A minimal non-supersymmetric E 6 Grand Unified Theory without intermediate symmetry Chandini Dash, 1, ∗ Snigdha Mishra, 1, † Sudhanwa Patra, 2, ‡ and Purushottam Sahu 2, § 1 Department of Physics, Berhampur University, Odisha-760007, India. 2 Department of Physics, Indian Institute of Technology Bhilai, Raipur-492015, India We consider a minimal renormalizable non-supersymmetric E6 Grand Unified Theory using only fundamental representation 27 for fermions and scalars. The proposed model, guided by TeV- scale vector-like fermions and scalars offer successful gauge unification even in the absence of any intermediate symmetry. Embedded with threshold corrections, it is shown to be compatible with the present experimental limit on proton decay lifetime. The unique feature of the model shows that, the GUT threshold corrections to the unification mass, is controlled by superheavy gauge bosons only, thereby minimising the uncertainty of the GUT predictions. The scalar and fermion leptoquarks residing in 27 representation can explain flavor physics anomalies like R(K * ) and R(D * ) as reported by the LHCb collaboration and the muon anomalous magnetic moment reported by the recent Muon g - 2 experiment at Fermilab. The model can also predict a sub-eV scale neutrino at one-loop level via exchange of W and Z gauge bosons via MRIS mechanism. PACS numbers: 12.60.Cn, 95.35.+d 1. Introduction: Standard Model (SM), a masterpiece woven by Glashow, Weinberg and Salam still remains the most treasured theory of particle physics with the discov- ery of Higgs boson at LHC. However with some unsolved puzzles associated with it, the Standard Model is unlikely to be the final theory, but an effective theory operative at a high scale. Many of the pressing issues can be ad- equately addressed in Grand Unified Theories (GUTs), with key predictions on experimental findings on non- zero neutrino masses, dark matter candidature, stability of proton as well as recent flavor physics anomalies etc. E 6 GUT [1, 2] is a plausible choice of unified theory of nature, since most of the nice features of the well known GUTs SU (5) [3] and SO(10) [4, 5] are inherent here through its embedding. It has the additional advantage of accommodating some exotic particles contained in the fundamental representation 27 F , which may circumvent the unsolved issues of particle physics. In the present study, we propose a non-supersymmetric E 6 GUT in its minimal version, as an unified theory to focus on some of these issues. The novel feature of the present work is that the proposed model, guided by TeV-scale extended SM scenario and GUT threshold cor- rections, is consistent with proton lifetime bound even in absence of any intermediate symmetry. Unlike the existing GUT models with threshold effects [6–9], the proposed model shows that, the threshold corrections to the unification mass, is controlled by superheavy gauge bosons only, thereby minimising the uncertainty of the GUT predictions. Further it has the potential to address flavor-physics anomalies, Muon g − 2 anomaly and light neutrino masses. This letter is organized as follows. In sec-2, the key in- gredients of the proposed model has been described tak- ing into account the renormalization group effects. In * Electronic address: dash25chandini@gmail.com † Electronic address: mishrasnigdha60@gmail.com ‡ Electronic address: sudhanwa@iitbhilai.ac.in § Electronic address: purushottams@iitbhilai.ac.in the next section, we focus on the uncertainty for the uni- fication mass and the GUT coupling due to threshold effects in tune with the predictions for proton lifetime. The subsequent section is devoted to the phenomeno- logical prediction with reference to the neutrino mass, B-physics anomalies and the muon anomalous magnetic moment. The concluding section briefly focuses on the salient features of the model. 2. Model framework: The fundamental representa- tion of E 6 i.e., the 27 F provides unified picture of SM plus additional particles as, 27 F = Q L (3, 2, 1/6) + u R (3, 1, 2/3) + d R (3, 1, −1/3) +ℓ L (1, 2, −1/2) + e R (1, 1, −1) + N R (1, 1, 0) +D L,R (3, 1, −1/3) + Ψ L,R (1, 2, −1/2) + S L (1, 1, 0) = 15 F (SM) + Others (1) where, the numbers inside parenthesis are quantum num- bers under SM gauge group (SU (3) C ,SU (2) L ,U (1) Y ). The proposed model contains the simplest symmetry breaking chain as, E 6 M U −→ SU (3) C ⊗ SU (2) L ⊗ U (1) Y ( SM ) M Z −→ SU (3) C ⊗ U (1) Q (2) Here E 6 GUT is spontaneously broken directly to the SM gauge symmetry G 321 at M U by SM singlet belonging to 27 H . The subsequent stage of symmetry breaking of SM to low energy theory is done at M Z scale by assigning non-zero VEV to the known SM Higgs doublet contained in 27 H . However gauge unification is not possible here like other existing non-SUSY GUT models in the absence of any intermediate symmetry. Therefore to achieve uni- fication, we introduce some exotic particles contained in the fundamental representation 27 F/H i.e., one copy of vector-like fermions D L,R (3, 1, −1/3), three copies of Ψ L,R (1, 2, −1/2) and three copies of sterile fermions N R (1, 1, 0), S L (1, 1, 0) as well as scalars s( 3, 1, 1/3) along with another conventional doublet φ(1, 2, −1/2), which are operative at a mass scale M I . It is noteworthy to mention that, to maintain minimality, we use only those arXiv:2109.12536v1 [hep-ph] 26 Sep 2021