SU(2)_R

SU(2)_R
Name	SU(2)_R
Type	Lie group

SU(2)_R SU(2)_R is a compact, simple Lie group that appears as a right-handed counterpart in extensions of Electroweak interaction models and in formulations of Grand Unified Theory candidates; it complements SU(2)_L in left–right symmetric constructions and features in discussions involving Parity (physics), CP symmetry, and chiral gauge structures. Historically motivated by attempts to restore parity in weak interactions, SU(2)_R has been invoked in models related to Pati–Salam model, SO(10), and Left–Right symmetric model frameworks and connects to searches at facilities such as the Large Hadron Collider and proposals like the International Linear Collider.

Introduction

The SU(2)_R factor commonly appears alongside SU(2)_L and U(1)_Y in left–right symmetric models developed to address parity violation observed in Wu experiment and to embed Weak interaction structure within unified schemes; seminal works by Mohapatra and Pati and Senjanović extended ideas from Glashow and Weinberg that underlie the Standard Model. SU(2)_R implementations interact with concepts from Neutrino oscillation phenomena, Seesaw mechanism, and the treatment of right-handed neutrinos appearing in Majorana fermion scenarios, influencing model-building in Beyond the Standard Model research pursued at institutions like CERN, Fermilab, and KEK.

Mathematical Structure

As a Lie group, SU(2)_R is isomorphic to the group of unit quaternions and shares structure with SO(3), possessing a three-dimensional Lie algebra spanned by generators satisfying su(2) commutation relations similar to those used by Pauli matrices and studied in the context of Representation theory (mathematics). The group admits a universal covering relation to Spin group constructions and fits into embeddings such as SU(2)_R × SU(2)_L ⊂ SO(4) and into larger groups like SO(10) and E6, linking to mathematical developments by Weyl, Cartan, and Dynkin. Topological features of SU(2)_R are relevant in instanton analyses analogous to those by Belavin–Polyakov–Schwartz–Tyupkin and in anomalies computed using methods related to Atiyah–Singer index theorem.

Role in Particle Physics and Gauge Theories

SU(2)_R gauges right-handed fermion doublets in left–right symmetric gauge groups such as SU(2)_L × SU(2)_R × U(1)_{B-L}, providing a framework to reinterpret parity restoration at high energies in models proposed by Pati–Salam model authors and elaborated by Mohapatra and Senjanović. It plays a role in embedding Hypercharge (Y) assignments and in realizing Electric charge formulae that relate to work by Georgi–Glashow and Weinberg (Weinberg–Salam model). Gauge bosons associated with SU(2)_R, often labeled W_R, interact with right-handed currents in processes analogous to those explored in Beta decay studies and searches influenced by experimental programs at SuperKEKB, LHCb, and ATLAS collaborations.

Representations and Symmetry Breaking

Fields transform under representations of SU(2)_R classified by spinor and vector types similar to those cataloged in Representation theory of Lie groups and structured via highest-weight methods introduced by Cartan and Weyl character formula. Spontaneous breaking of SU(2)_R down to subgroups often proceeds via Higgs sectors employing scalar multiplets similar in spirit to mechanisms used in the Higgs mechanism by Higgs, Englert, and Brout, or via triplet fields leading to Majorana mass terms as in the Type I Seesaw and Type II Seesaw constructions discussed by Minkowski and Schechter–Valle. Patterns of symmetry breaking relate to vacuum expectation values and to phase transitions considered in cosmological contexts by researchers like Kolb and Turner.

Phenomenological Implications and Experimental Searches

Phenomenology from SU(2)_R includes predictions of heavy charged and neutral gauge bosons (W_R, Z_R) whose mass scales are constrained by collider searches at ATLAS, CMS, and by precision measurements from LEP and SLAC National Accelerator Laboratory programs; limits inform models of neutrino mass generation explored by groups at CERN and Fermilab. Right-handed currents can affect flavor-changing processes investigated by Belle II, BaBar, and LHCb, and they impact neutrinoless double beta decay experiments like GERDA and KamLAND-Zen, interfacing with nuclear physics collaborations such as Majorana Demonstrator. Cosmological and astrophysical implications connect to baryogenesis scenarios like Leptogenesis studied by Fukugita and Yanagida, and to constraints from observations by Planck (spacecraft) and WMAP.

Extensions and Related Models

Extensions incorporating SU(2)_R appear in unified group constructions such as SO(10), E6, and in string-theory inspired frameworks studied by Green–Schwarz and Witten, sometimes combined with left–right parity from Parity doubling ideas discussed in Susskind-related contexts. Variants include asymmetric breaking chains and exotic representations encountered in models by Georgi and Glashow, and in phenomenological proposals linked to Composite Higgs scenarios and Technicolor-inspired frameworks of researchers like Weinberg (1979). Ongoing theoretical work engages communities at Perimeter Institute, Institute for Advanced Study, and major universities pursuing connections to Supersymmetry, Grand Unified Theory phenomenology, and to experimental programs at CERN and national laboratories.

Category:Lie groups Category:Gauge theories Category:Particle physics