Search

We present a determination of the ratio of kaon and pion leptonic decay constants in isosymmetric QCD (ISOQCD), ${f}_{K}/{f}_{\ensuremath{\pi}}$, making use of the gauge ensembles produced by the Extended Twisted Mass Collaboration with ${N}_{f}=2+1+1$ flavors of Wilson-clover twisted-mass quarks, including configurations close to the physical point for all dynamical flavors. The simulations are carried out at three values of the lattice spacing ranging from $\ensuremath{\sim}0.068$ to $\ensuremath{\sim}0.092\text{ }\text{ }\mathrm{fm}$ with linear lattice size up to $L\ensuremath{\sim}5.5\text{ }\text{ }\mathrm{fm}$. The scale is set by the particle data group (PDG) value of the pion decay constant, ${f}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=130.4(2)\text{ }\text{ }\mathrm{MeV}$, at the ISOQCD pion point, ${M}_{\ensuremath{\pi}}^{\text{ISO}\mathrm{QCD}}=135.0(2)\text{ }\text{ }\mathrm{MeV}$, obtaining for the gradient-flow scales the values ${w}_{0}=0.17383(63)\text{ }\text{ }\mathrm{fm}$, $\sqrt{{t}_{0}}=0.14436(61)\text{ }\text{ }\mathrm{fm}$ and ${t}_{0}/{w}_{0}=\phantom{\rule{0ex}{0ex}}0.11969(62)\text{ }\text{ }\mathrm{fm}$. The data are analyzed within the framework of SU(2) chiral perturbation theory without resorting to the use of renormalized quark masses. At the ISOQCD kaon point ${M}_{K}^{\text{ISO}\mathrm{QCD}}=494.2(4)\text{ }\text{ }\mathrm{MeV}$ we get $({f}_{K}/{f}_{\ensuremath{\pi}}{)}^{\text{ISO}\mathrm{QCD}}=1.1995(44)$, where the error includes both statistical and systematic uncertainties. Implications for the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{us}|$ and for the first-row Cabibbo-Kobayashi-Maskawa unitarity are discussed.

We present a calculation of the decays ${\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\gamma}}^{(*)}$ at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-${N}_{c}$ chiral perturbation theory. The numerical evaluation of the results is performed successively at LO, NLO, and NNLO, fitting the relevant low-energy constants to the available experimental data. We discuss the widths and decay spectra of ${\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ as well as ${\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{l}^{+}{l}^{\ensuremath{-}}$, with $l=e$, $\ensuremath{\mu}$.

Partial quenching allows one to consider correlation functions and amplitudes that do not arise in the corresponding unquenched theory. For example, physical $s$-wave pion scattering can be decomposed into $I=0$ and $2$ amplitudes, while, in a partially-quenched extension, the larger symmetry group implies that there are more than two independent scattering amplitudes. It has been proposed that the finite-volume quantization condition of L\"uscher holds for the correlation functions associated with each of the two-particle amplitudes that arise in partially-quenched theories. Using partially-quenched chiral perturbation theory, we show that this proposal fails for those correlation functions for which the corresponding one-loop amplitudes do not satisfy $s$-wave unitarity. For partially-quenched amplitudes that, while being unphysical, do satisfy one-loop $s$-wave unitarity, we argue that the proposal is plausible. Implications for previous work are discussed., Comment: 11 pages, 4 figures (v2: typos corrected, matches published version)

We present a calculation of the contribution of the Θ-term to the neutron and proton electric dipole moments using seven 2+1+1-flavor highly improved staggered quark ensembles. We also estimate the topological susceptibility for the 2+1+1 theory to be χQ=(66(9)(4) MeV)4 in the continuum limit at Mπ=135 MeV. The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The CP form factor F3 is calculated by expanding in small Θ. We show that lattice artifacts introduce a term proportional to a that does not vanish in the chiral limit, and we include this in our chiral-continuum fits. A chiral perturbation theory analysis shows that the N(0)π(0) state should provide the leading excited-state contribution, and we study the effect of such a state. Detailed analysis of the contributions to the neutron and proton electric dipole moment using two strategies for removing excited-state contamination are presented. Using the excited-state spectrum from fits to the two-point function, we find dnΘ is small, |dnΘ|≲0.01Θ¯ e·fm, whereas for the proton we get |dpΘ|∼0.02Θ¯ e·fm. On the other hand, if the dominant excited-state contribution is from the Nπ state, then |dnΘ| could be as large as 0.05Θ¯ e·fm and |dpΘ|∼0.07Θ¯ e·fm. Our overall conclusion is that present lattice QCD calculations do not provide a reliable estimate of the contribution of the Θ-term to the nucleon electric dipole moments, and a factor of 10 higher statistics data are needed to get better control over the systematics and possibly a 3σ result.

We use a dispersion representation based on unitarity and analyticity to study the low energy ${\ensuremath{\gamma}}^{*}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ process in the ${S}_{11}$ channel. Final state interactions among the $\ensuremath{\pi}N$ system are critical to this analysis. The left-hand part of the partial wave amplitude is imported from $\mathcal{O}({p}^{2})$ chiral perturbation theory result. On the right-hand part, the final state interaction is calculated through Omn\`es formula in $S$ wave. It is found that a good numerical fit can be achieved with only one subtraction parameter, and the eletroproduction experimental data of multipole amplitudes ${E}_{0+},{S}_{0+}$ in the energy region below $\mathrm{\ensuremath{\Delta}}(1232)$ are well described when the photon virtuality ${Q}^{2}\ensuremath{\le}0.1\text{ }\text{ }{\mathrm{GeV}}^{2}$.

The baryon axial vector current is computed in heavy baryon chiral perturbation theory in the large-${N}_{c}$ limit, where ${N}_{c}$ is the number of color charges. One-loop nonanalytic corrections of the order ${m}_{q}\mathrm{ln}{m}_{q}$ are comprised in the analysis, with contributions of both intermediate octet and decuplet baryon states, to all orders in the $1/{N}_{c}$ expansion of the axial vector current relevant for ${N}_{c}=3$. Theoretical expressions are obtained in the limit of vanishing decuplet-octet mass difference only, which allows one to carry out a full comparison with conventional heavy baryon chiral perturbation theory results for three flavors of light quarks and at the physical value ${N}_{c}=3$. Both approaches perfectly agree to all orders considered. Furthermore, a numerical analysis via a least-squares fit is performed in order to extract the values of the free parameters of the theory, using the experimental data available. The predictions of formalism are in good agreement with the experimental data.

The QCD axion remains experimentally viable in the mass range of $\mathcal{O}(10\text{ }\text{ }\mathrm{MeV})$ if (i) it couples predominantly to the first generation of SM fermions; (ii) it decays to ${e}^{+}{e}^{\ensuremath{-}}$ with a short lifetime ${\ensuremath{\tau}}_{a}\ensuremath{\lesssim}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{s}$; and (iii) it has suppressed isovector couplings, i.e., if it is piophobic. Remarkably, these are precisely the properties required to explain recently observed anomalies in nuclear deexcitations, to wit: the ${e}^{+}{e}^{\ensuremath{-}}$ emission spectra of isoscalar magnetic transitions of $^{8}\mathrm{Be}$ and $^{4}\mathrm{He}$ nuclei showed a ``bumplike'' feature peaked at ${m}_{{e}^{+}{e}^{\ensuremath{-}}}\ensuremath{\sim}17\text{ }\text{ }\mathrm{MeV}$. In this paper, we argue that on-shell emission of the QCD axion (with the aforementioned properties) provides an extremely well-motivated, compatible explanation for the observed excesses in these nuclear deexcitations. The absence of anomalous features in other measured transitions is also naturally explained: piophobic axion emission is strongly suppressed in isovector magnetic transitions and forbidden in electric transitions. This QCD axion hypothesis is further corroborated by an independent observation: a $\ensuremath{\sim}2--3\ensuremath{\sigma}$ deviation in the measurement of $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}})$ from the Standard Model theoretical expectation. This paper also includes detailed estimations of various axionic signatures in rare light meson decays, which take into account contributions from low-lying QCD resonance exchange, and, in the case of rare kaon decays, the possible effective implementations of $\mathrm{\ensuremath{\Delta}}S=1$ octet enhancement in chiral perturbation theory. These inherent uncertainties of the effective description of the strong interactions at low energies result in large variations in the predictions for hadronic signals of the QCD axion; in spite of this, the estimated ranges for rare meson decay rates obtained here can be probed in the near future in $\ensuremath{\eta}/{\ensuremath{\eta}}^{\ensuremath{'}}$ and kaon factories.

We calculate the spin-averaged amplitude for doubly virtual forward Compton scattering off nucleons in the framework of manifestly Lorentz invariant baryon chiral perturbation theory at complete one-loop order $O(p^4)$. The calculations are carried out both in the infinite and in a finite volume. The obtained results allow for a detailed estimation the finite-volume corrections to the amplitude which can be extracted on the lattice using the background field technique., 35 pages, 8 figures

Pion electro- and photoproduction off the nucleon close to threshold is studied in covariant baryon chiral perturbation theory at O(p3) in the extended-on-mass-shell scheme, with the explicit inclusion of the Δ(1232) resonance. The relevant low energy constants are fixed by fitting the available experimental data with the theoretical model. The inclusion of the Δ resonance as an explicit degree of freedom substantially improves the agreement with data and the convergence of the model.

Chiral perturbation theory (ChPT) is a low-energy effective field theory of QCD and also a nonlinear sigma model based on the symmetry breaking pattern ${\rm SU}(N_f)\times {\rm SU}(N_f)\to {\rm SU}(N_f)$. In the limit of massless $N_f$ quarks, we enumerate the independent operators without external sources in ChPT using an on-shell method, by counting and presenting the soft blocks at each order in the derivative expansion, up to ${\cal O}(p^{10})$. Given the massless on-shell condition and total momentum conservation, soft blocks are homogeneous polynomials of kinematic invariants exhibiting the Adler's zero when any external momentum becomes soft and vanishing. In addition, soft blocks are seeds for recursively generating all tree amplitudes of Nambu-Goldstone bosons without recourse to ChPT, and in one-to-one correspondence with the "low energy constants" which are the Wilson coefficients. Relations among operators, such as those arising from equations of motion, integration-by-parts, hermiticity, and symmetry structure, manifest themselves in the soft blocks in simple ways. We find agreements with the existing results up to NNNLO, and make a prediction at N$^4$LO., 31 pages, 2 figures and 6 tables. Mathematica codes added as ancillary files

We study the description of nucleons and diquarks in the presence of a uniform strong magnetic field within the framework of the two-flavor Nambu-Jona--Lasinio (NJL) model. Diquarks are constructed through the resummation of quark loop chains using the random phase approximation, while nucleons are treated as bound quark-diquark states described by a relativistic Fadeev equation, using the static approximation for quark exchange interactions. For charged particles, analytical calculations are performed using the Ritus eigenfunction method, which properly takes into account the breakdown of translation invariance that arises from the presence of Schwinger phases. Within this scheme, for definite model parametrizations we obtain numerical predictions for diquark and nucleon masses, which are compared with Chiral Perturbation Theory and Lattice QCD results. In addition, numerical estimations for nucleon magnetic moments are obtained., Comment: 31 pages, 4 figures

We present a calculation of $P\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{(*)}{\ensuremath{\gamma}}^{(*)}$ processes, where $P={\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}}$, at the one-loop level up to and including next-to-next-to-leading order (NNLO) in large-${N}_{c}$ chiral perturbation theory. The results are numerically evaluated successively at LO, NLO, and NNLO. The appearing low-energy constants are determined through fits to the available experimental data. We investigate the decay widths to real photons, the single-virtual transition form factors, and the widths of $P\ensuremath{\rightarrow}\ensuremath{\gamma}{l}^{+}{l}^{\ensuremath{-}}$, where $l=e$, $\ensuremath{\mu}$. Furthermore, we provide results for the slopes and curvatures of the transition form factors.

We report the results of a lattice quantum chromodynamics calculation of ${F}_{K}/{F}_{\ensuremath{\pi}}$ using M\"obius domain-wall fermions computed on gradient-flowed ${N}_{f}=2+1+1$ highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from $130\ensuremath{\lesssim}{m}_{\ensuremath{\pi}}\ensuremath{\lesssim}400\text{ }\text{ }\mathrm{MeV}$, four lattice spacings of $a\ensuremath{\sim}0.15$, 0.12, 0.09 and 0.06 fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the $a\ensuremath{\sim}0.06\text{ }\text{ }\mathrm{fm}$ ensemble is helpful, but not necessary to achieve a subpercent determination of ${F}_{K}/{F}_{\ensuremath{\pi}}$. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of ${F}_{{\stackrel{^}{K}}^{+}}/{F}_{{\stackrel{^}{\ensuremath{\pi}}}^{+}}=1.1942(45)$ with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of $|{V}_{us}|/|{V}_{ud}|=0.2311(10)$.

Experiments searching for the electric dipole moment (EDM) of the electron $d_e$ utilise atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to $d_e$. If the source of $CP$ violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce $CP$-odd semileptonic interactions, parametrised by the Wilson coefficient $C_{SP}$, and provide the dominant source of EDMs in paramagnetic systems instead of $d_e$. We evaluate the $C_{SP}$ coefficients induced by the leading hadronic sources of $CP$ violation, namely nucleon EDMs and $CP$-odd pion-nucleon couplings, by calculating the nucleon-number-enhanced $CP$-odd nuclear scalar polarisability, employing chiral perturbation theory at the nucleon level and the Fermi-gas model for the nucleus. This allows us to translate the ACME EDM limits from paramagnetic ThO into novel independent constraints on the QCD theta term $|\bar ��| < 3 \times 10^{-8}$, proton EDM $|d_p| < 2 \times 10^{-23}\,e\,{\rm cm}$, isoscalar $CP$-odd pion-nucleon coupling $|\bar g^{(1)}_{��NN}| < 4 \times 10^{-10}$, and colour EDMs of quarks $|\tilde d_u - \tilde d_d| < 2 \times 10^{-24}\,{\rm cm}$. We note that further experimental progress with EDM experiments in paramagnetic systems may allow them to rival the sensitivity of EDM experiments with neutrons and diamagnetic atoms to these quantities., 7 pages, 3 figures, version accepted for publication in Physical Review D

We present the calculation of the $K_{l3}$ form factors with $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action at the physical point on a large volume of (10.9 fm)$^3$ at one lattice spacing of $a = 0.085$ fm. We extract the form factors from 3-point functions with three different time separations between the source and sink operators to confirm suppression of excited state contributions. The form factors are calculated in very close to the zero momentum transfer, $q^2 = 0$, thanks to the large volume, so that stable interpolations to $q^2 = 0$ are carried out. Using our form factors, we obtain the form factor at $q^2 = 0$, $f_+(0) = 0.9603(16)(^{+14}_{\ -4})(44)(19)(1)$, where the first, second, and fifth errors are statistical, systematic errors from fit functions and the isospin breaking effect, respectively. The third and fourth errors denote the finite lattice spacing effects estimated from the renormalization factor and contribution beyond the leading order SU(3) chiral perturbation theory (ChPT). The result of $f_+(0)$ yields the Cabibbo-Kobayashi-Maskawa (CKM) matrix element, $|V_{us}| = 0.2255(13)(4)$, where the first error comes from our calculation and the second from the experiment. This value is consistent with the ones determined from the unitarity of the CKM matrix and the $K_{l2}$ decay within one standard deviation, while it is slightly larger than recent lattice calculations by at most 1.5 $\sigma$. Furthermore, we evaluate the shape of the form factors and the phase space integral from our results. We confirm that those results are consistent with the experiment, and also $|V_{us}|$ determined with our phase space integral agrees with the one in the above.

We calculate the complete $T$ matrices of pion-nucleon ($\ensuremath{\pi}N$) scattering to the third order in heavy baryon SU(3) chiral perturbation theory. The baryon mass in the chiral limit ${M}_{0}$ and the low-energy constants are determined by fitting to phase shifts of $\ensuremath{\pi}N$ and the experimental octet-baryon masses simultaneously. By using these constants, we obtain the pion-nucleon sigma terms, ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=(34.57\ifmmode\pm\else\textpm\fi{}11.85)\text{ }\text{ }\mathrm{MeV}$ . We also find a very small strangeness content of the proton, $y\ensuremath{\simeq}0$. The scattering lengths and the scattering volumes are predicted, which turn out to be in good agreement with those of other approaches and the available experimental data. The contributions from the third-order amplitudes are discussed in detail. We find that the contributions from the internal kaon lines of one-loop diagrams and the counterterms of the third order are sizeable. In addition, the issue of convergence is also discussed.

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

Baryon Chiral Perturbation Theory (BChPT) combined with the 1/Nc expansion is applied to the SU(3) vector currents. In terms of the xi power counting linking the low energy and 1/Nc expansions according to O(xi) = O(p) = O(1/Nc), the study is carried out to next-to-next-to-leading order, and it includes SU(3) breaking corrections to the |Delta S|= 1 vector charges, charge radii, and magnetic moments and radii. The results are obtained for generic Nc, allowing for investigating the various scalings in Nc.

We systematically calculate the isospin violating decay, ${D}_{s}^{*}\ensuremath{\rightarrow}{D}_{s}{\ensuremath{\pi}}^{0}$, with heavy meson chiral perturbation theory up to $\mathcal{O}({p}^{3})$ including the loop diagrams. The $\mathcal{O}({p}^{3})$ tree-level amplitudes contain four undetermined low energy constants. We use two strategies to estimate them. Using the nonanalytic dominance approximation, we get $\mathrm{\ensuremath{\Gamma}}[{D}_{s}^{*}\ensuremath{\rightarrow}{D}_{s}{\ensuremath{\pi}}^{0}]=8.{1}_{\ensuremath{-}2.6}^{+3.0}\text{ }\text{ }\mathrm{eV}$. Using the naturalness assumption, we obtain the range of the isospin violating decay width as [5.2, 11.7] eV. These two strategies give similar sizes. We find that the contribution of the $\mathcal{O}({p}^{3})$ corrections might be significant.

The RQCD collaboration proposed a projection method to remove the excited state contamination in lattice OCD calculations of nuclear form factors. The effectiveness of this method in removing the two-particle nucleon-pion-state contamination is examined using chiral perturbation theory. It is shown that the projection method has practically no impact in the calculation of the axial and induced pseudoscalar form factors. In the pseudoscalar form factor the projection method strongly enhances the nucleon-pion-state contamination. The generalized Goldberger-Treiman relation is satisfied even though large nucleon-pion-state contaminations are present in individual form factors. Therefore, the projection method is not a solution to the excited state problem in nucleon form factor calculations., Comment: 17 pages, 5 figures

Lorentz and CPT violation in hadronic physics must be tied to symmetry violations at the underlying quark and gluon level. Chiral perturbation theory provides a method for translating novel operators that may appear in the Lagrange density for color-charged parton fields into equivalent forms for effective theories at the meson and baryon levels. We extend the application of this technique to the study of Lorentz-violating and potentially CPT-violating operators from the minimal standard model extension. For dimension-4 operators, there are nontrivial relations between the coefficients of baryon-level operators related to underlying quark and gluon operators with the same Lorentz structures. Moreover, in the mapping of the dimension-3 operators from the quark and gluon level to the hadron level (considered here for the first time), many of the hadronic observables contain no new low-energy coupling constants at all, which makes it possible to make direct translations of bounds derived using experiments on one kind of hadron into bounds in a completely different corner of the hadronic sector. A notable consequence of this is bounds (at $10^{-15}$-$10^{-20}$ GeV levels) on differences $a^{\mu}_{B}-a^{\mu}_{B'}$ of Lorentz and CPT violation coefficients for $SU(3)_{f}$ octet baryons that differ in their structure by the replacement of a single valance $d$ quark by a $s$ quark. Never before has there been any proposal for how these kinds of differences could be constrained., Comment: 33 pages

The nucleon-pion-state contribution in the QCD 3-point function of the pseudoscalar density is calculated to leading order in chiral perturbation theory. It predicts a nucleon-pion-state contamination in lattice estimates for the pseudoscalar form factor $G_{\rm P}(Q^2)$ determined with the plateau method. Depending on the momentum transfer $Q^2$ the contamination varies between -20% and +50% for a source-sink separation of 2 fm. The nucleon-pion-state contamination also causes violations in the generalized Goldberger-Treiman relation among the pseudoscalar and the axial nucleon form factors, the dominant source being the nucleon-pion-state contamination in the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$. Comparing the chiral perturbation theory predictions with lattice results of the PACS collaboration we find reasonable agreement even for source-sink separations as small as 1.3 fm., Comment: 22 pages, 9 figures. Revised version: Minor changes in section III and IV, typos corrected, references added, results and conclusions unchanged. Matches version published in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1812.09191

Inspired by the discovery of the spin-$\frac{1}{2}$ doubly charmed baryon ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}$ and the subsequent theoretical studies of its magnetic moments, we study the magnetic moments of its spin-$\frac{3}{2}$ heavy quark spin symmetry counterparts, up to the next-to-leading order in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme. With the tree-level contributions fixed by the quark model while the two low energy constants $C$ and $H$ controlling the loop contributions determined in two ways: the quark model (case 1) and lattice QCD simulations together with the quark model (case 2), we study the quark mass dependence of the magnetic moments and compare them with the predictions of the heavy baryon chiral perturbation theory. It is shown that the difference is sizable in case 1, but not in case 2 due to the smaller low energy constants $C$ and $H$, similar to the case of spin-$\frac{1}{2}$ doubly charmed baryons. Second, we predict the magnetic moments of the spin-$\frac{3}{2}$ doubly charmed baryons and compare them with those of other approaches. The predicted magnetic moments in case 2 for the spin-$\frac{3}{2}$ doubly charmed baryons are closer to those of other approaches. In addition, the large differences in case 1 and case 2 for the predicted magnetic moments may indicate the inconsistency between the quark model and the lattice QCD simulations, which should be checked by future experimental or more lattice QCD data.

We present a lattice QCD calculation of the double-virtual neutral pion transition form factor, with the goal to cover the kinematic range relevant to hadronic light-by-light scattering in the muon $g\ensuremath{-}2$. Several improvements have been made compared to our previous work. First, we take into account the effects of the strange quark by using the ${N}_{f}=2+1$ coordinated lattice simulation gauge ensembles. Second, we have implemented the on-shell $\mathcal{O}(a)$ improvement of the vector current to reduce the discretization effects associated with Wilson quarks. Finally, in order to have access to a wider range of photon virtualities, we have computed the transition form factor in a moving frame as well as in the pion rest frame. After extrapolating the form factor to the continuum and to physical quark masses, we compare our results with phenomenology. We extract the normalization of the form factor with a precision of 3.5% and confirm within our uncertainty previous somewhat conflicting estimates for a low-energy constant that appears in chiral perturbation theory for the decay ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ at the next-to-leading order. With additional input from experiment and theory, we reproduce recent estimates for the decay width $\mathrm{\ensuremath{\Gamma}}({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$. We also study the asymptotic large-${Q}^{2}$ behavior of the transition form factor in the double-virtual case. Finally, we provide as our main result a more precise model-independent lattice estimate of the pion-pole contribution to hadronic light-by-light scattering in the muon $g\ensuremath{-}2$: ${a}_{\ensuremath{\mu}}^{\text{HLbL};{\ensuremath{\pi}}^{0}}=(59.7\ifmmode\pm\else\textpm\fi{}3.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$. Using in addition the normalization of the form factor obtained by the PrimEx experiment, we get the lattice and data-driven estimate ${a}_{\ensuremath{\mu}}^{\text{HLbL};{\ensuremath{\pi}}^{0}}=(62.3\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$.

We use lattice QCD to calculate the form factors ${f}_{+}({q}^{2})$ and ${f}_{0}({q}^{2})$ for the semileptonic decay ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\ell}\ensuremath{\nu}$. Our calculation uses six MILC asqtad $2+1$ flavor gauge-field ensembles with three lattice spacings. At the smallest and largest lattice spacing the light-quark sea mass is set to $1/10$ the strange-quark mass. At the intermediate lattice spacing, we use four values for the light-quark sea mass ranging from $1/5$ to $1/20$ of the strange-quark mass. We use the asqtad improved staggered action for the light valence quarks, and the clover action with the Fermilab interpolation for the heavy valence bottom quark. We use SU(2) hard-kaon heavy-meson rooted staggered chiral perturbation theory to take the chiral-continuum limit. A functional $z$ expansion is used to extend the form factors to the full kinematic range. We present predictions for the differential decay rate for both ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\mu}\ensuremath{\nu}$ and ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\tau}\ensuremath{\nu}$. We also present results for the forward-backward asymmetry, the lepton polarization asymmetry, ratios of the scalar and vector form factors for the decays ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\ell}\ensuremath{\nu}$ and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\ell}\ensuremath{\nu}$. Our results, together with future experimental measurements, can be used to determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$.

In this work, we employ the heavy hadron chiral perturbation theory to calculate the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ potentials to the next-to-leading order. The contact, the one-pion exchange, and the two-pion exchange interactions are all included in the calculation along with the mass splittings between the heavy quark spin symmetry partner states. Our result shows that neglecting the heavy quark symmetry violation effect may be misleading to predict the potentials between the charmed hadrons. We perform numerical analysis with three scenarios. In the first scenario, we relate the low-energy constants (LECs) in the contact terms of ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ to those of nucleon systems and reproduce the ${P}_{c}(4312)$ and ${P}_{c}(4440)$ as loosely bound states. In the second scenario, we vary the unknown LECs and find a small parameter region in which ${P}_{c}(4312)$, ${P}_{c}(4440)$ and ${P}_{c}(4457)$ can coexist as molecular states. In the third scenario, we include the coupled-channel effect on the basis of scenario II and notice that the three ${P}_{c}$ states can be reproduced as molecular states simultaneously in a large region of parameters. Our analytical results can be used for the chiral extrapolations in lattice QCD. With the lattice QCD results in the future as inputs, the identification of the ${P}_{c}$ states and predictions for other systems would be more reliable.

Using highly improved staggered quark (HISQ) ${N}_{f}=2+1+1$ MILC ensembles with five different values of the lattice spacing, including four ensembles with physical quark masses, we perform the most precise computation to date of the $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$ vector form factor at zero momentum transfer, ${f}_{+}^{{K}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}}(0)=0.9696(15{)}_{\mathrm{stat}}(12{)}_{\mathrm{syst}}$. This is the first calculation that includes the dominant finite-volume effects, as calculated in chiral perturbation theory at next-to-leading order. Our result for the form factor provides a direct determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|{V}_{us}|=0.22333(44{)}_{{f}_{+}(0)}(42{)}_{\mathrm{exp}}$, with a theory error that is, for the first time, at the same level as the experimental error. The uncertainty of the semileptonic determination is now similar to that from leptonic decays and the ratio ${f}_{{K}^{+}}/{f}_{{\ensuremath{\pi}}^{+}}$, which uses $|{V}_{ud}|$ as input. Our value of $|{V}_{us}|$ is in tension at the $2--2.6\ensuremath{\sigma}$ level both with the determinations from leptonic decays and with the unitarity of the CKM matrix. In the test of CKM unitarity in the first row, the current limiting factor is the error in $|{V}_{ud}|$, although a recent determination of the nucleus-independent radiative corrections to superallowed nuclear $\ensuremath{\beta}$ decays could reduce the $|{V}_{ud}{|}^{2}$ uncertainty nearly to that of $|{V}_{us}{|}^{2}$. Alternative unitarity tests using only kaon decays, for which improvements in the theory and experimental inputs are likely in the next few years, reveal similar tensions and could be further improved by taking correlations between the theory inputs. As part of our analysis, we calculated the correction to ${f}_{+}^{K\ensuremath{\pi}}(0)$ due to nonequilibrated topological charge at leading order in chiral perturbation theory, for both the full-QCD and the partially quenched cases. We also obtain the combination of low-energy constants in the chiral effective Lagrangian $[{C}_{12}^{r}+{C}_{34}^{r}\ensuremath{-}({L}_{5}^{r}{)}^{2}]({M}_{\ensuremath{\rho}})=(2.92\ifmmode\pm\else\textpm\fi{}0.31)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$.

The $s$-wave decay amplitude in the nonleptonic decay of baryons is analyzed within heavy baryon chiral perturbation theory in the $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ limit at one-loop order, where ${N}_{c}$ is the number of color charges. Loop graphs with octet and decuplet intermediate states are systematically incorporated into the analysis and the effects of the decuplet-octet mass difference are accounted for. There are $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ cancellations between different one-loop graphs as a consequence of the $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ spin-flavor symmetry of QCD baryons. The predictions of $\mathrm{large}\text{\ensuremath{-}}{N}_{c}$ baryon chiral perturbation theory are in very good agreement both with the expectations from the $1/{N}_{c}$ expansion and with the experimental data.

We show that the multicomponent meson systems can be described by chiral perturbation theory. We chiefly focus on a system of two pion gases at different isospin chemical potential, deriving the general expression of the chiral Lagrangian, the ground state properties and the spectrum of the low-energy excitations. We consider two different kinds of interactions between the two meson gases: one which does not lock the two chiral symmetry groups and one which does lock them. The former is a kind of interaction that has already been discussed in mutlicomponent superfluids. The latter is perhaps more interesting, because seems to be related to an instability. Although the pressure of the system does not show any instability, we find that for sufficiently strong locking, the spectrum of one Bogolyubov mode becomes tachyonic. This unstable branch seems to indicate a transition to an inhomogeneous phase., 13 pages, 5 figures

The nucleon-pion-state contribution to QCD two-point and three-point functions used in lattice calculations of the nucleon axial form factors are studied in chiral perturbation theory. For small quark masses this contribution is expected to be the dominant excited-state contamination at large time separations. To leading order in chiral perturbation theory the results depend on only two experimentally known low-energy constants and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the axial form factor $G_{\rm A}(Q^2)$ is at the 5 percent level for a source-sink separation of 2 fm and shows almost no dependence on the momentum transfer $Q^2$. In contrast, for the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$ the nucleon-pion-state contribution shows a rather strong dependence on $Q^2$ and leads to a 10 to 40 percent underestimation of $\tilde{G}_{\rm P}(Q^2)$ at small momentum transfers. The ChPT results can be used to analytically remove the nucleon-pion-state contribution from lattice data. Performing this removal for lattice data generated by the PACS collaboration we find agreement with experimental data and the predictions of the pion-pole dominance model. The removal works surprisingly well even for source-sink separations as small as 1.3 fm., Comment: 30 pages, 11 figures

We provide model-independent bounds on the rates of rare decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings, the nEDM arises at the two-loop level. The leading-order relativistic chiral perturbation theory calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counterterm-free result. This is an improvement upon previous estimates which used approximations in evaluating the two-loop contribution and were plagued by divergences. While constraints on the $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\ensuremath{\theta}$ term, our calculation means that whatever the origin of these couplings, the decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}2\ensuremath{\pi}$ will remain unobservable in the near future.

We show that the sigma/f_0(500) state with finite-temperature T corrections to its spectral properties included plays an essential role for the description of the scalar susceptibility chi_S, signaling chiral symmetry restoration. First, we use the O_4 linear sigma model as a test bed to derive the connection between chi_S and the sigma propagator and to check the validity and reliability of the approach where chi_S is saturated by the sigma/f_0(500) inverse self-energy, which we calculate at finite T to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal f_0(500) state generated in unitarized chiral perturbation theory (UChPT). Such an approach allows us to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the hadron resonance gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed and confirm the validity of the thermal f(0)(500) saturated approach and hence the importance of that thermal state for chiral symmetry restoration.

We investigate the finite size effect on pseudoscalar meson masses and decay constants using a subset of the "PACS10" configurations which are generated keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We have tried two kinds of analyses, fixing $\kappa$ values or measured axial Ward identity quark masses. Comparing the results on (5.4 fm$)^4$ and (10.8 fm$)^4$ lattices, we have found a sizable finite size effect on the pseudoscalar meson sector in the former analysis: a 2.1(8)%, 4.8(1.6)%, and 0.36(31)% finite size effect on $m_\pi$, $m_{\rm ud}$, and $f_\pi$, respectively, on the (5.4 fm$)^4$ lattice. For the latter analysis, the finite size effect on the pseudoscalar meson decay constants is 0.66(33)% for $f_\pi$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_\pi$. These values with two-sigma error bars are consistent with the predictions from the full one-loop SU(3) chiral perturbation theory, which are 0.20% for $f_\pi$, 0.08% for $f_K$, and 0.13% for $f_K/f_\pi$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision., Comment: 7 pages, 10 figures, published version

In this paper, we report on results for the $s$-wave scattering length of the $\ensuremath{\pi}\text{\ensuremath{-}}K$ system in the $I=3/2$ channel from ${N}_{f}=2+1+1$ lattice QCD. The calculation is based on gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about 230 to 450 MeV at three values of the lattice spacing. Our main result reads ${M}_{\ensuremath{\pi}}{a}_{0}^{3/2,\text{phys}}=\ensuremath{-}0.059(2)$. Using chiral perturbation theory we are also able to estimate ${M}_{\ensuremath{\pi}}{a}_{0}^{1/2,\text{phys}}=0.163(3)$. The error includes statistical and systematic uncertainties, and for the latter in particular errors from the extrapolation to the physical point.

In this paper we test the semi-local duality based on the method of Ref.[1] for calculating final-state interactions at varying number of colors ($N_C$). We compute the amplitudes by dispersion relations that respect analyticity and coupled channel unitarity, as well as accurately describing experiment. The $N_C$ dependence of the $\pi\pi\to\pi\pi$ scattering amplitudes is obtained by comparing these amplitudes to the one of chiral perturbation theory. The semi-local duality is investigated by varying $N_C$. Our results show that the semi-local duality is not violated when $N_C$ is large. At large $N_C$, the contributions of the $f_2(1270)$, the $f_0(980)$ and the $f_0(1370)$ cancel that of the $\rho(770)$ in the finite energy sum rules, while the $f_0(500)$ has almost no effect. This gives further credit to the method developed in Ref.[1] for investigating the $N_C$ dependence of hadron-hadron scattering with final-state interactions. This study is also helpful to understand the structure of the scalar mesons., Comment: 8 pages, 5 figures, several comments are added

Weak pion production off the nucleon at low energies has been systematically investigated in manifestly relativistic baryon chiral perturbation theory with explicit inclusion of the $\Delta$(1232) resonance. Most of the involved low-energy constants have been previously determined in other processes such as pion-nucleon elastic scattering and electromagnetic pion production off the nucleon. For numerical estimates, the few remaining constants are set to be of natural size. As a result, the total cross sections for single pion production on neutrons and protons, induced either by neutrino or antineutrino, are predicted. Our results are consistent with the scarce existing experimental data except in the $\nu_\mu n\to \mu^-n\pi^+$ channel, where higher-order contributions might still be significant. The $\Delta$ resonance mechanisms lead to sizeable contributions in all channels, especially in $\nu_\mu p\to \mu^- p\pi^+$, even though the considered energies are close to the production threshold. The present study provides a well founded low-energy benchmark for phenomenological models aimed at the description of weak pion production processes in the broad kinematic range of interest for current and future neutrino-oscillation experiments., Comment: 38 pages, 8 figures, 2 tables. Version to appear in PRD, with more discussions

Within the framework of the $U(3)$ chiral perturbation theory, we revisit the masses, decay constants and the mixing parameters of the light pseudoscalar mesons $\pi, K, \eta$ and $\eta'$. The low energy constants up to next-to-next-to-leading order are determined by including the light-quark mass dependences of the various quantities from different lattice QCD simulations and relevant phenomenological inputs. Then we study the finite-temperature behaviors of the masses of the light pseudoscalar mesons. The thermal behaviors of the $\eta$-$\eta'$ mixing angles in singlet-octet and quark-flavor bases are also explored. While the masses of the $\pi, K$, and $\eta$ are increased when increasing the temperatures, the mass of the $\eta'$ turns out to be slightly decreased in the low-temperature region.

We deliver lattice results for the $I=0$ $\pi\pi$ elastic $s$-wave scattering length calculated with the MILC $N_f=3$ flavors of the Asqtad-improved staggered fermions. The scattering phase shifts are determined by Luscher's formula from the energy-eigenvalues of $\pi\pi$ systems at one center of mass frame and four moving frames using the moving wall source technique. Our measurements are good enough to resolve the scattering length $a$ and effective range $r$, moreover, it allows us to roughly estimate the shape parameter $P$. Using our lattice results, the scattering length $a$ and effective range $r$ at the physical point are extrapolated by chiral perturbation theory. Our results are reasonably consistent with the Roy equation determinations and the newer experimental data. Numerical computations are carried out with two MILC fine ($a\approx0.09$~fm, $L^3 \times T = 40^3\times 96$) and one MILC superfine ($a\approx0.06$~fm, $L^3 \times T = 48^3\times 144$) lattice ensembles at three pion masses of $m_\pi\sim247~{\rm MeV}$, $249~{\rm MeV}$, and $314~{\rm MeV}$, respectively.

We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1{)}_{A}$ symmetries. For that purpose, we exploit QCD Ward identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ chiral perturbation theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1{)}_{A}$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in SU(3) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P=π, K, η). Recalling that there are three mass scales in this theory, mπ, mK and mη, 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 mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, 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 low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ. (Less)

The three-particle $N\pi\pi$-state contribution to the QCD two-point function of standard nucleon interpolating fields is computed to leading order in chiral perturbation theory. Using the experimental values for two low-energy coefficients the impact of this contribution on lattice QCD calculations of the nucleon mass is estimated. The impact is found to be at the per mille level at most and negligible in practice., Comment: 16 pages, 5 figures. V2: Error in eq. (A2) corrected, figures 3 to 5 updated, conclusions unchanged. Discussion of FV corrections expanded. Typos corrected, references added. Matches published version in Phys. Rev. D

We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cut-off effects. This finally yields a much smaller total error in the spectral projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility., Comment: 18 pages, 19 figures

We present an improved analysis of our lattice data for the $\ensuremath{\eta}--{\ensuremath{\eta}}^{\ensuremath{'}}$ system, including a correction of the relevant correlation functions for residual topological finite size effects and employing consistent chiral and continuum fits. From this analysis we update our physical results for the masses ${M}_{\ensuremath{\eta}}=557(11{)}_{\text{stat}}(03{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$ and ${M}_{\ensuremath{\eta}}^{\ensuremath{'}}=911(64{)}_{\text{stat}}(03{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$, as well as the mixing angle in the quark flavor basis $\ensuremath{\phi}=38.8(2.2{)}_{\text{stat}}(2.4{)}_{\ensuremath{\chi}\mathrm{PT}}^{\ensuremath{\circ}}$ in excellent agreement with other results from phenomenology. Similarly, we include an analysis for the decay constant parameters, leading to ${f}_{l}=125(5{)}_{\text{stat}}(6{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$ and ${f}_{s}=178(4{)}_{\text{stat}}(1{)}_{\ensuremath{\chi}\mathrm{PT}}\text{ }\text{ }\mathrm{MeV}$. The second error reflects the uncertainty related to the chiral extrapolation. The data used for this study has been generated on gauge ensembles provided by the European Twisted Mass Collaboration with ${N}_{f}=2+1+1$ dynamical flavors of Wilson twisted mass fermions. These ensembles cover a range of pion masses from 220 MeV to 500 MeV and three values of the lattice spacing. Combining our data with a prediction from chiral perturbation theory, we give an estimate for the physical $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ decay widths and the singly-virtual $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\gamma}}^{*}$ transition form factors in the limit of large momentum transfer.

Baryon chiral perturbation theory combined with the $1/{N}_{c}$ expansion is implemented for three flavors. Baryon masses, vector charges and axial vector couplings are studied to one-loop and organized according to the $\ensuremath{\xi}$-expansion, in which the $1/{N}_{c}$ and the low-energy power countings are linked according to $1/{N}_{c}=\mathcal{O}(\ensuremath{\xi})=\mathcal{O}(p)$. The renormalization to $\mathcal{O}({\ensuremath{\xi}}^{3})$ necessary for the mentioned observables is provided, along with applications to the baryon masses and axial couplings as obtained in lattice QCD calculations.

We calculate the masses and sigma terms of the doubly charmed baryons up to next-to-next-to-next-to-leading order [i.e., $\mathcal{O}({p}^{4})$] in a covariant baryon chiral perturbation theory by using the extended-on-mass-shell renormalization scheme. Their expressions both in infinite and finite volumes are provided for chiral extrapolation in lattice QCD. As a first application, our chiral results of the masses are confronted with the existing lattice QCD data in the presence of finite-volume corrections. Up to $\mathcal{O}({p}^{3})$, all relevant low-energy constants can be well determined. As a consequence, we obtain the physical values for the masses of ${\mathrm{\ensuremath{\Xi}}}_{cc}$ and ${\mathrm{\ensuremath{\Omega}}}_{cc}$ baryons by extrapolating to the physical limit. Our determination of the ${\mathrm{\ensuremath{\Xi}}}_{cc}$ mass is consistent with the recent experimental value by LHCb Collaboration, however, larger than the one by SELEX Collaboration. In addition, we predict the pion-baryon and strangeness-baryon sigma terms, as well as the mass splitting between the ${\mathrm{\ensuremath{\Xi}}}_{cc}$ and ${\mathrm{\ensuremath{\Omega}}}_{cc}$ states. Their quark mass dependences are also discussed. The numerical procedure can be applied to the chiral results of $\mathcal{O}({p}^{4})$ order, where more unknown constants are involved, when more data are available for unphysical pion masses.

Magnetic properties of octet baryons are investigated within the framework of chiral perturbation theory. Utilizing a power counting for large magnetic fields, the Landau levels of charged mesons are treated exactly giving rise to baryon energies that depend non-analytically on the strength of the magnetic field. In the small-field limit, baryon magnetic moments and polarizabilities emerge from the calculated energies. We argue that the magnetic polarizabilities of hyperons provide a testing ground for potentially large contributions from decuplet pole diagrams. In external magnetic fields, such contributions manifest themselves through decuplet-octet mixing, for which possible results are compared in a few scenarios. These scenarios can be tested with lattice QCD calculations of the octet baryon energies in magnetic fields., Comment: 25 pages, 9 figures

Rare weak decays of ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}K\ensuremath{\pi}$ have been investigated in the framework of the $U(3)$ chiral perturbation theory at the leading order. Our study shows that the branching ratio $\mathcal{B}({\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}K\ensuremath{\pi})$ is of the order of ${10}^{\ensuremath{-}11}$, which is far below the present experimental upper bound given by the BESIII Collaboration. By further analysis of ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{0}$, the ratio of isospin amplitudes is found, $|{A}_{1/2}/{A}_{3/2}|\ensuremath{\simeq}35$, which supports that the $\mathrm{\ensuremath{\Delta}}I=1/2$ transition enhancement, namely, the $\mathrm{\ensuremath{\Delta}}I=1/2$ rule, could be functional in ${\ensuremath{\eta}}^{\ensuremath{'}}$ weak decays.

Lattice QCD calculations with different staggered valence and sea quarks can be used to improve determinations of quark masses, Gasser-Leutwyler couplings, and other parameters relevant to phenomenology. We calculate the masses and decay constants of flavored pions and kaons through next-to-leading order in staggered-valence, staggered-sea mixed-action chiral perturbation theory. We present the results in the valence-valence and valence-sea sectors, for all tastes. As in unmixed theories, the taste-pseudoscalar, valence-valence mesons are exact Goldstone bosons in the chiral limit, at non-zero lattice spacing. The results reduce correctly when the valence and sea quark actions are identical, connect smoothly to the continuum limit, and provide a way to control light quark and gluon discretization errors in lattice calculations performed with different staggered actions for the valence and sea quarks., Comment: 8 pages, 9 figures, extended with more explanation. arXiv admin note: text overlap with arXiv:1311.6268

Recent ${N}_{f}=2+1$ lattice data for meson-meson scattering in the $p$-wave and with isospin $I=1$ are analyzed using a unitarized model inspired by chiral perturbation theory in the inverse-amplitude formulation for two and three flavors. Chiral extrapolations are performed that postdict phase shifts extracted from experiment quite well. In addition, the low-energy constants are compared to the ones from a recent analysis of ${N}_{f}=2$ lattice QCD simulations to check for the consistency of the hadronic model used here. Some inconsistencies are detected in the fits to ${N}_{f}=2+1$ data, in contrast to the previous analysis of ${N}_{f}=2$ data.

We calculate the form factors of the K→πlν semileptonic decays in three-flavor lattice QCD and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0.11 fm with four pion masses covering 290–540 MeV and a strange quark mass ms close to its physical value. By using the all-to-all quark propagator, we calculate the vector and scalar form factors with high precision. Their dependence on ms and the momentum transfer is studied by using the reweighting technique and the twisted boundary conditions for the quark fields. We compare the results for the semileptonic form factors with ChPT at next-to-next-to-leading order in detail. While many low-energy constants appear at this order, we make use of our data of the light meson electromagnetic form factors in order to control the chiral extrapolation. We determine the normalization of the form factors as f+(0)=0.9636(36)(-35+57) and observe reasonable agreement of their shape with experiment.