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The Paleozoic Era
Notes for the leader/teacher on the Earth science lesson plans The Paleozoic Era: With the Paleozoic Era, the life forms explode into complexity. It is important to continue to use simple stories with not too much detail. As you continue with this lesson, give impressions rather than detailed descriptions of the various life forms. There are so many interesting life forms that this alone will encourage students to continue their own research of the amazing creatures that came into existence. Dialogue for the lesson is included in bold and italics. Things you would do during the lesson are in CAPITAL LETTERS.
Prerequisites for presenting The Earth science lesson plans The Paleozoic Era: Intro to Clock of Eras; Hadean, Archaean, and Proterozoic presentations
Materials for The Earth science lesson plans The Paleozoic Era:
A clock of eras chart. Click here for a printable version
A blank or non-colored chart Click here for a printable version
Loose pieces for each of the Eras (You'll use four sections in this lesson: The Hadean, Archaean, the Proterozoic and the Paleozoic.)
(Optional: A large, black poster board or construction paper to use as a background.)
Templates for student follow-up
Presentation of The Earth science lesson plans The Paleozoic Era:
Review previous lesson(s) (SHOW BLANK CLOCK OF ERAS AND LAY DOWN EACH PERIOD AS YOU REVIEW THE NAMES.)
We've been learning about the Earth's creation using our Clock of Eras. So far we've learned about the Hadean Time, the Archaean Time and the Proterozoic Era. (PICK UP THE PROTEROZOIC AS YOU REVIEW ITS CHARACTERISTICS.)
The last Era was the Proterozoic. This was the time that the new cells were working with the sun to form an oxygen-rich atmosphere. It was the time the foraminiferans were removing the deadly mineral salts from the oceans. All of this activity was making just the right conditions for life.
(PLACE THE BLUE PALEOZOIC ERA ON THE BLANK CLOCK.)
The Paleozoic Era is colored blue on the Clock of Eras to remind us that all the new life, the oldest life forms on the planet, was in the water. After the foriminiferans took care of the salt problem, the seas were prepared for life forms. And well-prepared it was. There was literally an explosion of life forms at the beginning of the Paleozoic Era. The Cambrian Explosion marks the era with thousands of species of life forms in the ancient seas. It is this characteristic: life in the ancient sea, which makes the Paleozoic Era different from all the ones that came before it. You see, the cyanobacteria's makeup didn't just add oxygen to the atmosphere. It was an entirely new sort of structure: one that had a special container and a special "remembering" part called the nucleus. These new cells could join together to make different kinds of animals and plants. The tissues that made up these organisms were made to survive in a particular environment. Some would live on the bottom sediments, burrowing with tube-shaped bodies or walking with many tiny legs.
Others would live in the ocean column, developing fins for effective swimming. The Paleozoic Era is divided into six periods. Each period is very different from the one before or after it. The first of these was the Cambrian Period. The Cambrian Period had so many new life forms that it is often called the Cambrian Explosion. There were arthropods, mollusks, and echinoderms. The most famous animal of the Cambrian was the trilobite. It had more than 100 different species during the Cambrian Period. The plants of the Cambrian were simple one-celled algae. Sometimes algae cells lived together in a colony. As the Paleozoic Era continued through the other periods, new species developed.
Many new types of animal life appeared as the Paleozoic continued. One type, the cephalopod, was a mollusk that lived in the large opening at the end of their shell. As they grew, they would make a new, larger ring of shell at the open end. When they were ready to move out of their old ring, they made a thin wall behind them. These cephalopods had feet that grew out of their heads! Fish developed during the middle part of the Paleozoic Era. By the end of the Paleozoic, some organisms could live out of the water and were responsible for breaking down rocks and making soil. These were the lichens, a partnership between fungi and algae. The Paleozoic Era came to an end with a mass extinction. Something caused conditions on Earth to change dramatically. As much as 95% of the life on Earth died out at this time.
Follow-up for The Earth science lesson plans The Paleozoic Era:
Color or cut & paste the parts of the clock through the Paleozoic Era including labels.
Research particular periods of the Paleozoic. Make illustrations or dioramas to represent the periods.
Fossil Dig Activities
Research individual animals. Make models of the animal in its habitat.
Research the parts of a cell with emphasis on the cell wall and nucleus.
Finished with The Earth science lesson plans The Paleozoic Era? The next lesson is The Mesozoic.
The lesson before The Earth science lesson plans The Paleozoic is the Proterozoic
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Young Paleontologist Book and Fossil Set 25 children's books, 24 fossils and 100's of pages of online activities $84.95
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redpajama_set_name: RedPajamaCommonCrawl


text:
Lareina Joelle Wong
Videography · Los Angeles California United States
Born as Lareina Joelle Wong, Lareina has and continues to live a multicultural life. She was born in Kuala Lumpur, Malaysia and has lived in Hong Kong, San Diego, and currently, Los Angeles, as well as traveled abroad to many cities across mainland China, United Kingdom, France, Italy and Netherlands. Artistically talented, Lareina Joelle developed an advanced fluency of music at a young age, later transferring her talents to a variety of instruments and various art media. Lareina embraces planning. Her consistent drive and acceptance for nothing, but excellence is clearly apparent by completing high school at the age of 16, and graduating university with her B.A. at the unusual age of 19. Curious as a child, she experimenting with film, but it wasn't until college that she discovered and embraced her passion for storytelling in the art of filmmaking. In 2008, at 16 years of age and simultaneously completing high school as well as studying at a local college, Lareina was nominated for an Emmy Award for her Student Short Film, Voir Dire by the National Academy of Television Arts & Sciences. Fall of 2010, she began her undergraduate film studies at California State University Long Beach focusing in Film Direction. During that period directing several short films; The Psychiatrist, Mother's Love, and additionally was awarded the Hollywood Foreign Press Association Grant for her last undergraduate film, Geneius, which she wrote, directed and edited. Upon graduating in 2012 with her B.A. in Narrative Film Production, 'Cum Laude' honors, Lareina has directed and edited numerous projects consisting of narrative films (features and shorts), documentaries, series, promotional, commercial and corporate videos. Although Lareina has had many accomplishments thus far, she continues to challenge herself to become an excellent filmmaker while continuing her pursuit to become a director for major motion pictures. Hence, as of Fall of 2014, Lareina has been continuing her film and career education by attending graduate school at the renown USC Cinematic School of Arts to attain her M.F.A. in Film & Television Production.
Small Business Marketing Videos
Get in touch with Lareina Joelle Wong to get setup with a SmartShoot project!


C4DDev can be installed in two ways: Into your Cinema 4D plugins directory and as a command-line tool.
Head to the GitHub Releases page and download the latest release for your platform (Windows or macOS). Then unpack the directory into your Cinema 4D plugins directory.
You need either Python 2 or 3 installed on your system and the Pip package manager. Pip comes pre-installed with Python 3 on Windows, but with Python 2 you will need to run the get-pip.py script first. You may need to start the terminal with admin privileges to install Pip.
After this step, you can install the command-line tools by running the following command (again, you may need admin privileges).
Now you should be able to use the c4ddev command-line program.
source-protector  Protect .pyp files (requires APEX).


Members are asked to consider the appropriateness of their dress and are requested to wear appropriate smart casual attire when using the clubhouse. It is preferred that jeans are not worn, but it is recognised these may be appropriate on informal social occasions. Jogging suits, football shirts, vests and collarless shirts are not allowed. Tailored shorts may be worn, but abbreviated shorts and beach shorts are not allowed. No hats or caps or waterproofs are to be worn in the clubhouse.
Gentlemen are requested to wear jacket, collar and tie and Ladies appropriate dress when collecting prizes.The dress code for social events will be advertised with details of the event.


text:
Stationskwartier is het gebied rondom het huidige Station Breda nabij het centrum in Breda.

Het ligt tussen Belcrum en de Spoorbuurt Breda. Het is een onderdeel van Via Breda. Het moet een van de blikvangers van de stad worden. Station Breda is geheel vernieuwd met de nieuwe Openbaar Vervoer Terminal Breda. Het station heeft een transparant uiterlijk met zeven sporen gekregen. Ook is de busterminal verplaatst.

Vanaf 2018 doet de Beneluxtrein Breda aan en ontstaat er een verbinding tussen  Breda, Antwerpen en Brussel.

In het Stationskwartier komen onder andere winkels en kantoren. Het stationsgebouw is gerealiseerd van 2012 tot 2016. Plannen zijn er om ten westen van het Station Breda een World Trade Center Breda te bouwen. Deze plannen komen moeizaam van de grond. Wel is er zekerheid over een 66 meter hoog gerechtsgebouw waar ook het Openbaar Ministerie en de kinderbescherming zich zullen komen te vestigen. Parallel is het project Breda Vooruit ontwikkeld.

Externe link
 Stationskwartier

Wijk in Breda

redpajama_set_name: RedPajamaWikipedia


The British Columbia Civil Liberties Association appeared before the Parliamentary Standing Committee on Justice and Human Rights yesterday to demand changes to Bill C-55, which will allow emergency warrantless wiretaps of unlimited duration. The BCCLA urged Parliament to limit emergency warrantless wiretapping by the police to a 24-hour period.
In April 2012, the Supreme Court of Canada struck down as unconstitutional a section of the Criminal Code concerning warrantless wiretapping. Parliament is now considering how to make that section (s. 184.4) compliant with the Canadian Charter of Rights and Freedoms. Warrantless wiretaps are intended to deal with situations where there is such urgency that the police do not have time to go through the normal steps to obtain a warrant and the wiretap is immediately necessary to prevent serious harm.
The new bill is intended to address the problems identified by the Supreme Court. The Supreme Court said that the police are allowed to use warrantless wiretaps in truly urgent situations, but that the use of the wiretap without after-the-fact notice to the person being recorded is unconstitutional. In response, Bill C-55 introduces new notice and reporting requirements that bring the section in line with other wiretapping provisions in the Criminal Code. The warrantless wiretapping section is a unique provision in the Criminal Code, and one of only two sections that allow the state to listen in on private communications without a specific time limit and without approval from a judge.


Give yout BMW a sleek and aggressive with a Carbon Fiber Roof Spoiler.
A subtle addition, yet guaranteed to balance the proportions and enhance the look of your BMW.
These spoilers are made from the highest quality Carbon Fiber weave, and are designed to be hollow to reduce overall weight.
These roof spoilers apply with adhesive - NO DRILLING REQUIRED!
The spoiler is applied to the upper portion of the rear windshield with a permanent industrial adhesive (not included).
This item was originally made with an indentation for a logo, which we have modified for a cleaner look.
A faint outline of this indentation may be visible under certain angles of light.
If you think this will bother you, please do not order as returns are not accepted for this reason.
Note that the underside of the spoiler is not painted for a better installation surface.


text:
'We want art back, the new art of architecture'
Written by Nick Wright
Cloud Iron
by El Lissitzky
'A model of clear thinking and informed comment' - Nick Wright reviews the Imagine Moscow exhibition at the Design Museum.
"The position is this: the ecstatic period of the revolution is over. Now it's the working day — but art is holiday. And we want art back, the new art of architecture," artist and designer El Lissitzky declared in 1925. This intelligently conceived exhibition revisits that spirit of daring innovation and unbounded optimism which accompanied the accession to state power of Russia's working class, ushered in by the 1917 Russian revolution.
Buried deep in the Design Museum basement, a series of fluid spaces locate each of the designs for six utopian and uncompleted projects in an architectural, social, political and aesthetic context by assemblies of drawings, plans, documents and illustrations of the post-revolution period. In conception, Ivan Leonidov's 1927 Lenin Institute is simultaneously rooted in the technologies of the time and moulded by extravagantly utopian and untested technique. A pre-internet storehouse of knowledge and a radio station, it was to be served by a metropolitan aero-tram system. Its synthesis of architectural and political ambition hint that the global revolution might have progressed differently if the Comintern had had at its disposal both social media and television.
El Lissitzky's Iron Cloud (1923-1925) reworks, from the early years of the revolution, the model of integrated housing, transport, services and work with a new skyscraper technology which prefigures contemporary big-city style, while Boris Iofan's winning entry for the Palace of Soviets competition conveys something of the optimism of the time. Designed to be the tallest building in the world, topped by a 100-metre statue of Lenin, it was to sit on the site of Moscow's Cathedral of Christ the Saviour. The project started in 1931, just as Stalin warned that the USSR had a decade to prepare for Western invasion. But, by 1941, political realism allowed its uncompleted structures to be recycled to fortify the city against the nazi invaders. Later, the foundations became a swimming pool and now Russia's new bourgeoisie worship in a replica of the cathedral built on the site.
Lenin's statue in the Palace of the Soviets
The utopian spirit of these Soviet pioneers is predicated on a sense that transformed social relations produce a new human being. But, as the world revolution faltered, the bourgeoisie weaponised its fascist auxiliaries and, as the problems of building a socialist society demanded answers, new ways of transforming social actions presented themselves. The very magnitude of the problems necessitated prodigious efforts to mobilise the human and material resources of the socialist state. Thus there were over 100 entries for the competition to design a Commissariat of Heavy Industry, with Yakov Chernikhov's 1933 Architectural Fairytale echoing Lenin's telling phrase: "Communism is Soviet power plus the electrification of the whole country," while Konstantin Melnikov's two 40-story buildings, connected by a futuristic external escalator, were to be decorated with sculptures representing the successes of the first and second Five Year Plans.
The idea of communal living was rooted in the appropriation of the spacious dwellings of the bourgeoisie. Those utopian and revolutionary ideals were shaped to advance the liberation of women through their entry into social production more fully and to render domestic labour less oppressive. Communal kitchens, leisure facilities, laundries, nurseries and restaurants were conceived as state-sponsored instruments designed to enhance women's education and intellectual development. Nikolay Ladovsky's Communal House transmutes this into utopian form through a spiral structure echoing the dialectical thrust of Vladimir Tatlin's Monument to the Third International. The focus on healthy living for the whole person finds direct expression in Health Factory, Nikolay Sokolov's plan for a seaside complex designed to restore workers' productive well-being through structured vacations, recreation, sport and medicine.
Nikolay Ladovsky's Communal House
The one project which did reach completion in 1930 is Alexey Shchusev's Lenin Mausoleum, in which the Soviet leader's body lies in a sarcophagus designed by Konstantin Melnikov. Distinctive though the modernist building is, the materialist world view might be better served if successive Soviet leaders had done what Lenin asked and buried him alongside his mother. The contextual material to the exhibition is excellently presented, with useful accounts of debates in which architects and planners, artists and ideologues, futurists and functionaries argued out their competing priorities.
While there are examples of cold war and unreflective petit-bourgeois prejudice in the exhibition and the excellent accompanying book, in comparison to other stuff with which we are assailed this anniversary year, Imagine Moscow is a model of clear thinking and informed comment.
Runs until June 4, box office: designmuseum.org. This review was first published on morningstaronline.co.uk
Read 12289 times Last modified on Saturday, 28 October 2017 13:25
Latest from Nick Wright
Banners for Spain
Decoding the Culture of Capitalism
South Africa: The Art of a Nation
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Production Broadcaster will need to have good internet and experience with running streams. While we can teach and train the basics, you'll have to be a self-starting individual who enjoys being challenged. You are required to be online Mondays and Tuesdays at 4pm PST. You must have good communication skills and be fluent in English. You'll be working 8-12 hours a week.


IPPB Assistant Manager Question Paper: The Indian Post Payment Bank is going to announce the vacancies for Manager, Territory Officer and Assistant Manager as scale 1 and Scale 2 in the upcoming months. The selection will be done through the written examination and/ or interview. We will keep you informed about all the related updates regarding the direct recruitment on Bank Jobs.
Hence all those who are looking out for the extra study material have come just at the right place. Here we have assembled the IPPB Bank Scale 1 Previous Papers. Also along with them, Model Papers are available which are easy to download as well.
Latest Update: IPPB is going to conduct the Assistant Manager written examination 2019 in the upcoming months. Aspirants can download the IPPB Assistant Manager Previous Question Papers & Model Papers from here.
The previous papers are just the right material for those applicants who want to rest assured for their selection. The benefits of practicing the India Post Assistant Manager Previous Papers is that it helps to improve the accuracy of solving questions, gives subtle hints of most important topics, and follow the timeliness. Above all the difficulty level and how to cope with it can also be learned. You can find these papers below in the given table.
The model papers are way more different than the previous papers. The sample papers are provided by the teaching experts involved in the field over years. However, their expertise is really beneficial to be used in day to day practice. The regular practice with these IPPB Bank Sample Papers can improve the efficiency for learning the topics of the Syllabus and knowing the possibility of often asked questions.
Remarks: If you have any doubts regarding the IPPB Assistant Manager Question Papers, leave them in the comment section and we will get back to you. Also, you can receive the latest job notifications by subscribing our services.


text:
medici.tv launches dedicated broadcast platform for The Leeds International Piano Competition
Public vote for Audience Award opened to global audiences for the first time through this major new partnership
leedspiano2018.medici.tv
medici.tv's extensive coverage of The Leeds International Piano Competition, relaying the full Competition experience including performances from every round to more than 180 countries, begins today [8 August 2018] at leedspiano2018.medici.tv.
From today, audiences can enjoy the First Round performances of the 24 competitors who were selected from among 68 First Round pianists to go through to the next round in Leeds in September. Their progress can then be followed through 8 days of free live webcasts of the final rounds in Leeds between 6 to 15 September. All performances will also be available on demand for three years.
'The Leeds' and medici.tv will work together to deliver a rich digital experience on a dedicated new platform. As well as viewing every Competition performance for free, global audiences will also be able to experience the full atmosphere of the Competition through extensive behind-the-scenes coverage, interviews with the competitors and coverage of other events surrounding the Competition. Broadcaster Petroc Trelawny presents the live webcasts of the whole Competition and is joined by pianists Lucy Parham and former Leeds prize winner Noriko Ogawa for the Semis and Finals.
The new partnership will significantly extend the global reach of the Competition and bring the atmosphere and music-making of this most prestigious event to music lovers in more than 180 countries. It has been made possible thanks to the University of Leeds, a long-standing partner of The Leeds, which has extended its financial support to ensure that international audiences can experience everything that Competition has to offer.
In a major new development for both The Leeds and medici.tv, the global audience will be invited to vote online for the medici.tv Audience Award. This is the first time that worldwide audiences will be able to have a say at The Leeds. The international medici.tv vote will be verified and added to the vote from inside Leeds Town Hall and announced as part of the prize presentation which follows the second day of the Finals on Saturday 15 September. The winner of the inaugural medici.tv Audience Award will have a performance broadcast on medici.tv within the next three years.
Music communities around the world can also come together to follow news, blogs and interact on the newly-created medici.tv platform and via the hashtag #LeedsPiano on social media channels (Facebook, Instagram and Twitter).
Global streaming is one of the key innovations that are rejuvenating The Leeds under the artistic leadership of Paul Lewis and Adam Gatehouse, and is a key pillar of their new vision for the much enhanced Competition.
Held once every three years, The Leeds is one of the world's foremost music competitions. Since the first Competition in 1963, it has attracted the world's finest young pianists, drawn by the opportunities offered by the outstanding prize package, the challenge of demanding repertoire, a stellar jury – and a warm welcome from the City of Leeds. The roll call of eminent past winners and finalists includes many of the world's best-known pianists. The Competition's 1972 winner Murray Perahia became Patron in June 2017. Lang Lang is Global Ambassador and Dame Fanny Waterman was appointed Life President and Founder Director Emeritus in 2015.
Paul Lewis, co-Artistic Director of The Leeds, says: "The Leeds has introduced some outstanding pianists to the world over the past half century. Now, through the exceptional quality and reach of medici.tv's webcasts, we can share the extraordinary music-making of the Competition in real time and to more people than ever before."
Adam Gatehouse, co-Artistic Director of The Leeds, added: "We are thrilled to be working with medici.tv and our Senior Partner the University of Leeds to hugely extend the Competition's global reach and to share the Competition and the great city of Leeds with such diverse audiences in a new and exciting way. It is wonderful to be able to unite the global audience in voting to give one of our five Finalists the medici.tv Audience Award."
Hervé Boissière, Founder & Managing Director of medici.tv: "The Leeds has a long history of excellence and the Competition's world-class laureates have appeared regularly on medici.tv over the past ten years. We're thrilled to be able to help introduce the next generation of piano stars to music lovers around the globe and particularly excited to give fans worldwide the opportunity to engage with the Competition directly through the medici.tv Audience Award."
Following each live webcast, free replay of the various rounds and concerts will be available to online audiences until 16 September 2021, playable worldwide on all devices.


Everyone loves receiving gifts, but receiving a gift which is unique and personalised makes it a whole lot more special and memorable. We have a wonderful range of personalised kitchen gifts, gorgeous glassware and barware which include some great personalised gifts for men. Practical, personalised and precious, these unique kitchen gifts and kitchen accessories make excellent presents for special occasions such as personalised wedding gifts and anniversaries, why not check out our gorgeous range of personalised gifts for kids too.


This is Lubuntu 16.10's New Default Wallpaper - OMG! Ubuntu!
The new default wallpaper of Lubuntu 16.10 — yes, that's Lubuntu, don't get too excited! — has been unveiled.
The design, uploaded to the Ubuntu archives by Julien Lavergne, will ship as the default background on all new installations of the LXDE-based distribution from October.
Lubuntu's default wallpapers are typically reflective of the distribution's branding in that they use various blue gradients and shun busy, over complicated designs in favour of simplicity.
This cycle is no exception.
The jaggedy geometric layout of the new backdrop stands out as one of the more visually distinct to ship in recent years, with the wallpapers of Lubuntu 15.10 and 16.04 LTS both riffing off the similar angular wireframe motif.
The rich pinks and purples have been toned down a little, and more white elements introduced.
You don't have to install the latest Lubuntu 16.10 Alpha to get the wallpaper. We've uploaded the high-res version to Imgur.
I appreciate that news about the default background of an Ubuntu spin isn't exactly breaking, and I know that wallpaper choices aren't everyone's cup of tea.
But, hey, I also know that a lot of readers do take a keen interest in the branding and design of their computer (first impressions count and all that).
So if you like what you see, and want to make it your own wallpaper, click the Imgur preview a few rows above to nab yourself the full 3200 × 2000 version.


text:
Q: Erorr with drop specific rows with Pandas I'm trying to drop specific rows of my dataset, and I always have the same error. I have several candidates and I just want to work with two. I tried with "not in"condition, but when I need to visualize it used all the candidates.
I used the same formula to delete columns and it worked!
Any ideas?
Thanks
poll = poll.drop(["Alexandria Ocasio-Cortez","Amy Klobuchar","Andrew Yang","Barack Obama","Bernard Sanders","Beto O'Rourke","Bill de Blasio","Charles E. Schumer","Elizabeth Warren","Cory A. Booker","Eric Swalwell","Howard Schultz","Hillary Rodham Clinton","John K. Delaney","Jay Robert Inslee","John Hickenlooper","Kamala D. Harris","Julián Castro","Justin Amash","Marianne Williamson","Kirsten E. Gillibrand","Megan Rapinoe","Michelle Obama","Michael F. Bennet","Michael Bloomberg","Mike Pence","Mike Gravel","Nancy Pelosi","Pete Buttigieg","Oprah Winfrey","Nimrata R. Haley","Sherrod Brown","Seth Moulton","Steve Bullock","Tulsi Gabbard","Tom Steyer","Tulsi Gabbard","Wayne Messam"])

I also tried to by adding axis=1 at the end.
dataset:
https://projects.fivethirtyeight.com/polls-page/president_polls.csv

A: Assuming that this is your list of names,
namelist = ["Alexandria Ocasio-Cortez","Amy Klobuchar","Andrew Yang","Barack Obama","Bernard Sanders","Beto O'Rourke","Bill de Blasio","Charles E. Schumer","Elizabeth Warren","Cory A. Booker","Eric Swalwell","Howard Schultz","Hillary Rodham Clinton","John K. Delaney","Jay Robert Inslee","John Hickenlooper","Kamala D. Harris","Julián Castro","Justin Amash","Marianne Williamson","Kirsten E. Gillibrand","Megan Rapinoe","Michelle Obama","Michael F. Bennet","Michael Bloomberg","Mike Pence","Mike Gravel","Nancy Pelosi","Pete Buttigieg","Oprah Winfrey","Nimrata R. Haley","Sherrod Brown","Seth Moulton","Steve Bullock","Tulsi Gabbard","Tom Steyer","Tulsi Gabbard","Wayne Messam"]

poll is your dataframe, and the column that contains these names is called Candidates
Use this:
poll = poll[~poll['Candidates'].isin(namelist)]

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

The observation of the new baryon state $\Theta^+(1540)$ with
positive strangeness and minimal quark content $udud\bar{s}$
\cite{exp2003} has motivated intense theoretical investigations
 to clarify the quantum numbers and to understand the
under-structures of the exotic state
\cite{DiakonovPentaquark,ReviewPenta}. Although the pentaquark state
$\Theta^+(1540)$ can be signed to the top of the antidecuplet
$\overline{10}$ with isospin $I=0$, the spin and parity have not
been experimentally determined yet and no consensus has ever been
reached  on the theoretical side
\cite{DiakonovPentaquark,ReviewPenta}. The discovery has opened a
new field of strong interaction  and provides a new opportunity for
a deeper understanding of the low energy QCD especially when
multiquark states are involved. The magnetic moments of the
pentaquark states are
  fundamental parameters as their  masses, which have  copious  information  about the underlying quark
structures, can be used to distinguish the preferred
configurations from  various  theoretical models and  deepen our
understanding of the underlying dynamics.
 Furthermore, the magnetic moment of the pentaquark state $\Theta^+(1540)$ is an important ingredient
in studying the cross sections of the photo- or
electro-production, which can be used to determine the fundamental
quantum number of the pentaquark state $\Theta^+(1540)$, such
  as spin and parity \cite{HosakaPP,Nam04M}, and may be extracted from experiments eventually in the
future.

 There have been several works on the magnetic moments of the pentaquark state
  $\Theta^+(1540)$ \cite{Huang04M,Zhao04M,Kim04M,Nam04M,Zhu04M,Inoue04M,Bijker04M,Goeke04M,Hong04M,Delgado04M,Wang05M},
in this article, we take the point of view that the baryon
$\Theta^{+}(1540)$ is a diquark-diquark-antiquark
($[ud][ud]\bar{s}$) state with the quantum numbers $J=\frac{1}{2}$ ,
$I=0$ , $S=+1$, and study its magnetic moment with the QCD sum rules
in the external weak electromagnetic field (EFSR) and the light-cone
QCD sum rules (LCSR) respectively
\cite{Shifman79,Ioffe84,LightCone}. Different quark configurations
can be implemented with different interpolating currents, if the $u$
and $d$ quarks in the pentaquark state $\Theta^+(1540)$ are bound
into spin zero, color and flavor antitriplet $\bar{3}$ diquarks, we
can take the diquarks (for example, $\epsilon^{abc} u_b C\gamma_5
d_c$ with $J^P=0^+$ and $\epsilon^{abc} u_b C d_c$ with $J^P=0^-$ )
instead of the $u$ and $d$ quarks as the basic constituents to
construct the interpolating currents.

 The article is arranged as follows:   we derive the EFSR and LCSR for the magnetic moment of the
pentaquark state $\Theta^+(1540)$ in section II; in section III,
numerical results and discussions; section IV is reserved for
conclusion.

\section{EFSR and LCSR}
 Although for medium and asymptotic momentum transfers
 the  operator product expansion approach  can be applied for the form factors and moments of wave
 functions, at low momentum transfer,
 the standard operator product expansion approach cannot be  consistently  applied,
 as pointed out in the early work on photon
 couplings at low momentum for the nucleon  magnetic moments
 \cite{Ioffe84}. In Ref.\cite{Ioffe84}, the problem was solved by using a
 two-point correlation function in an external electromagnetic field, with
  vacuum susceptibilities introduced as parameters for
 nonperturbative propagation in the external field, i.e. the QCD  sum rules in the external field.
 As  nonperturbative vacuum properties, the susceptibilities can be
 introduced for both small and large momentum transfers  in the
 external fields. The alternative way
 is the light-cone QCD sum rules, which
  was firstly used to calculate the magnetic moments of the
nucleons in Ref.\cite{Braun89}. For more discussions about the
magnetic moments of the baryons in the framework of the LCSR
approach, one can consult Ref.\cite{Aliev}.

In the following, we write down  the two-point correlation functions
$\Pi_{EF\eta}(p)$ and $\Pi_{LC\eta}(p)$ for the EFSR and LCSR
respectively \cite{Matheus04},
\begin{eqnarray}
\Pi_{EF\eta}(p)&=& i\int d^4 x e^{ip\cdot x}\langle 0|T \{
\eta(x){\bar \eta}(0) \}|0\rangle_{F_{\mu\nu
} } \, , \nonumber \\
&=&\Pi_0(p) + \Pi_{\mu\nu} (p) F^{\mu\nu} +\cdots \, , \\
 \Pi_{LC\eta} (p, q)&=&  i\int d^4 x \, e^{i p x}
\langle\gamma(q)|T\{\eta(x) \bar \eta(0) \}|0\rangle ,
\end{eqnarray}
where
\begin{eqnarray}
\eta_1(x)&=&{1\over\sqrt{2}}\epsilon^{abc}\left\{\left[u_a^T(x) C
\gamma_5 d_b(x)\right] \left[u_c^T(x) C \gamma_5
d_e(x)\right]C\bar{s}^T_e(x) -
(u\leftrightarrow d)\right\} , \\
\eta_2(x)&=&{1\over\sqrt{2}}\epsilon^{abc}\left\{\left[u_a^T(x) C
d_b(x)\right] \left[u_c^T(x) C  d_e(x) \right ]C\bar{s}^T_e(x) -
(u\leftrightarrow
d)\right\}  , \\
 \eta(x)&=&\left\{t \eta_1(x) + \eta_2(x) \right\} .
\end{eqnarray}
Here the $\gamma(q)$ represents the external electromagnetic field
 $A_\mu (x)= \varepsilon_\mu e^{iq\cdot x}
$, the $\varepsilon_\mu$ is the photon polarization vector and the
field strength  $F_{\mu\nu}(x)=i( \varepsilon_\nu q_\mu
-\varepsilon_\mu q_\nu) e^{iq\cdot x}$. The $\Pi_0(p)$ is the
correlation function  without the external field $F_{\mu\nu}$ and
the $\Pi_{\mu\nu}(p)$ is the linear response term. The $a$, $b$, $c$
and $e$ are color indexes,  the $C=-C^T$ is the charge conjugation
operator, and the $t$ is an arbitrary parameter. The constituents $
\epsilon^{abc} u_b^T(x)C\gamma_5 d_c(x) $ represent the scalar
diquarks with $J^P=0^+$ and $ \epsilon^{abc} u_b^T(x)Cd_c(x)  $
represent the pseudoscalar diquarks  with $J^P=0^-$, we can denote
the $\eta_1(x)$ and $\eta_2(x)$ by S-type and P-type interpolating
current respectively according to the spin and parity of the
constituent diquarks. They both belong to the antitriplet $\bar{3}$
representation of the  color and flavor $SU(3)$ group,  and can
cluster together with diquark-diquark-antiquark  structure to give
the total spin and parity for the pentaquark state $\Theta^+(1540)$
$J^P={\frac{1}{2}}^+$ \footnote{We can write down the interpolating
currents for the other pentaquark states in the multiplets
$\overline{10}+8$ based on the Jaffe-Wilczek's diquark model in the
same way as we have done in Eqs.(3-5), then preform the operator
product expansion and take the current-hadron duality to obtain the
magnetic moments. Comparing with the magnetic moments in the
multiplets and detailed studies may shed light on the
under-structures and low energy dynamics of the pentaquark states.
However, the calculations of the operator product expansion for  a
number of correlation functions are tedious and beyond the present
work, this may be our next work.}. The scalar diquarks correspond to
the $^1S_0$ states of $ud$ quark system. The one-gluon exchange
force and the instanton induced force can lead to significant
attractions between the quarks in the $0^+$ channels
\cite{GluonInstanton}. The pseudoscalar diquarks do not have
nonrelativistic limit,  can be taken as  the $^3P_0$ states.

At the level of hadronic degrees of freedom, the linear response
term $\Pi_{\mu\nu}(p)$ can be written as
\begin{equation}
\Pi_{\mu\nu}(p)F^{\mu\nu} = i\int d^4x  e^{ip\cdot x}\langle 0\,|
\eta(x) \left\{ -i \int d^4y A_\mu(y) J^\mu(y)\right\}
\bar{\eta}(0)\,|\,0\rangle.
\end{equation}
According to the basic assumption of current-hadron duality in the
QCD sum rules  approach \cite{Shifman79}, we insert  a complete
series of intermediate states satisfying the unitarity   principle
with the same quantum numbers as the current operator $\eta(x)$
 into the correlation functions in
Eq.(2) and Eq.(6)  to obtain the hadronic representation. After
isolating the double-pole terms of the lowest pentaquark  states, we
get the following results,
\begin{eqnarray}
\Pi_{\mu\nu }(p)F^{\mu\nu} & = & -\int d^4x \int d^4y {d^4 k \over
(2\pi)^4} {d^4 k^\prime \over (2\pi)^4} \sum_{ ss^\prime} \frac{1}
{m^2_{\Theta^+} -k^2-i\epsilon}\frac{1} {m^2_{\Theta^+}
-{k^\prime}^2-i\epsilon} \nonumber \\ & & e^{ip\cdot x} A_\mu(y)
\langle 0 | \eta(x) | ks \rangle \langle ks | J^\mu(y) | k^\prime
s^\prime \rangle \langle k^\prime s^\prime | \bar{\eta}(0) | 0
\rangle+\cdots\, \nonumber\\
    & = & -F^{\mu\nu}f_0^2 \frac{F_1(0)+F_2(0)}{4(m_{\Theta^+}^2-p^2)^2} \{ {\hat p}
      \sigma_{\mu\nu} +\sigma_{\mu\nu} {\hat p} \}+\cdots ;
\end{eqnarray}
\begin{eqnarray}
\Pi_{LC\eta} (p, q) &=& -f_0^2\varepsilon^\mu\frac{{\hat
p}+m_{\Theta^+}}{p^2-m_{\Theta^+}^2} [F_1(q^2)\gamma_\mu
+\frac{i\sigma_{\mu\nu}q^\nu }{2m_{\Theta^+}}F_2(q^2)]\frac{{\hat p}+{\hat q}+m_{\Theta^+}}{(p+q)^2-m_{\Theta^+}^2} +\cdots  \nonumber \\
 &=&-
\frac{f_0^2\left[F_1(q^2)+
F_2(q^2)\right]}{(p^2-m_{\Theta^+}^2)((p+q)^2-m_{\Theta^+}^2)} {\hat
p}
{\hat \varepsilon} ({\hat p}+{\hat q}) +\cdots \nonumber\\
&=&\Pi_{LC} (p,
q)i\varepsilon_{\mu\nu\alpha\beta}\gamma_5\gamma^\mu\varepsilon^\nu
q^\alpha p^\beta+\cdots.
\end{eqnarray}
Here we  have used  the fix-point gauge  $x_\mu A^\mu(x)=0$,
$A_\mu(y)=-{1\over 2} F_{\mu\nu} y^\nu $, and the definition
$\langle 0| \eta(0) |\Theta^+ (p)\rangle =f_0 u(p)$. From the
electromagnetic form factors $F_1(q^2)$ and $ F_2(q^2)$ , we can
obtain the
 magnetic moment of the pentaquark state $\Theta^+(1540)$,
\begin{equation}
\mu_{\Theta^+}=\left\{ F_1(0)+F_2(0)\right\}
\frac{e_{\Theta^+}}{2m_{\Theta^+}}.
\end{equation}
 The linear response term $\Pi_{\mu\nu}(p)$ in the weak
external electromagnetic field $F_{\mu\nu}$  has three different
Dirac tensor structures,
\begin{equation}
\Pi_{\mu\nu}(p) =\Pi_{EF} (p) \left\{\sigma_{\mu\nu} {\hat p} +{\hat
p}\sigma_{\mu\nu}\right\} +\Pi_1(p)
i\left\{p_{\mu}\gamma_{\nu}-p_{\nu}\gamma_{\mu}\right\}{\hat p}
+\Pi_2(p) \sigma_{\mu\nu}  \, .
\end{equation}
The first structure has an odd number of $\gamma$-matrix and
conserves chirality, the second and third have even number of
$\gamma$-matrixes and violate chirality. In the original QCD sum
rules analysis of the nucleon magnetic
 moments \cite{Ioffe84}, the interval of dimensions (of the condensates) for the odd
structure is larger than the interval of dimensions for the even
structures, one may expect a better accuracy of the results obtained
from the sum rules with  the odd structure. In this article, the
spin of the pentaquark state $\Theta^+(1540)$ is supposed to be
$\frac{1}{2}$, just like the nucleon.  As in  our previous work
\cite{Wang05M},  we can choose  the first Dirac tensor structure
$\left\{\sigma_{\mu\nu} {\hat p} +{\hat p}\sigma_{\mu\nu}\right\}$
for analysis. The phenomenological spectral density of the EFSR in
Eq.(7) can written as,
\begin{equation}
\frac{\mbox{Im} \Pi_{EF} (s)}{\pi} = {1\over 4} \{F_1(0)+F_2(0)\}
f_0^2 \delta^\prime (s-m_{\Theta^+}^2) + C_{subtract} \delta
(s-m_{\Theta^+}^2) +\cdots\, ,
\end{equation}
where the first term corresponds to the magnetic moment of the
pentaquark state $\Theta^+(1540)$,  and is of double-pole. The
second term comes from the electromagnetic transitions between the
pentaquark state $\Theta^+(1540)$
 and the excited states (or high resonances),  and is of single-pole. Here we introduce the quantity  $C_{subtract}$ to represent
 the electromagnetic transitions between the ground pentaquark state and the high
 resonances, it may have   complex dependence  on the energy $s$ and high
 resonance masses. However, we have no knowledge about the high resonances,
 even the existence  of the ground pentaquark state $\Theta^+(1540)$
 is not firmly established, which is in contrast to the conventional baryons, in those channels we can use
 the experimental data as a guide in constructing the phenomenological spectral densities
 \cite{Nielsen05}. In practical manipulations, we can take the $C_{subtract}$ as
 an  unknown constant, and fitted to reproduce reliable values for
 the form factors $F_1(0)+F_2(0)$, we will revisit this subject
 in Eq.(19).
  The contributions from the higher
resonances and  continuum states  are suppressed after Borel
transform  and not shown explicitly for simplicity.  For the LCSR,
  we write down only the double-pole term explicitly in Eq.(8) which corresponds to
the magnetic moment of the pentaquark state $\Theta^+(1540)$, and
choose  the tensor structure
$\varepsilon_{\mu\nu\alpha\beta}\gamma_5\gamma^\mu\varepsilon^\nu
q^\alpha p^\beta$ for analysis \cite{Huang04M}. The contributions
from the single-pole terms which concerning the excited and
continuum states are suppressed after the double Borel transform,
and not shown explicitly for simplicity.

 The  calculation of the operator product expansion in the  deep Euclidean space-time region at the level of
quark and gluon degrees of freedom is
  straightforward and tedious, here technical details are neglected for simplicity,
  once  the analytical  results are obtained,
  then we can express the correlation functions at the level of quark-gluon
degrees of freedom into the following forms through dispersion
relation,
  \begin{eqnarray}
  \Pi_{EF}(P^2)&=& \frac{e_s}{\pi}\int_{m_s^2}^{s_0}ds
  \frac{{\rm Im}[A(s)]}{s+P^2}+
  e_sB(P^2)+\cdots\, , \\
\Pi_{LC}(p,q)&=& e_s\int_0^1 du
\left\{\frac{1}{\pi}\int_{m_s^2}^{s_0}ds
  \frac{{\rm Im}[C(s)]}{s-up^2-(1-u)(p+q)^2}+
  D(p,q) \right\}+\cdots\, ,
  \end{eqnarray}
where
\begin{eqnarray}
\frac{{\rm Im}[A(s)]}{\pi}&=&
-\frac{(5t^2+2t+5)s^4}{2^{14}5!4!\pi^8}+\frac{(5t^2+2t+5)s^3m_s\chi
\langle \bar{s}s\rangle}{2^{9}5!4!\pi^6} +\frac{(5+2t-7t^2)s\langle
\bar{q}q\rangle^2}{2^{9}3^2\pi^4}\nonumber \\
&&-\frac{(5+2t-7t^2)m_s \langle \bar{q}q\rangle^2 \langle
\bar{s}s\rangle
\chi}{2^{7}3^2\pi^2}-\frac{(5t^2+2t+5)s^2}{2^{17}4!\pi^6}\langle
\frac{\alpha_s GG}{\pi} \rangle , \nonumber \\
B(P^2)&=&\frac{(5t^2+2t+5)\langle \bar{q}q\rangle^4}{2^{5}3^3 P^4},
\nonumber \\
 \frac{{\rm Im}[C(s)]}{\pi}&=&
\frac{(5t^2+2t+5)s^4}{2^{12}5!4!\pi^8}-\frac{(5t^2+2t+5)s^3f
\psi(u)}{2^{13}5!\pi^6}+\frac{(7t^2-2t-5)s\langle
\bar{q}q\rangle^2}{2^{7}3^2\pi^4}\nonumber \\
&&-\frac{(7t^2-2t-5)\langle \bar{q}q\rangle^2f
\psi(u)}{2^{6}3\pi^2}+\frac{(5t^2+2t+5)s^2}{2^{15}4!\pi^6}\langle
\frac{\alpha_s GG}{\pi} \rangle  \nonumber \\
&&-\frac{(5t^2+2t+5)sf \psi(u)}{2^{14}3\pi^4}\langle
\frac{\alpha_s GG}{\pi} \rangle ,\nonumber \\
D(p,q)&=&-\frac{(5t^2+2t+5)\langle \bar{q}q\rangle^4}{2^{3}3^3
\left(-up^2-(1-u)(p+q)^2\right)^2}. \nonumber
\end{eqnarray}
From Eqs.(12-13), we can see that due to the special interpolating
current $\eta(x)$ ( see Eqs.(3-5)), the $u$ and $d$ quarks which
constitute the diquarks have no contributions to the magnetic moment
 though they have electromagnetic interactions with the external
field, the net contributions to the magnetic moment come from the
$s$ quark only, which is  different significantly from the results
obtained in Refs.\cite{Huang04M,Wang05M}, where
 all the $u$, $d$ and $s$ quarks have contributions. In Refs.\cite{Huang04M,Wang05M},
the  diquark-triquark type interpolating current $J(x)$ is used,
\begin{eqnarray}
J(x)={1\over \sqrt{2}} \epsilon^{abc} \left\{u^T_a(x) C\gamma_5 d_b
(x)\right\} \{ u_e (x) {\bar s}_e (x) i\gamma_5 d_c(x) - d_e (x)
{\bar s}_e (x) i\gamma_5 u_c(x)  \} \, .
\end{eqnarray}
Although the diquark-diquark-antiquark type and diquark-triquark
type configurations implemented by the interpolating currents
$\eta(x)$ and $J(x)$ respectively can give satisfactory masses for
the pentaquark state $\Theta^+(1540)$,  the resulting magnetic
moments are substantially different, once the magnetic moment can be
extracted from the electro- or photo-production experiments, we can
select the preferred  configuration. In this article, we have
neglected the contributions from the direct instantons as the
effects are supposed to be small.  In Ref.\cite{Forkel}, the authors
calculate the leading direct instanton contributions to the operator
product expansion of the nucleon correlation function with the Ioffe
current
\begin{eqnarray}
J_{p}(x)&=&\epsilon^{abc}[u^T_a(x)C\gamma_{\alpha}u_{b}(x)]\gamma_{5}
\gamma^{\alpha} d_{c}(x) \nonumber
\end{eqnarray}
in an external electromagnetic field, and find the instanton
contributions affect only the chiral odd sum rules which had
previously been considered unstable. The general form of the proton
current can be written as \cite{Baryon}
\begin{eqnarray}
J_p(x,t) &=&  \epsilon_{abc} \left\{ \left[ u_a^T(x) C d_b(x)
\right] \gamma_5 u_c(x) + t  \left[ u_a^T(x) C \gamma_5 d_b(x)
\right]  u_c(x) \right\},
\end{eqnarray}
in the limit $t=-1$, we recover the Ioffe current.
 In this article, we take the
value of the $t$ to be  $t=-1$ in Eq.(5). The pentaquark currents in
Eqs.(3-5) have the analogous Dirac structure as the baryon current
in Eq.(15), so the contributions from the direct instantons may not
affect significantly  about our analysis of the chiral even Dirac
structure in Eq.(10).
 Furthermore,
our previous  work on the pentaquark mass using the interpolating
current
\begin{eqnarray}
 J(x)&=&\epsilon^{abc}\epsilon^{def}\epsilon^{cfg}
   \{u_a^T(x)Cd_b(x)\}\{u_d^T(x)C\gamma_5 d_e(x)\}C\bar{s}_g^T(x)
   \nonumber
\end{eqnarray}
indicates  the direct instantons have neglectable contributions
\cite{WangMass}. The straightforward calculations and tedious
analysis about the direct instanton contributions to the magnetic
moment of the pentaquark state $\Theta^+(1540)$ will be our next
work.

 Here we will take a short
digression and make some discussion about the condensates and
light-cone amplitudes in Eqs.(12-13). The presence of the external
electromagnetic field $F_{\mu\nu}$ induces three new vacuum
condensates i.e. the vacuum susceptibilities in the QCD vacuum
\cite{Ioffe84},
\begin{eqnarray}
\langle  {\overline  q} \sigma_{\mu\nu} q  \rangle_{F_{\mu\nu}} =
e_q  \chi
F_{\mu\nu} \langle  {\overline  q}  q  \rangle \, , \nonumber \\
g_s \langle  \bar{q} G_{\mu\nu} q  \rangle_{F_{\mu\nu}} = e_q
\kappa F_{\mu\nu}
\langle  {\overline  q}  q  \rangle \, , \nonumber\\
g_s \epsilon^{\mu\nu\lambda\sigma} \langle  {\overline  q} \gamma_5
G_{\lambda\sigma} q  \rangle_{F_{\mu\nu}} = i e_q  \xi F^{\mu\nu}
\langle  {\overline  q}  q  \rangle \, , \nonumber
\end{eqnarray}
where $e_q$ is the quark charge, the $\chi$, $\kappa$ and $\xi$  are
the quark vacuum susceptibilities. The values with  different
theoretical approaches are different from each other, for a short
review,  one can see Ref.\cite{Wang02}. Here we shall adopt the
values $\chi=-4.4\, \mbox{GeV}^{-2}$, $\kappa =0.4$ and $\xi = -0.8$
\cite{Ioffe84,LightCone,Belyaev84}. In calculation,
 we have neglected the terms which concern the $ g_s \langle  \bar{q} G_{\mu\nu} q  \rangle$ and
 $g_s \epsilon^{\mu\nu\lambda\sigma}
\langle  {\overline  q} \gamma_5  G_{\lambda\sigma} q |0 \rangle$
induced   vacuum susceptibilities  as they are suppressed by large
denominators.  The photons can couple to the quark lines
perturbatively and nonperturbatively,
  which results in  two classes of diagrams. In the first class of diagrams,
  the photons couple to
the quark lines perturbatively through the standard QED, the second
class of diagrams involve the nonperturbative interactions of
photons with the quark lines, which are parameterized by  the photon
light-cone distribution amplitudes instead of the vacuum
susceptibilities.  In this article, the following two-particle
photon light-cone distribution amplitude has contributions to the
magnetic moment \cite{LightCone,photon},
\begin{eqnarray}
\langle \gamma (q)|\bar q(x) \gamma_\mu\gamma_5q(0)|0\rangle& =&
\frac{f}{4} e_q \epsilon_{\mu\nu\rho\sigma} \varepsilon^\nu q^\rho
x^\sigma \int_0^1 due^{iuqx} \psi(u) \, ,
\end{eqnarray}
where the $\psi(u)$ is the  twist--2 photon light-cone distribution
amplitudes.

We make  Borel transform  with respect to the variable $P^2$ in
Eq.(12) and double Borel transform  with respect to the variables
$p^2$ and $(p+q)^2$ in Eq.(13),
 \begin{eqnarray}
\Pi (M^2) \equiv \lim_{n,P^2 \rightarrow \infty} \frac{1}{\Gamma(n)}
(P^2)^{n} \left( - \frac{d}{d P^2} \right)^n \Pi (P^2), \\
{{\cal B}}^{M_1^2}_{(p+q)^2} {{\cal  B}}^{M_2^2}_{p^2} {\Gamma
(n)\over [ m^2 -(1-u)(p+q)^2-up^2]^n }= (M^2)^{2-n} e^{-{m^2\over
M^2}} \delta (u-u_0 ) ,
\end{eqnarray}
  with  $M^2 = P^2/n$ in Eq.(17) and
  $M^2=\frac{M_1^2M_2^2}{M_1^2+M_2^2}$,
$u_0\equiv\frac{M_1^2}{M_1^2+M_2^2}$ in Eq.(18). Finally we obtain
the sum rules,
\begin{eqnarray}
 \left\{F_1(0)+F_2(0)\right\}
(1+CM^2)f_0^2e^{-\frac{m^2_{\Theta^+}}{M^2}}&=&-4e_s AA, \\
\{ F_1(0)+F_2(0)\}f_0^2 e^{-\frac{m_{\Theta^+}^2}{M^2}}&=&-e_s BB,
\end{eqnarray}
where
\begin{eqnarray}
AA &=& -\frac{(5t^2+2t+5)M^{12}E_4}{2^{14}5!\pi^8}
+\frac{(5t^2+2t+5)m_s\chi \langle \bar{s}s\rangle
M^{10}E_3}{2^{11}5!\pi^6} \nonumber \\
&&+\frac{(5+2t-7t^2)\langle \bar{q}q\rangle^2M^6E_1}{2^{9}3^2\pi^4}
-\frac{(5+2t-7t^2)m_s \langle \bar{q}q\rangle^2 \langle
\bar{s}s\rangle \chi
M^4 E_0}{2^{7}3^2\pi^2}\nonumber\\
&&-\frac{(5t^2+2t+5)M^8E_2}{2^{16}4!\pi^6}\langle \frac{\alpha_s
GG}{\pi} \rangle  +\frac{(5t^2+2t+5)\langle
\bar{q}q\rangle^4}{2^{5}3^3 },  \nonumber\\
BB
&=&\frac{(5t^2+2t+5)M^{12}E_4}{2^{12}5!\pi^8}-\frac{(5t^2+2t+5)M^{10}E_3f
\psi(u_0)}{2^{15}5\pi^6}\nonumber\\
&&+\frac{(7t^2-2t-5)\langle
\bar{q}q\rangle^2M^6E_1}{2^{7}3^2\pi^4}-\frac{(7t^2-2t-5)\langle
\bar{q}q\rangle^2f
\psi(u_0)M^4E_0}{2^{6}3\pi^2}\nonumber \\
&&+\frac{(5t^2+2t+5)M^8E_2}{2^{14}4!\pi^6}\langle \frac{\alpha_s
GG}{\pi} \rangle  -\frac{(5t^2+2t+5)f
\psi(u_0)M^6E_1}{2^{14}3\pi^4}\langle \frac{\alpha_s GG}{\pi}
\rangle \nonumber \\
&&-\frac{(5t^2+2t+5)\langle \bar{q}q\rangle^4}{2^{3}3^3 },
\nonumber \\
E_n&=&1-exp\left(-\frac{s_0}{M^2}\right)\sum_{k=0}^{n}\left(\frac{s_0}{M^2}\right)^k\frac{1}{k!}\,
. \nonumber
\end{eqnarray}

The Borel transform in Eq.(17) can not eliminate the contaminations
to the correlation function from the single-pole terms, we introduce
 the parameter  $C$ which proportional to the  $C_{subtract}$ in Eq.(11) to the subtract the contaminations.
  We have no knowledge about the  electromagnetic transitions between the pentaquark state $\Theta^+(1540)$
 and the excited states (or high resonances), the $C$ can be taken as a free parameter, we  choose the suitable values for $C$ to
  eliminate the contaminations from  the single-pole terms to obtain the reliable  sum rules. The contributions from
  the single-pole terms may as large as or larger than the double-pole term, in practical calculations,
   the $C$ can be fitted to give stable sum rules with respect to
 variations  of the Borel parameter $M^2$ in a suitable interval. Taking  the $C$ as an  unknown constant has
 smeared the complex energy $s$ and high resonances masses dependence, which will certainly impair the
 prediction
 power. As final numerical results are insensitive to the
 threshold parameter $s_0$ and there realy exists a platform with the variations  of the Borel parameter $M^2$, the
 predictions still make sense.
   The double Borel transform in Eq.(18) can eliminate
  the single-pole terms naturally; for more discussions
about the double Borel transform, one can consult
Ref.\cite{Belyaev94}. Furthermore, from the correlation function
$\Pi_0(p)$ in Eq.(1), we can obtain the sum rules for the coupling
constant $f_0$ \cite{Matheus04},
\begin{equation}
f^2_0e^{-{m_{\Theta^+}^2\over M^2}}=CC,
\end{equation}

\begin{eqnarray}
CC &=&\frac{3(5t^2+2t+5)M^{12}E_5}{ 2^{11}7! \pi^8}
+\frac{(5t^2+2t+5)m_s\langle\bar{s}s\rangle M^{8}E_3}{2^{10}5!
\pi^6}+ \frac{(1-t)^2
M^{8}E_3}{2^{13}5!\pi^6}\langle \frac{\alpha_s GG}{\pi} \rangle \nonumber\\
& &+  \frac{(7t^2-2t-5)\langle \bar{q}q\rangle^2
M^{6}E_2}{2^{9}3^2\pi^4}- \frac{(5t^2+2t+5) m_s \langle
\bar{s}g_s\sigma  G s\rangle  M^{6}E_2}{2^{14}3^2\pi^6}
\nonumber\\
&  &+\frac{(7t^2-2t-5) m_s \langle\bar{s}s\rangle \langle \bar{q}
q\rangle^2M^{2}E_0}{2^{6}3^2\pi^2} +\frac{(5t^2+2t+5)\langle \bar{q}
q\rangle^4}{6^3}\, .\nonumber
\end{eqnarray}
 From above equations, we can obtain the sum rules for the form
 factor $F_1(0)+F_2(0)$,
\begin{eqnarray}
 \left\{F_1(0)+F_2(0)\right\}\left\{1+CM^2\right\} =-4 e_s \frac{
 AA} {CC} \,  , \\
 \left\{F_1(0)+F_2(0)\right\} =- e_s \frac{
 BB} {CC} \,  .
\end{eqnarray}

\section{Numerical Results and discussions}
In this article, we take the value of the parameter $t$ for the
interpolating current $\eta(x)$  to be $t=-1$, which can give stable
mass for the pentaquark state $\Theta^+(1540)$ (i.e.
$m_{\Theta^+}\approx 1540~MeV$) with respect to the variations of
the Borel mass $M^2$ in the considered interval $M^2=(2-3)GeV^2$
\cite{Matheus04}. The parameters for the condensates are chosen to
be the standard values, although there are some suggestions for
updating those values, for reviews, one can see Ref.\cite{Update},
$\langle \bar{s}s \rangle=(0.8\pm0.1) \langle \bar{u}u \rangle$,
$\langle \bar{q}q \rangle=\langle \bar{u}u \rangle=\langle \bar{d}d
\rangle=-(240\pm 10 MeV)^3$, $\langle \bar{s}g_s\sigma G s
\rangle=m_0^2\langle \bar{s}s \rangle$, $m_0^2=(0.8\pm0.1)GeV^2$,
$\chi=-(4.4\pm 0.4)GeV^{-2}$, $\langle \frac{\alpha_s GG}{\pi}
\rangle=(0.33GeV)^4$,
 $m_u=m_d=0$ and $m_s=(140\pm10) MeV$. Small variations of those condensates will not
 lead to large  changes about   the numerical
 values.  The threshold parameter $s_0$ is chosen to  vary between $(3.6-4.4) GeV^2$ to avoid possible contaminations from
 the high resonances and continuum states, which is shown in Fig.1 for $\langle \bar{s}s \rangle=0.8
   \langle \bar{u}u \rangle$,
$\langle \bar{q}q \rangle=-(240 MeV)^3$,  $m_0^2=0.8GeV^2$,
$\chi=-4.4GeV^{-2}$  and $m_s=140 MeV$. In the EFSR,  for $s_0=4.0
GeV^2$ and $M^2=(2-5)GeV^2$, we obtain the values
 \begin{eqnarray}
 F_1(0)+F_2(0)&=&-(0.18\pm 0.03) \, , \nonumber\\
 \mu_{\Theta^+}&=& -(0.18\pm 0.03) \frac{e_{\Theta^+}}{2m_{\Theta^+}}\, , \nonumber \\
  &=& -(0.11\pm 0.02)\mu_N,
  \end{eqnarray}
where the $\mu_N$ is the nucleon  magneton.
 From the Table 1,  we can see that although  the numerical values for
 the magnetic moment of the pentaquark  state $\Theta^+(1540)$  vary with theoretical
 approaches, they are small in general;  our numerical results
are consistent with most of the existing values of theoretical
estimations in magnitude, however, with negative sign. In Eq.(22),
the perturbative contributions are about $25\%$, the dominating
contributions come from the dimension-6 quark condensates terms
$\langle\bar{q}q\rangle^2$ , the contributions from the gluon
condensate $\langle \frac{\alpha_s}{\pi}GG\rangle$, dimension-12
quark condensate $\langle\bar{q}q\rangle^4$ are very small and can
be safely neglected. In calculation, other vacuum condensates are
neglected due to the suppression of the large denominators, the
truncation of the operator product expansion makes  sense.

For the conventional ground state mesons and baryons, due to the
resonance dominates over the QCD continuum contributions, the good
convergence of the operator product expansion, and the useful
experimental guidance on the threshold parameter $s_0$, we can
obtain the fiducial Borel mass region.  However, in the QCD sum
rules for the pentaquark states, the spectral density $\rho(s) \sim
s^m$ with $m$ larger than  the corresponding ones in the
 sum rules for the conventional baryons, larger $m$ means   stronger dependence on the
continuum or the threshold parameter $s_0$ \cite{Narison04,Zhu05}.
In Eq.(21), due to the huge continuum contributions, the  predicted
mass increases with the continuum threshold $s_0$, the QCD sum rules
cannot strictly indicate the existence of the resonance in the
spectral function,  the threshold parameter  $s_0$ has  to be fixed
ad hoc or intuitively. In  the finite energy sum rules (FESR)
approach, the exponential weight function $exp(-\frac{s}{M^2})$ is
replaced by $s^n$ in the numerical analysis. The FESR   correlate
the ground state mass and the QCD continuum threshold $s_0$, and
separate the ground state and QCD continuum contributions from the
very beginning, for  some pentaquark currents, there happen exist
reasonable stability regions  $s_0$ \cite{Narison04}. The weight
function $s^n$ enhances the continuum or the high mass resonances
rather than the lowest ground state, we must make sure that only the
lowest pole terms contribute to the FESR below the  $s_0$, in some
case, a naive stability region  $s_0$ can not guarantee    a
physically reasonable value for the $s_0$ \cite{Zhu05}. It is
obviously, as QCD models, the Laplace sum rules and the FESR have
both  advantages and shortcomings. Although the quantities $f^2_0
exp(-{m_{\Theta^+}^2\over M^2})$ in Eq.(19) and Eq.(21) have strong
dependence on the continuum threshold parameter $s_0$, the
dependence is eliminated in Eq.(22) which results in a net $s_0$
insensitivity;  it is far from the ideal case, where the $f^2_0
exp(-{m_{\Theta^+}^2\over M^2})$ are insensitive to the threshold
parameter $s_0$. From Fig.2, we can see that for the Borel parameter
$M^2=(2-5)GeV^2$, the contributions of the double-pole and
single-pole terms below the threshold $s_0=4.0GeV^2$ are dominating,
for example, the contributions of the continuum from the
$s_0=4.0GeV^2$ to a large interval $s_0=20.0GeV^2$ will not exceed
$30\%$ (comparing with the contributions below $s_0=4.0GeV^2$), the
lowest pole terms dominance still hold and we have the fiducial
Borel mass domain where the neglect of higher-order terms in the
short-distance expansion is justified while the nucleon pole terms
still dominate  over the continuum.

In the EFSR, the Borel transform can not eliminate the contributions
from the single-pole terms, on the other hand, we have no knowledge
about the transitions between the ground states $\Theta^+(1540)$
state and excited states (or high resonances), in practical
manipulations, we can introduce some free parameters which denote
the contributions from the single-pole terms and subtract them. In
choosing the parameter $C$ in Eq.(22), we must take care, in
general, the $C$ can be chosen to give the stable sum rules  with
respect to the variations of the Borel parameter $M^2$. Although the
uncertainty of the condensates, the neglect of the higher dimension
condensates, the lack of perturbative QCD corrections, etc, will
result in errors, we have stable sum rules for the magnetic moment,
furthermore, small variations of the condensates will not result in
large changes for the values,  the predictions are qualitative at
least. If the pentaquark state $\Theta^+(1540)$ can be interpolated
  by the linear superposition of the S-type and P-type diquark-diquark-antiquark current, $\eta(x)$,
  the predictions are quantitative and make sense.
Comparing with Ref.\cite{Wang05M}, the EFSR  with different
interpolating currents (standing for different configurations) can
lead to very different results for the magnetic moment, although
they can both give satisfactory masses for the pentaquark state
 $\Theta^+(1540)$.

 In the LCSR, the double Borel transform
is supposed to  eliminate the single-pole terms which concerning the
contaminations from high resonances  and continuum states, and gives
stable sum rules  with the variations of the Borel parameter $M^2$.
However, that is not the case, from Fig.3, we can see that the LCSRs
for the form factor $-[F_1(0)+F_2(0)]$ are sensitive to the
threshold parameter $s_0$, when $s_0>4.0 GeV^2$, the values of the
form factor $-[F_1(0)+F_2(0)]$ decrease drastically with the
increase of the Borel parameter $M^2$ and there will not appear the
platform. For $s_0=3.8GeV^2$, $M^2=(2-5)GeV^2$, $ \psi(u)=1$ and
$f=0.028 \mbox{GeV}^2$ \cite{LightCone,photon},
\begin{eqnarray}
 F_1(0)+F_2(0)&=&-(0.2-0.8) \, , \nonumber\\
 \mu_{\Theta^+}&=& -(0.2-0.8) \frac{e_{\Theta^+}}{2m_{\Theta^+}}\, , \nonumber \\
  &\approx& -(0.1-0.5)\mu_N.
  \end{eqnarray}
In above equations, we take the maximal variation  interval for the
values of the form factor $F_1(0)+F_2(0)$.

\begin{figure}
 \centering
 \includegraphics[totalheight=7cm]{Figure1.EPS}
 \caption{$|F_1(0)+F_2(0)|$ with the variations of the Borel Parameter $M^2$ for EFSR. }
\end{figure}

\begin{figure}
 \centering
 \includegraphics[totalheight=7cm]{Figure2.EPS}
 \caption{$|\frac{[\frac{AA}{CC}]_{s0=20.0GeV^2}-[\frac{AA}{CC}]_{s0=4.0GeV^2}}{[\frac{AA}{CC}]_{s0=4.0GeV^2}}|$ with the variations of the Borel Parameter $M^2$ for EFSR. }
\end{figure}

In the LCSR approach, the uncertainty of the photon light-cone
distribution amplitudes, keeping only the lowest-twist few terms of
two particles distribution amplitudes, the uncertainty of the
condensates, the neglect of the higher dimension condensates, the
lack of perturbative QCD corrections, etc, can lead to errors in the
predictions. The LCSRs for the form factor $F_1(0)+F_2(0)$ ( see
Eq.(23) and Eq.(25) ) are  very sensitive to the values of the
parameter $f$, small variations of the $f$ can lead to large changes
for the magnetic moment, which is shown in Fig.4. The inclusion of
the contributions from the direct instantons may improve the
stability of the LCSR, to our knowledge, there exist no such type
works on the magnetic moments of the baryon with the LCSR, this may
be our next work.  In this article, only the nonperturbative
interactions of the photons with the $s$ quark line of the form
$\langle \gamma (q)|\bar q(x) \gamma_\mu\gamma_5q(0)|0\rangle$ have
contributions to the magnetic moment which is different
significantly from the corresponding ones with the interpolating
current $J(x)$ in Eq.(14), where all the non-local matrix elements
$\langle \gamma (q)|\bar q(x) \sigma_{\mu\nu}q(0)|0\rangle$,
$\langle \gamma (q)|\bar q(x) \gamma_\mu\gamma_5q(0)|0\rangle$, $
\langle \gamma (q)|\bar q(x) \gamma_\mu q(0)|0\rangle$ have
contributions to the magnetic moment, and result in  more stable sum
rules \cite{Huang04M}. In the vector dominance model,
\begin{eqnarray}
f \simeq \frac{f_\rho m_\rho}{g_\rho}  \simeq 0.028 GeV^2,
\end{eqnarray}
with $g_\rho = 5.5$ and $f_\rho = 0.2 GeV$.  To the leading twist
accuracy,  the light-cone amplitude $ \psi(u) $ is a constant which
is set to be unity due to the normalization condition.
\begin{figure}
 \centering
 \includegraphics[totalheight=7cm]{Figure3.EPS}
 \caption{$-[F_1(0)+F_2(0)]$ with the variations of the Borel Parameter $M^2$ for LCSR. }
\end{figure}

\begin{figure}
 \centering
 \includegraphics[totalheight=7cm]{Figure4.EPS}
 \caption{$|F_1(0)+F_2(0)|$ for different $f$ with the variations of the Borel Parameter $M^2$ for  LCSR ($s_0=3.8GeV^2$). }
\end{figure}

 We choose different tensor
structures for analysis in different approaches i.e. the EFSR  and
the LCSR  with the same interpolating current $\eta(x)$, the
resulting different sum rules always lead to different predictions
\cite{Huang04M,Wang05M}. The LCSRs with  the interpolating current
$\eta(x)$ depend heavily on the values of the parameter $f$ and
sensitive to the threshold parameter $s_0$,   the values obtain from
the LCSR ( see Eq.(25)) are not as reliable as the corresponding
ones from the EFSR ( see Eq.(24)).
 When the experimental measurement of the magnetic moment of the
pentaquark state $\Theta^+(1540)$
  is possible in the  future, we might  be able  to test the theoretical
   predictions,  select
the preferred quark configurations.

  \begin{table}[ht]
         \caption{The values of $\mu_{\Theta^+}$ (in unit of $\mu_N$)}
         \begin{center}
         \begin{tabular}{c||c}
         \hline\hline
         Reference          & $\mu_{\Theta^+}$ \\
                            &  $(\mu_N)$  \\ \hline\hline
   \cite{Huang04M}         &   0.12 $\pm$ 0.06        \\ \hline
         \cite{Zhao04M}     &   0.08 $\sim$ 0.6        \\ \hline
         \cite{Kim04M} & 0.2$\sim$0.3     \\ \hline
     \cite{Nam04M}        & 0.2$\sim$0.5         \\ \hline
      \cite{Zhu04M}              & 0.08 or 0.23 or 0.19 or 0.37           \\ \hline
      \cite{Inoue04M}              & 0.4          \\ \hline
               \cite{Bijker04M}             & 0.38          \\ \hline
               \cite{Goeke04M}             &-1.19 or -0.33         \\ \hline
                \cite{Hong04M}             &0.71 or 0.56          \\ \hline
      \cite{Delgado04M}            &0.362          \\ \hline

                      \cite{Wang05M} &0.24$\pm$0.02           \\ \hline\hline
                   This Work &   -(0.11$\pm$ 0.02)        \\ \hline
         \end{tabular}
         \end{center}
         \end{table}
\section{Conclusion }

In summary, we have calculated  the magnetic moment of the
 pentaquark state  $\Theta^+(1540)$ as diquark-diquark-antiquark
($[ud][ud] \bar{s}$) state with both the  EFSR and LCSR. We choose
different tensor structures for analysis in different approaches
(i.e. the EFSR and the LCSR) with the same interpolating current ,
the resulting different sum rules always lead to different
predictions \cite{Huang04M,Wang05M}. The EFSRs for the magnetic
moment are stable with the variations of the Borel parameter $M^2$
and insensitive to the threshold parameter $s_0$ (See Fig.1 and
Fig.2); the LCSRs in this work depend heavily on the values of the
non-local matrix element $\langle \gamma (q)|\bar q(x)
\gamma_\mu\gamma_5q(0)|0\rangle$, small variations of the values $f$
can result in large changes about the magnetic moments. The values
from the EFSR are more reliable than the corresponding ones from the
LCSR. The numerical results from the EFSR are consistent with most
of the existing values of theoretical estimations in magnitude,
however, with negative sign, $\mu_{\Theta^+}= -(0.18\pm 0.03)
\frac{e_{\Theta^+}}{2m_{\Theta^+}}
  = -(0.11\pm 0.02)\mu_N$ . Comparing
with Ref.\cite{Wang05M}, the EFSR with different interpolating
currents (standing for different configurations) can lead to very
different results for the magnetic moment, although they can both
give satisfactory masses for the pentaquark state
 $\Theta^+(1540)$.   If the pentaquark state
$\Theta^+(1540)$ can be interpolated
  by the linear superposition of both S-type and P-type diquark-diquark-antiquark current $\eta(x)$,
  the predictions are quantitative and make sense.
   The  magnetic moments of the
baryons are  fundamental parameters as their masses, which have
copious  information  about the underlying quark structures,
different substructures can lead to
 very different results. The width of the pentaquark state $\Theta^+(1540)$ is so
narrow, when the
 small magnetic moment can be extracted from electro- or photo-production
experiments eventually in the  future, which may be used to
distinguish the preferred configurations  from various theoretical
models, obtain more insight into the relevant degrees of freedom and
deepen our understanding about  the underlying dynamics that
determines the properties of the exotic pentaquark states.

\section*{Acknowledgment}
This  work is supported by National Natural Science Foundation,
Grant Number 10405009,  and Key Program Foundation of NCEPU. The
authors are indebted to Dr. J.He (IHEP), Dr. X.B.Huang (PKU) and Dr.
L.Li (GSCAS) for numerous help, without them, the work would not be
finished.

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