Abstract:We propose new backgrounds of extra dimensions to lead to four-dimensional chiral models with three generations of matter fermions, that is T 2 /Z N twisted orbifolds with magnetic fluxes. We consider gauge theory on six-dimensional space-time, which contains the T 2 /Z N orbifold with magnetic flux, Scherk-Schwarz phases and Wilson line phases. We classify all the possible Scherk-Schwarz and Wilson line phases on T 2 /Z N orbifolds with magnetic fluxes. The behavior of zero modes is studied. We derive the number of zero modes for each eigenvalue of the Z N twist, showing explicitly examples of wave functions. We also investigate Kaluza-Klein mode functions and mass spectra.

We propose a new model which can simultaneously and naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo-Kobayashi-Maskawa matrix from the geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermions at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of the nondiagonal elements of fermion mass matrices is found to be severely restricted due to the geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy. a Recently, the ATLAS and CMS experimental groups of the CERN Large Hadron Collider (LHC) have announced the excess at 125 GeV, which is consistent with the Standard Model (SM) Higgs boson, with a local significance of 5σ after combining 7 TeV and 8 TeV data [1,2]. This amazing happening means that the mysteries behind the last missing piece of the SM are ready to be unveiled. But the SM still has many points which are unclear, in spite of lots of effort from physicists.One is called the "quark mass hierarchy problem". In the SM, we are forced to comply with a hierarchy of almost five orders of magnitude in Yukawa couplings of quarks for describing the suitable quark masses. Closely related to this issue, the SM cannot answer the mechanism behind the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes the strengths of generationchanging interactions in the SM. In addition to these two issues, we cannot explain why we introduce three copies of quarks whose quantum numbers are the same except for their masses and the degrees of mixings in the above interactions. Many attempts have been made to explain the issues within the four-dimensional (4D) Quantum Field Theory (QFT) framework with, including, for example, launching new continuous and/or discrete symmetries, introducing new matter and interactions, and discussing renormalization group (RG) effects from a theory at a (very) high energy scale compared to the electroweak (EW) scale.When we focus on the case in five dimensions (5D), where there is one additional spatial direction, we can find a new useful tool for tackling the above and other problems: geometry. Two of the most renowned studies which show the power of geometry are [3,4], where the authors proposed innovative ways for solving the hierarchy problem. Extra space can have a huge variety of structure, which are detected as differences from the 4D effective theory point of view. In a 5D QFT framework, we also find new mechanisms which we cannot find in 4D, for example, generating spontaneous gauge symmetry breaking with a global Wilson loop operator [5][6][7], and symmetry br...

Recently, deviations in flavor observables ofB → D ( * ) τν have been shown between the predictions in the Standard Model and the experimental results reported by BaBar, Belle, and LHCb collaborations. One of the solutions to this anomaly is obtained in a class of leptoquark model with a scalar leptoquark boson S 1 , which is a SU (3) c triplet and SU (2) L singlet particle with −1/3 hypercharge interacting with a quarklepton pair. With well-adjusted couplings, this model can explain the anomaly and be compatible with all flavor constraints. In such a case, the S 1 boson can be pair-produced at CERN's Large Hadron Collider (LHC) and subsequently decay as S * 1 → tτ , bν τ , and cτ . This paper explores the current 8 and 13 TeV constraints, as well as the detailed prospects at 14 TeV, of this flavor-motivated S 1 model. From the current available 8 and 13 TeV LHC searches, we obtain constraints on the S 1 boson mass for M S1 < 400 GeV -640 GeV depending on values of the leptoquark couplings to fermions. Then we study future prospects for this scenario at the 14 TeV LHC using detailed cut analyses and evaluate exclusion/discovery potentials for the flavor-motivated S 1 leptoquark model from searches for the (bν)(bν) and (cτ )(cτ ) final states. In the latter case, we consider several scenarios for the identification of charm jets. As a result, we find that the S 1 leptoquark origin of theB → D ( * ) τν anomaly can be probed with M S1 600/800 GeV at the 14 TeV LHC with L = 300/3000 fb −1 of accumulated data. One can also see that the 14 TeV LHC run II with L = 300 fb −1 can exclude the S 1 leptoquark boson up to M S1 ∼ 0.8 TeV at 95% confidence level, whereas a future 14 TeV LHC with L = 3000 fb −1 data has a potential to discover the S 1 leptoquark boson with its mass up to M S1 ∼ 1.1 TeV with over 5σ significance, from the (bν)(bν) and/or (cτ )(cτ ) searches.

We show bounds on five-and six-dimensional universal extra dimension (UED) models from the latest results of the Higgs searches at the LHC and from the electroweak precision data for the S and T parameters. We consider the minimal UED model in five dimensions and the ones in six dimensions, compactified on T 2 /Z 2 , T 2 /(Z 2 × Z 2 ), T 2 /Z 4 , S 2 , S 2 /Z 2 , the real projective plane, and the projective sphere. The highest possible ultraviolet cutoff scale for each UED model is evaluated from the electroweak vacuum stability by solving the renormalization group equation of the Higgs self-coupling. This scale turns out to be lower than the conventional one obtained from the perturbativity of the gauge coupling. The resultant 95% C.L. lower bounds on the first Kaluza-Klein scale from the LHC results and from the S, T analysis are 600 and 700 GeV in the minimal UED model, while those in the six-dimensional UED models are 800-1300 GeV and 900-1500 GeV, respectively.

We classify the combinations of parameters which lead three generations of quarks and leptons in the framework of magnetized twisted orbifolds on $T^2/Z_2$, $T^2/Z_3$, $T^2/Z_4$ and $T^2/Z_6$ with allowing nonzero discretized Wilson line phases and Scherk-Schwarz phases. We also analyze two actual examples with nonzero phases leading to one-pair Higgs and five-pair Higgses and discuss the difference from the results without nonzero phases studied previously.Comment: 28 pages (main body and references) + 65 pages (full list of classification), 22 tables (v1); typos corrected, problem in sentence fixed (v2