# Balasubramanian AnanthanarayanIndian Institute of Science | IISC

Balasubramanian Ananthanarayan

## About

207

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3,136

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Introduction

Balasubramanian Ananthanarayan currently works at Indian Institute of Science. Their most recent publication is 'An analytic representation of $F_K/F_{\pi}'.

**Skills and Expertise**

## Publications

Publications (207)

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 tha...

In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an automated package to derive the associated GKZ system for a given Feynman diagram and solve it in terms of hyperge...

We present new closed-form expressions for certain improper integrals of Mathematical Physics such as Ising, Box, and Associated integrals. The techniques we employ here include (a) the Method of Brackets and its modifications and suitable extensions and (b) the evaluation of the resulting Mellin-Barnes representations via the recently discovered C...

The pseudoscalar particles pions, kaons and the $\eta$-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 Weinber...

We determine the strange quark mass (ms) and quark mixing element |Vus|, and their joint determination from the Cabibbo suppressed hadronic τ decays in various perturbative schemes. We improve this analysis compared to the previous analysis based on the optimal renormalization or the renormalization group summed perturbation theory (RGSPT) scheme b...

In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an automated package to derive the associated GKZ system for a given Feynman diagram and solve it in terms of hyperge...

The transformation theory of the Appell F2(a,b1,b2;c1,c2;x,y) double hypergeometric function is used to obtain a set of series representations of F2 which provide an efficient way to evaluate F2 for real values of its arguments x and y and generic complex values of its parameters a,b1,b2,c1 and c2 (i.e. in the nonlogarithmic case). This study rests...

The analytic evaluation of multi-scale Feynman integrals is difficult due to the presence of various scales of the problem. When exact calculation is very difficult or impossible, systematic approximations may help. The strategy of expansion by regions is a useful method for obtaining the asymptotic analysis of multi-scale Feynman integrals. In thi...

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 $\tau$ 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...

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction.

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon g − 2 Theory Initiative to update the Standard Model prediction.

We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon g−2 Theory Initiative to update the Standard Model prediction.

In this special issue being brought in the centenary year of the birth of Yoichiro Nambu, we exemplify on his discovery of spontaneous symmetry breaking in elementary particle physics, and review precision pion physics in the present era. The notion of spontaneous symmetry breaking in elementary particle physics was introduced by Nambu, and found a...

We present the Olsson.wl Mathematica package which aims to find linear transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson in J. Math. Phys. 5, 420 (1964) in order to derive the analytic continuations of the Appell $F_1$ double hypergeometric series from the lin...

The Method of Brackets (MoB) is a technique used to compute definite integrals, that has its origin in the negative dimensional integration method. It was originally proposed for the evaluation of Feynman integrals for which, when applicable, it gives the results in terms of combinations of (multiple) series. We focus here on some of the limitation...

The transformation theory of the Appell $F_2(a,b_1,b_2;c_1,c_2;x,y)$ double hypergeometric function is used to obtain a set of series representations of $F_2$ which provide an efficient way to evaluate $F_2$ for real values of its arguments $x$ and $y$ and generic complex values of its parameters $a,b_1, b_2, c_1$ and $c_2$ (i.e. in the nonlogarith...

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational techniqu...

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop nonplanar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the method of cut Feynman diagrams comprising of the coproduct, the first entry condition and integrability condit...

The computational technique of N-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal three-point Feynman integral in various configurations. This shows the great simplicity and efficiency of the method in nonresonant cases (generic...

The method of using Hopf algebras for calculating Feynman integrals developed by Abreu et al. is applied to the two-loop non-planar on-shell diagram with massless propagators and three external mass scales. We show that the existence of the method of cut Feynman diagrams comprising of the coproduct, the first entry condition and integrability condi...

The computational technique of $N$-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal 3-point Feynman integral in various configurations. This shows the great simplicity and efficiency of the method in nonresonant cases (generic pr...

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, to our knowledge there is no systematic computational techniq...

The ASPIRE program, which is based on the Landau singularities and the method of Power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of scaling coming from the top facets. In this work, we relate the scaling having equal components of the top fac...

The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic propagator powers are expressed in terms of linear combinations of multiple hypergeometric series of the generalized Horn type. These results are derived from 9-fold Mellin-Barnes representations obtained from their dual conformal Feynman parameter repr...

High-statistics data on the e+e−→π+π− cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different data sets, especially the most precise ones, which have not been resolved so far. Additional independent constraints on the data are therefore of interest...

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...

High-statistics data on the $e^+e^-\to \pi^+\pi^-$ cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different datasets, especially the most precise ones, which have not been resolved so far. Additional independent constraints on the data are therefore...

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 Pad\'e approximants, we estimate the four-loop corrections to the static energy. We also employ the optimal renormalizatio...

The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic propagator powers are expressed in terms of linear combinations of multiple hypergeometric series of the generalized Horn type. These results are derived from 9-fold Mellin-Barnes representations obtained from their dual conformal Feynman parameter repr...

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses \(m_1,\, m_2\) and \(m_3\) and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella \(F_C^{(3)}\) function. The convergence regions of the new series contain re...

The three-loop QED mass-dependent contributions to the g−2 of each of the charged leptons with two internal closed fermion loops, sometimes called A3(6)(m1m2,m1m3) in the g−2 literature, is revisited using the Mellin-Barnes (MB) representation technique. Results for the muon and τ lepton anomalous magnetic moments A3,μ(6) and A3,τ(6), which were kn...

We present new analytic continuation formulas for the Appell $F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows quadratic transformations of the Gauss ${}_2F_1$ hypergeometric function to be used in the intermediate steps of the derivation. Such formulas are of relevance to loop calculations of quantum field theory where...

The three-loop QED mass-dependent contributions to the $g-2$ of each of the charged leptons with two internal closed fermion loops, sometimes called $A^{(6)}_3\left(\frac{m_1}{m_2}, \frac{m_1}{m_3}\right)$ in the $g-2$ literature, is revisited using the Mellin-Barnes (MB) representation technique. Results for the muon and $\tau$ lepton anomalous ma...

The ASPIRE program, which is based on the Landau singularities and the method of power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of scaling coming from the top facets. In this work, we relate the scaling having equal components of the top fac...

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 phy...

We use the method of brackets to evaluate quadratic and quartic type integrals. We recall the operational rules of the method and give examples to illustrate its working. The method is then used to evaluate the quadratic type integrals which occur in entries 3.251.1,3,4 in the table of integrals by Gradshteyn and Ryzhik and obtain closed form expre...

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 param...

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 l...

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 M...

We extend recently developed methods used for determining the electromagnetic charge radius and aμππ to obtain a determination of the electromagnetic form factor of the pion, FπV(t), in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, with the inclusion of precise inputs from both t...

We extend recently developed methods used for determining the electromagnetic charge radius and $a_\mu^{\pi\pi}$ to obtain a determination of the electromagnetic form factor of the pion, $F_\pi^V(t)$, in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, and with the inclusion of prec...

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 l...

We present an analytic representation of FK/Fπ as calculated in three-flavor 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 i...

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 $p^2=m_P^2$ ($P=\pi, K, \eta$). Recalling that there are three mass scales in this theory, $m_\pi$, $m_K$ and $m_\eta$, there are instances when t...

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...

Perturbative expansions appear to be divergent series in many phys- ically 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 or- ders. While this feature has little impact on physical predictions in...

We employ optimal renormalization group analysis to semi-leptonic -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 a...

We present an analytic representation of $F_K/F_\pi$ as calculated in three-flavoured two-loop chiral perturbation theory, and use it to extract values of the low energy constants $L^r_5$, $C^r_{14}+C^r_{15}$ and $C^r_{15}+2C^r_{17}$ by means of fitting with data from lattice simulations. Although for the calculation of the two-loop multi-scale int...

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,...

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 $\gamma$ 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 S...

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...

We employ optimal renormalization group analysis to semi-leptonic $\tau$-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 su...

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 con tribution 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...

The physics of the light flavoured sector is crucial to our understanding of the Standard Model. In this talk we briefly review the status of the determination of the strong coupling constant \(\alpha _S\), the light-quark masses and the mixing angles as summarized by recent lattice compilations. We also discuss advances in keystone quantities such...

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review...

We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the $s$-quark mass relevant in $\tau$-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 pert...

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 configur...

Form factors are important low-energy quantities and an accurate knowledge of these sheds light on the strong interactions. A variety of methods based on general principles have been developed to use information known in different energy regimes to constrain them in regions where experimental information needs to be tested precisely. Here we review...

The two-pion low-energy contribution to the anomalous magnetic moment of the muon, $a_\mu\equiv(g-2)_\mu/2$, 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 moments of the hadronic spectral functions are of interest for the extraction of the strong coupling and other QCD parameters from the hadronic decays of the τ lepton. We consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappin...

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, n...

Motivated by the discrepancies noted recently between the theoretical
calculations of the electromagnetic $\omega\pi$ 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 pr...

We consider the issue of the top quark Yukawa coupling measurement in a model
in dependent and general case with the inclusion of CP-violation in the
coupling. Arguably the best process to study this coupling is the associa ted
production of Higgs boson along with a $t\bar t$ pair in a machine like the
International Linear Collider (ILC). While det...

One of the most-studied signals for physics beyond the standard model in the production of gauge bosons in electron-positron collisions is due to the anomalous triple gauge boson couplings in the Zγ final state. In this work, we study the implications of this at the ILC with polarized beams for signals that go beyond traditional anomalous triple ne...

The two-pion contribution from low energies to the muon magnetic moment
anomaly, although small, has a large relative uncertainty since in this region
the experimental data on the cross sections are neither sufficient nor precise
enough. It is therefore of interest to see whether the precision can be
improved by means of additional theoretical info...

The moments of the hadronic spectral functions are of interest for the
extraction of the strong coupling $\alpha_s$ and other QCD parameters from the
hadronic decays of the $\tau$ lepton. Motivated by the recent analyses of a
large class of moments in the standard fixed-order and contour-improved
perturbation theories, we consider the perturbative...

We determine the strong coupling constant \alpha_s from the \tau hadroni
width using a renormalization group summed (RGS) expansion of the QCD Adler
function. The main theoretical uncertainty in the extraction of \alpha_s is due
to the manner in which renormalization group invariance is implemented, and the
as yet uncalculated higher order terms in...

We consider supersymmetric models in which the lightest Higgs scalar can
decay invisibly consistent with the constraints on the $126$~GeV state
discovered at the CERN LHC. We consider the invisible decay in the minimal
supersymmetric standard model~(MSSM), as well its extension containing an
additional chiral singlet superfield, the so-called next-...

The recently discovered scalar resonance at the LHC is now almost confirmed
to be a Higgs Boson, whose CP properties are yet to be established. At the ILC
with and without polarized beams, it may be possible to probe these properties
at high precision. In this work, we study the possibility of probing departures
from the pure CP-even case, by using...

Recent data from high statistics experiments that have measured the modulus
of the pion electromagnetic form factor from threshold to relatively high
energies are used as input in a suitable mathematical framework of analytic
continuation to find stringent constraints on the shape parameters of the form
factor at $t=0$. The method uses also as inpu...

We examine the large-order behaviour of a recently proposed
renormalization-group-improved expansion of the Adler function in perturbative
QCD, which sums in an analytically closed form the leading logarithms
accessible from renormalization-group invariance. The expansion is first
written as aneffective series in powers of the one-loop coupling, an...

Analyticity and unitarity techniques are employed to estimate Taylor coefficients of the pion electromagnetic form factor at t = 0 by exploiting the recently evaluated two-pion contribution to the muon (g -aEuro parts per thousand 2) and the phase of the pion electromagnetic form factor in the elastic region, known from pi pi scattering by Fermi-Wa...

The top polarization at the International Linear Collider (ILC) with transverse beam polarization is utilized in the process to probe interactions of the scalar and tensor type beyond the Standard Model and to disentangle their individual contributions. Confidence level limits of 90% are presented on the interactions with realistic integrated lumin...

A generalized top-spin analysis proposed some time ago in the context of
Standard Model and subsequently studied in varying contexts is now applied
primarily to the case of $e^+e^-\rightarrow t\bar{t}$ with transversely
polarized beams. This extends our recent work with new physics couplings of
scalar ($S$) and tensor ($T$) types. We carry out a co...