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Qaisar Shafi

Publications and source records attributed to Qaisar Shafi.

At least 19 recordsLinked to original sources
arXiv2026

Monopoles, Strings, Walls and Gravitational waves

The gauge symmetry breaking $SU(2) \to U(1) \to Z_2 \to 1$ successively produces monopoles, strings and domain walls bounded by strings (WBS), with the elementary monopole carrying a $U(1)$ magnetic flux twice as large as the elementary string. The elementary strings and subsequently WBS emit gravitational waves, and during their decay, the WBS yield a network of composite strings that carry the same $U(1)$ flux as the monopoles. Depending on the cosmological evolution, we provide the gravitational wave spectra generated by the elementary strings and WBS, in combination with the composite strings which are either effectively stable, quasistable, or metastable. These three scenarios are also realized in the symmetry breaking chain $SU(3) \to SO(3) \to Z_2 \to 1$. Both $SU(2)$ and $SU(3)$ have appeared in the literature as flavor gauge symmetries.

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arXiv2026

Magnetic monopoles and high frequency gravitational waves from quasi-stable strings

The spontaneous breaking of $SO(10)$ via flipped $SU(5)$ to the Standard Model yields a novel scenario in which the superheavy topologically stable GUT monopole carrying a single unit ($2\pi/e$) of Dirac magnetic charge emerges from the merger of a confined but topologically distinct monopole-antimonopole pair that are pulled together by a string. The $SO(10)$ breaking via the subgroup $SU(4)_c\times SU(2)_L\times SU(2)_R$, following a similar reasoning, produces a topologically stable monopole that carries two units ($4\pi/e$) of Dirac charge. We explore the cosmological consequences of this scenario by assuming that the monopoles and strings experience a limited number of inflationary $e$-foldings, before re-entering the horizon and ultimately forming a network of quasi-stable strings bounded by monopole-antimonopole pairs. We identify regions of the parameter space that yield an observable number density of the GUT monopole from the collapse of the appropriate string segments. The gravitational waves emitted by these quasi-stable cosmic strings lie in the Hz to kHz range, which can be tested in a number of proposed and ongoing experiments.

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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

Superconducting Strings in $E_6$

We discuss the appearance of superconducting strings in $E_6$ grand unification, keeping track of the magnetic monopole flux that precedes the formation of the string flux tube. This flux matching ensures compatibility with the quantum tunneling of a monopole-antimonopole pair on a metastable string. We identify two realistic $E_6$ models with superconducting (metastable) strings that also carry zero modes of the right handed Majorana neutrinos and dark matter particles. Depending on the symmetry breaking scale associated with the strings, the latter could be a source of observable gravitational waves, intermediate scale dark matter, and the observed baryon asymmetry via leptogenesis. Topologically stable superconducting strings also appear if the $E_6$ symmetry breaking leaves unbroken the $Z_2$ subgroup of $Z_4$, the center of $SO(10)$. The zero modes of the SM fermions are the charge carriers in this case. Finally, the flux matching condition ensures that the Aharanov-Bohm phase change in going around the metastable strings is an integer multiple of $2 \pi$ for all fields. The fields in the spinorial representation of SO(10) acquire a phase change of $\exp(\pm i\pi)$ if taken around the topologically stable $Z_2$ string.

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arXiv2025

Split supersymmetry and hybrid inflation in light of Atacama Cosmology Telescope DR6 data

Inspired by the recent measurement of the scalar spectral index, $n_s = 0.9743 \pm 0.0034$, by the Atacama Cosmology Telescope (ACT) DR6 data, we present an update on the split supersymmetry hybrid inflation model, also known as $\mu$-term hybrid inflation. The model employs a canonical K\"{a}hler potential but incorporates an additional renormalizable term in the superpotential $W$, which yields the MSSM $\mu$-term following supersymmetry breaking. This additional term in $W$ is responsible for a high reheat temperature, $T_r \gtrsim 10^{12}$ GeV, and consequently the necessity of split supersymmetry in this class of models. The predicted scalar spectral index is in excellent agreement with the ACT measurement and $r$, the tensor to scalar ratio, is estimated to be less than or of order $10^{-2} -10^{-3}$. For the running of the scalar spectral index we find $|dn_s/d \ln k| = O(10^{-4})$. With $T_r \gtrsim 10^{12}$ GeV, leptogenesis is readily implemented in this class of models. A wino-like LSP with mass of around 2 TeV is a plausible dark matter candidate.

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arXiv2025

Waterfall phase in supersymmetric hybrid inflation

We explore a class of realistic supersymmetric hybrid inflation models with a predicted scalar spectral index $n_s \approx 0.97-0.978$, which is in good agreement with the recent Atacama Cosmology Telescope (ACT) measurement. The waterfall field responsible for the gauge symmetry breaking in this scenario experiences some $e$-foldings during the inflationary epoch. The scalar perturbations associated with the waterfall field during this phase induce a stochastic gravitational wave spectrum that will be tested in the ongoing Pulsar Timing Array (PTA) measurements and in future experiments. In an $SU(5)$ setting an observable number density of the superheavy GUT monopole linked to the waterfall field can be realized.

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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

Supersymmetric Hybrid Inflation in light of Atacama Cosmology Telescope Data Release 6, Planck 2018 and LB-BK18

Supersymmetry-based hybrid inflation models (referred to as `spontaneously broken supersymmetry' by the Planck collaboration) are attractive for several reasons, including the appealing feature that inflation is associated with local gauge symmetry breaking in the early universe. Following the Planck collaboration's notation, the inflationary potential with sub-Planckian inflaton field values is given by: $V = \Lambda^4 [1 + \alpha_h \log(\phi / M_{Pl})] - m_{3/2} \Lambda^2 \phi + \Lambda^4 O((\phi / M_{Pl})^4)$. Here, $\Lambda = \sqrt{\kappa} M$ denotes the energy scale of inflation, $M$ is the gauge symmetry breaking scale, $\kappa$ is a dimensionless parameter that sets the inflaton mass ($\sqrt{2} \kappa M$), and $\alpha_h$ is determined from quantum corrections in terms of $\kappa$ and the underlying gauge group. A soft supersymmetry-breaking term proportional to the gravitino mass $m_{3/2}$ (~10 TeV) and linear in the inflaton field $\phi$ is also present during inflation. The final term in $V$ represents the leading-order supergravity correction. (Note that the last two terms were not taken into account in the Planck analysis.) We provide estimates for the parameters $\kappa$ (and $\alpha_h$) that yield a scalar spectral index $n_s$ in the range 0.96 to 0.98, which is fully consistent with recent P-ACT-LB measurements presented by the Atacama Cosmology Telescope, as well as earlier measurements by Planck. We recall that in the absence of the soft SUSY-breaking term proportional to $m_{3/2}$ in $V$, the spectral index $n_s = 1 - 1/N = 0.98$, where $N = 50$ denotes the number of e-foldings. The tensor-to-scalar ratio $r$ in this minimal model is tiny, but it can reach potentially observable values ($r \lesssim 0.01$) in non-minimal models.

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arXiv2025

Superheavy Metastable Strings in SO(10)

The spontaneous breaking of $SO(10)$ grand unified symmetry to $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)_\chi$ yields the GUT monopole as well as a comparably heavy $U(1)_\chi$ monopole which also carries $U(1)_Y$ flux. A metastable string scenario in this case requires that the $U(1)_\chi$ symmetry is necessarily broken close to the GUT scale, thus resulting in a dimensionless string tension $G \mu \sim 10^{-6}$. We show that the $\chi$ monopole does not carry any unconfined flux following the electroweak symmetry breaking. Coupled with $G \mu \sim 10^{-6}$, this metastable string network appears to provide a good fit to the recent Pulsar Timing Array data on the stochastic gravitational background. Gauge coupling unification, especially in the presence of low scale supersymmetry, determines the GUT scale and, in combination with constraints from proton decay experiments, one is able to constrain some of the key parameters in this setup. The breaking of $SO(10)$ via $SU(5) \times U(1)_\chi$ also yields superheavy metastable strings with no unconfined flux associated with the monopoles. Finally, we consider $SO(10)$ breaking via $SU(4)_c \times SU(2)_L \times U(1)_R$, $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ and flipped $SU(5)$ that yield metastable strings where the associated monopoles carry unconfined flux after the electroweak breaking.

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arXiv2025

Magnetic Monopoles and Exotic States in $SU(4)_c \times SU(2)_L \times SU(2)_R$

In the Pati-Salam gauge symmetry $SU(4)_c \times SU(2)_L \times SU(2)_R$ (4-2-2, for short), the observed quarks and leptons of each family reside in the bi-fundamental representations $(4,2,1)$ and $({\bar 4},1,2)$. There exist, however, the fundamental representations $(4,1,1)$, $(1,2,1)$ and $(1,1,2)$ and their hermitian conjugates, which show the presence, in principle, of yet to be discovered color triplets that carry electric charge $\pm{e/6}$, and color singlet particles with charges of $\pm{e/2}$. These Standard Model charges are in full accord with the fact that the 4-2-2 model predicts the presence of a topologically stable finite energy magnetic monopole that carries two quanta of Dirac magnetic charge, i.e., $4 \pi/e$, as well as color magnetic charge that is screened beyond the quark confinement scale. The 4-2-2 model therefore predicts the existence of exotic baryons, mesons and leptons that carry fractional ($\pm{e/2}$) electric charges. Since their origin lies in the fundamental representations of 4-2-2, these exotic particles may turn out to be relatively light, in the TeV mass range or so. The 4-2-2 magnetic monopole mass depends on the 4-2-2 symmetry breaking scale which may be as low as a few TeV.

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arXiv2025

C-parity, magnetic monopoles and higher frequency gravitational waves

We consider the spontaneous breaking of $SO(10)$ grand unified symmetry to the left-right symmetric model $SU(3)_c \times SU(3)_L \times SU(2)_R \times U(1)_{B-L}$ with C-parity also unbroken [$C$ converts $Q\to -Q$, where $Q$ is the electric charge operator in $SO(10)$.] This breaking produces the topologically stable GUT monopole as well as a GUT scale C-string. The subsequent breaking at an intermediate scale of C-parity produces domain walls bounded by C-strings, found by Kibble, Lazarides and Shafi. A limited number of inflationary $e$-foldings experienced during these breakings can yield an observable number density of primordial GUT monopoles. The C-strings also experience this inflationary phase, and the subsequent string-wall network decays through the emission of gravitational waves. We estimate the gravitational wave spectrum from these composite structures over a range of values of the domain wall tension $\sigma$. Depending on $\sigma$ the spectrum displays a peak in the higher frequency range between $10^2$ to $10^5$ Hz.

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arXiv2025

$\mathbf{\mu}$-Hybrid Inflation and Metastable Cosmic Strings in $\mathbf{SU(3)_c\times SU(2)_L\times SU(2)_R \times U(1)_{B-L}}$

We develop a scenario based on $\mu$-hybrid inflation within the framework of a left-right symmetric model defined by the gauge symmetry group $G_{3221} = SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. This model features a two-stage symmetry breaking to the Standard Model, with inflation occurring between the two stages, resulting in the dilution of primordial monopoles produced during the symmetry breaking of $SU(2)_R$ to $U(1)_R$. The second symmetry breaking gives rise to a network of metastable cosmic strings, which produces gravitational waves that can be observed by current and future experiments. A crucial aspect of this model is the inclusion of $R$-symmetry breaking terms in the superpotential, which helps explain the origin of the first symmetry breaking scale and ensures experimentally viable inflation with a minimal (canonical) K\"ahler potential. We show that the model successfully implements consistent inflation, leptogenesis, metastable cosmic strings, and gravitino dark matter, all in agreement with the observational data and constraints on reheating temperature from leptogenesis and gravitino overproduction bounds. We explore the potential embedding of $G_{3221}$ within the gauge symmetry $G_{422} = SU(4)_c \times SU(2)_L \times SU(2)_R$, and provide a brief discussion on the proton decay predictions, which can be tested by the upcoming experiments.

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arXiv2024

Induced gravitational waves, metastable cosmic strings and primordial black holes in GUTs

We explore the cosmological and astrophysical implications of a realistic hybrid inflation model based on flipped $SU(5)$. The model contains superheavy metastable cosmic strings arising from a waterfall field that encounters a limited number of $e$-foldings during the inflationary phase. In addition to the gravitational waves emitted by the metastable strings, there also appear scalar induced gravitational waves linked to the waterfall phase transition. These two independent sources of gravitational waves can yield a combined spectrum that is compatible with the recent PTA measurements, and with additional features that can be probed in future experiments. We also show the appearance of primordial black holes with mass on the order of $10^{29}$ g from the waterfall phase transition, and with an abundance that can be tested in the gravitational lensing experiments.

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arXiv2024

Kinetic Mixing, Proton Decay and Gravitational Waves in SO(10)

We present an $SO(10)$ model in which a dimension five operator induces kinetic mixing at the GUT scale between the abelian subgroups $U(1)_{B-L}$ and $U(1)_R$. We discuss in this framework gauge coupling unification and proton decay, as well as the appearance of superheavy quasistable strings with $G\mu \sim 10^{-8} - 10^{-5}$, where $\mu$ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for $G\mu$ values $\sim 4 \times 10^{-7} - 10^{-5}$, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to $G \mu$ values $\sim 10^{-8} - 2 \times 10^{-7}$, proton decay is expected to occur at a rate accessible in the Hyper-Kamiokande experiment. Finally, we present the gravitational wave spectrum emitted by effectively stable strings with $G\mu\approx 10^{-8}$ that have experienced a certain amount of inflation. This can be tested with future detectors in the $\mu$Hz frequency range.

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arXiv2024

Topological structures, dark matter and gravitational waves in $E_6$

We discuss the appearance of topological structures from the spontaneous breaking of $E_6$ to the Standard Model via its maximal subgroup $SO(10) \times U(1)_\psi$. They include dumbbells, metastable strings, as well as domain walls bounded by necklaces. We provide a novel scenario for producing metastable strings based on the symmetry breaking $U(1)_\psi \longrightarrow Z_8 \longrightarrow Z_4$. The metastable string arises from the merger of $Z_8$ strings that bound a domain wall. An unbroken gauge $Z_2$ symmetry from $SO(10)$ breaking yields viable stable dark matter candidates as well as topologically stable strings. We discuss the gravitational wave emission from two varieties of cosmic strings, namely the superheavy metastable ones and the intermediate scale topologically stable cosmic strings.

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arXiv2024

Primordial monopoles, black holes and gravitational waves

We show how topologically stable superheavy magnetic monopoles and primordial black holes can be generated at observable levels by the waterfall field in hybrid inflation models based on grand unified theories. In $SU(5) \times U(1)_\chi$ grand unification, the monopole mass is of order $4 \times 10^{17}$ GeV, and it carries a single unit ($2 \pi /e$) of Dirac magnetic charge as well as screened color magnetic charge. The monopole density is partially diluted to an observable value, and accompanied with the production of primordial black holes with mass of order $10^{17}$-$10^{19}$ g which may make up the entire dark matter in the universe. The tensor to scalar ratio $r$ is predicted to be of order $10^{-5}$ - $10^{-4}$ which should be testable in the next generation of CMB experiments such as CMB-S4 and LiteBIRD. The gravitational wave spectrum generated during the waterfall transition is also presented. The observed baryon asymmetry can be explained via leptogenesis.

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arXiv2024

Quantum tunneling in the early universe: Stable magnetic monopoles from metastable cosmic strings

We present a novel mechanism for producing topologically stable monopoles (TSMs) from the quantum mechanical decay of metastable cosmic strings in the early universe. In an $SO(10)$ model this mechanism yields TSMs that carry two units ($4π/e$) of Dirac magnetic charge as well as some color magnetic charge which is screened. For a dimensionless string tension parameter $Gμ\approx 10^{-9} - 10^{-5}$, the monopoles are superheavy with masses of order $10^{15} - 10^{17}$ GeV. Monopoles with masses of order $10^8 - 10^{14}$ GeV arise from metastable strings for $Gμ$ values from $\sim 10^{-22}$ to $10^{-10}$. We identify the parameter space for producing these monopoles at an observable level with detectors such as IceCube and KM3NeT. For lower $Gμ$ values the ultra-relativistic monopoles should be detectable at Pierre Auger and ANITA. The stochastic gravitational wave emission arises from metastable strings with $Gμ\sim 10^{-9}-10^{-5}$ and should be accessible at HLVK and future detectors including the Einstein Telescope and Cosmic Explorer. An $E_6$ extension based on this framework would yield TSMs from the quantum mechanical decay of metastable strings that carry three units ($6π/e$) of Dirac magnetic charge.

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arXiv2024

Muon g-2 and lepton flavor violation in supersymmetric GUTs

We present a class of supersymmetric (SUSY) GUT models that can explain the apparent discrepancy between the SM predictions and experimental values of muon g-2 while providing testable signals for lepton flavor violation in charged lepton decays. Moreover, these models predict LSP neutralino abundance that is compatible with the Planck dark matter bounds. We find that scenarios in the framework of $SU(4)_c\times SU(2)_L\times SU(2)_R$ unification, with additional symmetries to explain fermion masses and neutrino oscillations, provide interesting benchmarks for the search of SUSY by correlating a possible manifestation of it in dark matter, rare lepton decays and LHC signals.

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