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Low-Scale Quark-Lepton Unification

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Low-Scale Quark-Lepton Unification PHYSICAL REVIEW D 88, 057703 (2013) Low-scale quark-lepton unification Pavel Fileviez Pe´rez1 and Mark B. Wise2 1Particle and Astro-Particle Physics Division, Max Planck Institute for Nuclear Physics (MPIK), Saupfercheckweg 1, 69117 Heidelberg, Germany 2California Institute of Technology, Pasadena, California 91125, USA (Received 6 August 2013; published 30 September 2013) We investigate the possibility that quarks and leptons are unified at a low energy scale much smaller than the grand unified scale. A simple theory for quark-lepton unification based on the gauge group SUð4ÞC SUð2ÞL Uð1ÞR is proposed. This theory predicts the existence of scalar leptoquarks which could be produced at the Large Hadron Collider. In order to have light neutrinos without fine-tuning, their masses are generated through the inverse seesaw mechanism. DOI: 10.1103/PhysRevD.88.057703 PACS numbers: 12.10.Dm, 14.80.Sv I. INTRODUCTION our model and outline its main phenomenological consequences. In the Standard Model (SM) there are two types of In Sec. II we present the simplest model with quark- matter fields: the lepton and quark fields. The SM with lepton unification at a low scale that is consistent with the right-handed neutrinos describes all the measured properties experimental properties of quarks and leptons. In Sec. III of quarks and leptons. Grand unified theories based on we discuss the properties of the vector and scalar lepto- ð10Þ gauge groups, such as SU(5) or SO , provide one avenue quarks. Finally, we briefly summarize our main results for unifying the properties of quarks and leptons since in Sec. IV. quarks and leptons are part of the same representation of the gauge group. However, in this case the scale of 15 16 II. QUARK-LEPTON UNIFICATION unification is very high, MGUT 10 – GeV. An appealing approach to quark and lepton unification In models with QL unification based on the idea that was proposed by Pati and Salam in Ref. [1]. They used an leptons have the fourth color [1] the SM quarks and leptons ð Þ ð Þ SUð4ÞC gauge symmetry and the quarks and leptons are can be unified in the same multiplets: QL;‘L , uR;R , together in the fundamental representation of the gauge and ðdR;eRÞ. Therefore, naively one finds the following group. In this framework the leptons are the fermions with relations between quark and lepton masses: the fourth color. This idea also played a major role in grand M ¼ MD and M ¼ M ; (1) unification since the Pati-Salam gauge group is the maxi- u e d ð10Þ D mal subgroup of SO . This theory also predicts the where Mu, M , Me and Md are the up-quark, Dirac neutrino, existence of right-handed neutrinos needed for the seesaw charged lepton and down-quark masses, respectively. As is mechanism [2–6] of neutrino masses. well known, these relations are not consistent with In this paper we revisit the idea of quark-lepton (QL) experiment. unification based on the Pati and Salam paper where the We now construct the simplest model of quark-lepton leptons have the fourth color. We find a very simple ex- unification based on the gauge group tension of the SM based on the gauge group SUð4ÞC GQL ¼ SUð4Þ SUð2Þ Uð1Þ ; (2) SUð2ÞL Uð1ÞR, where quarks and leptons are unified in C L R the same representation. In addition to the SM fermions the which is consistent with experimental results on the prop- model contains three right-handed singlet fermions needed erties of quarks and leptons evading the unacceptable mass to generate Majorana neutrino masses through the inverse relations discussed above, and which allows the scale for seesaw mechanism. the symmetry breaking GQL ! GSM ¼ SUð3ÞSUð2ÞL Assuming near alignment of the quark and lepton Uð1Þ to be much smaller than the grand unification scale. generations the experimental limit on the branching ratio Y 0 ! Æ Ç SUð4Þ The fermion matter fields are in the representations for KL e implies that the scale of C breaking ! must be greater than 1000 TeV. See for example the studies u FQL ¼ ð4; 2; 0Þ; (3) in Refs. [7,8] for the constraints coming from meson de decays. This theory predicts the existence of vector and scalar leptoquarks. While the vector leptoquarks must be ÀÁ F ¼ uc c ð4; 1; À1=2Þ; (4) heavy, the scalar leptoquarks could be at the TeV scale u and give rise to exotic signatures at the Large Hadron ÀÁ ¼ c c ð4 1 1 2Þ Collider. In this article we discuss the spectrum of Fd d e ; ; = : (5) 1550-7998=2013=88(5)=057703(4) 057703-1 Ó 2013 American Physical Society BRIEF REPORTS PHYSICAL REVIEW D 88, 057703 (2013) Here we have chosen to work only with left-handed v1 1 v2 M ¼ Y3 pffiffiffi þ pffiffiffi Y4 pffiffiffi ; (14) fermion fields, as is common in discussions of grand d 2 2 6 2 unified theories. The gauge group GQL is spontaneously broken to GSM v1 3 v2 M ¼ Y3 pffiffiffi À pffiffiffi Y4 pffiffiffi : (15) by the vacuum expectation value of the scalar field, e 2 2 6 2 ÀÁ ¼ 0 ð4 1 1 2Þ u R ; ; = : (6) Here the vacuum expectation values that break GSM are v1 v2 Without loss of generality the vacuum expectation value hH0i¼pffiffiffi and hH0i¼pffiffiffi : (16) h 0 i¼ 2 2 2 canp beffiffiffi taken to be only in the fourth component, R 2 v= . The SM hypercharge Y is given by Since there are four independent Yukawa coupling pffiffiffi 6 matrices in the above equations we can generate acceptable ¼ þ masses for all the quarks and leptons. However, in order to Y R 3 T4; (7) achieve light Dirac neutrino masses one needs a severe D where T4 is the properly normalized SUð4ÞC generator, that fine-tuning between the two terms contributing to M when acting on the fundamental 4 representation is the in Eq. (13). See Ref. [11] for an alternative model using diagonal matrix the Pati-Salam symmetry. 0 1 It is useful to note that the renormalizable couplings of 100 0 B C the model contain an automatic global U(1) fermion matter 1 B 010 0C symmetry Uð1Þ where the matter charges of the fermion ¼ pffiffiffi B C F T4 B C: (8) fields F ¼ 1, F ¼ F ¼1. The scalar fields do not 2 6 @ 001 0A FQL Fu Fd 000À3 transform under this symmetry. Although this model can be consistent with experiment To break the gauge group down to the low-energy SUð3ÞC the fine-tuning needed to get very light Dirac neutrinos is Uð1ÞY gauge group in a way that can give acceptable not attractive. A modest extension of the fermion content fermion masses we add two more scalar representations, a of the model allows us to avoid this fine-tuning. Higgs doublet We can generate small Majorana masses for the light ÀÁ neutrinos if we add three new singlet left-handed fermionic T þ 0 H ¼ H H ð1; 2; 1=2Þ; (9) fields N and use the following interaction terms: È ð15 2 1 2Þ 1 and the scalar ; ; = , L ¼ þ þ H c ! QL Y5FuN NN : : (17) È È 2 È ¼ 8 3 þ T4H2; (10) For simplicity, we now discuss the neutrino sector in the È4 0 one-generation case. The discussion generalizes easily to which contains a second Higgs doublet H2. The new the three-generation case. Then, there are three left-handed scalars in È are the second Higgs doublet, the color octet neutrino fields (one each of , c and N) and the neutrino with the same weak quantum numbers as the Higgs dou- mass matrix reads as È ð8 2 1 2Þ 0 10 1 blet, 8 ; ; = SM, studied by Manohar and Wise in 0 D 0 M Ref. [9], and the scalar leptoquarks È3 ð3; 2; À1=6ÞSM ÀÁB CB C c B ð DÞT 0 D CB c C and È4 ð3; 2; 7=6ÞSM. These scalar leptoquarks do not N @ M M A@ A: (18) give rise to proton decay [10] at the renormalizable level D T 0 ðM Þ N since they do not couple to a quark pair. Proton decay D occurs at the dimension-six level. Here M is given by Eq. (13) and The Yukawa interactions in this theory are given by v D pffiffiffi M ¼ Y5 : (19) Y y 2 LQL ¼ Y1FQLFuH þ Y2FQLFuÈ þ Y3H FQLFd y By assigning the N fermion charge F ¼ 1 only the term þ Y4È FQLFd þ H:c:; (11) N proportional to breaks the matter symmetry. Hence it is which after symmetry breaking give rise to the following natural to take this parameter to be much smaller than the mass matrices for the SM fermions: other entries in the mass matrix. D D 1 In the limit when Mqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, M , the model has a heavy pv1ffiffiffi pffiffiffi pv2ffiffiffi Mu ¼ Y1 þ Y2 ; (12) D 2 D 2 c 2 2 6 2 Dirac neutrino with mass ðM Þ þðM Þ , where is paired with the linear combination v1 3 v2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D ¼ pffiffiffi À pffiffiffi pffiffiffi M Y1 Y2 ; (13) ¼ð D þ D Þ ð DÞ2 þð DÞ2 2 2 6 2 h M N M = M M : (20) 057703-2 BRIEF REPORTS PHYSICAL REVIEW D 88, 057703 (2013) ¼ 3 þ The orthogonal linear combination is the light Majorana leave color and the electromagnetic charge Q TL Y neutrino unbroken, i.e., only the neutral components of , H and H2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi get expectation values. D D D 2 D 2 l ¼ðM À M NÞ= ðM Þ þðM Þ : (21) III.
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