RESEARCH ARTICLE Algebraic Hyperstructure of Observable Elementary Particles Including the Higgs Boson Bijan Davvaz 1 • A. Dehghan Nezhad 1 • S. M. Moosavi Nejad 1 Received: 13 November 2015 / Revised: 20 June 2018 / Accepted: 5 September 2018 Ó Indian Academy of Sciences 2018 Abstract The standard model (SM) of particle physics is a gauge-field theoretical model, produced of two non-abelian gauge groups and one abelian gauge group. This model has proved to be extremely successful during the past three decades. The Higgs boson which plays a unique role in the SM was the last part of the SM that was experimentally verified in 2012. In the SM, all observable particles are classified into three generations of matter, i.e., hadrons, leptons and gauge vector bosons. In this paper it is shown that the leptons and gauge bosons along with the interac- tions between their members construct a weak algebraic hyperstructure. Weak algebraic hyperstructures or H v - structures introduced by Vougiouklis. The class of H v - structures is larger than the well-known one originated from the hypergroup in the sense of Marty. This new sight to the elementary particles would make a new arrangement to the elementary particles. Keywords Algebraic hyperstructure  H v -subgroup  Particle physics  Leptons  Gauge vector bosons 1 Introduction Hyperstructure theory was born in 1934 when Marty [1] defined hypergroups as a generalization of groups. Basic definitions and results about the hyperstructures can be found in [2, 3]. The theory of H v -structures has been introduced by Vougiouklis [4]. The concept of H v -struc- tures constitutes a generalization of the well-known algebraic hyperstructures (hypergroups, hyperrings, hypermodules). Actually, some axioms concerning the above hyperstructures are replaced by their corresponding weak axioms. Basic definitions and results about the H v - structures are given in [5, 6], see also [7–9]. The theory of H v -structures has many applications in Chemistry [10–13], Biology [14, 15] and Physics [16]. In the standard model (SM) of particle physics, all observable particles are categorized into three generations: hadrons, leptons and gauge bosons. These particles are listed in Table 1. Hadrons including the baryons and mesons are constructed from quarks, while leptons and gauge bosons do not have inner structures. According to the SM, quarks are the elementary particles which cannot be found freely and they are appeared in the combined structures of two or three ones. Triplex structures are called hadrons so the duplex structures including one quark and antiquark are known as mesons. Quarks are also classified into three generations, i.e., the first generation including the Up and Down flavors, the second generation consisting of the Strange and Charm quarks and the third generation which includes the Bottom and Top quarks. Since the variety of hadronic structures is so much, then the deter- mination of algebraic hyperstructure of quarks can be constructive to study the properties of hadrons. In [16], we provided a physical example of H v -structures associated with the leptons group. (The reader can see some properties of leptons in [17–20].) We considered this important group of the elementary particles and showed that this set along with the interactions between its mem- bers can be described by the algebraic hyperstructures. In the present work, we add the SM gauge bosons to the leptons set and show that they construct an algebraic hyperstructure. This extension makes the study more complicated. In the next section, we shall explain these sets & Bijan Davvaz davvaz@yazd.ac.ir 1 Yazd University, Yazd, Iran 123 Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. https://doi.org/10.1007/s40010-018-0553-z