Gauge invariance and quantization of Yang-Mills theories in extra dimensions

Novales‐Sánchez, H.; Toscano, J. J.

doi:10.1103/physrevd.82.116012

Cited by 34 publications

(157 citation statements)

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“…The extra dimensional approach is defined depending on the bulk geometry and the way in which the different fields are allocated on it. In particular, allowing gauge and matter fields of the standard model to propagate in the bulk gives rise to the universal extra dimensions (UEDs) scenarios [5]; in this approach, gauge invariance preservation at the higher dimensional level requires all gauge parameters to be also defined on the bulk [6]. In addition, to be consistent with the available experimental information, the submanifold corresponding to the extra dimensions is assumed to be suitably compactified.…”

Section: Introductionmentioning

confidence: 99%

“…Some theoretical aspects of these models have also been considered [14]. In this context, a comprehensive analysis of both the classical and quantum structure of Yang-Mills theories in the five dimensional S 1 /Z 2 -one UED (OUED) scenario was fully presented in a series of papers [6,7,15].…”

Section: Introductionmentioning

confidence: 99%

“…In each series, the zero modes of fields correspond to known fields of the standard model, whereas the zero modes of gauge parameters specify the * Electronic address: alopez@fcfm.buap.mx † Electronic address: emartinez@fcfm.buap.mx ‡ Electronic address: hnovales@fisica.ugto.mx § Electronic address: jtoscano@fcfm.buap.mx so-called standard gauge transformations (SGTs) [6,7]. These are gauge transformations underlying the lower dimensional theory, whose gauge parameters are the remainder of the gauge parameters defined on the bulk after compactification.…”

Section: Introductionmentioning

confidence: 99%

“…[6], a new classification of the gauge invariance underlying the four dimensional compactified theory was introduced: The SGTs and the nonstandard gauge transformations (NSGTs). The latter were defined in terms of the KK excited modes of the gauge parameters that propagate in the bulk.…”

Section: Introductionmentioning

confidence: 99%

“…[6,13,15], these theories must be consistently quantized since the excited KK states contribute to standard Green's functions (SGF) at the one-loop level, that is, to Green's functions with only zero modes in external legs. A remarkable result reported in these references was the proof that contributions from the extra dimension to the SGF are renormalizable at one-loop level.…”

Section: Introductionmentioning

confidence: 99%

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Yang-Mills theories with an arbitrary number of compactified extra dimensions

et al. 2014

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The well-known Yang-Mills theory with one S 1 /Z2 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 base manifold under consideration contains n spatial extra dimensions defined by n copies of the orbifold S 1 /Z2. 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 a 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Yang-Mills theories with an arbitrary number of compactified extra dimensions

et al. 2014

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One-loop helicity amplitudes for top quark pair production in Randall-Sundrum model

Zhu

Dai

et al. 2011

J. High Energ. Phys.

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In this paper, we show how to calculate analytically the one-loop helicity amplitudes for the process qq → tt induced by KK gluon, using the spinor helicity formalism. A minimal set of Feynman rules which are uniquely fixed by gauge invariance and the color representation of the KK gluon are derived and used in the calculation. Our results can be applied to a variety of models containing a massive color octet vector boson. Warped extra-dimension model proposed by Randall and Sundrum (RS) [1] is a popular model that can solve the hierarchy problem. When allowing the Standard Model (SM) field propagating in the extra dimension, the RS model provides many novel points of view for some problems, like hierarchy of fermion masses and the unification of gauge couplings. The first signal of the RS model may be the observation of KK gluon (first Kaluza-Klein excitation mode of SM gluon) as a resonant in the tt final state at the early LHC, simply because its production rate is large compare to the other KK particles [2]. Detailed study of total cross sections and the invariant mass distribution of tt production induced by KK gluon have been made in the literatures [2-8] at the Leading Order (LO) in QCD.Recently CDF collaboration reported a large top quark forward-backward asymmetry with integrated luminosity 5.3 fb −1 [9]. This 3.4 σ discrepancy with SM predictions [10,11] has motivated a lot of work in the theory community, cf. ref.[12] and references therein.One attractive explanation of the large anomalous forward-backward asymmetry is provided by the RS model. Within the RS framework, a realistic model has been constructed that has been shown to be able to explain the forward-backward asymmetry of top quark sector as well as bottom quark sector simultaneously [13]. This is realized by a careful choice of fermion localizations, so that there is a relatively light KK gluon with mass around 1.5TeV and large parity violation in the first generation of quark couplings. The authors of Ref. [13] have shown at the LO in QCD that the model they constructed can explain well the total asymmetry observed at the Tevatron by CDF [9], as well as the asymmetry at large top quark pair invariant mass region and large rapidity region [9].It's well known that LO prediction suffers from large scale uncertainty, and therefore is not appropriate for precision measurement, e.g., extraction of couplings between quark and KK gluon. Furthermore, tt production is known to have large K-factor at the Next-to-Leading Order (NLO) in QCD [14][15][16]. The large K-factor is partially taken into account in the Ref.[13] using a formalism proposed in [17]. Aiming at the precise prediction for the KK gluon mediated tt production, Ref.[18] calculated the interference of SM box diagrams and tree diagram of tt production induced by KK gluon. Furthermore, Ref.[19] consider the effects of KK gluon on tt production by gluon-gluon fusion. It was found that the contributions, although non-zero, are highly suppressed. For this reason, we focus our

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The Standard Model with one universal extra dimension

et al. 2013

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Effects of universal extra dimensions on Standard Model observables first arise at the oneloop level. The quantization of this class of theories is therefore essential in order to perform predictions. A comprehensive study of the SUC(3)×SUL(2)×UY(1) Standard Model defined in a space-time manifold with one universal extra dimension, compactified on the oribifold S 1 /Z2, is presented. The fact that the four-dimensional Kaluza-Klein theory is subject to two types of gauge transformations is stressed and its quantization under the basis of the BRST symmetry discussed. A SUC(3) × SUL(2) × UY(1)-covariant gauge-fixing procedure for the Kaluza-Klein excitations is introduced. The connection between gauge and mass eigenstate fields is established in an exact way. An exhaustive list of the explicit expressions for all physical couplings induced by the Yang-Mills, Currents, Higgs, and Yukawa sectors is presented. The one-loop renormalizability of the standard Green's functions, which implies that the Standard Model observables do not depend on a cutoff scale, is stressed. subject the KK excitations A (n)a µ [2]. In that paper, we also showed that the SM, or light, Green's functions (Green's functions whose external legs are all zero KK modes or, equivalently, SM fields) are renormalizable at the one-loop level. More recently, this fact was proven explicitly through the direct integration of the heavy KK excitations [3]. The cutoff insensitivity of light Green's functions at the one-loop level, which seems to be exclusive of UED models with one extra dimension, has already been pointed out in previous studies on some electroweak observables [4,5] and verified very recently [6] for the case of one-loop radiative corrections to the trilinear W W γ and W W Z vertices. One peculiarity of UED models is that the tree-level couplings among KK excited modes and zero modes involves strictly two or more KK excitations. This means that the electroweak observables are insensitive to virtual effects of KK excitations at tree level, although they can receive contributions at the one-loop level or higher orders. The main goal of this work is to present a comprehensive study of the vertices involved in the theory, for we think that this important predictive power of UED theories in five dimensions deserves especial attention. This theory would serve as a basis to estimate in an unambiguous way the impact of extra dimensions on electroweak observables. We will present a detailed study of the tree-level structure of the four-dimensional KK theory. Our results comprise a complete list of the Lagrangians characterizing the vertices generated by the compactified theory, including the definition of a gauge-fixing procedure for both the SGT and the NSGT.The rest of the paper has been organized as follows. In Sec. 2, the structure of the five-dimensional SM and the compactification of the extra dimension, including a gauge-fixing procedure, are discussed, whereas, in Sec. 3, a detailed list of the physical vertices of the theory is presented. In ...

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Gauge invariance and quantization of Yang-Mills theories in extra dimensions

Cited by 34 publications

References 70 publications

Yang-Mills theories with an arbitrary number of compactified extra dimensions

Yang-Mills theories with an arbitrary number of compactified extra dimensions

One-loop helicity amplitudes for top quark pair production in Randall-Sundrum model

The Standard Model with one universal extra dimension

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