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.Comment: 17 page

The order p8p^8 mesonic chiral Lagrangian

We derive the chiral Lagrangian at next-to-next-to-next-to-leading order (NNNLO) for a general number $N_f$ of light quark flavours as well as for $N_f=2,3$. We enumerate the contact terms separately. We also discuss the cases where some of the external fields are not included. An example of a choice of Lagrangian is given in the supplementary material.Comment: 23 pages, The file basis.pdf contains the full basis. Minor misprints corrected w.r.t. v

Book review: the Oxford handbook of Swedish politics edited by Jon Pierre

In this new edited volume, The Oxford Handbook of Swedish Politics, Jon Pierre brings together 50 contributors to describe and analyse Sweden’s past and contemporary political and constitutional settlement. Challenging romanticising interpretations of Sweden as an inherent beacon of prosperity and equality, this is a much-needed, well-organised and comprehensive collection that traces the evolution, development and possible twilight of the ‘Swedish model’, writes Carl Truedsson

Chiral Perturbation Theory at NNNLO

Chiral perturbation theory is a much successful effective field theory of quantum chromodynamics at low energies. The effective Lagrangian is constructed systematically order by order in powers of the momentum $p^2$, and until now the leading order (LO), next-to leading order (NLO), next-to-next-to leading order (NNLO) and next-to-next-to-next-to leading order (NNNLO) have been studied. In the following review we consider the construction of the Lagrangian and in particular focus on the NNNLO case. We in addition review and discuss the pion mass and decay constant at the same order, which are fundamental quantities to study for chiral perturbation theory. Due to the large number of terms in the Lagrangian and hence low energy constants arising at NNNLO, some remarks are made about the predictivity of this effective field theory.Comment: Prepared for submission to Symmetry, as invited contribution to the special issue Effective Field Theories - Chiral Perturbation Theory and Non-relativistic QF

The Characteristics of Patterns in Simple Discrete Reaction-Diffusion Systems of Different Dimensionality and Number of Species

The formation of smooth quasi-periodic patterns in static discrete reaction-diffusion systems of various kinds is here studied from a mathematical point of view. The regularity of the patterns can be attributed to the integrability of the system, so that, when searching for such patterns in a system, it is important to investigate whether or not there exist any conserved quantities. The work presented herein is an attempt to generalize a known method, which finds a mathematical representation of the reaction mechanisms allowing for a conserved quantity in the one-dimensional one-species case. It is shown that although the method does not generalize to higher spatial dimensionality, it is possible to generalize to an arbitrary number of species in one dimension, where the reaction mechanism is a generalization of that found in the known method. A fixed-point relation for the system is found and analyzed for an arbitrary number of species, whereas the stabilities and other characteristics of the fixed-points are studied for the two-species case. Numerical simulations show that quasi-periodic patterns indeed can exist along the spatial dimension of the two-species system, and have characteristics that agree with the developed theory. The stabilities in time of these patterns are unclear, since a static case of the reaction-diffusion dynamics is studied. It should be noted that the static case investigated is not uniquely defined by reaction-diffusion dynamics, so that the patterns, if stable, might be found so under some dynamics other than reaction-diffusion

The anomalous chiral Lagrangian at order p8p^8

We derive the order $p^8$ Lagrangian of odd intrinsic parity for mesonic chiral perturbation theory, and provide the resulting operator basis in the supplementary material. Neglecting the non-zero singlet trace, we find $999$ operators for a general number of quark flavours $N_f$, $705$ for $N_f=3$ and $92$ for $N_f=2$. Our numbers agree with those obtained through the Hilbert series approach in the literature. Including a singlet trace, as needed for the physical case of $N_f=2$, instead yields $1210$ operators for a general $N_f$, $892$ for $N_f=3$ and $211$ for $N_f=2$

Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment

We derive short-distance constraints for the hadronic light-by-light contribution (HLbL) to the anomalous magnetic moment of the muon in the kinematic region where the three virtual momenta are all large. We include the external soft photon via an external field leading to a well-defined Operator Product Expansion. We establish that the perturbative quark loop gives the leading contribution in a well defined expansion. We compute the first nonzero power correction. It is related to to the magnetic susceptibility of the QCD vacuum. The results can be used as model-independent short-distance constraints for the very many different approaches to the HLbL contribution. Numerically the power correction is found to be small.Comment: 6 page

Short-distance constraints on the hadronic light-by-light

The muon anomalous magnetic moment continues to attract interest due to the potential tension between experimental measurement [1,2] and the Standard Model prediction [3]. The hadronic light-by-light contribution to the magnetic moment is one of the two diagrammatic topologies currently saturating the theoretical uncertainty. With the aim of improving precision on the hadronic light-by-light in a data-driven approach founded on dispersion theory [4,5], we derive various short-distance constraints of the underlying correlation function of four electromagnetic currents. Here, we present our previous progress in the purely short-distance regime and current efforts in the so-called Melnikov-Vainshtein limit.Comment: Proceedings for "The XVth Quark Confinement and the Hadron Spectrum conference", Stavanger, Norway, August 202

Persistence of antibody response 1.5 years after vaccination using 7-valent pneumococcal conjugate vaccine in patients with arthritis treated with different antirheumatic drugs

Introduction: The aim of this study was to explore the persistence of an antibody response 1.5 years after vaccination with 7-valent pneumococcal conjugate vaccine in patients with rheumatoid arthritis (RA) or spondyloarthropathy (SpA) treated with different antirheumatic drugs. Methods: Of 505 patients initially recruited, data on current antirheumatic treatment and blood samples were obtained from 398 (79%) subjects after mean (SD, range) 1.4 (0.5; 1 to 2) years. Antibody levels against pneumococcal serotypes 23F and 6B were analyzed by using enzyme-linked immunosorbent assay (ELISA). Original treatment groups were as follows: (a) RA receiving methotrexate (MTX); (b) RA taking anti-TNF monotherapy; (c) RA taking anti-TNF+MTX; (d) SpA with anti-TNF monotherapy; (e) SpA taking anti-TNF+MTX; and (f) SpA taking NSAID/analgesics. Geometric mean levels (GMLs; 95% CI) and proportion (percentage) of patients with putative protective antibody levels >= 1 mg/L for both serotypes, calculated in different treatment groups, were compared with results 4 to 6 weeks after vaccination. Patients remaining on initial treatment were included in the analysis. Possible predictors of persistence of protective antibody response were analysed by using logistic regression analysis. Results: Of 398 patients participating in the 1.5-year follow up, 302 patients (RA, 163, and SpA, 139) had unchanged medication. Compared with postvaccination levels at 1.5 years, GMLs for each serotype were significantly lower in all groups (P between 0.035 and <0.001; paired-sample t test), as were the proportions of patients with protective antibody levels for both serotypes (P < 0.001; chi(2) test). Higher prevaccination antibody levels for both serotypes 23F and 6B were associated with better persistence of protective antibodies (P < 0.001). Compared with patients with protective antibody levels at 1.5 years, those not having protective antibody levels were older, more often women, had longer disease duration and higher HAQ and DAS, and had a lower proportion of initial responders to both serotypes. Concomitant anti-TNF treatment and MTX were identified as negative predictors of the persistence of protective antibodies among RA patients (P = 0.024 and P = 0.065, respectively). Only age 65 years or older (P = 0.017) and not antirheumatic treatment was found to be a negative predictor of protective antibodies in patients with SpA. Conclusions: After initial increase, 1.5 years after pneumococcal vaccination with 7-valent conjugate vaccine, postvaccination antibody levels decreased significantly, reaching levels before vaccination in this cohort of patients with established arthritis treated with different antirheumatic drugs. MTX and anti-TNF treatment predicted low persistence of protective immunity among patients with RA. To boost antibody response, early revaccination with conjugate vaccine might be needed in patients receiving potent immunosuppressive remedies