Shayan Ghosh - Academia.edu (original) (raw)
Papers by Shayan Ghosh
Computer Physics Communications
In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Me... more 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 hypergeometric functions using two equivalent algorithms, namely the triangulation method and the Gröbner deformation method. We present our code in the form of a Mathematica package FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the packages AMBRE and Olsson.wl as dependencies. As applications of the package, we find series solutions to the GKZ systems of several one-loop and two-loop Feynman integrals. These are included in the file Examples.nb that can be downloaded along with the package from GitHub.
arXiv (Cornell University), Dec 22, 2022
We show how the conic hull method, recently developed for the analytic and noniterative evaluatio... more We show how the conic hull method, recently developed for the analytic and noniterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and D = 4 − 2 .
Physical Review D
We show how the conic hull method, recently developed for the analytic and noniterative evaluatio... more We show how the conic hull method, recently developed for the analytic and noniterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the ϵ-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in ϵ of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the ϵ-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and D ¼ 4 − 2ϵ.
arXiv (Cornell University), Dec 17, 2021
The Method of Brackets (MoB) is a technique used to compute definite integrals, that has its orig... more 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 limitations of MoB and address them by studying the Mellin-Barnes (MB) representation technique. There has been significant process recently in the study of the latter due to the development of a new computational approach based on conic hulls (see Phys. Rev. Lett. 127, 151601 (2021)). The comparison between the two methods helps to understand the limitations of the MoB, in particular when termwise divergent series appear. As a consequence, the MB technique is found to be superior over MoB for two major reasons: 1. the selection of the sets of series that form a series representation for a given integral follows, in the MB approach, from specific intersections of conic hulls, which, in contrast to MoB, does not need any convergence analysis of the involved series, and 2. MB can be used to evaluate resonant (i.e. logarithmic) cases where MoB fails due to the appearance of termwise divergent series. Furthermore, we show that the recently added Rule 5 of MoB naturally emerges as a consequence of the residue theorem in the context of MB.
arXiv High Energy Physics - Phenomenology, Mar 27, 2020
<strong>Context</strong> The dataset contains the list of COVID Fake News/Claims whic... more <strong>Context</strong> The dataset contains the list of COVID Fake News/Claims which is shared all over the internet. <strong>Content</strong> Headlines: String attribute consisting of the headlines/fact shared. Outcome: It is binary data where 0 means the headline is fake and 1 means that it is true. <strong>Inspiration</strong> In many research portals, there was this common question in which the combined fake news dataset is available or not. This led to the publication of this dataset.
arXiv: Mathematical Physics, 2019
We use the method of brackets to evaluate quadratic and quartic type integrals. We recall the ope... more 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 expressions in terms of hypergeometric functions. The method is further used to evaluate the quartic integrals, entry 2.161.5 and 6 in the table. We also present generalization of both types of integrals with closed form expression in terms of hypergeometric functions.
arXiv: High Energy Physics - Phenomenology, 2017
We present an analytic representation of FK/FpiF_K/F_\piFK/Fpi as calculated in three-flavoured two-loop ch... more We present an analytic representation of FK/FpiF_K/F_\piFK/Fpi as calculated in three-flavoured two-loop chiral perturbation theory, and use it to extract values of the low energy constants Lr5L^r_5Lr5, Cr14+Cr15C^r_{14}+C^r_{15}Cr14+Cr15 and Cr15+2Cr17C^r_{15}+2C^r_{17}Cr15+2Cr17 by means of fitting with data from lattice simulations. Although for the calculation of the two-loop multi-scale integrals involved we have derived exact results using Mellin-Barnes theory, the representation presented in this letter is, for practical purposes, an approximation whose accuracy may be improved to any desired level without a significant increase in its complexity.
Machine Learning Techniques and Analytics for Cloud Security, 2021
arXiv: History and Philosophy of Physics, 2018
Pions were predicted by H. Yukawa as force carriers of the inter-nucleon forces, and were detecte... more 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 p...
arXiv: High Energy Physics - Theory, 2020
We present new analytic continuation formulas for the Appell F4(a,b;c,d;x,y)F_4(a,b;c,d;x,y)F4(a,b;c,d;x,y) double hypergeome... more We present new analytic continuation formulas for the Appell F4(a,b;c,d;x,y)F_4(a,b;c,d;x,y)F4(a,b;c,d;x,y) double hypergeometric series where d=a−b+1d=a-b+1d=a−b+1, which allows quadratic transformations of the Gauss 2F1{}_2F_1_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 they can been used, for instance, to obtain new series representations of the two-loop massive sunset Feynman diagram. The analytic continuation procedure introduced in this paper is also sufficiently general so as to find uses elsewhere.
J ute is one of the major industries in the eastern region of India, particularly in West Bengal.... more J ute is one of the major industries in the eastern region of India, particularly in West Bengal. Jute - the golden fibre, is a natural, renewable, biodegradable and eco-friendly product that meets all the standards of safepackagingin this era when the green marketing concept is gradually emerging in the globe. Government of India has given priority to the revival and development of the jute sector in its policy matrix. The steady decline in markets for traditional jute products forced the Governments and Jute Industry to take up programs for development of diversified jute products in the recent past. Besides attention is directed towards promotion of packaging material for conventional and new end-users with the emphasis on bio-degradable and eco-friendly attributes of jute as a natural fibre so that the jute industry does not depend primarily on mandatory packaging. The paper is an attempt to assess the performance of diversified jute products in front of marketing mix of the ind...
2021 International Conference on Computer Communication and Informatics (ICCCI), 2021
The year 2020, has seen the advent of a pandemic that has affected the world as we know it global... more The year 2020, has seen the advent of a pandemic that has affected the world as we know it globally. The origin reportedly from Wuhan, China, this pandemic is caused by COVID-19 which belongs to the family of Coronavirus. The increase of infection and mortality has shot up exponentially and has left mankind bewildered amongst the remains of the unseen disaster. During these times of hardship mankind has to face with a series of emotions. Analysis of all these emotions becomes a primary target for the well-being of an individual and mankind as a whole. The main motive of our study is to analyze these emotions correctly. Gathering these big chunks of data about this study from different social platforms like Twitter, Facebook, Instagram, etc. plays a major role. For this study we will be considering only the corona virus related tweets from Twitter. Analysis of all these tweets will give us a proper insight about the real emotions that the people has to face during these COVID-19 times. The main objective is to work with multinomial attributed to assess the sentiments more precisely. The next step is cleaning the data and labelling them for further processing. Hereafter a model is developed which is used to access the data and then predict the actual sentiment behind the tweet. The data is assessed using the binary-class and multi-class property with the cross-data evaluation of various machine learning algorithms to form the model. After tedious training of models, it is seen that the proposed model gives us a 96.58% accuracy with Support Vector Machine algorithm.
Data Driven Approach Towards Disruptive Technologies, 2021
Physical Review Letters, 2021
Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and... more 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 is no systematic computational technique of the multiple series representations of Nfold MB integrals for N > 2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained the method also allows, in general, the determination of a single master series for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this paper, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers.
Physical Review D, 2020
The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic ... more 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 representations. The individual terms in the presented expressions satisfy the differential equation that relates the double box in D dimensions to the hexagon in D +2 dimensions.
Physical Review D, 2021
The computational technique of N-fold Mellin-Barnes (MB) integrals, presented in a companion pape... more 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 propagator powers) as well as some of its subtleties in the resonant ones (for unit propagator powers). We confirm certain results in the physics and mathematics literature and provide many new results, some of them dealing with the more general massive oneloop conformal n-point case. In particular, we prove two recent conjectures that give the massive one-loop conformal n-point integral (for generic propagator powers) in terms of multiple hypergeometric series. We show how these conjectures, that were deduced from a Yangian bootstrap analysis, are related by a tower of new quadratic transformations in Hypergeometric Functions Theory. Finally, we also use our MB method to identify spurious contributions that can arise in the Yangian approach.
The European Physical Journal A, 2018
Leading (large) logarithms in non-renormalizable theories have been investigated in the recent pa... more 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.
Computer Physics Communications
In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Me... more 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 hypergeometric functions using two equivalent algorithms, namely the triangulation method and the Gröbner deformation method. We present our code in the form of a Mathematica package FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the packages AMBRE and Olsson.wl as dependencies. As applications of the package, we find series solutions to the GKZ systems of several one-loop and two-loop Feynman integrals. These are included in the file Examples.nb that can be downloaded along with the package from GitHub.
arXiv (Cornell University), Dec 22, 2022
We show how the conic hull method, recently developed for the analytic and noniterative evaluatio... more We show how the conic hull method, recently developed for the analytic and noniterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and D = 4 − 2 .
Physical Review D
We show how the conic hull method, recently developed for the analytic and noniterative evaluatio... more We show how the conic hull method, recently developed for the analytic and noniterative evaluation of multifold Mellin-Barnes (MB) integrals, can be extended to the case where these integrals have straight contours of integration parallel to the imaginary axes in the complex planes of the integration variables. MB integrals of this class appear, for instance, when one computes the ϵ-expansion of dimensionally regularized Feynman integrals, as a result of the application of one of the two main strategies (called A and B in the literature) used to resolve the singularities in ϵ of MB representations. We upgrade the Mathematica package MBConicHulls.wl which can now be used to obtain multivariable series representations of multifold MB integrals with arbitrary straight contours, providing an efficient tool for the automatic computation of such integrals. This new feature of the package is presented, along with an example of application by calculating the ϵ-expansion of the dimensionally regularized massless one-loop pentagon integral in general kinematics and D ¼ 4 − 2ϵ.
arXiv (Cornell University), Dec 17, 2021
The Method of Brackets (MoB) is a technique used to compute definite integrals, that has its orig... more 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 limitations of MoB and address them by studying the Mellin-Barnes (MB) representation technique. There has been significant process recently in the study of the latter due to the development of a new computational approach based on conic hulls (see Phys. Rev. Lett. 127, 151601 (2021)). The comparison between the two methods helps to understand the limitations of the MoB, in particular when termwise divergent series appear. As a consequence, the MB technique is found to be superior over MoB for two major reasons: 1. the selection of the sets of series that form a series representation for a given integral follows, in the MB approach, from specific intersections of conic hulls, which, in contrast to MoB, does not need any convergence analysis of the involved series, and 2. MB can be used to evaluate resonant (i.e. logarithmic) cases where MoB fails due to the appearance of termwise divergent series. Furthermore, we show that the recently added Rule 5 of MoB naturally emerges as a consequence of the residue theorem in the context of MB.
arXiv High Energy Physics - Phenomenology, Mar 27, 2020
<strong>Context</strong> The dataset contains the list of COVID Fake News/Claims whic... more <strong>Context</strong> The dataset contains the list of COVID Fake News/Claims which is shared all over the internet. <strong>Content</strong> Headlines: String attribute consisting of the headlines/fact shared. Outcome: It is binary data where 0 means the headline is fake and 1 means that it is true. <strong>Inspiration</strong> In many research portals, there was this common question in which the combined fake news dataset is available or not. This led to the publication of this dataset.
arXiv: Mathematical Physics, 2019
We use the method of brackets to evaluate quadratic and quartic type integrals. We recall the ope... more 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 expressions in terms of hypergeometric functions. The method is further used to evaluate the quartic integrals, entry 2.161.5 and 6 in the table. We also present generalization of both types of integrals with closed form expression in terms of hypergeometric functions.
arXiv: High Energy Physics - Phenomenology, 2017
We present an analytic representation of FK/FpiF_K/F_\piFK/Fpi as calculated in three-flavoured two-loop ch... more We present an analytic representation of FK/FpiF_K/F_\piFK/Fpi as calculated in three-flavoured two-loop chiral perturbation theory, and use it to extract values of the low energy constants Lr5L^r_5Lr5, Cr14+Cr15C^r_{14}+C^r_{15}Cr14+Cr15 and Cr15+2Cr17C^r_{15}+2C^r_{17}Cr15+2Cr17 by means of fitting with data from lattice simulations. Although for the calculation of the two-loop multi-scale integrals involved we have derived exact results using Mellin-Barnes theory, the representation presented in this letter is, for practical purposes, an approximation whose accuracy may be improved to any desired level without a significant increase in its complexity.
Machine Learning Techniques and Analytics for Cloud Security, 2021
arXiv: History and Philosophy of Physics, 2018
Pions were predicted by H. Yukawa as force carriers of the inter-nucleon forces, and were detecte... more 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 p...
arXiv: High Energy Physics - Theory, 2020
We present new analytic continuation formulas for the Appell F4(a,b;c,d;x,y)F_4(a,b;c,d;x,y)F4(a,b;c,d;x,y) double hypergeome... more We present new analytic continuation formulas for the Appell F4(a,b;c,d;x,y)F_4(a,b;c,d;x,y)F4(a,b;c,d;x,y) double hypergeometric series where d=a−b+1d=a-b+1d=a−b+1, which allows quadratic transformations of the Gauss 2F1{}_2F_1_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 they can been used, for instance, to obtain new series representations of the two-loop massive sunset Feynman diagram. The analytic continuation procedure introduced in this paper is also sufficiently general so as to find uses elsewhere.
J ute is one of the major industries in the eastern region of India, particularly in West Bengal.... more J ute is one of the major industries in the eastern region of India, particularly in West Bengal. Jute - the golden fibre, is a natural, renewable, biodegradable and eco-friendly product that meets all the standards of safepackagingin this era when the green marketing concept is gradually emerging in the globe. Government of India has given priority to the revival and development of the jute sector in its policy matrix. The steady decline in markets for traditional jute products forced the Governments and Jute Industry to take up programs for development of diversified jute products in the recent past. Besides attention is directed towards promotion of packaging material for conventional and new end-users with the emphasis on bio-degradable and eco-friendly attributes of jute as a natural fibre so that the jute industry does not depend primarily on mandatory packaging. The paper is an attempt to assess the performance of diversified jute products in front of marketing mix of the ind...
2021 International Conference on Computer Communication and Informatics (ICCCI), 2021
The year 2020, has seen the advent of a pandemic that has affected the world as we know it global... more The year 2020, has seen the advent of a pandemic that has affected the world as we know it globally. The origin reportedly from Wuhan, China, this pandemic is caused by COVID-19 which belongs to the family of Coronavirus. The increase of infection and mortality has shot up exponentially and has left mankind bewildered amongst the remains of the unseen disaster. During these times of hardship mankind has to face with a series of emotions. Analysis of all these emotions becomes a primary target for the well-being of an individual and mankind as a whole. The main motive of our study is to analyze these emotions correctly. Gathering these big chunks of data about this study from different social platforms like Twitter, Facebook, Instagram, etc. plays a major role. For this study we will be considering only the corona virus related tweets from Twitter. Analysis of all these tweets will give us a proper insight about the real emotions that the people has to face during these COVID-19 times. The main objective is to work with multinomial attributed to assess the sentiments more precisely. The next step is cleaning the data and labelling them for further processing. Hereafter a model is developed which is used to access the data and then predict the actual sentiment behind the tweet. The data is assessed using the binary-class and multi-class property with the cross-data evaluation of various machine learning algorithms to form the model. After tedious training of models, it is seen that the proposed model gives us a 96.58% accuracy with Support Vector Machine algorithm.
Data Driven Approach Towards Disruptive Technologies, 2021
Physical Review Letters, 2021
Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and... more 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 is no systematic computational technique of the multiple series representations of Nfold MB integrals for N > 2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained the method also allows, in general, the determination of a single master series for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this paper, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers.
Physical Review D, 2020
The off-shell massless six-point double box and hexagon conformal Feynman integrals with generic ... more 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 representations. The individual terms in the presented expressions satisfy the differential equation that relates the double box in D dimensions to the hexagon in D +2 dimensions.
Physical Review D, 2021
The computational technique of N-fold Mellin-Barnes (MB) integrals, presented in a companion pape... more 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 propagator powers) as well as some of its subtleties in the resonant ones (for unit propagator powers). We confirm certain results in the physics and mathematics literature and provide many new results, some of them dealing with the more general massive oneloop conformal n-point case. In particular, we prove two recent conjectures that give the massive one-loop conformal n-point integral (for generic propagator powers) in terms of multiple hypergeometric series. We show how these conjectures, that were deduced from a Yangian bootstrap analysis, are related by a tower of new quadratic transformations in Hypergeometric Functions Theory. Finally, we also use our MB method to identify spurious contributions that can arise in the Yangian approach.
The European Physical Journal A, 2018
Leading (large) logarithms in non-renormalizable theories have been investigated in the recent pa... more 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.