arXiv subjects

B. Ananthanarayan

Publications and source records attributed to B. Ananthanarayan.

At least 37 records · Page 2Linked to original sources

arXiv2019

New Series Representations for the Two-Loop Massive Sunset Diagram

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses m1, m2 and m3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella Fc function. The convergence regions of the new series contain regions of interest to physical problems. These include some ranges of masses and squared external momentum values which make them useful from Chiral Perturbation Theory to some regions of the parameter space of the Minimal Supersymmetric Standard Model. The analytic continuation results presented on the Lauricella series could be used in other settings as well.

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arXiv2019

Pion form factor and low-energy hadronic contribution to muon $g-2$ by analytic extrapolation: consistency and sensitivity tests

The largest error in the theoretical determination of the muon anomalous magnetic moment is due to the low-energy hadronic vacuum polarization, which cannot be calculated by perturbative QCD and requires nonperturbative techniques. Recently, an accurate determination of the low-energy two-pion contribution to muon $g-2$ has been obtained by a parametrization-free analytic continuation of the pion vector form factor from other kinematical regions. In this work we compare the results of the analytic continuation with direct determinations at low momenta from experiment and lattice QCD. We also explore the sensitivity of the method to the timelike data on the modulus of the form factor used as input, by extending the input region to energies up to 0.76 GeV.

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arXiv2019

Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry

We introduce a novel approach for solving the problem of identifying regions in the framework of Method of Regions by considering singularities and the associated Landau equations given a multi-scale Feynman diagram. These equations are then analyzed by an expansion in a small threshold parameter via the Power Geometry technique. This effectively leads to the analysis of Newton Polytopes which are evaluated using a Mathematica based convex hull program. Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions like potential and Glauber. Several one-loop and two-loop examples are studied and benchmarked using our algorithm which we call ASPIRE.

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arXiv2018

Pion electromagnetic form factor at high precision with implications to $a_μ^{ππ}$ and the onset of perturbative QCD

We extend recently developed methods used for determining the electromagnetic charge radius and $a_μ^{ππ}$ to obtain a determination of the electromagnetic form factor of the pion, $F_π^V(t)$, in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, and with the inclusion of precise inputs from both timelike and spacelike regions. On the unitarity cut, below the first inelastic threshold we use the precisely known phase of the form factor, known from $ππ$ elastic scattering via the Fermi-Watson theorem, and above the inelastic threshold a conservative integral condition on the modulus. We also use as input the experimental values of the modulus at several energies in the elastic region, where the data from $e^+e^-\to π^+π^-$ and $τ$ hadronic decays are mutually consistent, as well as the most recent measurements at spacelike momenta. The experimental uncertainties are implemented by Monte Carlo simulations. At spacelike values $Q^2=-t>0$ near the origin, our predictions are consistent and significantly more precise than the recent QCD lattice calculations. The determinations at larger $Q^2$ confirm the late onset of perturbative QCD for exclusive quantities. From the predictions of $|F_π^V(t)|^2$ on the timelike axis below 0.63 GeV, we obtain the hadronic vacuum polarization (HPV) contribution to the muon anomaly, $a_μ^{ππ}|_{\leq 0.63\gev} = (132.97\pm 0.70)\times 10^{-10}$, using input from both $e^+e^-$ annihilation and $τ$ decay, and $a_μ^{ππ}|_{\leq 0.63 \gev} = (132.91\pm 0.76)\times 10^{-10}$ using only $e^+e^-$ input. Our determinations can be readily extended to obtain such contributions in any interval of interest lying between $2 m_π$ and 0.63 GeV.

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arXiv2018

Pion Interactions and the Standard Model at High Precision

Pions were predicted by H. Yukawa as force carriers of the inter-nucleon forces, and were detected in 1947. Today they are known to be bound states of quarks and anti-quarks of the two lightest flavours. They satisfy Bose statistics, and are the lightest particles of the strong interaction spectrum. Determination of the parameters of the Standard Model, including the masses of the lightest quarks, has only recently reached high precision on the lattice. Pions are also known to be pseudo-Goldstone bosons of spontaneously broken approximate axial-vector symmetries, and a probe of their properties and interactions at high precision tests our knowledge of the strong interactions. While also being a probe of the solution of the strong interactions on the computer, which is known as lattice gauge theory. Despite their long history, there are significant experimental and theoretical challenges in determining their properties at high precision. Examples include the lifetime of the neutral pion, and the status of their masses and decay widths in effective field theories. Pion-pion scattering has been studied for several decades using general methods of field theory such as dispersion relations based on analyticity, unitarity and crossing. Knowledge from these theoretical methods are used to confront high precision experimental data, and to analyze them to extract information on their scattering and phase shift parameters. This knowledge is crucial for estimating the Standard Model contributions to the anomalous magnetic moment of the muon, which is being probed at Fermilab in ongoing experiments. Other sensitive tests include the rare decay of the eta meson into three pions, which represents an isospin violating decay. The present article briefly reviews these important developments.

physics.hist-ph↗

arXiv2018

Analytic representations of $m_K$, $F_K$, $m_η$ and $F_η$ in two loop $SU(3)$ chiral perturbation theory

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in $SU(3)$ chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at $p^2=m_P^2$ ($P=π, K, η$). Recalling that there are three mass scales in this theory, $m_π$, $m_K$ and $m_η$, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for $m_π$ and $F_π$, the pion mass and decay constant. We provide fully analytic exact expressions for $m_K$ and $m_η$, the kaon and eta masses, and $F_K$ and $F_η$, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for $m_K$, $F_K$, $m_η$ and $F_η$ that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for $m_π$ and $F_π$ may be obtained, the latter having been used in conjunction with the results for $F_K$ to produce a recently published analytic representation of $F_K/F_π$.

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arXiv2018

Analytic representation of $F_K/F_π$ in two loop chiral perturbation theory

We present an analytic representation of $F_K/F_π$ as calculated in three-flavour two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how approximations may be made to obtain relatively compact analytic representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.

hep-ph↗

arXiv2018

Leading Logarithms of the Two Point Function in Massless O(N) and SU(N) Models to any Order from Analyticity and Unitarity

Leading (large) logarithms in non-renormalizable theories have been investigated in the recent past. Besides some general considerations, explicit results for the expansion coefficients (in terms of leading logarithms) of partial wave amplitudes and of scalar and vector form factors have been given. Analyticity and unitarity constraints haven been used to obtain the expansion coefficients of partial waves in massless theories, yielding form factors and the scalar two-point function to five-loop order in the O(4)/O(3) model. Later, the all order solutions for the partial waves in any O(N+1)/O(N) model were found. Also, results up to four-loop order exist for massive theories. Here we extend the implications of analyticity and unitarity constraints on the leading logarithms to arbitrary loop order in massless theories. We explicitly obtain the scalar and vector form factors as well as to the scalar two-point function in any O(N) and SU(N) type models. We present relations between the expansion coefficients of these quantities and those of of the relevant partial waves. Our work offers a consistency check on the published results in the O(N) models for form factors, and new results for the scalar two-point function. For the SU(N) type models, we use the known expansion coefficients for partial waves to obtain those for scalar and vector form factors as well as for the scalar two-point function. Our results for the form factor offer a check for the known and future results for massive O(N) and SU(N) type models when the massless limit is taken. Mathematica notebooks which can be used to calculate the expansion coefficients are provided as ancillary files.

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arXiv2018

Inclusive spin-momentum analysis and new physics at a polarized electron-positron collider

We consider the momentum distribution and the polarization of an inclusive heavy fermion in a process assumed to arise from standard-model (SM) $s$-channel exchange of a virtual $γ$ or $Z$ with a further contribution from physics beyond the standard model involving $s$-channel exchanges. The interference of the new physics amplitude with the SM $γ$ or $Z$ exchange amplitude is expressed entirely in terms of the space-time signature of such new physics. Transverse as well as longitudinal polarizations of the electron and positron beams are taken into account. Similarly, we consider the cases of the polarization of the observed final-state fermion along longitudinal and two transverse spin-quantization axes which are required for a full reconstruction of the spin dependence of the process. We show how these model-independent distributions can be used to deduce some general properties of the nature of the interaction and some of their properties in prior work which made use of spin-momentum correlations.

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arXiv2017

Perturbative Expansions in QCD Improved by Conformal Mappings of the Borel Plane

Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients exhibit a factorial growth at large orders. While this feature has little impact on physical predictions in QED, it can have nontrivial consequences in applications of perturbative QCD at moderate energies. In particular, it affects the theoretical error in the extraction of the strong coupling $α_s$ from hadronic $τ$ decays, despite progress of perturbative calculations available at present to four loops. We discuss a new type of perturbative expansion for QCD correlators, which uses instead of the standard powers of the coupling a new set of expansion functions. These functions are defined by means of an optimal conformal mapping of the Borel complex plane, which implements the known features of the high-order divergence in terms of the lowest Borel-plane singularities. The properties of the expansion functions resemble those of the expanded correlators, by exhibiting in particular the singular behaviour of the correlators at $α_s=0$. We prove the good convergence properties of the new expansions on mathematical models that simulate the physical polarization function for light quarks and its derivative (the Adler function), in various prescriptions of renormalization-group summation.

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arXiv2017

An Analytic Analysis of the Pion Decay Constant in Three-Flavoured Chiral Perturbation Theory

A representation of the two-loop contribution to the pion decay constant in $SU(3)$ chiral perturbation theory is presented. The result is analytic upto the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of $F_π$ and $M_π^2$ in the strange quark mass in the isospin limit, and perform the matching of the chiral SU(2) and SU(3) low energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.

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arXiv2017

Electromagnetic charge radius of the pion at high precision

We present a determination of the pion charge radius from high precision data on the pion vector form factor from both timelike and spacelike regions, using a novel formalism based on analyticity and unitarity. At low energies, instead of the poorly known modulus of the form factor, we use its phase, known with high accuracy from Roy equations for $ππ$ elastic scattering via the Fermi-Watson theorem. We use also the values of the modulus at several higher timelike energies, where the data from $e^+e^-$-annihilation and $τ$-decay are mutually consistent, as well as the most recent measurements at spacelike momenta. The experimental uncertainties are implemented by Monte-Carlo simulations. The results, which do not rely on a specific parametrization, are optimal for the given input information and do not depend on the unknown phase of the form factor above the first inelastic threshold. Our prediction for the charge radius of the pion is $r_π=(0.657 \pm 0.003) \fm $, which amounts to an increase in precision by a factor of about 2.7 compared to the PDG average.

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arXiv2017

Optimal renormalization and the extraction of strange quark mass from semi-leptonic $τ$-decay

We employ optimal renormalization group analysis to semi-leptonic $τ$-decay polarization functions and extract the strange quark mass from their moments measured by the ALEPH and OPAL collaborations. The optimal renormalization group makes use of the renormalization group equation of a given perturbation series which then leads to closed form sum of all the renormalization group-accessible logarithms which have reduced scale dependence. Using the latest theoretical inputs we find $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm GeV}) = 74.47 \pm 7.77~{\rm MeV}$ for ALEPH and OPAL data respectively.

hep-ph↗

arXiv2017

An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two-mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files, which may serve as pedagogical supplements to the methods described in this paper.

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arXiv2016

Optimal renormalization and the extraction of the strange quark mass from moments of the $τ$-decay spectral function

We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the $s$-quark mass relevant in $τ$-decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass $m_s(2{\rm GeV}) = 106.70 \pm 9.36~{\rm MeV}$ and $m_s(2{\rm GeV}) = 74.47 \pm 7.77~{\rm MeV}$ from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

hep-ph↗

arXiv2016

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

The two-pion low-energy contribution to the anomalous magnetic moment of the muon, $a_μ\equiv(g-2)_μ/2$, expres sed as an integral over the modulus squared of the pion electromagnetic form fac tor, 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 $e^+e^-$ annihilation and $τ$-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 $a_μ$ from below 0.63 GeV the value $(133.258 \pm 0.723)\times 10^{-10}$, which amounts to a reduction of the theoretical error by about $6 \times 10^{-11}$.

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arXiv2015

Invisible decays of the heavier Higgs boson in the minimal supersymmetric standard model

We consider the possibility that the heavier CP-even Higgs boson~($H^0$) in the minimal supersymmetric standard model (MSSM) decays invisibly into neutralinos in the light of the recent discovery of the 126 GeV resonance at the CERN Large Hadron Collider (LHC). For this purpose we consider the minimal supersymmetric standard model with universal, non-universal and arbitrary boundary conditions on the supersymmetry breaking gaugino mass parameters at the grand unified scale. Typically, scenarios with universal and nonuniversal gaugino masses do not allow invisible decays of the lightest Higgs boson~($h^0$), which is identified with the $126$ GeV resonance, into the lightest neutralinos in the MSSM. With arbitrary gaugino masses at the grand unified scale such an invisible decay is possible. The second lightest Higgs boson can decay into various invisible final states for a considerable region of the MSSM parameter space with arbitrary gaugino masses as well as with the gaugino masses restricted by universal and nonuniversal boundary conditions at the grand unified scale.The possibility of the second lightest Higgs boson of the MSSM decaying into invisible channels is more likely for arbitrary gaugino masses at the grand unified scale. The heavier Higgs boson decay into lighter particles leads to the intriguing possibility that the entire Higgs boson spectrum of the MSSM may be visible at the LHC even if it decays invisibly, during the searches for an extended Higgs boson sector at the LHC. In such a scenario the nonobservation of the extended Higgs sector of the MSSM may carefully be used to rule out regions of the MSSM parameter space at the LHC.

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arXiv2014

Constraints on the $ωπ$ form factor from analyticity and unitarity

Motivated by the discrepancies noted recently between the theoretical calculations of the electromagnetic $ωπ$ form factor and certain experimental data, we investigate this form factor using analyticity and unitarity in a framework known as the method of unitarity bounds.We use a QCD correlator computed on the spacelike axis by operator product expansion and perturbative QCD as input, and exploit unitarity and the positivity of its spectral function, including the two-pion contribution that can be reliably calculated using high-precision data on the pion form factor. From this information, we derive upper and lower bounds on the modulus of the $ωπ$ form factor in the elastic region. The results provide a significant check on those obtained with standard dispersion relations, confirming the existence of a disagreement with experimental data in the region around 0.6 GeV.

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