arXiv subjects

F. A. Chishtie

Publications and source records attributed to F. A. Chishtie.

At least 19 recordsLinked to original sources

arXiv2026

Finite-Field QED Corrections to Vacuum Birefringence and Magnetar Polarization Transport

We study low-energy photon propagation in a constant magnetic field within the finite-field one-loop Heisenberg--Euler framework and apply the resulting mode-dependent refractive indices to magnetar polarization transport. In a centered-dipole model, the polarization-limiting radius is unchanged to better than $10^{-12}$ because mode decoupling occurs at $\sim10^2R_{\rm NS}$, where $B\ll B_{\rm cr}$. Near the surface, however, the weak-field Cotton--Mouton expression overestimates the accumulated birefringent phase by up to a factor $2.9$ at $10^{15}$~G. At the plasma--vacuum resonance, finite-field corrections reduce the resonance density by $32\%$ and raise the adiabatic conversion energy by $14\%$ for 1E~1547.0$-$5408; the corresponding changes are factors $2.6$ and $1.37$ for 1RXS~J1708$-$4009, and factors $9.7$ and $2.13$ for SGR~1806$-$20, the latter controlled by the strong-field asymptote. The parallel-mode magnetic response remains positive and exhibits a broad maximum near $17B_{\rm cr}$. Its strict $\mathcal O(α)$ expansion is monotonic, indicating that the detailed position and profile of the maximum are not controlled beyond the present approximation and require higher-loop assessment. These results identify vacuum-resonance observables as the most sensitive channel for testing finite-field QED in magnetars.

astro-ph.HE↗

arXiv2026

Lambert W Function Framework for Graphene Nanoribbon Quantum Sensing: Theory, Verification, and Multi-Modal Applications

We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W)=We^W$, provides exact analytical solutions to transcendental equations governing quantum confinement. Operating near the branch point singularity at $z=-1/e$ yields sensitivity enhancement factors scaling as $(z-z_c)^{-1/2}$, achieving 35-fold enhancement when the operating point lies within $δ=0.001$ of the branch point. Comprehensive numerical verification confirms: (i) all seven bound states for strength parameter $R=10$ satisfy the constraint $u^2+v^2=R^2$ to machine precision; (ii) the theoretical band gap formula $E_g=2π\hbar v_F/(3W)$ is analytically equivalent to the independently determined empirical relation $E_g=1.38/W$~eV$\cdot$nm, establishing the validity of the FSW-GNR analogy; (iii) a universal sensitivity factorization $S_X = \mathcal{G}_k \cdot η_{\rm enh} \cdot \mathcal{P}_X$ applies across biomedical (SARS-CoV-2, inflammatory markers, cancer biomarkers), environmental (CO$_2$, CH$_4$, NO$_2$, N$_2$O, H$_2$O), and physical (strain, magnetic field, temperature) sensing modalities. This unified framework provides analytically predictable design principles for next-generation graphene quantum sensors. The framework is analytic and predictive rather than microscopic or experimental: band-structure and adsorption parameters are taken as inputs from tight-binding, first-principles, and experimental sources, and the framework returns closed-form sensitivity and design relations built upon them. Reported detection limits are labelled throughout as either literature-demonstrated device values or values predicted by the present framework.

cond-mat.mes-hall↗

arXiv2023

Modelling of COVID-19 Using Fractional Differential Equations

In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel Bernoulli used an elementary version of compartmental modeling to find the effectiveness of deliberate smallpox inoculation on life expectancy. We have used the well-known SIR (Susceptible, Infected and Recovered) model of Kermack & McKendrick to extend the analysis further by including exposure, quarantining, insusceptibility and deaths in a SEIQRDP model. Further, we have generalized this model by using the solutions of Fractional Differential Equations to test the accuracy and validity of the mathematical modeling techniques against Canadian COVID-19 trends and spread of real-world disease. Our work also emphasizes the importance of Personal Protection Equipment (PPE) and impact of social distancing on controlling the spread of COVID-19.

physics.soc-ph↗

arXiv2021

The Fourier Transform of the Continuous Gravitational Wave Signal

The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multi-messenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large amounts of data need to be integrated to achieve desired sensitivity. Contemporary searches use ingenious ad-hoc methods to reduce computational complexity. In this paper we provide analytical expressions for the Fourier transform of realistic pulsar signals. This provides description of the manifold of pulsar signals in the Fourier domain, used by many search methods. We analyze the shape of the Fourier transform and provide explicit formulas for location and size of peaks resulting from stationary frequencies. We apply our formulas to analysis of recently identified outlier at 1891.76 Hz.

gr-qc↗

arXiv2021

Renormalization Mass Scale and Scheme Dependence in the Perturbative Contribution to Inclusive Semileptonic $b$ Decays

We examine the perturbative calculation of the inclusive semi-leptonic decay rate $Γ$ for the $b$-quark, using mass-independent renormalization. To finite order of perturbation theory the series for $Γ$ will depend on the unphysical renormalization scale parameter $μ$ and on the particular choice of mass-independent renormalization scheme; these dependencies will only be removed after summing the series to all orders. In this paper we show that all explicit $μ$-dependence of $Γ$, through powers of ln$(μ)$, can be summed by using the renormalization group equation. We then find that this explicit $μ$-dependence can be combined together with the implicit $μ$-dependence of $Γ$ (through powers of both the running coupling $a(μ)$ and the running $b$-quark mass $m(μ)$) to yield a $μ$-independent perturbative expansion for $Γ$ in terms of $a(μ)$ and $m(μ)$ both evaluated at a renormalization scheme independent mass scale $I\!\!M$ which is fixed in terms of either the "$\overline{MS}$ mass" $\overline{m}_b$ of the $b$ quark or its pole mass $m_{pole}$. At finite order the resulting perturbative expansion retains a degree of arbitrariness associated with the particular choice of mass-independent renormalization scheme. We use the coefficients $c_i$ and $g_i$ of the perturbative expansions of the renormalization group functions $β(a)$ and $γ(a)$, associated with $a(μ)$ and $m(μ)$ respectively, to characterize the remaining renormalization scheme arbitrariness of $Γ$. We further show that all terms in the expansion of $Γ$ can be written in terms of the $c_i$ and $g_i$ coefficients and a set of renormalization scheme independent parameters $τ_i$.

hep-ph↗

arXiv2020

Multi-color photometry and parameters estimation of Jupiter-sized exoplanets; TRES-3b, WASP-2b and HATP-30b

Precise and frequent photometric follow-up studies of transit light curves are indispensable when accurately characterizing extrasolar planets. We present new multi-wavelength photometry of three transiting "Hot Jupiters", TrES-3b, WASP-2b and HAT-P-30b (WASP-51b). Data were acquired from an 0.8 meter telescope at Tarleton State University. When combined with literature data, allowed us to redetermine system parameters in a corresponding way. We developed GCX reduction pipeline and TAP, modeling and light curve fitting package to analyze the extracted light curves. We then used weighted mean results to estimate the parameters from BVRI filters for three exoplanetary systems and compared them to previous results. We concluded our determined parameters are agreed with previous studies. From our study, TreS-3b with a mass of Mp = 1.773 Mjup and Rp = 1.305 Rjup appears slightly less massive, while HAT-P-30b, which has a mass of Mp = 0.7006Mjup and Rp = 1.5109Rjup appears to be a bloated "Hot Jupiter". Additionally, we compared the results of our broadband photmetric analysis with the previous studies to search for transit depth wavelength dependence. We found a flat spectrum across optical wavelengths (except WASP-2b in R-band) for TrES-3b and WASP-2b, indicating the presence of clouds in their atmospheres. ForWASP-2b, Rp/R* value was 0.14215 which was 0.14$σ$ higher than in the previous work. HAT-P-30b had a significantly larger radius in B filter with Rp = 0.161246Rjup, resulting from Rp/R* = 0.1334, which was secondarily confirmed by the atmospheric scale height value, H = 1450km, indicating that HAT-P-30b is an inflated "Hot Jupiter".

astro-ph.EP↗

arXiv2020

Transformation of scalar couplings between Coleman-Weinberg and MS schemes

The Coleman-Weinberg (CW) renormalization scheme for renormalization-group improvement of the effective potential is particularly valuable for CW symmetry-breaking mechanisms (including the challenging case of models with multiple scalar fields). CW mechanism is typically studied using models with classical scale invariance which not only provide a possibility for an alternative symmetry breaking mechanism but also partially address the gauge hierarchies through dimensional transmutation. As outlined in our discussion section, when the couplings are not large, models with CW symmetry-breaking mechanisms have also been shown to naturally provide the strong first-order phase transition necessary for stochastic gravitational wave signals. A full understanding of the CW-MS scheme transformation of couplings thus becomes important in the era of gravitational wave detection and precision coupling measurements. A generalized Coleman-Weinberg (GCW) renormalization scheme is formulated and methods for transforming scalar self-couplings between the GCW and MS (minimal-subtraction) renormalization schemes are developed. Scalar $λΦ^4$ theory with global $O(4)$ symmetry is explicitly studied up to six-loop order to explore the magnitude of this scheme transformation effect on the couplings. The dynamical rescaling of renormalization scales between the GCW and MS schemes can lead to significant (order of 10\%) differences in the coupling at any order, and consequently GCW-MS scheme transformation effects must be considered within precision determinations of scalar couplings in extensions of the Standard Model.

hep-ph↗

arXiv2020

Renormalization Scheme and Mass Scale Independence

We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that results in a cancellation between the implicit and explicit dependence on these parameters. The resulting perturbative expansion is consequently independent of these arbitrary parameters. We illustrate this by considering R, the cross section for e+e- -> hadrons.

hep-ph↗

arXiv2019

A Systematic Expansion of Running Couplings and Masses

As an alternative to directly integrating their defining equations to find the running coupling $a(μ)$ and the running mass $m(μ)$, we expand these quantities in powers of $\ln\left(\fracμ{μ^\prime}\right)$ and their boundary values $a(μ^\prime)$ and $m(μ^\prime)$. Renormalization group summation is used to partially sum these logarithms. We consider this approach using both the $\overline{MS}$ and 't Hooft renormalization schemes. We also show how the couplings and masses in any two mass independent renormalization schemes are related.

hep-th↗

arXiv2017

Renormalization Scheme Dependence and Renormalization Group Summation

We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter $μ$ cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher order radiative corrections is absorbed by the behaviour of the running coupling.

hep-ph↗

arXiv2017

Renormalization Scheme Dependence and the Renormalization Group Beta Function

The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is related to a change in the mass scale $μ$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expansion for a physical quantity $R$ terminates.

hep-ph↗

arXiv2017

The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V'(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".)

hep-th↗

arXiv2014

The Canonical Structure of the Superstring Action

We consider the canonical structure of the Green-Schwarz superstring in $9 + 1$ dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in $2 + 1$ and $3 + 1$ dimensions. A key feature of this structure is that the primary Fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac Bracket (DB) then the second group of primary Fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary Fermionic first class constraints can be used to find the generator of a local Fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space-time to see if the Fermionic gauge symmetry can be made simpler than it is in $2 + 1$, $3 + 1$ and $9 + 1$ dimensions. With a $3 + 3$ dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first class Fermionic constraint.

hep-th↗

arXiv2013

Treatment of a System with Explicitly Broken Gauge Symmetries

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.

hep-th↗

arXiv2013

A Massive Non-Abelian Vector Model

The introduction of a Lagrange multiplier field to ensure that the classical equations of motion are satisfied serves to restrict radiative corrections in a model to being only one loop. The consequences of this for a massive non-Abelian vector model are considered.

hep-th↗

arXiv2011

Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?

We consider the effective potential $V$ in the standard model with a single Higgs doublet in the limit that the only mass scale $μ$ present is radiatively generated. Using a technique that has been shown to determine $V$ completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL) contributions to $V$ using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling $x$, the quartic coupling of the Higgs field $y$, the SU(3) gauge coupling $z$, and the $SU(2) \times U(1)$ couplings $r$ and $s$). We then employ the two loop RG functions with the three couplings $x$, $y$, $z$ to sum the next-to-leading-log (NLL) contributions to $V$ and then the three to five loop RG functions with one coupling $y$ to sum all the $N^2LL...N^4LL$ contributions to $V$. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction (MS) scheme to their form in the CW scheme. The Higgs mass can then be determined from the effective potential: the $LL$ result is $m_{H}=219\;GeV/c^2$ decreases to $m_{H}=188\;GeV/c^2$ at $N^{2}LL$ order and $m_{H}=163\;GeV/c^2$ at $N^{4}LL$ order. No reasonable estimate of $m_H$ can be made at orders $V_{NLL}$ or $V_{N^3LL}$. This is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of $m_H$. The mass $163\;GeV/c^2$ is argued to be an upper bound on $m_H$.

hep-ph↗

arXiv2010

Summing Radiative Corrections to the Effective Potential

When one uses the Coleman-Weinberg renormalization condition, the effective potential $V$ in the massless $ϕ_4^4$ theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the $(p+1)$ order renormalization group function determine the sum of all the N$^{\mbox{\scriptsize p}}$LL order contribution to $V$ to all orders in the loop expansion. We discuss here how, in addition to fixing the N$^{\mbox{\scriptsize p}}$LL contribution to $V$, the $(p+1)$ order renormalization group functions also can be used to determine portions of the N$^{\mbox{\scriptsize p+n}}$LL contributions to $V$. When these contributions are summed to all orders, the singularity structure of \mcv is altered. An alternate rearrangement of the contributions to $V$ in powers of $\ln ϕ$, when the extremum condition $V^\prime (ϕ= v) = 0$ is combined with the renormalization group equation, show that either $v = 0$ or $V$ is independent of $ϕ$. This conclusion is supported by showing the LL, $\cdots$, N$^4$LL contributions to $V$ become progressively less dependent on $ϕ$.

hep-th↗

arXiv2009

Radiative Corrections in Vector-Tensor Models

We consider a two-form antisymmetric tensor field ϕminimally coupled to a non-abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term \frac{μ^2}{2} \tr (ϕ\wedge ϕ) for the tensor field eliminates degrees of freedom associated with this field. Explicit one loop calculations show that an additional coupling m\tr(ϕ\wedge F) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term \frac {μ^2}{2} \tr (ϕ\wedge\star ϕ) and coupling m\tr(ϕ\wedge \star F). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.

hep-th↗