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M. S. A. Alam Khan

Publications and source records attributed to M. S. A. Alam Khan.

9 recordsLinked to original sources
arXiv2025

Investigating non-local contributions in $B_{s} \to ϕ\bar{\ell} \ell$ including higher-twist effects

We analyze the impact of higher-twist three-particle $B_s$-meson light-cone distribution amplitudes (LCDAs) on the non-local form factors for the $B_s\to ϕ\bar{\ell} \ell$ transition focusing on the `charm-loop' contribution within the light-cone sum rule (LCSR) framework. To analytically continue these charm-loop contributions into the kinematically allowed region of the decay, we employ a hadronic dispersion relation that incorporates intermediate resonant states such as the $ϕ,\,J/Ψ$ and $ψ(2S)$ mesons. Here, the LCSR predictions serve as inputs, supplemented by experimental data from two-body decays $B_s \to ϕ~+$ resonance states. Our results indicate that the inclusion of twist-5 and twist-6 LCDAs enhances the non-local form factors by approximately an order of magnitude compared to previous estimates, due to partial disruption of cancellation among different twist contributions. This leads to a dilepton invariant mass-squared ($q^2$)-dependent correction to the Wilson coefficient $C_9$, which is higher than, but still consistent with the Standard Model prediction without the non-factorizable charm-loop corrections within uncertainties. Additionally, we update the local form factors to include contributions from higher-twist three-particle $B_s$-meson LCDAs. The phenomenological implications, particularly for the differential branching fraction and angular observables, are also discussed.

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arXiv2023

Renormalization group improved determination of light quark masses from Borel-Laplace sum rules

We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale dependence of the finite order perturbative series for the renormalization group (RG) invariant quantities such as spectral function, the second derivative of the polarization function of the pseudoscalar current correlator, and its Borel transformation. In addition, the convergence of the spectral function is significantly improved by summing all running logarithms and kinematical $π^2$-terms. Using RGSPT, we find $m_s(2 GeV)=104.34_{-4.21}^{+4.23}\hs\MeV$, and $m_d(2 GeV)=4.21_{-0.45}^{+0.48}\hs\MeV$ leading to $m_u(2 GeV)=2.00_{-0.40}^{+0.33}\hs\MeV$.

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arXiv2023

Renormalization group improved determination of $α_s$, $m_c$, and $m_b$ from the low energy moments of heavy quark current correlators

We determine $α_s$, $m_c$, and $m_b$ using the relativistic quarkonium sum rule and the renormalization group summed perturbation theory (RGSPT). Theoretical uncertainties, especially originating from the variation of the renormalization scale, are considerably reduced for the higher moments. Our determinations using RGSPT are also found to be stable with respect to the use of $\overline{\text{MS}}$ quark mass for the condensate terms. We obtain $α_s^{\left(n_f=5\right)}(M_Z)=0.1171(7)$, $\overline{m}_c=1281.1(3.8)\hspace{.4mm}\mathrm{MeV}$, and $\overline{m}_b=4174.3(9.5)\hspace{.4mm}\mathrm{MeV}$.

hep-ph↗
arXiv2023

Renormalization Group Improvement and QCD Sum Rules

We summarize the results obtained for the quark masses (u,d,s,c, and b) in Refs.~\cite{AlamKhan:2023ili,AlamKhan:2023kgs} and strong coupling ($α_s$) using renormalization group (RG) improvement of the theoretical expressions and experimental inputs that enter in the QCD sum rules. We obtain $m_{u}(2 GeV)=2.00_{-0.40}^{+0.33}$ MeV, $m_{d}(2 GeV)=4.21_{-0.45}^{+0.48}$ MeV, and $m_{s}(2 GeV)=104.34_{-4.24}^{+4.32}$ MeV using Borel Laplace sum rules for the divergence of the axial vector currents. The relativistic sum rules for the moments of the heavy quark currents lead to the determination of $α_s(M_Z)=0.1171(7)$, $\overline{m}_{c}=1281.1(3.8)$ MeV and $\overline{m}_{b}=4174.3(9.5)$ MeV.

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arXiv2023

The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods

The perturbative QCD static potential and ultrasoft contributions, which together give the static energy, have been calculated to three- and four-loop order respectively, by several authors. Using the renormalization group, and Padé approximants, we estimate the four-loop corrections to the static energy. We also employ the optimal renormalization method and resum the logarithms of the perturbative series in order to reduce sensitivity to the renormalization scale in momentum space. This is the first application of the method to results at these orders. The convergence behaviour of the perturbative series is also improved in position space using the Restricted Fourier Transform scheme. Using optimal renormalization, we have extracted the value of $Λ^{\overline{\textrm{MS}}}_{\textrm{QCD}}$ at different scales for two active flavours by matching to the static energy from lattice QCD simulations.

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arXiv2023

Renormalization group improved $m_s$ and $\vert V_{us}\vert$ determination from hadronic $τ$ decays

We determine the strange quark mass ($m_s$) and quark mixing element $\vert V_{us}\vert $, and their joint determination from the Cabibbo suppressed hadronic $τ$ decays in various perturbative schemes. Compared to the previous analysis based on the optimal renormalization or the renormalization group summed perturbation theory (RGSPT) scheme, we have improved this analysis by replacing the theoretical longitudinal contributions with phenomenological parametrization, and the RGSPT coefficients are used for the dimension-4 Adler functions. The improved analysis results in the extraction of $m_s(2\,\mathrm{GeV})=98\pm19\,\mathrm{MeV}$ and $\vert V_{us}\vert=0.2191\pm0.0043$ from the RGSPT scheme.

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arXiv2023

Renormalization group summation and analytic continuation from spacelike to timeline regions

Analytic continuation of the perturbative series from spacelike to timelike regions is performed using renormalization group summed perturbation theory (RGSPT). This method provides an all-order summation of kinematic ``$π^2$-terms'' accessible from a given order of a perturbative series. The impact of the summation of these terms is studied for Higgs boson decay and electromagnetic R-ratio in the perturbative QCD. Results obtained using RGSPT have improved convergence behavior in addition to significantly reduced renormalization scale dependence compared to fixed-order perturbation theory (FOPT). The higher-order behavior using the Padé approximant is also studied for processes considered.

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arXiv2023

Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model

The pseudoscalar particles pions, kaons and the $η$-particle are considerably lighter than the other hadrons such as protons or neutrons. Their lightness was understood as a consequence of approximate chiral symmetry breaking. This led to current algebra, a way to express the relations imposed by the symmetry breaking. It was realized by Weinberg that because of their low mass, it is possible to formulate a purely pionic (effective) field theory at experimental energies, which carries all information on the (non-perturbative) dynamics, symmetries, and their spontaneous breaking of quantum chromodynamics (QCD) and allows for systematic calculations of observables. In this review, we trace these developments and present recent activities in this field. We make the connection to other effective theories, more generally introduced by Wilson, as approximate field theories at low energies. Indeed, principles and paradigms introduced first for pions have become ubiquitous in particle physics and the standard model. Lastly, we turn to the latest development where the present (fundamental) standard model itself is considered as an effective field theory of a - yet to be formulated - even more fundamental theory. We also discuss important techniques that were developed in order to turn chiral perturbation theory into a predictive framework and briefly review some connections between lattice QCD and chiral perturbation theory (ChPT).

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