text:
Sol Phryne was a ferry of Sol Maritime Services Ltd. She was bought by the Palestine Liberation Organisation and sunk on 16 February 1988.

Sol Phryne was built in Japan in 1948 as Taisetsu Maru.

From 1967 to 1974, she was owned by Efthymiades Line and used for regular ferry duties between Greek islands as Eolis. In 1974, she was purchased by Sol Maritime Services Ltd., renamed Sol Phryne and was then used in the Middle East, notably evacuating Palestinian guerrillas from Beirut in 1982. She was sunk during an attempt to ferry Palestinian deportees to Haifa, Israel.

Voyage
The 6,151-ton Sol Phryne was purchased in some secrecy by the Palestine Liberation Organization and renamed Al Awda ("the Return"). The PLO planned to symbolically ferry 135 Palestinian deportees and, if they accepted the short notice invitation, hundreds of journalists and other observers, to the Israeli port city of Haifa for a "journey of return", echoing the 1947 journey of .

Israeli Defence Minister Yitzhak Rabin stated that Israel would oppose the voyage "in whatever ways we find," while Prime Minister Yitzhak Shamir labeled the journey "a declaration of war".

A different, chartered ship had been scheduled to sail from Piraeus on 9 February, but the departure was postponed several times because Greek ship owners feared commercial retaliations from Israel if their vessel was used. With this difficulty chartering a ship, on 13 February 1988 the PLO purchased the Sol Phryne in Limassol, Cyprus at auction for $600,000. By the time of the sinking the crew of the ship had not been informed of the new owners.

On 15 February, three high-ranking military officials of the PLO were assassinated in Limassol by a remote-controlled bomb planted on their car.

18 hours later, on the night of 15 February, a limpet mine attached to the hull exploded and holed a fuel tank of the Sol Phryne, flooding it and causing the ship to list. No casualties were reported but this ended the attempt.  Yassar Arafat alleged that this was done by Israeli frogmen but did not provide any evidence to support his claim, The Sol Phryne was raised and transferred to Bijela, in Yugoslavia.
As Time reported, "Israel officially denied complicity in the car bombing but hardly bothered to conceal its role in disabling the ferry" and suspicions of Israeli involvement were further reinforced when Israeli Transport Minister Chaim Corfu threatened that, if a further attempt was made by the PLO, "its fate will be the same". Fuad al-Bitar, Athens representative of the PLO told an Athens news conference that "it is clear that the only one interested" in the sabotage was Israel. In July 2008, Haaretz referred to this attack, without admitting Israeli responsibility, in the context of the scheduled and ultimately successful Free Gaza Movement voyage which broke Israel's siege of Gaza.

Three claims of responsibility were made, two of them being:
 an anonymous caller, claiming to be from the Palestine Salvation Front because "rejected many times Yasir Arafat's idea to arrange this propaganda trip" - denied by Abdul Hadi al-Nahhad for the Damascus-based group and by the PLO.
 a telephone call received by the Associated Press claimed the attack for the Jewish Defence League

Israel's responsibility
In 2011 the Journalists Dan Margalit, Ronen Bergman published a book, in which they claimed that Israel's Shayetet 13 unit, was responsible for the bombing of the Sol Phryne. And that Israel's Minister of Education Yoav Galant was the commander of the operation.

See also

Gaza flotilla raid

References

External links
 U.S. leftists confirm plans to sail to Gaza to break siege, Haaretz
 S/S Taisetsu Maru (Swedish)

International maritime incidents
Espionage scandals and incidents
Ship bombings
Maritime incidents in 1988
Ships built by Mitsubishi Heavy Industries
1948 ships
Palestine Liberation Organization
Israeli–Palestinian conflict


Military researchers in the United States are trying to create super-warriors by focusing on the tongue.
Researchers at the Florida Institute for Human and Machine Cognition hope to turn fiction into reality by giving army rangers 360-degree unobstructed vision at night and allowing Navy Seals to sense sonar in their heads while maintaining normal vision underwater.
The device, known as "Brain Port", was pioneered more than 30 years ago by Dr Paul Bach-y-Rita, a University of Wisconsin neuroscientist.
Bach-y-Rita began routing images from a camera through electrodes taped to people's backs, discovering that the tongue was a superior transmitter.
A narrow strip of red plastic connects the Brain Port to the tongue, where 144 microelectrodes transmit information through nerve fibres to the brain.
Dr Anil Raj, the project's lead scientist, said instead of holding and looking at compasses and bulky hand-held sonar devices, the divers can process the information through their tongues.
In testing, blind people found doorways, noticed people walking in front of them and caught balls.
A version of the device, expected to be commercially marketed soon, has restored balance to those whose vestibular systems in the inner ear were destroyed by antibiotics.
Michael Zinszer, a Navy diver and director of Florida State University's Underwater Crime Scene Investigation School, took part in testing using the tongue to transmit an electronic compass and an electronic depth sensor while in a swimming pool.
He said: "You are feeling the outline of this image. I was in the pool, they were directing me to a very small object and I was able to locate everything very easily."
Underwater crime scene investigators might use the device to identify search patterns, signal each other and "see through our tongues, as odd as that sounds", Zinszer said.
Raj said the objective for the military was to keep Navy divers' hands and eyes free.
"It will free up their eyes to do what those guys really want to, which is to look for those mines and see shapes that are coming out of the murk."
Sonar is the next step. A lot depends on technological developments to make sonar smaller - hand-held sonar is now about the size of a lunch box.
"If they could get it small enough, it could be mounted on a helmet, then they could pan around on their heads and they could feel the sonar on their tongues with good registration to what they are seeing visually," Raj said.
The research at the Florida institute, the first to research military uses of sensory augmentation, is funded by the US defence department.


I had some downtime last Wednesday afternoon and decided to bake cookies for my evening yoga class. Well, and let's be honest…for my own personal enjoyment too! I tend to always use the same cookie recipes and wanted to try something new with a fall twist. I found a recipe for pumpkin oatmeal cookies that sounded perfect. I decided to divide the batter in half and mix chocolate chips into one batch and white chocolate chips and dried cranberries into the other.
The cookies were a huge hit with my yogis and I cannot even count how many I have eaten over the past few days. Addictive. The texture is definitely more on the soft side and the cookies have to bake a little longer than normal. I am a fan of soft cookies anyway and I think the texture totally fits with the pumpkin flavor. The cookie dough includes a heavy dose of pumpkin pie spice that really give these their fall flavor. These cookies will become a seasonal favorite in our house!
In a medium bowl, whisk together flour, baking soda, cinnamon, pumpkin pie spice, and salt.
In the bowl of a stand mixer, fitted with the paddle attachment (or in a large bowl with a handheld mixer), beat butter and sugar on medium-high speed until lightened in color and fluffy, 3 minutes. Add in eggs and vanilla and mix well. Add in pumpkin puree and mix until combined. Reduce mixer speed to low and add in dry ingredients. Finally, add in oats until just combined.
Divide batter in two and add chocolate chips into one half and white chocolate and cranberries into the other.
Using a spoon, drop about 2 tablespoon rounds onto prepared baking sheets, about 2-3 inches apart. Bake 12-14 minutes or until slightly browned. You may need to rotate the baking sheets halfway through depending on the temperature of your oven. Allow to cool before transferring to a wire rack.


text:
Q: How to get the value of inner html data for storing the value to database How do I get this JavaScript variable data to PHP, so that I can insert Latitude and Longitude data to the database or any other way to get the user's location and store it in the database.

<!DOCTYPE html>

Click the button to get your coordinates.

  <button onclick="getLocation()">Try It</button>

A: it seems like you need to use AJAX to pass the value of your javascript variable to PHP.
In your HTML file (index.html)
index.html

<button onclick="getLocation()">Try It</button>

In your ajax file (ajax-processor.php)
$lat = $_POST['lat'];
$long = $_POST['long'];

//your code to insert to the database here using the $lat and $long variable

Make sure that the URL for the PHP file is correct.
You may read more about AJAX and how to pass data from JavaScript to PHP in my blog post: https://www.davidangulo.xyz/website-development/how-to-pass-value-from-javascript-to-php/

redpajama_set_name: RedPajamaStackExchange


Greetngs and Welcome to the Hill!
It's a great time to be a Hilltopper, but an even greater time to be a student in our College of Health and Human Services at WKU! With the positive hiring trends in both the health and human service sectors, these are exciting and dynamic times for our students and our graduates.
We welcome you to become involved in the numerous opportunities and experiences provided by our faculty and staff. Our mission in the CHHS is to inspire the discovery and application of knowledge in health and human services. We hope that you take advantage of your college experience at WKU by exploring the programs, resources, service learning opportunities as well as study abroad experiences that are available to you.
"Experiential learning", or "learning from doing" enhances positive outcomes, including enhanced student learning, on-time graduation, and seamless transition into the workforce. Hands-on application of knowledge can help to build a student's skills and networks, as well as offer valuable professional experience. Here in the CHHS, we have long been conducting experiential learning. However, we are poised to take the learning experience that students receive in CHHS to an even higher level that not only enhances learning, but also positions them for success after graduation.


Christian Bauer is an innovative and modern company with a rich tradition and history.
The brand offers its customers an attractive range of engagement and wedding rings made from high-quality raw materials such as gold and platinum, and carefully selected diamonds.
Each ring is unique and made with precision by goldsmiths who have years of experience. High quality and special comfort are the result of extended experience gained by the Christian Bauer company. The innovative products are characterised by modern and elegant design.
Timeless elegance and innovative production technology characterise the brand, Christian Bauer.


text:
New Ferrari 488 GT Modificata is a limited edition track days-only supercar
The new, limited edition Ferrari 488 GT Modificata takes its technology from the 288 GT3 and 488 GTE, the pushes to achieve its full athletic potential. That potential is exclusively for use during track days and at Ferrari Club Competizioni GT events.
The Ferrari 488 GT Modificata takes its name from the Ferrari jargon meaning better performance. It takes its prowess from the genes of the 488 GT3 and the 488 GTE. It also has new technologies, mainly linked to the powertrain, that are no longer limited by the FIA Balance of Performance.
The 488 GTE competes in the World Endurance Championship. Ferrari calls the 488 GT3 the "queen of GT racing". The 488 GT3 has delivered 350 wins and 630 podiums at national and international races as well as the FIA World Endurance Championship Drivers', Teams' and Manufacturers' titles. The 488 GTE has won the 24 Hours of Le Mans and the Petit Le Mans. Ferrari tuned the new model at the Nordschleife.
It's powered by a twin-turbo V8 that delivers 690 horsepower. Ferrari says that it does all that by utilizing new high-performance mapping that doesn't compromise the car's predicted reliability. The car's gearbox is available with different transmission ratios. The clutch is made of carbon fiber.
Ferrari has given the car unique high-downforce aerodynamics that shift the position of the car forward. This positioning generates higher downforce without increasing drag, allowing the model to be more efficient than its racing counterparts. The car has downforce of over 2,204 pounds at 142 mph.
The car's body is made almost entirely of carbon fiber. It has an aluminum roof and uprights.
Ferrari has given the 488 GT Modificata the 488 GTW's suspension. The braking system was developed in partnership with Brembo and features low residual torque calipers that are fitted to world championship cars. Its antilock brake system comes from the 488 GT3 Evo 2020, with specific settings.
Each model comes standard with a V-Boz acquisition system, which combines with Bosch's telemetry data acquisition system and allows data to be downloaded directly onto a USB stick.
A high-resolution rearview camera is also standard.
Customers will be able to nearly fully customize their 488 GT Modificata. It will initially only be for drivers who, in recent years, have participated in Competizioni GT with Ferrari or Club Competizioni GT.
The 488 GT Modificata will be admitted to Club Competizioni GT events. In 2021, customers will have the chance to participate in five events at tracks including Virginia International Raceway, Monza, Watkins Glen, Suzuka, Nurburgring, and Finali Mondiali.
PrevPreviousRefreshed 2021 Lincoln Nautilus gets a new interior aimed at elevating the model
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redpajama_set_name: RedPajamaCommonCrawl


text:
Holiday, Episode
Epic Mickey Offers No Choice
It's that time of year again.
Since you should know by now that I have the Christmas week off and you showed up anyway, I guess we're all going to be sitting in silence for the next five minutes while you contemplate how much you appreciate me.
(10 seconds of silence)
Oh, fine. Here's some clips.
Darksiders Edit
And what right does War have to be angsty about his life? He's fucking War! He's never had to queue up at the job center or pine after ex-girlfriends who left him for a surfer; he just breaks things! If I were War, and I'd just hoisted a seven-foot demon into the air and chopped him in half with a single swing, I wouldn't stand there scowling, I'd go, "Fucking hell! Did anyone see that? I am squirting machismo out of my nipples over here! I am a monster truck that walks like a man!"
Dark Void Edit
After two years of this, I thought I was immune to being disappointed by games. Whoops, that's my entire opinion on Dark Void given away in one sentence, isn't it?
Mass Effect 2 Edit
Off-roading around random planets is now replaced by scanning the surface from orbit, launching probes to extract resources, which is as interesting as it sounds, and it sounds like this: bwwwhhhhaaaaaaaahhhhhhh.
Aliens vs Predator Edit
This is Aliens vs. Predator, though, so there are Predators, too, who show up now and then to a chorus of "WHAT THE FUCK WAS THAT?" from nearby human NPCs. And I'm waiting for someone to reply, "It's a fucking Predator, you moron!" The human race has only encountered them like 50 times. Did no one document anything? Didn't at least one survivor put an entry on his fucking LiveJournal?
Battlefield: Bad Company 2 Edit
A better name for the Modern Warfare thing would be Deranged Paranoid Power Fantasy For Right-Wing Shut-ins Who Would Blow Their Own Nuts Off The Moment They Were Handed An Actual Firearm And Probably Already Have Done Shooter.
Final Fantasy XIII Edit
Some people have told me that FF13 gets good about 20 hours in. You know that's not really a point in its favor, right? Put your hand on a stove for 20 hours and yeah, you'll probably stop feeling the pain, but you'll have done serious damage to yourself.
Red Steel 2 Edit
But anyway, here's Red Steel 2, and I've got to admit, this is probably the best motion-control combat I've seen on the Wii. Of course, it still isn't very good. It's like being the best at jerking off to your sister in the shower: you only won because no one else entered, and you probably shouldn't have been doing it in the first place.
Dead to Rights: Retribution Edit
You play the preposterously named Jack Slate, a cop so close to the edge he has to wear a safety harness, who surgically implants rare steaks into his muscles, and who missed a golden opportunity when he chose policing rather than opening a roofing business. Someone murdered his father, so he's out searching for answers, and he's letting his gun do the talking, and his gun only knows one very loud word!
Monster Hunter Tri Edit
But I guess calling it Hunter/Gatherer of Innocent Young Dinosaurs Pathetically Mewling Their Last as the Memory of Their Mother's Warmth Drifts Away to Be Replaced by the Unforgiving Coldness of. . ., oh fuck it, let's just call it You Bastard.
Alan Wake Edit
It's like a crime drama about a detective who can only concentrate when he's around pastry, so every week the crime has to conveniently take place in a bakery or within walking distance of a pie shop.
Crackdown 2 Edit
And joining online random games is like walking into an aviary full of nitrous oxide and trying to play Scrabble with the kookaburras while they stand around having sex with your mum.
Shadow of the Colossus Edit
It creates an effective contrast, like riding a bike down a long and peaceful country road and every other hundred yards the bike turns into a bear.
Metroid: Other M Edit
On an educated guess, though, the evil guy was probably the one with the evil moustache.
Halo: Reach Edit
...and the story is focused on a small commando unit whose members spend the entire game having a prolonged "Who can have the noblest death?" competition. Oh, come on, this isn't a spoiler. They wouldn't characterize this many NPCs if they weren't gonna pick them off like After Eight mints. The very first image in the game is a brief flash-forward depicting your helmet lying discarded in the dust of battle-scarred terrain. What the fuck do you think happens in the end? Your character thrillingly and climatically gets a little bit hot?
Dead Rising 2 Edit
What I like about it is it's a true water cooler game, and I'm not taking about all that Facebook game bollocks where you can boast to all your friends because you stuck a radish up an imaginary cow's arse.
Enslaved: Odyssey to the West Edit
If you said to me "sci-fi reimagining of another culture's mythology mostly concerned with robots," I would immediately think Too Human and punch you in the bollocks for reminding me of it.
Star Wars: The Force Unleashed II Edit
So I look forward to seeing how the fanboys justify The Force Unleashed II, because it is the most grossly offensive and mishandled application of intellectual property since the Schindler's List Easy-Bake Oven!
April Fools 2010 Edit
(speaking very slowly with ticking clock in the background)
Ay, in the very temple of Delight
Veil'd Melancholy has her sovran shrine,
Though seen of none save him whose strenuous tongue
Can burst Joy's grape against his palate fine;
His soul shall taste the sadness of her might,
And be among her cloudy trophies hung.
This episode has no addenda.
Retrieved from "https://zeropunctuation.fandom.com/wiki/Holiday_2010?oldid=14111"


text:
\section{Introduction}
Lattice calculations have started extracting phenomenologically
relevant results with high precision and controlled uncertainties
\cite{Davies:2003ik}.  This requires simulations with dynamical
quarks, lattice actions with small discretization errors and good
control over perturbative corrections.  Effective field theory methods
are an important tool to achieve these goals. They enable a judicious
design of lattice actions with small discretization errors.  On the
other hand, the complicated form of improved lattice actions puts a
burden on perturbative calculations required to match the output of
lattice simulations to continuum physics.  For the matching to be
meaningful, perturbative calculations have to be performed with {\it
  exactly the same} action and operators, with which the
non-perturbative simulations are done.

The purpose of the present paper is to compute the matching
coefficients of the four-fermion $\Delta S=2$ operators relevant for
$K-\bar K$ mixing for the Asqtad lattice action, an improved staggered
fermion action used in many of the current simulations with dynamical
quarks. The strength of $K-\bar K$ mixing is determined by the matrix
element $\langle \bar K | (\bar s d)_{V-A} (\bar s d)_{V-A} | K
\rangle \sim B_K(\mu)$, where $\mu$ is the renormalization scale.  The
determination of $B_K(\mu)$ has become an important goal of lattice
simulations, since a precise value of this parameter translates into a
stringent constraint on the unitarity triangle.  The current
constraint is dominated by theoretical uncertainties, the largest
being the uncertainty in the value of $B_K$ \cite{Charles:2004jd}.
The experimental input comes from $K\rightarrow\pi\pi$ decays and has
percent level precision \cite{Eidelman:2004wy}.

Results of lattice calculations for $B_K(2~{\rm GeV})$ have been
summarized in \cite{Hashimoto:2004hn,Wingate:2004xa}; a central value
of $ B_K(2~{\rm GeV}) = 0.58(4)$ from quenched determinations was
advocated in \cite{Hashimoto:2004hn}. The uncertainty associated with
this value does not include the systematic error induced by quenching,
i.e.~neglecting the effects of dynamical fermions. The errors from
quenching are presumed to be of the order of 15\%, but are very hard
to estimate reliably \cite{Sharpe:1998hh}. In order to go beyond this
accuracy, the calculation needs to be performed with dynamical
fermions. The virtue of the improved action for which we perform our
calculation is that it allows for precise calculations with light,
dynamical quarks.  The action is used by the MILC collaboration
\cite{Bernard:2001av} and consists of the Asqtad discretization of
staggered quarks \cite{Lepage:1998vj,Orginos:1999cr} coupled to a
Symanzik improved gluon action \cite{Luscher:1985zq}.

The nonperturbative calculation of the matrix elements of the lattice
operators on the MILC dynamical configurations was discussed in
\cite{Gamiz:2004qx}, along with preliminary results for the bare $B_K$
parameter. Together with the matching coefficients given in this
paper, these results determine the renormalized continuum value
$B_K(\mu)$ \cite{CDGSW05}.

In \cite{Becher:2002if} two of us suggested an approach to lattice
perturbation theory that allows an efficient separation of energy
scales that appear in matching calculations -- the inverse lattice
spacing, which plays the role of the ultraviolet cut-off, and the
physical masses and momenta.  As a result of this scale separation, we
are able to treat the complicated integrals that appear in lattice
perturbation theory by algebraic means.  The approach allows a very
high degree of automation, thereby circumventing the complexity of
improved lattice actions to a certain degree. We have used this method
in \cite{Becher:2003fu} to compute the one-loop relation between the
bare lattice mass and the pole mass for the Asqtad action. In the
present paper we compute the matching coefficient for $\Delta S = 2$
four-fermion operators for the Asqtad action, using the algebraic
technique \cite{Becher:2002if} as well as numerically. The agreement
of the results obtained using these two completely different
techniques provides a strong check on the calculation.

The lattice-to-continuum matching coefficients for the $\Delta S=2$
four-quark operators have been previously calculated for the standard,
unimproved, discretization of staggered fermions
\cite{Ishizuka:1993fs}, as well as for a class of improved
staggered actions \cite{Lee:2003sk}. While none of these results is
directly relevant for the Asqtad action, we have checked that we
reproduce the known result for the unimproved action, once we switch off
all improvement terms.

The rest of the paper is organized as follows. In the next Section we
give the discretization of the four-fermion operators. In Section
\ref{sec:match} we discuss how the matching is performed and give the
result for each of the relevant Feynman diagrams. In Section
\ref{sec:TI} we include the tadpole improvement terms. We present our
results for the matching coefficients that relate bare lattice
operators to continuum ${\overline {\rm MS}}$ operators in Section
\ref{sec:results}.  Finally, in the last Section we summarize our
results and compare the size of the perturbative corrections found for
different staggered actions.

\section{Staggered and naive lattice operators}

For energy scales below the charm quark mass, the continuum effective
Hamiltonian relevant for $K-\bar K$ mixing reads \cite{Buras:1990fn}
\begin{equation}\label{Heff}
   H_{\rm eff}^{\rm weak} = \frac{G_F^2 m_W^2}{16\pi^2} C(\mu)\, Q(\mu),
\end{equation}
where
\begin{equation}
    Q = (\bar s d)_{V-A}\,(\bar s d)_{V-A}.
\label{qcont}
\end{equation}
The possibility to describe $K-\bar K$ mixing by a single operator is
a consequence of the $V-A$ structure of weak interactions and the
Fierz identities that facilitate expressing any relevant four-quark
operator in canonical form (\ref{qcont}).

Lattice simulations of the $K-\bar K$ mixing require introducing the
operator $Q$ on the lattice. It is convenient to perform the
perturbative calculations with naive instead of staggered quarks and
to carry out the spin-diagonalization and the reduction from the sixteen
to four doublers (or ``tastes'') afterwards.  We use the standard
discretization for the staggered four-quark operators and now show how
these operators can be rewritten in terms of the naive fermion field.

The naive fermion field $\psi$ and the staggered field
$\chi$ at lattice site $n=(n_1,n_2,n_3,n_4)$ are related by
\begin{align}
\psi(n)&=\Gamma_n \,\chi(n) &
\bar\psi(n)&=\bar\chi(n)\,\Gamma_n^\dagger \label{eq:psi}
\end{align}
where
\begin{equation}
\Gamma_n=(\gamma_1)^{n_1}\,(\gamma_2)^{n_2}\,(\gamma_3)^{n_3}\,(\gamma_4)^{n_4} \,.
\end{equation}
We choose a Hermitian representation of the Euclidean Dirac algebra with
\begin{align}
\left \{ \gamma_i, \gamma_j \right\}&=2\delta_{ij} & &\text{and} &\gamma_5&=\gamma_1\,\gamma_2\,\gamma_3\,\gamma_4 \,.
\end{align}

When written in terms of staggered fermions, the quark action becomes
spin diagonal and three of the four components of the quark field
$\chi$ can be dropped. In perturbation theory it is more convenient to
keep all components, and replace $n_f\rightarrow n_f/4$ at the end
of the calculations to obtain the result for the single component
field.

The fields $\chi(2N+A)$ are collected into a set of Dirac fields
$q(2N)$ that live on the even lattice sites and are spread over a unit
hypercube \cite{Gliozzi:1982ib, Kluberg-Stern:1983dg,Sharpe:1993ur}
($A_\mu=0$ or 1, $\mu=1\dots 4$)
\begin{equation}
q(2N)_{\alpha i j}=\frac{1}{8}\sum_A (\Gamma_A)_{\alpha,i}\; \chi_j(2N+A)\,.
\end{equation}
The index $\alpha$ is the Dirac index of the new field and $i$ the
``taste'' index. The second taste index $j$ runs over the components
of the field $\chi$. Staggered fermions have only one component, while
the four component of the naive field give rise to $4\times4$
tastes. Bilinear quark operators with spin structure $\gamma_S$ and taste structure $\xi_T=\Gamma_T^*$ (with $T$ again on the unit hypercube) are
\begin{multline}
\bar q(2N) (\gamma_S\otimes \xi_T) q(2N)\\=\frac{1}{16}\,\sum_{A,B} \bar\chi(2N+A) \;\chi(2N+B)\, \frac{1}{4}{\rm tr}( \Gamma_A^\dagger\,\gamma_S \Gamma_B\,\Gamma_T^\dagger ) \,.
\end{multline}
Since the quark fields in the operators are at different lattice
points, they need to be connected by Wilson lines in order to make the
operators gauge invariant. We suppress these Wilson lines, but it is
understood that gauge strings among all possible shortest paths
connecting the quark fields are inserted and the operator is divided
by the number of paths.  Using (\ref{eq:psi}) we rewrite the operator
in terms of the naive fermion field:
\begin{multline}
\bar q(2N) (\gamma_S\otimes \xi_T) q(2N) \\
=\frac{1}{16}\,\sum_{A,B} \bar\psi(2N+A)\,\Gamma_A\, \Gamma_B^\dagger\,\psi(2N+B)\, \frac{1}{4}{\rm tr}( \Gamma_A^\dagger\,\gamma_S \Gamma_B\,\gamma_T^\dagger )\,.
\end{multline}
 Let us write out the vector and axial currents at $N=0$ with unit taste structure in
terms of the naive quark field $\psi(n)$. We find
\begin{multline}
 \bar q\, (\gamma_\mu\otimes 1)\, q
= \frac{1}{16}\sum_{A} \delta_{A_\mu,0} \\ \left[
  \bar\psi(A)\gamma_\mu\psi(A+\hat\mu)+\bar\psi(A+\hat\mu)\gamma_\mu\psi(A)\right]\,, \label{eq:Amu}
\end{multline}
and ($\overline{A}=(1,1,1,1)-A$)
\begin{multline}
 \bar q\, (\gamma_\mu\gamma_5\otimes 1)\, q
= \frac{1}{16}\sum_{A} \delta_{A_\mu,0} \\ \left[
  \bar\psi(A)\gamma_\mu\gamma_5\psi(\overline{A+\hat\mu})+\bar\psi(\overline{A})\gamma_\mu\gamma_5\psi(A+\hat\mu)\right] \,.\label{eq:Vmu}
\end{multline}
In the continuum limit, the massless staggered action has a
$SU(4)_L\times SU(4)_R$ chiral symmetry (for a single staggered field)
and one would naively expect to find fifteen Goldstone bosons after
chiral symmetry breaking, corresponding to the fifteen traceless taste
matrices.  However, this symmetry is explicitly broken to an axial
$U(1)$ symmetry by terms in the action proportional to the lattice
spacing squared.  The generator of the remaining axial symmetry is the
matrix $\gamma_S\otimes\xi_T=\gamma_5\otimes\gamma_5$. In our case,
this implies that only the kaon with taste structure $\gamma_5$
becomes massless in the chiral limit. For this reason, the simulation
is done with currents having $\xi_T=\gamma_5$ taste structure and not
the unit matrix as in (\ref{eq:Amu}) and (\ref{eq:Vmu}).  However, it
has been shown that the result for diagrams in which the fermions in
the operators are not contracted are identical for the Dirac and taste
structures $\Gamma\otimes \Gamma'$ and $\Gamma\gamma_5\otimes
\Gamma'\gamma_5$ \cite{Sharpe:1993ur}.\footnote{The reason is that in
  this case, one can view the four fermions as four different quark
  flavors and perform separate axial $U(1)$ transformations on each
  field.} For our perturbative calculation we will thus use
(\ref{eq:Vmu}) instead of the vector current $\gamma_\mu\otimes
\gamma_5$ and (\ref{eq:Amu}) in place of $\gamma_\mu\gamma_5\otimes
\gamma_5$.

The operator $Q$ for which we want to perform the matching calculation
is a product of two $V-A$ currents. We will see that QCD corrections
to bare lattice four-quark operators affect the vector and axial parts
differently; as a consequence currents of the form $V+A$ are
generated. A minimal set of lattice operators that matches to the
continuum and closes under renormalization consists of 4 scalar and 2
pseudoscalar operators. Schematically these operators are
\begin{align}
&\begin{aligned}
Q_{1} &= (\bar s^a d^a)_V (\bar s^b d^b)_V, &
\phantom{o}& Q_{2}= (\bar s^a d^b)_V (\bar s^b d^a)_V, \nonumber\\
 Q_{3} &= (\bar s^a d^a)_A (\bar s^b d^b)_A, &
\phantom{o}& Q_4 = (\bar s^a d^b)_A (\bar s^b d^a)_A,
\end{aligned} \label{ques}\\
&\begin{aligned}
& Q_{5} = (\bar s^a d^a)_V (\bar s^b d^b)_A+(\bar s^a d^a)_A (\bar s^b
d^b)_V, \\
& Q_{6}= (\bar s^a d^b)_V (\bar s^b d^a)_A+(\bar s^a d^b)_A (\bar s^b d^a)_V\,.
\end{aligned}
\end{align}
$V$ and $A$ are the vector and axial currents with taste structure
$\xi_T=\gamma_5$. The color indices $a,b$ indicate which fields are
connected by Wilson lines. The pseudoscalar operators $Q_{5,6}$ only
mix amongst themselves and their $K-\bar K$ matrix element vanishes,
because of parity. In the following we will therefore only consider
the renormalization of the operators $Q_{1-4}$.

The above operators are used in the nonperturbative calculation of the
matrix elements by the HPQCD collaboration \cite{Gamiz:2004qx,
  CDGSW05}. In contrast to the lattice action, these operators are not
Symanzik improved.

\section{Matching calculation\label{sec:match}}

To perform the matching we calculate a physical quantity in the
continuum and on the lattice, expand around the continuum limit, and
adjust the Wilson coefficients of the lattice operators in such a way
that they reproduce the continuum result. Specifically, we determine
the bare lattice Wilson coefficients from the quark-quark scattering
amplitude
\begin{align}
{\cal A}= Z^2 C^{\rm bare}_{i} \langle O^{\rm bare}_i \rangle= Z^2 C_{i}\,Z_{ij} \langle O_j \rangle =
Z_{\rm lat}^2 C^{\rm lat}_{i} \langle O^{\rm lat}_i \rangle\, ,\label{eq:matching}
\end{align}
where $Z$ and $Z_{\rm lat}$ are on-shell quark wave-function
renormalizations and $\langle O \rangle$ is the amputated four-quark
Green's function with an insertion of the operator $O$. The
lattice-to-continuum matching coefficients are independent of the
quantity chosen to perform the matching. At one-loop order, it is
simplest to regulate infrared divergencies with a gluon mass and to
calculate the scattering amplitude of massless quarks at zero external
momentum.

At tree level in the continuum limit, the operators $Q_i$ are
identical to their continuum counterparts; this implies that no tree
level matching is required.  At one loop the matching coefficients
$C_i^{\rm lat}$ are obtained by calculating the difference between the
lattice and continuum one-loop diagrams. In the difference, the
infrared divergencies cancel. Below we present such a calculation for
the set of lattice operators described above.

For unimproved staggered fermions the renormalization of the axial
current operator with
$\gamma_S\otimes\xi_T=\gamma_\mu\gamma_5\otimes\gamma_5$ is finite and
identical in the continuum and on the lattice. This happens because it
renormalizes in the same way as the vector current with unit taste
structure $\gamma_\mu\otimes 1$ which has exactly the same form as the
quark-gluon coupling in the Lagrangian.  Because of the improvement
terms, this is not true for the Asqtad action and we will need to
evaluate the matching not only for the four-quark operators but also
for the current.

The matching calculation requires computing matrix elements
of certain operators in lattice perturbation theory; to do so
 we
use the approach described in \cite{Becher:2002if,Becher:2003fu}.
In those  references an expansion of the lattice integrals
around the continuum limit is introduced by utilizing the
technique of asymptotic expansions.
The asymptotic expansion  around the continuum limit
splits the lattice diagrams into two parts: (i) a soft part which is
obtained by evaluating continuum loop integrals (in analytic regularization)
and is independent of
the discretization and (ii) a hard part which depends on the
discretization but is independent of particle masses and momenta.
The proximity of the soft part of the lattice loop integrals
and the continuum integrals in dimensional regularization
permits significant simplifications when computing the difference
of the lattice and continuum Green's functions required for
matching calculations.

There are five diagrams (plus permutations) that contribute at ${\cal
  O}(\alpha_s)$ to the quark-quark scattering amplitude; they are
shown in Fig.~\ref{fig:graphs}.  To present the result of the
calculations, we introduce the following notation for the difference
of the lattice and continuum one-loop matrix elements of the
four-fermion operators: \begin{equation} \delta \langle Q^{i} \rangle_\alpha =
\left ( \frac{\alpha_s}{4\pi} \right ) \left (\frac{\mu a}{2} \right
)^{2\epsilon} \sum \limits_{j=1}^4 q_{\alpha,j}^{i} Q^{j}, \end{equation} where
the label $\alpha$ refers to a particular diagram shown in
Fig.~\ref{fig:graphs}.  The spacetime dimension is $d=4-2\epsilon$,
$\mu$ is the renormalization scale in the ${\overline {\rm MS}}$
subtraction scheme and $a$ the lattice spacing. In what follows, we
split the matrices $q_{i}$ into soft and hard pieces. We give the
result for each diagram separately. We hope that the results for the
individual diagrams will be useful for readers performing similar
calculations in the future.

\subsection{Soft part}
 As a first step in the matching calculation, we compute  the
difference between the soft parts of lattice matrix elements
and the  result derived  in
dimensional regularization. To obtain the full result, we later add
the hard part for a given lattice action. Technically the soft part is
obtained by evaluating the continuum diagrams shown in Fig.~\ref{fig:graphs},
first in dimensional and then in analytic
regularization. The calculation is simplified by noting that a
difference between the two regulators can only arise from
ultraviolet divergent loop integrals.

Below we give the results for the {\em difference} of the
soft parts of the matrices $q$ and the corresponding
continuum diagrams. Since the
diagrams 4 and 5 in Fig.~\ref{fig:graphs}  do not have continuum analog, their
contribution to the soft part is zero:
$q_4^{\rm soft}=q_5^{\rm soft}= 0$.
For diagram $1$, we derive
\begin{equation*}
q_{1}^{\rm soft} = \left (
\begin{array}{cccc}
C_F f_{11}^{(1)} & 0 & 0 & 0 \\
\frac{f_{11}^{(1)}}{2} & -\frac{f_{11}^{(1)}}{2N} & 0 & 0 \\
0 & 0 & C_F f_{11}^{(1)} & 0 \\
0 & 0 & \frac{f_{11}^{(1)}}{2} & -\frac{f_{11}^{(1)}}{2N}   \\
\end{array}
\right )\,.
\end{equation*}
The variable $N=3$ denotes the number of colors, $C_F=(N^2-1)/2N$
and
\begin{eqnarray}
&& f_{11}^{(1)} = -2\,(1+\xi)\,\left(\frac{1}{\epsilon } -
\frac{1}{\delta}\right) +1 - 2\xi\,.
\end{eqnarray}
The parameter $\delta$ is an intermediate analytic regulator, which
will drop out in the sum of the hard and soft part
\cite{Becher:2002if}. Setting the gauge parameter $\xi=0$, one obtains
the result in Feynman gauge while $\xi=-1$ corresponds to Landau gauge. For
details on our notation and method of calculation, we refer the reader
to \cite{Becher:2003fu}.

For diagrams 2 and 3 in Fig.~\ref{fig:graphs} we obtain,
\begin{equation*}
q_{2}^{\rm soft} = \left (
\begin{array}{cccc}
-\frac{f_{11}^{(2)}}{2N}  & \frac{f_{11}^{(2)} }{2}
& -\frac{f_{13}^{(2)}}{2N}  & \frac{f_{13}^{(2)}}{2} \\
\frac{ f_{11}^{(2)}}{2} & -\frac{f_{11}^{(2)}}{2N}
& \frac{f_{13}^{(2)}}{2}  & -\frac{f_{13}^{(2)}}{2N}  \\
 -\frac{f_{13}^{(2)}}{2N} & \frac{f_{13}^{(2)}}{2}
&  -\frac{f_{11}^{(2)}}{2N} & \frac{f_{11}^{(2)}}{2} \\
\frac{f_{13}^{(2)}}{2} & -\frac{f_{13}^{(2)}}{2N}
&  \frac{f_{11}^{(2)}}{2} & -\frac{f_{11}^{(2)}}{2N}
\end{array}
\right ),
\end{equation*}
\begin{equation*}
q_{3}^{\rm soft} = \left (
\begin{array}{cccc}
-\frac{f_{11}^{(3)}}{2N}  & \frac{f_{11}^{(3)} }{2}
& -\frac{f_{13}^{(3)}}{2N}  & \frac{f_{13}^{(3)}}{2} \\
0 & C_F f_{11}^{(3)}
& 0  & C_F f_{13}^{(3)}   \\
 -\frac{f_{13}^{(3)}}{2N} & \frac{f_{13}^{(3)}}{2}
&  -\frac{f_{11}^{(3)}}{2N} & \frac{f_{11}^{(3)}}{2}  \\
0 & C_F f_{13}^{(3)}
&  0 & C_F f_{11}^{(3)}
\end{array}
\right ),
\end{equation*}
where
\begin{eqnarray}
&& f_{11}^{(2)} = -f_{11}^{(3)}+6=\left(5+2\xi \right )\left(
\frac{1}{\epsilon}-\frac{1}{\delta} \right ) +\frac{15}{2} + 2\xi,
\nonumber \\
&& f_{13}^{(2)} =f_{13}^{(3)}=3\left
(\frac{1}{\epsilon}-\frac{1}{\delta} \right ) +\frac{5}{2}.
\end{eqnarray}
To evaluate the continuum diagrams, a prescription for the treatment
of $\gamma_5$ and the extension of the Fierz identities to
$d$-dimensions \cite{Dugan:1990df,Buras:1989xd,Herrlich:1994kh} has to
be adopted. We use naive dimensional regularization for $\gamma_5$ and
treat the evanescent operators exactly as in \cite{Buras:1990fn}, to
be compatible with the results for the Wilson coefficients given in
these references. Note that with this prescription, the operators
$Q_1\propto\gamma_\mu\otimes\gamma_\mu$ and
$Q_3\propto\gamma_\mu\gamma_5\otimes\gamma_\mu\gamma_5$ also mix into
operators with Dirac structure $1\otimes1$, $\gamma_5\otimes\gamma_5$
and $\sigma_{\mu\nu}\otimes\sigma_{\mu\nu}$. We do not give the result
for this mixing, since it drops out in the sums $Q_1+Q_3$ and
$Q_2+Q_4$ which are relevant for our matching calculation. However,
separating the vector and axial contributions also in the soft part
allows us to read off the current renormalizations from the first
diagram in Fig.~\ref{fig:graphs} and provides additional consistency
checks, such as cancellation of $\delta$-poles and gauge invariance of
the sum of hard and soft parts.

In addition to the diagrams shown in Fig.~\ref{fig:graphs}, we have
to account for the external leg corrections, given by the wave
function renormalization of the massless quarks. This correction is
 universal in that it does not depend on the operator under
consideration.  We obtain
\begin{equation}
{\delta Z}^{(1)} O_i|_{\rm soft} =C_F \left(
\frac{2}{\epsilon }- \frac{2}{\delta} +1 \right) (1+\xi) O_i,
\end{equation}
where $Z^2_{\rm lat} - Z^2$=$\frac{\alpha_s}{\pi}\,\delta Z^{(1)}+\dots$
is the difference between the lattice (soft part only) and the on-shell
quark wave function renormalization constant. This difference
vanishes in Landau gauge, which is a consequence of the
fact that in this gauge the continuum quark wave function
renormalization is finite.

Note that the coefficients of the $1/\epsilon$ and $1/\delta$ pieces
in all the equations above
are exactly opposite. The $1/\delta$-divergences will cancel against
those of the hard parts. The fact that the above differences do not
depend on any infrared scales (the gluon mass in our case) shows
that the result of a matching calculation is process independent.

\begin{figure}
\begin{center}
\begin{tabular}{ccc}
\includegraphics[width=0.12\textwidth]{diag1} &
\includegraphics[width=0.12\textwidth]{diag2} &
\includegraphics[width=0.12\textwidth]{diag3}
\end{tabular}
\begin{tabular}{cccc}
\includegraphics[width=0.12\textwidth]{diag4} &
\includegraphics[width=0.12\textwidth]{diag6} &
\end{tabular}
\end{center}
\caption{Current-current diagrams. The diagrams on the second line do not have a continuum analog. Not shown are additional diagrams that can be obtained by flipping one of the above diagrams horizontally or vertically.}\label{fig:graphs}
\end{figure}

\subsection{Hard part}

We now give the result of our calculation of the hard part.
This amounts to presenting the matrices $q_{\alpha}$
for the five diagrams in Fig.~\ref{fig:graphs}.
The symmetry factors for each of the
diagrams are included. We begin with naive unimproved
fermions coupled to unimproved glue.

The result for the hard part of the first three diagrams in
Fig.~\ref{fig:graphs}, has the same structure as was found for
the soft part:

\begin{align*} q_{1}^{\rm hard} &= \left (
\begin{array}{cccc}
C_F d_{11}^{(1)} & 0 & 0 & 0  \\
\frac{d_{11}^{(1)}}{2} & -\frac{d_{11}^{(1)}}{2N} & 0 & 0 \\
0 & 0 & C_F d_{33}^{(1)} & 0 \\
0 & 0 & \frac{d_{33}^{(1)}}{2} & -\frac{d_{33}^{(1)}}{2N}
\end{array}
\right )\,,
\end{align*}
where
\begin{align}
 d_{11}^{(1)} &=
- \frac{2(1+\xi)}{\delta} -3.53 - 2.38\,\xi, \nonumber \\
 d_{33}^{(1)} &=
- \frac{2(1+\xi)}{\delta}  -3.62 + 0.695\,\xi \,,
\end{align}
and
\begin{align*}
q_{2}^{\rm hard} &= \left (
\begin{array}{cccc}
-\frac{d_{11}^{(2)}}{2N}  & \frac{d_{11}^{(2)} }{2}
& -\frac{d_{13}^{(2)}}{2N}  & \frac{d_{13}^{(2)}}{2}  \\
\frac{ d_{11}^{(2)}}{2} & -\frac{d_{11}^{(2)}}{2N}
& \frac{d_{13}^{(2)}}{2}  & -\frac{d_{13}^{(2)}}{2N}\\
 -\frac{d_{13}^{(2)}}{2N} & \frac{d_{13}^{(2)}}{2}
&  -\frac{d_{11}^{(2)}}{2N} & \frac{d_{11}^{(2)}}{2} \\
\frac{d_{13}^{(2)}}{2} & -\frac{d_{13}^{(2)}}{2N}
&  \frac{d_{11}^{(2)}}{2} & -\frac{d_{11}^{(2)}}{2N}
\end{array}
\right ), \,
 \nonumber\\ &\nonumber \\
q_{3}^{\rm hard} &= \left (
\begin{array}{cccc}
-\frac{d_{11}^{(3)}}{2N}  & \frac{d_{11}^{(3)} }{2}
& -\frac{d_{13}^{(3)}}{2N}  & \frac{d_{13}^{(3)}}{2}   \\
0 & C_F d_{11}^{(3)}
& 0  & C_F d_{13}^{(3)}  \\
 -\frac{d_{13}^{(3)}}{2N} & \frac{d_{13}^{(3)}}{2}
&  -\frac{d_{11}^{(3)}}{2N} & \frac{d_{11}^{(3)}}{2}  \\
0 & C_F d_{13}^{(3)} &  0 & C_F d_{11}^{(3)}
\end{array}
\right ),
\end{align*}
with
\begin{align}
 d_{11}^{(2)} &=-d_{11}^{(3)} =
\frac{(5+2\xi)}{\delta} +0.157 + 0.689\xi, \nonumber \\
 d_{13}^{(2)} &=d_{13}^{(3)} =
\frac{3}{\delta} -0.341,
\end{align}

The remaining two diagrams have no continuum analogue. We obtain
\begin{align*}
q_{i=4,5}^{\rm hard} &=\left (
\begin{array}{cccc}
C_F\,d_{11}^{(i)} & 0  & 0 & 0\\
d_{21}^{(i)} & \!\!\!C_F\,d_{22}^{(i)}-\frac{d_{21}^{(i)}}{N} \!\!\! & 0 & 0  \\
0 & 0 &   C_F\,d_{33}^{(i)} & 0  \\
0 & 0 & d_{43}^{(i)} &\!\!\!C_F\,d_{44}^{(i)}-\frac{d_{43}^{(i)}}{N}\!\!\! \\
\end{array}
\right )\,,
\end{align*}
with entries
\begin{align}
d_{11}^{(4)} &= 16.06+18.38\xi, \nonumber \\
d_{21}^{(4)} &= 1.18 + 1.69\xi, \nonumber\\
d_{22}^{(4)} &= 13.70 + 15.00\xi,\\
d_{33}^{(4)} &= 12.23+12.23\xi, \nonumber \\
d_{43}^{(4)} &= -0.73-1.38\xi, \nonumber \\
d_{44}^{(4)} &= 13.70 + 15.00\xi, \nonumber
\end{align}
\begin{align}
d_{11}^{(5)} &= -73.40-9.19\,\xi ,  \nonumber\\
d_{21}^{(5)} &= -2.20-0.85\xi, \nonumber\\
d_{22}^{(5)} &= -48.9-7.50\xi, \\
d_{33}^{(5)} &= -24.47 - 6.12\xi, \nonumber\\
d_{43}^{(5)} &=1.57+0.69\xi, \nonumber \\
d_{44}^{(5)} &= -48.9-7.50\xi. \nonumber
\end{align}
We also give the result for the hard part
fermion wave function renormalization on the lattice:
\begin{eqnarray}
{\delta Z}^{(1)}\, O_{i}|_{{\rm hard}} && =C_F
\Big (
-10.614 -11.928\,\xi
+ \frac{2(1+\xi)}{\delta}
\nonumber \\
&&
+\left[24.466 + 6.117\,\xi  \right] \Big )\, O_i.
\label{zhardN}
\end{eqnarray}
We have separated out the tadpole
contribution in (\ref{zhardN}) in square brackets. In Landau gauge
this contribution exactly cancels against the tadpole improvement
term.

We now give the results for the entries of the matrices for the
case of Asqtad action.
In this case, as explained in \cite{Becher:2003fu},
we expand
in the improvement terms, for both quark and gluon actions.
We use half of the highest order terms as the numerical error estimate
and multiply the last term of the series by $2/3$ to resum the higher
order contributions that behave like an alternating geometric series
with expansion parameter $1/2$ (see \cite{Becher:2003fu} for details).
We find
\begin{align}
 d_{11}^{(1)} &=
- \frac{2(1+\xi)}{\delta} -3.00(1) - 2.379\,\xi, \nonumber \\
 d_{33}^{(1)} &=
- \frac{2(1+\xi)}{\delta} + 0.81(4)  + 0.695\,\xi \nonumber \\
 d_{11}^{(2)} &=-d_{11}^{(3)}= \frac{(5+2\xi)}{\delta} +2.79(10)+0.689\xi, \nonumber \\
 d_{13}^{(2)} &=d_{13}^{(3)}= \frac{3}{\delta}+2.10(9), \nonumber \\ &\nonumber\\
 d_{11}^{(4)} &= 18.54(6) +18.38\xi, \nonumber \\
d_{21}^{(4)} &=1.73(1)+1.69 \xi, \nonumber\\
d_{22}^{(4)} &=15.09(3)+15.00\xi, \\
d_{33}^{(4)} &=12.23+12.23 \xi, \nonumber \\
d_{43}^{(4)} &=-1.43(2)-1.38\xi, \nonumber \\
d_{44}^{(4)} &=15.09(3)+15.00 \xi, \nonumber \\ &\nonumber\\
 d_{11}^{(5)} &= -58.0(5)-9.19\,\xi , \nonumber \\
 d_{21}^{(5)} &= -2.06-0.84\,\xi , \nonumber \\
 d_{21}^{(5)} &= -39.1(3)-7.50\,\xi , \nonumber \\
 d_{33}^{(5)} &= -20.3(1) - 6.12\,\xi ,\nonumber \\
 d_{43}^{(5)} &= 1.56(1)+0.69\,\xi , \nonumber \\
 d_{44}^{(5)} &= -39.1(3)-7.50\,\xi . \nonumber
\end{align}
The gauge dependent part is the same as in the unimproved case because
the improvement terms in the action are transverse \cite{Becher:2003fu}.

For the Asqtad action, the wave function renormalization
contribution is:
\begin{eqnarray}
{\delta Z}^{(1)}\, O_{i}|_{{\rm hard}} && =C_F
\Big (
-14.3(2) -11.28\,\xi
+ \frac{2(1+\xi)}{\delta}
\nonumber \\
&&
+\left[ 30.1(6)
+ 5.47 \xi \right] \Big )\,O_i.
\label{zhard}
\end{eqnarray}

The renormalization of the axial and vector current can be read off
from the above expressions. In both cases it is given by one half of
the corresponding entries in the matrices $q_i$ for diagrams 1, 4 and
5 in Fig.~\ref{fig:graphs} and the contribution due to the wave
function renormalization.  As discussed earlier in this section,
the discretized version of the axial current that we use in this paper
renormalizes identically to the unimproved quark-gluon vertex.  As a
consequence, the lattice-to-continuum matching coefficient for the
axial current should be equal to unity for the unimproved action, to
all orders in $\alpha_s$. Using the results presented above, it is
easy to verify this at the one-loop level.

\subsection{Matching coefficients from a different method\label{sec:method2}}

Most of the diagrams needed in the determination of the matching
coefficients for four-fermion operators can be calculated from the
renormalization coefficients for bilinears operators, as was first
pointed out by Martinelli \cite{Martinelli84}. The method has been
generalized to Landau-gauge operators in \cite{Sharpe:1993ur}, general
local operators in \cite{GBS96} and staggered gauge invariant
operators in \cite{Lee:2003sk}.

\begin{figure}
\begin{center}
\begin{tabular}{ccccc}
\includegraphics[width=0.12\textwidth,angle=180]{current1.ps} &&
\includegraphics[width=0.12\textwidth,angle=180]{current2.ps} &&
\raisebox{0.027\textwidth}
{\includegraphics[width=0.12\textwidth,angle=180]{current3.ps}}
\end{tabular}
\end{center}
\caption{Current diagrams.}\label{fig:bilgraphs}
\end{figure}

In Fig.~\ref{fig:graphs}, we did not show mirrored diagrams and did
not display the color structure of the four-quark operators. Also, we
have not indicated from which of the two currents the gluons in
diagrams 4 and 5 are emitted. Listing all possibilities, one ends up
with 16 diagrams of type 4 and 6 of type 5. Only 8 of the 16 diagrams
of type 4 and 2 of the 6 diagrams of type 5 are genuine four-fermion
contributions. All other diagrams factor into a product of a one-loop
current renormalization diagram times a tree level current.
Furthermore, only half of the remaining diagrams contribute to the
mixing between operators whose bilinears have identical
taste-structure, which is all that is relevant for matrix elements
involving external states of definite taste. One cannot avoid
calculating the genuine four-fermion diagrams, but the result for the
other topologies can be obtained from the diagonal renormalization
coefficients for bilinears operators using Fierz and charge
conjugation transformations as described in \cite{Lee:2003sk}.  Apart
from the 5 genuine four-fermion diagrams, the calculation reduces to
the evaluation of the current renormalization diagrams in
Fig.~\ref{fig:bilgraphs} and the universal wave function
renormalization of the massless quarks. In Fig.~\ref{fig:bilgraphs},
the crossed circle denotes the insertion of any bilinear with structure
$(\gamma_S\otimes\xi_T)$. The calculation is further simplified by
noting that the corrections are identical if the operators are multiplied
by $(\gamma_5\otimes\gamma_5)$ due to the axial symmetry, as stressed
above.

For diagonal four-fermion operators (with identical taste and spin
structure in both bilinears) this procedure gives us a $35\times35$
matrix from which we can extract the $2\times2$ block describing the
mixing between $[\gamma_{\mu}\otimes\gamma_5]
[\gamma_{\mu}\otimes\gamma_5]$ and
$[\gamma_{\mu}\gamma_5\otimes\gamma_5]
[\gamma_{\mu}\gamma_5\otimes\gamma_5]$. This block is related to the
$4\times4$ matrix in (\ref{match}) by including the appropriate color
factors as explained in \cite{Lee:2003sk}.

We have done the calculation of the matching coefficients for the
$\Delta S=2$ four-quark operators using the method described above and
evaluating the integrals numerically instead of algebraically. In all
cases we find full agreement with the direct evaluation of the
diagrams. This independent calculation of the matching coefficients
provides a non-trivial check of the validity of our results.
In addition, we have also performed the calculation for the HYP
actions used in \cite{Lee:2003sk} and reproduce the result for the
matching matrix given in that reference.

\section{Tadpole improvement\label{sec:TI}}

Quite generally one finds that perturbative corrections in lattice
regularization are larger than those encountered in continuum
calculations, e.g. in the ${\overline {\rm MS}}$ scheme. The large
corrections typically arise from the additional diagrams that would be
absent in the continuum, in our case the fourth and fifth diagram in
Fig.~\ref{fig:graphs}. Since the size of the corrections is scheme
dependent they are not by themselves meaningful. Instead of just
working with the bare lattice parameters one can try to absorb the
large perturbative corrections into a redefinition of the basic
parameters of the theory, such as coupling constant, quark masses,
Wilson coefficients of the weak Hamiltonian, etc. Such techniques are
also used in the continuum, for example in the context of Heavy-Quark
Effective theories: the perturbative results for inclusive heavy hadron decay
rates get large perturbative corrections if they are expressed in
terms of the heavy quark pole mass but the corrections are much
smaller if one uses a more suitable mass definition
\cite{Bigi:1997fj,Czarnecki:1997sz,Hoang:1998ng}.  Similar ideas are
behind the so-called ``physical'' couplings and optimal scale setting
prescriptions, introduced quite some time ago \cite{Brodsky:1982gc}.

The large effects of the tadpole diagrams can be canceled by tadpole
improvement \cite{Lepage:1992xa}. Tadpole improvement is achieved by
working with an action in which all gauge links are divided by an
average link $u_{0}$. In the simulation the average link is determined
numerically, while it is evaluated perturbatively
in the matching calculation. We define
\begin{equation}
u_0=1-\alpha_s\,u_0^{(1)}+\dots.
\end{equation}
 The average link receives large
perturbative corrections which then cancel out the large contributions
from the tadpole diagrams. In this section we give the tadpole
improvement terms relevant for our calculation. Some care is required
because different variants of tadpole improvement are used in the
literature. First of all, two different definitions of the the  mean link $u_0$ are common: the mean link in Landau gauge
\begin{equation}
u_0 =\left\langle \frac{1}{3}\,{\rm Re}\,{\rm Tr}\,U_{n,\mu} \right\rangle_{\xi=-1}\label{eq:meanLink}
\end{equation}
or the fourth root of the average plaquette
\begin{equation}
u_0^P=\left\langle \frac{1}{3}\,{\rm Re}\,{\rm Tr}\, U_{n,\mu}\,U_{n+\mu,\nu}\,U^{\dagger}_{n+\mu+\nu,\mu}\,U^{\dagger}_{n+\nu,\nu} \right\rangle^{1/4}\,.
\end{equation}
The second definition is somewhat simpler since no gauge fixing is
required and it is what MILC is using in their simulations with the
Asqtad action. Furthermore, MILC divides the $L$-link terms in the
action and operators not by $u_0^L$ as \cite{Lepage:1992xa} but by
$u_0^{L-1}$ and absorbs a power of $u_0$ into the fermion mass. With
their prescription no tadpole improvement factor is present in the
fermion part of the naive unimproved action
\cite{Orginos:1999cr}.\footnote{We thank C.~Bernard for pointing this
  out to us.} Since the fermion mass does not enter our calculation,
the difference between the two prescriptions merely amount to a
rescaling of the fermion field and leads to identical results for the
matching coefficients we calculate.

If we divide the $L$-link terms by $u_0^L$, the tadpole improvement
contribution from the current operators is
\begin{equation}
q^{({\rm tad})}=4\pi u_0^{(1)}\left(
\begin{array}{cccc}
6 & 0  & 0 & 0 \\
0 & 4 &  0 & 0  \\
0 & 0  & 2 & 0 \\
0 & 0 &  0 & 4
\end{array}\right)\,.
\label{eqs:tadsop}
\end{equation}
In addition, there is a tadpole improvement correction to the square
of the wave function renormalization
\begin{align}
\delta Z^{\rm tad}_{\rm unimp.}\,Q_i&=-8\pi u_0^{(1)}\,Q_i\,, \nonumber \\
\delta Z^{\rm tad}_{\rm Asqtad}\,Q_i&=-18\pi u_0^{(1)}\,Q_i\,.
\label{eqs:z2}
\end{align}

The results given in the next section are obtained with $u_0$ defined
as the mean link in Landau gauge (\ref{eq:meanLink}). However, using
the explicit form of the tadpole improvement terms given above the
prescription can easily be changed.

\section{Wilson coefficients of the lattice operators\label{sec:results}}

The Wilson coefficients of the lattice operators can now be read off
by imposing that the four-quark scattering amplitudes are equal in the
continuum and on the lattice. Clearly, the solution to the matching
equation (\ref{eq:matching}) is in general not unique since there are
many different discretizations of the same continuum operator. In the
present case, the two $(\bar s d)_{V-A}\,(\bar s d)_{V-A}$ operators
with different color structure become equivalent in the continuum
limit where they are related by a Fierz transformation. The matching
condition will thus not fix the Wilson coefficients of the operators
with different color structure individually. To be specific, at tree level
the matching conditions impose only three relations
\begin{align}
C_{1}^{{\rm latt}}&=C_{3}^{{\rm latt}}+{\mathcal O}(\alpha_s) \,, \nonumber\\
C_2^{{\rm latt}}&=C^{{\rm latt}}_4+{\mathcal O}(\alpha_s) \,, \\
C^{{\rm cont}}&=C_{1}^{{\rm latt}}+C_{2}^{{\rm latt}} +{\mathcal O}(\alpha_s)\,,\nonumber
\end{align}
among the four lattice operator Wilson
coefficients. Here, $C^{{\rm cont}}$ is the Wilson coefficient of the
continuum operator $Q$, while $C_i^{{\rm latt}}$ are the coefficients
of $Q_i$.

In lattice simulations, the quarks in the operator $Q$ are treated as
four distinct flavors \cite{Sharpe:1986xu}. In this case, there is no
ambiguity: the effective continuum Hamiltonian contains operators
$Q_i^{\rm cont}$ that are the continuum limit of each $Q_i$. Also,
instead of writing relations among coefficients, it is more convenient
to rewrite the result of the matching in the form
\begin{equation}
Q_i^{\rm cont}\equiv \sum_{j=1}^4\,C_{ij} Q_j^{\rm lat},
\end{equation}
where ``$\equiv$'' means equality at the level of matrix elements, see
(\ref{eq:matching}). The 4 by 4 matrix $C_{ij}$ has a perturbative
expansion
\begin{equation}
C_{ij}=\delta_{ij}+\left ( \frac{\alpha_s}{\pi} \right )
\,C_{ij}^{(1)}+\dots
\end{equation}
and is obtained from the results for the graphs in the previous section by
\begin{align}
C_{ij}^{(1)} &=-\frac{1}{4}\left[{\delta Z}^{(1)} \delta_{ij}+
\left (\frac{a\mu}{2} \right )^{2\epsilon}\sum \limits_{\alpha}
q_{\alpha,j}^{i} + \delta Z^{(1)}_{ij}\right] \, . \label{match}
\end{align}
Here $\delta Z^{(1)}$ stands for the wave function
renormalization and  $Z_{ij}=\delta_{ij}+\frac{\alpha_s}{\pi} Z^{(1)}_{ij}$
is the matrix of the ${\overline {\rm MS}}$ renormalization constants
 for the operators
$Q^{\rm cont}_i$ in the continuum. For the purposes of
computing $C_{ij}^{(1)}$, the role of this matrix
 is to remove any residual $1/\epsilon$ dependence in (\ref{match}).
Using the results for the matrices $q_{\alpha}$
given in the previous section, it is straightforward
to compute the matching coefficients. We split the matrix $C_{ij}^{(1)}$ into
 three parts
\begin{equation}
C^{(1)} = \ln \left (\frac{a\mu}{2} \right )\,\gamma^{(1)} + C^{(1)}_C+C^{(1)}_U.
\end{equation}
Here, $\gamma^{(1)}$ is the universal one-loop anomalous dimensions matrix of the operators $Q_i$:
\begin{equation}
\gamma^{(1)} = \left (
\begin{array}{cccc}
0 & 0  & \frac{1}{2} & -\frac{3}{2}   \\
-\frac{3}{4}& \frac{9}{4}& -\frac{3}{4}& -\frac{7}{4} \\
\frac{1}{2}& -\frac{3}{2}& 0& 0 \\
-\frac{3}{4}& -\frac{7}{4}& -\frac{3}{4}& \frac{9}{4}
\end{array}
\right ).
\end{equation}

The remainder $C_{C}+C_{U}$ depends on the lattice action and we give
it for three cases: (a) Asqtad fermion and improved gauge action, (b)
Asqtad fermion with plaquette gluon action, (c) standard action, no
improvement. The reason for splitting the remainder into two pieces
which are not separately gauge invariant, is as follows. Occasionally,
simulations are performed with operators that are obtained by dropping
the links that connect fermions on different sites. The simulations
with these gauge non-invariant operators are performed in Landau gauge
and their matching coefficients can be extracted from our calculation.
To obtain them, we need to account for the contributions from graphs
$1-3$ in Fig.~\ref{fig:graphs}, the wave function renormalization
contributions as well as the tadpole improvement for the wave function
given in (\ref{eqs:z2}).  We denote the corresponding matching matrix
by $C_{C}$.  The remainder, denoted by $C_{U}$ is the contribution
from graphs 4 and 5 which arises from the link fields in the current
operator and the operator tadpole improvement term given in
(\ref{eqs:tadsop}).  We give the matrices $C_{C,U}$ in Landau gauge;
their sum is gauge invariant.

For the Asqtad and improved gauge action, we
find
\begin{align}
C_{C}^{(1a)} &= \left (
\begin{array}{cccc}
2.83(14) & -0.75 & 0.38(1) & -1.15(2)  \\
-1.25(1) & 4.33(10) & -0.58(1) & -1.34(3)  \\
0.38(1) & -1.15(2) & 2.59(15) & -0.75  \\
-0.58(1) & -1.34(3) & -1.34(2) & 4.36(10)
\end{array}
\right ), \nonumber\\ & \\
C_{U}^{(1a)} &= \left (
\begin{array}{cccc}
2.08(5) & 0 & 0 & 0  \\
0.29 & 0.98(3) & 0 & 0  \\
0 & 0 & 0 & 0  \\
0 & 0 & -0.20(1) & 1.14(3)
\end{array}
\right ).\nonumber
\end{align}
These results are obtained after tadpole improvement with the ``mean
link in Landau gauge'' definition of the improvement parameter,
$u_0^{(1)}=0.750(2)$ for the improved gluon action and
$u_0^{(1)} = 0.97432$ for the unimproved action. For Asqtad with the standard
plaquette gluon action, the result is
\begin{align}
C_{C}^{(1b)} &= \left (
\begin{array}{cccc}
2.33 & -0.75 & 0.34 & -1.03  \\
-1.18 & 3.61(1) & -0.51 & -1.20  \\
0.34 & -1.03 & 2.09 & -0.75  \\
-0.51 & -1.20 & -1.27 & 3.64(1)
\end{array}
\right ), \nonumber\\ & \\
C_{U}^{(1b)} &= \left (
\begin{array}{cccc}
2.97 & 0 & 0 & 0  \\
0.32 & 1.43 & 0 & 0  \\
0 & 0 & 0 & 0  \\
0 & 0 & -0.20 & 1.60  \\
\end{array}
\right ).\nonumber
\end{align}
Notice that case (b) is not equivalent to what is considered in
\cite{Lee:2003sk}. These authors employ a different discretization of
the operators using insertions of fattened links to make the operators
gauge invariant while we are using thin links. Also, their fermion
action is similar but not identical to the fermion part of the Asqtad
action.

Without any improvement terms in the action, we get
\begin{align}
C_{C}^{(1c)} &= \left (
\begin{array}{cccc}
-0.81 & -0.75 & 0.18 & -0.54  \\
-0.85 & -0.5 & -0.27 & -0.63  \\
0.18 & -0.54 & 0.25 & -0.75  \\
-0.27 & -0.63 & -0.46 & -0.63
\end{array} \right ) ,  \nonumber\\
& \\
C_{U}^{(1c)} &= \left (
\begin{array}{cccc}
3.83 & 0 & 0 & 0  \\
0.47 & 1.86 & 0 & 0  \\
0 & 0 & 0 & 0  \\
0 & 0 & -0.38 & 2.14
\end{array} \right ) .  \nonumber
\end{align}
The matrices for the unimproved action agree with
the known results in the literature \cite{Ishizuka:1993fs,Lee:2003sk}.

We write the finite correction to the normalization of the
axial-vector current in the form $Z_A=1+\frac{\alpha_s}{\pi} \delta
Z_A$ and obtain
\begin{align}
  \delta Z_A^{(a)}&=1.17(7), & \delta Z_A^{(b)}&=0.921, & \delta
  Z_A^{(c)}&=0.
\end{align}
The current renormalization happens to be identical for the gauge
invariant and non-invariant operators in Landau gauge. This occurs
because in this gauge, the contribution of the fourth graph vanishes
and the contribution from fifth graph gets canceled by tadpole
improvement.

\section{Summary and discussion}

We have calculated the matching of the Wilson coefficients in the
$\Delta S=2$ flavor changing effective Hamiltonian from the continuum
to the lattice for the Asqtad lattice action. Together with
non-perturbative calculations of the $K-\bar K$ matrix element of
the lattice operators, our results determine the amount of indirect CP
violation in the kaon system. The matrix elements are currently being
evaluated by the HPQCD and UKQCD collaborations \cite{Gamiz:2004qx,CDGSW05}.
The calculation uses the configurations with $n_f=2+1$ dynamical flavors
generated by the MILC collaboration.

Previous calculations of the quantity $B_K$, which determines the
strength of $K-\bar K$ mixing, were performed in the quenched
approximation. This induces an essentially unknown and
irreducible systematic error into the result. Precise simulations with
{\em dynamical} fermions are necessary in order to be able to make
full use of the experimental data on $K-\bar K$ mixing to constrain
the CKM matrix elements entering the effective Hamiltonian. Among the
currently available fermion actions, only staggered actions allow for
simulations with low statistical errors at small quark masses.
However, the unimproved staggered action suffers from large
taste-changing interactions. The Asqtad action, for which we have performed
the matching, has been designed to reduce these as well as other
cut-off effects.

We have performed our calculation with two independent methods. First,
we have evaluated the diagrams in two different ways: by directly
calculating the various diagrams and by first separating off the part
which can be inferred from the renormalization of the current
operators. Second, we have evaluated the lattice integrals both
algebraically and numerically.  For the algebraic evaluation, we have
expanded the diagrams around the continuum limit.  This produces a set
of lattice tadpole integrals which we then reduced to a minimal set of
master integrals using computer algebra. The agreement between these
two rather different methods provides a strong check on our results.

We find that the size of one-loop corrections to the tree level
matching for the Asqtad action is very similar to what is found with
unimproved staggered and other improved staggered actions, such as the
HYP action \cite{Lee:2004qv}. In quenched calculations at a lattice
spacing $1/a=1.6~{\rm GeV}$, the shift in the value of the bare $B_K$
due to ${\cal O}(\alpha_s)$ corrections is around 10\% for all these
actions \cite{CDGSW05}.  In dynamical simulations with the Asqtad
action the shift turns out to be over 15\% at the same lattice
spacing, simply because the value of the strong coupling is much
larger for $n_f=3$ than for $n_f=0$ dynamical flavors. Also, it turns
out that the values for the matching coefficients are not very
sensitive to the improvement of the gluon action. Switching off the
gluon improvement terms in the Asqtad action changes the entries of
the one-loop matching matrix by less than 20\% and the changes are
even smaller for the larger elements on the diagonal. The motivation for
using an improved staggered action in the calculation of $B_K$ is not
to reduce the size of the one-loop corrections, which are already small
in the unimproved case, but to correct the large ${\cal O}(a^2)$
scaling violations that highly affect the unimproved case; see
\cite{Gamiz:2004qx,CDGSW05} for further discussion.

The situation is different for the calculation of other weak matrix
elements relevant in the study of CP-violating effects in the
kaon system. For the unimproved staggered action, Sharpe and Patel
\cite{Sharpe:1993ur} found very large perturbative corrections for
operators with scalar and tensor Dirac structure. The contributions
are large even after tadpole improvement, which casts doubt on the
perturbative expansion for the unimproved action. The corrections are
reduced to an acceptable level with the HYP action
\cite{Hasenfratz:2001hp} and operators which are made gauge invariant
by the insertion of fattened links \cite{LS02, Lee:2003sk}. In
order to check whether these large corrections are present for the
Asqtad action with standard four-quark operators, we have analyzed the
mixing of scalar operators.  We find that the corrections are small
with the improved action. The suppression arises because the
improvement terms reduce taste-changing interactions. In Appendix
\ref{sec:scalar} we present the results for the mixing of scalar
operators and discuss the suppression of the large contributions in
more detail.

The absence of anomalously large one-loop corrections suggests that
the two-loop corrections to our results should be reasonably small.
However, in order to reduce the uncertainty in dynamical calculations
to the level of a few per-cent, a two-loop matching calculation will
be necessary.

{\bf Acknowledgments} We are grateful to Christine Davies and Andreas
Kronfeld for discussions and comments on the manuscript. We thank the
KITP in Santa Barbara and the INT in Seattle where part of this work
was carried out for their hospitality and financial support. This
research was supported in part by the U.S.\ Department of Energy
contracts DE-AC02-76CH03000, DE-FG03-94ER-40833 and the Outstanding
Junior Investigator Award DE-FG03-94ER-40833, and by the Alfred P.
Sloan Foundation. E.G.\ is indebted to the European Commission for a
Marie-Curie Grant No.\ MEIF-CT-2003-501309. Fermilab is operated by
Universities Research Association Inc., under contract with the U.S.\
Department of Energy.

redpajama_set_name: RedPajamaArXiv


Throughout history, Cambridgeshire (including Huntingdon and Peterborough) has figured in many of the conflicts which have shaped our nation. Doomed Roman legionaries marched from Longthorpe to defeat by Boudicca's Iceni; Saxons and Danes fought over the edges of the Danelaw; the Normans came this way to crush Hereward's Fenland resistance; in the Civil War it provided the defended frontier between Parliamentarian and Royalist; in Napoleonic times French prisoners of war were incarcerated here; and in the twentieth century its flat expanses were home to numerous airfields and missile bases. This book describes the function and purpose of these defensive structures and reveals the evidence which many of these major events left on the ground: the earthworks of hill forts, medieval castles and moats; the masonry of later forts and strong-houses; drill halls and militia barracks; and the lines of anti-invasion defences from 1940.


text:
Iran Launches New Ballistic Missiles- Obama Evades Truth, Says Not Deal Violation
by Jeff Dunetz | Mar 8, 2016 | Foreign Policy/Terrorism, Israel, Politics
Iran launched several ballistic missiles across the country today in violation of United Nations Security Council resolution (UNSCR) 2231, and despite what the administration says, it's a violation of the P5+1 nuclear deal. They showed the launch on state television and bragged that efforts by their "main enemies" could not halt the program:
Brigadier General Amir Ali Hajizadeh, commander of the IRGC's [Revolutionary Guard] aerospace arm, said sanctions would not stop Iran developing its ballistic missiles, which it regards as a cornerstone of its conventional deterrent. "Our main enemies are imposing new sanctions on Iran to weaken our missile capabilities… But they should know that the children of the Iranian nation in the Revolutionary Guards and other armed forces refuse to bow to their excessive demands," the IRGC's website quoted Hajizadeh as saying. A state television report showed a missile being fired from a fortified underground silo at night time. The presenter said it was a medium-range Qiam-1 missile, and the test took place in the early hours of Tuesday.
When nuclear negotiations began the Obama administration dispatched officials to the Hill to ask Congress to back off plans to pressure the Iranians, and in exchange promised that any final deal would include a rollback of Iran's ballistic missile program. The Iranians not only refused to discuss making ballistic missile concessions – at one point Zarif literally laughed in the face of American negotiators who tried to bring it up – and instead began quietly moving to get relief from ballistic missile sanctions.
Days before the final round of Vienna talks the U.S. military community expressed alarm at rumors that U.S. negotiators would make concessions on ballistic missiles. Joint Chiefs Chairman Gen. Martin Dempsey told lawmakers "we should under no circumstances relieve pressure on Iran relative to ballistic missile capabilities and arms trafficking" and Defense Secretary Ash Carter echoed that the U.S. "want[s] them to continue to be isolated as a military and limited in terms of the kinds of equipment and material they are able to procure."
At Vienna U.S. diplomats nonetheless ceded to a particular Iranian interpretation of UNSCR 1929 under which Iran was entitled to relief from ballistic missile sanctions, and agreed to lift the U.N.-imposed embargo on ballistic missiles in 8 years' time. The concession was a diplomatic choice not justified by the text of the UNSCR, and American diplomats were subsequently criticized for not holding their position. Iranian FM Zarif bragged after Vienna that the international ban on Iranian missile R&D had been transformed into a "non-binding restriction" and Iranian Deputy FM Abbas Araghchi vowed to buy weapons from wherever possible… [and] to provide weapons to whomever and whenever it considers appropriate."
After Vienna the administration fell back on promising that it would aggressively push back against Iranian missile development while the eight year ban was still in effect. President Obama declared in his post-Vienna speech that "restrictions on ballistic missile technology will remain for eight years… we are not taking the pressure off Iran with respect to arms and with respect to ballistic missiles" . Secretary Kerry was asked on Face the Nation why the U.S. was lifting ballistic missile restrictions and snapped back "actually, we're not… [w]e have to have those. And they add on to additional mechanisms that we have to hold them accountable on arms and missiles."
Since then the Iranians have launched ballistic missiles every few weeks. The State Department has assured reporters they will aggressively respond to this latest Iranian ballistic missile test.
There is only one reason for Iran to develop these missiles-to deliver warheads to far away locations, which is why the UN banned the rogue regime from developing them. This is not the first time Iran has fired ballistic missiles.
The Obama administration claims the firing of missiles did not violate the p5+1 nuke deal. But they admit that if true the missile firings violates UNSCR 2231, the resolution which among other things approved the P5+1 deal. Paragraph 3 of Annex B of resolution 2231 (2015) calls upon Iran not to undertake any activity related to ballistic missiles designed to be capable of delivering nuclear weapons, including launches using such ballistic missile technology. So since the two are part of the same UN resolution one can argue that violating one part is violating the whole thing. Or to put on another way saying that it doesn't violate the P5+1 deal is a trick of semantics.
Foreign Relations Committee Chairman Bob Corker (R-Tenn.) said Tuesday that both the United States and the United Nations must show that the reported tests will have "swift and immediate consequences."
"The administration's hesitancy and the council's refusal to act after multiple violations last fall must not be repeated now that Iran appears ready to test the will of the international community with the nuclear agreement in place," he added.
Sen. Tom Cotton (R-Ark.) suggested that Obama was to blame for Iran's behavior, saying that "it's clear our enemies no longer fear the United States" and Iran is "throwing dirt in the face of the entire free world."
But with is number one goal being the protection of his foreign policy legacy, so far President Obama has refused to punish Iran for their illegal acts.
The State Department is still giving reporters conflicting background on yesterday's out-of-nowhere declaration from the IAEA that the nuclear deal places new limits on what the Agency is allowed to report about Iran's nuclear program, which would be the exact opposite of the administration's promise of unprecedented transparency. There's an AP report out of Vienna that suggests the Russians are coordinating with the Iranians on the issue.
An Asylum Officer Said She Won't Enforce "Immoral" Asylum Standards At The US-Mexico Border (Hamed Aleaziz/BuzzFeed News) memeorandum


text:
Facebook signs up partners for German news product, but Springer baulks
Nadine Schimroszik and Klaus Lauer
This article was published more than 6 months ago. Some information may no longer be current.
Facebook signed up a string of German media partners on Monday to provide content for a local news product, but the publisher of the country's best-selling newspaper said it would not take part on terms it dismissed as derisory.
Described as a "dedicated venue for journalistic content", Facebook News will feature reporting from heavyweight weeklies Die Zeit and Der Spiegel, and daily newspapers including the Frankfurter Allgemeine Zeitung, Handelsblatt and Tagesspiegel.
"Part of our user base wants to read more news," Jesper Doub, Facebook's director of news partnerships in Europe, told reporters.
But Axel Springer, the publisher backed by private equity house KKR that puts out the Bild tabloid and conservative broadsheet Die Welt said it would not be joining.
"Attempts by some platforms on the one hand to position themselves as news media, and on the other to fob off publishers with inadequate remuneration, are problematic," a spokesman for Axel Springer said.
Springer said it preferred to rely on European copyright rules that allow all publishers to receive an appropriate share of remuneration.
The broadside comes shortly after an unprecedented week-long news blackout by Facebook for its users in Australia over legislation that requires tech platforms to pay traditional news publishers to show their content.
Facebook agreed to restore its Australian news pages after wringing concessions on the legislation, including a mechanism to take disputes to arbitration.
It has since said it will invest $1 billion in news over the next three years.
Facebook News has already launched in the United States and Britain, and will follow soon in France, added Doub.
He did not disclose financial terms for the partnerships backing the German launch of Facebook News, which will also feature several regional newspaper partners as well as fashion, motoring and sports publishers.
"We are delighted to try out new ways to reach our readers with quality journalism in close partnership with platforms like Facebook," Spiegel Group Managing Director Stefan Ottlitz said in a statement.


Get Smart: Lowest Priced New Home in Corolla – Loaded with Smart Home Technology & A Pool!
This beautiful new construction home, located in the Monteray Shores community in Corolla, NC is offered by Homes by Eillu. It has just been finished and is "move in" ready to be personalized with all your decorative furniture and touches. The attention to details is already apparent in the high end fixtures and finishes that will remain timeless. Think granite counter tops, fully tiled baths, and custom cabinets. This is one home you must see – such a great value and offered at $399,900.
The home, located at 848 Golden Bluff Way, Corolla NC 27927, is 2087 square feet with 459 square feet of decks/porches. There are 4 bedrooms, 3.5 baths. The generous 12×24' Cape May fiberglass pool is fully fenced with a concrete deck. Grab some deck chairs, a table, and your BBQ to get the party started. The pool area is already wired for outdoor speakers, so bring your phone with all your music.
This home is technologically advanced with the latest smart home features. There are various sensors in the home which are connected to the smart hub. Of course, you can also control the features using your smart phone too. The smart home devices included with the home are light controls, keyless entry, automated thermostats that maximize energy efficiency and allow you to control them from anywhere in the world (with internet connection). There is also a front entry camera. This will allow you to answer the door with your smart phone even if you are thousands of miles away. You can also view the image to get real time status of the front door area. There is a water leak sensor to alert you should a leak be detected when you are not at home or even if you are home for faster response. The home comes pre-wired for audio/speakers in the great room, rec room, pool and deck area. Each room comes hard wired for high speed internet and smart tv's. There is wireless internet and USB charging built into the power outlets in the great room, master BR, rec room and kitchen. These features are convenient and allow the owner to take advantage of IoT (Internet of Things) today and in the future.
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The second floor, or top floor is the open floor plan or "great room" with high ceilings, dramatic pendant lights, chandelier and decorative fans. The luxury vinyl floor is waterproof and has the look of wood but will last for years with no maintenance.
The generous kitchen will delight the chef in the family with a bar area that allows the family to converse and watch the cooking action. The kitchen has the latest style gray custom cabinets with granite counter tops and all Whirlpool stainless steel appliances (electric range, refrigerator, microwave, and dishwasher). The under mount stainless steel sink has a pull-out spray faucet to make filling that large pots for pasta or crabs easy.
The living area has an electric fireplace with custom stone work as the focal point. There are two sliders out to the deck which spans the entire back of the home and overlooks the pool. There is a large dining area to comfortably seat your family and guests. This floor also has a powder room or half bath.
Perhaps more important than the state of the art interior features and the things you see are the things you don't see but will appreciate for years to come. The home is designed with high end materials to last for years. The sofit and fascia are maintenance free. The windows, front door with sidelights are Pella energy efficient and the heat pump/AC is 13 seer. There is a 50 gallon quick recovery water heater so no one will end up with a cold shower. The electric panel is 200 Amps, the wiring is copper, the plumbing is non-corrosive PVC. The yard is landscaped and includes motion sensor outdoor lights. The siding is LP smart siding that comes with a 5/50 year warranty.
This home includes a 4 year New Home American Home Shield Warranty (click here for what's covered) and a 1 year Builder Warranty.
Monteray Shores is a wonderful well established community that offers many amenities such as Tennis Courts, Community Pool, Club house with lounge area, Basketball Court, Playground and two Sound side Piers and waterfront small craft launch area. Centrally located in Corolla, it is only few minutes from the Sound and the Ocean; it is close to all shopping, restaurants and local attractions. This fun beach home is perfectly suitable for a second home or vacation rental. You can read more about the community of Monteray Shores here.
Homes by Eillu has many new construction packages available. Call today to schedule an appointment to view this home or visit our next project.


The ESPRIT CAM user event of the year – ESPRIT World happening June 3-7, 2019. Located on the beautiful St. Johns River, the event kicks off at the Hyatt Regency in Jacksonville, Florida. Join us for a week packed with in-depth ESPRIT training sessions, plus Boot Camp built for beginners.
Learn our best tips and tricks, get direct access to our application engineers and spend 1-on-1 time working on your specific projects. You'll also network with industry peers and colleagues as we celebrate in style with exclusive parties and special events.


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Diamond Frances Paintings
The Library Exhibitions
17 May – 21 June 2021
Open every day 9am-5pm
An emotive and intimate series from painter, Diamond Frances, who documents her life through portraits of her family and loved ones at different stages of their lives.
Diamond Frances grew up in Austria. She moved to London and graduated with a BA (Hons) Fine Art from the Slade School in 2005 and has exhibited in Germany, Austria, United States and England. Diamond Frances is married, has three children and lives in Bow, East London where she also holds a studio. Her daughter was born with a rare chromosomal disorder.
Frances's works are subjective and intuitive, they display their own reality and internal logic. She produces paintings with an emotional quality; photographs and family snapshots frequently serve as a skeleton from which works evolve. Meaning is unsure and the nature of her practise hovers on the edge of the communicable. Her inspiration comes from and through the process of work itself. Different styles and media including painting, collage, drawing and assemblage are an essential feature of her work.
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In the spring of 1980, Rev. Ralph Volpe, Senior Pastor of Central Assembly of God, had the vision for a Christian school. After examining several Christian schools and going through much curriculum, a course of operation was established. His son, Rev. Richard Volpe, was hired to be the head Administrator of Central Christian Academy.
In 1981, the Family Life Center was ready to house the new school. The school building, complete with ten classrooms, a library, offices, kitchen, and a gym, was to be home for Central Christian Academy.
In 1981, Central opened its doors to educate its first students. That first year, there were twenty-four students that attended Central Christian, and a grade configuration of K – 9. Several of the classes were combined. There were four full-time teachers. The total school budget was $32,000.00.
The school grew, and the second year went to tenth grade, with forty-eight students.
Rev. Richard Volpe continued as Administrator, and after the third year, and an enrollment of 60, became the children's minister of Central Assembly of God Church.
Don O'Hare was hired as Administrator in 1984. The fourth year of operation saw enrollment increase to 90, and the next year to 130. More teachers were hired, and eventually we had one teacher for each class. Two rooms above the kitchen and new office space were added. In 1994, Central Christian Academy was granted full accreditation by the International Christian Accrediting Association.
In 1997, a computer lab and a teacher's lounge were added to the school.
In 2001, the classrooms were networked together with the office. Also that year, Central Assembly of God voted to expand its facility on McGovern Road. The addition was completed in 2003.
In the fall of 2003, after nearly 20 years of service, Don O'Hare resigned as Administrator, and Rev. Stephen Getchell was selected to take his place. Rev. Getchell served the school for one and one-half years.
In December of 2004, Rev. Getchell was elected Senior Pastor of Central Assembly of God Church, and Don O'Hare returned as interim Administrator until July 2007.
Kate Fisher was hired as administrator in July 2007.
The school is currently at capacity with almost 250 students ranging from nursery through eighth grade.
God's faithfulness has been apparent in providing finances, personnel, and a facility. It is the continued purpose of Central Christian Academy to honor Jesus Christ, believing that an education in which Christ is central will influence the entire course of a student's life.
May God continue to bless Central Christian Academy, as we look to the future.


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How to manage multiple Instagram accounts in one app?
Sep 07, 2021 Sheriff Subair 13 min
InstagramTips/How toTools
Managing multiple Instagram accounts for your brand can seem like a hellish task.
From trying to figure out how to manage the tons of messages you receive daily to deciding the best strategy for posting your content on the platform. From brainstorming ways to grow your Instagram profiles and then wondering if your business growth reflects your effort.
No one can blame you for wondering if anyone can manage multiple Instagram accounts. And if it's worth it to do so.
Well, I can tell you that you can manage multiple Instagram accounts. And with the right execution, you can drive your business forward with them.
In this post, I'll show you how to add and manage your Instagram profiles using the Instagram app. And then introduce you to Sociality.io, our social media management platform, that will assist you in managing your Instagram accounts.
Can you manage multiple Instagram accounts in one app?
Here's how to start managing multiple Instagram accounts using the Instagram app
Step up your Instagram marketing game with Sociality.io
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I'll first answer this question: Can you have multiple Instagram accounts?
The answer is yes. You can have more than one Instagram account. In fact, Instagram doesn't put a limit on the number of Instagram accounts you can create. So, you're free to create 20 different Instagram profiles as long as you provide an email address for each one of them.
But would you be able to manage all of them in one Instagram app?
Not exactly. You can only have up to five different Instagram accounts on one app, that you can switch between without logging out of them.
This means that if you have just three Instagram accounts, you can easily add the accounts to your app and switch between them seamlessly. But if you have 6 Instagram accounts, you'll need to log out of one of the five accounts already added in order to access the sixth one.
So yes, you can create as many Instagram accounts as you like. But if you have more than five profiles to grow, switching between them can quickly become a frustrating chore.
1. Add your different accounts to the Instagram app
If you want to manage multiple Instagram accounts on the Instagram app, you'll need to add the accounts first. Here's how to go about that.
Open the Instagram app on your iPhone or Android phone.
Now, go to your profile page. You'll get there by tapping your profile picture at the bottom right corner of your screen.
Tap the hamburger menu icon at the top right corner of your screen, then tap the settings icon at the bottom of the menu that slides out.
Scroll to the bottom of the list and tap on Add Account.
Two options will slide up from the bottom of your screen. You can either choose to Log Into An Existing Account or Create a New Account.
If you already have an Instagram account ready, click on the first option and enter the login information of the account you want to add i.e your username and password.
Tap login, and you've successfully added an Instagram account to the Instagram app.
But if you don't have one yet, tap the second option to begin the process of creating a new Instagram account.
Follow the steps above for each new account you want to add. Remember that the limit is five.
2. Switch between different accounts on the Instagram app
Once you've added your Instagram accounts to the app, switching between them is a breeze. Follow these steps to switch between your Instagram accounts.
On your profile page, tap on your username on the top left corner of your screen. This will bring up a list of added accounts. You could also hold your profile picture on the bottom right corner of your screen to show you your added accounts.
Choose which one you want to use and the selected account will open.
You can switch back and forth between any of your added accounts whenever you want.
3. Post to multiple accounts on the Instagram app
There's no point in adding all these accounts if you'll not be able to post content on them, right? You can share content with your different Instagram accounts using the app.
To post to an account, switch to the desired account and post your content as usual.
Unfortunately, you can't schedule your Instagram posts using the app. But there are two other options you could try apart from setting an alarm on your phone.
There is a limit to how much account management you can do with your Instagram app.
Unless you have low expectations for your Instagram campaigns, you can only go so far with managing your Instagram accounts on the Instagram app.
For starters, Instagram's five account rule puts a limit on how many profiles you can manage at once. And creates the inconvenience of having to log out of one profile in order to add another one.
Granted. If you do not have up to five accounts, this rule doesn't affect you that much. We can't all have a gazillion Instagram accounts like Nike.
But let's assume that you found out that the best time to post on your three accounts are 1 pm, 6 pm, and 2 am respectively. This most likely means you'll have to set an alarm on your phone so that you'll remember to post at the right time.
One more trivial task vying for your attention — all because the Instagram app doesn't have a scheduling feature.
And that's not all it doesn't have.
Instagram analytics is an important feature for the Instagram app, especially for brands like yours that need business profiles. But if you want a deep dive into the data behind your Instagram numbers, Instagram's in-built analytics feature will come up short.
For instance, this tool doesn't allow you…
In order to deal with messages and mentions across your social media accounts, you'll need to jump from one account. That's time-wasting, and I'm sure you don't need anyone to tell you that time is money.
So, in order to stop losing money, you need a system that helps you become more efficient with your time.
Sociality.io is that solution.
Sociality.io is a social media management platform that allows you to schedule your social media content, analyze and report the content's performance, track conversations about your brand, and so much more.
Let's start with the Instagram messaging feature. If your Instagram engagement is in chaos — understandable if you manage two or more accounts — you could be creating dissatisfaction in your audience.
But with Sociality.io's Instagram messaging feature, you'll receive all your messages in one team inbox, saving the need for you to jump from one profile to another.
In this inbox, you'll be able to view and reply to your audience reactions to your stories, reply publicly or privately to your post comments
I talked about time earlier. Sociality.io's Instagram messaging feature has more features that'll help you save it. For instance, you can assign conversations to certain members of your team. And have access to ready-to-use messaging templates that'll increase your customer satisfaction and free up your time.
That is not the only way Sociality.io helps you manage your Instagram accounts more efficiently.
I already mentioned how the inability to schedule your Instagram posts can be a pain in the neck. Well, it won't be with Sociality.io. This is because you'll be able to create a content calendar and schedule your posts to go out at specific times.
Actually, this calendar is not limited to Instagram. It is a social media calendar. So if your brand is on multiple social media platforms, you'll be able to plan your content in one place.
There are other features in Sociality.io that provide you with more functionalities that the Instagram app can't give you.
Like the Listen module which tracks the latest news about your brand on Instagram.
And the Competitor Analysis module allows you to research your competitors so that you can make more accurate strategic decisions.
And the Report module allows you to generate and export the performance report of your Instagram accounts in minutes.
You can have all these and more with Sociality.io.
And that's why I'm excited to let you know of Sociality.io's mobile application. It gives you access to desktop-level social media management features on your ios or android. So, if you want to track your Instagram performance on the go, you can download the Sociality.io mobile application from the Google PlayStore or the App Store.
Having multiple Instagram accounts allows you to reach different segments of your target audience on a platform that has one billion monthly active users.
But in order to maximize the gains of owning multiple Instagram accounts, you need to effectively manage all your accounts.
This is where Sociality.io's social media management platform can help you. You'll be able to manage all your social media accounts without switching between platforms.
You can join them by activating your 14-day free trial here. No credit card required.
Sheriff Subair
Sheriff is a SaaS-focused content marketer 👨💻 His goal is to assist every reader to solve their problem, one sentence at a time 👌 He is a direct-to-the-point producer with aim of providing useful information.
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