % LQ structed at the LHC. This signature can be a smoking gun confidence level is set√ as 830 GeV (840 GeV) by the re- − for the lepton number violation because no lepton number cent CMS result at s = 7 TeV with 5.0 fb 1 integrated is taken away by invisible particles. There is no irreducible luminosity [7] (See also Refs. [8]). background in principle because the SM conserves the lep- The leptoquark induces various LFV processes. At ton number. It would be also very rare that the SM process the tree level, four- operators (two left-handed lep- mimics the signal process because the leptons in the signal tons and two left-handed quarks) are generated by inte- γµµ γ events are too energetic to be produced in the SM process. grating leptoquarks out. Operators (eL L)(uL µuL) and µ It should be emphasized that the event rate of the pro- (ν γ ν ′ )(d γµ s ) are strongly constrained by the µ-e ℓL ℓ L L L cess is not necessarily suppressed though the full pro- conversion search and the K decay measurement, cess picks up all new coupling constants relevant to the respectively [9]. For the benchmark√ point in Appendix A, µ ∗ 2 −11 small neutrino masses (namely, Ys, , and YL). One rea- we have |(Y ) (Y )µ |/(4 2 G m ) = 6.1 × 10 and L e1 √L 1 F LQ son for that is because the process in Fig. 2 does not have ∗ − | ′ |/ 2 ≲ 7 2 2 (YL)ℓ1(YL)ℓ 2 (4 2 GF mLQ) 10 which satisfy con- suppressions with the two-loop factor 1/(16π ) and with −5 −2 straints shown in Ref. [9], where GF = 1.17×10 GeV . down-type quark masses, which are used for tiny neu-

18002-p.2 Hadron Physics Symposium 2012

A A benchmark point

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d 1.0 × 10 0 0  ÄÉ Ê   =  − . × −2 , ¼ Ys  0 0 1 2 10  (4b) ` −2 −4 Ä 0 −1.2 × 10 −3.8 × 10 µ = , = , = . Figure 2. The same-signed charged lepton signature without 1 TeV mLQ 1 TeV mDQ 4 TeV (4c) missing energy at the LHC. The benchmark point gives the following values: 2 2 2 sin 2θ23 = 1, sin 2θ13 = 0.1, sin 2θ12 = 0.87, δ = 0, ≃ ∆ 2 = . × −3 2 > ∆ 2 = m1 0, m31 2 4 10 eV 0, and m21 . × −5 2 ff trino masses. The other reason is that on-shell produc- 7 6 10 eV . The e ective mass relevant for the neu- ≃ . × −3 tions of a diquark and leptoquarks are utilized as σ(dd → trinoless is (Mν)ee 1 5 10 eV. [∑ ] → → ℓ 2 S DQ)BR(S DQ S LQS LQ) ℓ,i BR(S LQ LuiL) ; even if a partial decay width is controlled by a small coupling References → ℓ constant (e.g., S LQ LuiL via (YL)ℓi), its branching ratio becomes sizable when the total decay width is also con- [1] M. Kohda, H. Sugiyama and K. Tsumura, Phys. Lett. trolled by small coupling constants. In this scenario, the B 718, 1436 (2013). cZBM seems the new physics model which is the most [2] K. S. Babu and C. N. Leung, Nucl. Phys. B 619, 667 easily probed at the LHC and takes us to the top of the (2001). energy frontier. [3] D. Aristizabal Sierra, M. Hirsch and S. G. Kovalenko, For the benchmark point shown in the Appendix A, the Phys. Rev. D 77, 055011 (2008). decay branching ration for S DQ → S LQS LQ is 85 %. Then, [4] P. Fileviez Perez and M. B. Wise, Phys. Rev. D 80, 15 % (7 %) of S LQ decays into a quark (a top quark) 053006 (2009). associated with an or a . Decays into an up [5] K. S. Babu and C. Macesanu, Phys. Rev. D 67, 073010 quark are negligible for the bench mark point. The de- (2003). cay into a lepton might not be reliable because it gives [6] A. Zee, Nucl. Phys. B 264, 99 (1986); K. S. Babu, missing neutrinos. Even if S LQ decays into a top quark, Phys. Lett. B 203, 132 (1988). hadronic decays (68 %) of W± from the top quark decay [7] S. Chatrchyan et al. [CMS Collaboration], Phys. Rev. have no missing energy. As a result, the cross section for D 86, 052013 (2012). L#V events√ without missing energy is about 0.18 fb at the [8] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B LHC with s = 14 TeV for the benchmark point. 709, 158 (2012) [Erratum-ibid. 711, 442 (2012)]; Eur. Phys. J. C 72, 2151 (2012); S. Chatrchyan et al. [CMS Collaboration], JHEP 1212, 055 (2012). 4 Conclusions [9] M. Carpentier and S. Davidson, Eur. Phys. J. C 70, 1071 (2010). [10] R. Benbrik and C. -K. Chua, Phys. Rev. D 78, 075025 We have studied a model for neutrino mass generation (2008). with the scalar leptoquark S LQ and diquark S DQ. Tiny Ma- [11] J. Adam et al. [MEG Collaboration], Phys. Rev. Lett. jorana neutrino masses are induced at the two-loop level 107, 171801 (2011). where the colored particles are involved in the loop. [12] O. Cakir and M. Sahin, Phys. Rev. D 72, 115011 The model gives a distinctive signature at the LHC, (2005); T. Han, I. Lewis and Z. Liu, JHEP 1012, 085 − ′− (2010). namely pp → S DQ → S LQS LQ → ℓ ℓ j j without miss- ing energy, which would be a clear evidence of the lepton [13] S. Chatrchyan et al. [CMS Collaboration], Phys. number violation. We have shown that the lepton num- Lett. B 704, 123 (2011). ber violating process is not suppressed in this model while [14] M. Bona et al. [UTfit Collaboration], JHEP 0803, Majorana neutrino masses are highly suppressed. 049 (2008).

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