Adjoint Representation Of SU Research Articles

All-loop group-theory constraints for four-point amplitudes of SU(N), SO(N), and Sp(N) gauge theories

In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop order L) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers of N). Using an iterative process, we systematically construct the L-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (for L ≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (for L ≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory.

Mono-Higgs and Mono-Z Production in the Minimal Vector Dark Matter Model

The minimal vector dark matter is a viable realization of the minimal dark matter paradigm. It extends the standard model by the inclusion of a vector matter field in the adjoint representation of SU(2)L. The dark matter candidate corresponds to the neutral component of the new vector field (V0). Previous studies have shown that the model can explain the observed dark matter abundance while evading direct and indirect searches. At colliders, the attention has been put on the production of the charged companions of the dark matter candidate. In this work, we focus on the mono-Higgs and mono-Z signals at Hadron colliders. The new charged vectors (V±) are invisible unless a dedicated search is performed. Consequently, we assume that the mono-Higgs and mono-Z processes correspond to the pp→hV+,0V−,0 and pp→ZV+,0V−,0 reactions, respectively. We show that, while the pp→hV+,0V−,0 is more important, both channels may produce significant signals at the HL-LHC and colliders running at s=27 TeV and 100 TeV, probing almost the complete parameter space.

Computable conditions for order-2 CP symmetry in NHDM potentials

We derive necessary and sufficient conditions for order-2 CP (CP2) symmetry in N-Higgs-doublet potentials for N > 2. The conditions, which are formulated as relations between vectors that transform under the adjoint representation of SU(N) under a change of doublet basis, are representation theoretical in nature. Making use of Lie algebra and representation theory we devise an efficient, computable algorithm which may be applied to decide whether or not a given numerical potential is CP2 invariant.

Exploring the phenomenology of weak adjoint scalars in minimal R-symmetric models

We examine the phenomenology of the scalar fields in weak and Higgs sectors of minimal R-symmetric models, in particular the ‘swino’ and ‘sbino’, the scalar partners to the chiral fields that marry the electroweak gauge bosons in Dirac gaugino models. These fields are in adjoint representations of SU(2) and U(1) and have both CP-even and CP-odd components. The interactions of these new states are summarized, and decay widths are computed analytically to one loop order. We discuss the tree level contributions of these new states to the mass spectrum of MSSM sfermions. We also explore production cross sections and decay signatures at colliders for several chosen benchmarks. We find that large regions of parameter space are unconstrained by present collider data.

Useful relations among the generators in the defining and adjoint representations of SU(N)

There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric tensor $d_{abc}$ that arises in the study of the SU(N) Lie algebra, one can also consider relations that involve the adjoint representation matrix, $(D^a)_{bc}=d_{abc}$. In this review, we summarize many useful relations satisfied by the defining and adjoint representation matrices of SU(N). A few relations special to the case of N=3 are highlighted.

Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions

A recent work (arXiv:1811.04930) proposed a SU(2) gauge theory for optimal doping criticality in the cuprate superconductors. The theory contains $N_h$ Higgs fields transforming under the adjoint representation of SU(2), with $N_h=1$ for the electron-doped cuprates, and $N_h=4$ for the hole-doped cuprates. We investigate the strong-coupling dynamics of this gauge theory, while ignoring the coupling to fermionic excitations. We integrate out the SU(2) gauge field in a strong-coupling expansion, and obtain a lattice action for the Higgs fields alone. We study such a lattice action, with O($N_h$) global symmetry, in an analytic large $N_h$ expansion and by Monte Carlo simulations for $N_h=4$ and find consistent results. We find a confining phase with O($N_h$) symmetry preserved (this describes the Fermi liquid phase in the cuprates), and Higgs phases (describing the pseudogap phase of the cuprates) with different patterns of the broken global O($N_h$) symmetry. One of the Higgs phases is topologically trivial, implying the absence of any excitations with residual gauge charges. The other Higgs phase has $\mathbb{Z}_2$ topological order, with `vison' excitations carrying a $\mathbb{Z}_2$ gauge charge. We find consistent regimes of stability for the topological Higgs phase in both our numerical and analytical analyses.

Search for Type-III SeeSaw heavy lepton with the ATLAS Detector at the LHC using TeV up to 140 fb–1

A search of heavy leptons N0 and L± pair production predicted by the Type-III SeeSaw mechanism is presented. This mechanism extends the Standard Model, introducing at least two new triplets of fermionic fields with zero hypercharge in the adjoint representation of SU(2)l, resulting in two heavy Dirac charged leptons and a heavy Majorana neutral lepton. This search uses data collected by the ATLAS detector at the Large Hadron Collider in protonproton collision at a centre-of-mass energy of 13 TeV, with an integrated luminosity up to 140 fb−1 corresponding to the full Run-2 dataset recorded between 2015-2018.The analysis focuses on all the possible production and boson decay channels of these heavy leptons, which are assumed to be degenerate in mass. The search is based on the separate optimization of each lepton multiplicity final state, considering 2, 3, 4 or more than 5 leptons. The power of the leptonic channels lies in the low expected background from Standard Model processes. Different control and signal regions are defined for each final state, designed to be orthogonal one each other. Good agreement between the number of events in data and Standard Model predictions is observed.The results are translated into exclusion limits on heavy lepton masses with a 95% confidence level using statistical uncertainties only. Assuming the branching ratios to all lepton flavours to be equal, a lower limit of 560 GeV is obtained.

Focus point gauge mediation without a severe fine-tuning

We consider focus point gauge mediation within the framework of the next-to-minimal supersymmetric standard model, which substantially reduces the degree of finetuning for the electroweak symmetry breaking. The milder fine-tuning is realized by a messenger field in the adjoint representation of SU(5) gauge group with SU(3)c octet being heavy. Our model has a simple ultraviolet completion. The fine-tuning measure Δ can be as small as 40-50 without any contradiction with LHC constraints.

Classification of compactified su(Nc) gauge theories with fermions in all representations

We classify su(Nc) gauge theories on {mathrm{mathbb{R}}}^3times {mathbb{S}}^1 with massless fermions in higher representations obeying periodic boundary conditions along {mathbb{S}}^1 . In particular, we single out the class of theories that is asymptotically free and weakly coupled in the infrared, and therefore, is amenable to semi-classical treatment. Our study is conducted by carefully identifying the vacua inside the affine Weyl chamber using Verma bases and Frobenius formula techniques. Theories with fermions in pure representations are generally strongly coupled. The only exceptions are the four-index symmetric representation of su(2) and adjoint representation of su(Nc). However, we find a plethora of admissible theories with fermions in mixed representations. A sub-class of these theories have degenerate perturbative vacua separated by domain walls. In particular, su(Nc) theories with fermions in the mixed representations adjoint⊕fundamental and adjoint⊕two-index symmetric admit degenerate vacua that spontaneously break the parity mathcal{P} , charge conjugation mathcal{C} , and time reversal mathcal{T} symmetries. These are the first examples of strictly weakly coupled gauge theories on {mathrm{mathbb{R}}}^3times {mathbb{S}}^1 with spontaneously broken mathcal{C} , mathcal{P} , and mathcal{T} symmetries. We also compute the fermion zero modes in the background of monopole-instantons. The monopoles and their composites (topological molecules) proliferate in the vacuum leading to the confinement of electric charges. Interestingly enough, some theories have also accidental degenerate vacua, which are not related by any symmetry. These vacua admit different numbers of fermionic zero modes, and hence, different kinds of topological molecules. The lack of symmetry, however, indicates that such degeneracy might be lifted by higher order corrections. Finally, we study the general phase structure of adjoint⊕fundamental theories in the small circle and decompactification limits.

On rational R-matrices with adjoint SU(n) symmetry**Dedicated to the memory of Petr Petrovich Kulish.

Using the representation theory of Yangians we construct the rational R-matrix which takes values in the adjoint representation of SU(n). From this we derive an integrable SU(n) spin chain with lattice spins transforming under the adjoint representation. However, the resulting Hamiltonian is found to be non-Hermitian.

Seminatural gauge mediation from product group unification

We propose a focus point gauge mediation model based on the product group unification (PGU), which solves the doublet-triplet splitting problem of the Higgs multiplets. In the focus point gauge mediation, the electroweak symmetry breaking scale can be naturally explained even for multi-TeV stops. It is known that the focus point behavior appears if a ratio of the number of SU(2) doublet messengers to that of SU(3) triplet messengers is close to 5/2. Importantly, this ratio (effectively) appears in our scenario based on the PGU, if the messenger field is an adjoint representation of SU(5) gauge group. Therefore, our focus point scenario is very predictive. It is also pointed out the gravitino can be dark matter without spoiling the success of the thermal leptogenesis. The absence of the SUSY CP-problem is guaranteed in the case that the Higgs B-term vanishes at the messenger scale.

Doubly-charged Higgs and vacuum stability in left-right supersymmetry

We present an analysis of supersymmetric left-right symmetric models with Higgs fields lying in the adjoint representation of SU(2) R . These models feature a doubly-charged Higgs boson which gets its mass only at the loop level. We present, for the first time, a complete one-loop calculation of this mass and show that contributions that have been neglected so far can shift it by a few hundreds of GeV. We then combine this observation with LHC bounds deduced from extra charged gauge boson and doubly-charged Higgs boson searches. In particular, we point out that existing limits get substantially modified by the presence of singly-charged Higgs bosons that are also predicted in these models. In addition, we address constraints stemming from vacuum stability considerations and show how the considered class of models could be ruled out at the next LHC run in the absence of any signal.

Calculating the Annihilation Rate of Weakly Interacting Massive Particles

We develop a formalism that allows one to systematically calculate the weakly interacting massive particle (WIMP) annihilation rate into gamma rays whose energy far exceeds the weak scale. A factorization theorem is presented which separates the radiative corrections stemming from initial-state potential interactions from loops involving the final state. This separation allows us to go beyond the fixed order calculation, which is polluted by large infrared logarithms. For the case of Majorana WIMPs transforming in the adjoint representation of SU(2), we present the result for the resummed rate at leading double-log accuracy in terms of two initial-state partial-wave matrix elements and one hard matching coefficient. For a given model, one may calculate the cross section by finding the tree level matching coefficient and determining the value of a local four-fermion operator. The effects of resummation can be as large as 100% for a 20TeV WIMP. However, for lighter WIMP masses relevant for the thermal relic scenario, leading-log resummation modifies the Sudakov factors only at the 10% level. Furthermore, given comparably sized Sommerfeld factors, the total effect of radiative corrections on the semi-inclusive photon annihilation rate is found to be percent level. The generalization of the formalism to other types of WIMPs is discussed.

Nonuniversal gaugino masses and seminatural supersymmetry in view of the Higgs boson discovery

I consider models with non-universal gaugino masses at the gauge coupling unification scale, taking into account the Higgs boson discovery. Viable regions of parameter space are mapped and studied in the case of non-universality following from an F-term in a linear combination of singlet and adjoint representations of SU(5). I consider, in particular, "semi-natural" models that have small \mu, with gaugino masses dominating the supersymmetry breaking terms at high energies. Higgsino-like particles are then much lighter than all other superpartners, and the prospects for discovery at the Large Hadron Collider can be extremely challenging.

Heavy squarks and light sleptons in gauge mediation. From the viewpoint of 125 GeV Higgs boson and muon g − 2

In the framework of gauge mediation models, we investigate scenarios with heavy squarks and light sleptons, motivated by the recent discovery of the Higgs boson and the deviation of the muon anomalous magnetic moment (g − 2) from the SM prediction. We show that only models with a messenger multiplet in the adjoint representation of SU(5) GUT gauge group are the unique possibility that sleptons are light enough to explain the muon g − 2 in the minimal setup. We also show that, if there is an additional source of the Higgs soft masses, the muon g − 2 can be explained with messenger multiples in the fundamental representation of SU(5) with the help of the light higgsino. Some phenomenological aspects of these models are also discussed.

Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes at all loop orders

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints that arise from group theory alone. These constraints break into subsets associated with irreducible representations of the symmetric group S_n, which allows them to be presented in a compact and natural way. Using an iterative approach, we derive the constraints for six-point amplitudes at all loop orders, extending earlier results for n=4 and n=5. We then decompose the four-, five-, and six-point group-theory constraints into their irreducible S_n subspaces. We comment briefly on higher-point two-loop amplitudes.

SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders

Color-ordered amplitudes for the scattering of n particles in the adjoint representation of SU(N) gauge theory satisfy constraints arising solely from group theory. We derive these constraints for n=5 at all loop orders using an iterative approach. These constraints generalize well-known tree-level and one-loop group theory relations.

Light-front Hamiltonian and path integral formulations of large N scalar [formula omitted

Recently Grinstein, Jora and Polosa (2009) [5] have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. ʼt Hooft (1974) [6]). This theory admits a Bethe–Salpeter equation describing the discrete spectrum of qq¯ bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.

On the origin of neutrino masses

We discuss the simplest mechanisms for generating neutrino masses at tree level and one loop level. We find a significant number of new possibilities where one can generate neutrino masses at the one-loop level by adding only two new types of representations. These models have renormalizable interactions that automatically conserve baryon number. Adding to the minimal standard model a scalar color octet with SU(3)⊗SU(2)⊗U(1) quantum numbers, (8,2,1/2), and a fermionic color octet in the fundamental or adjoint representation of SU(2), one can generate neutrino masses in agreement with experiment. Signals at the LHC and constraints from flavor violation are briefly discussed.

On the problem of multiple M2 branes

A simplified version of 3d BL theory is considered, which allows any number N of M2 branes in d=11. The underlying 3-algebra structure is provided by degenerate U(N) Nambu bracket [X,Y,Z] = tr(X) [Y,Z] + tr(Y) [Z,X] + tr(Z) [X,Y], the corresponding f^{abcd} is not totally antisymmetric and extended supersymmetry of the action remains to be checked. All the fields, including auxiliary non-propagating gauge fields, are in adjoint representation of SU(N) and the only remnant of 3-algebra structure is an octuple of gauge singlets, acquiring vacuum expectation value in transition to D2 branes in d=10.