arXiv subjects

Saurabh K. Shukla

Publications and source records attributed to Saurabh K. Shukla.

9 recordsLinked to original sources

arXiv2026

The topological non-Abelian string in the extended ${\rm SU}(N) \otimes {\rm U}(1)$ gauge sector

We study the topological non-Abelian string and its classical stability in models with two Higgs fields to achieve the symmetry breaking of ${\rm SU}(N) \otimes {\rm U}(1)_X\to {\rm SU}(N-1) \otimes {\rm U}(1)_{X^\prime}$. The topological origin is due to the global $\widetilde {\rm U}(1)$ symmetry and its breaking in the scalar potential. The most generic winding configurations of arbitrary integers of $(n_1\,, n_2)$ are considered. The stability of the topological string is analyzed based on the time-dependent perturbations to the string background and numerical solutions to the coupled Helmholtz equations of the perturbed Fourier modes. We present the constraints on the stable regions for the $(n_1\,, 0)$ configuration (or equivalently the $(0\,, n_2)$ configuration). For the general winding configurations of $(n_1\neq 0\,, n_2\neq 0)$, we point out the stable regions only exist in the semilocal limit of the large mixing angle of $\vartheta_N\to \fracπ{2}$.

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arXiv2026

Revisiting ${\rm SU}(5)$ Yukawa Sectors Through Quantum Corrections

This article revisits the validity of tree-level statements regarding the Yukawa sector of various minimal-renormalisable $SU(5)$ frameworks at the loop level. It is well-known that an $SU(5)$ model with only the $45_{\mathrm{H}}$ dimensional irreducible representation~(irrep) contributing to the Yukawa sector is highly incompatible in yielding the low-energy observables. However, this study shows that when one-loop corrections from heavy degrees of freedom are included in the various Yukawa vertices, the model can reproduce the charged fermion mass spectrum and mixing angles within the assumed experimental uncertainty. The fitted Yukawa couplings remain within the perturbative range. The scenario also necessitates mass splitting among various scalars of $45_{\mathrm{H}}$ dimensional irrep, with some of the scalars' mass deviating significantly from the matching scale $(M_{GUT})$, collectively providing substantial threshold corrections. The effect of the lightest scalar on the RGE evolution of the SM parameters has also been considered. It is shown that this scenario reproduces the SM spectrum at low energy. As an extension, the minimal $SU(5)$ model with only the $45_{\mathrm{H}}$ irrep is augmented with the $15_{\mathrm{H}}$-dimensional irrep, which also successfully reproduces the observed charged and neutral fermion mass spectra. Finally, the study considers an alternative $SU(5)$ model incorporating both $5_{\mathrm{H}}$ and $15_{\mathrm{H}}$ irreps, which also yields the desired fermion mass spectra and mixing angles. This work demonstrates the viability of a minimal $SU(5)$ Yukawa sector in different setups when quantum corrections are considered.

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arXiv2026

Small-instanton effects in an atlas of KSVZ axion models

We investigate small-instanton contributions to the axion potential across a range of KSVZ models containing vector-like quarks~(VQs), using naive dimensional analysis. We consider scenarios containing a single VQ, multiple identical copies, and sets of distinct VQs, requiring in each case that the gauge couplings remain perturbative up to the Planck scale under the two-loop gauge running. The associated fermion zero-mode content varies between these cases, requiring different combinations of mass insertions and scalar--Yukawa contractions for its saturation. Increasing the copies of VQs can render the instanton-size integral dominated by instantons of the smallest size, corresponding to the scale near the ultraviolet~(UV) cut-off. The resulting contribution then becomes sensitive to the UV completion and the induced potential can compete with, or dominate over, the ordinary QCD contribution. Assuming that the QCD and small-instanton potentials are aligned, we determine the resulting axion-mass shift and its consequences for the axion--photon coupling. When the small-instanton induced susceptibility becomes comparable to or larger than the QCD susceptibility, the physical axion mass of $m_a$ is enhanced at fixed decay constant~$f_a$, while the axion-photon of $g_{aγγ}$ coupling remains controlled by $f_a$ and the anomaly ratio of $E/N$. The standard QCD relation among $m_a$, $f_a$ and $g_{aγγ}$ is consequently modified, opening new regions of the $(m_a,g_{aγγ})$ plane for axion searches.

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arXiv2026

Scalar-induced Neutrinoless Double Beta Decay in $SU(5)$

We discuss the role of heavy scalar fields in mediating neutrinoless double beta decay $(0νββ)$ within the $SU(5)$ Grand Unified Theory framework, extended suitably to include neutrino mass. In such a minimal realistic $SU(5)$ setup for fermion masses, the scalar contributions to $0νββ$ are extremely suppressed as a consequence of the proton decay bound. We circumvent this problem by imposing a discrete ${\cal Z}_3$ symmetry. However, the scalar contributions to $0νββ$ remain suppressed in this $SU(5) \times {\cal Z}_3$ model due to the neutrino mass constraint. We find that the $0νββ$ contribution can be enhanced by extending the scalar sector with an additional $\mathbf{15}$-dimensional scalar representation with suitable ${\cal Z}_3$ charge. Such an extension not only yields realistic fermion mass spectra but also leads to experimentally testable predictions in upcoming ton-scale $0νββ$ searches, which can be used as a sensitive probe of the new scalars across a broad range, from LHC-accessible scales up to $\sim 10^{10}\,\text{GeV}$.

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arXiv2025

Unravelling the Scalar Sector of Grand Unification: Phenomenology & Implications

Grand Unified Theories (GUTs) based on groups like $SO(10)$ and $SU(5)$ unify Standard Model (SM) fermions into irreducible representations (irreps), and predict additional scalar fields beyond the SM Higgs. In $SO(10)$ GUTs, the scalar fields can arise from irreps contributing to the Yukawa sector at the renormalisable level, such as $10_{\mathrm{H}}$, $120_{\mathrm{H}}$, and $\overline{126}_{\mathrm{H}}$, or from $16_{\mathrm{H}}$ in non-renormalisable interactions. The direct implications of these scalars include the violation of baryon and lepton number, enabling processes such as nucleon decays, neutron-antineutron oscillation, and potentially accounting for the observed baryon asymmetry of the universe. We systematically analyse their couplings to SM fermions, identifying diquark and leptoquark interactions vertices involving all scalars residing in $10_{\mathrm{H}}$, $120_{\mathrm{H}}$, $\overline{126}_{\mathrm{H}}$, and $16_{\mathrm{H}}$ and comprehensively assess their contributions to nucleon decay, neutron-antineutron oscillation, quark flavour violation, and baryogenesis. Constraints on the masses of these scalars, derived from experimental bounds on the aforementioned processes, are also estimated. Conventional GUTs rely on multiple scalar irreps to avoid unrealistic fermion mass relations; for example, minimal $SU(5)$ with $5_{\mathrm{H}}$ predicts degenerate down-quark and charged-lepton masses. We demonstrate that quantum corrections from heavy scalars in a minimally extended $SU(5)$ model can lift this degeneracy, thereby reducing the arbitrariness in the scalar sector, which has been called as indirect impact. This thesis provides a comprehensive examination of the scalar sector's role in GUTs, establishing connections between UV-complete models and observable phenomena.

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arXiv2025

Constraining scalars of $16_H$ through proton decays in non-renormalisable $SO(10)$ models

Non-renormalisable versions of $SO(10)$\, based on irreducible representations with lesser degrees of freedom, are free of running into the catastrophe of non-perturbativity of standard model gauge couplings in contrast to the renormalisable versions having tensors with many degrees of freedom. $16_H$ is the smallest representation, participates in Yukawa Lagrangian at the non-renormalisable level, contributing to the charged and neutral fermion masses, and has six distinct scalars with different $B-L$ charges. We computed the leptoquark and diquark couplings of different pairs of scalars stemming from all possible decomposition of the term resulting from the coupling of $16_{H}$ with the ${\mathbf{16}}$ dimensional fermion multiplet of $SO(10)$,\, i.e. $\frac{\mathbf{16}\,{\mathbf{16}}\,16_{H}\,16_{H}}Λ$. Computing the tree and loop level contribution of different pairs to the effective dimension six, $B-L$ conserving operators, it turns out only three pairs, viz $σ\big(1,1,0\big)- T\big(3,1,\frac{1}{3}\big)$, and $H\big(1,2,-\frac{1}{2}\big)-Δ\big(3,2,\frac{1}{6}\big)$, and $H-T$ can induce proton decay at tree level. Assuming that the Yukawa couplings of the $16_{H}$ are comparable to those of the $\overline{126}_{H}$ of a realistic $SO(10)$ model and setting the cutoff scale to the Planck scale typically constrains the $B-L$ breaking scale to be $4\sim 5$ orders of magnitude less than the cutoff scale $(Λ)$. Moreover, analysing the branching pattern of the leading two-body decay modes of the proton, we observed a preference for the proton to decay into second-generation mesons due to the hierarchical nature of Yukawa couplings. In a realistic $SO(10)$\, scenario, we find that $M_T >10^{8}$ TeV, while $M_Δ$ could be as light as a few TeV$s$.

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arXiv2024

Quantum corrections and the minimal Yukawa sector of $SU(5)$

It is well-known that the $SU(5)$ grand unified theory, with the standard model quarks and leptons unified in $\overline{5}$ and $10$ and the electroweak Higgs doublet residing in $5$ dimensional representations, leads to relation, $Y_d=Y_e^T$, between the Yukawa couplings of the down-type quarks and the charged leptons. We show that this degeneracy can be lifted in a phenomenologically viable way when quantum corrections to the tree-level matching conditions are taken into account in the presence of one or more copies of gauge singlet fermions. The 1-loop threshold corrections arising from heavy leptoquark scalar and vector bosons, already present in the minimal model, and heavy singlet fermions can lead to realistic Yukawa couplings provided their masses differ by at least two orders of magnitude. The latter can also lead to a realistic light neutrino mass spectrum through the type I seesaw mechanism if the colour partner of the Higgs stays close to the Planck scale. Most importantly, our findings demonstrate the viability of the simplest Yukawa sector when quantum corrections are considered and sizeable threshold effects are present.

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arXiv2023

Spectrum of colour sextet scalars in realistic SO(10) GUT

Incorporation of the standard model Yukawa interactions in a grand unified theory (GUT) often predicts varieties of new scalars that couple to the fermions and lead to some novel observational effects. We assess such a possibility for the colour sextet diquark scalars within the realistic renormalizable models based on $SO(10)$ GUT. The spectrum consists of five sextets: $Σ\sim (6,1,-\frac{2}{3})$, $S \sim (6,1,\frac{1}{3})$, $\overline{S}\sim(\overline{6},1,-\frac{1}{3})$, ${\cal S}\sim(6,1,\frac{4}{3})$ and $\mathbb{S}\sim(\overline{6},3,-\frac{1}{3})$. Computing explicitly their couplings with the quarks, we evaluate their contributions to the neutral meson-antimeson mixing and baryon number-violating processes like neutron-antineutron oscillation. The latter arises because of a $B-L$ violating trilinear coupling between the sextets which also contributes to some of the quartic couplings and perturbativity of the same leads to strong limits on the sextet masses. Using the values of the $B-L$ breaking scale and Yukawa couplings permitted in the realistic models, we derive constraints on the masses of these scalars. It is found that $Σ$ along with any of the remaining sextets cannot be lighter than the $B-L$ breaking scale, simultaneously. In the realm of realistic models, this implies no observable $n$-$\bar{n}$ oscillation in near future experiments. We also point out a possibility in which sub-GUT scale $Σ$ and a pair of $S$, allowed by the other constraints, can viably produce the observed baryon asymmetry of the universe.

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arXiv2022

Anatomy of scalar mediated proton decays in $SO(10)$ models

Realistic models based on the renormalizable grand unified theories have varieties of scalars, many of which are capable of mediating baryon ($B$) and lepton ($L$) number non-conserving processes. We identify all such scalar fields residing in ${\bf 10}$, $\overline{\bf 126}$ and ${\bf 120}$ dimensional irreps of $SO(10)$ which can induce baryon and lepton number violating interactions through the leading order $d=6$ and $d=7$ operators. Explicitly computing their couplings with the standard model fermions, we derive the effective operators including the possibility of mixing between the scalars stemming from a given representation. We find that such interactions at $d=6$ are mediated by only three sets of scalars: $T(3,1,-1/3)$, ${\cal T} (3,1,-4/3)$ and $\mathbb{T}(3,3,-1/3)$ and their conjugates. In the models with ${\bf 10}$ and $\overline{\bf 126}$, only the first has appropriate couplings to mediate the proton decay. While ${\cal T}$ and $\mathbb{T}$ can induce baryon number violating interactions when ${\bf 120}$ is present, ${\cal T}$ does not contribute to the proton decay at tree level because of its flavour antisymmetric coupling. Three additional colour triplets and their conjugates can mediate nucleon decay via $d=7$ operators which violate also the $B-L$. We give general expressions for partial widths of proton in terms of the fundamental Yukawa couplings and use these results to explicitly compute the proton lifetime and branching ratios for the minimal non-supersymmetric $SO(10)$ model based on ${\bf 10}$ and $\overline{\bf 126}$ Higgs. We find that the proton preferably decays into $\overlineν\, K^+$ or $μ^+\, K^0$ and list several distinct features of scalar mediated proton decay. If the latter dominates over the gauge mediated contributions, the proton decay spectrum provides a direct probe to the flavour structure of the underlying grand unified theory.

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