arXiv subjects

Shaikh Saad

Publications and source records attributed to Shaikh Saad.

At least 19 recordsLinked to original sources

arXiv2026

Large Language Model-Assisted Framework for BSM Model Building

Recent advances in artificial intelligence (AI), particularly large language models (LLMs), have created new opportunities for natural-language interaction with scientific software, but reliable theoretical model building still requires deterministic symbolic calculations. We present \texttt{bsm_agent}, an open-source symbolic framework for beyond the Standard Model (BSM) model building that combines a deterministic physics backend with an LLM chat interface. Starting from the SM field content and a user-specified set of additional scalars and/or fermions, the package constructs renormalizable Lagrangian, performs gauge-anomaly checks, expands operators into component fields, and derives electroweak symmetry breaking stationary conditions and tree-level mass matrices. The key novelty of the framework is that all of these tasks are performed automatically once the user specifies the quantum numbers of the new fields through a natural-language interface, eliminating the need for manual model construction. The symbolic calculations are performed entirely by the Python backend to ensure the correctness and reproducibility of the physics results; the LLM is used only as an orchestration layer that interprets natural-language requests, manages confirmation steps for ambiguous inputs, triggers backend tools, and formats report-ready summaries. The package supports three provider classes: local Ollama inference, remote self-hosted model servers accessed through the implemented remote provider interface, and commercial hosted APIs via OpenAI and Anthropic. This separation between conversational control and deterministic computation preserves reproducibility while making interactive BSM model construction substantially more convenient.

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arXiv2026

Weak Triplet Models of Neutrino Magnetic Moments

Experimental limits on neutrino magnetic moments remain several orders of magnitude above the predictions of the Standard Model; therefore, any future detection would provide unambiguous evidence for new physics. In models with Dirac neutrinos, however, mechanisms that enhance the magnetic moment typically generate excessively large neutrino masses. Recently, it has been argued that in frameworks where neutrinos mix with weak-triplet Dirac fermions, the magnetic moment can be decoupled from the neutrino mass. In this work, we revisit this possibility and show that sizable enhancements remain highly nontrivial to realize naturally. We demonstrate that, although the minimal realization allows the magnetic moment to be decoupled from the neutrino mass, obtaining an observable enhancement requires a delicate adjustment of the model parameters. Moreover, in extended scenarios, the decoupling no longer persists: the magnetic moment and neutrino mass become intrinsically linked, such that attempts to enhance the former inevitably induce large contributions to the latter.

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arXiv2026

Towards Precision Neutrino Fits in GUTs: Relevance of One-Loop Finite Corrections

In this work, we perform a dedicated analysis of fermion mass fits in the minimal $SO(10)$ grand unified theory (GUT), going beyond the tree-level approximation by incorporating one-loop finite corrections to the neutrino mass matrix. We show that parameter regions that successfully reproduce all fermion masses and mixings at tree level can lead to significant deviations in neutrino masses and leptonic mixing parameters once the radiative corrections are included. These results expose a limitation of conventional tree-level fitting procedures and highlight the sensitivity of neutrino observables to loop effects. Since in the minimal $SO(10)$ GUT the same set of Yukawa parameters simultaneously governs quark masses, charged lepton masses, and neutrino properties, these radiative corrections propagate across all fermion sectors, reshaping the viable parameter space in a highly non-trivial and correlated manner. We find that the largest corrections to the masses and mixing angles are of order $\mathcal{O}(30\%)$-$\mathcal{O}(40\%)$, therefore, cannot be neglected. In light of the current precision of neutrino oscillation measurements, and the expected improvements from ongoing and future experiments, we demonstrate that the inclusion of one-loop effects is essential for a consistent and reliable exploration of the parameter space, with important implications for the predictivity of $SO(10)$ GUTs.

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arXiv2026

Reality-constrained Minimal Yukawa Structure in SO(10) GUT

We investigate the minimal Yukawa sector of grand unified theories based on $\mathrm{SO}(10)$ symmetry, consisting of a Higgs structure with representations $\mathbf{10}_{\mathbb{R}}\oplus \mathbf{120}_{\mathbb{R}}\oplus\mathbf{126}$. In this framework, where $\mathbf{10}_\mathbb{R}$ and $\mathbf{120}_{\mathbb{R}}$ are real scalars, we derive the associated $\mathrm{SO}(10)$ reality conditions for their weak-doublet constituents -- both by explicit computation and an analytic reframing into a Pati-Salam-like description -- to revisit previously reported fermion mass relations. Our analysis revises these earlier results, in particular by introducing a relative sign difference between the reality constraints on the two weak doublets in $\mathbf{120}_{\mathbb{R}}$, yielding a new parameter (a magnitude) in the fermion mass relations. Our formalism is fully general and provides a systematic framework for deriving Clebsch-Gordan coefficients and implementing reality constraints for arbitrary parent-daughter representation pairs of $\mathrm{SO}(10)$ and its Pati-Salam subgroup. Incorporating these corrections, we perform an extensive numerical scan of the parameter space and find that the model successfully reproduces SM fermion masses and mixings, including recent precision measurements of solar oscillation parameters by JUNO. It accommodates both octants of $\theta_{23}$ while mildly disfavoring $\delta_\mathrm{PMNS}\sim (140^\circ,220^\circ)$. The model predicts a strongly hierarchical right-handed neutrino spectrum $(10^{5},10^{12},10^{15})$ GeV and a neutrinoless double beta decay parameter $m_{\beta\beta}\sim 3$-$4$ meV, just below future experimental sensitivity. Proton decay is dominated by $p\to\pi^+\overline{\nu}$ and $p\to\pi^0 e^+$, making these channels testable in upcoming experiments.

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arXiv2025

TeV Scale Quark-Lepton Unification

We propose a quark-lepton symmetric Pati-Salam (PS) model based on the gauge group $SU(2)_L \times SU(2)_R \times SU(4)_C$ with an $E_6$-inspired particle spectrum which naturally accommodates a multi-TeV leptoquark gauge boson $X_\mu(3,1,\frac{2}{3})$. A softly broken $Z_2$ symmetry plays a crucial role in realizing this scenario, under which the Standard Model (SM) fermions are even, while new vector-like fermions present in the model are odd. A notable feature of this model is that the PS gauge boson $X_\mu$ itself is $Z_2$-odd, causing it to couple exclusively between SM fermions and the vector-like fermions, except in the right-handed down-quark sector, where mixing is induced by the soft breaking of $Z_2$. This structure leads to helicity suppression of tree-level meson decays mediated by $X_\mu$, with helicity-unsuppressed contributions arising only via one-loop diagrams. We show that $X_\mu$ can be as light as 1.1 TeV while being compatible with all flavor-violating constraints. However, mass relations among the $(W'^\pm_\mu, Z'_\mu, X_\mu)$ gauge bosons push the $X_\mu$ mass limit up to 4.3 TeV from the stringent LHC bounds on the $Z^\prime$ mass. This comparatively low PS-breaking scale opens up promising collider opportunities for probing the leptoquark gauge boson, as well as the distinctive signature of vector-like down-type quarks carrying an unusual baryon number of $2/3$. The model can be further tested via lepton flavor-violating processes induced by the leptoquark gauge boson, such as $\mu \to e \gamma$, $\mu \to e e e$, and $\mu$-$e$ conversion in nuclei. Neutrino masses arise in the model through dimension-seven operators at tree-level, as well as from dimension-five operators via one-loop diagrams.

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arXiv2025

Neutrino masses, $\delta_\mathrm{PMNS}$, and $m_{\beta\beta}$ in SO(10)

We explore the leptonic sector of a recently proposed supersymmetric SO(10) model with supersymmetry breaking in the 3-10 TeV range. A new ingredient in this work is the requirement that the observed baryon asymmetry is explained via non-thermal leptogenesis, which can be realized in a large class of supersymmetric hybrid inflation models including SO(10). We provide estimates for the masses of the three Standard Model neutrinos (with the lightest mass $m_1\approx 5$ meV) as well as the three right-handed neutrinos ($M_1\approx 10^9$ GeV and $M_{2,3}\approx 10^{13}$ GeV). The best fit estimate for the leptonic CP violating parameter $\delta_\mathrm{PMNS}\approx 235^\circ$, and the value of the neutrinoless double beta decay mass parameter $m_{\beta\beta}\approx 0.18$ meV. A numerical analysis broadens the predicted range for $\delta_\mathrm{PMNS}$ ($100^\circ$-$300^\circ$), but leaves largely intact the predictions for the six (light and heavy) neutrino masses and $m_{\beta \beta}$. Our statistical analysis, which yields the likelihood-predicted ranges of the observables, is fully consistent with JUNO's newly released first measurement of reactor neutrino oscillations in the $\Delta m^2_{12}$-$\sin^2\theta_{12}$ plane, with JUNO improving the precision by a factor of 1.6 relative to the combination of all previous measurements. The implementation of successful non-thermal leptogenesis allows us to provide estimates for the inflaton mass ($m_\chi \approx 7\times 10^{9}$ GeV) and the reheating temperature ($T_\mathrm{RH}\approx 4\times 10^6$ GeV).

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arXiv2025

Neutrino Mass Induced $n$-$\overline{n}$ Oscillation

The Georgi-Glashow model is the simplest possible attempt at grand unification. However, due to its particle content, the model preserves a global $U(1)_{B-L}$ symmetry, where $B$ and $L$ are baryon and lepton numbers, respectively. It thus leaves neutrinos massless just as the Standard Model does. The extensions of the Georgi-Glashow model that break lepton number by two units, i.e., scenarios with $|\Delta L|=2$ operator(s), naturally generate potentially viable Majorana neutrino masses. Since the dynamics that yields $|\Delta L| = 2$ interactions unavoidably induces $|\Delta B| = 2$ transitions via $B\!-\!L$ breaking, these extensions consequentially lead to intriguing processes such as neutron--antineutron ($n$--$\overline{n}$) oscillation. We investigate this intrinsic connection between neutrino mass generation and $n$--$\overline{n}$ oscillation within a number of representative extensions of the Georgi-Glashow model that can yield realistic neutrino masses and mixing parameters. These extensions include the tree-level seesaw mechanism realizations of the Type I, II, and III varieties, as well as the one-loop and two-loop radiative neutrino mass models.

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arXiv2025

Updated Running Quark and Lepton Parameters at Various Scales

In the light of the recent Particle Data Group (PDG) release, we revisit the running quark and lepton Yukawa couplings, together with the quark mixing parameters, across a range of energy scales. The 2024 PDG determinations of low-energy fermion masses feature significantly smaller uncertainties, resulting from a reduced estimate of systematic errors compared to the more conservative treatment in the 2022 analysis. To assess the impact of these changes, we present running parameters obtained using both the 2022 and 2024 datasets, within the frameworks of the Standard Model (SM) and its minimal supersymmetric extension (MSSM). The evolved values, along with their associated $1\sigma$ uncertainties, are given within the SM framework at benchmark scales of $M_Z$ and $10^3$, $3\cdot 10^3$, $10^4$, $10^5$, $10^7$, $10^9$, $10^{12}$, and $10^{16}$ GeV. Within the MSSM, we additionally provide GUT-scale results for different choices of $\tan\beta$, assuming supersymmetry breaking scales of 3 and 10 TeV, including an approximate way for taking supersymmetric loop threshold corrections into account. We furthermore discuss implications of the updated results for constructing and testing theories beyond the SM.

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arXiv2025

A new perspective on the CMSSM: Yukawa Unification, DM and the SUSY scale

What does third family ($t$-$b$-$\tau$) Yukawa unification, a typical prediction from embedding the Standard Model (SM) fermions in 16-plets of a $\mathrm{SO}(10)$ GUT, imply for the scale of the supersymmetric (SUSY) partners? Which neutralino dark matter (DM) candidate can be realized, and how large is the DM relic density? In this work, we address these questions in a simplified SUSY-breaking framework: the Constrained Minimal Supersymmetric Standard Model (CMSSM). To this end, we recast the parameter space of the CMSSM in a way that for all parameter points the SM-like Higgs mass is correctly reproduced. Considering fixed $\tan\beta$ and $\mathrm{sgn}(\mu)$, for every point in the $(x:=\frac{M_{1/2}}{m_0},y:=\frac{A_0}{m_0})$ parameter plane ranges for all observables are predicted. This provides a new perspective on where in parameter space different types of DM are realized, and which value of the SUSY scale is required in order to explain the observed mass of the SM Higgs boson. In our analysis we consider and compare two strategies: grid scans over the $(x,y,\tan\beta)$ parameter region and MCMC sampling. We find both techniques yield similar results. For $t$-$b$-$\tau$ unification within $5\,\%$ or $10\,\%$, we find $\mu<0$, the SUSY spectrum showing a characteristic pattern, and the SUSY scale around $\mathcal{O}(10)\,\mathrm{TeV}$. The extra MSSM Higgses are the lowest lying new states at $\sim 2\div 3\,\mathrm{TeV}$ (with discovery potential at the HL-LHC), the $\mathcal{O}(10)\,\mathrm{TeV}$ stops and gluino are in reach of a possible FCC-hh, while bino DM has a mass above $2.5\,\mathrm{TeV}$, is overabundant, and effectively unobservable in planned direct and indirect detection experiments. The DM relic density requires a dilution factor of $10<\mathcal{D}<1000$, implying non-standard cosmology that could leave its imprints in the stochastic gravitational wave background.

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arXiv2025

Beyond Neutrino Mass: Observable $n$-$\overline{n}$ Oscillations in UV Complete Seesaw Models

Next-generation experiments, such as the Deep Underground Neutrino Experiment and the European Spallation Source, are set to improve sensitivity to neutron-antineutron oscillation, a direct probe of $\Delta B = 2$ baryon number violation, with particularly significant gains expected at the latter. The discovery of such a rare $\Delta B = 2$ process would indicate physics beyond the Standard Model and could point to specific unified theories that allow observable $n-\overline{n}$ transitions. We accordingly examine $n-\overline{n}$ oscillations within a unified framework that accounts for charged fermion masses and generates viable neutrino masses via the seesaw mechanism. More specifically, we show that $n-\overline{n}$ oscillations can arise from two specific topologies within two distinct $SU(5)$ scenarios. One topology requires a presence of two color-sextet scalars in the Type II seesaw framework, whereas the other involves a scalar sextet and a color-octet fermion in the Type III seesaw framework. While the former topology can be realized in the $SO(10)$/Pati-Salam frameworks, the latter finds a natural embedding in $SU(5)$, which constitutes one of the key novelties of our work. Remarkably enough, the same dynamics responsible for fermion masses also induces baryon number violation, thus linking $n-\overline{n}$ oscillations to the flavor structure of the theory. We show that, given a TeV-scale mass for one of the colored states, upcoming searches for such $\Delta B = 2$ processes can probe for a presence of the other colored states with masses up to $10^{11}\,\mathrm{GeV}$, well beyond the reach of colliders. This positions $n-\overline{n}$ oscillations as a rare low-energy portal to grand unification and ultra-heavy new physics.

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arXiv2025

One Phase to Rule Them All: Spontaneous CP Violation and Leptogenesis in SO(10)

We present a renormalizable $SO(10)$ grand unified theory with a minimal Yukawa sector consisting of a $126_H$, a real $10_H$ and a real $120_H$, where $CP$ violation has a spontaneous origin. We show that the Yukawa sector in this setup, which consists of only 19 real parameters, is capable of simultaneously reproducing the observed fermion masses and mixings, including neutrino oscillations, as well as the baryon asymmetry of the Universe via thermal leptogenesis. In this framework, $CP$ is spontaneously broken when a $CP$-odd Higgs field $54_H$, used for GUT symmetry breaking, acquires a non-zero vacuum expectation value. All $CP$-violating phases, including the Dirac phases $\delta_\mathrm{CKM}$ and $\delta_\mathrm{PMNS}$, the neutrino Majorana phases, as well as those responsible for leptogenesis, arise solely from a single complex parameter in the Higgs potential. The proposed minimal setup predicts a normal ordering of neutrino masses, with the atmospheric mixing angle $\theta_{23}$ preferred in the first octant and the leptonic $\delta_{\mathrm{PMNS}}$ lying in the range $(-38^\circ,\, +31^\circ)$. The fermion fits in our scenario further yield a strongly hierarchical mass spectrum for the three right-handed neutrinos, $(M_1,\,M_2,\,M_3) \sim \left(10^{5},\, 10^{12},\, 5\cdot 10^{14}\right)~\mathrm{GeV}$, which is shown to result in successful $N_2$-dominated leptogenesis, consistent with current cosmological data.

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arXiv2025

Fermion masses and mixings in supersymmetric SO(10) with third-generation quasi-Yukawa unification

We discuss the charged and neutral fermion masses and mixings in a supersymmetric SO(10) model with a minimal Higgs sector consisting of the multiplets $10_H$, $45_H$, and $16_H + \overline{16}_H$. In addition to the renormalizable Yukawa couplings involving the Higgs 10-plet, we include non-renormalizable Yukawa couplings, which are important for reproducing with good accuracy the observed masses and mixings in the quark and lepton sectors. We identify a preferred solution which is compatible with third family quasi-Yukawa unification, namely $y_t \approx y_b \approx 0.73 y_{\tau}$ at the unification scale, with the MSSM parameter $\tan\beta \sim 58$. Acceptable solutions with lower $\tan\beta$ values are also realized in our framework, and we provide an example with $\tan \beta =10$. Based on our fits, the masses for the three right-handed neutrinos turn out to be $\left(M_1,M_2,M_3\right)\sim \left(10^9, 8\cdot 10^{12}, 9\cdot 10^{12}\right) \mathrm{GeV}$. We briefly discuss the metastable and quasistable string scenarios that can be realized in this class of supersymmetric SO(10) models.

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arXiv2025

Non-Renormalizable SU(5) GUTs: Leptoquark-Induced Neutrino Masses

We revisit the doublet-triplet splitting problem within the $SU(5)$ gauge group framework to advocate a viable regime with the light scalar leptoquark of the doublet-triplet splitting notoriety that is compatible with the current experimental bounds on partial proton decay lifetimes. We explicitly demonstrate, through a consistent use of higher-dimensional operators, how to implement suppression of baryon number violating interactions of the aforementioned color triplet. Our study thus offers an alternative approach to the doublet-triplet splitting problem as it removes a need for an extreme mass hierarchy between the partners residing in the same representation. We furthermore pursue two different extensions of two distinct symmetry breaking scenarios of $SU(5)$, one with a $24$-dimensional representation and the other one with a $75$-dimensional representation, to produce comparative study of novel consequences for the gauge coupling unification and the one-loop level neutrino mass generation. Our results point towards qualitatively novel $SU(5)$ scenarios, where the light scalar leptoquarks, responsible for the neutrino mass generation, might be even accessible at colliders and thus serve as an accelerator accessible portal to the high-scale physics.

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arXiv2025

Metastable Cosmic Strings and Gravitational Waves from Flavour Symmetry Breaking

Metastable cosmic strings (MSCSs) are among the best-fitting explanations of the 2023 pulsar timing array (PTA) signal for gravitational waves at nanohertz frequencies. We propose the novel possibility that a network of MSCSs generating this signal originates from the multi-step spontaneous breaking of a gauged flavour symmetry. As a specific example, we construct a model of $SU(2)$ flavour symmetry in the context of $SU(5)$ grand unification, where the $SU(2)$ acts exclusively on the first two generations of the matter 10-plet, such that it is ``right for leptons'' and allows for large lepton mixing. The model explains the mass hierarchies of the Standard Model fermions, and predicts the string scale of the MSCSs in a range compatible with the 2023 PTA signal. Cosmic inflation is associated with the latter step of (two-step) family symmetry breaking, and the phase transition ending inflation generates the cosmic string network.

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arXiv2024

Ultraviolet Completion of a Two-loop Neutrino Mass Model

The Zee-Babu model is an economical framework for neutrino mass generation as two-loop quantum corrections. In this work, we present a UV completion of this model by embedding it into an $SU(5)$ unified framework. Interestingly, we find that loop-induced contributions to neutrino masses arising from colored scalars are just as important as those from color-neutral ones. These new states, which are required from gauge coupling unification and neutrino oscillation data to have masses below $\mathcal{O}(10^3)$ TeV, may be accessible to future collider experiments. Additionally, the model can be probed in proton decay searches. Our Markov chain Monte Carlo analysis of model parameters shows a high likelihood of observable $p \rightarrow e^+ \pi^0$ decay signal in the first decade of Hyper-Kamiokande operation. The model predicts a vector-like down-type quark at the TeV scale, utilized for realistic fermion mass generation and gauge coupling unification. The model is UV-complete in the sense that it is a unified theory which is realistic and asymptotically free that can be extrapolated to the Planck scale.

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arXiv2024

Leptogenesis in SO(10) with Minimal Yukawa sector

In prior studies, a very minimal Yukawa sector within the $SO(10)$ Grand Unified Theory framework has been identified, comprising of Higgs fields belonging to a real $10_H$, a real $120_H$, and a $\overline{126}_H$ dimensional representations. In this work, within this minimal framework, we have obtained fits to fermion masses and mixings while successfully reproducing the cosmological baryon asymmetry via leptogenesis.The right-handed neutrino ($N_i$) mass spectrum obtained from the fit is strongly hierarchical, suggesting that $B-L$ asymmetry is dominantly produced from $N_2$ dynamics while $N_1$ is responsible for erasing the excess asymmetry. With this rather constrained Yukawa sector, fits are obtained both for normal and inverted ordered neutrino mass spectra, consistent with leptonic CP-violating phase $\delta_\mathrm{CP}$ indicated by global fits of neutrino oscillation data, while also satisfying the current limits from neutrinoless double beta decay experiments. In particular, the the leptonic CP-violating phase has a preference to be in the range $\delta_\mathrm{CP}\simeq (230-300)^\circ$. We also show the consistency of the framework with gauge coupling unification and proton lifetime limits.

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arXiv2024

Unified Origin of Inflation, Baryon Asymmetry, and Neutrino Mass

In this work, we present a unified theoretical framework that simultaneously addresses some of the most intriguing puzzles in particle physics and cosmology, namely the origins of neutrino mass, baryon asymmetry, and cosmic inflation. In our model, inflation is driven by a combination of the Standard Model Higgs, the type II seesaw Higgs responsible for neutrino mass generation, and the unified symmetry-breaking Higgs field. During inflation, non-zero values of the latter field ensure the absence of the monopole problem. The baryon asymmetry is generated through the Affleck-Dine mechanism, facilitated by the non-zero angular motion in the phase of a complex scalar field, which is part of the inflaton. We find that the successful parameter region for generating baryon asymmetry through a renormalizable term in the scalar potential requires a rather heavy type II seesaw triplet, with a mass well beyond the TeV scale. Inflationary observables, in particular, the spectral index is in excellent agree with experimental observation, whereas tensor-to scalar ratio is expected to be probed by the future LiteBIRD and CMB-S4 missions.

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arXiv2024

Explaining PTA Results by Metastable Cosmic Strings from SO(10) GUT

In a recent paper (see https://doi.org/10.1103/PhysRevD.108.095053), we have demonstrated that the 2023 PTA results, which hint at a stochastic gravitational wave (GW) background at nanohertz frequencies, point towards a promising model-building route for realizing $SO(10)$ Grand Unification with embedded inflation. The proposed supersymmetric scenario solves the doublet-triplet splitting without fine-tuning, accounts for charged fermion and neutrino masses, avoids conflicts with current proton decay bounds, and includes only representations no larger than the adjoint. It features multi-step breaking of $SO(10)$ to the Standard Model gauge symmetry, with inflation embedded such that metastable cosmic strings are produced at the end of inflation. This cosmic string network generates a stochastic GW background that can explain the PTA results. In this paper, we provide a detailed analysis of the singled out GUT model class, focusing on how the gauge coupling unification condition affects the scales of multi-step $SO(10)$ breaking and the preferred GW spectra. The lowest breaking scale, linked to inflation, the generation of right-handed neutrino masses for the seesaw mechanism, and metastable cosmic string production, coincides with the range suggested by the PTA results.

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