I. Sentitemsu Imsong

Bio: I. Sentitemsu Imsong is an academic researcher from Indian Institute of Science. The author has contributed to research in topics: Unitarity & Perturbative QCD. The author has an hindex of 10, co-authored 24 publications receiving 213 citations.

Extrapolation and unitarity bounds for the $B \to \pi$ form factor

Abstract: We address the problem of extrapolating the vector form factor $f_{B\pi}^+$, which is relevant to $B\to \pi\ell u_\ell$ decays, from the region of small to the region of large momentum transfer. As input, we use the QCD light-cone sum rule at small momentum transfer. We carry out a comprehensive Bayesian uncertainty analysis and obtain correlated uncertainties for the normalization and shape parameters of the form factor. The $z$-series parametrization for $f_{B\pi}^+$ is employed to extrapolate our results to large momentum transfer, and to compare with the lattice QCD results. To test the validity of our extrapolation we use the upper and lower bounds from the unitarity and positivity of the two-point correlator of heavy-light quark currents. This correlator is updated by including the NNLO perturbative term and the NLO correction to the quark condensate contribution. We demonstrate that an additional input including the form factor, its first and second derivative calculated at one value of momentum transfer from the light-cone sum rules, considerably improves the bounds. This only holds when the correlations between the form factor parameters are taken into account. We further combine our results with the latest experimental measurements of $B\to \pi \ell u_\ell$ by the BaBar and Belle collaborations, and obtain $|V_{ub}|= (3.32^{+0.26}_{-0.22}) \cdot 10^{-3}$ from a Bayesian analysis.

Theory of unitarity bounds and low-energy form factors

Abstract: We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the Kl3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

Precise determination of the low-energy hadronic contribution to the muon g-2 from analyticity and unitarity: An improved analysis

Abstract: The two-pion low-energy contribution to the anomalous magnetic moment of the muon, ${a}_{\ensuremath{\mu}}\ensuremath{\equiv}(g\ensuremath{-}2{)}_{\ensuremath{\mu}}/2$, expressed as an integral over the modulus squared of the pion electromagnetic form factor, brings a relatively large contribution to the theoretical error, since the low accuracy of experimental measurements in this region is amplified by the drastic increase of the integration kernel. We derive stringent constraints on the two-pion contribution by exploiting analyticity and unitarity of the pion electromagnetic form factor. To avoid the poor knowledge of the modulus of this function, we use instead its phase, known with high precision in the elastic region from Roy equations for pion-pion scattering via the Fermi-Watson theorem. Above the inelastic threshold we adopt a conservative integral condition on the modulus, determined from data and perturbative QCD. Additional high precision data on the modulus in the range 0.65--0.71 GeV, obtained from ${e}^{+}{e}^{\ensuremath{-}}$ annihilation and $\ensuremath{\tau}$-decay experiments, are used to improve the predictions on the modulus at lower energies by means of a parametrization-free analytic extrapolation. The results are optimal for a given input and do not depend on the unknown phase of the form factor above the inelastic threshold. The present work improves a previous analysis based on the same technique, including more experimental data and employing better statistical tools for their treatment. We obtain for the contribution to ${a}_{\ensuremath{\mu}}$ from below 0.63 GeV the value $(133.258\ifmmode\pm\else\textpm\fi{}0.723)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which amounts to a reduction of the theoretical error by about $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

Abstract: The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor F(t) at asymptotic spacelike momenta t(= -Q(2)) < 0 We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from pi pi elastic scattering, and the modulus measured from threshold up to 3 GeV by the BABAR Collaboration The method leads to almost model-independent upper and lower bounds on the spacelike form factor Further inclusion of the value of the charge radius and the experimental value at -245 GeV2 measured at JLab considerably increases the strength of the bounds in the region Q(2) less than or similar to 10 GeV2, excluding the onset of the asymptotic perturbative QCD regime for Q(2) < 7 GeV2 We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

Abstract: The recently evaluated two-pion contribution to the muon g - 2 and the phase of the pion electromagnetic form factor in the elastic region, known from pi pi scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t = 0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations, and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, = (0.435 +/- 0.005) fm(2) and F(-1.6 GeV2) = 0.243(-0.014)(+0.022), we obtain the allowed ranges 3.75 GeV-4 less than or similar to c less than or similar to 3.98 GeV-4 and 9.91 GeV-6 less than or similar to d less than or similar to 10.46 GeV-6 for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

B→Vℓ+ℓ− in the Standard Model from Light-Cone Sum Rules

Abstract: We present B q → ρ, B q → ω, B q → K ∗, B s → K ∗ and B s → ϕ form factors from light-cone sum rules (LCSR) at $$ \mathcal{O}\left({\alpha}_s\right) $$ for twist-2 and 3 and $$ \mathcal{O}\left({\alpha}_s^0\right) $$ for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-4 (and 5) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for B → K ∗ll angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low q 2 as well as combined fits to LCSR and lattice results covering the entire kinematic range for B q → K ∗, B s → K ∗ and B s → ϕ. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for B → K ∗γ as well as B → K ∗l+l− and B s → ϕμ + μ − at low dilepton invariant mass. Employing our B → (ρ,ω) form factor results we extract the CKM element |V ub| from the semileptonic decays B → (ρ, ω)lν and find good agreement with other exclusive determinations.

Three-pion contribution to hadronic vacuum polarization

Abstract: We address the contribution of the $3\pi$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^+e^-\to 3\pi$ amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon $(g-2)_\mu$, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances $\omega$ and $\phi$, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for $(g-2)_\mu$ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying $\gamma^*\to3\pi$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^+e^-\to 3\pi$ data sets. Overall, we obtain $a_\mu^{3\pi}|_{\leq 1.8\,\text{GeV}}=46.2(6)(6)\times 10^{-10}$ as our best estimate for the total $3\pi$ contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the $2\pi$ channel below $1\,\text{GeV}$, this covers nearly $80\%$ of the total HVP contribution, leading to $a_\mu^\text{HVP}=692.3(3.3)\times 10^{-10}$ when the remainder is taken from the literature, and thus reaffirming the $(g-2)_\mu$ anomaly at the level of at least $3.4\sigma$. As side products, we find for the vacuum-polarization-subtracted masses $M_\omega=782.63(3)(1)\,\text{MeV}$ and $M_\phi=1019.20(2)(1)\,\text{MeV}$, confirming the tension to the $\omega$ mass as extracted from the $2\pi$ channel.

g − 2 of charged leptons, α ( M Z 2 ) , and the hyperfine splitting of muonium

Abstract: Following updates in the compilation of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\text{hadrons}$ data, this work presents reevaluations of the hadronic vacuum polarization contributions to the anomalous magnetic moments of the electron (${a}_{e}$), muon (${a}_{\ensuremath{\mu}}$) and tau lepton (${a}_{\ensuremath{\tau}}$), to the ground-state hyperfine splitting of muonium and also updates the hadronic contributions to the running of the QED coupling at the mass scale of the $Z$ boson, $\ensuremath{\alpha}({M}_{Z}^{2})$. Combining the results for the hadronic vacuum polarization contributions with recent updates for the hadronic light-by-light corrections, the electromagnetic and the weak contributions, the deviation between the measured value of ${a}_{\ensuremath{\mu}}$ and its Standard Model prediction amounts to $\mathrm{\ensuremath{\Delta}}{a}_{\ensuremath{\mu}}=(28.02\ifmmode\pm\else\textpm\fi{}7.37)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, corresponding to a muon $g\ensuremath{-}2$ discrepancy of $3.8\ensuremath{\sigma}$.