### Speaker

Prof.
Johan Bijnens
(Lund University)

### Description

Recent progress in mesonic Chiral Perturbation Theory at finite volume
and/or with twisted boundary conditions will be discussed. Topics include
the finite volume at two-loop order calculations of masses and decay constants
for the pseudoscalar of the normal case for two and three flavours [1],
partially quenched three flavour [2] and the case for different patterns of
spontaneous symmetry breaking [3].
Twisted boundary conditions lead to extra terms in Ward identities and form-factors which affects finite volume corrections and relations often used. This will be discussed for a number of cases, the older work [4] and the application to $K_{\ell3}$ for staggered partially quenched [5]. Vector two-point functions relevant for the $g-2$ HVP calculation will be treated at two-loop order [6] allowing a better estimnate of twisting and finite volume corrections.
[1] Finite Volume at two-loops in Chiral Perturbation Theory,
J. Bijnens and T. Rössler,[arXiv:1411.6384] JHEP 1501 (2015) 034
[2] Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation
Theory through NNLO in the Meson Sector,
J. Bijnens and T. Rössler, [arXiv:1508.07238] JHEP 1511 (2015) 097
[3] Finite Volume and Partially Quenched QCD-like Effective Field Theories,
J. Bijnens and T. Rössler, [arXiv:1509.04082] JHEP 1511 (2015) 017
[4] Masses, Decay Constants and Electromagnetic Form-factors with
Twisted Boundary Conditions, J. Bijnens and J. Relefors,
[arXiv:1402.1385] JHEP 05 (2014) 015
[5] C. Bernard, J. Bijnens, E. Gamiz and J. Relefors, work in progress
[6] J. Bijnens and J. Relefors, work in progress

### Primary author

Prof.
Johan Bijnens
(Lund University)