text:
\section{Introduction}

Physics beyond the standard model (SM) has been studied extensively in many years.
One of the simplest extensions of SM is to introduce exotic leptons in addition to the SM matters.
They are assumed to have the same quantum numbers under the SM gauge symmetries as the SM leptons.
In general, they have vector-like masses and couple to the SM leptons via Yukawa interactions.

Such extra leptons are often motivated by the excess of the experimental result of the anomalous magnetic moment of the muon (muon $g-2$)~\cite{g-2_bnl2010} against the SM prediction~\cite{g-2_hagiwara2011,g-2_davier2010}.
The discrepancy between the experimental value and its SM prediction is more than 3$\sigma $ levels as $a_{\mu }^{{\rm exp}} - a_{\mu }^{{\rm SM}} = (26.1 \pm 8.0) \cdot 10^{-10}$~\cite{g-2_hagiwara2011} or $(28.7 \pm 8.0) \cdot 10^{-10}$~\cite{g-2_davier2010}, depending on the estimation of the leading hadronic contributions to the theoretical value.
This excess may suggest the existence of new physics in the electroweak scale.
A solution is provided by the models in which the muon Yukawa interaction is generated through the mixing with the extra leptons~\cite{Kannike:2011ng,Dermisek:2013gta}.
The 3$\sigma $ discrepancy is solved when they are relatively light.

The extra leptons are searched for through direct productions at colliders or measurements of the precision observables.
In particular, they can affect the interactions among the SM particles.
When the extra leptons have vector-like masses and couple to the SM leptons, they generally contribute to the SM lepton couplings with the $W$, $Z$, and Higgs bosons (see e.g., Ref.~\cite{Kannike:2011ng}).
These contributions depend on flavors.
Those to the electron couplings have been constrained by the electroweak precision observables (EWPOs)~\cite{ALEPH:2005ab}.
On the other hand, the muon interactions may include sizable corrections, if the extra leptons solve the muon $g-2$ anomaly (see Refs.~\cite{Kannike:2011ng,Dermisek:2013gta}).
Such a flavor non-universality is realized by the Yukawa interactions between the extra leptons and the SM ones.
Thus, the effects of the extra leptons may be probed as non-universalities of the SM lepton interactions.

In this letter, we investigate the precision observables that are sensitive to the lepton non-universality.
In particular, we focus on the flavor universality between the electron and muon interactions with the $W$ and $Z$ bosons.
Currently, they are constrained most severely by EWPOs~\cite{delAguila:2008pw}.
In this letter, we discuss the leptonic pion decay, $\pi \to \ell \nu _{\ell} $, which is also sensitive to the lepton universality~\cite{Kumar:2013qya}.
Its measurement as well as the SM prediction is very accurate and expected to be improved in the near future.
It will be shown that the pion decay can provide a better probe of the non-universality than EWPOs.
Furthermore, it provides a complementary information in determining the lepton couplings with the $W$ bosons.

This letter is organized as follows.
In the first part of this letter, corrections to the lepton couplings with the $W$ and $Z$ bosons are studied in a model-independent way.
The leptonic pion decay is sensitive to the flavor universality of the $W\ell\nu$ couplings as shown in Sec.~\ref{sec:pion}.
We discuss current status and future prospects of the corrections to the $W\ell\nu$ couplings.
On the other hand, the lepton non-universality is already limited by EWPOs.
In particular, they contribute to the theoretical value of the Fermi constant, $G_F$, the $W$ decay width, and the $Z$ couplings with the leptons.
The first two observables are sensitive to the corrections to the $W\ell\nu$ couplings, while the last one restricts those to the $Z\ell\ell$ interactions.
The $Z\ell\ell$ coupling is naively correlated with that of the $W$ boson.
However, the relation  depends on details of the extra lepton models (see e.g., Ref.~\cite{Kannike:2011ng}).
Thus, the contributions to the $W$ and $Z$ bosons are discussed seprately in Sec.~\ref{sec:ewpo}.
We show the result of searching for the electron/muon flavor universality in Sec.~\ref{sec:result}.
It is applied to a model of the extra leptons in Sec.~\ref{sec:model}.
The last section is devoted to the conclusion.

\section{Pion Decay}\label{sec:pion}

First of all, let us define the correction to the $W\ell\nu$ coupling.
The interaction among the $W$ boson, the left-handed charged lepton and the neutrino is
\begin{equation}
 \mathcal{L} = \frac{g}{\sqrt{2}} \Delta g^{W \ell \nu} \,
 \bar{\ell }_L \gamma ^{\mu } \nu _{\ell }\, W^+ _{\mu } + {\rm h.c.},
 \label{eq:lagW}
\end{equation}
where $g$ is the SU(2)$_L$ gauge coupling, and $\ell = e$, $\mu $.
The coefficient $\Delta g^{W \ell \nu}$ is decomposed into the SM value and its correction as
\begin{equation}
 \Delta g^{We\nu _e} = 1 - \delta g^{We\nu _e}, ~~~~
 \Delta g^{W \mu \nu  _{\mu }} = 1 - \delta g^{W \mu \nu  _{\mu }},
 \label{eq:corrW}
\end{equation}
where the unity in the right-hand side corresponds to the SM prediction.
The lepton universality is preserved when $\Delta g^{We\nu _e} = \Delta g^{W \mu \nu  _{\mu }}$.
It is realized in SM due to the hypothesis that the leptons have identical gauge charges and their chiralities mix only via the Higgs interactions.
It can be violated by the new physics contributions.
They are represented by $\delta g^{W \ell \nu}$ $(\ll 1)$.

One of the most sensitive probes of the electron--muon flavor universality is provided by the leptonic decay of the pion, $\pi \to \ell \nu _{\ell }$~\cite{Bryman:2011zz,Kumar:2013qya}.
The decay proceeds via the $W$ boson exchange, and thus, the rate is sensitive to $\delta g^{W \ell \nu}$.
A ratio of the electric and muonic decays, $\pi \to e \nu _e / \mu \nu _{\mu }$, is represented as (cf.~Refs.~\cite{Kinoshita:1959ha,Marciano:1976jc,Cirigliano:2007xi})
\begin{align}
  R_{\pi \to e/\mu } &=
  \frac{\Gamma (\pi \to e \nu_e (\gamma ))}{\Gamma (\pi \to \mu \nu_{\mu } (\gamma ))}
  = \left| \frac{\Delta g^{We\nu _e}}{\Delta g^{W \mu \nu  _{\mu }} } \right| ^2
  \frac{m_e ^2 }{m_{\mu }^2}
  \left( \frac{1- m_e ^2/m_{\pi} ^2}{1- m_{\mu }^2/m_{\pi } ^2} \right) ^2
  (1+\delta R_{\pi \to e/ \mu } )
  \notag \\
  & \simeq
  (1- 2\delta g^{We\nu _e} + 2 \delta g^{W \mu \nu  _{\mu }}  )
  R_{\pi \to e/\mu }^{{\rm SM}},
  \label{eq:deltapi}
\end{align}
where $R_{\pi \to e/\mu }^{{\rm SM}}$ is the SM prediction.
Although radiative corrections $\delta R_{\pi \to e/ \mu }$ could also depend on $\Delta g^{W \ell \nu}$, the effect is sufficiently small and neglected here.
It is stressed that the ratio is not polluted by hadronic uncertainties.
It is calculated with a high accuracy as~\cite{Bryman:2011zz,Kumar:2013qya,Kinoshita:1959ha,Marciano:1976jc,Cirigliano:2007xi}\footnote
{
In Ref.~\cite{Cirigliano:2007ga}, two-loop contributions of $\mathcal{O} (e^2 p^4)$ are calculated within the chiral perturbation theory.
The SM prediction becomes $(1.2352 \pm 0.0001) \times 10^{-4}$, which is more accurate than Eq.~\eqref{eq:decaypi1}.
Here, we adopt a conservative result.
Anyway, the accuracy of the theoretical prediction is much better than that of the experimental result.
}
\begin{equation}
 R_{\pi \to e/\mu }^{{\rm SM}} = (1.2351 \pm 0.0002) \times 10^{-4}.
 \label{eq:decaypi1}
\end{equation}
Thus, the uncertainty of the SM prediction is 0.02\%.

On the other hand, the experimental result of the leptonic pion decay has been reported as~\cite{Beringer:1900zz}
\begin{equation}
 R_{\pi \to e/\mu }^{{\rm exp}} = (1.230 \pm 0.004) \times 10^{-4},
 \label{eq:decaypi2}
\end{equation}
where the results of TRIUMF~\cite{Britton:1992pg} and PSI~\cite{Czapek:1993kc} are averaged by PDG~\cite{Beringer:1900zz}.
The precision of the current experimental result is 0.3\%.
It is larger by an order of magnitude than the theoretical prediction.
There are ongoing experiments that can improve the experimental precision.
Two experiments are in progress at TRIUMF~\cite{AguilarArevalo:2010fv} and PSI~\cite{Pocanic:2003pf}, which are expected to achieve an accuracy of 0.05--0.06\% or better for $R_{\pi \to e/\mu }$.
Also, the PEN experiment~\cite{PEN} have accumulated $>10^7$ events of $\pi \to e\nu$ and $>10^8$ events of $\pi \to \mu \to e$ during 2008--2010.
The analysis of those data is under way to determine $R_{\pi \to e/\mu }$.
The precision goal is about 0.05\%~\cite{Kumar:2013qya}, which is comparable to TRIUMF and PSI.

From the theoretical prediction and the experimental result, the correction to the $W\ell\nu$ coupling is limited in the range:
\begin{equation}
 \delta g^{W \mu \nu  _{\mu }} - \delta g^{We\nu _e} = (-2.0 \pm 1.6) \times 10^{-3}.
 \label{eq:senst1}
\end{equation}
Since the experimental result is consistent with the theoretical prediction, the correction must be suppressed.
If the uncertainty of the experimental value can be reduced to be 0.05\% in future, the correction is determined as
\begin{equation}
 \delta g^{W \mu \nu  _{\mu }} - \delta g^{We\nu _e} = (-2.0 \pm 0.3) \times 10^{-3},
 \label{eq:senst2}
\end{equation}
where the central value is fixed to be that in Eq.~\eqref{eq:senst1}.
Thus, it is found that the sensitivity of the correction to the $W\ell\nu$ coupling is expected to be improved by a factor of 5 or more.
It is also stressed that the pion decay determines $\delta g^{W \mu \nu  _{\mu }}$ {\it minus} $\delta g^{We\nu _e}$.
The relative sign comes from Eq.~\eqref{eq:deltapi}, where the ratio of the decay channels is considered.

Let us comment on the $K$ and $\tau$ decays.
Their leptonic decays are also sensitive to the lepton universality.
Current experimental results of the $K$ decay have reached a precision of 0.4\% at KLOE~\cite{Ambrosino:2009aa} and NA62~\cite{Goudzovski:2010uk}.
The sensitivity is expected to achieve 0.1\% in the near future~\cite{Goudzovski:2010uk}.
The SM prediction is estimated very accurately~\cite{Cirigliano:2007xi}.
The correction to the $W\ell\nu$ coupling is limited as $\delta g^{W \mu \nu  _{\mu }} - \delta g^{We\nu _e} = (2.2 \pm 2.0) \times 10^{-3}$ (cf., \cite{Pich:2013lsa}).
The accuracy is expected to become about $5\times 10^{-4}$ in future.
It is worse by a factor of 2 than Eq.~\eqref{eq:senst2}.
On the other hand, the current precision of the $W\ell\nu$ coupling from the $\tau$ decay is $\delta g^{W \mu \nu  _{\mu }} - \delta g^{We\nu _e} = (-1.8 \pm 1.4) \times 10^{-3}$ \cite{Pich:2013lsa}.
This accuracy is better than that of Eq.~\eqref{eq:senst1}.
The future sensitivity may be expected to be $5\times 10^{-4}$, according to the estimation for the SuperB project~\cite{Bona:2007qt}.
Since the pion decay is most sensitive to the lepton universality in future, we focus on it in this letter.

\section{Electroweak Precision}\label{sec:ewpo}

Measurements of the $Z$ boson decays have been used to test SM and constrain the new physics.
This is often called the electroweak precision test (EWPT).
In particular, contributions to the SM lepton couplings with the $W$ and $Z$ bosons are constrained.
When the lepton couplings are modified, there are mainly three types of the contributions to EWPOs.
The couplings to the $Z$ boson are constrained by the measurements of the $Z$ boson decaying to leptons.
Those to the $W$ boson contribute to the determination of the Fermi constant $G_F$ through
the measurements of the lifetime of the muon.
Also, they change the decay width of the $W$ boson.
In this section, we study these observables to restrict the lepton flavor universality.

Let us first focus on the $W\ell\nu$ coupling, which is directly correlated with the leptonic pion decay.
Since the Fermi constant $G_F$ is determined by the lifetime of the muon, it is affected by corrections to the $W e \nu _e$ and $W \mu \nu _{\mu }$ couplings.
The contribution to $G_F$ is represented as
\begin{equation}
 G_F = G^{\text{SM }}_F +  \frac{g^2}{4\sqrt{2} m_W^2} \Delta \bar{\delta } _G,
\end{equation}
where $G^{\text{SM}}_F$ is the SM prediction.
Effects of the new physics are denoted by $\Delta \bar{\delta } _G$.
When there are corrections to the $W\ell\nu$ coupling \eqref{eq:corrW}, it becomes
\begin{align}
 \Delta \bar{\delta } _G = -( \delta g^{We\nu _e} +  \delta g^{W \mu \nu  _{\mu }}) .
 \label{eq:corrGF}
\end{align}
It is noticed that $\delta g^{W \mu \nu  _{\mu }}$ has the same sign as $\delta g^{We\nu _e}$.
This is contrasted to the decays of the pion (or $K$, $\tau$), as shown in Eq.~\eqref{eq:deltapi}.
The correction to the Fermi constant affects the $Zff$ couplings, and the mass and decay width of the $W$ boson.

The corrections to the $W\ell\nu$ coupling also contributes to the decay width of the $W$ boson, $\Gamma_W$, through the decay channel, $W \to \ell\nu_\ell$.
The correction to $\Gamma_W$ is represented as
\begin{equation}
 \Gamma_W = \Gamma_W^{\text{SM }} + \frac{G_F m_W^3}{6\sqrt{2}\pi} \Delta \bar\delta_{\Gamma W},
\end{equation}
where $\Gamma_W^{\text{SM }}$ is the SM prediction.
The corrections to the $W\ell\nu$ coupling \eqref{eq:corrW} induce $\Delta \bar\delta_{\Gamma W}$ as
\begin{align}
 \Delta \bar\delta_{\Gamma W} = - 2( \delta g^{We\nu _e} +  \delta g^{W \mu \nu  _{\mu }}) .
 \label{eq:corrGW}
\end{align}
We checked that this contribution is subdominant in EWPT compared to Eq.~\eqref{eq:corrGF}.

Next, let us consider the interaction between the $Z$ boson and the charged leptons.
The effective $Zff$ coupling, $g^{Z\ell\ell}_{L, R}$, is defined as
\begin{equation}
  \mathcal{L} =
  \frac{e}{s_W c_W}
  \bar{\ell }
  \left[ g^{Z\ell\ell}_L \gamma ^{\mu } P_L + g^{Z\ell\ell}_R \gamma ^{\mu } P_R \right]
  \ell\, Z_{\mu } + {\rm h.c.},
\end{equation}
where $e = \sqrt{4\pi\alpha}$, $s_W = \sin \theta _W$ and $c_W = \cos \theta _W$ with the Weinberg angle $\theta _W$, and $P_{L(R)}$ is the left- (right-) handed projection operator.
The $Z$ boson decay observables are affected by the new physics through these effective couplings as well as $G_F$.

In this letter, we focus on corrections to the left-handed interaction, $g^{Z\ell\ell}_L$.
It is decomposed into the SM value and its correction as
\begin{equation}
 g^{Zee}_L = \left.g^{Zee}_L\right|_{\rm SM} + \delta g^{Zee}_L, ~~~~
 g^{Z\mu\mu}_L = \left.g^{Z\mu\mu}_L\right|_{\rm SM} + \delta g^{Z\mu\mu}_L,
 \label{eq:corrZLL}
\end{equation}
where $\left.g^{Z\ell\ell}_L\right|_{\rm SM}$ is the SM prediction.
The new physics contribution $\delta g^{Z\ell\ell}_L$ is related to the $W\ell\nu$ coupling \eqref{eq:corrW}.
However, details depend on new physics models (see e.g., Ref.~\cite{Kannike:2011ng}).
On the other hand, $\delta g^{Z\ell\ell}_R$ is independent of the left-handed coupling.
For instance, in the extra lepton model which will be discussed later, $\delta g^{W \ell \nu} =  \delta g^{Z\ell\ell}_L$ is approximately satisfied, while the contributions to $\delta g^{Z\ell\ell}_R$ can be suppressed.

The lepton flavor universality is studied by EWPT via the above contributions. In this letter, the following observables are considered:
\begin{align}
&\text{line-shape and FB asymmetry : }
 \Gamma _Z,~\sigma _h^0, ~R_f, ~A^f_{\text{FB}} ~(f= e, \mu , \tau ), \notag \\
& \tau ~\text{polarization : }
A_{\tau },~A_e, \notag \\
& b ~\text{and}~ c ~\text{quarks : }
R_f, ~A^f_{\text{FB}}, A_f ~(f=b, c), \notag \\
&\text{SLD results : }
A_f ~(f= e,\mu ,\tau) , \notag \\
& W~\text{mass and width : }
m_W, ~\Gamma _W. \label{eq:obs}
\end{align}
The experimental results and their correlation coefficients are found in Ref.~\cite{ALEPH:2005ab}, while the measurements of the mass and width of the $W$ boson are updated by Tevatron~\cite{Group:2012gb}.
Since the correlation coefficients of the $W$ boson observables are not available, we simply assume that they are independent of each other and the other observables.

The experimental values are compared with the theoretical predictions.
The latter includes the contributions from SM and the new physics.
Because of the high precision of the experimental values, it is important to include higher-order corrections in the SM calculations.
Recently, the full EW two-loop contributions of the closed fermion loops are completed~\cite{Awramik:2003rn, Awramik:2006uz, Awramik:2008gi, Freitas:2013dpa, Freitas:2014hra}.
We use the fitting formulae of EWPOs obtained in Ref.~\cite{Freitas:2014hra}, which also include other radiative corrections.
On the other hand, the new physics contributes to EWPOs through Eqs.~\eqref{eq:corrGF}, \eqref{eq:corrGW} and \eqref{eq:corrZLL}.
Eqs.~\eqref{eq:corrGF} and \eqref{eq:corrZLL} are taken into account by using the fitting formulae explored in Ref.~\cite{Cho:1999km, Cho:2011rk}, while Eq.~\eqref{eq:corrGW} is included by modifying them.
In the theoretical calculations, the following SM inputs are used~\cite{Beringer:1900zz,g-2_davier2010}:
\begin{align}
&m_t = 173.07 \pm 0.52 \pm 0.72, \\
&m_H = 125.9 \pm 0.4, \\
&\alpha _s(m_Z) = 0.1185 \pm 0.0006, \\
&\Delta \alpha ^{(5)}_{\text{had}}(m_Z) = 0.02757 \pm 0.00010.
\end{align}
In addition, the $Z$ boson mass $m_Z$, the Fermi constant $G_F$ and the fine structure constant $\alpha $ are $m_Z = 91.1876 \pm 0.0021$, $G_F = 1.1663787(6) \times 10^{-5}$ and $\alpha = 1/137.035999074$, respectively \cite{Beringer:1900zz}.
In the analysis, we take $m_Z$, $G_F$ and $\alpha$ as constant values, since their uncertainties are sufficiently small.
In order to limit the lepton non-universality, we perform the global $\chi ^2$ fit of the above 21 observables.
The result is shown in the next section.

\section{Result}\label{sec:result}

In this section, current bounds and future prospects of the lepton universality are discussed.
Those of the pion decay are obtained in Eqs.~\eqref{eq:decaypi1} and \eqref{eq:decaypi2}.
In Fig.~\ref{fig:constraint}, the current bound and future sensitivity are displayed by the orange and red regions, respectively.
The axes are $\delta g^\ell_L \equiv \delta g^{W \ell \nu}$ with $\ell = e, \mu$.
The SM prediction corresponds to $\delta g^\ell_L = 0$.
Here, 95\% CL regions are shown.
The central value of the future sensitivity is set to be that of the current result \eqref{eq:senst1}.
It is found that, for a given $\delta g^{We\nu _e}$, the sensitivity is expected to be improved by a factor of 5 or more in the future.

On the other hand, the current limit at 95\% CL from EWPOs (Sec.~\ref{sec:ewpo}) is shown by the blue region.
Here, only $\delta g^{W \ell \nu}$ is considered, and $g^{Z\ell\ell}_L$ is assumed to be zero.
Thus, the contributions to $G_F$ \eqref{eq:corrGF} and $\Gamma_W$ \eqref{eq:corrGW} are taken into account.
The limit is mainly determined by the former.
The uncertainty is smaller than the current result of the pion decay (also those from $K$ and $\tau$).
However, it is found that the pion decay can have a better sensitivity to probe the lepton universality in the future, as observed by comparing the red and blue bands.

Furthermore, it is stressed that, in the figure, the slope of the band is different between the pion decay and EWPOs.
The former depends on $\delta g^{W \mu \nu  _{\mu }} - \delta g^{We\nu _e}$, while the latter on $\delta g^{W \mu \nu  _{\mu }} + \delta g^{We\nu _e}$.
Obviously, the couplings cannot be determined separately if we use only one measurement.
However, if we combine these two results, it is possible to determine $\delta g^{W \mu \nu  _{\mu }}$ and $\delta g^{We\nu _e}$ individually without assuming new physics models.
The corrections are restricted at 95\% CL in the range:
\begin{align}
-1.1 \times 10^{-3} < \delta g^{We\nu _e} < 3.5 \times 10^{-3}, ~~~~~
-3.1 \times 10^{-3} < \delta g^{W \mu \nu _{\mu }} < 1.5 \times 10^{-3}.
\end{align}
The error is dominated by the experimental uncertainty of the pion decay.
In future, the pion decay rate will be measured accurately.
The error is expected to be reduced by a factor of 2, where the experimental uncertainty of EWPOs dominates the error.
Hence, the pion decay can play a complementary role in determining the contributions to the electron and muon interactions with the $W$ boson.

Finally, let us consider a case when $\delta g^{Z \ell\ell}_L = \delta g^{W \ell \nu _{\ell }} \equiv \delta g^\ell_L$ is satisfied.
This corresponds to the extra lepton model in the next section.
When the lepton coupling to the $Z$ boson is tightly correlated with that to the $W$ boson, EWPT constrains $g^{Z ee}_L$ and $g^{Z \mu\mu}_L$ individually.
In Fig.~\ref{fig:constraint}, the 95\% CL limit from EWPOs is shown by the circle with the black dashed line.
Since the experimental result of the $Z \to e^+ e^-$ decay is accurate, the constraint on $ \delta g^{W e \nu _e }$ is tightened compared to the blue region.
However, the EWPT accuracy of $\delta g^{Z \mu\mu}_L$ is comparable to that of $\delta g^{W \mu  \nu _{\mu } }$, and thus, the limit does not change so much for the muon couplings.
It is found that the EWPT limit on the lepton non-universal coupling with the $W$ and $Z$ boson is currently more severe than the bound from the pion decay.
However, the lepton non-universal coupling, especially of the muon, can be probed more sensitively by the pion decay in the near future.

\vspace*{5mm}
\begin{figure}[htbp]
\begin{center}
 \includegraphics[width=8cm]{fig.eps}
 \end{center}
 \caption{Constraint and sensitivity of the contribution to the lepton non-universal coupling to the $W$ (and $Z$) boson.
 The axes are $\delta g^\ell_L \equiv \delta g^{W \ell \nu}$ with $\ell = e, \mu$.
 The orange and blue regions are currently allowed at 95\% CL by $R_{\pi \to e/\mu }$ and EWPOs, respectively.
 The red region is a future sensitivity from $R_{\pi \to e/\mu }$ (Eq.~\eqref{eq:senst2}), where the central value is chosen to be the same as the current result (Eq.~\eqref{eq:senst1}).
 If $\delta g^{Z \ell\ell}_L = \delta g^{W \ell \nu _{\ell }} \equiv \delta g^\ell_L$ is satisfied by the new physics model, EWPOs provide a more tight limit.
 The region in the circle with the black dashed line is allowed at 95\% CL.}
 \label{fig:constraint}
\end{figure}

\section{Extra Lepton Model} \label{sec:model}

Let us apply the result in the previous section to an extra lepton model~\cite{Kannike:2011ng,Dermisek:2013gta}.
We introduce SU(2)$_L$ vector-like doublets $(L_L \oplus L_R)$ and singlets $(E_L \oplus E_R)$, which are coupled only to the muon.
It is assumed that the $(L_L \oplus L_R)$ and $(E_L \oplus E_R)$ have the same quantum numbers as the left- and right-handed SM leptons, respectively.
Their interaction and mass terms are given as
\begin{align}
 \mathcal{L} =
 &
 - \bar{\ell}_{L} Y_{\mu } \ell_{R} H
 - \bar{\ell}_{L} \lambda _E E_R H
 - \bar{L}_L \lambda _L \ell_{R} H
 - \lambda  \bar{L}_L E_R H
 - \bar{\lambda } H^{\dagger }\bar{E}_L L_R \notag \\
 &
 - M_L \bar{L}_L L_R
 - M_E \bar{E}_L E_R + \rm{h.c.},
\end{align}
where $\ell$ denotes the SM lepton, and $H$ is the Higgs boson.
The terms in the first line represent the Yukawa interactions, while those in the second line are vector-like mass terms.
The components of the SU(2)$_L$ doublets and singlets are represented as
\begin{equation}
 \ell _{L} = \begin{pmatrix}
                  \nu _{\mu } \\
                  \mu _{L} \\
             \end{pmatrix},~~~
 \ell_R = \mu _R,~~~
 L_{L,R} =  \begin{pmatrix}
                  L^0 _{L,R} \\
                  L^- _{L,R} \\
             \end{pmatrix},~~~
 H = \begin{pmatrix}
            0 \\
            v + \frac{h}{\sqrt{2}} \\
       \end{pmatrix},
\end{equation}
where $v \simeq 174\,{\rm GeV}$ is the vacuum expectation value of the Higgs field.
After the electroweak symmetry is broken, the mass term of the charged leptons becomes
\begin{equation}
 -\mathcal{L}_{\rm mass} =
 (\bar{\mu }_{L}, \bar{L}^-_{L},\bar{E}_L) \mathcal{M}_{\mu } \begin{pmatrix} \mu _{R} \\ L^-_{R} \\ E_R  \\ \end{pmatrix} + \rm{h.c.},
\end{equation}
where $\mathcal{M}_{\mu}$ is the $3 \times 3$ mass matrix for the muon and the vector-like leptons,
\begin{equation}
 \mathcal{M}_{\mu} =
 \begin{pmatrix}
    Y_{\mu } v & 0 & \lambda _E v \\
    \lambda _L v & M_L & \lambda v \\
    0 & \bar{\lambda } v & M_E \\
 \end{pmatrix}.
 \label{eq:modelY}
\end{equation}
This matrix is diagonalized by unitary matrices $U_{L,R}$ as
\begin{equation}
  U_L ^{\dagger} \mathcal{M}_{\mu} U_R = \text{diag}(m_{\mu }, m_{\ell_2} ,m_{\ell_3}).
  \label{eq:mixmat}
\end{equation}
Here, $m_{\mu }$ is the muon mass, and $m_{\ell_{2,3}}$ are the heavy lepton masses in the mass eigenstate basis.

In this letter, we study the lepton non-universal coupling to the $W$ boson and the left-handed one to the $Z$ boson.
They are determined by $U_L$.
In the limit of $\lambda _E v$, $\lambda _L v$, $\bar{\lambda } v$, $\lambda v  \ll M_E$, $M_L$, it is approximately written as
\begin{align}
 &U_L =
 \begin{pmatrix}
     1 - v^2 \frac{\lambda _E^2}{2M_E^2}
   & - v^2
     \left(
       \frac{\lambda _E}{M_L}
       \frac{\bar{\lambda } M_E + \lambda M_L}{M_E^2 - M_L^2 } -
       \frac{Y_{\mu }\lambda _L}{M_L^2}
     \right)
   & v \frac{\lambda _E}{M_E} \\
     - v^2 \frac{\bar{\lambda } \lambda _E M_L - Y_{\mu } \lambda _L M_E}{M_L^2 M_E }
   & 1 - v^2 \frac{(\lambda M_E + \bar{\lambda } M_L )^2}{2(M_E^2 - M_L^2 )^2}
   & v \frac{\lambda M_E + \bar{\lambda } M_L }{M_E^2 - M_L^2} \\
     - v \frac{\lambda _E}{M_E}
   & - v \frac{\lambda M_E + \bar{\lambda } M_L }{M_E^2 - M_L^2}
   & 1 - v^2 \frac{\lambda _E^2}{2M_E^2}
       - v^2 \frac{(\lambda M_E + \bar{\lambda } M_L )^2}{2(M_E^2 - M_L^2 )^2} \\
 \end{pmatrix}.
 \label{eq:appmat}
\end{align}
After the diagonalization, the muon couplings to the $W$ and $Z$ bosons are modified.\footnote{The Higgs coupling is also modified from the SM prediction~\cite{Kannike:2011ng}.}
The corrections become
\begin{align}
\delta g^{W \mu \nu _{\mu }}
&= - \left[ (U_L)_{11} -1 \right]
\simeq \frac{1}{2} \left( \frac{\lambda _E v}{M_E} \right) ^2, \notag \\
\delta g^{Z \mu \mu}_L
&= \frac{1}{2} (U^{\dagger }_L)_{13}(U_L)_{31}
\simeq \frac{1}{2} \left( \frac{\lambda _E v}{M_E} \right) ^2.
\label{eq:corrEL}
\end{align}
It is noticed that both are determined by $(\lambda _E v / M_E)^2$, and
$\delta g^{W \mu \nu _{\mu}} = \delta g^{Z\mu\mu}_L$ is satisfied approximately.\footnote
{
The right-handed coupling $\delta g^{Z\mu\mu}_R$ also receives a correction, $\sim (\lambda_L v/M_L )^2$.
It is suppressed when $M_L$ is larger or $\lambda_L$ is small.
We neglects its contribution to EWPOs, for simplicity.
}
On the other hand, there is no correction to the electron coupling with the SM bosons, since the extra leptons do not couple to the electron in Eq.~\eqref{eq:modelY}.

The result in the previous section is applied to Eq.~\eqref{eq:corrEL}.
From Fig.~\ref{fig:constraint}, the constraint on $(\lambda _E v / M_E)^2$ is derived.
Currently, the most tight limit is imposed by EWPT.
The bound is estimated at 95\% CL as\footnote
{
The contribution to the muon $g-2$ depends also on other parameters in the extra lepton models.
See Refs.~\cite{Kannike:2011ng,Dermisek:2013gta} for the explicit formula.
}
\begin{align}
  - 1 \times 10^{-3} \lesssim
  \left( \lambda _E v / M_E \right )^2 \lesssim
  3 \times 10^{-3}.
\end{align}
The result is consistent with zero, i.e., the SM prediction.
This is stronger than the limit from the pion decay (also from the $K$ and $\tau$ decays).
In the near future, the pion decay can have a better sensitivity to the coupling.
The error of $(\lambda _E v / M_E)^2$ will be reduced to be about $1 \times 10^{-3}$ at 95\% CL, which is better by a factor of 2 than EWPT.
Thus, the search for the lepton non-universality with the leptonic pion decay can compete with the limit with EWPT.

Finally, let us touch on other extra lepton models.
If the contribution to the muon coupling to the $Z$ boson is suppressed with keeping those to the $W$ boson sizable, the pion decay not only has a better sensitivity, but also provides a complimentary information in determining the corrections to the $W\ell\nu$ coupling, as mentioned in the previous section.

\section{Conclusion}

In this letter, we discussed the lepton flavor non-universal coupling to the $W$ and $Z$ bosons.
Here, the left-handed lepton interactions are considered.
The electron/muon coupling to the $W$ boson is currently constrained by EWPT.
We showed that the ratio of the leptonic pion decay, $R_{\pi \to e/\mu }$, is expected to be more sensitive to the non-universality in the near future.
Furthermore, it was found that the ratio is complimentary to determine the electron and muon non-universal couplings individually without assuming new physics models.

We applied the result to an exotic lepton model.
In the model, the left-handed muon coupling with the $Z$ boson is tightly correlated with that with the $W$ boson, and the EWPT limit is severe.
It was discussed that the pion decay will be able to compete with or be better than the EWPT result.
Thus, the measurement of the leptonic pion decay is expected to play an important role in searching for effects of the exotic lepton models.

\section*{Acknowledgements}
This work was supported by JSPS KAKENHI Grant No.~23740172 (M.E.) and 25-10486 (T.Y.).
The work of T.Y. is supported by a JSPS Research Fellowship for Young Scientists
and by an Advanced Leading Graduate Course for Photon Science grant.

\providecommand{\href}[2]{#2}
\begingroup\raggedright

redpajama_set_name: RedPajamaArXiv


text:
Four more employment precincts to drive jobs, boost education and create innovation
Home-grown IT giant Atlassian is set to become an anchor tenant at Sydney's Sydney Innovation and Technology Precinct located at Central-Eveleigh with NSW Premier Gladys Berejiklian today announcing initiatives across four employment precincts.
Ms Berejiklian and Treasurer Dominic Perrottet joined Atlassian Co-CEO Scott Farquhar to announce Atlassian and the NSW Government have reached an agreement in principle for the tech leader to create a new home for their Sydney headquarters near Central Station.
"The Sydney Innovation and Technology Precinct will become the digital destination for all of Australia with thousands of people working and learning, and I am delighted Atlassian will be part of this future," Ms Berejiklian said.
"We have a record low unemployment rate of 3.9 percent in NSW but we will not rest on our laurels. We will create 250,000 new jobs across the next four years, and these employment precincts will play an important role contributing to that total."
Ms Berejiklian revealed key initiatives in three other precincts:
A statement of intent has been signed with three universities to create the Liverpool Health and Innovation Precinct based around the $740 million redeveloped Liverpool Hospital. This precinct will be a partnership between the South Western Sydney Local Health District, University of New South Wales, University of Wollongong and Western Sydney University and the Ingham Institute for Applied Medical Science.
$12.5 million in funding to develop a Nuclear Medicine and Technology Hub in partnership with the Australian Nuclear Science Technology Organisation in Lucas Heights in Sydney's south which will create up to 5000 jobs.
The creation of an integrated Central Coast Education and Employment Precinct around a revitalised Gosford CBD with increased education and job opportunities.
"These precincts will bring together universities, major hospitals, industry leaders and startups to deliver more job opportunities across Sydney and the Central Coast," Ms Berejiklian said.
"We want Western and South Western Sydney and the Central Coast to have the best jobs and the best education opportunities, and these new precincts will deliver that."
Treasurer Dominic Perrottet said creating the environment for innovation and entrepreneurship would provide opportunity for the next generation.
"It's vital we take advantage of the strong economic position NSW is in to create opportunity for the future and keep growing NSW," Mr Perrottet said.
"We have Australia's most diverse economy, and one of the great strengths of NSW is our ability to innovate and develop new businesses both for today but also for the next generation."
These four precincts are in addition to six other major precincts that the Government is delivering across NSW:
Western Sydney Airport Aerospace and Defence Industries Precinct.
Westmead Health and Education Precinct.
Randwick Health and Education Precinct.
Williamtown Defence Aerospace and Aviation Precinct.
Parkes Special Activation Precinct.
Wagga Wagga Special Activation Precinct.

redpajama_set_name: RedPajamaCommonCrawl


NK vs CD: The fourth match of Super Smash 2018-19 is between Northern Knights and Central Districts which is scheduled today. The match will start at 6:00 AM GMT, 11:30 AM IST on 27th December 2018. The venue of the match is at Bay Oval, Mount Maunganui.
This is the first match for Central Districts. Northern Knights have won their first match in the series and it is their second match. Hence in today's match NK vs CD, it is predicted that Northern Knights will win against Central Districts.


text:
Die Liste gibt den Fortschreibungsstand vom 15. April 2020 wieder und umfasst 25 Baudenkmäler.

Baudenkmäler nach Ortsteilen

Oberickelsheim

|}

Geißlingen

|}

Rodheim

|}

Ehemalige Baudenkmäler

|}

Siehe auch
 Liste der Bodendenkmäler in Oberickelsheim

Einzelnachweise

Anmerkungen

Literatur

Weblinks

!
Oberickelsheim
Baudenkmaler Oberickelsheim

redpajama_set_name: RedPajamaWikipedia


text:
Flaw Leaves Online Citibank Customers Vulnerable
By: Dennis Fisher | January 08, 2002
A security vulnerability in an online payment site run by Citibank may be leaving sensitive customer data exposed and leaving the door wide open for crackers.
The flaw in Citibanks c2it.com site enables any logged-in user of the site to access other users accounts and transfer cash, view credit-card and bank data, and even cover his tracks when hes finished.
The vulnerability, known as cross-site scripting, is a common one and has been well-publicized for nearly two years. It involves a flaw in the way dynamically generated Web pages are created that enables an attacker to enter malicious code into form fields and retrieve data from remote Web servers.
The c2it vulnerability was discovered by Dave deVitry, a security researcher who focuses on cross-site scripting problems. He first notified Citibank of the problem in September and published an advisory about C2it to the Bugtraq mailing list Monday.
He said the flaw is relatively simple to exploit—and simpler to fix.
"Its easy to exploit from a technology perspective," deVitry said. "One only really needs to know Javascript. To pull off a heist seamlessly, youd have to have [a secure Web server] somewhere, but still, [its] easy."
In a longer version of the advisory that is posted on his Web site, deVitry cites two separate attacks that are possible and provides sample scripts for accomplishing them. He also describes how an attacker could potentially mask his actions on c2it by corrupting the sites transaction history page.
C2it enables users to send electronic payments via accounts that are attached to a credit card or bank account. Its privacy policy has a long section concerning the sites security and the measures taken to prevent compromises of customer data.
"Security and privacy are the pillars upon which c2it service was built, and we are proud of the innovations we have made to protect members data and personal identities throughout every component of the c2it service," the statement reads in part.
deVitry recommends that Citibank shut down c2it.com until the issue is fixed and warns users to steer clear of the service until the vulnerability is remedied.
He also said that although Citibank on Tuesday implemented a partial fix for the problem, the companys slow response to such a serious issue is troubling.
"What Im most surprised at is their lack of an aggressive fix for this," deVitry said. "Of course, they never should have had these holes in the first place. If they missed this simple security hole, imagine what else they could have missed."
Attempts to reach Citigroup Inc.s Citibank unit for comment were unsuccessful.
Previous Fixes for Cracks in Windows
Next Study: Hold Vendors Liable for Security Breaches


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redpajama_set_name: RedPajamaGithub


Mrs Micklewright is the teacher in our class who works closely with Mrs Full, our targetted learning support. Planning time in year 1 is covered by Mrs Kellman and Mrs Hattersley who teach us French, PE and Music each week.
Year One begins our journey into Key Stage One, so it's a very important year. We do lots of hands on leaning through our inspiring and creative curriculum. We are a busy class who are enthusiastic about learning and enjoy new challenges. We are always Safe, Ready and Respectful.
Our morning sessions concentrate on building English, Phonics and Maths skills. Our afternoon sessions are dedicated to the remainder of the curriculum, which is usually delivered through a topic, changed each half term.
Read with us every day! Ask us questions about our books to make sure we understand everything we're reading.
Encourage us to write our common exception words in our blue books every week. Putting these words into sentences will help us to understand what we're writing and make our writing better in school.
Let us play Doodle Maths! Completing our '5 a day' will help us in our quest to become super mathematicians!
Mrs Micklewright will be on the playground every morning, so please see her then if you have any concerns or questions about our learning. Alternatively, please book an appointment with reception.


As a leader of a small or medium-sized business, there's no doubt you're wearing many hats. You're likely involved in every aspect of your business - including the technology that runs it - and you're trying to stretch your internal resources to the max.
However, we all know that as a small business leader, your time is best spent focused on running your business…not on managing technology. Leave that to a partner you can trust - one that can help you address your immediate technology needs while helping you achieve your long term goals; one that understands the importance of delivering cost-effective solutions and building long-term, personal relationships.


BENICIO DEL TORO as the brutal enforcer Lado in "Savages." ©Universal Studios.
(L to R) Chon (TAYLOR KITSCH) and his closest friend, Ben (AARON JOHNSON), ready for war in "Savages." ©Universal Studios.
(L to R) Ben (AARON JOHNSON), DEA agent Dennis (JOHN TRAVOLTA) and Chon (TAYLOR KITSCH) in "Savages." ©Universal Studios.
Brutal enforcer Lado (BENICIO DEL TORO) and his boss, Elena (SALMA HAYEK), in "Savages." ©Universal Studios.
(L to R) Chon (TAYLOR KITSCH), O (BLAKE LIVELY) and Ben (AARON JOHNSON) in "Savages." ©Universal Studios.


text:
Michigan legislature committees subpoena election evidence from Detroit and nearby suburb
"Election integrity should not be a partisan issue, this information needs to be preserved," State Senator Ruth Johnson said
Updated: December 16, 2020 - 8:02pm
Subpoena to Detroit City Clerk.pdf
Subpoena to Livonia City Clerk.pdf
Concerned about possible election evidence being destroyed, members of a joint session of the Michigan Legislature's House and Senate oversight committees on Tuesday voted to issue subpoenas to Detroit and the nearby suburb of Livonia demanding they surrender hard drives, emails, absentee voter counting board laptops and other election-related materials.
One Senate Democrat reportedly joined his Republican colleagues in supporting the subpoenas.
A Nov. 28 order memo from the State Bureau of Elections had followed the same protocol as prior elections and ordered the deletion by November 30 of "E-Pollbook laptops and flash drives … unless a petition for recount has been filed and the recount has not been completed, a post-election audit is planned but has not yet been completed, or the deletion of the data has been stayed by an order of the court or the Secretary of State."
Tracy Wimmer, director of Media Relations for Michigan Secretary of State Jocelyn Benson, a Democrat, told Just the News in a statement Thursday that she rejected Republicans' concerns about the deletion memo.
"The Bureau of Elections memo sent to clerks is the same memo that has been sent to clerks for years, including under the administration of now state senator Ruth Johnson," Wimmer said. "Republican House and Senate legal counsel were provided this information days ago. The fact that members of their party is choosing to ignore these truths in a press release demonstrates they have no interest in preserving the integrity of our elections or democracy."
Michigan State Senator Ruth Johnson--the Republican cited by Wimmer who also supports the subpoena effort, told Just the News she had previously signed the same deletion order while she was secretary of state but the unusual nature of the 2020 election meant circumstances had changed.
"Election integrity should not be a partisan issue, this information needs to be preserved while there are ongoing lawsuits, audits, and Oversight committee review of the November election," Johnson said. "Only after these activities are concluded should this information be deleted for data privacy reasons."
"All information and records need to be preserved to ensure proper review and oversight of the election can occur," Michigan State Senator Aric Nesbitt, a Republican, told Just the News in a statement. "There must be complete confidence in our election security and vote counting process."
Read the subpoenas to the two Michigan cities below.
Reporter Daniel Payne contributed to this report.


Some say life is not a sprint but a marathon. We say, forget that! We want to see as many places and hunt as many creatures as we can and that takes speed! Part of the Badlands Ultralight Series, the Sprint features our latest and greatest Ripstop material, Badlands Airtrack™ Suspension and tons of organization. Sorry, you can no longer blame your lack of speed on your hunting pack.


What is the next step for moving forward on the intensification of the Williamsville Main Street plan and what will you do to demonstrate growing Kingston as a livable, sustainable city during your 4 years on Council?
Intensification of the Princess Street corridor should be an integral part of our housing strategy. I believe in and support the Williamsville Main Street plan, and will support proposals to redevelop underutilized properties along Princess Street. While I support intensification, I believe that a careful approach must be taken so that we create a pedestrian-friendly streetscape. That could include greater setbacks from the sidewalk, stepping the building back every few stories to minimize the scale of taller structures, including ground-level retail spaces, and including green space. Combined with intensification, a pedestrian friendly streetscape will also be beneficial to area businesses, with increased foot traffic and a larger customer base.
Pedestrian friendly, walkable, transit supportive communities are sustainable and livable communities. I believe in the development of neighbourhoods with a mixture of low, medium, and high density residential and neighbourhood commercial land uses, plus adequate green space and recreational opportunities. Mixed use zoning and combining medium and high density residential with single family homes allows residents to walk to amenities, provides the density required to support transit service, and is a more efficient way to use available land.
2018 rental housing vacancy rate is 0.7%, the lowest in Canada. What steps will you take to increase the supply of housing?
This really ties in with the first question, and part of the solution to increasing our rental housing stock is to increase density. Higher density buildings can potentially offer lower rents since the fixed costs – one of the big ones being land acquisition – can be spread across more units. In Williamsville specifically, higher density residential along the Princess Street corridor will alleviate pressure on the existing housing stock in the established neighbourhoods. There is an increasing demand for student housing due to increased enrollment at Queen's University and the proposed student-oriented developments will help prevent more single-family homes and smaller apartment buildings in the neighbourhood from being turned into student rentals.
I'm also a supporter of bylaw amendments to permit secondary suites of all types throughout the City. That could include basement apartments, detached apartment units (Garden homes), or apartments over detached garages/carriage houses. Consideration must be taken to ensure that proposed secondary suites comply with the Building Code and Property Standards, that adequate off-street parking is available, and that proposed detached structures don't adversely affect the character of established neighbourhoods. Secondary suites in private homes are typically less expensive than other types of rental accommodation, potentially filling an important gap in the market. The possibility of earning income from a secondary suite can also make homeownership a reality for more Kingstonians, especially with changes to CMHC rules allowing secondary suite income to be considered on a mortgage application.
Social housing is another concern of many, with a years-long waiting list for units. This is unacceptable. We have a vast amount of vacant land in Kingston owned by the Provincial and Federal Governments – land that is unused and untaxed, yet taxpayer money is spent on maintenance and upkeep. The potential to acquire some of that land for the construction of additional social housing units should be explored, as acquiring the land inexpensively from another level of Government reduces cost and allows us to construct more units for the same amount of money.
What is the next step for moving forward on the Kingston airport expansion and what will you do to expand air service during your 4 years on Council? For example, which is a higher priority, another Canadian airline to compete with Air Canada or an American airline to access new US markets?
Another Canadian airline (Porter?) would be a more realistic first option to pursue. The challenge with trying to attract an American airline will likely be competition from the airports in Watertown, Syracuse, and Ogdensburg, NY. Watertown is only an hour away – Can we be competitive enough on price and service to bring enough passengers through the Kingston airport?
What is the next step for moving forward on the intensification of JCB corridor expansion and new bridge and its linkage to the Third Crossing….and what will you do to encourage that growth during your 4 years on Council?
The Third Crossing and the increased number of commuters passing through the area is going to be a great opportunity for new and existing businesses to grow. In addition to providing the traffic necessary to support intensification and new business growth along JCB, a revitalization of Montreal Street could also take place, being an important North/South route that many commuters crossing the new bridge will use to get downtown.
Existing developments on JCB are very automobile-centric being an industrial and formerly rural area. If the opportunity for a new residential development arises, I would like to see a mixed use, pedestrian and transit friendly development. Development of new retail and services to support new residential in the area must also be encouraged.
I'm also supportive of constructing the Leroy Grant Drive extension if traffic volume and patterns warrant it once the Third Crossing is built. This will help avoid downtown-bound traffic from cutting through the established Kingscourt and Williamsville neighbourhoods.
What is your solution to the lack of parking inventory in downtown Kingston? What is your financial plan for creating new parking spaces to add to the City's inventory to promote local retail?
In situations where surface parking is removed to support new development, negotiations should always take place with developers to provide an adequate number of public parking spaces. Ideally this should happen with no or minimal cost to the City.
Surface parking alone won't be able to solve our inventory problem, especially since not every surface parking space removed due to development will be replaced. A new parking structure is something that will have to be seriously considered, possibly on the Byron or McKee lots on Queen Street. The cost to build a new multi-level parking structure is substantial and will need to be considered when assessing development charges and when adjusting parking rates.
Reducing demand for parking downtown is the other piece of the puzzle. Further improvements to Kingston Transit including the development of Park and Ride lots in other areas of the City and the development of safe cycling infrastructure (including secure bicycle parking!) can reduce the demand for parking downtown, while enabling residents to make more sustainable commuting choices. These are lower cost options compared to building a new multi-level parking structure, and could delay that expenditure or reduce the size needed.
Prev PostMemorial Centre Revitalization – Let's Finish the Job!
Build Up – Not Out!
Memorial Centre Revitalization – Let's Finish the Job!
Copyright © 2019 Andre Imbeault.


text:
Ribble, families meet to push rare diseases legislation
Katherine Lymn
Families of kids like Zoe and Jason, who both have extremely rare chromosome disorders, often resort to Facebook groups and other parents to figure out the best care for their children.
Only roughly 200 other people are known to have 9-year-old Zoe's disorder, Tetrasomy 18p, and there are 184 people with confirmed cases of what Jason has, a microduplication of the 15th chromosome.
Mothers of the two children met Friday morning at Appleton's Pierce Park with Wisconsin Congressman Reid Ribble, who wanted to raise awareness of the families' struggles and point to how legislation, the 21st Century Cures Act, could help. The House has passed the bill but the Senate hasn't done anything with it yet, said Ribble, the representative for Wisconsin's 8th Congressional District. The legislation would help streamline the process of getting new cures and treatments from researchers to those who need them.
The legislation would remove some barriers for information-sharing among providers, open up new research opportunities and get new drugs to the market faster.
With every new doctor, Zoe's mom, Cathy LaFrombois, said, "you're faced with the difficult task of having to educate our doctor about the condition because it's so rare."
The legislation, LaFrombois said, "would take down barriers for us."
Appleton mother Amy Ziglinksi said 7-year-old Jason has weak muscles, is on the autism spectrum and has ADD because of a chromosome disorder. He's also fructose-intolerant, so Ziglinski is constantly checking ingredient lists and Jason has a stomachache multiple times a week.
She's hopeful about a tablet Jason could take that would allow him to eat fructose without the pain. The legislation could fund the tablet's research and development, she said.
LaFrombois, of Greenville, hopes the legislation can help unite families with children with rare disorders.
"There are so many of us out there that we don't need to feel isolated," she said.
— Katherine Lymn: 920-993-1000, ext. 7232, or klymn@postcrescent.com; on Twitter @kathlymn


Haven't heard of Hex Media? That should change. We are large supporters of film and the horror genre in particular and we are even bigger fans of supporting independent horror. Hex Media is a genre focused indie company formed by Dubliners Lawrie Brewster and Sarah Daly, both passionate fans and two incredibly talented people. We've just got word on their new film and have the deets below. Make sure to check it out, as well as their prior work over here, follow them on twitter here, and support indie film!
The latest poster for director Lawrie Brewster's Gothic Noir THE OWLMAN: CHAPTER 2 (also known as THE BLACK GLOVES) firmly cements the film's status as the next instalment in his Owlman franchise.
Ahead of the release of the 1940s-set chiller, Hex Studios has also shared a series of portraits, giving fans a glimpse of the film's cast of characters.
Watch this space for more updates on the film's release, slated for early Spring this year.


The origin of Delft Blue dates back to the start of the 17th century. In addition to spices, the VOC (Dutch East India Company) ships also brought black blue on white decorated porcelain from China. This porcelain soon became popular with the wealthy. When imports came to a halt as a result of the civil war in China, the Dutch potteries saw an opportunity and began the production of Delft Blue, which is today known as a typical Dutch product all over the world. Our assortment of Delft Blue consists of contemporary and unique classic Delft Blue pottery, designs inspired by Delft Blue and home accessories with Delft Blue prints.
include the Delfts Blond tableware by Blond Amsterdam and the popular Delft Blue vase.
Delft Blue is not only limited to pottery. The Delft Blue cuff links include a small Delft Blue tile, but also the Delft Blue shoulder bag, laptop bag and wine cooler bag have a fresh Delft Blue imprint. Beautiful products!
A print of Delft Blue tiles adorns the Dutch Designer Chair and the Dutch Designer Whiteboard, attractive accessories for the home. And for those who want Delft Blue on their walls, we even have Delft Blue wallpaper (available in different colours).
Dutch icons come together in the two Delft Blue piggy banks: the hand-painted Miffy piggy bank and the inexpensive Miffy cube piggy bank. Typically Dutch and playful at the same time.


According to the Resource Obscurantism Department, space pirate attacks are increasing and their new Space Pirate Protection Program is designed to protect travelers. The Shredded Orphans find the ROD's new SP3 requirements inconvenient at best.
Come space tripping with the Shredded Orphans seismic rock band. The music industry slaves: Lix, Ophelia, Mac, Chitto and Justice, make their way to Seachellis 17 for a concert they've been dying to play.
The only hitch in their plans is the runaway slave, Mercy, hiding on the ship and their encounter with space pirates. Now they have no means to get Mercy to a safe off-grid planet and Justice is more than a little stressed.
Lix hasn't come away from the space pirate encounter unscathed. His injuries will definitely make playing the scheduled concert on Seachellis 17 difficult.
Will this seal the Shredded Orphans fate? What happens when you mix space pirates and Shredded Orphans? Find out in The Shredded Orphans and the Space Pirates.
Fans of Joss Whedon's Firefly, Rockne S. O'Bannon's Farscape and Grant Naylor's Red Dwarf will love this science fiction comedy adventure!
Sonya Rhen is an author of science fiction, poetry and other fiction books. She was born, raised and still resides in the Pacific Northwest with her husband and two children. She also shares her home with two dogs, two cats and a lonely catfish.


text:
Thymianá (engelska: Thymiana) är en ort i Grekland.   Den ligger i prefekturen Chios och regionen Nordegeiska öarna, i den östra delen av landet,  km öster om huvudstaden Aten. Thymianá ligger  meter över havet och antalet invånare är . Den ligger på ön Chios.

Terrängen runt Thymianá är kuperad västerut, men österut är den platt. Havet är nära Thymianá åt sydost. Den högsta punkten i närheten är Kakia Rachi,  meter över havet,  km väster om Thymianá.  Närmaste större samhälle är Chios,  km norr om Thymianá.

Klimatet i området är tempererat. Årsmedeltemperaturen i trakten är  °C. Den varmaste månaden är juli, då medeltemperaturen är  °C, och den kallaste är februari, med  °C. Genomsnittlig årsnederbörd är  millimeter. Den regnigaste månaden är december, med i genomsnitt  mm nederbörd, och den torraste är augusti, med  mm nederbörd.

Kommentarer

Källor

Orter i Nordegeiska öarna


Swift Systems is a leading IT service provider in the Maryland area. While they had a functioning website and were seeing decent traffic to it, they weren't seeing the organic search traffic they wanted.
Swift Systems knew that they needed to rank higher in the keywords that were relevant to their customers and their business. That's where New North came in.
New North worked with Swift Systems to create and implement an SEO strategy that would boost their ranking for relevant keywords and drive an increase in organic traffic. This involved research to determine the most relevant keywords for targeting, creating a keyword sitemap, and implementing optimization strategies. Additionally, New North created additional content in the form of blog posts and pages to target long tail keywords. The results were 103 first page keyword rankings, 74 of which were overall #1 rankings, and a 12.2% increase in visibility.


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David Friedman, President Donald Trump's nominee for U.S. ambassador to Israel, has managed to anger Jewish Voice for Peace, J Street, U.S. Rep. Jan Schakowsky (D-Ill.) and the Union for Reform Judaism. It's a safe bet that every Jewish leftist who ever cut a check to the New Israel Fund is enduring sleepless nights. Friedman must be doing something right.
They are the political leaders who made Iran a nuclear power, and their party has nominated U.S. Rep. Keith Ellison (D-Minn.) to head its national committee despite Ellison's past ties to the Nation of Islam and his defense of its anti-Semitic leader, Louis Farrakhan.
The legacy of Obama and Kerry is changing the calculus of American Jewish voters. The political apostasy has caused families to rupture and friendships to unravel, exacerbated by Trump's unanticipated victory.
The intensity is palpable as seen in Peter Beinart's questioning Jared Kushner's Jewishness in The Forward. Liberal Jews not only believe they have a monopoly on the moral high ground, but their corrupted perspective of tikkum olam (repairing the world) justifies action that has made the world a more dangerous place for Jews and Christians.
Lara Friedman's use of her blog in The Hill to impugn David Friedman's loyalty is a reckless reinforcement of anti-Semitic stereotypes.
If David Friedman is appointed ambassador to Israel, he will swear an oath of allegiance to the U.S., not the state of Israel.
J Street, which even Obama eventually silenced, giving the group's seat at the progressive table to a revamped Israel Policy Forum, has been further discredited on Capitol Hill by the emergence of the CUFI Action Fund, a Christians United for Israel (CUFI)-affiliated lobby group.
Abraham H. Miller is an emeritus professor of political science, University of Cincinnati, and a distinguished fellow with the Haym Salomon Center. Paul Miller is president and executive director of the Haym Salomon Center.


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Question: What Does Multiple Periods Of Employment Mean?
1 What does multiple period of employment mean?
2 What does employment period mean?
3 What is multiple employment?
4 What is a base period employer?
5 What is a good answer for reason for leaving job?
6 What does minimum employment period mean?
7 What is the $600 Cares Act?
8 What are base period wages?
9 What is a notice period?
10 Why having multiple careers is good?
11 Is it good to have multiple jobs?
12 How do you do dual employment?
13 What do I put for current employer?
14 What is standard base period?
15 What does next to last employer mean?
What does multiple period of employment mean?
More Definitions of Period of Employment Period of Employment means the number of months that the Officer has been an employee of the Company. Period of Employment means the period of time between the Effective Date and the date on which the Executive's employment terminates.
What does employment period mean?
Employment Period means the period commencing on the Effective Date and ending on the second anniversary of such date. Employment Period means the period of Employee's employment with the Company governed by the terms and provisions of this Agreement.
What is multiple employment?
Having multiple careers is the growing trend in the late 20th century and early 21st century whereas a career comprises the work activities that can be identified with a particular job or profession These multiple careers can either be concurrent (where a worker has two simultaneous careers) or sequential (where a
What is a base period employer?
The base period employer claim is sent to any employer or employers who paid wages to the claimant during the base period. The base period is defined as the first four of the last five completed calendar quarters. Its sole purpose is to determine the employer's chargeability.
You might be interested: Readers ask: • What Is Equal Employment Opportunity?
What is a good answer for reason for leaving job?
How to answer "Why do you want to leave your current job?"
Be clear about your reasons for exiting.
Keep your answer short.
Stay positive.
Be honest without being too detailed.
"I don't like the company."
"I'd like more pay."
"I'm bored at work/I don't like the job."
"I don't like the hours at my job."
What does minimum employment period mean?
Under the Fair Work Act, there is a requirement that in order to make an unfair dismissal claim against an employer, a dismissed employee must have served a "minimum employment period" of 6 months, or 12 months if the employer employs fewer than 15 employees.
What is the $600 Cares Act?
Unemployment Benefits under the CARES Act In short: FPUC provided an extra $600 weekly benefit for all weeks of unemployment between April 5, 2020 and July 31, 2020, in addition to the benefit amount an individual would otherwise be entitled to receive under state law.
What are base period wages?
All states use a base period, or base year, to determine whether laid off workers have earned enough wages to qualify for UI benefits. A base period is typically four calendar quarters. (The calendar quarters are January through March, April through June, July through September, and October through December.)
What is a notice period?
When an employee leaves a job they usually have to work a notice period. A notice period is the amount of time an employee has to work for their employer after they resign, are dismissed or made redundant.
You might be interested: Quick Answer: How To Do Self Employment Taxes?
Why having multiple careers is good?
BENEFITS OF HAVING MULTIPLE CAREERS Some reasons you may choose to have multiple careers: For personal growth and autonomy. 40% of independent workers in a study by And Co said their main reason for becoming an independent freelancer was for "personal growth." The second most-cited reason was "flexibility."
Is it good to have multiple jobs?
If you have two separate jobs (like consulting, or multiple part-time jobs), then your income could be more secure than with just one job. If one company goes out of business, for example, you'll still have income from other work. You can keep income coming in at the same time that you get your business up and running.
How do you do dual employment?
The moonlighting clause must be added and signed with the free consent of both the employer and employee. The employer has to make sure that the employment agreement clearly mentions dual employment as a ground for termination of employment.
What do I put for current employer?
The meaning of current employer simply means the employer where you currently work. So, if you work for XYZ Company, that would be your current employer. However, if you worked for XYZ Company and no longer work there or at that company, then you would not list them.
What is standard base period?
The "Standard" Base Period uses the wages earned in the first four of the last five completed calendar quarters prior to the beginning date of the UI claim. The "Alternate" Base Period uses the wages earned in the four most recently completed calendar quarters.
You might be interested: What To Call The Employment Of A Disabled Person?
What does next to last employer mean?
A notice is sent to the last employer of an individual who has filed a new or additional claim. It advises the employer that the person has filed for unemployment benefits. If the individual has not worked sixteen weeks for the last employer, a notice is also sent to the next-to-last employer.


Cobble Hill Nosy Neighbors 500 Piece Puzzle Are the Nosy Neighbors bothering the cute little kitty? These cute black lab puppies just want to have some fun with their furry friend. They even brought 625012520683 14.99 Calendars.com https://www.calendars.com/Nosy-Neighbors-500-Piece-Puzzle/prod201500015572/?
Are the Nosy Neighbors bothering the cute little kitty? These cute black lab puppies just want to have some fun with their furry friend. They even brought a ball of yarn over! Nothing cuter than cats and dogs who get along!
14.0" x 10.0" x 2.38"


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Fresno State to lead dairy innovation project with $1.8M USDA grant
The push to develop new products in the nation's leading dairy state is also the impetus behind a new, three-year $1.8 million grant from the U.S. Department of Agriculture Agricultural Marketing Service aimed at dairy business innovation.
Graduate student Daniel Olmos is channeling his love of science and food to integrate two of his favorite campus farm products into his graduate research project.
Working with food science and nutrition faculty Dr. Carmen Licon Cano, the Fresno-native Olmos is creating a new, wine-infused cheese product that he hopes to produce at the campus creamery for the Gibson Farm Market, and later potentially on a larger scale.
"When you try to produce cheese and wine, there is a fair bit of chemistry and microbiology to consider," Olmos said. "An infused cheese like this is an artisanal product that you might see produced in Spain or other parts of the world, so it's exciting to consider its potential here. Dairy products are exciting to work with since they're very functional, nutritious and delicious."
Licon will work with Dr. Susan Pheasant, director of the Institute for Food and Agriculture at Fresno State, to coordinate a program that will position students, faculty, staff and campus facilities to support industry partners in California, Oregon and Washington to launch a newly-created Pacific Coast Coalition for dairy processors.
Visit Fresno State News to read more.
(Dr. Carmen Licon Cano, left, and Dr. Susan Pheasant)


From Stonehenge to the Pyramids to the Great Wall of China, the world is full of ancient stone monuments. To us, though, the most amazing achievements are structures built entirely from one stone. We've already told you about one such place, but there's another, larger example — 11 other examples, in fact. These are the mind-blowing underground churches of Lalibela, Ethiopia.
There's some dispute between historians about if Ethiopia or Armenia was the first country to convert to Christianity, but the edge probably goes to Ethiopia, which was then called Abyssinia. Sometime around 330 C.E., Emperor Ezana embraced the religion and declared his to be a Christian nation. His decision simply followed his countrymen's lead, while the Armenian ruler who allegedly made a similar declaration about 30 years prior had a hostile country full of would-be converts to contend with. More significantly, we can place Ezana's conversion quite precisely in time from firsthand accounts — the Armenian version, by contrast, was only told a century or so after it happened.
All that is to say that Christianity has been in Ethiopia for a long, long, long time, so it's probably not very surprising that some of the most mind-blowing early Christian churches were built right here. In the region called Lalibela — named after the emperor who purportedly commissioned the churches — you can find no fewer than 11 of these churches carved directly into the mountains. Emperor Lalibela wanted to build a "New Jerusalem" in his country, and these remarkable churches were the best way to do it. The largest of them, Bet Medhane Alem, is also in the record books as the largest church carved from a single monolith. Bet Golgotha houses a replica of Jesus's tomb and of the manger where Mary gave birth, and Bet Giyorgis is perhaps the most iconic of all the churches with its singular cruciform design.
Lalibela reigned from 1181 to 1221, but the churches he (probably) built are still in use today. They attract about 100 thousand visitors per year, many of whom make the pilgrimage on foot. In other words, the emperor was successful in making his New Jerusalem. Even to people who don't practice Ethiopian Orthodox Christianity, these monuments are a major draw, with thousands coming from all over the world to explore the above-ground structures and below-ground tunnels.
When the UNESCO World Heritage Site program began in 1978, the rock-hewn churches of Lalibela were one of the inspirations — and one of the first 12 sites to be protected by the UN. Tourism to the country has been on the rise ever since, and in 2015, Ethiopia was named the World's Best Tourism Destination by the European Council on Tourism and Trade. But with that increased traffic come unexpected side effects, as the structures face erosion over time and the price of admission increases. But Ethiopia isn't just home to eight other UNESCO sites besides the churches of Lalibela; it's also got bubbling hot springs, volcanoes with exposed lava pools, and beautiful, mountainous views. And up in those mountains? More churches.
Fewer tourists visit the country's other rock-hewn churches, these located in the Tigray region. That might be because in order to get to them, you literally have to scale a cliff. But these are also where some of the oldest Christian churches in the world can be found. In Lalibela, 12th- and/or 13th-century laborers started from the top and worked their way down. In Tigray, the workers were using 4th-century technology, and they carved the churches into the sides of the mountain instead. If you really want to lean into your all-church tour of the country, you totally can — other iconic places of worship include Debre Birhan Selassie, a 17th-century church with a more familiar architectural style but plastered on the inside with stunningly detailed frescos. More modern churches quite literally stand out in fluorescent pinks and yellows and prove themselves worth a pilgrimage as well.
If you can't make it to Africa in the near future, you can at least get a closer look at these unique locations in the photography book "Ethiopia: The Living Churches of an Ancient Kingdom." We choose books we think you'll like based on the articles you read. If you purchase through these links, Curiosity will receive a portion of the proceeds.


TurnKey Vacation Rentals has raised $21 million in Series C funding.
The company has raised a total of $41 million since 2013 with this latest round led by Adams Street Partners as well as existing investors Altos Ventures, Silverton Partners and angel investors.
TurnKey claims to be the third-largest vacation rental property management company in the US and is expanding further with plans to open offices in Phoenix and Panama City as well as Oregon.
The company, which was founded in 2012, also says it plans to double the number of properties it manages in 2017 as well as further develop its technology platform.
TurnKey is introducing virtual tours, floorplans and 3D models of its homes.
The vacation rental specialist raised seed funding of $1.5 million in August 2013 followed by a larger round of $3 million just under a year later and a $10 million round in March 2016.
The vacation rental sector continues to develop at a fast pace as well as attract investor attention.
GuesttoGuest raised $35 million recently and acquired competitor HomeExchange.
Meanwhile, AccorHotels entered negotiations to by US-based Travel Keys.


All of us at FFL wish all our dealers a happy and restful Thanksgiving holiday!
We wish to remind you all that while we have prepared for high demand, there may be unexpected orders which could drive stocks to low levels. Also, this busy time of year coupled with unpredictable winter weather may delay holiday shipments! We strongly encourage you to plan in advance for last-minute holiday inventory needs. Our order team is eager to assist you through the holiday crush. Please visit your portal, call us, or email us whenever you need help. Below is a link to a map of holiday shipping cut off times. Please reference this document when taking into account holiday orders. Happy Holidays!


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No room for Champions League stupidity warns Arsenal star
The situation for Arsenal in the Champions League competition right now is still very precarious and even another positive result against one of the pre-tournament favourites to win the whole thing might not be enough to get the Gunners into the knockout phase.
Winning at home against Bayern Munich has certainly given Arsenal a chance though and it has obviously given the players a major morale boost. But our Brazil international defender Gabriel is a little concerned that it might have gone to our heads.
So the centre back has warned his team mates in an Arsenal.com report that despite keeping the Germans from scoring at home and hitting them brilliantly on the break, we must be extra careful about how we try to get forward at the Allianz arena tomorrow. Gabriel wants everyone to keep in their minds that a draw would not be too bad and that we do not need to push for all three points.
But he also feels confident ahead of the game and after nobody expected us to beat Bayern after losing the opening two games with Dinamo Zagreb and Olympiacos, he knows that anything is possible, as long as the Gunners approach it in the right way.
He said, "I think we feel more confident within the competition than after the first two games. We had two defeats and we felt a bit down but the group is very strong, so we managed to overcome that and we managed to recover against a great team that will probably fight to win the competition as well.
"With this victory, we managed to get up and running and realise that anything is possible in football, thanks to the confidence and ability of all the players.
"I think at home we were able to impose ourselves a lot more. We attacked a bit more but I think when we play away, we also have to have a slightly different outlook.
"That doesn't mean we'll spend the whole game defending. We're a big team, we're Arsenal and we need to attack because we need the result.
"But we need to attack with intelligence and make sure we don't suffer a defeat and complicate our situation for the rest of our competition."
So it sounds like it will be a difficult balancing act for Arsenal in Munich, but can we get it right and can we really get out of this group?
Updated: November 3, 2015 — 3:07 pm
BabyPlease
Don't worry baby Please
We have quality on a daily
We won't mess up
Arsenal doesn't do Europa League. We will beat Bayern.
This is our year
Fatboy Gooney
Please baby please!
It wasn't meeeeeeeee!!
That was my long lost twin, who you caught in the sack with your sister! ???? On a dailyyyy ????
Listen baby pleeeeeease!
(Door slams)
Nooooooooooo!! ??? baby please!! ???
* 6 months of psychiatric help later!
And your left with the side effects of "listen baby please!"
Ks-Gunner
We need to play for a draw. Better safe then srry.
Uzi Ozil
Bellerin will miss Bayerns game according to report…..Arsenal need to appease to the injury gods….Anyway, hoping Debuchy show us what he got…..We got him to replace Sagna. Started his career pretty well until injuries set in…I remember the game against Mancity last season. He played so well in that game…We conceded a goal when he was injured in that game…Hector came into the team and He has been awesome……
Debuchy show us what you got tomorrow, Rise to the occasion…We dont wanna be screwed. Come onnnnnnnnnnnnnnnnnnnnnnnnnnnnnn!
We need to be alert and focus in munich, there is no room for complacency! Lets play as we did at the emirates and we will be ok! Coyg!
NY_Gunner
I have faith in the fellas to come away with the 3 points. And as soon as we get past Bayern, the only teams I see as real threats to us are Barca and Atletico Madrid…And Maybe City.
Lethal Prince 9
We have shown last season that we can handle City.
I really thank God that Wenger is not u derives pleasure in under-estimating teams @ ur own detriment or foolhadiness. To be real champions and not strong contenders,arsenal would have to see each team it comes across as a treat. Am sure u must have whispered something to wenger in the game against monaco last season. I can bet he doesn't have your number dis season…
I really thank God that Wenger is not u who derives pleasure in under-estimating teams @ ur own detriment or foolhadiness. To be real champions and not strong contenders,arsenal would have to see each team it comes across as a treat. Am sure u must have whispered something to wenger in the game against monaco last season. I can bet he doesn't have your number dis season…
Bare bones!
___________Giroud
______Sanchez Ozil Campbell
________Cazorla Coquelin
Monreal Koscielny Mertesacker Debuchy
____________Cech
@Twig
If we're gonna roll with Debuchy, we need Gabe in the line up.
trophygunner
As if we've got options.
ozildatrequartista
According 2 my fortuneteller the game at bayern is either a 2 all draw or a last gasp a 3-2 arsenal win. Giroud will get a sitter at the death n either bury it or send it 2 row Z.
By the way that ashley young is such a knob. Smthn's definately wrong with 'im. All he's missing now is the goggles, the webbed feet n the oxygen tank. Then he's all set.
Listen Baby Please
The right side is in good hands with Campbell and Debuchyyyy on a dailyyyy, so don't worryyyy because they are top qualityyyy
kelleson
Now that Bellerin is injure and Debuchy will be call opon in the starting XI we need Gabriel to replace Mert in dat defence becos of his pace. My lineup
Debuchy……. Gabriel….. Koscieny…. Monreal
Cazorla ………… Coquelin
Campbell…..
….. Ozil………. Sanchez……….
we can do it with dis selection. Coquelin and Gabriel should try to avoid early yellow card. We can defeat Bayern with this team.
Atid on Josh Kroenke shows exactly how out of touch the Kroenke family is


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The Best Writing Desks of 2022: A Foundation For Your Practice
April 6, 2022 December 21, 2021 by Austin Carroll
Your writing space is your sanctuary — a little sliver of the world where you can dream, imagine, and create as you please. While it doesn't need to be anything fancy, it should feel cozy and joyful, inspiring you to perform your best work. The best writing desks are an excellent way to make the space your own, providing a foundation for all those big ideas and artistic endeavors.
Technically, any desk you write on can be considered a writing desk. But the following options expertly blend classic writing desk features (like woodgrain surfaces and convenient nooks) with more modern necessities. Whether you're a novelist, journalist, or hobbyist seeking a more personalized writing environment, these desks will help you put pen to paper — or fingers to keyboard — in comfort and style.
The Best Writing Desks
My Writing Desk Review Process
Here's a quick overview of my top recommendations. Click the links to automagically leap to my in-depth analysis.
The best writing desk overall: IKEA HEMNES
The best writing desk on a budget: Amazon Basics Study Desk
The best traditional writing desk: Walker Edison Writing Desk
The best workstation for writers: Eureka Ergonomic SS140B
The best standing desk for writers: Steelcase Solo
Let's start with a look at the best writing desk overall. Then, we'll check out a few specialty options.
IKEA HEMNES
The best writing desk overall
Desktop is solid pine
Features a spacious 48-inch surface
Cabinet and drawers provide plenty of storage
Includes a touch of fiberboard
Maker: IKEA | Dimensions: W48″ x D21.5″ x H29″ | Materials: Solid Pine, Fiberboard | Finish: Brown | Price: $199
Many writers dismiss IKEA as a cheap, low-quality retailer without any options worth considering. While I understand this sentiment (cheap often means low-quality), I've encountered many excellent products from the Swedish furniture store. The IKEA HEMNES illustrates this beautifully.
The IKEA HEMNES is a gorgeous, study-style writing desk built from a slab of genuine pine. It also incorporates a touch of fiberboard in inconspicuous areas like under the drawer and on the back panel. While some furniture purists detest any use of engineered wood, the fiberboard makes this desk much more cost-effective without sacrificing the premium look and feel.
Concerning storage, the desk comes with one right-side drawer and a left-side cabinet. Although you can use these as you please, the drawer is perfect for stashing pens and paper, while the cabinet is ideal for larger items.
One of the best parts about the desk is its size. The solid pine surface measures 48 inches wide. This generous surface area ensures plenty of room to stretch out with notes and various equipment. The desk also sits at a reasonable 29 inches tall. Since the industry average of 30 inches is too high for most users, this is a nice touch that's more comfortable and ideal for postural health.
You will have to assemble the HEMNES yourself, but that's the norm for these types of desks. If assembly isn't your forte, IKEA partners with TaskRabbit, meaning you can have it professionally assembled at your home or office for a nominal fee. Although some online reviewers mention issues during or shortly after assembly, I haven't encountered this myself.
The good news? Should anything go wrong, the HEMNES comes with an unbeatable 1-year return policy and 10-year warranty. It's the best writing desk your hard-earned money can buy.
Amazon Basics Study Desk
The best writing desk on a budget
Affordable $60 price tag
Folding design is extremely versatile
Lower-quality materials prone to minor defects
Quite small, with no drawers or nooks
Maker: Amazon Basics | Dimensions: W40″ x D20″ x H30″ | Materials: Chipboard, Steel | Finish: Natural, Wood | Price: $60
No matter how you feel about Amazon, there's no denying the eCommerce company's convenience and exceptional pricing. The brand's new Amazon Basics lineup channels this philosophy into physical goods, and the Study Desk fits the narrative to a tee.
This desk comes in at roughly $60 and features a foldable frame that's ready to go seconds after arriving at your door. Even though it lacks "extras" like drawers, the minimal design is quite elegant, and the two color options fit into any room.
Of course, the tradeoff is a lower-quality chipboard surface that's prone to dents and edge wear. But even with the more fragile surface, only a small percentage of reviewers encounter issues. Meanwhile, the steel frame is surprisingly robust and sturdy, even if the weld points look a little weak.
Amazon assigns the desk a whopping 200-pound weight capacity, which may be possible but is probably a little overgenerous. Considering the materials and craftsmanship, I'd recommend sticking closer to half of that.
My biggest grievance with the Amazon Basics Study Desk has to be its small size. I suppose the 40-inch width and 20-inch depth could be considered a boon for small rooms, but it doesn't give you much space to work with. The desk also sits 30 inches high, which is standard but still quite tall. I recommend pairing with the Amazon Basics footrest (here's the one I use), as it provides better ergonomics and postural support at a similarly great price.
Walker Edison Writing Desk
The best traditional writing desk
Beautiful rustic finish
Central drawer offers easy storage
Durable design; rated for up to 100 pounds
Tedious multi-hour assembly process
Private-label design; lacks a traditional warranty
WALKER EDISON
Maker: Walker Edison | Dimensions: W46″ x D20″ x H30″ | Materials: MDF, Laminate | Finish: Barnwood, Brown, Grey, Marble, Walnut, White Oak | Price: $149
The Walker Edison features a classy, minimal aesthetic that looks straight out of an 1800s farmhouse. It's constructed from a high-quality MDF, or engineered wood, and comes with a durable laminate top available in several finishes. Underneath, you'll find a criss-cross pattern that plays double duty — providing structural integrity and a charming rustic aesthetic.
My favorite design element on the Walker Edison is its center drawer, which provides just enough room to tuck in your notebooks and supplies. If you write with just a laptop, you can even fit that in there, ensuring a clean desktop that looks as great in the office as it does in the den. Meanwhile, the horizontal pull makes it easy to open and close the drawer while providing a modern pop of silver to contrast the traditional wood design.
Concerning measurements, the Walker Edison comes in around 4 feet long, which is probably the best size for most users. It strikes an ideal balance, offering enough length for your gear without overburdening its surroundings.
It's important to note that Walker Edison deals primarily in private-labeled products. In other words, another company built the desk and branded it with Walker Edison's labeling. It's not an uncommon practice (Amazon Basics does the same thing), but Walker Edison chooses not to warranty its private-labeled products outside the standard 30-day return period. While this is an unfortunate oversight, I don't believe it should pose an issue for most users.
The biggest complaint among reviewers is the desk's tedious assembly process. I haven't gone hands-on with this particular desk, but from what I can gather, installation is best left to a handy person who can fix or adjust any issues that arise. While frustrating, it still doesn't outweigh Walker Edison's attractive design and reliable craftsmanship.
Eureka Ergonomic SS140B
The best workstation for writers
Features a sleek, two-tone design
Rated for up to 200 pounds; backed by a 5-year warranty
Comes with a side shelf, monitor mount, and pegboard organizer
Lacks the traditional writing desk aesthetic
The 30-inch height is a little tall for some users
Maker: Eureka Ergonomic | Dimensions: W55″ x D23.5″ x H30″ | Materials: Engineered Wood, Steel | Finish: Archaize Brown, Wood | Price: $189.99
Eureka Ergonomic is among my favorite office desk manufacturers. The business creates dozens of attractive, durable models for a range of users. This particular model — the SS140B — isn't just stunning, but loaded with features to enhance your writing workflow.
The first thing you'll notice about the desk is the side shelf, which has three levels for accessories and (optionally) your desktop computer. The top shelf is all-black, which creates a striking separation between the desktop's wood grain. You'll also notice a pegboard on either side of the desk, a thoughtful inclusion that lets you hang notes and peripherals within easy reach. Lastly, there's the monitor riser, which holds your display at a more appropriate, ergonomic level.
Aside from its array of add-ons and accessories, the most unique thing about the SS140B is its modular design. You can attach the side shelf and monitor mount on either side, meaning the layout is entirely up to you. No matter how you piece it together, the unit also remains as solid as stone, capable of carrying 200 pounds, no problem.
Even though you can configure your SS140B, the desk is still designed for the modern office. It lacks the traditional writing desk elements seen on IKEA's HEMNES and Walker Edison's Writing Desk, and I've found that it works best when used as a computer workstation rather than a standalone writing space.
I may sound like a broken record here, but the SS140B's 30-inch height is — like others on this list — too tall. If you're not 6 feet or taller, I recommend a footstool. Eureka Ergonomic is happy to sell you one for a paltry $29.99.
Steelcase Solo
The best standing desk for writers
Suitable for all users
Promotes a more healthful writing environment
Simple Touch controller adjusts the desk's height 25 inches with a single press
Pricey, starting at $699
Lacks programmable height presets
Maker: Steelcase | Dimensions: W48″ x D24″ x H" | Materials: Laminate, Steel | Finish: Archaize, Arctic White, Ash Noce, Clay Noce, Clear Oak, Storm Noce, Virginia Walnut | Price: $699
Steelcase creates the best writing chair, so it's not surprising to see the company features on this list of best writing desks. The funny thing is, you don't even need a chair for this desk (though you'll probably want one). That's because the Steelcase Solo is a standing desk, moving from 22.5 inches to 48.5 inches high at the push of a button.
Because of its unique adjustability, the Solo isn't your typical writer's desk. It doesn't have any nifty drawers or shelves, and the modern design doesn't evoke that traditional writing-by-the-fireplace imagery. But what it lacks in aesthetics, it makes up for in ergonomic bliss.
The Solo is suitable for every height. Users as short as 5 feet and as tall as 7 feet can sit or stand at the desk and write to their heart's content. Better yet, you can swap between the two, counteracting the harmful effects of sedentary sitting and promoting circulation for boosted productivity.
Although you can select from various finishes, the Solo always comes with a laminate top and three-stage legs that move up and down via a Simple Touch controller. With all these elements working in tandem, the Solo can accommodate up to 360 pounds — or about 6,000 Moleskine notebooks stacked towards the heavens.
Of course, the Steelcase Solo is pricey. The desk starts at $699 and goes up to $840, depending on its kit. But I find its health-oriented benefits, performance-enhancing features, and 15-minute assembly worth the price.
I'm a freelance writer by trade, and I have years of experience writing about ergonomics and office gear. I've gone hands-on with many of today's most popular office desk brands, including IKEA, Eureka Ergonomic, and Steelcase. For this guide on the best writing desks, I combined that knowledge with a fresh round of research and consideration.
Here's a look at my process and the criteria used to determine which desks make it to the top of the list.
1. Sizing. A spacious surface allows you to spread out and reduce clutter. I usually recommend a minimum width of 42 inches and a depth of 20 inches, though writers with smaller rooms can get away with less.
2. Ergonomics. The best desk for writers is only useful so long as it helps you sit down and write. For that, it should be comfortable, with a smooth tabletop surface and a maximum 30-inch height (26 inches is my sweet spot, albeit hard to find). Adjustable legs, drawers, and shelves are other things to look out for, as they let you customize the workspace to your specific needs.
3. Design. Writing desks are traditionally wooden, with little nooks and crannies for stashing things like pens and writing pencils. Although modern writing desks vary in material and desk, they should maintain a sophisticated look and feel that suits your writing workflow.
4. Durability. Most writing desks aren't worth your time — they're flimsy and easily damaged. That's why it's crucial to seek out natural wood and metal finishes when possible, as well as manufacturer warranties that cover any potential issues.
5. Pricing. Few of us fit the starving artist stereotype, but that doesn't mean we can drop hundreds on a brand new writing desk. I tried to include the best writing desks in every price range, ensuring a quality selection for folks with $50 and $500.
Although many excellent desks failed to make this list, that only serves as a testament to the quality of these options. I'm confident in recommending every model on this list, and I firmly believe that they represent the best desks for writing.


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