An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Ananthanarayan, B.; Bijnens, Johan; Ghosh, Shayan; Hebbar, Aditya

doi:10.1140/epja/i2016-16374-8

Cited by 12 publications

(21 citation statements)

References 38 publications

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“…For special cases, with up to two distinct mass scales, closed form results are available [13][14][15]. 1 With two mass scales not falling into the threshold or pseudothreshold configurations [2], or with three distinct mass scales, the sunsets cannot be written in terms of elementary functions. In fact, the sunset diagram with three different masses and arbitrary p 2 cannot even be expressed entirely in terms of multiple polylogarithms.…”

Section: ð3þmentioning

confidence: 99%

“…In this work, we therefore present the full analytic expressions valid for the kaon and eta masses and decay constants in terms of double infinite series involving two mass ratios, thus completing the program first initiated in [20] of evaluating the three mass scale sunset diagrams in SUð3Þ ChPT. 2 Here, we present only the results, and the complete derivation will be given in an upcoming paper [23]. An overview of the method used is given in [2], and detailed descriptions can be found in [24,25].…”

Section: ð3þmentioning

confidence: 99%

“…2 Here, we present only the results, and the complete derivation will be given in an upcoming paper [23]. An overview of the method used is given in [2], and detailed descriptions can be found in [24,25].…”

Section: ð3þmentioning

confidence: 99%

“…In a recent publication, the important ratio F K =F π was evaluated in a scheme that allows for the derivation of compact analytic approximations in two loop chiral perturbation theory (ChPT) [1], based on the Mellin-Barnes (MB) approach detailed in [2]. In a prior work, a different scheme was employed to obtain analytic approximations of m π and F π in SUð3Þ ChPT at two loops [3].…”

Section: Introductionmentioning

confidence: 99%

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Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
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In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in SUð3Þ chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p 2 ¼ mRecalling 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 lowenergy 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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Section: ð3þmentioning

confidence: 99%

Section: ð3þmentioning

confidence: 99%

Section: ð3þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
Self Cite
16
0
20
1
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“…In Appendix C we list a series of new sums, which simplify the recent results on the sunrise diagram of Ref. [79].…”

Section: Introductionmentioning

confidence: 99%

Iterated elliptic and hypergeometric integrals for Feynman diagrams

Ablinger

Blümlein

Freitas

et al. 2018

Journal of Mathematical Physics

117

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We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as 2 F 1 Gauß hypergeometric functions at rational argument. In some cases, integrals of this type can be mapped to complete elliptic integrals at rational argument. This class of functions appears to be the next one arising in the calculation of more complicated Feynman integrals following the harmonic polylogarithms, generalized polylogarithms, cyclotomic harmonic polylogarithms, square-root valued iterated integrals, and combinations thereof, which appear in simpler cases. The inhomogeneous solution of the corresponding differential equations can be given in terms of iterative integrals, where the new innermost letter itself is not an iterative integral. A new class of iterative integrals is introduced containing letters in which (multiple) definite integrals appear as factors. For the elliptic case, we also derive the solution in terms of integrals over modular functions and also modular forms, using q-product and series representations implied by Jacobi's ϑ i functions and Dedekind's η-function. The corresponding representations can be traced back to polynomials out of Lambert-Eisenstein series, having representations also as elliptic polylogarithms, a q-factorial 1/η k (τ ), logarithms and polylogarithms of q and their q-integrals. Due to the specific form of the physical variable x(q) for different processes, different representations do usually appear. Numerical results are also presented.

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Chiral perturbation theory: reflections on effective theories of the standard model

2023

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

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An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Cited by 12 publications

References 38 publications

Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
Self Cite
16
0
20
1
View full text Add to dashboard Cite

Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
Self Cite
16
0
20
1
View full text Add to dashboard Cite

Iterated elliptic and hypergeometric integrals for Feynman diagrams

Chiral perturbation theory: reflections on effective theories of the standard model

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An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Cited by 12 publications

References 38 publications

Analytic representations of mK , FK , mηAnanthanarayan1, Bijnens2, Friot3 et al. 2018Phys. Rev. DSelf Cite160201View full textAdd to dashboardCite

Analytic representations of mK , FK , mηAnanthanarayan1, Bijnens2, Friot3 et al. 2018Phys. Rev. DSelf Cite160201View full textAdd to dashboardCite

Iterated elliptic and hypergeometric integrals for Feynman diagrams

Chiral perturbation theory: reflections on effective theories of the standard model

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Product

Resources

About

Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
Self Cite
16
0
20
1
View full text Add to dashboard Cite

Analytic representations of mK , FK , mη
Ananthanarayan
¹
,
Bijnens
²
,
Friot
³

et al. 2018
Phys. Rev. D
Self Cite
16
0
20
1
View full text Add to dashboard Cite