Tensor gauge boson dark matter extension of the electroweak sector

The existence of dark matter is explained by a new, massive, neutral, non-symmetric, rank-2 tensor gauge boson (Zμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upmu \upnu }}$$\end{document}-boson). The Zμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upmu \upnu }}$$\end{document}-boson can be predicted by the tensor gauge boson extension of the Electro Weak (EW) theory, proposed by Savvidy (Phys Lett B 625:341, 2005). The non-symmetric rank-2 tensor Zμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upmu \upnu }}$$\end{document} can be decomposed into a symmetric (Z(μν))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{(\upmu \upnu )}})$$\end{document} and anti-symmetric (Z[μν])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{[\upmu \upnu ]}})$$\end{document} part. Based on the non-Lagrangian formulation for the free sector of the R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {R}_{\textrm{2}}$$\end{document}-theory proposed recently by Criado et al. (Phys Rev D 102:125031, arXiv:2010.02224, 2020), our massive anti-symmetric tensor field Z[μν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{[\upmu \upnu ]}}$$\end{document} corresponds to the massive symmetric spinor field Zαβγδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upalpha \upbeta \upgamma \updelta }}$$\end{document} in the (2,0) irrep. For the massive Zαβγδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upalpha \upbeta \upgamma \updelta }}$$\end{document} with the Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{\textrm{2}}$$\end{document}-symmetric Higgs portal couplings to a Standard Model (SM) particle, we compute the self-annihilation cross-section of the Zαβγδ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{\upalpha \upbeta \upgamma \updelta }}$$\end{document} dark matter and calculate its relic abundance. We also study the SM-SM particle scattering due to the exchange of the massive-Z(μν)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Z}_{{(\upmu \upnu )}}$$\end{document} symmetric field at a high energy scale. This proposition may have far reaching applications in astrophysics and cosmology.

More recently, Masi [73] proposed a new criterion to extend the SM of particle physics from a straightforward algebraic conjecture: that the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley-Dickson algebras, from complex numbers to octonions and sedenions. The exceptional symmetry group G(2) that could solve the dark matter problem can be identified from the automorphism of octonion (and sedenion) algebra.
Belyaev et al. [74,75] introduced the Fermion Portal Vector Dark Matter: a new class of renormalisable models, consisting of a dark SU(2) D (Dark-Isospin) gauge sector connected to the SM through a vector-like fermion mediator without the need for a Higgs portal. In these models, the dark matter candidate is a massive vector boson.
The Feynman rules for spin-2 fields were derived by Weinberg more than half a century ago in the R 2 -representation [77]. No Lagrangian formulation for the free sector of this theory is known. Recently, Criado et al. [76] proposed a very useful reformulation of Weinberg's original idea based on the symmetric multispinor formulation: Criado's Effective Field Theory (EFT) allows for consistent computations of physical observables for general-spin dark matter particles, although it does not admit a Lagrangian description [76].
A satisfactory theory of higher-spin gauge fields was constructed by Savvidy [78][79][80][81]. Building on this theory, the present paper investigates the possibility that the occurrence of dark matter can be explained by a new, neutral, nonsymmetric tensor gauge boson (the Z μν -boson, of a mass of 2.85 TeV) that can be predicted by the tensor gauge boson extension of the Electro Weak (EW) [78][79][80][81]. Based on the non-Lagrangian formulation for the free sector of the R 2theory proposed recently by Criado et al. [76], our massive anti-symmetric tensor field Z [μν] corresponds to the massive symmetric spinor field Z αβγδ in the (2,0) irrep. For the massive Z αβγδ with the Z 2 -symmetric Higgs portal couplings to the SM particle, we compute the self-annihilation crosssection of the Z αβγδ -boson-dark matter, and calculate its relic abundance. We also study the SM-SM particles scattering due to the exchange of a massive symmetric tensor Z μν field at a high energy scale. The current proposition may have far reaching applications in astrophysics and cosmology.

Non-Abelian tensor gauge bosons dark matter
Following Savvidy [78][79][80][81], we first consider a model whereby the SU(2) L group is extended to higher spins but the U(1) Y group is not extended. The W ± , Z gauge bosons receive their higher-spin descendance: and the doublet of complex Higgs scalars appear together with their higher-spin partners: The Lagrangian that describes the interaction of the tensor gauge bosons with the scalar fields and tensor bosons is: where In Eqs. (3) and (4), Y is the hypercharge, so the electric charge is Q = T 3 + Y/2, and, for isospinor fields, T i = τ i /2. In the Lagrangian (3), g 2 is the tensor gauge boson coupling constant, and is a real positive parameter. The three terms in the first line of (3) represent the standard electroweak model, and the rest of the terms represent the higher-spin generalisation of this model. Therefore, all the parameters of the SM are incorporated in the tensor extension. When the scalar fields acquire the vacuum expectation value η, then and the third term in the second line of Eq. (3) generates the masses of the tensor (W ± ,Z 0 ) gauge bosons: Thus all the intermediate spin-2 bosons acquire the same mass: The rest of the terms in Eq. (3) describe the interaction between old and new particles [78][79][80][81]. We note that the Lagrangian (3) is invariant under the simultaneous extended gauge transformations of the bosonic matter fields ϕ λ1 and tensor gauge fields A μλ1 The transformation law of the bosonic matter fields ϕ λ1 is homogenous; however, that of the the tensor gauge fields A μλ1 is inhomogeneous. As shown from the higher-spin extension of the SM [78][79][80][81], the general formulation of the extended gauge transformation for the arbitrary tensor gauge fields A μλ1...λs and bosonic matter fields ϕ λ1...λs can correctly define the corresponding field strengths and the invariant Lagrangian. The non-Abelian tensor gauge boson Z μν , given by Eq. (7) is a real field. The tensor boson Z μν , therefore, is its own antiparticle. For this reason, field Z μν has no electrical charge. In this article, we propose this neutral tensor gauge boson Z μν as a new dark matter candidate.

The R 2 -representation of the anti-symmetric second-rank tensor gauge fieldZ [μν]
The second-rank tensor gauge fieldZ α μν , which, according to the theory expounded in [78][79][80][81], is an arbitrary nonsymmetric tensorZ α μν =Z α νμ , does not coincide with the graviton. This is because has different gauge symmetries and interactions. Note that, for the spin-2 particles in the (1,1) representation of the Lorentz group L 0 (e.g., gravitons), the field is a symmetric rank-2 tensor [76]. The rank-2 tensor Z μν can be decomposed into a symmetricZ (μν) ) and an anti-symmetric (Z [μν] ) part: This decomposition is not generally true for tensors of rank 3Z μνλ and above: tensors of these ranks have more complex symmetries. The symmetric and anti-symmetric parts have the same information of the arbitrary non-symmetricZ μν field. This means thatZ (μν) andZ [μν] fields have the same spin (s), mass (m), coupling constant (gZ ), and all the other quantum numbers. Our anti-symmetric tensor fieldZ α [μν] will be in the R 2 -representation. The symmetric multispinor formulation developed in Ref. [76] is based on the known two-component spinor formalism [82][83][84]. The proposed Effective Field Theory (EFT) allows for consistent computations of physical observables for general-spin dark matter particles, although it does not admit a Lagrangian description [76]. The representation R 2 to which spin-2 belongs is defined as the subspace of (2,0) ⊕ (0,2) for whichZ † L =Z R . The irreps (2,0) and (0,2) are minimal in the sense that they contain exactly the necessary number of degrees of freedom [76]. In free R 2 theory, the massive spin-2 field in the (2,0) irrep is given by: . . α 4 is a symmetrized multi-index built from twocomponent spinor indices, and s is the particle spin. The indices (α) transform in the (1/2,0) irrep of the Lorentz group L 0 , (for details of the symmetric multispinor formulation (see Appendix A, Refs. [76,84], and Refs. [82,83]).

The interactions of theZ-dark matter field
Konitopoulos and Savvidy [86] analyzed the interaction between two tensor currents caused by the exchange of these tensor gauge bosons. They found that all the negative-norm states are excluded from the spectrum of the second-rank massless non-symmetric tensor gauge field A μν , due to the gauge invariance of the theory. They thus came to the conclusion that the theory does indeed respect unitarily at the free level. In our description, hovered, perturbative unitarity is unavoidably broken at some high energy scale , above the Z μν particle mass. Following [76], below the energy scale -much higher than the particle mass, m, and the electroweak energy scale, EW -the only degrees of freedom present are those of the SM and the spin-2 dark matter particles. The interactions between the spin-2 dark matter particles and the SM particles can be described by an EFT that incorporates the effects of the new physics at through Lorentz-invariant local operators whose effects are suppressed by inverse powers of . We define the effective cutoff scale as follows: where gZ is the dark matter coupling, and the mass MZ is derived from Eq. (9). We expect that the perturbative unitarity is broken in processes of energy E ≈ . From Eq. (25), we obtain the upper limit for the validity of the theory. Furthermore, the perturbative unitarity condition gZ < 4π is given by Eq. (25) for MZ < . The Z αβγδ -dark matter particle must be stable. This can be achieved by imposing the Z 2 -symmetry. The Z αβγδ natural dark matter candidate is Z 2 -odd, while all the SM particles are Z 2 -even. Now, the effective interacting Hamiltonian density is given by: Based on [76], since a spin-s field carries an effective dimension of = s + 1, the lowest dimension of the Lorentzinvariant local operators linear in the spinorZ field is N = 1+3s. Hence the Z 2 -violating interaction H Linear in Eq. (26) is:  (27) where N = 1 + 3s = 7, (for spin s = 2).
Z αβγ δ is the spin-2 dark matter field in the (2,0) irrep; Linear is an energy scale of the Z 2 -violating linear interactions of theZ dark matter field with the SM particles; B μν and W i μν are the U(1) Y and SU(2) L field strengths, respectively. The coefficients c B and c W are arbitrary in principle. The object σ μν αβ projects rank-2 tensors B μν and W i μν into their (1,0) subspace. Note that, unlike the case for spin-2 particles in the (1,1) representation (e.g., gravitons), in Eq. (27), linear interactions with fermions and scalars are absent at the leading order due to Lorentz symmetry [84]. Interaction (27) yields to the decay of the Z αβγδ field to EW vector gauge bosons VV. The total decay width of the massive spin-2 particle to EW vector gauge bosons VV is given by: For Z 2 -violating interactions at a large energy scale Linear , the spin-2 particle becomes metastable. The term H Portal in Eq. (26) is the Z 2 -symmetric Higgs portal: whereZ αβγ δ is the spin-2 dark matter field in the (2,0) irrep, φ is the Higgs doublet, and gZ is the dark matter coupling. The interaction is mediated by a quartic coupling between two Higgs and two spin-2 dark matter particles [76].

The annihilation cross-section of theZ-dark matter field
Based on [76], the total annihilation cross-section times the relative velocity ofZ -dark matter to SM particles is given by: where MZ is derived from Eq. (9); gZ is the coupling constant, and m f , and g v are the SM-fermion mass and SM-vector gauge boson coupling, respectively. The annihilation cross-sections (32), (33), and (34) follow from the Z 2 -symmetric Higgs portal given by Eq. (30), and calculated from Reference [76] for the case of real coupling constant gZ and spin-2 dark matter particles. Equations (33) and (34) correspond to the s-wave (∼ u 0 rel ) dark matter annihilation for bosons; Eq. (32) corresponds to the p-wave annihilation (∼ u 2 rel ) for fermions. The annihilation ofZ -dark matter particle to SM-fermions is thus velocity-suppressed (u 2 rel < 1). Therefore, the total annihilation cross section (31) becomes: Following [87], for the proposedZ -dark matter, the relic density should be: where σ u rel ≈ 0.83 pb. Analysis of the three-year Wilkinson Microwave Anisotropy Probe (WMAP) data suggests that the density of dark matter is DM h 2 = 0.102 ± 0.009 (where DM = ρ DM /ρ crit , with ρ crit being the density corresponding to a flat universe [88], and h being the Hubble constant, in units of 100 km s −1 · Mpc −1 ) [89]. More recently, Aghanim et al. (Planck Collaboration, 2020) [87] suggested that the density of dark matter is about DM h 2 ∼ 0.12. A cold dark matter candidate produced at the LHC should, therefore, have this annihilation cross section. This quantity leads us to the second method of measuring the coupling of dark matter from SM particles: through the search for the products of dark matter annihilation or decay originating from high-density regions of the Universe, such as the center of galaxies [90]. Since the WMAP results provide good information about σ u rel , the uncertainties in this approach stem from our sketchy knowledge of the exact density of dark matter in the center of galaxies, and from the difficulty of separating the dark matter annihilation signal from possible background signals. From the total annihilation cross section Eq. (35), the mass of theZ -dark matter is given by: Assuming (σ u rel ) total ≈ 0.83 pb = 2, 1315977 × 10 −9 GeV −2 , from the requirement of relic abundance and g 2 Z = 0.4, g V = 0.6, we obtain the following value for the mass of Z -dark matter: 6 SM-SM particle scattering due to the exchange of a massive, symmetric second-rank tensor gauge field Z (μν) at a high energy scale The symmetric part of Eq. (10) is the symmetric gauge field Z μν =Z νμ . The spin (s), mass (m), coupling constant (g 2 ), and all the other quantum numbers of this field are the same as those of the anti-symmetric tensor fieldZ [μν] . The symmetric gauge fieldZ (μν) is in the (1,1) representation of the Lorentz group L 0 . TheZ (μν) field does not coincide with the graviton because its gauge symmetries and interactions differ from those of the graviton. Based on Savvidy [78][79][80][81]86], the Lagrangian for the symmetric spin-2 particle of mass MZ Sym ≈ 2.85T eV has the Fierz-Pauli form: whereZ (μν) is the linearized field. The higher-order terms describe the self-interactions of theZ (μν) field. Furthermore, for the symmetricZ (μν) field, we impose the traceless con-ditionZ μ μ = 0. The interaction term with the SM fields is: where, η μν is the Minkowski metric, and the factors within the parentheses are the stress-energy tensors T (s) μν for the SM particles of different spins(s = 0, 1/2, 1) [91]. As such, (s) is the SM Lagrangian for the particles of spin-s. Since the spin sum of theZ Sym polarisation: with is traceless, the terms proportional to (s) in Eq. (40) do not contribute [91] (Explicit expressions for the various spins can be found in Ref. [92]). Equation (41) is the effective coupling constant, and Sym is the cut-off energy scale of the EFT symmetric tensor generalisations of the EW theory. We note that Sym does not need to be the same with the cutoff energy scale of the EFT symmetric spinor version of the non-symmetric tensor generalisations of the EW theory (see above). Based on Haiying Cai et al. [91], for a generic scattering process B 1 + B 2 → B 3Z Sym where B 1,2,3 are the SM particles, the amplitude squared after the solid angle integration of the process is given by: At high energies, above the EW scale EW , we find that all amplitudes squared scale as follows: where g s is an appropriate SM coupling, and s = p B 1 + p B 2 2 . The only exception is the process hh → hZ Sym , for which the amplitude is a constant: where the Higgs mass m h = 125 GeV, and the EW vacuum expectation value υ ≈ 246 GeV. For the SM fermionfermion processf 1 f 2 → VZ Sym with the SM vector gauge bosons V, the total amplitude squared is calculated using the Feynman Rules [93,94]: where g v is the weak coupling. The decay width of the symmetric spin-2 particle Z Sym of a mass of 2.85 TeV is governed by the Lagrangian in Eq. (40): The three partial decay widths describe decay to scalar h, fermion f and vector particles V respectively.

Discussion
The second-rank tensor gauge field Z μν , which in the Lagrangian theory [78][79][80][81] described in Sect. 2 is an arbitrary non-symmetric tensor Z μν = Z νμ , does not coincide with the graviton, because it has different gauge symmetries and interactions. Note that, for the spin-2 particles in the (1,1) representation of the Lorentz group L 0 (e.g., gravitons), the field is a symmetric rank-2 tensor [76]. The rank-2 tensor Z μν can be decomposed into a symmetric, Z (μν) and an anti-symmetric, Z [μν] part. The proposed EFT allows for consistent computations of physical observables for general-spin dark matter particles, although it does not admit a Lagrangian description [76]. Our heavy anti-symmetric tensor field Z [μν] corresponds to the massive symmetric spinor field Z αβγδ in the (2,0) irrep by Eq. (16). For this reason, for the symmetric spinor field Z αβγδ , we follow a non-Lagrangian formulation of the EFT in Sects. 3-5. On the other hand, the symmetric gauge field Z (μν) is in the (1,1) representation of the Lorentz group L 0 . Therefore, in Sect. 6, we follow a Lagrangian formulation of the EFT.
Based on [76], the collider constraints of our non-Lagrangian effective framework for the symmetric spinor fieldZ are quite similar to the usual Higgs-portal DM models [95][96][97][98]. In these models, the only way to produce DM in colliders is by first producing Higgs bosons, either on-shell or off-shell, which subsequently decay into DM: pp → hB → ZZ B (where B represents visible SM states). The prospect of a DM signal then crucially depends on the mass of the DM. If the DM mass is M DM ≤ m h /2, the Higgs boson can decay to DM on-shell. This is an invisible decay. The SM Higgs boson decays predominantly to visible channels. The only invisible decay channel of the Higgs boson is to neutrinos: BR SM (h → inv) = BR SM (h → 4ν) ≈ 10 −3 . This decay can be neglected. BSM contributions can significantly alter the invisible decay rate of the Higgs boson. Here, the symmetric spinor fieldZ is much heavier than M DM > m h /2, and the Higgs boson in pp → hB →ZZ B has to be virtual. In this case, DM production is suppressed by g 2 For the symmetric spin-2 particle Z Symm , the Lagrangian formulations allow. The collider constraints are quite similar to those of the massive Kaluza-Klein (KK) graviton models [25,30,31,99]. The heavy symmetric spin-2 particle Z Symm can be produced from quark/anti-quark scattering at the LHC, and then decay into the SM particles (as we showed in Sect. 6). Based on Kang and Lee [99], we may also constrain non-universal lepton and photon couplings by the photon energy distribution from the process e + e − → γZ Symm . Following [99], the squared amplitude for e + e − → γZ Symm , is as follows: where, For c γ = c e , the squared amplitude behaves like s/ 2 Symm . This shows that unitarity is violated at a lower energy. A similar phenomenon was observed in the Quantum Chromodynamics (QCD) process, qq → gZ Symm [100][101][102][103][104]: in the latter, c g = c q would give rise to a similar dependence of the corresponding squared amplitude on the centre of mass energy [99].
The Dijet and dilepton searches at the LHC can constrain relatively heavy spin-2 resonances [105,106]. Although not sensitive enough, the Initial State Radiation (ISR) photon or jet + heavy Dijet resonances may have the potential to constrain non-universal quark and gluon couplings by the jet-transverse momentum p T distribution from the qq → g Z Symm process at the LHC and future hadron colliders [105].
Direct detection bounds from XENON1T [107,108], LUX [109], PandaX [110], etc., are most stringent for weak-scale or heavier dark matter. As a general feature, the necessary values of coupling gZ for the correct DM abundance to be generated through freeze-out are excluded by the bounds on invisible decays of the Higgs boson for M DM < mh/2, and by direct detection experiments for 6 GeV < M DM < 1 TeV.

Conclusions
We suggest that a new, neutral, non-symmetric tensor gauge boson (Z μν -boson) can explain the existence of dark matter in our Universe. The non-symmetric Z μν -boson can be predicted by the tensor gauge boson extension of the Electro Weak (EW) theory proposed by Savvidy. Based on the non-Lagrangian formulation for the free sector of the R 2 -theory proposed recently by Criado et al. our massive antisymmetric tensor field Z [μν] corresponds to the massive symmetric spinor field Z αβγδ in the (2,0) irrep. For the massive Z αβγδ with the Z 2 -symmetric Higgs portal couplings to the SM particle, we compute the self-annihilation cross-section of the Z αβγδ -boson-dark matter, and calculate its relic abundance. We also study the SM-SM particle scattering due to the exchange of a massive, Z μν -symmetric boson at a high energy scale. This proposition may have far-reaching applications in astrophysics and cosmology.
Acknowledgements I would like to thank the anonymous referee for the useful comments and suggestions.

Data Availability Statement
This manuscript has associated data in a data repository. [Authors' comment: The datasets generated during and/or analyzed during the current study are available from the author on request.] Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecomm ons.org/licenses/by/4.0/. Funded by SCOAP 3 . SCOAP 3 supports the goals of the International Year of Basic Sciences for Sustainable Development.