29 research outputs found
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 , 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 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 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 order mesonic chiral Lagrangian
We derive the chiral Lagrangian at next-to-next-to-next-to-leading order
(NNNLO) for a general number of light quark flavours as well as for
. 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
The anomalous chiral Lagrangian at order
We derive the order 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
operators for a general number of quark flavours , for and
for . 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 , instead yields operators for a general ,
for and for
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
Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
The hadronic light-by-light contribution to the muon anomalous magnetic
moment depends on an integration over three off-shell momenta squared ()
of the correlator of four electromagnetic currents and the fourth leg at zero
momentum. We derive the short-distance expansion of this correlator in the
limit where all three are large and in the Euclidean domain in QCD.
This is done via a systematic operator product expansion (OPE) in a background
field which we construct. The leading order term in the expansion is the
massless quark loop. We also compute the non-perturbative part of the
next-to-leading contribution, which is suppressed by quark masses, and the
chiral limit part of the next-to-next-to leading contributions to the OPE. We
build a renormalisation program for the OPE. The numerical role of the
higher-order contributions is estimated and found to be small.Comment: 53 pages, analytical results as FORM output included as results.txt,
some references added, misprints corrected, one figure change
Short-distance HLbL contributions to the muon g-2
The current discrepancy between the Standard Model prediction and
the experimental value of the muon anomalous magnetic moment could be a hint
for the existence of new physics. The hadronic light-by-light contribution is
one of the pieces requiring improved precision on the theory side, and an
important step is to derive short-distance constraints for this quantity
containing four electromagnetic currents. Here, we derive such short-distance
constraints for three large photon loop virtualities and the external fourth
photon in the static limit. The static photon is considered as a background
field and we construct a systematic operator product expansion in the presence
of this field. We show that the massless quark loop, i.e. the leading term, is
numerically dominant over non-perturbative contributions up to next-to-next-to
leading order, both those suppressed by quark masses and those that are not.Comment: Proceedings for talk given at 23rd International Conference in
Quantum Chromodynamics (QCD 20), 27 October - 30 October 2020, Montpellier -
F
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