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 leptoquarks and diquarks? Hiroaki Sugiyama1 1Department of Physics, University of Toyama, Toyama 930-8555, Japan Abstract. We investigate a model in which tiny neutrino masses are generated at the two-loop level by using scalar leptoquark and diquark multiplets. The diquark can be singly produced at the LHC, and it can decay into a pair of leptoquarks through the lepton number violating interaction. Subsequent decays of the two leptoquarks can provide a clear signature of the lepton number violation, namely two QCD jets and a pair of same-signed charged leptons 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 particles 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 particle physics, the addition of the Ma- S α 3 1 −1=3 1 1=3 jorana mass term of neutrinos (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 beta decay is extremely important because it gives ev- SU(2)L, and hypercharge Y = −1=3. We also introduce a idence that neutrinos are Majorana particles. Such pro- scalar diquark multiplet S DQ whose baryon 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 baryon number conservation is imposed to the mental than light neutrino masses as the L#V parameter at model such that the proton 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 n o therefore the production cross sections are not so signif- c α α α ∗ L = − L (Y )` i σ Q + (` )c (Y )` u (S ) icant at the LHC. However, new particles in the loop Yukawa ` 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 hadron colliders. 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 quarks. Then, the SU(2)L part- 0 = y 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 y ν = (U ) ` ν` , 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 (` = e; µ, τ) spectively. Under the SM gauge group, the S is as- LQ and the down-type quark 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. Thisis an Open Access article distributed under the terms of the Creative Commons Attribution License 2. 0 , which permits unrestricted use, dist ribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20134918002 EPJ Web of Conferences ff At the loop level, e ects of leptoquarks on charged ` ! ` γ ¯ lepton transitions, i.e., i j , have also been stud- ½ ½ ¿ ¿ Ë ied [10]. Since we assume that S has the Yukawa inter- Ë LQ ÄÉ ÄÉ ¾ = ¿ action only with the left-handed quarks (namely YR 0), Ë É the contribution from the top quark loop does not give a large enhancement of ` ! ` γ. Then, the branch- i j d d ´d µ ´d µ Ê Ä Ä Ê µ ! γ µ ! γ = ª ª ing ratio of e is calculated as BR( e ) Ä µ ´ ¼ ( ) Ä Ì 2 Ñ Ñ ¼ y µ ´Y ´Y µ Y µ ´ 2 4 i × Ä j Ä 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 neutrino oscillation 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 0 ν ν c σ ! The neutrino mass term 2 (Mν)`` `L ( `0 L) in the fla- duction crossp section (dd S DQ) is about 5 fb at the vor basis is generated by a two-loop diagram in Fig. 1 in- LHC withp 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 neutral current ∗ y processes in the down-type quark sector. Especially, it 0 = + µ ; (Mν)`` 24 (YL)`i md (Ys)i j Ii j md (YL) j`0 (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)``0 ) 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 Tevatron and ergy.