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\title{\begingroup\textfont1=\seventeenbi \scriptfont1=\twelvebi
\scriptfont0=\twelvebf \scriptfont2=\twelvebsy
\seventeenbf Hard gluon emission from colored scalar pairs\break
in $e^+e^-$ annihilation\endgroup}

\author{\fourteenrm Ken-ichi Hikasa}
\address{Department of Physics, Tohoku University\break
Aoba-ku, Sendai 980-77, Japan}
\author{\fourteenrm Junji Hisano}
\address{Department of Physics, Tokyo Institute of Technology\break
Oh-okayama, Meguro-ku, Tokyo 152, Japan}

\vskip\frontpageskip\centerline{\fourteenrm ABSTRACT

We study QCD correction to the pair production of colored scalar
particles in electron-positron annihilation
with an emphasis on gluon emission in the final state.
We discuss the usefulness of working in a ``quasi-two-body'' frame and
present the helicity amplitudes for the process.
We compare the final state configuration with fermion pair production
and find that the three-jet fraction for the scalars shows quantitative
difference from that for fermions.

\vfil\break

\chapter{Introduction}

The known elementary particles are either spin-1/2 fermions
(quarks and leptons) or spin-1 gauge bosons.  No elementary spin-0 particle
has been found to date.  Yet, scalar particles appear in most field theory
models of particles.  Higgs bosons are the key ingredient for
electroweak symmetry breaking in the standard model and its extensions.
Supersymmetry predicts a scalar partner for each fermion degree of freedom,
thus the existence of three generations of squarks and sleptons.
Grand unified $E_6$ model contains  colored scalar particles which may be
interpreted either as leptoquarks or diquarks.

Many of these scalars can be pair produced in $e^+e^-$ annihilation with a
cross section comparable to or somewhat smaller than that for fermions.
Experimental searches for these particles have been extensively performed%
\ref{Particle Data Group, L.~Montanet {\it et al.}, \PRD50, 1173 (1994).}.

\REF\Schwinger{J.~Schwinger, {\it Particles, Sources, and Fields}, Vol.~II
(Addison-Wesley, Mass., 1973), Chapter 5-4.}
\REF\DH{M.~Drees and K.~Hikasa, \PLB252, 127 (1990).}

If the scalar particle is colored (like the squark and leptoquark),
the cross section is modified by QCD corrections.
The calculation of the ${\cal O}(\alpha_s)$ correction is essentially
the same as scalar QED one-loop calculation which is known for a long time.%
  \footnote{A detailed description can be found in Ref.~\Schwinger.  A
  typographical error is corrected in Ref.~\DH.}
The ${\cal O}(\alpha_s)$ correction for the scalar pair production is
numerically quite important.
In the high energy limit, the total correction
factor for scalar pair production is {\it four\/} times larger than
that for fermion pair production\keepspacefactor\refm@rk\DH:
$$ \sigma(e^+e^-\to \zeta\bar\zeta(g)) =
\sigma_0 \biggl( 1 + 3\,{C_{\!R}\alpha_s\over\pi} \biggr) \;, \eq@@\eq$$
where $\sigma_0$ is the lowest-order cross section and
$C_{\!R}$ is the second-order SU(3) Casimir eigenvalue
(4/3 for the fundamental representation like squarks or leptoquarks).
We use the notation $\zeta$ to represent a generic colored scalar
particle in the representation $R$.
At lower energies, especially in the threshold region, the correction
factor becomes even larger.

The total ${\cal O}(\alpha_s)$ correction consists of two parts,
one-loop virtual correction to the lowest order process
$e^+e^-\to \zeta\bar\zeta$ and real gluon emission correction
$e^+e^-\to \zeta\bar\zeta g$, both of which are infrared divergent.
This divergence is cancelled when the two contributions are added.
Essential for this cancellation is only the part of the three-body phase
space where the gluon is soft
(or collinear to one of the scalars when the scalar mass goes to zero).
The rest of the three-body phase space corresponds to the final state
with a hard gluon which may be observed as a separate jet
(``three-jet'' final state).

The gluon emission process in scalar top quark pair production
has been studied by Beenakker, H\"opker, and Zerwas\ref{W.~Beenakker,
R.~H\"opker, and P.~M. Zerwas, \PLB349, 463 (1995).}, who calculated the
fully differential cross section for $e^+e^-\to \tilde t \bar{\tilde t} g$.
In the present paper, we derive the cross section in a different Lorentz
frame (``quasi-two-body'' frame) in which the helicity amplitudes have a
simple interpretation.  We then extend their analysis and compare the
three-jet cross sections with those for scalar and fermion pair production
processes.

The QCD correction we calculate in this paper is just the effects arising
from gluon gauge interactions.
In the supersymmetric standard model there are additional interactions with
the same strength involving gluinos.  The gluino coupling contribution
to the virtual ${\cal O}(\alpha_s)$ correction is discussed by
Arhrib, Capdequi-Peyranere, and Djouadi%
\ref{A.~Arhrib, M.~Capdequi-Peyranere, and A.~Djouadi, \PRD52, 1404 (1995).}.

\chapter{Lowest-Order Cross Section}

We consider the process $e^+e^-\to \zeta\bar\zeta$ which occurs via
$s$-channel $\gamma$ or $Z$ exchange.   Additional $t$ or $u$-channel
exchanges have to be included for selectron (or electron sneutrino)
production or a leptoquark if it couples to electrons with a nonnegligible
Yukawa coupling.

In this section we list the lowest-order amplitude and cross section
for completeness.  The Feynman graph is shown in Fig.~1.
The amplitude is found to be (see Fig.~1 for the momentum assignments)
$$ {\cal M}_0  = {e^2\over s} \,H^\mu\,(p-\bar p)_\mu \;,\eq@@\eq$$
with
$$ H^\mu =  -Q_\zeta\, \bar v(\bar p_e) \gamma^\mu  u(p_e)
+ {T_{3\zeta}-Q_\zeta\sin^2\!\theta_W\over\cos^2\!\theta_W\sin^2\!\theta_W} \,
{s\over s-m_Z^2} \,\bar v(\bar p_e) \gamma^\mu (v_e - a_e\gamma_5) u(p_e)
\;.\eq@@\eq$$
Here $s$ is the $e^+e^-$ c.m.\ energy squared,
$Q_\zeta$ and $T_{3\zeta}$ are the electric charge and the third component
of weak isospin of $\zeta$, and
$$ v_e = -{1\over4} + \sin^2\!\theta_W\;,\qquad a_e = -{1\over4} \;.\eq@@\eq$$
We will neglect the electron mass throughout the paper.

For longitudinally polarized electrons with polarization $P$ colliding
with unpolarized positrons, the cross section can be written
$$d\sigma = {1+P\over 4}\, d\sigma_+
+ {1-P\over 4}\, d\sigma_- \;,\eq@@\eq$$
where $d\sigma_\pm$ denotes the cross section for the $e^-_R e^+_L$ and
$e^-_L e^+_R$ initial states.  We find
$$ {d\sigma_\pm\over d\cos\theta} = {\pi d_R\alpha^2\beta^3\over 2s} H_\pm^2
\,\sin^2\!\theta \;,\eq@@\eq$$
with
$$ H_\pm =  -Q_\zeta
+ {(v_e {\mp} a_e)(T_{3\zeta} {-} Q_\zeta\sin^2\!\theta_W)
\over \cos^2\!\theta_W \sin^2\!\theta_W}{s\over s-m_Z^2} \;.\eq@@\eq$$
Here,  $d_R$ is the dimension of the color SU(3) representation of $\zeta$
(3 for the fundamental representation), and
$$\beta = \sqrt{1-4m^2/s} \;,\eq@@\eq$$
with $m$ being the $\zeta$ mass.  The $\beta^3$ factor reflects the
$P$ wave threshold.  The total cross section is
$$\sigma_\pm  = {2\pi d_R\alpha^2\beta^3\over 3s} H_\pm^2 \;,\eq@@\eq$$
which we will denote by $\sigma_{0\pm}$.

\chapter{${\cal O}(\alpha_s)$ correction}

\section{Virtual one-loop correction}

Feynman diagrams for the process $e^+e^-\to\zeta\bar\zeta$ at
${\cal O}(\alpha_s)$ are depicted in Fig.~2.  The diagrams (a)--(c)
are the one-particle-irreducible vertex corrections.  The mixed four-point
vertex in (b) and (c)
appears because the scalar kinetic term has two covariant derivatives.
The diagrams (d) and (e) are $\zeta$ self-energy corrections, and the
diagrams (f)--(h) show the counterterm contribution.

We regularize the ultraviolet divergence by dimensional reduction%
  \footnote{Naive dimensional regularization gives the same physical
   results, although the finite parts of the renormalization constants
   differ.}
with $D=4-2\epsilon$, and the infrared singularity by an infinitesimal
gluon mass $\lambda$.  This procedure does not cause problems with gauge
invariance since the diagrams do not contain non-Abelian gauge vertices.

We adopt the on-shell renormalization scheme to
determine the counterterms.  The mass and wave function renormalization
constants for $\zeta$ are found to be
$$\eqalignno{
&\displaystyle{\delta m^2\over m^2} = - {C_{\!R}\alpha_s\over 4\pi}
\left[ 3 \left(\displaystyle{1\over\epsilon}  -\gamma_E + \log4\pi \right)
-3\log \displaystyle{m^2\over\mu^2} + 7 \right] \;,&\eq@@\eq\cr
&Z_\zeta-1 = {C_{\!R}\alpha_s\over 4\pi}
\left[ 2 \left(\displaystyle{1\over\epsilon}  -\gamma_E + \log4\pi \right)
-2\log \displaystyle{\lambda^2\over\mu^2} \right] \;,&\eq@@\eq\cr}$$
where $\mu$ is the renormalization scale and $\gamma_E$ is the Euler constant.

We write the $\zeta\bar\zeta\gamma$ vertex function in the form
$-ieQ_\zeta \Lambda_\mu$ with
$$ \Lambda_\mu = F(q^2) (p-\bar p)_\mu \;.\eq@@\eq$$
(See Fig.~2 for the definition of the momenta.)
Up to the order we work, the $\zeta\bar\zeta Z$ vertex can be
writtten as
$${-ie(T_{3\zeta}-Q_\zeta\sin^2\!\theta_W)\over\cos\theta_W\sin\theta_W}
\Lambda_\mu \eq@@\eq$$
with the same $\Lambda_\mu$.
At the lowest order we have  $F(q^2)=1$.

The counterterm for the vertex can be found using the Ward
identity.  The same result is obtained by requiring no
${\cal O}(\alpha_s)$ correction at $q^2=0$, {\it i.e.}, $F(0)=1$.
Expanding the form factor as
$$ F(q^2) =  1 + {C_{\!R}\alpha_s\over 2\pi} f(q^2) \;,\eq@@\eq$$
we find for $q^2>4m^2$
\begingroup
\def\+{{+}}
\def\-{{-}}
$$\eqalignno{
f(q^2) &=
\biggl(-{1\+\beta^2\over 2\beta}
\log{1\+\beta\over 1\-\beta} + 1 \biggr) \log{m^2\over\lambda^2} \cr\noalign{\vskip 3\jot }
&\quad + {1\+\beta^2\over\beta} \biggl[ \Li2(1\-\beta\over 1\+\beta)
- \log{2\beta\over 1\+\beta}\log{1\+\beta\over 1\-\beta}
- {1\over4}\log^2{1\+\beta\over1\-\beta} + {\pi^2\over3} \biggr]\cr\noalign{\vskip 3\jot }
&\quad + {1\+\beta^2\over\beta}\log{1\+\beta\over 1\-\beta} -2 \cr\noalign{\vskip 3\jot }
&\quad + i\pi \, {1\+\beta^2\over 2\beta} \biggl(\log{m^2\over\lambda^2}
+ \log{4\beta^2\over 1\-\beta^2} -2 \biggr) \;.&\eq@@\eq\cr}$$
\REF\tHV{G.~'t~Hooft and M.~Veltman, \NPB153, 365 (1979).}
Here $\mathop{\rm Li_2}(x)$ is the dilogarithm (Spence) function%
\footnote{For a convenient expansion for numerical evaluation of
dilogarithm, see Ref.~\tHV.}
$\mathop{\rm Li_2}(x)=-\int_0^x dt\,\log(1-t)/t$.
At ${\cal O}(\alpha_s)$, the lowest order cross section is multiplied by the
factor
$$ 1 + {C_{\!R}\alpha_s\over\pi}\, \Re f(s) \;.\eq@@\eq$$
The infrared singularity is cancelled by real gluon emission,
to which we now turn.
\endgroup

\section{Real gluon emission}

The Feynman diagrams for the process $e^+e^-\to \zeta\bar\zeta g$
at the lowest order are shown in Fig.~3.  The amplitudes are found to
be
$${\cal M} =
{e^2 g_s T^a\over s}\, H^\mu
\left[ {(p-\bar p+k)_\mu p_\alpha \over  p{\cdot}k}
- {(p-\bar p-k)_\mu \bar p_\alpha \over \bar p{\cdot}k}
- 2g_{\mu\alpha} \right] \;\epsilon^{*\alpha} \;.\eq@@\eq$$
Here $T^a$ is the SU(3) generator in the representation $R$.

We calculate the cross section for this process in two methods, with
agreeing results.  One is the conventional trace technique.  The other
method is a helicity amplitude technique described in Appendix A.

The differential cross section may be parametrized by four variables.
We find it convenient to use the following four:

\itemitem{$\tau$ :} $\zeta\bar\zeta$ c.m.\ energy squared normalized to $s$,
$\tau=(p+\bar p)^2/s$;
\itemitem{$\Theta$ :} angle between the $e^-$ and the gluon
in the $e^+e^-$ c.m.\ frame;
\itemitem{$\theta$ :} angle between the $\zeta$ and the gluon
in the $\zeta\bar\zeta$ c.m.\ frame;
\itemitem{$\phi$ :} azimuthal angle between the $e^-$ and the $\zeta$ with
respect to the gluon, measured from the $e^-$ to the $\zeta$ direction
(common to both frames).

The use of these variables is motivated by the fact that the amplitude
can be split into two subprocesses $e^+e^-\to V^*$ ($V^*=\gamma$, $Z$)
and $V^*\to \zeta\bar\zeta g$, and the latter process can be most
conveniently evaluated in the $\zeta\bar\zeta$ c.m.\ frame.  The detail
and the result for the helicity amplitudes may be found in Appendix A.

The polarized cross section is
$$\eqalignno{
&{d\sigma_\pm \over d\tau\,d\cos\Theta\,d\cos\theta\,d\phi}
=  {d_R\alpha^2 H_\pm^2 \over 8 s}\,{C_{\!R}\alpha_s\over\pi}\, v (1-\tau)\cr\noalign{\vskip 3\jot }
&\qquad\times\biggl\lbrace
A (1+\cos^2\Theta) + B (1-3\cos^2\Theta )
+ C \sin\Theta\cos\Theta\cos\phi + D \sin^2\Theta \cos2\phi
\biggr\rbrace\;,\cr&&\eq@@\eq\cr}$$
where
$$\eqalignno{
A &= 1 + {2\beta^2 \tau v^2 \sin^2\!\theta\over
(1-\tau)^2 (1-v^2\cos^2\!\theta)^2} \;,&\eq@@\eqa\cr\noalign{\vskip 3\jot }
B &= {2 \tau v^4 \sin^2\!\theta \cos^2\!\theta \over
(1-\tau)^2 (1-v^2\cos^2\!\theta)^2} \;,&\eq@@\eqb\cr\noalign{\vskip 3\jot }
C &= -{4\sqrt\tau v^2\sin\theta\cos\theta
\bigl[ \beta^2-v^2+(1+\tau)v^2\sin^2\!\theta\bigr]
\over (1-\tau)^2(1-v^2\cos^2\!\theta)^2} \;,&\eq@@\eqc\cr\noalign{\vskip 3\jot }
D &= -{2\tau v^2\sin^2\!\theta(\beta^2-v^2\cos^2\!\theta)\over
(1-\tau)^2(1-v^2\cos^2\!\theta)^2}  \;.&\eq@@\eqd\cr}$$
Here
$$ v = \sqrt{ 1 - 4m^2/ \tau s} \eq@@\eq$$
is the velocity of $\zeta$ in the $\zeta\bar\zeta$ c.m.\ frame.

If one integrates the cross section over the whole 3-body phase space,
one encounters infrared divergence coming from soft-gluon region.  We
separate this region from the rest by the condition that the gluon
energy $k^0<\omega$, where the cutoff $\omega$ is infinitesimally small.

In this region, we regularize the divergence by giving an infinitesimal mass
$\lambda$ to the gluon, which satisfies $\lambda\ll\omega$.  We recalculate
the amplitude with finite mass.  The amplitude factorizes into the
lowest-order part and the soft gluon factor.
Since a very soft gluon does not alter the kinematics of the $\zeta\bar\zeta$
state, we can also integrate
over the soft gluon phase space ignoring momentum conservation.
Integrate over this soft-gluon region, we find the cross section
\begingroup
\def\+{{+}}
\def\-{{-}}
$$\eqalignno{\sigma_{\rm soft} &= \sigma_0 {C_{\!R}\alpha_s\over\pi}\,
\Biggl\{ \biggl({1\+\beta^2\over2\beta} \log{1\+\beta\over 1\-\beta} -1\biggr)
          \log{4\omega^2\over\lambda^2}
\cropen{10pt} &\qquad\quad
         +{1\+\beta^2\over\beta}\biggl[
           \Li2({1\-\beta\over 1\+\beta})
         - \log{2\beta\over1\+\beta}\log{1\+\beta\over 1\-\beta}
           -{1\over4}\log^2{1\+\beta\over 1\-\beta} - {\pi^2\over6} \biggl]
\cropen{10pt} &\qquad\quad
        + {1\over\beta}\log{1\+\beta\over 1\-\beta}
         \Biggr\} \;,&\eq@@\eq\cr}$$
where $\sigma_0$ is the lowest-order cross section.

For the rest of the phase space, we can set the gluon mass to zero.
We first integrate over $\Theta$, $\phi$ to find
$${d\sigma_\pm\over d\tau\,d\cos\theta}
= \sigma_{0\pm}\,{C_{\!R}\alpha_s\over\pi }\,{v(1-\tau)\over \beta^3}\,
\biggl[1 + {2\beta^2 \tau v^2 \sin^2\!\theta\over
(1-\tau)^2 (1-v^2\cos^2\!\theta)^2}\biggr] \;,\eq@@\eq$$
which we will use to study the event configuration in the next section.
The integrated cross section is
$$\eqalignno{\sigma_{\rm hard} &= \sigma_0 {C_{\!R}\alpha_s\over\pi}\,
\Biggl\{ \biggl({1+\beta^2\over2\beta} \log{1\+\beta\over 1\-\beta} -1\biggr)
          \log{m^2\over4\omega^2}
\cropen{10pt} &\qquad\quad
         +{1+\beta^2\over\beta}\biggl[
          2\,\Li2({1\-\beta\over 1\+\beta})
         + 2\,\Li2(-{1\-\beta\over 1\+\beta})
          -\log{2\over1\+\beta}\log{1\+\beta\over 1\-\beta}
\cropen{10pt} &\qquad\qquad\qquad\quad
          + {1\over2} \log^2{1\+\beta\over 1\-\beta} - {\pi^2\over6} \biggr]
 -3\log{4\over 1\-\beta^2} - 4\log\beta
\cropen{10pt} &\qquad\quad
        - {1\over4\beta^3}\, (3+\beta^2)(1-\beta^2)
          \log{1\+\beta\over 1\-\beta}
        + {1\over2\beta^2}(3+7\beta^2)
         \Biggr\} \;.&\eq@@\eq\cr}$$

The $\omega$ dependence cancels out when these two cross sections are summed.
The infrared divergence is cancelled by adding the virtual one-loop
correction discussed in the previous subsection.

\section{Total correction}

The ${\cal O}(\alpha_s)$ corrected cross section for
$e^+e^-\to \zeta\bar\zeta (g)$ can thus be written as
$$\sigma=\sigma_0\,\biggl[ 1 + {C_{\!R}\alpha_s\over\pi}\Delta \biggr] \;,\eq@@\eq$$
where
$$ \Delta = {1\over\beta}\,A(\beta)
       + {1\over4\beta^3}(-3\+10\beta^2\+5\beta^4)\log{1\+\beta\over 1\-\beta}
       + {3\over2\beta^2}(1\+\beta^2)  \;,\eq@@\eq$$
with
$$\eqalignno{
A(\beta) &= (1+\beta^2)\biggl[
          4 \,\Li2({1\-\beta\over 1\+\beta})
        + 2 \,\Li2(-{1\-\beta\over 1\+\beta})
        - 3\log{2\over 1\+\beta}\log{1\+\beta\over 1\-\beta}
\cropen{10pt} &\qquad\qquad\quad
       - 2 \log\beta\log{1\+\beta\over 1\-\beta} \biggr]
 - 3\beta\log{4\over 1 \- \beta^2}  - 4\beta \log\beta\;.&\Eqn\eqA\cr}$$
This may be compared with the corresponding formulas for the pair production
of a colored fermion pair via vector and axial vector currents (the detail
on the latter may be found in Appendix C)
$$\eqalignno{ \Delta_V &= {1\over\beta}\,A(\beta)
       + {33+22\beta^2-7\beta^4\over 8\beta(3-\beta^2)}
            \log{1\+\beta\over 1\-\beta}
       + {3(5-3\beta^2)\over 4(3-\beta^2)}  \;.&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta_A &= {1\over\beta}\,A(\beta)
       + {1\over 32\beta^3}\,(21+59\beta^2+19\beta^4-3\beta^6)
            \log{1\+\beta\over 1\-\beta} \cr\noalign{\vskip 3\jot }
&\quad + {3\over 16\beta^2}\,(-7+10\beta^2+\beta^4)  \;.&\eq@@\eq\cr}$$

The dependence on $\beta$ of the cross section normalized to its
lowest order value is shown in Fig.~4.  The corresponding quantities
for fermion pair production are also shown for comparison.
The correction for scalars is larger than that for fermions via vector
current for all values of $\beta$.  The correction for fermions via
axial current is equal to that for vector current at the high energy
limit (which reflects the chiral symmetry in this limit), but approaches
the scalar curve at small $\beta$.  This latter behavior reflects the fact
that spin does not play an important role in the nonrelativistic region.
The difference of the vector current result is due to its $S$-wave
dynamics contrast to the $P$ wave behavior of the others.

At the high energy limit $\beta\to 1$, one finds
$$ \Delta = 3 \;,\qquad \Delta_V=\Delta_A={3\over4} \;.\eq@@\eq$$
The correction for the scalar pair is four times larger.
Near the threshold, one has
$$ \Delta \simeq \Delta_A \simeq {\pi^2\over2\beta}-2 \;,\qquad
   \Delta_V \simeq {\pi^2\over2\beta}-4 \;.\eq@@\eq$$
The terms proportional to $1/\beta$ are the consequence of Coulomb gluon
exchange.

It is well known that perturbation expansion in $\alpha_s$
breaks down very near the threshold and one has to sum over ladder
Coulomb gluon diagrams\keepspacefactor\refm@rk{\Schwinger}.
For the case of scalar pair production with the $P$ wave threshold
behavior, the lowest-order cross section is propotional to $\beta^3$,
which is modified to $\beta^2$ by the ${\cal O}(\alpha_s)$ correction.
The nonperturbative contribution further enhances the cross section
and leads to a constant cross section at the threshold\Ref\BFK{I.~I. Bigi,
V.~S. Fadin, and V.~Khoze, \NPB377, 461 (1992).}.
In the nonrelativistic approximation with the Coulomb potential (one gluon
exchange approximation), the cross section is
$$ \sigma_\pm = {2\pi^2 d_R\alpha^2\over 3s}\,H_\pm^2 \,
{C_{\!R}\alpha_s\bigl(\beta^2+{1\over4}C_{\!R}^2\alpha_s^2\bigr)
\over \bigl[1 -\exp(-\pi C_{\!R}\alpha_s/\beta)\bigr]} \;,\eq@@\eq$$
which gives at the threshold
$$ \Delta = {\pi^2 C_{\!R}^2\alpha_s^2\over 4 \beta^3} \;.\eq@@\eq$$
This effect becomes important only at very near threshold, $\beta\sim 0.1$,
however.

\endgroup

If one approaches closer to the threshold, one will encounter $P$-wave
$\zeta\bar\zeta$ bound states, similar to charmonium and bottomonium
resonances.
These states are expected to be less pronounced than the fermion bound
states, since the resonance formation cross section is proportional
to the derivative of the wave function at the origin and is suppressed
by a factor of $\alpha_s^2$ compared to the fermion bound states.
In the Coulomb potential approximation, this subthreshold cross section
is given by\keepspacefactor\refm@rk{\BFK}
$$ \sigma_\pm = {\pi^2 d_R \alpha^2\over 12}\,H_\pm^2
\bigl(C_{\!R}\alpha_s\bigr)^5
\mathop{\textstyle\sum}\limits_{n=2}^\infty {n^2-1\over n^5}
\delta(s-M_n^2) \;,\eq@@\eq$$
where $M_n = 2m - C_{\!R}^2\alpha_s^2 m/4n^2$.  This Coulombic approximation
ignores the effect of confinement and is not adequate especially for
higher bound states.  One needs to solve Schr\"odinger equation with
a realistic color-force potential to obtain the cross section in the
resonance region.

If $\zeta$ has a short lifetime with $\Gamma \mathrel{\mathpalette\@versim>} \alpha_s^2 m$,
it does not live long enough to form a bound state.
There will be only a smooth bump or shoulder instead of the resonances
at the threshold.  The situation will be similar to the case for the
top quark pair production\ref{V.S. Fadin and V.A. Khoze,
\JETPL46, 525 (1987); \SJNP48, 309 (1988);\unskip\nobreak\hskip\parfillskip\break
M. Strassler and M. Peskin, \PRD43, 1500 (1991).}
and the cross section can be calculated quite reliably within perturbative
QCD.

\chapter{Jet configuration}

In this section we study the shape of the three-body final state
$\zeta\bar\zeta g$ when the gluon is `visible'.  We compare various
distributions with those for the more familiar final state of a fermion-pair
plus a gluon.

To define the final state configuration, it is convenient to use
Lorentz-invariant kinematic variables.  We use the following
Dalitz variables
$$ x = {2p{\cdot}k \over s}\;,\qquad
\bar x = {2\bar p{\cdot}k \over s}\;,\eq@@\eq$$
for which the phase space density is constant.  The $\zeta\bar\zeta g$
cross section is (we drop the subscript $\pm$ from here on)
$${d\sigma\over dxd\bar x} = \sigma_0\,{C_{\!R}\alpha_s\over\pi}\,{1\over\beta}\,
\left[ {2\over\beta^2}
- \left({1\over x} + {1\over \bar x}\right)
+ {1+\beta^2\over 2}\,{1\over x\bar x}
-{1-\beta^2\over 4} \,\left({1\over x^2}+{1\over \bar x^2}\right)\right]
\;.\eq@@\eq$$
The infrared singularity arises when the gluon energy is very small,
$x\sim\bar x\sim0$.  At the high energy limit, additional singularity
arises from the region of the phase space in which the gluon momentum
is parallel to that of $\zeta$ or $\bar\zeta$.  This collinear region
is characterized as $x\sim 0$ or $\bar x\sim 0$.  In these singular regions,
it is practically impossible to observe the existence of the extra gluon
in the final hadron system.  We therefore treat the $^{^(}\!\bar\zeta{}^{^)}+\rm gluon$
system as a $^{^(}\!\bar\zeta{}^{^)}$ jet when the $^{^(}\!\bar\zeta{}^{^)} g$ invariant mass
is sufficiently close to the $\zeta$ mass.

We thus divide the three-body phase space into the two-jet
and three-jet regions.  The two-jet region is defined as
$$ x < x_c \qquad\hbox{or}\qquad \bar x < x_c \eq@@\eq$$
and the rest is the three-jet region.  The two-jet cross section
is the sum of the $\zeta\bar\zeta$ cross section and the $\zeta\bar\zeta g$
cross section in the two-jet region.

In the high energy limit $\beta\to 1$, the integrated three-jet cross section
is found to be
$$\sigma_{\rm 3j}/\sigma_0 =
{C_{\!R}\alpha_s\over\pi}\biggl[ 2 \Li2(x_c) + \log^2 x_c -{\pi^2\over6}
- 2 (1-x_c)\log{1-x_c\over x_c} + (3-2x_c)(1-2x_c) \biggr]\;,\eq@@\eq$$
whereas for fermions (both vector and axial) we have
$$\eqalignno{\sigma_{\rm 3j}/\sigma_0 &=
{C_{\!R}\alpha_s\over\pi}\biggl[ 2 \Li2(x_c) + \log^2 x_c -{\pi^2\over6} \cr\noalign{\vskip 3\jot }
&\qquad\qquad
- {1\over2} (1-x_c)(1-3x_c)\log{1-x_c\over x_c} + {5\over4}(1-2x_c) \biggr]
\;.&\eq@@\eq\cr}$$
In Fig.~5, we show the three-jet fraction as a function of $x_c$.
(Here and in the following figures, we plot $\sigma_{\rm 3j}$ normalized to
the ${\cal O}(\alpha_s)$ total cross section, not to the lowest-order
cross section.)
The three-jet fraction for the scalar is larger than that for the fermion
at large $x_c$ but becomes smaller at small $x_c\mathrel{\mathpalette\@versim<} 0.1$.
The approximate form for small $x_c$ is
$$\sigma_{\rm 3j}/\sigma_0 \simeq {C_{\!R}\alpha_s\over\pi}
\biggl[\log^2 x_c + 2 \log x_c + 3 -{\pi^2\over6}\biggr]
\eq@@\eq$$
for scalars, and
$$\sigma_{\rm 3j}/\sigma_0 \simeq {C_{\!R}\alpha_s\over\pi}
\biggl[ \log^2 x_c + {3\over2} \log x_c + {5\over4} -{\pi^2\over6}\biggr]\eq@@\eq$$
for fermions.  These predictions are not reliable at very small $x_c$
since higher order contributions become important.

The three-jet fraction for finite $m$ has a very complicated expression
and we do not write down the analytic expression here.  Instead, we show
the numerical result for $\sigma_{\rm 3j}/\sigma$ for several values of
$\beta$ in Fig.~6.
For a fixed value of $x_c$, the three-jet fraction rapidly decreases
as $\beta$ becomes smaller.  Hard gluon emission is much suppressed
when one approaches to the threshold.  This suppression comes from the
available phase space and from the structure of the gluon-emission vertex.
The large QCD enhancement near the threshold can be attributed to two-jet
configuration and one can assume that most events in the threshold region
have no extra jets in experimental searches for new colored scalar particles.

Toward the threshold region, the three-jet fraction in Fig.~6 for scalar
pairs becomes similar to that for fermion pairs from axial current.
The fermion pair from vector current shows a different behavior.  This again
reflects the fact that spin of the particle is not important in the
nonrelativistic region.

In jet analyses in $e^+e^-$ physics, one normally uses a jet-defining
algorithm by combining momentum of hadrons and compares the result with
the corresponding quantity in the quark-gluon system.  A commonly adopted
prescription uses the invariant mass of the hadron system to define a jet.
To conform with this algorithm, we may use the invariant mass variables
$$ y = {(p+k)^2\over s} \;,\qquad \bar y = {(\bar p+k)^2\over s} \;,\eq@@\eq$$
instead of $x$ and $\bar x$.  These variables are related by
$$ y = x +{m^2\over s} \;,\qquad \bar y = \bar x +{m^2\over s}
\;.\eq@@\eq$$
The definition of three-jet events in terms of $y$ is
$$ y > y_c \qquad\hbox{and}\qquad \bar y > y_c \;.\eq@@\eq$$
The three-jet fraction as a function of $y_c$ is shown in Fig.~7.

So far we have assumed that we can somehow distinguish
a $\zeta$-jet and a gluon jet.  If this is not the case, we need to
treat the three final particles in a democratic way and define the
three-jet region as
$$ y > y_c \qquad\hbox{and}\qquad \bar y > y_c \qquad\hbox{and}\qquad
y_g > y_c \;,\eq@@\eq$$
where $y_g = (p+\bar p)/s$.  Since the region $y_g \to 0$ (or
$y_g \to 4m^2/s$) contains no singularity, this definition does not
lead to significant modification of the result for small $y_c$.
In the high energy limit $\beta\to 1$, the three-jet fraction is found to be
$$\eqalignno{\sigma_{\rm 3j}/\sigma_0 &=
{C_{\!R}\alpha_s\over\pi}\biggl[ 2 \Li2({y_c\over 1-y_c})
+ \log^2{1-y_c\over  y_c} -{\pi^2\over6} \cr\noalign{\vskip 3\jot }
&\qquad\qquad
- 2 (1-2y_c)\log{1-2y_c\over y_c} + 3(1-y_c)(1-3y_c) \biggr] \;,&\eq@@\eq\cr}$$
whereas for fermions (both vector and axial) we have
$$\eqalignno{\sigma_{\rm 3j}/\sigma_0 &=
{C_{\!R}\alpha_s\over\pi}\biggl[  2 \Li2({y_c\over 1-y_c})
+ \log^2{1-y_c\over  y_c} -{\pi^2\over6} \cr\noalign{\vskip 3\jot }
&\qquad\qquad
- {3\over2} (1-2y_c)\log{1-2y_c\over y_c} + {1\over4}(1-3y_c)(5+3y_c)
\biggr]\;.&\eq@@\eq\cr}$$

\chapter{Conclusions}

We have studied ${\cal O}(\alpha_s)$ QCD correction to colored scalar
pair production in $e^+e^-$ annihilation.  Emphasis is put on gluon
emission in the final state.  We compared the configuration of the
three-jet final state with those in fermion pair production and found
that the two cross sections are quantitatively quite different.  This
has to be taken into account in the search and study of production of
scalar particles such as squarks and leptoquarks at LEP-2 and
future linear colliders.

In calculating the helicity amplitudes $e^+e^-\to \zeta\bar\zeta g$,
we found that it is convenient to decompose the amplitude into two
subprocesses $e^+e^-\to V^*$ ($V^*=\gamma$, $Z$) and
$V^*\to \zeta\bar\zeta g$.  The amplitudes take a simple form if one
works in two different Lorentz frames, the $e^+e^-$ c.m.\ frame for the
former and the $\zeta\bar\zeta$ c.m.\ frame in the latter.  In particular,
working in the ``quasi-two-body'' frame in the latter $1\to 3$ subprocess
allows one to take advantage of the strong constraints of rotational
invariance on two-body states.

\ack

One of us (J.H.) is a fellow of the Japan Society for the Promotion of
Science.
This work is partly supported by Grant-in-Aid for Scientific Research
(no.~06640369) from the Japan Ministry of Education, Science, Sports, and
Culture.

\vfil\break

\Appendix{A}{Helicity amplitudes for $e^+e^-\to \zeta\bar\zeta g$}

A number of formulations%
\ref{See {\it e.g.},
P. de Causmaecker {\it et al.}, \NPB206, 53 (1982);\unskip\nobreak\hskip\parfillskip\break
Zh. Xu, D.-H. Zhang, and L. Chang, \NPB291, 392 (1987);\unskip\nobreak\hskip\parfillskip\break

S.~J. Parke and T.~R. Taylor, \PL157B, 81 (1985);
{\bf174}, 465(E) (1986);\unskip\nobreak\hskip\parfillskip\break
A.~Kersch and F.~Scheck, \NPB263, 475 (1986);\unskip\nobreak\hskip\parfillskip\break
J.~F. Gunion and Z.~Kunszt, \PL161B, 333 (1985);\unskip\nobreak\hskip\parfillskip\break
R.~Kleiss and W.~J. Stirling, \NPB262, 235 (1985);\unskip\nobreak\hskip\parfillskip\break
K.~Hagiwara and D.~Zeppenfeld, \NPB274, 1 (1986);\unskip\nobreak\hskip\parfillskip\break
F.~A. Berends and W.~Giele, \NPB294, 700 (1987);\unskip\nobreak\hskip\parfillskip\break
V.~Barger, J.~Ohnemus, and R.J.N. Phillips, \PRD35, 166 (1987).}
to calculate helicity amplitude
\ref{M.~Jacob and G.~C. Wick, \AP7, 404 (1959).} are found in the literature.
Most of them are particularly suited for many-body final states and
numerical evaluation of the amplitudes.  The technique we employ here is
a method%
\ref{K.~Hikasa, to appear.}
based on spherical-vector basis, which is suited for manual analytic
calculations and gives amplitudes with clear physical interpretation.
The method is most useful for $2\to 2$ body processes (also $1\to 2$,
$2\to 1$).   In these processes, angular momentum conservation strongly
constrains the form of the amplitudes.  In our technique, this constraint
can be explicitly extracted in the form of a Wigner $D$ function which
depends on the scattering angles.  This part represents
the variation of the amplitude which is imposed by kinematics.
The rest of the amplitude contains purely dynamical information.

In general, the helicity amplitude for the process
$$ a (p_a, \lambda_a) + b (p_b, \lambda_b) \to
c (p_c, \lambda_c) + d (p_d, \lambda_d) $$
($\lambda_a$ is the helicity of the particle $a$, {\it etc.})
in the c.m.\ frame can be written as
$$ {\cal M} = \widetilde{\cal M}(E_{\rm c.m.},\cos\theta; \{\lambda\}) \,
d^{J_0}_{\lambda_i,\lambda_f}(\theta) \, e^{i(\lambda_i-\lambda_f)}\phi
\;, \eq@@\eq$$
where $\lambda_i=\lambda_a-\lambda_b$, $\lambda_f=\lambda_c-\lambda_d$,
$J_0=\max(\lambda_i,\lambda_f)$, and ($\theta$, $\phi$) are the scattering
angles (in the frame $\vec p_a$ is along the $z$ axis, $\vec p_c$ is
in the direction ($\theta$, $\phi$)).  The $d^J_{\lambda\lambda'}$ is
the Wigner $d$ function.  The last two factors in this formula
represent the ``minimal'' angular distribution imposed by the kinematics.
The physical meaning of $J_0$ is the smallest allowed angular momentum
for the process.  The $\cos\theta$ dependence of $\widetilde{\cal M}$
comes from higher partial waves with $J>J_0$.
If the process has only one partial wave $J$ ({\it e.g.} for two-body
decays or $e^+e^-\to \mu^+\mu^-$), the whole angular dependence can
be extracted in the form of $d^J$ and the $\phi$-dependent phase factor.

This technique can be applied to the process we consider if we note the
following two points:

\item{1)} The amplitude can be decomposed into two parts:
 (A) production of a virtual
vector boson $V^*$, $e^+e^-\to V^*$ ($V=\gamma$ or $Z$); (B) the virtual
vector boson decaying to $\zeta\bar\zeta g$.  The helicity amplitude
for the whole process is the product of the two amplitudes with a fixed
$V^*$ helicity ($\lambda_V=\pm1$, $0$), which are then summed over:
$$ {\cal M}= - \mathop{\textstyle\sum}\limits_{V}{1\over s-m_V^2}
\mathop{\textstyle\sum}\limits_{\lambda_V=\pm1,0}
{\cal M}(e^-e^+\to V^*)\,{\cal M}(V^*\to \zeta\bar\zeta g) \;.\eq@@\eq$$
(Note that we need three polarization states for both $\gamma^*$ and $Z^*$.
A fourth (scalar) polarization state need not be included since $V^*$
couples to a conserved current.)

\item{2)} The helicity amplitude for the second $1\to 3$ process
$V^* (q) \to \zeta (p) + \bar\zeta (\bar p) + g (k) $ can be treated
in the same way as $2\to2$ processes if one works in the ``quasi-two-body''
frame, the c.m.\ frame
of {\it two\/} of the final particles ({\it e.g.} $\zeta\bar\zeta$),
not in the $V^*$ c.m.\ frame.  This frame is related to the $e^+e^-$
c.m.\ frame by a boost along the gluon direction.

First, we list the helicity
amplitudes for $V^* (q,\lambda_V) \to \zeta (p) + \bar\zeta (\bar p)
+ g (k,\lambda) $ (note that the scalar particles have zero helicities).
We take the $V^*$ (and $g$) direction as the $z$ axis, and $\zeta$
direction as ($\theta$, $\phi$).  We follow the Jacob-Wick convention
to fix the phase of the fermion/vector wave functions.  The amplitudes
can be written as
$${\cal M}(V^*\to\zeta\bar\zeta g) = g_f g_s T^a \widetilde{\cal M}\;,\eq@@\eq$$
with
$$g_f=\cases{ Q_\zeta e & for $V=\gamma$, \cr
            e (T_{3\zeta}-Q_\zeta\sin^2\!\theta_W)/\sin\theta_W \cos\theta_W
                 & for $V=Z$,\cr}\eq@@\eq$$
and $\widetilde{\cal M}$ given by the following:

\noindent $\lambda_n \equiv \lambda_V - \lambda = \pm2$
$$\widetilde{\cal M} =
{2 \tau v^2 \sin^2\theta\over (1-\tau)(1-v^2\cos^2\theta)}
  e^{i\lambda_n\phi}\;,\eq@@\eq$$

\noindent $\lambda_n \equiv \lambda_V - \lambda = \pm1$
$$\widetilde{\cal M} = \mp {2\sqrt{2\tau} v^2 \sin\theta\cos\theta\over
(1-\tau)(1-v^2\cos^2\theta)}  e^{i\lambda_n\phi}\;,\eq@@\eq$$

\noindent $\lambda_n \equiv \lambda_V - \lambda = 0$
$$\widetilde{\cal M} =
-{2 \tau v^2 \sin^2\theta\over (1-\tau)(1-v^2\cos^2\theta)} - 2 \;.\eq@@\eq$$

The helicity amplitude for $e^- e^+ \to V^*$ is simpler.  We take the $V^*$
direction as the $z$ axis and the $e^-$ direction lying on the $xz$ plane
(with a positive $x$ component).  The angle between the two directions
is denoted by $\Theta$.  This choice is made to relate the two
frames by the boost along the $z$ axis, under which the helicity of $V^*$
does not change.  The amplitude conserves electron chirality so that only
$\lambda_i=\lambda(e^-) - \lambda(e^+) = \pm1$ is allowed.
$${\cal M}= (-1)^{\lambda_V} g_i \sqrt{2s}\, d^1_{\lambda_i\lambda_V}(\Theta)
\;,$$
with
$$g_i=\cases{ -e & for $V=\gamma$, $\lambda_i=\pm1$,\cr
            e (v_e\mp a_e)/\sin\theta_W \cos\theta_W
                 & for $V=Z$, $\lambda_i=\pm1$.\cr}\eq@@\eq$$
The explicit form of the $d$ functions needed is
$$d^1_{\lambda\mu}(\Theta) =
\cases{ {1\over2}(1+\lambda\mu\cos\Theta) & $|\lambda|=|\mu|=1$,\cr
-{\lambda\over\sqrt2}\sin\Theta & $|\lambda|=1$, $\mu=0$.\cr}\eq@@\eq$$

\Appendix{B}{Three-body phase space}

The differential cross section can be calculated from the helicity amplitudes
with the Lorentz-invariant three-body phase space
\def\DP#1{{d^3#1\over (2\pi)^3 2 #1^0}}
$$ d\Phi_3 = (2\pi)^4\delta^4(q-p-\bar p-k)\,\DP{p}\DP{\bar p}\DP{k} \;,\eq@@\eq$$
which in terms of the kinematic variables defined in Section~3 is
$$ d\Phi_3 = {sv(1-\tau)\over 1024\pi^4}\,
d\tau\, d\cos\Theta\, d\cos\theta\, d\phi \;,\eq@@\eq$$
where $1-\beta^2<\tau<1$, and $v=(1-4m^2/\tau s)^{1/2}$ is the $\zeta$
velocity in the $\zeta\bar\zeta$ c.m.\ frame.
(We have integrated over one azimuthal angle on which the cross section
has trivial dependence.)

Two of the kinematic variables, $\tau$ and $\theta$, specify the
final state configuration and the other two determine the orientation
of the configuration with respect to the initial beam axis.
Integrating over $\Theta$ and $\phi$ one has
$$ d\Phi_3 = {sv(1-\tau)\over 256\pi^3}\, d\tau\, d\cos\theta  \;.\eq@@\eq$$

For analytic integration over the three-body phase space for $m\neq0$,
it is easier to use ($\cos\theta$, $v$) as the integration
variables, for which the integration region is $0<v<\beta$,
$-1<\cos\theta<1$.
$$ d\Phi_3 = {s(1-\beta^2)\over 128\pi^3}\,{v^2(\beta^2-v^2)\over(1-v^2)^3}
\, dv\,d\cos\theta \;.\eq@@\eq$$

The variables ($x$, $\bar x$) have a special property
that the phase space factor is constant (Dalitz variables).
$$ d\Phi_3 = {s\over 128\pi^3} dx\,d\bar x \;.\eq@@\eq$$
The translation is made using
$$ \tau = 1-x-\bar x \;,\qquad v\cos\theta = -{x-\bar x\over x+\bar x}
\;.\eq@@\eq$$
The physical phase space region is bounded by the inequality
$$ x\bar x(1-x-\bar x) -{m^2\over s} (x+\bar x)^2 > 0 \;.\eq@@\eq$$

\Appendix{C}{Formulas for fermion pair production}

\REF\VectorC{B.~L. Ioffe, \PL78B, 277 (1978);\unskip\nobreak\hskip\parfillskip\break
G.~Grunberg, Y.~J. Ng, and S.-H.~H. Tye, \PRD21, 62 (1980);
{\bf 36}, 311(E) (1987).}
\REF\AxialC{%
J.~Jers\'ak, E.~Laermann, and P.~M. Zerwas, \PRD25, 1218 (1982);\unskip\nobreak\hskip\parfillskip\break
A.~Djouadi, \ZPC39, 561 (1988);\unskip\nobreak\hskip\parfillskip\break
J.~G. K\"orner, A.~Pilaftsis, and M.~M. Tung, \ZPC63, 575 (1994).}

\begingroup
\def\+{{+}}
\def\-{{-}}
We collect results for the familiar process of fermion pair production
$e^+e^-\to F\bar F(g)$\keepspacefactor\refm@rk{\Schwinger,\VectorC,\AxialC} in this
Appendix.  These results have been independently calculated by us.
The $ F\bar F\gamma$ and $F\bar FZ$ vertices in the lowest order have the
form
$$ -ieQ_F \gamma_\mu \quad\hbox{and}\quad -{ie\over\cos\theta_W\sin\theta_W}
 \gamma_\mu(v_F - a_F\gamma_5) \;,\eq@@\eq$$
with
$$\eqalignno{
v_F&={1\over2}\bigl[T_{3}(F_L)+T_{3}(F_R)\bigr]-Q_F\sin^2\!\theta_W \;,
&\eq@@\eq\cr\noalign{\vskip 3\jot }
a_F&= {1\over2}\bigl[T_{3}(F_L)-T_{3}(F_R)\bigr] \;.&\eq@@\eq\cr}$$
At ${\cal O}(\alpha_s)$, the correction factor is common for the photon and
the vector part of the $Z$ current.  The axial part of the $Z$ current
is modified differently if $m_F\neq0$.  We write the general Lorentz
structure of the vector and axial vertices for on-shell fermions
$$\Gamma_\mu = F_1^V(q^2) \gamma_\mu + F_2^V(q^2) i\sigma_{\mu\nu}q^\nu/m_F
\eq@@\eq$$
for the vector current and
$$\Gamma_\mu^5 = F_1^A(q^2) \gamma_\mu\gamma_5 + F_2^A(q^2) q_\mu \gamma_5
/m_F \eq@@\eq$$
for the axial current.
We have retained only terms appearing at ${\cal O}(\alpha_s)$, {\it i.e.},
terms allowed by $CP$ invariance and vector current conservation.
We normalize the vertices such that $F_1^{V,A}=1$ at the lowest order.
$F_2^{V,A}$ do not appear in this order.

We write the ${\cal O}(\alpha_s)$ corrected vertices as
$$\eqalignno{F_1^{V,A}(q^2) &= 1 + {C_{\!R}\alpha_s\over 2\pi} f_1^{V,A}(q^2)
\;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
F_2^{V,A}(q^2) &=  {C_{\!R}\alpha_s\over 2\pi} f_2^{V,A}(q^2)
\;.&\eq@@\eq\cr}$$
We find the renormalized vector form factors for $q^2>4m_F^2$
$$\eqalignno{
f_1^V &=
\biggl( - {1+\beta^2\over 2\beta} \log{1\+\beta\over 1\-\beta}+1\biggr)
\log{m_F^2\over\lambda^2}\cr\noalign{\vskip 3\jot }
&\quad +{1+\beta^2\over\beta}\biggl[  \Li2({1\-\beta\over1\+\beta})
+  \log{1\+\beta\over2\beta} \log{1\+\beta\over 1\-\beta}
- {1\over4} \log^2{1\+\beta\over1\-\beta} + {\pi^2\over3} \biggr]\cr\noalign{\vskip 3\jot }
&\quad +{1+2\beta^2\over2\beta}\log{1\+\beta\over1\-\beta} - 2 \cr\noalign{\vskip 3\jot }
&\quad + i\pi\biggl[ {1+\beta^2\over 2\beta}\biggl(
\log{m_F^2\over\lambda^2} + \log{4\beta^2\over1\-\beta^2}\biggr)
-{1+2\beta^2\over 2\beta}\biggr] \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
f_2^V &= {1-\beta^2\over4\beta}
\biggl(-\log{1\+\beta\over 1\-\beta}+i\pi\biggr) \;,&\eq@@\eq\cr}$$
where $ \beta = (1-4m_F^2/ q^2)^{1/2} $ .  We have used on-mass-shell
renormalization condition such that $F_1^V(0)=1$.  Once the prescription
for the vector vertex is fixed, there is no freedom to choose a
renormalization condition for the axial vertex because of electroweak
gauge symmetry.  In particular, $F_1^A(0)$ {\it deviates\/} from unity.
The axial form factors are found to be
$$\eqalignno{
f_1^A &=
\biggl( - {1+\beta^2\over 2\beta} \log{1\+\beta\over 1\-\beta}+1\biggr)
\log{m_F^2\over\lambda^2}\cr\noalign{\vskip 3\jot }
&\quad +{1+\beta^2\over\beta}\biggl[  \Li2({1\-\beta\over1\+\beta})
+  \log{1\+\beta\over2\beta} \log{1\+\beta\over 1\-\beta}
- {1\over4} \log^2{1\+\beta\over1\-\beta} + {\pi^2\over3} \biggr]\cr\noalign{\vskip 3\jot }
&\quad +{2+\beta^2\over2\beta}\log{1\+\beta\over1\-\beta} - 2 \cr\noalign{\vskip 3\jot }
&\quad + i\pi\biggl[ {1+\beta^2\over 2\beta}\biggl(
\log{m_F^2\over\lambda^2} + \log{4\beta^2\over1\-\beta^2}\biggr)
-{2+\beta^2\over 2\beta}\biggr] \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
f_2^A &= {1-\beta^2\over 4\beta} \biggl[ (2+\beta^2)
\biggl( -\log{1\+\beta\over 1\-\beta}+i\pi\biggr) + 2\beta \biggr] \;.&\eq@@\eq\cr}
$$
The second form factor $F_2^A$ represents the pseudoscalar part of the
axial current and does not contribute to the reaction we are interested in
as long as the electron mass is neglected.

The differential cross section for the 3-body $F\bar Fg$ final state
is for the vector current
$$\eqalignno{{d\sigma^V_\pm\over d\tau\,d\cos\theta}
&= \sigma_{0\pm}^V\,{C_{\!R}\alpha_s\over\pi}\,
{v(1-\tau)\over \beta(3-\beta^2)}\,\cr\noalign{\vskip 3\jot }
&\quad\times
\biggl[ {1+v^2\cos^2\!\theta\over 1-v^2\cos^2\!\theta}
+ {2(3-\beta^2)\tau v^2\sin^2\!\theta\over
(1-\tau)^2 (1-v^2\cos^2\!\theta)^2 }\biggr]\;,&\eq@@\eq\cr}$$
and for the axial current
$$\eqalignno{{d\sigma_\pm^A\over d\tau\,d\cos\theta}
&= \sigma_{0\pm}^A\,{C_{\!R}\alpha_s\over\pi}\,
{v(1-\tau)\over 2\beta^3}\,\cr\noalign{\vskip 3\jot }
&\quad\times
\biggl[ {2-\beta^2+v^2\cos^2\!\theta\over 1-v^2\cos^2\!\theta}
+ {4\beta^2\tau v^2\sin^2\!\theta\over
(1-\tau)^2 (1-v^2\cos^2\!\theta)^2 }\biggr]\;,&\eq@@\eq\cr}$$
with the lowest order cross sections
$$\eqalignno{
\sigma_{0\pm}^V &= {8\pi d_R\alpha^2\over 3s}\,H_{V\pm}^{2}
{\beta(3-\beta^2)\over 2} \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\sigma_{0\pm}^A &= {8\pi d_R\alpha^2\over 3s}\,H_{A\pm}^{2}
{\beta^3} \;.&\eq@@\eq\cr}$$
Here $H_{V\pm}$ and $H_{A\pm}$ are given by
$$\eqalignno{
H_{V\pm} &= - Q_F
+ {(v_e {\mp} a_e) v_F
\over \cos^2\!\theta_W \sin^2\!\theta_W}{s\over s-m_Z^2} \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
H_{A\pm} &=  {(v_e {\mp} a_e) a_F
\over \cos^2\!\theta_W \sin^2\!\theta_W}{s\over s-m_Z^2} \;.&\eq@@\eq\cr}$$

In terms of the Dalitz variables, we have for the vector current
$$\eqalignno{{d\sigma_\pm^V\over dx\,d\bar x}
&= \sigma_{0\pm}^V\,{C_{\!R}\alpha_s\over\pi}\,{1\over\beta}\,
\biggl[ {1\over 3-\beta^2} \biggl({\bar x\over x}+{x\over\bar x}\biggr) \cr\noalign{\vskip 3\jot }
&\qquad\qquad\qquad - \left({1\over x} + {1\over \bar x} \right)
+ {1+\beta^2\over 2}\,{1\over x\bar x}
-{1-\beta^2\over 4} \,\left({1\over x^2}+{1\over \bar x^2}\right)\biggr]
\;,\qquad&\eq@@\eq\cr}$$
and for the axial vector current
$$\eqalignno{{d\sigma_\pm^A\over dx\,d\bar x}
&= \sigma_{0\pm}^A\,{C_{\!R}\alpha_s\over\pi}\,{1\over\beta}\,
\biggl[ {3-\beta^2\over 4\beta^2} \biggl({\bar x\over x}+{x\over\bar x}\biggr)
+ {1-\beta^2 \over 2\beta^2} \cr\noalign{\vskip 3\jot }
&\qquad\qquad\qquad - \left( {1\over x} + {1\over \bar x}\right)
+ {1+\beta^2\over 2}\,{1\over x\bar x}
-{1-\beta^2\over 4} \,\left({1\over x^2}+{1\over \bar x^2}\right)\biggr]
\;.\qquad&\eq@@\eq\cr}$$

The total ${\cal O}(\alpha_s)$ correction can be written as the sum of
the three contributions, virtual, soft, and hard corrections.  We list each
correction term for the scalar-pair production for comparison
$$\eqalignno{
\Delta_{\rm virtual} &= {1\over\beta} A_v(\beta)
+ {1+\beta^2\over\beta} \log{1+\beta\over 1-\beta} - 2 \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta_{\rm soft} &= {1\over\beta} A_s(\beta)
+ {1\over\beta}\log{1+\beta\over 1-\beta} \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta_{\rm hard} &= {1\over\beta} A_h(\beta)
- {1\over 4\beta^3}(3+\beta^2)(1-\beta^2) \log{1+\beta\over 1-\beta}
+ {1\over 2\beta^2}(3+7\beta^2) \;,\qquad&\eq@@\eq\cr}$$
where we have collected the ``dilogarithmic'' part (dilogarithm and
double log terms) into the functions $A_i$ ($i=v$, $s$, $h$)
$$\eqalignno{
A_v(\beta) &= \biggl(-{1\+\beta^2\over 2}
\log{1\+\beta\over 1\-\beta} + \beta \biggr) \log{m^2\over\lambda^2} \cr\noalign{\vskip 3\jot }
&\quad + (1 +\beta^2) \biggl[ \Li2(1\-\beta\over 1\+\beta)
- \log{2\beta\over 1\+\beta}\log{1\+\beta\over 1\-\beta}
- {1\over4}\log^2{1\+\beta\over1\-\beta} + {\pi^2\over3} \biggr] \;,\cr
&&\eq@@\eq\cr
A_s(\beta) &= \biggl({1\+\beta^2\over2} \log{1\+\beta\over 1\-\beta}
  -\beta\biggr) \log{4\omega^2\over\lambda^2} \cr\noalign{\vskip 3\jot }\noalign{\goodbreak}
&\quad  +(1 +\beta^2)\biggl[\Li2({1\-\beta\over 1\+\beta})
         - \log{2\beta\over 1\+\beta}\log{1\+\beta\over 1\-\beta}
           -{1\over4}\log^2{1\+\beta\over 1\-\beta} - {\pi^2\over6} \biggl]
\;,\cr &&\eq@@\eq\cr
A_h(\beta) &= \biggl({1\+\beta^2\over2} \log{1\+\beta\over 1\-\beta}
 -\beta\biggr) \log{m^2\over4\omega^2} \cr\noalign{\vskip 3\jot }
&\quad +(1 +\beta^2) \biggl[ 2\,\Li2({1\-\beta\over 1\+\beta})
         + 2\,\Li2(-{1\-\beta\over 1\+\beta})
          -\log{2\over1\+\beta}\log{1\+\beta\over 1\-\beta} \cr\noalign{\vskip 3\jot }
&\qquad\qquad\qquad
+ {1\over2} \log^2{1\+\beta\over 1\-\beta} - {\pi^2\over6} \biggr]
 - 3\beta\log{4\over 1 \- \beta^2}  - 4\beta \log\beta\;.&\eq@@\eq\cr}$$
The function $A(\beta)$ in \eqA\ is the sum of these three
$$ A(\beta) = A_v(\beta) + A_s(\beta) + A_h(\beta) \;.\eq@@\eq$$

Turning to the fermion-pair production, it is found that the dilogarithmic
terms are exactly the same as for the scalar-pair production.  For the vector
part we find
$$\eqalignno{
\Delta^V_{\rm virtual} &= \Re f_1^V + {6\over 3-\beta^2} \Re f_2^V \cr\noalign{\vskip 3\jot }
&= {1\over\beta} A_v(\beta)
+ {\beta(4-\beta^2)\over 3-\beta^2} \log{1+\beta\over 1-\beta} - 2 \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta^V_{\rm soft} &= {1\over\beta} A_s(\beta)
+ {1\over\beta}\log{1+\beta\over 1-\beta} \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta^V_{\rm hard} &= {1\over\beta} A_h(\beta)
+ {9-2\beta^2+\beta^4\over 8\beta(3-\beta^2)}\log{1+\beta\over 1-\beta}
+ {39-17\beta^2\over 4(3-\beta^2)} \;,&\eq@@\eq\cr}$$
and for the axial part
$$\eqalignno{
\Delta^A_{\rm virtual} &= {1\over\beta} A_v(\beta)
+ {2+\beta^2\over 2\beta} \log{1+\beta\over 1-\beta} - 2 \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta^A_{\rm soft} &= {1\over\beta} A_s(\beta)
+ {1\over\beta}\log{1+\beta\over 1-\beta} \;,&\eq@@\eq\cr\noalign{\vskip 3\jot }
\Delta^A_{\rm hard} &= {1\over\beta} A_h(\beta)
+ {1\over 32\beta^3}(21-5\beta^2+3\beta^4-3\beta^6)\log{1+\beta\over 1-\beta}
\cr\noalign{\vskip 3\jot } &\quad + {1\over 16\beta^2}(-21+62\beta^2+3\beta^4) \;.&\eq@@\eq\cr}$$

\endgroup

\refout\vfil\break
\p@genumfalse
\FIG\figone{Feynman diagram for $e^+e^-\to\zeta\bar\zeta$ at the lowest
order.}
\FIG\figtwo{Feynman diagrams for $e^+e^-\to\zeta\bar\zeta$ at
${\cal O}(\alpha_s)$.}
\FIG\figthree{Feynman diagrams for $e^+e^-\to\zeta\bar\zeta g$.}
\FIG\figfour{Total ${\cal O}(\alpha_s)$ correction to the pair production
cross section of scalar pair (solid); fermion pair via vector current (dash);
fermion pair via axial current (dotted).  All curves are for particles
in the fundamental color representation ($C_{\!R}=4/3$) and the strong
coupling constant $\alpha_s=0.12$.}
\FIG\figfive{Three-jet fraction for scalar (solid) and fermion (dashed)
at the high energy limit, for $\alpha_s=0.12$ and $C_{\!R}=4/3$.}
\FIG\figsix{Three-jet fraction for scalar (solid), fermion-vector (dashed),
and fermion-axial (dotted) for $\beta=0.4$, 0.6, 0.8, and 1.0$,
\alpha_s=0.12$ and $C_{\!R}=4/3$.}
\FIG\figseven{Same as Fig.~\figsix, but as a function of a jet-defining
variable $y_c$.}
\figout
\vfil\break
\vfil
$$\epsfbox{fig1.eps}$$
\vfil\break
\epsfysize=550pt
$$\epsfbox{fig2.eps}$$
\vfil\break
$$\epsfbox{fig3.eps}$$
\vfil\break
\epsfxsize=400pt
$$\epsfbox{fig4.eps}$$
\vfil\break
\epsfxsize=400pt
$$\epsfbox{fig5.eps}$$
\vfil\break
\epsfxsize=400pt
$$\epsfbox{fig6.eps}$$
\vfil\break
\epsfxsize=400pt
$$\epsfbox{fig7.eps}$$
\bye

redpajama_set_name: RedPajamaArXiv


text:
Nisshin (日親, October 14, 1407 – October 21, 1488) was a Nichiren Buddhist priest during the Muromachi period in Japan. He is the son of Hinaya Shigetsugu. Nisshin was the first to use the concept of "fuju fuse" (不受不施義) which is to neither give nor receive alms. He received the posthumous name Kudō Shigeruin (久遠成院).

Biography
Nisshin was born in Kazusa province on October 14, 1407. After receiving instruction from his paternal uncle Nichiei, Nisshin entered Hokekyo-ji. In 1427, Nisshin travelled towards the capital stopping at various temples along the way in Kamakura, Kyoto, and other such cities. As he did so, he spread his teachings. In 1433 he continued towards Hizen province as a head priest of the Nakayamonryū lineage with some followers. However, due to harsh shakubu preachings, Nisshin himself was heavily opposed and eventually expelled from the Nakayamonryū lineage.  Then in 1437 as Nisshin made his way still towards the capital, he opened Honpō-ji. Along the way, he was also able to convert many temples into those following the Nichiren school of Buddhism. In doing such, he gained the opportunity to preach to the shōgun of the time, Ashikaga Yoshinori. Nisshin used this time to preach about not giving alms to temples. This talk unfortunately aggravated the shōgun so that he placed a ban upon Nisshin's sermons.

Nisshin, of course, couldn't stop himself from spreading his teachings and violated the ban. In 1440, he was imprisoned as punishment for breaking the ban and his temple destroyed. He continued to preach even during his imprisonment. As the legend goes, during his imprisonment, Nisshin had a pot put over his head to shut him up. It's said not even a scolding hot pot could make Nisshin stop sermonizing. This story became known as the tale of the "pot-wearing saint" or sometimes referred to as "the pot-wearing Nisshin."

In 1441, during the Kakitsu era, there was the Kakitsu uprising. This uprising saw the assassination of the 6th shōgun. Because of this, Nisshin was able to escape his imprisonment and began rebuilding his temple Honpō-ji. The year 1460 however saw the destruction of Honpō-ji once again. This was because Nisshin had continued to preach despite the previous ban on his actions. The temple was destroyed and Nisshin was summoned to the capital by the 8th shōgun, Ashikaga Yoshimasa. Nisshin was escorted by Chiba Mototane to Kyoto. He was taken to the residence of Hosokawa Mochikata to be imprisoned this time. While imprisoned there, he made the acquaintance of Hon'ami Honkō (Kiyonobu), of the distinguished Hon'ami family of sword experts., who became his devout follower. The two were both able to become free from their imprisonment thanks to the collaboration of local lords. These lords also frequently gave to Honpō-ji. Nisshin continued preaching in Honpō-ji until his death in 1488 at the age of 82 years-old.

Fuju Fuse
Most famous of Nisshin's practices was that of the Fuju Fuse—refusing to accept or give donations to others outside of the Hokke lineages. This practice was meant to portray an image of self-sustaining and self-governing ability within the sect. In doing so, Nisshin's line had not only regained some power to the organization but began to set a competitive tone against legal authorities. This would add fuel to the later fires of movements to remove more power from Buddhist organizations and the subsequent destruction of temples.

Personality
Nisshin was greatly revered for his skill in his monastic life. Virtuous Deeds, written by Honji-in Nissho, gave a hagiographical recount of his life, frequently highlighting his swift understanding of teachings as well as his strong ability to convert others. Nisshin had followed heavily in the footsteps of Japanese priest Nichiren—founder of Nichiren Buddhism—taking up a willful suffering for the Lotus Sutra or practicing "admonishing of the state" as Nichiren had. Nisshin had faced imprisonment for three days for his admonishing, which he met with thankful pleasure in being able to serve the Lotus Sutra so sacrificially. Out of respect to Nichiren's original views, he wished to preserve the exclusivity of the organization to maintain its purity regardless of intra-sect opposition.

Temples
Nisshin established the Honpō-ji temple in 1436, the temple represents a branch of the prevalent Nichiren buddhist sect. Honpō-ji was originally located at Higashi-no-toin Ayanokoji. The temple was destroyed in a fire in 1440, by the Shōgun Yoshinori. The temple was rebuilt in 1455 near Shijo Takakura by Emperor Go-Hanazono. In 1460, the hapless fate of the burning of the Honpō-ji temple arose again. The arson was an order given by the shōgun Ashikaga Yoshimasa, whose reasons for the fire rested on propagandistic affairs. The temple however, achieved reconstruction and relocated to Sanjo Madenokoji in 1460. The temple was prosperous for a period of time, but faced another twist of fate when it had to relocate once again. It was later rebuilt near the Ichijo Modoribashi bridge along the narrow Horikawa river. Honpō-ji's final and current location resides near Ogawa Teranouchi. The temple is also extremely renowned because its relocation was enforced during the period of the reconstruction and reorganization of the city by Toyotomi Hideyoshi in 1587. Jojakko-ji temple was also founded in (1561-1617) by Nisshin and is located in the Arashiyama area. It is a well known Nichiren sect temple and was the place where Nisshin spent his life in retirement in 1596.

References

1407 births
1488 deaths
Nichiren Buddhist monks

redpajama_set_name: RedPajamaWikipedia


Nigerian Hip Hop sensation and multiple award winning act, Panshak Henry Zamani also known as Ice Prince is set to release two mega hits on the Spinlet platform.
The songs, Aboki and More which are set for local and international release once again features the music icon at his very best.
Aboki is an up-tempo hip hop classic which is bound to get Ice's fans hitting the dance floor. More which is set for international release is a mellow acoustic ballad. Both songs not only showcase the sensitive, emotional side of Ice Prince but also celebrate the rich culture of Nigeria.
Ice Prince expressed gratitude for the support received from the brand and promised more super hits for his fans." Right from my days in Jos, music has been my own personal journey through the world. And everywhere I go on this journey, I just want to spread the love and positive change and make a difference with my music, Its very important to me to be able to do this and I'll always be grateful to Spinlet for making it happen, he concluded.


This guide is meant to tackle all the "How do I prepare for an interview with X team" questions, since 90% of the preparation is the same regardless of the industry or product group that you are interviewing for.
The fit part of the interview (anything not talking about markets or brain teasers) will be the longest and will carry the most weight. To prepare for the fit part, look hard at your resume for possible questions that could be asked (e.g. I see you studied abroad in China, how was it?). Prepare answers and try to come up with an interesting story rather than "China was really cool. Great experience".
Given that fit is so important, some of you might be tempted to not bother much with technicals. Big mistake. Technicals are there to differentiate candidates. If there are two candidates who are about equal in the fit category, you are going to take the one that either A) has a skill set you want (p.e. computer science) or B) knows more technicals. Technicals also help to show commitment to the industry.
First thing I recommend is that you read and download the Vault Guide to Finance Interviews. A quick Google search would reveal several other links should this one go down in the future. The guide is excellent in providing a basic understanding of several products and different types of questions that you could be asked.
Reading the Market Wizards books or Come Into My Trading Room by Alex Elder could also be beneficial to get an idea of what goes on in the equity markets. Market Wizards is candid interviews with top traders, and Elder's book is one of those "learn how to trade books". None of these books will give you much technical knowledge of the "you calculate the WACC by…", but the point of reading them is to give you a better sense of what people look for when they trade stocks.
The Financial Times is probably the best financial newspaper -try to read the Lex column on the back page-, but let's focus on the WSJ since that is what most people have access to. If you only have 30 minutes of free time a day and can only get your information from one source-read the front cover of the WSJ, the front page of The Marketplace section, and the Money and Investing section. The Marketplace section can be used to generate a stock pick or a talk about why a specific event makes an industry look attractive.
Your primary focus should be the money and investing section. Read the front page, Heard of the Street (back page), Moving the Market, and any article on currencies or commodities. The idea is to get a general sense of what is happening in the markets along with investor's general mindset (the driving forces). That way when you tell the interview what is your view of the economy you can provide some examples—I think Energy will be a very big sector with higher commodity prices, demand from China and India, Potash, BHP. Maybe mention a growth number you picked up in your reading about the increase in demand for Iron ore, whatever. The idea is to have a 2-3 investment "themes" and examples of those themes playing out.
Apart from the WSJ/FT, there are plenty of other sources of information, like Pimco.com -for fixed income research-, Abnormalreturns.com, seekingalpha.com, etc. These sites would keep you up to date with current events and provide plenty of investment ideas to talk about during an interview.
When it comes to the specific stock question, have at least 2 choices. You should know the stocks P/E ratio (historically high or low), Sales, Net Income, Operating Margin, products, risks to their business, areas where they are growing, what are their strengths—brand name, international exposure, and things that they have done recently. You can try to pick a stock and then steer the interview back to the general economy. So touch on its P/E ratio and comment on whether it was cheap or expensive, then say areas they were growing, some of their strengths, and how events in the general economy would affect it going forward.
You should have an idea of the current levels for all of the below, as well as what their price movements looked like over the last 6-9 months and , if possible, the market sentiment behind the moves—all of which becomes very easy if you actively follow the markets-. You should also note their support and resistance levels and events that could force them out of their ranges.
The S&P 500, The Dow Jones, Oil, Gold, 2 yr UST, 5 yr UST, 10yr UST, 30yr UST, Fed Funds Rate, O/N Libor, 3-month Libor, 6 month Libor, USD,GBP,JPY,EUR,AUD.
If you were to follow the assigned reading and keep up to date with the markets, you would probably be fine for any research interview. If you have an interview that is geared towards a particular industry, you are not expected to know everything about it, but do have the basics covered. Know what factors is the industry particularly sensitive to, main risks that companies in the sector face, or the nature of the relationship with suppliers or customers. Google or wikipedia can probably give you more than you need on this.
If someone asks you if you know about X, always respond with "I have done some reading so I know a little bit, I know that X and Y about Z. Show the interviewer your knowledge by talking about it—it may lead to more detailed questions, but if you are honest and humble about it those detailed questions that you don't know won't hurt you. If you get a question you don't know, admit you don't know it, offer some guesses with your reasoning behind them and then politely ask the interviewer what the answer is. Even if you know a great deal about a topic, it's always safer to play it humble and let your answers reveal your knowledge. If you walk into an interview with a cocky know it all attitude, there is a good chance you will get mind fucked with technicals and not get the job even if you get them all right. A matter of fit.


text:
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redpajama_set_name: RedPajamaCommonCrawl


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text:
Q: How to make two elements always stay at the same height? I have two
* one is an image one a piece of text. I need the bottom of the text to align with the bottom of the text at a relative scale. I can make them both align with margin-top but not when I change the window size.

A: If you have both elements inside a div you can simply use flexbox to align them.
PS: you should provide us with some code in order to make your question more clear.
Take a look at this guide to understand more how flexbox works.
Your code should look something like this:
HTML:

Something...

CSS:
.container {
    display: flex;
    align-items: center;
}

A: There are several ways to do this, one simple way would be to put both elements inside a div container and apply the following styles.
.elements-container{
    display: flex;
    align-items: flex-end;
    justify-content: flex-start;
 }

Note that you can adjust the justify content,see this link from css-tricks for more information, as well as add a width attribute to the container as per your needs. Hope this helped in some way.

redpajama_set_name: RedPajamaStackExchange


The children put on fine display of food from around the World showcasing their creations and presenting their knowledge and skills to parents and family members.
Holly class made English Afternoon Tea with scones and cucumber sandwiches, Oak class made delicious Chinese spring rolls and Sycamore class displayed their project work and photos.
The children thoroughly enjoyed showing their work and what they have learned over the past few weeks to parents and grandparents.
Oak Class children enjoying their spring rolls!
Sycamore children displaying their project work.
Parents looking at the project work.


The Maritime Gallery was established by the Otago Maritime Society. They still work with us today to help share the seafaring stories of Otago.
The Union Steam Ship Company (USSCo), also known as "the Southern Octopus", was formed in 1875 by James Mills. It offered both passenger and cargo services. By 1914, it was one of the largest shipping companies in the world.
The gallery has numerous builders' models of significant USSCo ships. These and other local, national and international vessels highlight advances in shipbuilding techniques, the importance of trade routes and war-time service.
Presiding over the centre of the space is the fin whale skeleton, collected by Captain Jackson Barry in 1882. Barry toured the whale around New Zealand, charging people to dine in its mouth, before giving it to the Museum.


text:
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EU: Policing: member states get ready for the first "European Data Quality Day"
Policing Databases Council of the EU EU
With the forthcoming interconnection of a host of EU databases for policing and migration, a lot more data on a lot more people will be available to a far greater number of authorities and officials than at present. However, EU databases are riddled with errors. As part of its proposal for a "European Police Partnership", the German Presidency is planning a "European Data Quality Day" which will aim to improve "the quantity and quality of data" held in the Europol Information System and the Schengen Information System.
Full-text of the document
NOTE from: Presidency to: Working Party on JHA Information Exchange (IXIM): Questionnaire preparing the first European Data Quality Day (EDQD) (10422/20, LIMITE, 9 September 2020, pdf)
With the European Police Partnership (EuPP), the Presidency is promoting the common understanding that freedom and security in the EU require effective and trustworthy cooperation between all police authorities. Within the existing legal framework, instruments should be used more effectively in a spirit of partnership. To that end, the exchange of relevant information – all available information, in best possible quality – between law enforcement authorities is a priority. It is only through even closer cooperation that we can combat growing threats more effectively throughout Europe.
As part of this initiative, we aim to encourage Member States' authorities (especially police, but also justice authorities), Frontex and Europol to make greater use of the European law enforcement databases and enter more data. However, the initiative is not linked to issues that are currently being discussed separately, such as the Foreign Terrorist Fighters (FTF) lists/ Schengen Information System(SIS) issue (about the integration of lists of FTF into the SIS).
In order to raise and maintain awareness of the importance of providing high quality data, we have planned a European Data Quality Day (EDQD), which we hope will become a recurrent European initiative.
Information exchange between police authorities of the Member States relies on sufficient and validated data in the different systems. The SIS – as the most widely used and largest information sharing system for security (and border management) in Europe – and the Europol Information System (EIS) that contains information on serious international crimes, suspected and convicted persons, criminal structures, and offences and the means used to commit them are the most important systems for (cross-border) police searches in the Member States.
A closer look however reveals certain shortcomings that illustrate the need to improve the quality and coverage of the data collected. Tragic cases that have caught the public's attention have highlighted the insufficient availability of important national information in European databases. It seems that input into the EIS and SIS varies considerably between Member States. Even when legal restrictions subjecting the conditions of issue and the proportionality of European arrest warrants to an independent and objective review are taken into account, the ratio of national to Europe-wide arrest warrants needs improvement.
The EDQD is dedicated to improving the quantity and quality of the data in the EIS and SIS. Validated data is not only a key factor in investigations, but also a precondition of data protection, so as to avoid false positive matches and further actions based on false information.
Please send your replies to the questions listed below to IXIM.DE2020@bmi.bund.de and ixim@consilium.europa.eu by 1 October 2020 COB.
To identify and to further specify possible areas of action, we rely on your input and would therefore ask you to answer the following questions.
I. SIS
1) General
i. How many alerts does your Member State enter into the SIS? Please provide the figures as of 1 January 2018 until 1 September 2020 for the categories listed below and the number of new inserted alerts for the categories listed below for the years 2017, 2018 and 2019.
Article 26 of Regulation (EU) 2018/1861 (SIS Police Regulation)
Article 32 of the SIS Police Regulation
Article 36 of the SIS Police Regulation (persons)
Article 24 of Regulation (EU) 2018/1861 (SIS Borders Regulation)
Article 36 of the SIS Police Regulation (objects)
ii. How do these numbers relate to the number of corresponding national alerts?
iii. What measures have been taken in your Member State to improve the amount and quality of your national data sets in the SIS (e.g. changes in legislation, advertising, campaigns and training)? Have improvements in this respect been achieved at national level in recent years?
iv. Can you provide best practice recommendations?
v. Which data quality tools are you using at technical level in your Member State (e.g. pre-defined code tables)? Which processes do you apply to improve data quality (e.g. instructions for end-users)?
vi. When a database check is carried out, is the SIS automatically queried in addition to the national databases (e.g. default settings, instructions)?
vii. Are there obligations or default settings so that (new) national alerts in certain national databases are automatically transferred to the SIS?
viii. Are there automations to ensure that supplementary information (such as photographs and fingerprints or person-related remarks) are uploaded to the SIS (if available in national databases)?
ix. Which improvements could still be made at national or EU level to ensure that more national data sets are entered into the SIS? How? Please explain.
2) Ratio of arrest warrants/alerts entered into the SIS to arrest warrants/alerts not entered into the SIS
i. How many national arrest warrants are currently active in your Member State? How many of these national arrest warrants concern murder, grievous bodily harm, organised or armed robbery, rape, sexual exploitation of children and child pornography?
ii. How many of those arrest warrants have been turned into European arrest warrants pursuant to Council Framework Decision 2002/584/JHA of 13 June 2002 on the European arrest warrant and the surrender procedures between Member States?
iii. Can you give reasons for the differences in the figures (ratio of national to European-wide arrest warrants)? Differences might result e.g. from legal restrictions, judicial workflows, etc. Please explain.
iv. How many of those European arrest warrants are entered into the SIS?
3) Additional alert categories
i. How does the use of other alerts (alerts inserted into the SIS by the police authorities) under Articles 32 or 36 of the SIS Police Regulation (discreet and specific checks) relate to the use of national alerts on missing persons, travelling sex offenders and foreign terrorist fighters? Can you give reasons for the differences in the figures related to the different phenomenological areas (even ratio of national to SIS alerts)?
ii. In which areas of serious and organised crime do you also use alerts issued nationally by police authorities, e.g. alerts under Articles 32 or 36 of the SIS Police Regulation (i.e. alerts other than arrest warrants)?
iii. How many alerts issued nationally by police authorities did you enter in 2019 in these areas of offending?
iv. How many of these alerts issued nationally by police authorities have been transferred to the SIS at European level?
v. Why, if applicable, have national alerts issued nationally by police authorities not been transferred to the SIS?
EIS – ratio of national data sets to data sets contributed to the EIS
1) How many data sets does your Member State contribute to the EIS? What is the ratio of national data sets to data sets contributed to the EIS?
2) What measures have been taken in your Member State to improve the amount and quality of your national data sets in the EIS (e.g. advertising, campaigns, technical solutions and training)? Have improvements in this respect been achieved at national level in recent years?
3) Can you provide best practice recommendations?
4) When a database check is carried out, is the EIS automatically queried in addition to the national databases (e.g. default settings, instructions)?
5) Are there obligations or default settings so that (new) alerts in certain national databases are automatically transferred to the EIS?
6) Is there further potential for improvement in the use of the EIS related to quantity (national/international)? If yes, please explain.
EDQD
1) Do you have preferences for media that could be taken on board with a view to an EDQD action day (e.g. information sites in police intranets, pop-up windows on personal work stations or the national SIS interface when logging in, etc.)? Do you have any other ideas for the planned EDQD?
2) As the EDQD is not supposed to be a one-off event, but rather aims at sustainable improvements in data quality and might demonstrate a need for legal changes (at national level): what long-term measures would you propose to achieve a more efficient use of the SIS and EIS?
See: NOTE from: Presidency to: Working Party on JHA Information Exchange (IXIM): Questionnaire preparing the first European Data Quality Day (EDQD) (10422/20, LIMITE, 9 September 2020, pdf)
EU: Exports of "dual-use" technology: Council's updated negotiating position
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text:
Бэньси́-Маньчжу́рский автономный уезд () — автономный уезд в городском округе Бэньси, провинция Ляонин, КНР. Уезд назван по озеру Бэньсиху.

История
В 1906 году был создан уезд Бэньси (本溪县). В 1952 году он был расформирован, а его земли перешли под юрисдикцию города Бэньси.

В 1956 году уезд Бэньси был создан вновь; его власти разместились в городе Бэньси. В 1960 году правление уезда переехало в посёлок Сяоши.

В 1989 году уезд Бэньси был преобразован в Бэньси-Маньчжурский автономный уезд.

Административное деление
Уезд делится на 1 уличный комитет, 10 посёлков и 1 волость.

Ссылки

Автономные уезды провинции Ляонин


text:
Mission,Vision & Values
Times Education Student Visa Allowance
Times Education Student Visa Allowance Application
Charles Shiao
Times Education Founder & Chief Executive Officer
Ms. May Wunnacharoensri
Managing Director & Principal Executive Officer
Mr. Attila Gaspar
Chief Compliance Officer & Principal Executive Officer
Heidi Reid
Chief Academic Officer
Dr. Tshepiso Makara
Principal Executive Officer
Ms. Ivy Chung
Mr. Jonathan Huang
Chief Public Relations Officer
Ms. Gia Jia
IIBT Board of Governors
CR Mel Congerton
Deputy Mayor, City of Swan
Mel Congerton is a Deputy Mayor at the City of Swan, where he previously served for 16years, including four years as Deputy Mayor. Cr Mel is passionate about delivering positive outcomes to residents in the Whiteman Ward and the broader City of Swan.Cr Mel is also a small business owner, and is committed to supporting local businesses to ensure that they thrive and reach their full potential.
Graham Quirk
Former 16th Lord Mayor of Brisbane (2011-2019)
After thirty-four years in public life including eight years as Lord Mayor of Brisbane, GrahamQuirk resigned from office in 2019 to pursue other interests and have more family time. Since leaving the role as Lord Mayor, Graham has been appointed to the Board of InfrastructureAustralia and to the Board of Racing Queensland. He is also CEO of Grace Education andMigration.
As Lord Mayor of Brisbane Graham Quirk introduced a number of initiatives relating to the promotion of International Students including an Ambassador Program and Conducted severalInternational Student Friendship Ceremonies generally attended by around 700 students on each occasion.
Graham Quirk was also Chairman of the Council of Mayors of South East Queensland for 8years. He oversaw an Olympics 2032 Preferability and Full Feasibility study for South EastQueensland which has now resulted in Federal and State Government support for the bid.Graham was continuing to support the bid in a voluntary capacity pre Covid 19.Graham is a Graduate of the Australian Institute of Company Directors.
Dr Tshepiso Makara has over 15 years of experience in Tertiary Education teaching and assessment, research, leadership and industry engagement. Specialising in Finance,Accounting, Economics and Entrepreneurship, Tshepiso has held various Academic positions at several universities and Higher Education Private Providers in Australia and overseas.
Tshepiso has extensive knowledge in tertiary education leadership and management. She is also involved in ongoing cross-university research collaborations with local universities and international universities, and has several ABDC A-ranked journal publications. Prior to joining Academia, Tshepiso worked as an Auditor for the Botswana Unified Revenue Services as well as an International Trade Officer for First National Bank Botswana.On a more personal level, Tshepiso is a mother to two teenage boys and sings in the church worship team.
Dr. Tracy Hopkins
Doctorate in Business Administration, MBA, Master of Training and Development
Dr Tracy Hopkins is a creative achiever with a wide range of experiences, qualifications, and interests. Tracy has an in-depth understanding of business strategic moves and its management as she has built and sold businesses in the past 20 years including an RTO anda student recruitment agent. Besides this, Tracy has served in school, business, and RTO boards.
She has won several business awards over the years for her business, demonstrating her credibility in business. Tracy is currently working as a Project Manager for Helping MindsRecovery College and has been a Sessional Academic at Curtin University for eight years teaching in the School of Management.She holds a Doctorate in Business Administration, MBA, Master of Training and Development,Post-graduate Diploma in Social Science (Developmental Studies), Bachelor of Social Science(Children and Family Studies) and CIV 40116 TAE.
Mathilda Joubert
Director of Excellence and Innovation at Sheridan College, Perth
Mathilda Joubert is Director of Excellence and Innovation at Sheridan College, Perth. She is an experienced educational leader, Board Director, advisor, trainer, lecturer, consultant and researcher, specialising in creativity and innovation, curriculum development, teaching and learning, learning theory, process improvement and the management of change. She brings strong expertise in higher education compliance, accreditation, course development, course review and higher education management acquired through serving in a range of higher education roles at Warwick University, theOpen University, the University of London, Edith Cowan University and Sheridan College.
Mathilda has been a long-term advisor to the Australian, Lithuanian and British governments on creativity in education, including serving as the expert advisor for Critical and Creative Thinking Skills to the Australian Curriculum, Assessment and Reporting Authority. She currently serves on the WesternAustralian Executive of the Australian Council for Educational Leadership, is an accredited SchoolImprovement Advisor for the Australian Council for Educational Research, a Director of GeelongBaptist College and a reviewer for the International Journal of Educational Research and the ThinkingSkills and Creativity Journal. She is a strategic thinker with strong business acumen and experience of running own business and securing/managing multiple funded grants and projects.
Mathilda is a true cross-disciplinarian with multiple VET, Bachelor and Master degree qualifications in diverse fields including music, languages, education, cognitive neuropsychology and business, and currently completing her PhD in Education at the University of Western Australia. She has published widely on creativity and innovation and is a regular speaker at academic and industry conferences. Ona more personal level, Mathilda is a committed Christian, happily married, mum of two teenagers and enjoys singing in the West Australian Symphony Orchestra Chorus.
Grace Yu
Grace Education Founder/ Brisbane Lord Mayor's Charitable Trust Ambassador
As the Founder of Grace Education, Grace is well known for her breadth of knowledge and expertise in international education. Grace has been actively involved in promoting international education, servicing the local community and assisting numerous new migrants and their families.
Grace's philosophy is to treat others with sincerity and help others with knowledge and wisdom. Since founding, Grace Education has been able to help tens of thousands of international students prepare for their studies in Australia.
Grace has constantly been involved in helping and promoting the local Chinese and Taiwanese communities in Brisbane. In 2015 she was appointed as an Ambassador of the Brisbane Lord Mayor'sCharitable Trust (LMCT). As an ambassador of LMCT, Grace organized many community fundraising events that provided support to many disadvantaged communities. Grace was elected as President of the Australian Taiwanese Chamber of Commerce Queensland (ATCCQ) in 2019.Now, even after 26 years, Grace continues to follow her passion of helping those in need with the vision of expanding Grace Education even more globally to help more of those in need.
Mr Charles Shiao, Founder and CEO of Times Education since 2014, and Director of its individual colleges. Times Education disseminates advanced education concepts with the core of education training, consulting, educational resource development, project planning and promotion. It controls and operates one Higher Education, five Australian accredited Vocational Colleges and two ELICOSInstitutes with campuses across Sydney, Brisbane and Perth.Charles' vast experience within this sector includes student recruitment, developing articulation pathways to universities, project management for offshore partnerships and business development which have all contributed to a comprehensive understanding of the industry at both the operational and strategic levels.Charles' advocacy for change and innovation has led to many new projects and developments within the Group. He aims to bring his years of experience to bear on expanding Times Education's role in-servicing its communities, and exploring how the education group can also improve opportunities for international students from all walks of life.
As an integrated group, Times Education focuses on training, consulting, resource development, project planning and promoting an advanced educational philosophy to ensure your future.
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Email: info@timesedu.com.au
> About our company
> Mission, vision and values
> Our colleges
2021 Tourism Training Australia Trainer of the year. What a significant milestone
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TOKYO, Nov 30 — French President Emmanuel Macron will discuss the Renault-Nissan alliance's future with Japan's prime minister at the G20 summit in Argentina today, seeking to defuse a brewing diplomatic row over the balance of power inside the partnership.
The auto alliance is facing the biggest test of its 19-year existence after the ousting of Nissan Motor Co Chairman Carlos Ghosn, who was arrested last week for suspected financial misconduct.
Tokyo authorities on Friday approved the maximum 10-day extension of Ghosn's detention, Japanese media said. Prosecutors have to file charges against Ghosn, 64, by Dec. 10 or arrest him on suspicion of fresh crimes to keep him in custody.
Tokyo prosecutors declined to comment. Nissan did not immediately respond to a request for comment.
Ghosn's detention in Tokyo has left the Franco-Japanese auto alliance without a leader and an advocate for the French government, which has a 15 per cent stake in Renault and has said it wants to retain the current capital structure for the alliance.
Renault controls Nissan through its 43 per cent stake, while Nissan holds a non-voting 15 per cent stake in its partner.
An official in the French presidency said Macron would discuss the alliance with Prime Minister Shinzo Abe at midday in Buenos Aires, but gave no further details.
Meeting in Paris last week, Japanese Industry Minister Hiroshige Seko and French Finance Minister Bruno Le Maire reaffirmed the two countries' support for the alliance.
A few days later, however, Le Maire said on French television that he and Seko agreed that keeping the alliance's current capital structure was desirable – an agreement the Japanese minister denied making.
The Mainichi Shimbun daily reported today that Seko had sent a rare letter of protest to Le Maire for the remarks.
Officials at Japan's Ministry of Economy, Trade and Industry said they could not immediately comment on the reported letter. A French finance ministry official said Le Maire's office had no comment.
Ghosn's arrest, including for allegedly under-reporting his income, has triggered new attempts by Nissan to shake off what it considers Renault's outsized control of it, adding to problems at Macron's Elysee.
As economy minister, Macron had masterminded the French government's surprise increase of its Renault stake in 2015, raising alarm bells inside Nissan that the Elysee was out to wield more influence over the Japanese company.
The auto alliance, which also includes Japan's Mitsubishi Motors Corp, for its part "emphatically reiterated" its commitment to the partnership yesterday after executives met in Amsterdam for the first time since Ghosn's arrest.