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The renormalizable extension of a pure Yang-Mills theory with Lorentz violation is characterized by the CPT-Even $(k_F)_{\mu \nu \lambda \rho}$ and the CPT-Odd $(k_{AF})_\mu$ constant Lorentz coefficients. In this paper, the one-loop structure of the theory up to second order in these Lorentz violating coefficients is studied using the BFM-gauge. Results for the diverse beta functions are derived and contrasted with those given in the literature at first order in these parameters. Special emphasis is putted on the beta function $\beta(g)$, which is studied in both mass-independent and mass-dependent renormalization schemes. It is found that in a mass-independent scheme the $(k_{AF})_\mu$ Lorentz coefficient does not contribute to the $\beta(g)$ function, but it does in a mass-dependent scheme with contributions that are gauge-dependent and IR divergent., Comment: 21 pages, 3 figures

The impact of the CPT-Odd electroweak gauge sector of the Standard Model Extension on the anomalous magnetic moment of charged leptons is studied. This gauge sector is characterized by the $(k_1)_\mu$ and $(k_2)_\mu$ Lorentz coefficients, which have positive mass dimension because they are associated with a $U_Y(1)$-invariant and with an $SU_L(2)$-invariant dimension-three operators, respectively. They belong to the category of relevant interactions, which have strong effects on low-energy observables. We find that the contribution to the anomalous magnetic dipole moment of the electron can be up to fourteen orders of magnitude greater than that of the muon and up to sixteen orders greater than that of the tau. Using the experimental data for the electron, we obtain an upper bound of $\left|k^2_1-0.79 k_1\cdot k_2 +0.27 k^2_2\right|<1.31\times 10^{-19} m^2_e $. The Lorentz coefficient $(k)_{AF}$ of the Carroll-Field-Jackiw's QED is given by a linear combination of the $(k_1)_\mu$ and $(k_2)_\mu$ vectors. Assuming that $|k^2_1|, |k^2_2|\gg |k^2_{AF}|$ and taking $(k)_{AF}=0$, which implies that $(k_1)_\mu$ and $(k_2)_\mu$ are collinear, we obtain upper bounds of $|k_1^2|<7.2\times 10^{-21}m^2_e$ and $|k_2^2|<3.2\times 10^{-19}m^2_e$., Comment: 15 pages, 3 figures

The renormalizable extension of a pure Yang-Mills theory with Lorentz violation is characterized by the CPT-Even $(k_F)_{\mu \nu \lambda \rho}$ and the CPT-Odd $(k_{AF})_\mu$ constant Lorentz coefficients. In this paper, the one-loop structure of the theory up to second order in these Lorentz violating coefficients is studied using the BFM-gauge. Results for the diverse beta functions are derived and contrasted with those given in the literature at first order in these parameters. Special emphasis is putted on the beta function $\beta(g)$, which is studied in both mass-independent and mass-dependent renormalization schemes. It is found that in a mass-independent scheme the $(k_{AF})_\mu$ Lorentz coefficient does not contribute to the $\beta(g)$ function, but it does in a mass-dependent scheme with contributions that are gauge-dependent and IR divergent., Comment: 21 pages, 3 figures

A bound on the CPT-odd four vector coefficient $k^\mu_\phi$ that appears in Higgs sector of the Minimal Standard Model Extended (MSME) is presented. The analysis is based on the contributions arising from the sector in question to the anomalous dipole moment for leptons calculated at the one loop level, for which an analytical expression is obtained. The largest contribution of this Lorentz violating coefficient is on the lightest lepton, which results as a consequence of a strong non-decoupling effect. By using the experimental uncertainty of the electron anomalous dipole moment we predict that $|k^2_{ \phi\,R}|<3.29\times 10^{-29}$ GeV$^2$., Comment: 10 pages, 2 figures

Lorentz-violating Yukawa couplings lying within the renormalizable part of the SME generate Lorentz-invariant one-loop contributions to electromagnetic moments of fermions. These proceedings provide a discussion on such contributions and present bounds on SME coefficients from experimental data on electromagnetic moments. Constraints as restrictive as $\sim10^{-14}$ are found., Comment: Presented at the Ninth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, May 17-26, 2022

Yukawa couplings from the Lorentz- and $CPT$-violating Standard Model Extension induce quantum contributions to the magnetic and electric moments of quarks, which are calculated in the present paper. Then we take advantage of the high sensitivity measurements of the proton and neutron electromagnetic moments (EMM), suitable to search for tiny effects of new physics, to constrain coefficients parametrizing Lorentz violation, reaching bounds as restrictive as $10^{-23}$., Comment: 8 pages, 2 figures, 1 table

The self-interacting $\lambda\phi^{4}$ scalar field theory is a warhorse in quantum field theory. Here we explore the one-loop order impact from one universal extra dimension, $S^{1}/\mathbb{Z}_{2}$, to the self-energy and four point vertex functions associated to this theory. Such effects come as an infinite number of UV divergences corresponding to an infinite superposition of excited KK particles around the loop. We show that dimensional regularisation is adequate enough to control them in terms of the product of the one dimensional inhomogenous Epstein zeta function times the gamma function. From the analytical properties of these functions, the UV divergences are extracted and the counterterms defined; the latter turn out to be of canonical dimension four at the Lagrangian level. We use both, the MS-scheme and a mass-dependent subtraction scheme to remove divergences. Only the latter manifestly satisfy the decoupling theorem., Comment: 20 pages, 6 figures, submitted to J. Phys. G: Nucl. Part. Phys

The self-interacting $\lambda\phi^{4}$ scalar field theory is a warhorse in quantum field theory. Here we explore the one-loop order impact from one universal extra dimension, $S^{1}/\mathbb{Z}_{2}$, to the self-energy and four point vertex functions associated to this theory. Such effects come as an infinite number of UV divergences corresponding to an infinite superposition of excited KK particles around the loop. We show that dimensional regularisation is adequate enough to control them in terms of the product of the one dimensional inhomogenous Epstein zeta function times the gamma function. From the analytical properties of these functions, the UV divergences are extracted and the counterterms defined; the latter turn out to be of canonical dimension four at the Lagrangian level. We use both, the MS-scheme and a mass-dependent subtraction scheme to remove divergences. Only the latter manifestly satisfy the decoupling theorem., Comment: 20 pages, 6 figures, submitted to J. Phys. G: Nucl. Part. Phys

Kaluza-Klein fields characterizing, from a four-dimensional viewpoint, the presence of compact universal extra dimensions would alter low-energy observables through effects determined by some compactification scale, $R^{-1}$, since the one-loop level, thus being particularly relevant for physical phenomena forbidden at tree level by the Standard Model. The present paper explores, for the case of one universal extra dimension, such new-physics contributions to Higgs decays $h^{(0)}\to q^{(0)}_\alpha q^{(0)}_\beta$, into pairs of quarks with different flavors, a sort of decay process which, in the Standard Model, strictly occurs at the loop level. Finite results, decoupling as $R^{-1}\to \infty$, are calculated. Approximate short expressions, valid for large compactification scales, are provided. We estimate that Kaluza-Klein contributions lie below predictions from the Standard Model, being about 2 to 3 orders of magnitude smaller for compactification scales within $1.4\,{\rm TeV}

A comprehensive analysis on the photon self-energy, the fermion self-energy, and the fermion vertex function is presented at one loop in the context of quantum electrodynamics (QED) with 1 extra dimension. In 5-dimensional theories, characterized by an infinite number of Kaluza-Klein fields, one-loop amplitudes involve discrete as well as continuous sums, $\sum^\infty_{n=1}\int d^4k$, that could diverge. Using dimensional regularization, we express such sums as products of gamma and Epstein functions, both defined on the complex plane, with divergences arising from poles of these functions in the limit as $ D \to 4$. Using the analytical properties of the Epstein function, we show that the ultraviolet divergences generated by the Kaluza-Klein sums can be consistently renormalized, which means that the corresponding renormalized quantities reduce to the usual ones of QED at the limit of a very large compactification scale $R^{-1}$. The main features of QED at the one-loop level were studied. We use the mass-dependent $\mu$-scheme to calculate, in QED with an arbitrary number $n$ of extra dimensions, a beta function fulfilling all desirable physical requirements. We argue that in this type of theories, with a large mass spectrum covering a wide energy range, beta functions should not be calculated by using mass-independent renormalization schemes. We show that the beta function is finite for any energy $\mu$. In particular, it reduces to the usual QED result $e^3/12\pi^2$ for $m\ll \mu \ll R^{-1}$ and vanishes for $m\gg \mu$, with $m$ the usual fermion mass. Throughout the work, the decoupling nature of all our results obtained from the analytical properties of the Epstein function is stressed., Comment: Accepted for publication in Physical Review D, 24 pages, 6 figures

The effective-Lagrangian description of Lorentz-invariance violation provided by the so-called Standard-Model Extension covers all the sectors of the Standard Model, allowing for model-independent studies of high-energy phenomena that might leave traces at relatively-low energies. In this context, the quantification of the large set of parameters characterizing Lorentz-violating effects is well motivated. In the present work, effects from the Lorentz-nonconserving Yukawa sector on the electromagnetic moments of charged leptons are calculated, estimated, and discussed. Following a perturbative approach, explicit expressions of leading contributions are derived and upper bounds on Lorentz violation are estimated from current data on electromagnetic moments. Scenarios regarding the coefficients of Lorentz violation are considered. In a scenario of two-point insertions preserving lepton flavor, the bound on the electron electric dipole moment yields limits as stringent as $10^{-28}$, whereas muon and tau-lepton electromagnetic moments determine bounds as restrictive as $10^{-14}$ and $10^{-6}$, respectively. Another scenario, defined by the assumption that Lorentz-violating Yukawa couplings are Hermitian, leads to less stringent bounds, provided by the muon anomalous magnetic moment, which turn out to be as restrictive as $10^{-14}$., Comment: 21 pages, 17 figures, 6 tables

Universal extra dimensions, presumably observable at some high-energy scale, would modify low-energy observables, being particularly relevant for physical processes forbidden at tree level by the Standard Model. We address the Kaluza-Klein contributions from the 5-dimensional Standard Model to the anomalous magnetic moment and to branching ratios of electromagnetic decays of the top quark. In accordance with present bounds on the compactification scale, contributions to both quantities are found to be at least 3 orders of magnitude below Standard-Model predictions., Comment: 11 figures, 31 pages. arXiv admin note: text overlap with arXiv:1704.07339

We construct a consistent quantum field theory of a dimensionally reduced self-interacting scalar field. The Kaluza-Klein dimensional reduction on the well-known $\Phi^{4}$ scalar theory, on a certain $(4+n)$ spacetime with an arbitrary number of extra dimensions, induces a four dimensional reduced theory with scalar fields: the zeroth mode (`light' field) and an infinite number of KK-excited modes (`heavy' fields). This theory is quantized by Hamiltonian path integral methods. It is shown, from first principles, that non-trivial measure factors at the level of the functional measure are absent even if the whole set of heavy fields is taken into account. Hints on the regularization and renormalization process are briefly discussed., Comment: 7 pages, 5 figures

The transition from formulations with extra dimensions to Kaluza-Klein theories, aimed at extending the Standard Model, bears the ingredients of hidden symmetries and the Kaluza-Klein mechanism for mass generation. We explore these essential aspects in detail, and find that much can be said about them with no reference to the specific geometry of compact extra dimensions: the low-energy theory is determined, included dynamic variables and symmetries; mass terms arise; eigenfunctions that define Kaluza-Klein fields are fixed by the appropriate choice a Casimir invariant; there is a set of Kaluza-Klein pseudo-Goldstone bosons. Throughout our presentation, similarities and differences among spontaneous symmetry breaking, commonly present in conventional Standard Model extensions, and what happens in Kaluza-Klein theories are signaled and discussed., Comment: 7 pages

We construct an effective Lagrangian for Yang-Mills theories with $n$ extra dimensions. We start from a field theory governed by the extra-dimensional Poincar\'e group ISO$(1,3+n)$ and by the extended gauge group $SU(N,{\cal M}^{4+n})$, characterized by an unknown energy scale $\Lambda$ and assumed to be valid at energies far below this scale. Assuming that the size of the extra dimensions is much larger than the distance scale at which this theory is valid, we construct an effective theory with symmetry groups ISO$(1,3)$, $SU(N,{\cal M}^{4})$. Such theories are connected by a canonical transformation that hides the extended symmetries ISO$(1,3+n)$, $SU(N,{\cal M}^{4+n})$ into the standard ISO(1,3), $SU(N,{\cal M}^{4})$, thus generating KK gauge masses. Using a set of orthogonal functions $\{f^{(\underline{0})}, f^{(\underline{m})}(\bar x)\}$, defined by the Casimir invariant $\bar{P}^2$ of the translations subgroup $T(n)\subset$ISO$(n)$, we expand the degrees of freedom of ISO(1,3+n), $SU(N,{\cal M}^{4+n})$ in general Fourier series, whose coefficients are the degrees of freedom of ISO(1,3), $SU(N,{\cal M}^{4})$. These functions, which correspond to the projection on the basis $\{|\bar{x} \big >\}$ of the discrete basis $\{|0\big >,|p^{(\underline{m})}\big >\}$ generated by $\bar {P}^2$, are central to define the effective theory. Components along the ground state $f^{(\underline{0})}=\big <\bar x|0\big>$ do not receive mass at the compactification scale, so they are identified with the standard Yang-Mills fields; components along excited states $f^{(\underline{m})}=\big<\bar x|p^{(\underline{m})}\big>$ receive mass at this scale, so they correspond to KK excitations. Associated with any direction $|p^{(\underline{m})}\neq0\big>$ there are a massive gauge field and a pseudo-Goldstone boson. We stress resemblances of this mass-generating mechanism with the Englert-Higgs mechanism., Comment: 18 pages. arXiv admin note: text overlap with arXiv:1603.03128

We construct a consistent quantum field theory of a dimensionally reduced self-interacting scalar field. The Kaluza-Klein dimensional reduction on the well-known $\Phi^{4}$ scalar theory, on a certain $(4+n)$ spacetime with an arbitrary number of extra dimensions, induces a four dimensional reduced theory with scalar fields: the zeroth mode (`light' field) and an infinite number of KK-excited modes (`heavy' fields). This theory is quantized by Hamiltonian path integral methods. It is shown, from first principles, that non-trivial measure factors at the level of the functional measure are absent even if the whole set of heavy fields is taken into account. Hints on the regularization and renormalization process are briefly discussed., Comment: 7 pages, 5 figures

We study radiative corrections on the photon propagator from the electroweak sector of the minimal Lorentz- and $CPT$-violating Standard Model Extension. We derive the most general Lorentz-violating ghost sector from BRST symmetry and renormalization theory. We introduce a Lorentz-violating nonlinear gauge that simplifies both the Higgs and gauge-sector extensions, which can be helpful in radiative corrections. At one loop, these sectors contribute to the $CPT$-even part of the photon propagator, characterized by the Riemann-type tensor $(k_F)_{\alpha\beta\mu\nu}$. We give exact results for the contributions to the SO(1,3) irreducible parts of $(k_F)_{\alpha \beta \mu \nu}$, namely, the Weyl-type tensor $(\hat{k}_F)_{\alpha \beta \mu \nu}$, the Ricci-type tensor $(k_F)_{\alpha \beta}$, and the curvature-type scalar $k_F$. In the Yukawa sector, one-loop contributions are ultraviolet finite, but most of them are unobservable due to finite renormalization. The only observable effect is a contribution proportional to $(k_F)_{\alpha \beta}$ that emerges via a dimension-6 term that is observer and gauge invariant. In the Higgs and gauge sectors, all the irreducible parts of the corresponding Riemann-type tensors receive divergent contributions, so they are observable. The only finite contribution corresponds to the dimension-6 term. We think of these contributions as radiative corrections to the renormalized tensors and assume that both effects are of the same order of magnitude to find bounds from vacuum birefringence and compare with the literature. Bounds on $(k_F)_{\alpha \beta}$ contributions, innocuous to birefringence, are also derived using limits on the renormalized tensor from Laser-Interferometer-Gravitational-Wave-Observatory data. We compare these bounds with the literature. Beta functions associated with $(\hat{k}_F)_{\alpha \beta \mu \nu}$ and $(k_F)_{\alpha \beta}$ are derived., Comment: Accepted for publication in Physical Review D, 33 pages, 5 figures

We construct an effective Lagrangian for Yang-Mills theories with $n$ extra dimensions. We start from a field theory governed by the extra-dimensional Poincar\'e group ISO$(1,3+n)$ and by the extended gauge group $SU(N,{\cal M}^{4+n})$, characterized by an unknown energy scale $\Lambda$ and assumed to be valid at energies far below this scale. Assuming that the size of the extra dimensions is much larger than the distance scale at which this theory is valid, we construct an effective theory with symmetry groups ISO$(1,3)$, $SU(N,{\cal M}^{4})$. Such theories are connected by a canonical transformation that hides the extended symmetries ISO$(1,3+n)$, $SU(N,{\cal M}^{4+n})$ into the standard ISO(1,3), $SU(N,{\cal M}^{4})$, thus generating KK gauge masses. Using a set of orthogonal functions $\{f^{(\underline{0})}, f^{(\underline{m})}(\bar x)\}$, defined by the Casimir invariant $\bar{P}^2$ of the translations subgroup $T(n)\subset$ISO$(n)$, we expand the degrees of freedom of ISO(1,3+n), $SU(N,{\cal M}^{4+n})$ in general Fourier series, whose coefficients are the degrees of freedom of ISO(1,3), $SU(N,{\cal M}^{4})$. These functions, which correspond to the projection on the basis $\{|\bar{x} \big >\}$ of the discrete basis $\{|0\big >,|p^{(\underline{m})}\big >\}$ generated by $\bar {P}^2$, are central to define the effective theory. Components along the ground state $f^{(\underline{0})}=\big <\bar x|0\big>$ do not receive mass at the compactification scale, so they are identified with the standard Yang-Mills fields; components along excited states $f^{(\underline{m})}=\big<\bar x|p^{(\underline{m})}\big>$ receive mass at this scale, so they correspond to KK excitations. Associated with any direction $|p^{(\underline{m})}\neq0\big>$ there are a massive gauge field and a pseudo-Goldstone boson. We stress resemblances of this mass-generating mechanism with the Englert-Higgs mechanism., Comment: 18 pages. arXiv admin note: text overlap with arXiv:1603.03128

The transition from formulations with extra dimensions to Kaluza-Klein theories, aimed at extending the Standard Model, bears the ingredients of hidden symmetries and the Kaluza-Klein mechanism for mass generation. We explore these essential aspects in detail, and find that much can be said about them with no reference to the specific geometry of compact extra dimensions: the low-energy theory is determined, included dynamic variables and symmetries; mass terms arise; eigenfunctions that define Kaluza-Klein fields are fixed by the appropriate choice a Casimir invariant; there is a set of Kaluza-Klein pseudo-Goldstone bosons. Throughout our presentation, similarities and differences among spontaneous symmetry breaking, commonly present in conventional Standard Model extensions, and what happens in Kaluza-Klein theories are signaled and discussed., Comment: 7 pages

The fundamental description of nature, beyond the Standard Model (SM), may include heavy neutrinos that mix and thus allow processes in which lepton flavor is not preserved. We investigate the impact of charged currents that couple heavy gauge bosons to heavy neutrinos and SM leptons on lepton-flavor-violating decays of SM leptons into three charged leptons, with no final-state neutrinos. We implement our expressions for the leading contributions to ${\rm Br}(l_\alpha\to l_\beta\,l_\sigma\,l_\sigma)$, which hold for either Dirac or Majorana neutrinos, to the trilepton decay $\mu\to3e$, of the muon, and so determine sets of masses of heavy neutrinos and the heavy gauge boson, within GeVs to few TeVs, that are consistent with the upper bounds provided by the SINDRUM Collaboration. We find, however, that constraints dictated by the upper bound on ${\rm Br}(\mu\to e\gamma)$, from the MEG Collaboration, are more stringent. We utilize such parameters to find that the contributions to tau decays are $\sim10^{-15}-10^{-13}$, well below bounds from $B$ factories. The mixing of heavy and SM charged bosons is also investigated. We find that current experimental data from MEG and SINDRUM would allow mixing angles as large as $\sim10^{-2}$, for a relatively light new charged boson, but the expected sensitivity of the Mu3e experiment would be capable of setting an upper bound on this angle as small as $\sim10^{-4}$ if the mass of this boson is within the range of few TeVs., Comment: Accepted for publication in Journal of Physics G, 26 pages, 12 figures, 4 tables, several new elements were added for this version of the manuscript, the whole discussion was improved as well

The radiative correction to beta function is comprehensively studied at 1 loop in the context of universal extra dimensions. Instead of using cutoffs to regularize 1-loop divergences, the dimensional regularization scheme is used. Large momenta effects are removed from physical amplitudes by adjusting the parameters of the appropriate counterterms. The use of a SU(N)-covariant gauge-fixing procedure is stressed. 1-loop contributions of KK excitations are characterized by discrete KK sums and continuous momenta sums, which can diverge. Two types of UVs are identified, one arising from poles of the gamma function and associated with short-distance effects in the usual 4-dimensional spacetime manifold, and the other emerging either from poles of the 1-dimensional Epstein function or from the gamma function, and corresponding to short-distance effects in the compact manifold. We address the cases of 5 and 4+n dimensions (n>1) separately. In 5 dimensions the 1-dimensional Epstein function is convergent, so the usual counterterm renormalizes the vacuum polarization function. For 4+n dimensions, the 1-dimensional Epstein function is divergent, so renormalization is implemented by interactions of canonical dimension higher than 4, already present in the effective theory. The polarization function is renormalized using both mass-dependent and mass-independent schemes, with extra-dimensions effects decoupling in the former case but not in the latter. The beta function is calculated for an arbitrary number of extra dimensions. Our main result is that Yang-Mills theory remains perturbative at 1 loop, which is in disagreement with the results obtained in the literature by using a cutoff regulator, which suggest that Yang-Mills theory in more than 4 dimensions ceases to be perturbative. We emphasize the advantages of a mass-dependent scheme in this type of theories, in which decoupling is manifest., Comment: 30 pages

The signal strength of the $gg \to H \to \gamma \gamma$ reaction in $pp$ collisions at the LHC is studied within the context of the SM with UED. The impact of an arbitrary number $n$ of UED on both the $gg\to H$ and $H\to \gamma \gamma$ subprocesses is studied. The 1-loop contributions of Kaluza-Klein excitations to these subprocesses are proportional to discrete and continuous sums, which can diverge. By implementing dimensional regularization, it is shown that discrete regularized sums can naturally be expressed as multidimensional Epstein functions, and that divergences, if exist, emerge through the poles of these functions. It is found that continuous sums converge, but the discrete ones diverge, with the exception of the $n=1$ case, in which the 1-dimensional Epstein function converges. It is argued that divergences that arise from discrete sums for $n\geq 2$ are genuine UV divergences, since they correspond to short-distance effects in the compact manifold. Then, the amplitudes are renormalized in a modern sense by incorporating interactions of canonical dimension higher than four that allow us to generate the required counterterms, which are determined using a $\overline{\rm MS}$-like renormalization scheme. We find that the $gg\to H$ subprocess is quite sensitive to both the size and the dimension of the compact manifold, but the SM prediction for $H\to \gamma \gamma$ subprocess is practically unchanged. In the $n=1$ case, it is found that the experimental constraint on the compactification scale $R^{-1}\geq 1.5$ TeV allow us to reproduce the experimental limit on the signal strength $1.01\leq \mu^{(1)}_{\gamma \gamma}\leq 1.2$. In the $n\geq 2$ cases, it is found that the experimental limit on $\mu^{(n)}_{\gamma \gamma}$ leads to stronger lower bounds for the compactification scale given by $R^{-1}\geq 1.55, 2.45, 3.57, 5.10, 7.25$ TeVs for $n=2, 4, 6, 8, 10$, respectively., Comment: 31 pages, 5 figures

We construct an effective theory for the SM with extra dimensions. We start from a theory governed by the extra-dimensional groups ISO$(1,3+n)$ and $G_{\rm SM}({\cal M}^{4+n})=SU_C(3,{\cal M}^{4+n})\times SU_L(2,{\cal M}^{4+n})\times U_Y(1,{\cal M}^{4+n})$, characterized by an unknown energy scale $\Lambda$ and valid at energies far below this scale. Assuming that the extra dimensions are much larger than the distance scale of this theory, we construct an effective theory with symmetry groups ISO(1,3), $G_{\rm SM}({\cal M}^{4})$. The theories are connected by a canonical transformation that hides ISO$(1,3+n)$, $G_{\rm SM}({\cal M}^{4+n})$ into ISO(1,3), $G_{\rm SM}({\cal M}^{4})$; KK fields receive mass. Using a set of orthogonal functions $\{f^{(\underline{0})},f^{(\underline{m})}\}$, generated by the Casimir invariant $\bar{P}^2$ associated with the translations subgroup $T(n)\subset$ISO$(n)$, we expand the degrees of freedom of ISO$(1,3+n)$, $G_{\rm SM}({\cal M}^{4+n})$ in general Fourier series, whose coefficients are the degrees of freedom of ISO(1,3), $G({\cal M}^{4})$. These functions, which correspond to the projection on $\{|\bar{x}\big>\}$ of the discrete basis $\{|0\big>,|p^{(\underline{m})}\big>\}$ of $\bar{P}^2$, are central to define the effective theory. Components along the ground state $f^{(\underline{0})}=\big <\bar x|0\big>$ do not receive mass at the compactification scale, so they are the SM fields; components along excited states $f^{(\underline{m})}=\big<\bar x|p^{(\underline{m})}\big>$ get mass at this scale, so they are KK excitations. For any direction $|p^{(\underline{m})}\neq0\big>$ there are a massive gauge field and a pseudo-Goldstone boson. We stress resemblances of this mass-generating mechanism with the Englert-Higgs mechanism and discuss physical implications. We include a full catalog of Lagrangian terms that can be used to calculate Feynman rules., Comment: 46 pages; content and discussion have been improved

Violation of $CP$ invariance is a quite relevant phenomenon that is found in the Standard Model (SM), though in small amounts. This has been an incentive to look for high-energy descriptions in which $CP$ violation is increased, thus enhancing effects that are suppressed in the SM, such as the electric dipole moments (EDMs) of elementary particles. In the present investigation, we point out that charged currents in which axial couplings are different from vector couplings are able to produce one-loop contributions to EDMs of charged leptons if neutrinos are massive and if these currents violate $CP$. We develop our discussion around charged currents involving heavy neutrinos and a $W'$ gauge boson coupling to SM charged leptons. Using the most stringent bound on the electron EDM, provided by the ACME Collaboration, we determine that the upper bound on the difference between axial and vector currents lies within $\sim10^{-10}$ and $\sim10^{-7}$ for heavy-neutrino masses between $0.5\,{\rm TeV}$ and $6\,{\rm TeV}$ and if the $W'$ mass is within $0.45\,{\rm TeV}-7\,{\rm TeV}$. This possibility is analyzed altogether with the anomalous magnetic moments of charged leptons, among which we estimate, for the $\tau$ lepton, an anomalous magnetic moment contribution between $\sim10^{-8}$ and $\sim10^{-10}$ for neutrino masses ranging from $0.5\,{\rm TeV}$ to $6\,{\rm TeV}$ and a $W'$ mass between $0.45\,{\rm TeV}$ and $7\,{\rm TeV}$. The general charged currents are also used to calculate the branching ratio for $\mu\to e\gamma$, which gets suppressed if the set of masses of heavy neutrinos is quasidegenerate. In a scenario of nondegenerate neutrino masses, we find that regions of neutrino and $W'$ masses in which the contributions to this flavor changing branching ratio are lower than the current upper bound exist. We show that such regions can be widened if the $W'$ gauge boson mass is larger., Comment: 14 pages; 4 figures; accepted by Physical Review D for publication; we found a problem with our calculations, so this revised version includes corrections, modifications to analyses, a whole new section, and an improved discussion

We construct an effective theory for the SM with extra dimensions. We start from a theory governed by the extra-dimensional groups ISO$(1,3+n)$ and $G_{\rm SM}({\cal M}^{4+n})=SU_C(3,{\cal M}^{4+n})\times SU_L(2,{\cal M}^{4+n})\times U_Y(1,{\cal M}^{4+n})$, characterized by an unknown energy scale $\Lambda$ and valid at energies far below this scale. Assuming that the extra dimensions are much larger than the distance scale of this theory, we construct an effective theory with symmetry groups ISO(1,3), $G_{\rm SM}({\cal M}^{4})$. The theories are connected by a canonical transformation that hides ISO$(1,3+n)$, $G_{\rm SM}({\cal M}^{4+n})$ into ISO(1,3), $G_{\rm SM}({\cal M}^{4})$; KK fields receive mass. Using a set of orthogonal functions $\{f^{(\underline{0})},f^{(\underline{m})}\}$, generated by the Casimir invariant $\bar{P}^2$ associated with the translations subgroup $T(n)\subset$ISO$(n)$, we expand the degrees of freedom of ISO$(1,3+n)$, $G_{\rm SM}({\cal M}^{4+n})$ in general Fourier series, whose coefficients are the degrees of freedom of ISO(1,3), $G({\cal M}^{4})$. These functions, which correspond to the projection on $\{|\bar{x}\big>\}$ of the discrete basis $\{|0\big>,|p^{(\underline{m})}\big>\}$ of $\bar{P}^2$, are central to define the effective theory. Components along the ground state $f^{(\underline{0})}=\big <\bar x|0\big>$ do not receive mass at the compactification scale, so they are the SM fields; components along excited states $f^{(\underline{m})}=\big<\bar x|p^{(\underline{m})}\big>$ get mass at this scale, so they are KK excitations. For any direction $|p^{(\underline{m})}\neq0\big>$ there are a massive gauge field and a pseudo-Goldstone boson. We stress resemblances of this mass-generating mechanism with the Englert-Higgs mechanism and discuss physical implications. We include a full catalog of Lagrangian terms that can be used to calculate Feynman rules., Comment: 46 pages; content and discussion have been improved

One-loop Standard Model observables produced by virtual heavy Kaluza-Klein fields play a prominent role in the minimal model of universal extra dimensions. Motivated by this aspect, we integrate out all the Kaluza-Klein heavy modes coming from the Yang-Mills theory set on a spacetime with an arbitrary number, $n$, of compact extra dimensions. After fixing the gauge with respect to the Kaluza-Klein heavy gauge modes in a covariant manner, we calculate a gauge independent effective Lagrangian expansion containing multiple Kaluza-Klein sums that entail a bad divergent behavior. We use the Epstein-zeta function to regularize and characterize discrete divergences within such multiple sums, and then we discuss the interplay between the number of extra dimensions and the degree of accuracy of effective Lagrangians to generate or not divergent terms of discrete origin. We find that nonrenormalizable terms with mass dimension $k$ are finite as long as $k>4+n$. Multiple Kaluza-Klein sums of nondecoupling logarithmic terms, not treatable by Epstein-zeta regularization, are produced by four-dimensional momentum integration. On the grounds of standard renormalization, we argue that such effects are unobservable., Comment: 16 pages, slight change in title, new references added

An exact calculation of the Higgs boson decays $H\to q_i q_j$ mediated by flavor changing neutral currents is presented in the context of the Standard Model. Using up-to-date experimental data, branching ratios of the order of $10^{-7}$, $10^{-8}$, $10^{-8}$, and $10^{-15}$ are found for the $\bar{b}s+\bar{s}b$, $\bar{b}d+\bar{d}b$, $\bar{s}d+\bar{d}s$, and $\bar{c}u+\bar{u}c$ decay modes, respectively., Comment: Revised version accepted in J. Phys. G: Nucl. Part. Phys

In models with extended scalar sectors with several Higgs multiplets, such as Higgs triplet models, the $Z$ gauge boson can have nondiagonal couplings to charged Higgs bosons. In a model-independent way, we study the potential contributions arising from such theories to the CP-violating trilinear neutral gauge boson couplings $ZZ^*\gamma$, $ZZ\gamma^*$, and $ZZZ^*$, which are parametrized by four form factors: $h^Z_{1,2}$, $f_4^\gamma$, and $f_4^Z$, respectively. Such form factors can only be induced if there are at least two nondegenerate charged Higgs scalars and an imaginary phase in the coupling constants. For the masses of the charged scalar bosons we consider values above 300 GeV and find that the form factors can reach the following orders of magnitude: $|h_1^Z|\sim 10^{-5}-10^{-4}$, $|h_2^Z|\sim 10^{-7}-10^{-6}$, $|f_4^\gamma|\sim 10^{-5}-10^{-3}$ and $|f_4^Z|\sim 10^{-6}-10^{-5}$, though there could be an additional suppression factor arising from the coupling constants. We also find that the form factors decouple at high energies and are not very sensitive to a change in the masses of the charged scalar bosons. Apart from a proportionality factor, our results for the $f_4^Z$ form factor, associated with the $ZZZ^*$ vertex, is of the same order of magnitude than that induced via nondiagonal neutral scalar boson couplings in the framework of a two-Higgs doublet model., Comment: 13 pages, 8 figures

The $Z\to \gamma \gamma$ and $Z\to gg$ decays are studied in the context of the renormalizable version of the Standard Model Extension. The $CPT$-odd $\bar{\psi}\gamma_5 \gamma^\mu b_\mu\psi$ bilinear interaction, which involves the constant background field $b_\alpha$ and which has been a subject of interest in literature, is considered. It is shown that the $Z\to \gamma \gamma$ and $Z\to gg$ decays, which are strictly zero in the standard model, can be generated radiatively at the one-loop level. It is found that these decays are gauge invariant and free of ultraviolet divergences, and that the corresponding decay widths only depend on the spatial component of the background field $b$., Comment: A few references corrected

An exact calculation of the Higgs boson decays $H\to q_i q_j$ mediated by flavor changing neutral currents is presented in the context of the Standard Model. Using up-to-date experimental data, branching ratios of the order of $10^{-7}$, $10^{-8}$, $10^{-8}$, and $10^{-15}$ are found for the $\bar{b}s+\bar{s}b$, $\bar{b}d+\bar{d}b$, $\bar{s}d+\bar{d}s$, and $\bar{c}u+\bar{u}c$ decay modes, respectively., Comment: Revised version accepted in J. Phys. G: Nucl. Part. Phys

In models with extended scalar sectors with several Higgs multiplets, such as Higgs triplet models, the $Z$ gauge boson can have nondiagonal couplings to charged Higgs bosons. In a model-independent way, we study the potential contributions arising from such theories to the CP-violating trilinear neutral gauge boson couplings $ZZ^*\gamma$, $ZZ\gamma^*$, and $ZZZ^*$, which are parametrized by four form factors: $h^Z_{1,2}$, $f_4^\gamma$, and $f_4^Z$, respectively. Such form factors can only be induced if there are at least two nondegenerate charged Higgs scalars and an imaginary phase in the coupling constants. For the masses of the charged scalar bosons we consider values above 300 GeV and find that the form factors can reach the following orders of magnitude: $|h_1^Z|\sim 10^{-5}-10^{-4}$, $|h_2^Z|\sim 10^{-7}-10^{-6}$, $|f_4^\gamma|\sim 10^{-5}-10^{-3}$ and $|f_4^Z|\sim 10^{-6}-10^{-5}$, though there could be an additional suppression factor arising from the coupling constants. We also find that the form factors decouple at high energies and are not very sensitive to a change in the masses of the charged scalar bosons. Apart from a proportionality factor, our results for the $f_4^Z$ form factor, associated with the $ZZZ^*$ vertex, is of the same order of magnitude than that induced via nondiagonal neutral scalar boson couplings in the framework of a two-Higgs doublet model., Comment: 13 pages, 8 figures

The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based manifold under consideration contains $ n $ spatial extra dimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In this approach, we present the gauge structure and the mass spectrum of the effective four-dimensional theory. We introduce the concept of standard and nonstandard gauge transformations of the effective theory, and explicitly identify the emergence of massive vector fields in the same number as massless ('pseudo-Goldstone') scalars in the compactified theory, verifying that a Higgs-like mechanism operates in the compactification process. It is found that, in contrast with the one UED scenario, in cases with two or more UEDs there emerge massive scalar fields. Besides, at phase-space level, the Hamiltonian analysis yields that the higher-dimensional and compactified theories are classically equivalent using the fundamental concept of canonical transformation. This work lays the ground for a wider study on these theories concerning their quantization and predictive power at the level of quantum fluctuations., Comment: Minor changes in the Introduction, and some typos corrected

The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based manifold under consideration contains $ n $ spatial extra dimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In this approach, we present the gauge structure and the mass spectrum of the effective four-dimensional theory. We introduce the concept of standard and nonstandard gauge transformations of the effective theory, and explicitly identify the emergence of massive vector fields in the same number as massless ('pseudo-Goldstone') scalars in the compactified theory, verifying that a Higgs-like mechanism operates in the compactification process. It is found that, in contrast with the one UED scenario, in cases with two or more UEDs there emerge massive scalar fields. Besides, at phase-space level, the Hamiltonian analysis yields that the higher-dimensional and compactified theories are classically equivalent using the fundamental concept of canonical transformation. This work lays the ground for a wider study on these theories concerning their quantization and predictive power at the level of quantum fluctuations., Comment: Minor changes in the Introduction, and some typos corrected

The $Z\to \gamma \gamma$ and $H\to \gamma \gamma \gamma$ decays are strictly forbidden in the Standard Model, but they can be induced by theories that violate Lorentz symmetry or the CPT theorem. By assuming that a nonvanishing $Z\gamma \gamma$ vertex is induced in some context of new physics, and by analyzing the reaction $H\to \gamma Z^*\to \gamma \gamma \gamma$ in the $Z$ resonance, we obtain an estimation for the branching ratio of the $H\to \gamma \gamma \gamma$ decay. Specifically, it is found that $BR(H\to \gamma \gamma \gamma)\lesssim BR(H\to \gamma Z)BR_{Exp}(Z\to \gamma \gamma)$, which is of the order of $10^{-7}$., Comment: 4 pages, 1 figure

The lepton flavor violating decay of the Higgs boson $H\to l_Al_B$ is studied within two qualitatively different extensions of the Yukawa sector: one renormalizable and the other nonrenormalizable; both incorporating Lorentz violation in a model-independent fashion. These extensions are characterized by Yukawa-like matrices, the former by a constant Lorentz 2-tensor $Y^{AB}_{\mu \nu}$, whereas the latter by a constant Lorentz vector $Y^{AB}_\mu$. It is found that the experimental constraints on the decays $l_A\to l_B\gamma$ severely restrict lepton flavor violating Higgs signals in the renormalizable scenario. In this context, it is found that $BR(H\to \mu^\pm e^\mp)$ and $BR(H\to \tau^\pm \mu^\mp)$ cannot be larger than $10^{-18}$ and $10^{-11}$, respectively. In the nonrenormalizable scenario, transitions mediated by the Higgs or the $Z$ gauge boson are induced at tree level, and we find mild restrictions on lepton flavor violation. Using the experimental limits on the three-body decays $l_A \to l_B \bar{l}_Cl_C$ to constraint the vector $Y^{AB}_\mu$, it is found that the branching ratio for the decays $H\to \mu^\pm e^\mp$ is of about $4\times 10^{-9}$, more important, a branching ratio of $7\times 10^{-4}$ is found for the $\tau^\pm \mu^\mp$ mode. Accordingly, the decay $H \to \tau^\pm \mu^\mp$ could be at the reach of future measurements. The lepton flavor violating decays of the $Z$ gauge boson were also studied. In the renormalizable scenario, it was found the undetectable branching ratios $BR(Z\to \mu^\pm e^\mp)<5.7\times 10^{-21}$ and $BR(Z\to \tau^\pm \mu^\mp)<2.0\times 10^{-12}$. In the nonrenormalizable scenario, it was found that $BR(Z\to \mu^\pm e^\mp)<0.67\times 10^{-12}$ and $BR(Z\to \tau^\pm \mu^\mp)<1.12\times 10^{-7}$. Although the latter branching ratio is relatively large, it still could not be within the range of future measurements., Comment: Updated to essentially match published version

The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based manifold under consideration contains $ n $ spatial extra dimensions defined by $ n $ copies of the orbifold $ S^{1} / Z_{2}$. In this approach, we present the gauge structure and the mass spectrum of the effective four-dimensional theory. We introduce the concept of standard and nonstandard gauge transformations of the effective theory, and explicitly identify the emergence of massive vector fields in the same number as massless ('pseudo-Goldstone') scalars in the compactified theory, verifying that a Higgs-like mechanism operates in the compactification process. It is found that, in contrast with the one UED scenario, in cases with two or more UEDs there emerge massive scalar fields. Besides, at phase-space level, the Hamiltonian analysis yields that the higher-dimensional and compactified theories are classically equivalent using the fundamental concept of canonical transformation. This work lays the ground for a wider study on these theories concerning their quantization and predictive power at the level of quantum fluctuations., Comment: Minor changes in the Introduction, and some typos corrected

El objetivo de este artículo es estudiar los cambios en la productividad y sus elementos determinantes -cambio técnico y cambio en eficiencia- de una muestra de explotaciones lecheras cubanas ubicadas en el municipio de San José de las Lajas. Con este propósito se calculan índices Malmquist de productividad con técnicas DEA y datos correspondientes al período 2006-08. Asimismo, se asumen rendimientos variables a escala y se utiliza una orientación al producto. Se consideraron dos insumos y dos productos. Los resultados indican que debido a una caída de la productividad de las explotaciones lecheras durante el periodo 2006-2007, que no fue compensada por el incremento ocurrido durante el lapso 2007-2008, todo el periodo de estudio, del 2006 al 2008, reflejó una pequeña reducción de la productividad, que fue ocasionada en su totalidad por un ligero retroceso tecnológico. Este resultado es explicado, parcialmente, por un aumento del número de vacas en el año 2007 que no se expresó proporcionalmente en la producción correspondiente a ese año.

The lepton flavor violating decay of the Higgs boson $H\to l_Al_B$ is studied within two qualitatively different extensions of the Yukawa sector: one renormalizable and the other nonrenormalizable; both incorporating Lorentz violation in a model-independent fashion. These extensions are characterized by Yukawa-like matrices, the former by a constant Lorentz 2-tensor $Y^{AB}_{\mu \nu}$, whereas the latter by a constant Lorentz vector $Y^{AB}_\mu$. It is found that the experimental constraints on the decays $l_A\to l_B\gamma$ severely restrict lepton flavor violating Higgs signals in the renormalizable scenario. In this context, it is found that $BR(H\to \mu^\pm e^\mp)$ and $BR(H\to \tau^\pm \mu^\mp)$ cannot be larger than $10^{-18}$ and $10^{-11}$, respectively. In the nonrenormalizable scenario, transitions mediated by the Higgs or the $Z$ gauge boson are induced at tree level, and we find mild restrictions on lepton flavor violation. Using the experimental limits on the three-body decays $l_A \to l_B \bar{l}_Cl_C$ to constraint the vector $Y^{AB}_\mu$, it is found that the branching ratio for the decays $H\to \mu^\pm e^\mp$ is of about $4\times 10^{-9}$, more important, a branching ratio of $7\times 10^{-4}$ is found for the $\tau^\pm \mu^\mp$ mode. Accordingly, the decay $H \to \tau^\pm \mu^\mp$ could be at the reach of future measurements. The lepton flavor violating decays of the $Z$ gauge boson were also studied. In the renormalizable scenario, it was found the undetectable branching ratios $BR(Z\to \mu^\pm e^\mp)<5.7\times 10^{-21}$ and $BR(Z\to \tau^\pm \mu^\mp)<2.0\times 10^{-12}$. In the nonrenormalizable scenario, it was found that $BR(Z\to \mu^\pm e^\mp)<0.67\times 10^{-12}$ and $BR(Z\to \tau^\pm \mu^\mp)<1.12\times 10^{-7}$. Although the latter branching ratio is relatively large, it still could not be within the range of future measurements., Comment: Updated to essentially match published version

The $Z\to \gamma \gamma$ and $H\to \gamma \gamma \gamma$ decays are strictly forbidden in the Standard Model, but they can be induced by theories that violate Lorentz symmetry or the CPT theorem. By assuming that a nonvanishing $Z\gamma \gamma$ vertex is induced in some context of new physics, and by analyzing the reaction $H\to \gamma Z^*\to \gamma \gamma \gamma$ in the $Z$ resonance, we obtain an estimation for the branching ratio of the $H\to \gamma \gamma \gamma$ decay. Specifically, it is found that $BR(H\to \gamma \gamma \gamma)\lesssim BR(H\to \gamma Z)BR_{Exp}(Z\to \gamma \gamma)$, which is of the order of $10^{-7}$., Comment: 4 pages, 1 figure

El objetivo de este artículo es estudiar los cambios en la productividad y sus elementos determinantes -cambio técnico y cambio en eficiencia- de una muestra de explotaciones lecheras cubanas ubicadas en el municipio de San José de las Lajas. Con este propósito se calculan índices Malmquist de productividad con técnicas DEA y datos correspondientes al período 2006-08. Asimismo, se asumen rendimientos variables a escala y se utiliza una orientación al producto. Se consideraron dos insumos y dos productos. Los resultados indican que debido a una caída de la productividad de las explotaciones lecheras durante el periodo 2006-2007, que no fue compensada por el incremento ocurrido durante el lapso 2007-2008, todo el periodo de estudio, del 2006 al 2008, reflejó una pequeña reducción de la productividad, que fue ocasionada en su totalidad por un ligero retroceso tecnológico. Este resultado es explicado, parcialmente, por un aumento del número de vacas en el año 2007 que no se expresó proporcionalmente en la producción correspondiente a ese año.

Lorentz violation emerged from a fundamental description of nature may impact, at low energies, the Maxwell sector, so that contributions from such new physics to the electromagnetic vertex would be induced. Particularly, nonbirefringent $CPT$-even effects from the electromagnetic sector modified by the Lorentz- and $CPT$-violating Standard Model Extension alter the structure of the free photon propagator. We calculate Lorentz-violating contributions to the electromagnetic vertex, at the one-loop level, by using a modified photon propagator carrying this sort of effects. We take the photon off shell, and find an expression that involves both isotropic and anisotropic effects of nonbirefringent violation of Lorentz invariance. Our analysis of the one-loop vertex function includes gauge invariance, transformation properties under $C$, $P$, and $T$, and tree-level contributions from Lorentz-violating nonrenormalizable interactions. These elements add to previous studies of the one-loop contributions to the electromagnetic vertex in the context of Lorentz violation in the photon sector. Finally, we restrict our analysis to the isotropic case and derive a finite contribution from isotropic Lorentz violation to the anomalous magnetic moment of fermions that coincides with the result already reported in the literature., Comment: 11 pages, 2 figures, some references added

We examine Lorentz-violating effects that could appear through deviations of the Standard Model gauge couplings WWgamma and WWgammagamma. These new physics effects are explored on the gamma gamma -> WW reaction at the International Linear Collider. In particular, the associated helicity amplitudes are computed in the context of the Standard Model Extension (which is a model-independent approach to CPT and Lorentz violation) and the Effective Lagrangian Model (which incorporates new physics effects that respect CPT and Lorentz violation). We perform an exhaustive study of the polarized differential cross sections to stand out effects related to Lorentz symmetry violation, where it is evidenced that the effects of Lorentz symmetry violation are more sensitive to the presence of the b constant background field. We found that for the $(\pm,\pm,(L,T+T,L))$ polarization state, only Standard Model Extension and Effective Lagrangian Model contribute at the lowest order, however, both types of new physics effects are clearly distinguished, being dominant the convoluted cross section of the Standard Model Extension in around 4 orders of magnitude. For this polarization state, at the last stage of operation of International Linear Collider, it is expected an integrated luminosity of 10^3 fb^{-1}, finding around of 2 events for a Lorentz-violating energy scale of 32 TeV., Comment: 25 pages and 23 figures. arXiv admin note: substantial text overlap with arXiv:1305.4265

Low-energy Lorentz-invariant quantities could receive contributions from a fundamental theory producing small Lorentz-violating effects. Within the Lorentz-violating extension of quantum electrodynamics, we investigate, perturbatively, the contributions to the one-loop $ff\gamma$ vertex from the $CPT$-violating axial coupling of a vector background field to fermions. We find that the resulting vertex function has a larger set of Lorentz structures than the one characterizing the usual, Lorentz invariant, parametrization of the $ff\gamma$ vertex. We prove gauge invariance of the resulting one-loop expression through a set of gauge invariant nonrenormalizable operators introducing new-physics effects at the first and second orders in Lorentz violation, and which generate tree-level contributions to the $ff\gamma$ vertex. Whereas loop contributions involving parameters that violate Lorentz invariance at the first order are $CPT$-odd, those arising at the second order are $CPT$-even, so that contributions to low-energy physics are restricted to emerge for the first time at the second order. In this context, we derive a contribution to anomalous magnetic moment of fermions, which we use to set a bound on Lorentz violation., Comment: 13 pages, 1 figure, 1 table, a couple of references were added

Physics beyond the Fermi scale could show up through deviations of the gauge couplings predicted by the electroweak Yang-Mills sector. This possibility is explored in the context of the International Linear Collider (ILC) through the helicity amplitudes for the gamma e -> W nu_e reaction to which contributes the trilinear WWgamma coupling. The new physics effects on this vertex are parametrized in a model-independent fashion through an effective electroweak Yang-Mills sector, which is constructed by considering two essentially different sources of new physics. In one scenario, Lorentz violation will be considered exclusively as the source of new physics effects. This type of new physics is considered in an extension of the Standard Model that is known as the Standard Model Extension (SME), which is an effective field theory that contemplates CPT and Lorentz violation in a model-independent fashion. Any source of new physics that respects the Lorentz symmetry, will be considered within the general context of the well known Conventional Effective Standard Model (CESM) extension. Both the SME and the CESM descriptions include gauge invariant operators of dimension higher than four, which, in general, transform as Lorentz tensors of rank higher than zero. Whereas in the former theory observer Lorentz invariants are constructed by contracting these operators with constant Lorentz tensors, in the latter the corresponding Lorentz invariant interactions are obtained contracting such operators with products of the metric tensor. We focus our study on the possibility of experimentally distinguish both types of new physics effects on the WWgamma vertex. It is found that for a new physics scale of the same order of magnitude and under determined circumstances, both types of new physics effects will be clearly distinguished., Comment: 18 pages and 25 figures

One-loop effects of Standard Model (SM) extensions comprising universal extra dimensions are essential as a consequence of Kaluza-Klein (KK) parity conservation, for they represent the very first presumable virtual effects on low-energy observables. In this paper, we calculate the one-loop CP-even contributions to the SM WWgamma and WWZ gauge couplings produced by the KK excited modes that stand for the dynamical variables of the effective theory emerged from a generalization of the SM to five dimensions, in which the extra dimension is assumed to be universal, after compactification. The employment of a covariant gauge-fixing procedure that removes gauge invariance associated to gauge KK excited modes, while keeping electroweak gauge symmetry manifest, is a main feature of this calculation, which is performed in the Feynman 't Hooft gauge and yields finite results that consistently decouple for a large compactification scale. After numerical evaluation, our results show to be comparable with the one-loop SM contributions and well within the reach of a next linear collider., Comment: 25 pages, 6 figures, new references added, typos corrected

Compactified Yang-Mills theories with one universal extra dimension were found [arXiv:1008.4638] to exhibit two types of gauge invariances: the standard gauge transformations (SGTs) and the nonstandard gauge transformations (NSGTs). In the present work we show that these transformations are not exclusive to compactified scenarios. Introducing a notion of hidden symmetry, based on the fundamental concept of canonical transformation, we analyse three different gauge systems, each of which is mapped to a certain effective theory that is invariant under the so-called SGTs and NSGTs. The systems under discussion are: (i) four dimensional pure $SU(3)$ Yang-Mills theory, (ii) four dimensional $SU(3)$ Yang-Mills with spontaneous symmetry breaking, and (iii) pure Yang-Mills theory with one universal compact extra dimension. The canonical transformation, that induces the notion of hidden symmetry, maps objects with well defined transformation laws under a gauge group $G$ to well defined objects under a non-trivial subgroup $H \subset G$. In the case where spontaneous symmetry breaking is present, the set of SGTs corresponds to the group into which the original gauge group is broken into, whereas the NSGTs are associated to the broken generators and can be used to define the unitary gauge. For the system (iii), the SGTs coincide with the gauge group $ SU(N,\cal{M}^{4}) $, whereas the NSGTs do not form a group; in this system the 'fundamental' theory and the effective one are shown to be classically equivalent., Comment: 26 pages, title has changed, some comments and clarifications added, some references added

Lorentz violation emerged from a fundamental description of nature may impact, at low energies, the Maxwell sector, so that contributions from such new physics to the electromagnetic vertex would be induced. Particularly, nonbirefringent $CPT$-even effects from the electromagnetic sector modified by the Lorentz- and $CPT$-violating Standard Model Extension alter the structure of the free photon propagator. We calculate Lorentz-violating contributions to the electromagnetic vertex, at the one-loop level, by using a modified photon propagator carrying this sort of effects. We take the photon off shell, and find an expression that involves both isotropic and anisotropic effects of nonbirefringent violation of Lorentz invariance. Our analysis of the one-loop vertex function includes gauge invariance, transformation properties under $C$, $P$, and $T$, and tree-level contributions from Lorentz-violating nonrenormalizable interactions. These elements add to previous studies of the one-loop contributions to the electromagnetic vertex in the context of Lorentz violation in the photon sector. Finally, we restrict our analysis to the isotropic case and derive a finite contribution from isotropic Lorentz violation to the anomalous magnetic moment of fermions that coincides with the result already reported in the literature., Comment: 11 pages, 2 figures, some references added

We examine Lorentz-violating effects that could appear through deviations of the Standard Model gauge couplings WWgamma and WWgammagamma. These new physics effects are explored on the gamma gamma -> WW reaction at the International Linear Collider. In particular, the associated helicity amplitudes are computed in the context of the Standard Model Extension (which is a model-independent approach to CPT and Lorentz violation) and the Effective Lagrangian Model (which incorporates new physics effects that respect CPT and Lorentz violation). We perform an exhaustive study of the polarized differential cross sections to stand out effects related to Lorentz symmetry violation, where it is evidenced that the effects of Lorentz symmetry violation are more sensitive to the presence of the b constant background field. We found that for the $(\pm,\pm,(L,T+T,L))$ polarization state, only Standard Model Extension and Effective Lagrangian Model contribute at the lowest order, however, both types of new physics effects are clearly distinguished, being dominant the convoluted cross section of the Standard Model Extension in around 4 orders of magnitude. For this polarization state, at the last stage of operation of International Linear Collider, it is expected an integrated luminosity of 10^3 fb^{-1}, finding around of 2 events for a Lorentz-violating energy scale of 32 TeV., Comment: 25 pages and 23 figures. arXiv admin note: substantial text overlap with arXiv:1305.4265