arXiv subjects

Johan Bijnens

Publications and source records attributed to Johan Bijnens.

At least 55 records · Page 3Linked to original sources

arXiv2017

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and $n\bar n$-oscillations

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of $ππ$-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

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arXiv2017

The Pion Mass and Decay Constant at Three Loops in Two-Flavour Chiral Perturbation Theory

A calculation of the pion mass and decay constant at NNNLO in two-flavour chiral perturbation theory is presented. The results are cross-checked by using both the exponential and square root parameterizations of the Goldstone matrix field, as well as by comparing to the known leading log coefficients of the two quantities. A small numerical study of the quark mass dependence is performed, and for a physical quark mass there is good agreement with lower order results.

hep-ph↗

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.

hep-ph↗

arXiv2017

Twisted finite-volume corrections to $K_{l3}$ decays with partially-quenched and rooted-staggered quarks

The determination of $|V_{us}|$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$ which can be calculated precisely on the lattice. We provide the one-loop partially quenched chiral perturbation theory expressions both with and without including the effects of staggered quarks for all form factors at finite volume and with partially twisted boundary conditions for both the vector current and scalar density matrix elements at all $q^2$. We point out that at finite volume there are more form factors than just $f_+$ and $f_-$ for the vector current matrix element but that the Ward identity is fully satisfied. The size of the finite-volume corrections at present lattice sizes is small. This will help improve the lattice determination of $f_+(q^2=0)$ since the finite-volume error is the dominant error source for some calculations. The size of the finite-volume corrections may be estimated on a single lattice ensemble by comparing results for various twist choices.

hep-lat↗

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.

hep-ph↗

arXiv2016

Chiral Perturbation Theory at Finite Volume and/or with Twisted Boundary Conditions

In this talk we discuss a number of ChPT calculations relevant for lattice QCD. These include the finite volume corrections at two-loop order for masses and decay constants. The second part is about hadronic vacuum polarization where we present the two-loop ChPT estimate for the disconnected and strange quark contributions. We also present the finite volume corrections at two-loop order. The final part is the one-loop finite volume with twisted boundary conditions contribution to $f_+(q^2)$ and the full $K_{\ell3}$ amplitude

hep-lat↗

arXiv2016

Connected, Disconnected and Strange Quark Contributions to HVP

We calculate all neutral vector two-point functions in Chiral Perturbation Theory (ChPT) to two-loop order and use these to estimate the ratio of disconnected to connected contributions as well as contributions involving the strange quark. We extend the ratio of $-1/10$ derived earlier in two flavour ChPT at one-loop order to a large part of the higher order contributions and discuss corrections to it. Our final estimate of the ratio disconnected to connected is negative and a few % in magnitude.

hep-lat↗

arXiv2016

Pion light-by-light contributions to the muon $g-2$

This paper contains some new results on the hadronic light-by-light contribution (HLbL) to the muon $g-2$. The first part argues that we can expect large effects from disconnected diagrams in present and future calculations by lattice QCD of HLbL. The argument is based on the dominance of pseudo-scalar meson exchange. In the second part, we revisit the pion loop HLbL contribution to the muon anomalous magnetic moment. We study it in the framework of some models studied earlier, pure pion loop, full VMD and hidden local symmetry for inclusion of vector mesons. In addition we study possible ways to include the axial-vector meson. The main part of the work is a detailed study of how the different momentum regions contribute. We derive a short distance constraint on the $γ^*γ^*\toππ$ amplitude and use this as a constraint on the models used for the pion loop. As a byproduct we present the general result for integration using the Gegenbauer polynomial method.

hep-ph↗

arXiv2016

Masses, decay constants and electromagnetic form-factors with twisted boundary conditions

We discuss some of the effects of twisted boundary conditions in finite volume using continuum SU(3) Chiral Perturbation Theory. We point out how broken cubic symmetry affects the definitions of quantities such as form-factors. Using the $π^+$ as an example, we give one loop results for the mass, decay constants and electromagnetic form-factor and illustrate how the relevant Ward identities are satisfied.

hep-lat↗

arXiv2015

ChPT meets lattice: finite volume and partial quenching for masses, decay constants and VEVs at NNLO

We discuss finite volume effects and partial quenching for Chiral Perturbation Theory in the mesonic sector. The effects are computed in terms of analytical expressions for masses, decay constants and vacuum expectation values (VEVs) to two-loop order. Numerical examples are presented for a number of interesting and relevant cases. All numerical programs are publically available, the prospects of a combination of these studies with lattice gauge theory computations are discussed briefly.

hep-lat↗

arXiv2015

Hadronic light-by-light contribution to $a_μ$: extended Nambu-Jona-Lasinio, chiral quark models and chiral Lagrangians

This talk discusses our old work on the hadronic light-by-light contribution to the muon anomalous magnetic moment and some more recent contributions. I discuss the various contributions starting with pseudo-scalar meson exchange, the quark- and pion-loop, as well as scalar and $a_1$-exchange. For the $π^0$-exchange I point out a possible large enhancement when only connected contributions are included. For the quark-loop I include some comments about the more recent estimates of this contribution. The pion-loop is discussed in more detail, in particular I discuss our unpublished work on including effects from $a_1$ and the polarizability.

hep-ph↗

arXiv2015

Leading logarithms for mesons and nucleons

This talk describes the work done in calculating leading logarithms in massive effective field theories. We discuss shortly leading logarithms in renormalizable theories and how they can be calculated using only one-loop calculations in effective field theories. The remainder of the talk discusses masses, decay constants, condensates and anomalous processes in mesonic effective field theories like Chiral Perturbation Theory and the expansion of the nucleon mass.

hep-ph↗

arXiv2015

Finite Volume and Partially Quenched QCD-like Effective Field Theories

We present a calculation of the meson masses, decay constants and quark-antiquark vacuum expectation value for the three generic QCD-like chiral symmetry breaking patterns $SU(N_F)\times SU(N_F)\to SU(N_F)_V$, $SU(N_F)\to SO(N_F)$ and $SU(2N_F)\to Sp(2 N_F)$ in the effective field theory for these cases. We extend the previous two-loop work to include effects of partial quenching and finite volume. The calculation has been performed using the quark flow technique. We reproduce the known infinite volume results in the unquenched case. The analytical results can be found in the supplementary material. Some examples of numerical results are given. The numerical programs for all cases are included in version 0.54 of the CHIRON package. The purpose of this work is the use in lattice extrapolations to zero mass for QCD-like and strongly interacting Higgs sector lattice calculations.

hep-lat↗

arXiv2015

Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.

hep-lat↗

arXiv2015

Leading chiral logarithms for the nucleon mass

We give a short introduction to the calculation of the leading chiral logarithms, and present the results of the recent evaluation of the leading logarithm series for the nucleon mass within the heavy baryon theory. The presented results are the first example of leading logarithm calculation in the nucleon ChPT. We also discuss some regularities observed in the leading logarithmical series for nucleon mass. The talk has been presented at "Quark Confinement and the Hadron Spectrum XI".

hep-ph↗

arXiv2015

Leading logarithms for the nucleon mass

Within the heavy baryon chiral perturbation theory approach, we have studied the leading logarithm behaviour of the nucleon mass up to four-loop order exactly and we present some results up to six-loop order as well as an all-order conjecture. The same methods allow to calculate the main logarithm multiplying the terms with fractional powers of the quark mass. We calculate thus the coefficients of $m^{2n+1}\log^{(n-1)}(μ^2/m^2)$ and $m^{2n+2}\log^n(μ^2/m^2)$, with $m$ the lowest-order pion mass. A side result is the leading divergence for a general heavy baryon loop integral.

hep-ph↗

arXiv2015

Finite Volume at Two-loops in Chiral Perturbation Theory

We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.

hep-lat↗

arXiv2014

CHIRON: a package for ChPT numerical results at two loops

This document describes the package CHIRON which includes two libraries, chiron itself and jbnumlib. CHIRON is a set of routines useful for two-loop numerical results in Chiral Perturbation Theory (ChPT). It includes programs for the needed one- and two-loop integrals as well as routines to deal with the ChPT parameters. The present version includes everything needed for the masses, decay constants and quark-antiquark vacuum-expectation-values. An added routine calculates consistent values for the masses and decay constants when the pion and kaon masses are varied. In addition a number of finite volume results are included: one-loop tadpole integrals, two-loop sunset integrals and the results for masses and decay constants. The numerical routine library jbnumlib contains the numerical routines used in chiron. Many are to a large extent simple C++ versions of routines in the CERNLIB numerical library. Notable exceptions are the dilogarithm and the Jacobi theta function implementations. This paper describes what is included in CHIRON v0.50.

hep-ph↗