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text:
Jummah 1st 1:15 / 2nd 1:45
Upcoming Prayer At The Mosque
1 February 2023 - Zuhr: 13:15
Zuhr
Jama'ah
View monthly prayer times
Prayer Hall For Men & Women
Madrasah For Children
Ladies Educational Classes
Islamic Marriage Registration Service
Decades of Muslim worship
The history of Newham North Islamic Association (NNIA) dates back to 1974 when it was established to cater for the religious, social and cultural needs of a growing Muslim community in Newham, east London. Since the early 1990s, Green Street Mosque has been the home of NNIA.
The mosque was one of the first to offer facilities for Muslim worshippers in the city's borough and also became the first organisation in Newham to provide a dedicated and equally equipped facility for women.
From humble beginnings, over almost 50 years, the centre has been extended and modernised to cope with the growing demands of the thriving local population. The mosque is also able to support people with special needs, such as offering wheelchair access and lifts to different floors.
We are a non-profit organisation and registered as charity.
The Green Street Masjid is mainly run by volunteers, including people from a wide range of backgrounds and professions. We are very grateful for the hard work and dedication of the trustees and management committee.
The vast experience of our committee allows the mosque to deliver many excellent services to the local – and wider – community.
We also rely on the work of the Imams of the mosque, who lead the prayer, as well as the teachers at the madrassha.
Apart from our role in the Masjid, members of NNIA play an active part in the wider community, including such activities as enabling school visits and forming an excellent relationship with the local police.
Green Street Masjid also supports UK and overseas charities and our work has been featured in local newspapers many times.
As part of a wider community, we are affiliated with and connected to:
The Standing Advisory Council on Religious Education (SCARE): An independent advisory body for the provision of Local Authority religious education.
Newham Mosque Alliance: An advocate of interfaith, inter-religious dialogue and of multiculturalism.
The Muslim Council of Britain (MCB): The UK's largest and most diverse national Muslim umbrella organisation.
Faithful Friends: A group that aims to build friendships between people of different faiths.
Union of Muslim Organisations (UMO): A group that raises awareness, educates and promotes better relationships between different religious and racial groups.
We are proud that Green Street Masjid has an open-door policy and we welcome everyone. Please do drop-in at the centre or contact us to find out more.
Green Street Mosque 2023 © All rights reserved
Designed by Jarilo Design

redpajama_set_name: RedPajamaCommonCrawl


text:
Book Gene for Your Next Event
Hip Hop Fit Transformations
Creating filtered version of banner image.
Hip-Hop Fit with Gene Hicks
DiabetesSisters hosted its first program of 2019 on January 11th: New Year, New You: Hip Hop Fit with Gene Hicks in Woodridge, IL. A group of over 50 participants listened to guest speakers Samantha Doty, RD, LDN, CDE, CCP and Amanda Przybyla, RDN, LDN, CCP, from Livongo, speak about the value of physical activity and its relationship to blood sugar management before enjoying an exercise dance session.
DiabetesSisters recognizes and appreciates the support of AstraZeneca, Janssen, Livongo, Novo Nordisk, and the Boehringer Ingelheim-Lilly Alliance as sponsors of Minority Initiative programs.
Small Business Development Center	— SBDC at JJC
Hip Hop Fit with Gene Hicks
A new Bolingbrook business is dancing to the beat! Kate Ryan and Gene Hicks officially opened Hip Hop Fit with Gene Hicks on February 10, 2016. For the past six years, Gene had been teaching his exclusive Hip Hop Fit classes at area gyms and built up a loyal following. It was rewarding for him to watch people reach their fitness goals and transform their lives from the workout he created. The positive feedback and support from clients gave the couple encouragement to start their own studio and bring Hip Hop Fit to a larger audience.
Hip Hop Fit classes are easy-to-follow, dance based workouts. The studio offers Hip Hop workouts in 60 minute sessions, six days per week. They also offer martial arts based classes and are planning to add a Latin Fusion class. Additional workout formats will be added as the studio expands. Kate said, "Gene's Hip Hop Fit workouts are exciting and challenging, yet anyone at any ability level can enjoy success in the class because he makes the moves so simple and easy to follow." She explained that Gene also brings high-energy to his classes to create a fun, party-like workout.
Participants must be ages 14 and up for Hip Hop Fit classes. However, children of all ages are welcome at Kickboxing and Family Hip Hop Fit classes. Clients may purchase a a month-to-month membership or simply pay a drop-in rate as they attend a class.
A ribbon cutting ceremony was held by the Bolingbrook Area Chamber of Commerce on April 26, 2016 at the studio. The guests in attendance admired the large studio space that is available for classes.
While in the planning stages for their business, they reached out to the Illinois Small Business Development Center at Joliet Junior College for assistance with their start-up. They consulted with Michael McClinton, SBDC business advisor, to receive guidance with developing a business plan.
Kate said, "Michael helped us to finish up our business plan by providing excellent feedback. He also helped connect us with ACCION Chicago and prepared us to be ready for the process of applying for a start-up loan with them." She added, "He was there with us from the beginning and supported us throughout the startup process by always being available to answer questions and give insightful feedback."
Hip Hop Fit with Gene Hicks is located at 526 East Boughton Road in Bolingbrook, Illinois. For more information and a class schedule, call (630) 312-8732 or visit their website at: www.hiphopfit.net/
Mike said, "The success of Hip Hop Fit is proof that dreams do come true with hard work, dedication and continued encouragement." He continued, "Gene and Kate are a great team and I see nothing but success in their future."
The Illinois SBDC at JJC offers consultations, resources and seminars to assist entrepreneurs with the start-up or expansion of their business. To learn more about the Illinois SBDC at JJC call (815) 280-1400 or email sbdc@jjc.edu.
The Illinois SBDC at JJC is funded in part through a cooperative agreement with the U.S. Small Business Administration, the Department of Commerce and Economic Development, and Joliet Junior College.
The Lewis Flyer	— Roslyn Summerville and Barbara Kaluzny
Professor to Host Dance Night
Roslyn Summerville, Public Relations Editor
Barbara Kaluzny, Contributor
Bored and don't know what to do?
Sick and tired of doing homework?
Or maybe you just want to get out there and meet some new people.
Well, if any of those apply to you, then you should head on over to the D'Arcy Great Room on Wednesday, Oct. 23 for a night of learning the cha-cha, just make sure to wear shoes with less traction for better spinning and twirling abilities. The event will be held from 7:30- 8:30 p.m.
Dr. George Miller, chair and professor to the philosophy department at Lewis University, has been hosting these dance nights on campus for the past few years.
The dance nights came about because Miller was taking dance classes in ballroom and hip hop. He thought that the energy in his dance lesson room was great, and wanted to duplicate that experience for Lewis students.
The instructor who is going to teach the cha-cha is Norman Landrum, who has been a ballroom dance instructor for over 13 years. He runs a studio called Norm's Dance Family, and teaches ballroom dance classes weekly at the Bolingbrook Park District.
This isn't the first time Landrum has been invited to teach students at Lewis. Previously, he's been here to teach the hustle, rumba, and the swing.
Miller thinks that it is important for students to partake in physical activity. He is known for having his students do physical activity before and during his classes because he has found "that studies have shown that students who exercise are actually better students."
"I don't think 20 year olds should be sitting around. I don't think anybody should be sitting around for that matter," Miller said. "I think that energy is better served doing something positive instead of negative."
The room in De La Salle for the previous dance night, which was hip hop taught by Gene Hicks who produces, performs and hosts events all over the Midwest, was filled from wall to wall with students dancing for the hour. One of Miller's students, junior biology major Ariel Colman, was there to experience all of the high energy.
"I liked the [hip hop] dance night a lot. It was a lot of fun going, and it gives people a chance to just relax and dance," Colman said. "I will be going to the next one, and it definitely is something I recommend for people to do."
Colman thought the dancing was a great way to get rid of the stress from studying. The dance night was just like she expected it to be, which she says was "fun and upbeat."
"We have a lot of fun dancing in [Miller's] class, so I wasn't expecting anything less for hip hop night," she said.
The next dance night is going to be held on Dec. 5, and it will be a ballroom and hip hop mix with Hicks making another appearance.
© 2019 Hip-Hop Fit with Gene Hicks. All Rights Reserved.


6:23 | New Company commander Ron Christmas found lax discipline when he arrived at An Hoa base. This was something he could fix because he loved training, that and his 106mm recoilless rifle.
Naval ROTC graduate Ron Christmas took a Marine commission and headed to Camp LeJeune where he learned basic facts of leadership. One is that you share all hardships with your men. Another, unique to the Marines, is that everyone is trained as a rifleman.
Platoon leader Ron Christmas was a stickler for training, even on his first deployment, and all his men who were up for promotion passed their test. From the Mediterranean, he went to the Caribbean, where a beautiful sunset changed his life.
When Ron Christmas was assigned to the Marine Barracks in Washington, he was surrounded by tradition at the Marines' oldest post. It was there that he met Blackie, a most unusual member of the garrison.
When Ron Christmas was assigned to Vietnam, he was so excited to be going that he studied the Vietnamese language at his own expense. When he arrived in country, he reluctantly took the command of a service company.
When Gen. Westmoreland decided to move around and reinforce certain units in Operation Checkers, Captain Ron Christmas found himself just outside of the city of Hue in a camp where hostiles owned the high ground.
Believing there would be an uprising among the populace, Ho Chi Minh and Gen. Giap planned a general offensive for the Tet New Year in 1968. There was no uprising, but Ron Christmas would see some of the nastiest fighting of the war as a result.
What Marine Captain Ron Christmas knew, as he assembled a relief convoy, was that action was reported in Hue. What he and others didn't know was that the North Vietnamese Army had infiltrated the entire city.
Marines were trained for jungle warfare in Vietnam, but Captain Ron Christmas found himself in a house-to-house urban battle in Hue. He prevailed using lance corporal ingenuity and PFC power, along a handy 106mm recoilless rifle.
As Ron Christmas fought to capture the Capitol building in the battle for Hue, the sight of an enemy flag angered him. Even though it was forbidden, as soon as he secured the site, he raised an American flag to boost the morale of his men.
Always looking for a bit of humor for relief, Captain Ron Christmas and his men had some fun in a posh toy room in a captured mansion. What they found in another well appointed house was an eye-opening stash of brandy. Both were great morale boosters.
Ordered to take ground across a bridge in Hue, Captain Ron Christmas used a barrage of smoke rounds to cover a dash across the span. After holding long enough to move across vital units, he found that his men were disappointed they had to withdraw.
It was Friday the Thirteenth when a North Vietnamese soldier fired an RPG at Ron Christmas. Dodging a direct hit, his legs were wounded badly enough to cause his evacuation. Unfortunately, he became lost in the medical system.
Ron Christmas tells the story of a Marine who kept getting wounded, and kept returning to battle because he couldn't desert the men that he considered to be his brothers. That, he says, is the true meaning of Semper Fidelis.
Under the rules of the Marine Corps at the time, Ron Christmas should have been discharged after he was wounded in Vietnam. As he recovered his strength, he was able to avoid a medical exam until he got in line with some inductees.
Marine Ron Christmas reflects on the basic principles of urban warfare, which he learned on the fly in the battle for Hue. He felt blessed in his later career as he received many rewarding assignments.
One of the men that Reed was with had a .45 Auto handgun, which was one of the only guns left that had any ammunition in it. Reed remembers that he had to know how to use his gun like it was second nature, and how that helped him in his Viet Cong approach. Part 4 of 4.
When he saw the weapons the Vietnamese infantry had, American Advisor Nat Robb thought he was in World War II. M-16's were on the way but, in the meantime, the untested unit had to fight. There was little activity at first, but it was just a matter of time.


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Aristotle's Journey to Europe: A Synthetic History of the Role Played by the Islamic Empire in the Transmission of Western Educational Philosophy Sources from the Fall of Rome through the Medieval Period
umi-ku-2277_1.pdf (3.504Mb)
Cloud, Randall R.
Educational Leadership and Policy Studies
This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
After the fall of Rome, how did the work and words of the ancient Greek philosophers make their way, textually and intellectually, into later European thought? There were two primary and obvious paths that this Greek literature could have taken to reach medieval Europe after the split of the Roman Empire into east and west sectors, but these two potential paths functionally became, instead, dual roadblocks to its transmission. In the western portion of the former Roman Empire, there was an overwhelming passive indifference to Greek philosophy coupled with a decline of culture generally in Western Europe during the so-called Dark Ages. In the eastern portion of the former Roman Empire, the attitude toward Greek philosophy was tempered by the imperial authority of Constantinople and eastern Christianity, and ranged from cautious acceptance to occasionally active censorship. In response to the research question, here is my thesis: The Islamic Empire of the Middle Ages was the primary and indispensable force behind the preservation, transmission and acceptance of the Greek philosophical tradition to later European thinking. I will contend that without the influence of Muslim scholars during the medieval period, the foundational impact of Greek philosophy on later Western philosophy (including specifically, Western sources of educational philosophy) may have been greatly reduced (or potentially lost), used differently, and/or forced to find other sources of transmittal. My research will pursue the historical connections between classical Greece and pre-Renaissance Europe on three interrelated levels--textual, philosophical, and cultural. First, I will examine the textual transmission of specific works by Plato and Aristotle, looking at the translation and transmission work done over time and through several language and cultural groups. Second, I will seek to find how the ideas of Plato and Aristotle were used and transmitted, moving from text to philosophical patterns of thinking. Third, I will look more broadly at the acceptance of philosophical inquiry and the development of critical thinking within culture itself, in Greek, Arabic, and Latin settings, to see how the often competing ideas of faith and reason play out over the course of our historical framework.
Dissertations [4276]
Education Dissertations and Theses [1068]


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Tag: family summer vacation ideas
The Resort at Paws Up Welcomes Austin Grill Master Evan LeRoy for BBQ-U
Comfortable around a live fire from a young age, Chef Evan LeRoy's culinary experiences range from fine dining at Hudson's on the Bend to barbecue at Hill Country Barbecue. LeRoy was named as one of Zagat's 30 Under 30 rising stars in the Austin culinary scene. LeRoy has appeared on Burgers, Brew & Que and Food Porn and gained the title of Austin Grill Master on the Travel Channel.
In 2017, LeRoy opened the barbecue truck LeRoy and Lewis, with a rotating menu of nontraditional meats and cuts and a working motto of "new school barbecue, old school service." LeRoy has also traveled to Australia and Russia to train and work with prospective pit masters and is known for his openness to teaching and sharing smoking secrets. We are thrilled to have him this year for BBQ-U on June 22–24, 2018. We had a chance to sit down with LeRoy for a quick interview.
The last time you visited Paws Up was in 2016, correct? Tell us a little about your favorite memory on our ranch.
Correct. I took a hike through the woods one morning and saw a bald eagle for the first time in my life. Also, the last day of archery with my wife was fun and competitive.
What activity are you most excited about trying on property?
I'm most interested in doing some fishing this trip. I was not able to do that last time, and it seems like fun.
How did you become interested in barbecue?
I've been interested in barbecue for a long time. Since I was a kid cooking in the backyard with my dad. It's more than an interest growing up in Texas—it's an ingrained part of our culture.
Can you tell us about the dual smoker, which we hear you're bringing to Paws Up? And why it's called "the twins"?
Between leaving Freedmen's (my last BBQ job) and opening LeRoy and Lewis, I taught some classes to keep me busy, keep money coming in and to stay relevant in the barbecue scene. I liked the idea of cooking with people and connecting with people over BBQ on a deeper level. One of my students was Sheldon Mason from Montana. He has his own pop-up BBQ business, and he designed the pits for capacity and travel—as two back-to-back smokers that mirror one another.
Can you explain what you mean by "new school barbecue"?
As the next generation of Texans who are carrying this tradition of barbecue into the next decades, it's our responsibility to put our own stamp on it, improve it and give it to those who come after us. New school BBQ is about taking the method and soul of BBQ and injecting new life into it with updates on classic cuts, global flavor profiles and modern hospitality.
What is your favorite thing to cook at home?
Vegetables, mostly in pasta and stir fries. I like to keep it simple and use herbs from my garden. I also use a lot of eggs.
What is your favorite cooking show on television?
Used to be Good Eats. Now it's Mind of a Chef.
Is there something you've never grilled that you want to attempt?
I've never cooked a fish I caught on the beach or on a shore. I would love to do that.
What travel destination is next on your bucket list?
Germany, Hawaii, Italy.
If you could cook alongside one barbecue chef, who would it be?
I would love to cook with Tootsie Tomanetz from Snow's BBQ in Lexington, TX.
From the Grammys to Glamping Robbie Fulks Kicks Off Campfire Stars
From the Grammys to Glamping, Robbie Fulks will be heading to The Resort at Paws Up for Campfire Stars at Paws Up on June 19–23. Robbie is a singer, recording artist, instrumentalist, composer and songwriter. His most recent release, 2017's Upland Stories, earned year's-best recognition from National Public Radio and Rolling Stone among many others, as well as two Grammy® nominations for folk album and American roots song. We were lucky to sit down with Robbie for a chat.
Your last record, Upland Stories, was nominated for two Grammys in 2017. Did that bring your career more exposure?
It's definitely helped. I've been playing at more places where people are listening respectfully as opposed to throwing bottles at my head. (laughs)
Did you attend the ceremony?
I was there with the whole family. The bigger ceremony is telecast and that was the part I was expecting not to enjoy, but it was amazing. Beyoncé and Bruno Mars and all these people are great singers. It was like a positive presentation of the state of popular music today and the production was done very well.
You performed at Paws Up during Montana Master Grillers 2015. What were your experiences at Paws Up like?
It was super memorable. As far as gigs go, usually you travel someplace and you're in and out, but at Paws Up, somebody picks you up and takes you out into the woods and you're there for three or four days. And the amenities are unbelievable. You can hike. You can rappel. The food is unbelievable and the staff is really kind.
Do you have songs in mind that you will play during Campfire Stars?
No, not at all. The way that it works best for me is to go in and respond to the situation, to keep it in the moment. If you plan too much in advance, the audience can read it and it can seem scripted and gets a little bit robotic sometimes.
What would you tell young people at Campfire Stars who might want to start playing music themselves?
For me, music was a great thing to have early in life because it set up music as a verb, not as something that you just go and witness. It's something participatory as well. It's something that can be meaningful about where you live and what your ancestry is. So I try to reflect that now when I play.


This past weekend was a great weekend. We did not go on a fun summer getaway, nor had some extravagant party night out.
A huge thing that we did – uncluttered our apartment. It took 4 hours on Saturday, and created 3 huge blue Ikea bags of donations taken to the Salvation Army (and another big bag of books waiting its turn).
Some people love redecorating their homes, we love removing unnecessary things and creating more space, and the light feeling that it brings. I think the small sizes of NYC apartments is a great incentive to be creative and save yourself from the plague that is consumerism.
I have a rule of thumb for anything material that I have: clothes, books, other things: if you haven't used it in 6-12 months, just get rid of it. Sean used to be somewhat sentimental towards his old tshirts (what is it with guys and tshirts?) but then he realized that most of clothes in the closet that he never wore anymore were out of style, or too big or wrong fit. And he also changed his thinking, realizing that things that he does not use will benefit someone else who actually needs them.
One thing that we are still working on is greeting cards and other memorabilia: we love the notes, but there's a big box of cards just sitting there. I'm looking for a way to digitize them, so we still have all the notes and memories, but don't have to hold on to the actual cards (maybe create some cool craft project out of them and gift it).
Curious to hear tips on this, and on uncluttering living spaces in general.


The applicant must hold a baccalaureate degree, preferably a B.F.A. degree or its equivalent based upon experience and proof of technical and aesthetic abilities.
Portfolio containing 20 digital images of artwork. Fifteen images must focus on the major studio area of application and five images must demonstrate drawing abilities. Please include a numbered slide identification sheet.
Each digital image must be in jpeg format set for maximum resolution to compliment your work (CDs with PowerPoint presentations are acceptable). All images and presentation modes must be compatible with both Mac and PC formats.
Artist statement supporting the applicant's work.
Statement of purpose in which the applicant expresses interests, intentions, and expectations for wanting to attend graduate school generally, and more specifically, the M.F.A. program at the University of South Dakota.
Three letters of recommendation from professionals associated with the applicant's work and abilities.
One official transcript verifying receipt of an undergraduate degree and previous graduate credit earned.
Application for Assistantship, if desired.
TOEFL Scores in the Test of English as Foreign Language. A minimum score of 550 is required for entrance into The University of South Dakota.
Finalists in the applicant review process will receive a phone interview as part of the review process. Following the review, students will receive a letter stating if they are accepted or denied into the M.F.A. program.
The Master of Fine Arts degree program is a 60 credit hour terminal degree that involves a 3 years of residential intensive study. In addition to meeting all the graduation requirements of the Graduate School, M.F.A. candidates must satisfy all degree program requirements, including the passing of a preliminary oral examination, presentation of a comprehensive thesis exhibition, completion of a final oral examination, and the passing of the written ACAT Art Exit Exam.


This post contains affiliate links. Read our disclosure policy here.
Kids like this may be strident and pushy about how they think things should be done. But they don't always realize how their words are affecting others around them. They don't realize how other people view their behavior.
To help, we can talk about some different ways to think before you speak and the impact your words can have on others. My favorite lesson to use with children is the Chrysanthemum Lesson. It's simple yet visually it makes a big impact.
Tell the children to pay attention to whether the characters in the book were using kind words or when a character was using mean words.
As you read the book, every time a character says something mean to Chrysanthemum, have the students wrinkle up a piece of their paper heart to represent how mean words impact others.
Every time her parents said something kind and loving to her, have them smooth out the paper heart a little bit and try to repair it.
At the end of the book try and spread out the heart as much as possible and repair it either using tape or Band-Aids.
Compare the paper heart that you set aside at the beginning at all to the ones that were wrinkled during the story. Invite children to notice how different they are.
Highlight that even when you say sorry and apologize, it still has a lasting effect. You can smooth out the wrinkled heart as much as you can but it still is always going to look a little bit wrinkled from your mean words and your mean actions.
Ms. Bossy - Ms. Bossy tells people how to draw and create art. That's SO not fun.
My Little Pony - Here's a clip where quiet Fluttershy becomes overbearing and bossy. You've got to find a happy medium between being too passive and being mean and rude to your friends.
Recess isn't so fun if someone is bossing you around. But what happens when one brave souls stands up and says no?
A great book about how your words can fill or empty someone's imaginary bucket. This book can even be integrated into a whole positive behavior system in a classroom or a whole school. Such a great read!


Norman's new book will be out April 30, 2019. You can preorder a copy now.
Please see Readings & Workshops at Norman Fischer Books for his tour schedule.
Talks from the 2019 Winter Practice Period at Tassajara are still being posted. Search for "Tassajara" (below left) to bring them up.
two new poems by Norman Fischer, at Talisman Magazine.
"I can see the necessity for applying a negative dialectic to all religious thought and practice. It's necessary to keep things honest. In order to have some faith, you absolutely have to doubt. You have to wonder whether yesterday's truth still applies today. You have to ask if it does or not. Be willing to tear down today's truth to find something, if anything, behind it. This makes life—and religion—alive."


Last edited by gldtn; 10-20-2005 at 04:59 PM..
you have replaced gab_redirect.php file and you are still getting the same error?
Geek, a few more redirection problems..
I tried to setup a Individual Scripts and Ad Blocks and the Standard Banner and Text type of ad blocks works but the rotating ad blocks seems to have a problem. It rotates the banners and when you click on it, it opens a new window.. but doesn't take you anywhere.


text:
\section{Introduction}
The determination of the pole associated to the  $\sigma$ resonance  (or $f_0(600)$)  is known  to be a   difficult problem. The pole is situated deep in the complex plane, its influence in the physical region is masked to a certain extent by the nearby Adler zero  and, until recently,  the experimental data on  $\pi\pi$ scattering
  at low energies were quite poor.  This explains why the values reported by PDG \cite{PDG2006} for the mass and width of  $\sigma$  cover a very large interval.

During the last years,  Chiral Perturbation Theory (ChPT) and Roy equations led to an accurate description of $\pi\pi$ scatering at low energies  \cite{ACGL, CGL}. In  particular, the scattering length $a_0^0$ and the effective range parameter  $b_0^0$ of the isoscalar $S$-wave given in \cite{CGL}:
\begin{equation}\label{abCGL}
 a_0^0=0.220 \pm 0.005, \quad\quad b_0^0=0.276 \pm 0.006\,,
\end{equation}
have remarquably small uncertainties.

 The formalism based on Roy equations  was shown recently  \cite{CCL} to control also the analytic extrapolation of the $\pi\pi$ amplitude in the complex plane, leading to precise values for the mass and width of $\sigma$:
\begin{equation}\label{CCL}
M_\sigma = 441\,^{+16}_{-8}\, {\rm MeV}, \quad \quad \Gamma_\sigma/2= 272\,^{+9}_{-12.5} \, {\rm MeV}.
\end{equation}
In the standard method  of detecting resonances, the experimental data on the partial wave with the quantum numbers of the resonance  play an important role. Unlike this,
 the prediction (\ref{CCL})  was obtained without using  experimental data on the isoscalar  $S$-wave at low energies: the amplitude  was calculated below 800 MeV, and also in the complex plane, from Roy equations, using experimental input at higher energies and theoretical results on the pion-pion scattering \cite{CGL}. Roy equations provide a very suitable framework in this case, compensating the lack of experimental data on $\pi\pi$ scattering at low energies by theoretical information.

Recently \cite{NA48},  NA48/2 Collaboration  measured the phase shift difference $\delta_0^0-\delta_1^1$ at low energies from  $K_{e4}$
 decay,  with a  precision much greater than that of the older experiments
 \cite{Rosselet, Pislak}. This revived the interest in
the determination of the scattering length $a_0^0$ and the
 pole associated to $\sigma$ by direct analytic extrapolation of the $\pi\pi$ scattering data. In \cite{GMPY}
  the authors propose a
  representation of the isoscalar $S$-wave $t_0^0(s)$ based on an  expansion in powers of a conformal mapping variable. To account for the theoretical
 uncertainties related to analytic continuation,
 two  parametrizations  were
 considered, the difference between them being interpreted as a systematic theoretical  uncertainty of the method. In the framework discussed in \cite{GMPY},  the mass and width of $\sigma$ are obtained with an accuracy comparable to that quoted in (\ref{CCL}).

In the present work we focus on the problem of systematic uncertainties within this approach. We note that the class of functions used in  \cite{GMPY}, although based on a convergent expansion, is still quite narrow when the expansion is restricted to a few terms. By enlarging the class of admissible analytic functions used for fitting the data,  the theoretical bias is reduced and
 a more realistic estimate of the uncertainties in the position of the $\sigma$ pole is obtained. In the present work we apply this idea,  by using  a large sample of analytic parametrizations of the $\pi\pi$ amplitude, suitable at low energies.  A short description of the method and some results were given already in \cite{ICScadron}.

In the next section we discuss several parametrizations of the $\pi\pi$ isoscalar $S$-wave, which satisfy analyticity and elastic unitarity. In the next two sections  we apply these parametrizations for fitting the data on the phase shift $\delta_0^0$: in section 3 we consider only the data from $K_{e4}$ decay, and in section 4 we include data up to the $K\bar{K}$ threshold. From  the  admissible parametrizations of the isoscalar $S$-wave we
 find the threshold parameters $a_0^0$ and $b_0^0$ and the location of the $\sigma$ pole. Our conclusions are summarized in  section 5.

\section {The isoscalar $S$-wave at low energy}
 We consider the $\pi\pi$ isoscalar $S$-wave $t_0^0(s)$, which is an analytic function in the $s$-plane cut along $s\ge 4  M_\pi^2$ and $s \le 0$. We assume that  $t_0^0(s)$ is the pure strong amplitude, where all the isospin breaking corrections  are neglected. As in \cite{ACGL}-\cite{CCL}, we take for  $M_\pi$ and $M_K$ the masses of the charged pion and charged kaon, respectively.

Neglecting the inelasticity due to the 4$\pi$ channel below 1 GeV,  unitarity implies that the relation
\begin{equation} \label{unit}
 \mbox{Im} \left[\frac{1}{t_0^0(s+i\epsilon)}\right] = - i \rho(s),\quad\quad\quad \rho(s)=\sqrt{1-  4 M_\pi^2/s},
\end{equation}
is valid up to  the threshold for $K\bar K$ production, $s= 4 M_K^2$.
From (\ref{unit}) it follows that the function $\psi(s)$, defined by
\begin{equation}\label{t00}
t_0^0(s)= \frac{1}{\psi(s)- i \rho(s)},
\end{equation}
is real in the elastic region:
\begin{equation}\label{imag}
\mbox{Im} \psi(s+i\epsilon) =0,\quad \quad \quad   4 M_\pi^2 \le s < 4 M_K^2,
\end{equation}
and is related to the phase shift $\delta_0^0(s)$ by:
\begin{equation}\label{delta00}
 \psi(s)=\rho(s)\, \mbox{cot}\delta_0^0(s).
\end{equation}
 Since the  amplitudes are analytic functions of real type, Eq. (\ref{imag}) means that
 $\psi(s)$ has no discontinuity across the elastic unitarity cut.
The definition (\ref{t00}) shows also that $\psi(s)$ has poles at the points where $t_0^0(s)$ has zeros. The amplitude is expected to vanish below threshold at a point $s_A$, related to the so-called  Adler zeros.   ChPT to lowest order predicts $s_A=M_\pi^2/2$. Assuming that $t_0^0(s)$  does not have other  zeros in the complex plane, the product $(s- s_A) \psi(s)$ is analytic
in the $s$-plane cut for  $s \le 0$ and  $s\ge 4 M_K^2$. The effective range expansion amounts to
  expanding the function $\psi(s)$
 in powers of $q^2=(s/4- M_\pi^2)$ around the threshold $q^2=0$, where it is regular.  However, the branch point $s=0$ limits the convergence of this expansion  to the circle $|q^2|< M_\pi^2$.
\subsection {Method of conformal mappings}\label{conf}
 The domain of convergence of a power series can be enlarged by expanding the function in powers of a variable which  conformally maps a part of the holomorphy domain onto the interior of a disk. The use of conformal mappings in particle  physics was first discussed in  \cite{Confmap, CutDeo1}; in the context of the effective range  expansion for partial waves a conformal mapping was used in \cite{CutDeo};  more recently, the method was applied  for the description of exclusive semileptonic  $B$ decays \cite{CaLeNe} and in perturbative QCD \cite{CaFi}.  As shown in \cite{Confmap},  the asymptotic rate of convergence of the series in the physical region is optimal if the amplitude is expanded in powers of the variable which  mapps the entire holomorphy domain onto a disk. Since the disk is the natural convergence domain of the power series, the new expansion will converge in the whole analyticity domain, up to its boundary.

Consider the variable
\begin{equation}\label{wa}
 w(s,\alpha )=\frac{\sqrt{s}- \alpha \sqrt{4 M_K^2-s}}{\sqrt{s} + \alpha \sqrt{4 M_K^2-s}},
\end{equation}
where  $\alpha >0$ is arbitrary. The function  $w(s, \alpha)$ transforms the $s$-plane cut along $s\le 0$ and $s\ge 4 M_K^2$ onto the unit disk
$|w|<1$ in the complex plane $w= w(s,\alpha )$,  such that $w(4 M_K^2,\alpha )=1$ and $w(0, \alpha)=-1$. In  \cite{GMPY}  the authors adopt the expansion
\begin{equation}\label{psiYgen}
\psi(s)= \frac{M_\pi^2}{s-s_A} \left[ \frac{2 s_A} {M_\pi\sqrt{s}}+ B_0+B_1 w(s, \alpha) +B_2 w(s, \alpha)^2+\ldots\right]
\end{equation}
with  the particular choice  $\alpha=1$. In Eq. (\ref{psiYgen}), the first term in parantheses, added to the expansion in powers of  $w(s,\alpha)$, compensates the singularity of $\rho(s)$ at $s=0$ in the denominator of (\ref{t00}),  removing an unphysical singularity  of $t_0^0(s)$ on the real axis  which would appear otherwise.

 A slightly  different form was also used in  \cite{GMPY}:
\begin{equation}\label{psiY}
\psi(s)= \frac{M_\pi^2}{s-s_A}\frac{\mu_0^2-s}{\mu_0^2} \left[ \frac{2  s_A}{M_\pi\sqrt{s}}+ B_0+B_1 w(s,1 )+B_2 w(s, 1)^2+\ldots \right],
\end{equation}
where the factor $(\mu_0^2-s)$ displays explicitly the energy  where the  phase shift $\delta_0^0$  passes through $\pi/2$, according to (\ref{delta00}).  This factor is useful for fitting narrow resonances  but, as we shall show, it is not suitable for broad resonances like $\sigma$.

 The power expansions in (\ref{psiYgen}) and (\ref{psiY}) converge in the disk $|w|<1$  and, for a large number of terms,  these parametrizations are equivalent. However, when the series are truncated at a finite number of terms, (\ref{psiYgen}) and (\ref{psiY}) lead to different results. This difference is interpreted
  in  \cite{GMPY} as a systematic uncertainty of theoretical nature,  which should be added to the statistical errors. In the present work we develop this idea, presenting  other admissible analytic parametrizations of the amplitude.

A first generalization  is to expand $\psi(s)$ in powers of $w= w(s,\alpha )$, for an arbitrary $\alpha$, as in (\ref{psiYgen}).
 By varying $\alpha$, one changes the point mapped to the origin of the $w$-plane and the position of the intervals where experimental data are available. Some examples  are shown in Fig. 1.  As we shall see, the flexibility offered by the parameter $\alpha$  allows us to describe the peculiar structure of the isoscalar $S$-wave near the inelastic $K\bar K$ threshold.

\begin{figure}[thb]\label{wgen}\begin{center}\vspace{0.3cm}
\includegraphics[width=4.5cm]{circwa036.eps}\hspace{0.5cm}\includegraphics[width=4.5cm]{circwa1.eps}\hspace{0.5cm}\includegraphics[width=4.5cm]{circwa4.eps}
\end{center}
\caption{The disk $|w|<1$ in the complex plane  $w=w(s,\alpha)$ defined in (\ref{wa}), for $\alpha=0.36$ (left), $\alpha=1$ (center)  and $\alpha=4$ (right). The thick segments indicate the regions where experimental data are available from $K_{e4}$ decay \cite{NA48}-\cite{Pislak} and  the process $\pi N\to\pi\pi N$ (cf. the compilation of data made in \cite{PY 2005}), respectively; the circle shows  the $\sigma$ pole  on the second Riemann sheet from \cite{CCL}.}\end{figure}

\subsection{Alternative procedure for ghost removal}\label{CM}
The singularity at $s=0$ of the phase space factor $\rho(s)$  in (\ref{t00}) can be alternatively eliminated  if
the term $i \rho(s)$ is replaced by a function which is analytic in the $s$-plane cut along $s\ge 4 M_\pi^2$ and has the imaginary part equal to $\rho(s)$ on the upper edge of the cut. In the context of effective range approximation, Chew and Mandelstam \cite{ChMa} defined such a function, vanishing at threshold,  by a once subtracted dispersion relation. For convenience, we  consider the loop function  of ChPT, $\bar{J}(s, M_\pi^2)$, written as
 \begin{equation}\label{J}
\bar{J}(s, M_\pi^2) =\frac{2}{\pi}+\frac{\rho(s)}{\pi} \ln\left[\frac{\rho(s)-1}{1 + \rho(s)}\right],
\end{equation}
 which vanishes at the origin, $J(0, M_\pi^2)=0$, and satisfies the relation
\begin{equation}\label{ImJ}
\mbox{Im}\, \bar{J}(s+i\epsilon, M_\pi^2)= \rho(s), \quad\quad s\ge 4 M_\pi^2.
\end{equation}
If we define the function  $\psi_1(s)$ by:
\begin{equation}\label{t001}
t_0^0(s)= \frac{1}{\psi_1(s) - \bar{J}(s, M_\pi^2)},
\end{equation}
the unitarity relation (\ref{unit}) and  Eq. (\ref{ImJ}) show that  $\psi_1(s)$ is real for  $4 M_\pi^2\le s < 4 M_K^2$, where it is  related to the phase shift $\delta_0^0$ by
\begin{equation}\label{delta001}
 \psi_1(s)= \rho(s)\, \mbox{cot}\delta_0^0(s)+ \mbox{Re}\,\bar{J}(s, M_\pi^2)\,.
\end{equation}
 The reality property implies also that  $\psi_1(s)$ is analytic in the $s$-plane cut for $s\le 0$ and $s \ge 4 M_K^2$,  except for the pole  at $s=s_A$, and can be expanded as
\begin{equation}\label{psi1}
\psi_1(s)= \frac{M_\pi^2}{s-s_A}\left[B_0+B_1\, w(s,\alpha )+B_2 \,w(s,\alpha )^2+\ldots \right],
\end{equation}
in powers of the  variable (\ref{wa}). We remark that the compensating term $2 s_A/M_\pi^2\sqrt{s}$ appearing in  (\ref{psiYgen}) is no longer
 necessary in (\ref{psi1}), since the  function $\bar{J}(s, M_\pi^2)$ is by definition regular at $s=0$.

 \subsection{$S$-matrix factorization}\label{DT}

 Other parametrizations of $t_0^0(s)$ are obtained by including some information about  its behaviour  near the $K\bar{K}$ threshold.  We do this by expressing the $S$-matrix element
\begin{equation} \label{S00}
S_0^0(s) =  1+ 2 i \rho(s) t_0^0(s)
\end{equation}
 as a
  product
\begin{equation}\label{DalitzTuan}
S_0^0(s)= S_{\rm rest}(s) S_{f_0}(s),
\end{equation}
where each factor satisfies elastic  unitarity ($|S_{\rm rest}(s)|=| S_{f_0}(s)|=1$) below the $K\bar K$ threshold.
 The multiplication of the two $S$-matrices amounts to the following addition rule for the corresponding amplitudes:
\begin{equation}\label{t}
t_0^0(s)= t_{\rm rest}(s)+  t_{f_0}(s) +  2 i\rho(s)\ t_{\rm rest}(s)\ t_{f_0}(s),
\end{equation}
where
\begin{equation}\label{tS}
t_{\rm rest}(s)= \frac{S_{\rm rest}(s)-1}{2 i\rho(s)}, \quad\quad
t_{f_0}(s)=\frac{S_{f_0}(s)-1}{2 i\rho(s)}.
\end{equation}
 Crossing symmetry  implemented by Roy equations \cite{CGL} implies that the expansion of the partial
  wave amplitude around $s=0$ starts with
\begin{equation} \label{ts0}
t_0^0(s)= t_0 + t_1 s + t_2 s^{3/2}+ O(s^2)\,,
\end{equation}
where $t_0$ is nonzero.
In order to cancel the singularity of the factor $\rho(s)$ at $s=0$ in  (\ref{t}), either
 $t_{\rm rest}(s)$ or  $t_{f_0}(s)$ must vanish at $s=0$, but not both (since, cf. (\ref{ts0}),
 the full amplitude does not have a zero there). We choose to set $t_{f_0}(0)=0$, taking   for this amplitude the expression\begin{equation}\label{tf0}
 t_{f_0}(s)= \frac{k_1 s } {\kappa -s- k_1 s \,\bar{J}(s, M_\pi^2) -(k_2+k_3 s) \bar{J}(s, M_K^2)},\end{equation}
where $\bar{J}(s, M_\pi^2)$ is defined in (\ref{J}) and $\bar{J}(s, M_K^2)$ is obtained  replacing   $M_\pi$ in $\rho(s)$ by $M_K$. We note that by taking
\begin{equation}\label{kappaCohen}
 \kappa = 1.01, \quad  k_1 = 0.08, \quad k_2 = -1.09, \quad k_3 = 1.16,
\end{equation}
the modulus of the corresponding $S$-matrix, $S_{f_0}(s)$, is close, in the range $2 M_K < \sqrt{s} < 1.16$ GeV,  to the elasticity $\eta_0^0(s)$ measured in \cite{Cohen}, while for
 \begin{equation}\label{BES1u}
\kappa =  1.15, \quad  k_1 = 0.11, \quad k_2 =  0.39, \quad k_3 = 0.03,\end{equation}
\begin{equation}\label{BES1l}
\kappa =  1.41, \quad  k_1 = 0.24, \quad k_2 = -0.73, \quad k_3 = 1.72, \end{equation}
  $|S_{f_0}(s)|$ is close,  in the same range, to the upper/lower edges of the  band of the elasticity $\eta_0^0$  extracted from  the decay $J/\psi\rightarrow\phi\pi\pi$ \cite{BESf0}.

For our purpose, the specific form adopted for  $t_{f_0}(s)$  is not a limitation, since the total amplitude contains the additional term $t_{\rm rest}(s)$.    Elastic unitarity, $|S_{\rm rest}(s)|=1$, implies that $t_{\rm rest}(s)$ can be written, for instance, as
\begin{equation}\label{trest}
  t_{\rm rest}(s)=\frac{1}{\psi_{\rm rest}(s) -i \rho(s)}\,,
  \end{equation}
with $\psi_{\rm rest}$  analytic in the $s$-plane cut along $s\le 0$ and $s \ge 4M_K^2$, except for a pole  at  $s=s_1$, where $t_{\rm rest}(s_1)=0$ (from (\ref{t}) and (\ref{tf0}) it follows that $s_1$ is close to the Adler zero $s_A$).  Therefore, we can write $\psi_{\rm rest}(s)$ as:
\begin{equation}\label{psirest}
\psi_{\rm rest}(s)= \frac{M_\pi^2}{s-s_1} \left[ \frac{2 s_1}{M_\pi \sqrt{s}}+ B_0+B_1 w(s,\alpha ) +B_2 w(s,\alpha )^2+\ldots \right],
\end{equation}
where  $w(s,\alpha )$ is defined in (\ref{wa}). Alternatively, we can use for  $t_{\rm rest}(s)$ an expression similar to (\ref{t001}), involving the function $\bar{J}(s,M_\pi^2)$.

 Other admissible parametrizations are obtained if we assume that   $t_{\rm rest}(s)$ is almost regular near $s=4M_K^2$. Since the next branch point, at $s=4 M_\eta^2$,   is known to have a weak effect,  we can neglect at low energies the right hand cut of  $\psi_{\rm rest}(s)$,  and expand it as
\begin{equation}\label{psirest1}
\psi_{\rm rest}(s)= \frac{M_\pi^2}{s-s_1} \left[ \frac{2 s_1}{M_\pi \sqrt{s}}+ B_0+B_1 w_1(s,\alpha ) +B_2 w_1(s,\alpha )^2+\ldots \right],
\end{equation}
where the variable
\begin{equation}\label{w1a}
 w_1(s,\alpha )=\frac{ \sqrt{s} - \alpha }{\sqrt{s}+ \alpha},\quad\quad \alpha>0,
\end{equation}
maps the $s$-plane cut only for $s\le 0$ onto the disk $|w_1|<1$ of the complex plane $w_1=w_1(s,\alpha)$.

 The expressions given in this subsection are examples of possible analytic parametrizations of the amplitude at low energies. Following an idea of Dalitz and Tuan \cite{DaTu}, in some phenomenological analyses \cite{BuggZou} the individual $S$-matrices in the product (\ref{DalitzTuan}) are associated to specific resonances. However, in our work we use the factorization  (\ref{DalitzTuan})  only for mathematical purposes: by isolating a factor with a rapid variation near the  $K\bar K$ threshold, we expect a better convergence for the expansion of the remaining part,  $t_{\rm rest}(s)$. This part, which is fixed by the low energy data, contributes to both the elasticity $\eta_0^0(s)= |S_0^0(s)|$ and the phase shift $\delta_0^0$ above the $K\bar K$ threshold. So, the behaviour of $t_0^0$  above this point is  left free in our fits.
\section{Fits of the data from $K_{e4}$ decay}

We consider first the data on the difference  $\delta_0^0-\delta_1^1$ measured below 0.4 GeV from $K_{e4}$ decay \cite{NA48}-\cite{Pislak}. The $P$-wave phase shift $\delta_1^1$
is known with precision in this energy range \cite{CGL, PY 2005}, allowing an accurate extraction of  $\delta_0^0$.
 As shown recently \cite{Gasser}, the phase shift measured in $K_{e4}$ decay differs from the pure strong phase shift $\delta_0^0(s)$ by an isospin  correction overlooked so far, accounting for the differences between the masses of the charged and neutral mesons, and between the quark masses  $m_u$ and $m_d$.  The correction evaluated in  ChPT to one-loop reads \cite{Gasser}:
\begin{equation}\label{isocorr}
\Delta[\delta_0^0(s)]= \frac{1}{32 \pi F_0^2} \{(4 \Delta_\pi +s)\rho (s)+(s-M_{\pi^0}^2) \left(1+\frac{3}{2 R}\right) \rho_0(s) -(2 s-M_\pi^2) \rho(s)\},
\end{equation}
where $\rho (s)$ is defined in (\ref{unit}) and
\begin{equation}
 \Delta_\pi =M_\pi^2 -M_{\pi^0}^2, \quad \rho_0(s)=\sqrt{1-4 M_{\pi^0}^2/s}, \quad R=\frac{m_s-\hat{m}}{m_d-m_u}\,,\quad\hat{m}=(m_u+m_d)/2\,.
\end{equation}
With the estimate R=37 $\pm$ 4 given in  \cite{Gasser}, the correction $\Delta[\delta_0^0(s)]$ amounts to a fraction of a degree in the whole experimental range.  This correction  was subtracted  from the  phase shift derived from $K_{e4}$ data, in order to obtain the pure strong phase shift $\delta_0^0(s)$.

  The total number of points from the $K_{e4}$ experiments is 21 (5 points from  \cite{Rosselet}, 6 from  \cite{Pislak} and 10 from  \cite{NA48}). As in \cite{GMPY}, we increased the experimental error on the last point in \cite{Pislak}   by 50\%.  For the 10 data from the NA48/2 experiment we used the covariance matrix  published recently in \cite{NA48}.
We fitted these data with the parametrizations described in section 2.

\begin{figure}\label{FitsKe4}\begin{center}
  \includegraphics[width=7.5cm]{delta00Ke4Fits.eps}\hspace{0.4cm} \includegraphics[width=7.5cm]{delta00Ke4FitsExtrap.eps}
  \caption{Left: phase shift  $\delta_0^0$ derived from $K_{e4}$ decay, fitted with the 16 parametrizations described in the text. Right: extrapolation of the fits above the experimental range.}\end{center}
\end{figure}

 In our analysis, the positive number $\alpha$, specifying  the conformal variables (\ref{wa}) and (\ref{w1a}), together with the parameters $\kappa$ and $k_i$ appearing in (\ref{tf0}), represent the input which defines an admissible class.  To account for the uncertainty in the position of the Adler zero, $s_A$ was varied between $0.4 M_\pi^2$ and $0.6 M_\pi^2$.
In each admissible class, the coefficients  $B_i$ of the expansion in  powers of the conformal variable are free. They are determined by fitting the low energy data.

We investigated a large class of combination of input parameters, from which we retained
 16 admissible parametrizations: the first three  are based on Eqs. (\ref{t00}) and (\ref{psiYgen}), with $\alpha=1$, $\alpha=0.36$ and  $\alpha=4$, respectively. The value  $\alpha=0.36$ is special, since, as seen in Fig. 1, it maps the  experimental range relevant in $K_{e4}$ decay onto a symmetric interval around the origin $w=0$. According to general theorems \cite{CutDeo}, this variable
 gives the best approximation of data in the experimental range. On the other hand, for $\alpha$ greater than 1 (for instance, $\alpha=4$) the variable $w(s,\alpha)$  maps the region close to the branch point $s=4 M_K^2$ near the origin of the $w$-plane (see right panel of Fig. 1). As we shall see,  the expansion  (\ref{psiYgen}) is then  more suitable at higher energies.

The next three parametrizations are  based on Eqs. (\ref{t001}) and (\ref{psi1}), with the same choices $\alpha=1$, $\alpha=0.36$ and  $\alpha=4$. The difference from the previous fits is the way of eliminating the singularity at $s=0$ of the phase space $\rho(s)$  in the denominator of $t_0^0(s)$.

  The remaining ten
 parametrizations are based on the $S$-matrix factorization discusssed in subsection \ref{DT}.  In three of them  we take the parameters $\kappa$ and $k_i$ from (\ref{BES1u})  and  the expansion (\ref{psirest1}), with  $\alpha=0.36$, $\alpha=1$ and  $\alpha=4$, and in the next two we  use  the same parameters $\kappa$ and $k_i$  and  the expansion (\ref{psirest}), with  $\alpha=0.36$ and $\alpha=1$. In other two cases we use the parameters $\kappa$ and $k_i$ from (\ref{BES1l}) and  the expansion (\ref{psirest1}) with  $\alpha=0.36$ and $\alpha=1$,
  while in the last three  parametrizations we take the parameters $\kappa$ and $k_i$ from  (\ref{kappaCohen}), using either  the expansion (\ref{psirest})  with  $\alpha=1$ and $\alpha=0.36$, or the expansion (\ref{psirest1}) with $\alpha=0.36$.

 We obtained good fits of the 21 experimental points with 2 free parameters, $B_0$ and $B_1$, in the expansion in powers of the conformal variables. The values of $\chi^2$ are very similar for all the fits, although the parametrizations  are quite different. The values of $\chi^2$ and the optimal parameters  are given in Table 1, for $s_A$ (or $s_1$) fixed at $0.5 M_\pi^2$ (note that if $s_1=0.5 M_\pi^2$,  the position $s_A$ of the Adler zero, resulting from the fits, is slightly different: for the last 10 fits given in Table 1, $s_A$ varied between  $0.42 M_\pi^2$ and $0.47 M_\pi^2$). The values of  $\chi^2$ decrease by about 0.4 if we take into account the theoretical uncertainty associated to the isospin correction \cite{Gasser}. For simplicity we indicate only the central values of the parameters, omitting the statistical errors.

\begin{table}\label{TableKe4}\begin{center}\vskip0.3cm
\begin{tabular}{rcccccl}
Nr. &  $\chi^2$ & $B_0$ & $B_1$ & $a_0^0$ & $b_0^0$ & $\sqrt{s_\sigma}\, (\mbox{MeV}) $\\\hline
1.&  21.7&    7.5&  -15.1&   0.216& 0.278&  459 + 259 i \\
2.&  21.5&   14.6&  -12.4&   0.214& 0.282&  445 + 259 i \\
3.&  21.9&  -16.4&  -37.1&   0.217& 0.275&  473 + 261 i \\
4.&  20.9&    7.7&  -20.2&   0.212& 0.287&  412 + 237 i \\
5.&  20.6&   17.2&  -16.5&   0.210& 0.292&  401 + 231 i \\
6.&  21.2&  -35.0&  -60.3&   0.214& 0.284&  422 + 246 i \\
7.&  21.5&   14.6&    -14.8& 0.214& 0.281&  443 + 262 i \\
8.&  21.7&   5.8&   -18.8&   0.215& 0.278&  455 + 261 i \\
9.&  21.8&  -25.3&  -47.9&   0.216& 0.276&  465 + 260 i \\
10.& 21.6&   15.2&  -12.8&   0.215& 0.280&   451 + 264 i \\
11.& 21.8&   7.8&  -15.5&    0.216& 0.277&  466 + 264 i \\
12.& 21.5&   15.0&  -15.3&   0.214& 0.281&  448+ 264 i \\
13.& 21.7&   5.9&  -19.5&    0.216& 0.277&  459 + 262 i \\
14.& 21.8&   7.8&  -15.5&    0.216& 0.277&  465 + 263 i \\
15.& 21.6&   15.1&  -12.8&   0.215& 0.280&  450 + 263 i \\
16.& 21.4&   14.5&  -14.8&   0.214& 0.282&  443 + 261 i \\\hline
\end{tabular}\caption{Results of the fits of the data from $K_{e4}$ decay \cite{NA48}-\cite{Pislak}, using the 16 parametrizations  described in the text.}\end{center}\end{table}

The quality of the fits is seen in Fig. 2. Although the fits are almost indistinguishable in the experimental range, they exhibit large differences when extrapolated to higher energies. This illustrates the well-known phenomenon of instability of analytic extrapolation \cite{Ciulli}. We note that the lowest curves in the right panel of Fig. 2  correspond to the fits 4, 5 and 6 in Table 1, obtained with  the parametrization (\ref{t001})-(\ref{psi1}). In particular, the fits no. 4 and 5, corresponding to the choices $\alpha=1$  and $\alpha=0.36$ in (\ref{psi1}), exhibit a plateau at low values of $\delta_0^0(s)$.  The  increase of the phase shift required by the high energy data (see below) is  obtained, for instance, with the choice $\alpha=4$ in the expansion (\ref{psiYgen}), or by using parametrizations based on the $S$-matrix factorization described in subsection 2.3.

In Table 1 we give for each fit the central values of $a_0^0$ and $b_0^0$ and the position $s_\sigma$ of the $\sigma$ pole on the second Riemann sheet, obtained by analytic extrapolation to the threshold and into the complex plane (as shown in \cite{CCL},  $s_\sigma$ is the solution of the equation $S(s_\sigma)=0$ on the first sheet).

Taking the average of the 16 admissible values for $m_\sigma=\sqrt{s_\sigma}= M_\sigma -i\Gamma_\sigma/2$,  we obtain:
\begin{equation}\label{sigmaKe4}
M_\sigma=447 \pm 7\, \mbox{(stat)} \,\,^{+25}_{-46} \,\mbox{(syst)} \,\, \mbox{MeV},\quad \Gamma_\sigma/2= 258 \pm 6\, \mbox{(stat)}\, \,^{+10}_{-26}\, \mbox{(syst)}\,\, \mbox{MeV},
\end{equation}
where the systematic error is defined, as in \cite{GMPY}, such as to cover all the admissible fits (the uncertainty in the Adler zero produces a small error, of about 4 MeV in  $M_\sigma$ and 3 MeV in $\Gamma_\sigma/2$).

The pole positions given in Table 1 are
shown in Fig. \ref{sigmamass}, together with the results reported in  \cite{CCL}, \cite{GMPY} and \cite{KPY 2007}.  Note that the three isolated points, with small values of $M_\sigma$ and  $\Gamma_\sigma$, correspond to the fits 4, 5 and 6 in Table 1, which are based on the parametrization (\ref{t001})-(\ref{psi1}). As we mentioned, they lead to a bad behaviour of the phase shift at higher energies, in spite of the fact that they provide very good fits of the data from $K_{e4}$ decay.  From Table 1 it is seen that these parametrizations (especially 4 and 5) give low values   for    $a_0^0$ and large values  for $b_0^0$.

In this Section we obtained  good fits of the phase shift measured from $K_{e4}$ decay. However,  the extrapolation of the phase shift above the experimental region is not acceptable for many of them. Therefore, we  can not take
 the results of this Section as final. In particular,  the narrow range  spanned by most of the widths $\Gamma_\sigma$  in Fig.  \ref{sigmamass} may signal a  bias. In the next Section we shall improve the description of $t_0^0(s)$  by including data on the phase shift at higher energies.

\begin{figure}\label{sigmamass}\begin{center}
  \includegraphics[width=12cm]{sigmamass_Fits.eps}
  \caption{Positions of the $\sigma$ pole obtained by the analytic extrapolation of the parametrizations used for fitting various sets of data, compared with   Refs. \cite{CCL}, \cite{GMPY} and \cite{KPY 2007} (from the last reference we show the value  obtained with  isospin corrected $K_{e4}$ data).}
\end{center}\end{figure}

\section{Inclusion of high energy data}

\begin{table}\label{TableHyams}\begin{center}\vskip0.3cm
\begin{tabular}{rcccccccr}
Nr. &  $\chi^2$ &   $\chi^2_{Ke4}$ &  $B_0$ & $B_1$ & $B_2$ & $a_0^0$ & $b_0^0$ & $\sqrt{s_\sigma}\, (\mbox{MeV}) $\\\hline
1.&  37.7& 24.3  &  7.8&  -23.5& -20.6 &  0.233&  0.261     & 486 + 312 i \\
2.&  32.9& 22.8  &   -20.3&  -61.5&  -23.9 & 0.226& 0.271   & 462 + 298  i \\
3.&  32.6& 22.6  &  -37.3&  -84.6&  -29.6 &  0.225&  0.272   & 461 + 296 i \\
4.&  32.7&  22.2 &    1.3&  -52.3&  -39.9 & 0.222  &  0.271  & 458 + 265 i \\
5.&  33.9& 21.8 &   -52.8&  -105.8& -26.0  &  0.207  & 0.283   & 442 + 234 i \\
6.&  32.4& 22.1 &    9.3&  -12.0& -  &  0.220   & 0.274   & 457 + 281 i \\
7.&  33.7&22.9  &  -2.2&    -20.3& - & 0.228  & 0.272   & 454 + 303 i \\
8.&  33.9&  21.8  &  13.1  & -12.2  & -  &   0.215    & 0.278  & 454 + 267 i \\
9.&  38.0& 21.8  &5.2 &  -19.9 & -  &   0.213   &  0.278  & 456 + 256 i \\
10.&  32.1&21.5  & 18.8  &-12.9  & - &  0.216   &  0.281  & 441 + 272 i \\
11.& 31.9& 21.6  & 12.4  & -13.9  & -  &  0.216    &  0.279  &  446 + 267 i \\
12.& 32.1& 21.9  &  7.4&  -15.5&-  &   0.219  &  0.276  &  450 + 274 i \\
13.& 32.7& 22.6  &  -9.5&  -29.3& -  &  0.225   &  0.272  &  455 + 295 i \\\hline
\end{tabular}\caption{Results of the fits of the 40 data points of set I, using the 13 parametrizations described in the text.}\end{center}\end{table}

The difference $\delta_0^0(s)-\delta_0^2(s)$   is measured at  $s=M_K^2$ from the decay $K\to\pi\pi$ \cite{Aloisio}. However, in  this case the radiative corrections are very large  \cite{Cirigliano} and the extraction of the strong phase shift  $\delta_0^0$ is still uncertain \cite{Colangelo}. For this reason, we shall not use as input in our analysis this datum.

 Experimental data  at higher energies are available from  the  $\pi N\to\pi\pi N$ process \cite{Hyams, Proto}.
 We considered  two sets of data below the $K\bar K$ threshold:
\begin{itemize}
\item set I, which consists from 40 data points: 21  from  $K_{e4}$ decay \cite{NA48}-\cite{Rosselet} and  19  from the CERN-Munich experiment \cite{Hyams};
\item  set II, which consists from 32 data points: 21 from  $K_{e4}$ decay \cite{NA48}-\cite{Rosselet}  and a collection of 11 data points from $\pi N\to\pi\pi N$ \cite{Proto}, given in Eq. (2.13) of \cite{PY 2005}.
\end{itemize}

 As in the previous section, we investigated a large number of parametrizations, but rejected many of them since they gave bad fits. For instance, the choice $\alpha=0.36$ (or other values  $\alpha<1$) in the expansions (\ref{psiYgen}) and (\ref{psi1}) was not admissible, leading to high values of $\chi^2$ (such parametrizations can not exhibit the rapid increase of the phase shift above 900 MeV). Also, the parametrization (\ref{psiY}), considered in \cite{GMPY}, proved to be not acceptable: with 3 free parameters, $\mu_0$, $B_0$ and  $B_1$, we obtained  $\chi^2=45.6$ for the 40 points of set I, and  $\chi^2=34.6$ for the 32 points of set II. We recall that  expressions  which display the energy where the phase shift passes through $\pi/2$ are often used
 for fitting narrow resonances.  However, they are not suitable for broad resonances like $\sigma$.

We finally  retained 13 admissible parametrizations:  the first three  are based on Eqs. (\ref{t00}) and (\ref{psiYgen}), with $\alpha=1$, $\alpha=4$ and  $\alpha=6$, respectively.
The next two  are  based on Eqs. (\ref{t001}) and (\ref{psi1}), with the  choices $\alpha=1$ and  $\alpha=4$.
  The remaining eight
 parametrizations are based on the $S$-matrix factorization discusssed in subsection \ref{DT}: in four cases we use  the values $\kappa$ and $k_i$ from (\ref{kappaCohen}), and either the expansion (\ref{psirest}) with  $\alpha=1$, $\alpha=4$ and $\alpha=0.5$, respectively, or the expansion (\ref{psirest1})  with  $\alpha=1$. In the next three cases we use  the parameters $\kappa$ and $k_i$ from (\ref{BES1u}), and either the expansion  (\ref{psirest}) with  $\alpha=0.2$, or  the expansion  (\ref{psirest1}), with  $\alpha=0.5$ and $\alpha=1$. Finally, in  the last parametrization  we take the values of $\kappa$ and $k_i$ from (\ref{BES1l}) and the expansion (\ref{psirest1})  with $\alpha=4$.

  For the first five parametrizations we used 3 nonzero coefficients,  $B_0$, $B_1$ and $B_2$, in the expansion in powers of the conformal variables,  and for the last eight we obtained good fits with 2 nonzero coefficients,  $B_0$ and  $B_1$. As in the previous Section,  we took into account the uncertainty in the position of the Adler zero, by allowing in each case $s_A$ to vary between 0.4 $M_\pi^2$ and 0.6 $M_\pi^2$.

 The results of the fits (for $s_A$ or $s_1$ fixed at $0.5 M_\pi^2$) are presented in Tables 2 and 3, for the sets I and II, respectively.  For completeness, we show also in column 3  the contribution to the $\chi^2$ of the 21 points from $K_{e4}$ decay.  By comparing Tables 2 and 3 with Table 1 we notice that the description of the $K_{e4}$ data,  measured by their contribution to the total $\chi^2$, is now slightly worse than in the fits restricted to the data from $K_{e4}$ decay:  constraining the behaviour at high energies leads to a small deterioration of the description of the low energy data. The quality of the fits is shown in Fig. \ref{delta00HyamsPY}, and in  Fig. 5 we show an expanded view of the energy region covered by $K_{e4}$ decay. As expected from the previous discussion,  the various parametrizations are no longer indistinguishable, as were those obtained from fitting only the $K_{e4}$ data in Fig. 2.

\begin{table}\label{TablePY}\begin{center}\vskip0.3cm
\begin{tabular}{rcccccccr}
Nr. &  $\chi^2$ &   $\chi^2_{Ke4}$ &  $B_0$ & $B_1$ & $B_2$ & $a_0^0$ & $b_0^0$ & $\sqrt{s_\sigma}\, (\mbox{MeV}) $\\\hline
1.&  28.6& 22.8  & 5.4&  -29.0& -20.9 &  0.225&  0.267     & 494 + 279 i \\
2.&  24.8& 22.4  &   -26.6&  -71.8&  -27.1 & 0.223& 0.272   & 470 + 287  i \\
3.&  24.4& 22.3  &  -45.9&  -97.4&  -33.0 &  0.223&  0.273   & 469 + 285 i \\
4.&  25.1 & 22.0 &  -0.3&  -56.6&  -41.3 & 0.218  &  0.273  & 466 + 251 i \\
5.&  24.6& 22.2 &   -56.6&  -111.1& -26.9  &  0.205  & 0.284   & 446 + 229 i \\
6.&  23.9& 21.8 &    7.4&  -16.3& -  &  0.215   & 0.277  & 466 + 259 i \\
7.&  24.3&22.5  &  -6.2&    -25.3& - & 0.224  & 0.272   & 462 + 293 i \\
8.&  24.7&  22.1  &  12.5&   -16.9& -  &   0.208    & 0.281  & 463 + 242 i \\
9.&  26.6& 22.9  &  1.0&   -28.8& -  &   0.204   &  0.282  & 465 + 225 i \\
10.& 23.2&21.6  &  20.1&  -16.8& - &  0.210  &  0.284  & 448 + 254 i \\
11.& 23.2& 21.8  &  11.6&  -18.7& -  &  0.209    &  0.283  &  453 + 246 i \\
12.& 23.1& 21.8  &  4.8&  -20.8&-  &   0.213  &  0.279  &  458 + 253 i \\
13.& 23.5& 22.0  &  -21.1&  -43.3& -  &  0.219   &  0.274  &  466 + 272 i \\\hline
\end{tabular}\caption{Results of the fits of the 32 data points of set II, using the 13 parametrizations described in the text.}\end{center}\end{table}

Taking the average of the values of the threshold parameters $a_0^0$ and $b_0^0$  given in Tables 2 and 3,  weighted with the ratio $\chi^2/{\rm N_{dof}}$,  we obtain, for the two sets:
\begin{eqnarray}\label{abHyams}
&&a_0^0=0.220 \pm 0.005\, \mbox{(stat)} \pm 0.013 \,\mbox{(syst)} \pm 0.003 (s_A) \quad \mbox{(I)} \nonumber \\
&&a_0^0=0.215 \pm 0.005\, \mbox{(stat)} \pm 0.011 \,\mbox{(syst)} \pm 0.003 (s_A)\quad \mbox{(II)}
\end{eqnarray}
and
\begin{eqnarray}\label{abPY}
&&b_0^0= 0.275 \pm 0.006 \mbox{(stat)}^{+0.009}_{-0.014}\mbox{(syst)}\pm 0.004 \,(s_A)\quad \mbox{(I)} \nonumber \\
&&b_0^0= 0.277 \pm 0.006 \mbox{(stat)}^{+0.007}_{-0.010}\mbox{(syst)}\pm 0.004 \,(s_A) \quad \mbox{(II)}.
\end{eqnarray}
If we combine these determinations we obtain the values
\begin{equation}\label{abfinal}
a_0^0=0.218 \pm 0.014, \quad\quad \quad b_0^0=0.276 \pm  0.013,\end{equation}
which are fully consistent  with the results  obtained from ChPT and low energy theorems for $\pi\pi$ scattering \cite{CGL}, quoted in (\ref{abCGL}).

\begin{figure}\label{delta00HyamsPY}
  \includegraphics[width=7.5cm]{delta00Hyams.eps}\hspace{0.5cm}
\includegraphics[width=7.5cm]{delta00PY.eps} \caption{Left: fits of the data in set I ($K_{e4}$ data \cite{NA48}-\cite{Pislak}  plus the CERN-Munich data \cite{Hyams} below the $K\bar K$ threshold). Right:  fits of the data in set II ($K_{e4}$ data  plus a selection of data from $\pi N\to\pi\pi N$, given in  \cite{PY 2005}).}
\end{figure}

Before discussing the results for the $\sigma$ pole, let us make a few comments on the phase shift $\delta_0^0(s)$ shown in Fig. 4. It was advocated in some papers, for instance \cite{KPY 2007}, that the phase shift of the isoscalar $S$-wave exhibits a "hump" at energies around 800 MeV,  before starting the rapid increase near the $K\bar K$ threshold.   As seen from  Fig. 4, no hump is seen in the fits of the data in the set I, while  a weak hump appears only in a few fits of the data in set II. This proves that the hump seems to be an artefact of special parametrizations used for fitting the data (in particular, the expression (\ref{psiY}) displays a pronounced hump if a small number of coefficients $B_i$ is kept in the expansion). As discussed in \cite{HLAzore}, this shape is in conflict with the forward dispersion relation for the $\pi\pi$ amplitude of isospin $I=0$.

It is of interest to calculate with our parametrizations the value of  $\delta_0^0$  at  $\sqrt{s}=M_K$.  We recall that  the phase shift difference  $\delta_0^0(s)-\delta_0^2(s)$ at this energy can be extracted  from the decay $K\to\pi\pi$. However, as we mentioned in section 4, in this case the isospin breaking corrections are large and the extraction of the strong phase shift  $\delta_0^0$ is still unclear. For this reason  we did not use this information as input in our fits. Using the parameters given in Tables 2 and 3 and taking the averages of the admissible values in the two sets we obtain:
\begin{eqnarray}\label{deltamk}
&&\delta_0^0(M_K^2)= 38.9^\circ \pm 0.6^\circ\, \mbox{(stat)} ^{+ 1.7^\circ}_{-1.4^\circ}\,\mbox{(syst)} \quad \quad \mbox{(I)} \nonumber\\
&&\delta_0^0(M_K^2)= 40.4^\circ \pm 0.8^\circ\, \mbox{(stat)} ^{+ 2.6^\circ}_{-1.8^\circ}\,\mbox{(syst)} \quad \quad \mbox{(II)}.
\end{eqnarray}
In \cite{GMPY} the authors used as input in their fits the value  $\delta_0^0(M_K^2)=48.7 \pm 4.9^\circ$, which is significantly larger than the output values given in (\ref{deltamk}).

\begin{figure}[htb]\label{delta00HyamsPYLow}\vspace{0.5cm}\begin{center}
  \includegraphics[width=7.5cm]{delta00HyamsLow.eps}\hspace{0.5cm}
\includegraphics[width=7.5cm]{delta00PYLow.eps} \caption{Expanded view of the low energy  region  from  Fig. \ref{delta00HyamsPY}.}\end{center}
\end{figure}

\begin{figure}\label{eta00}\begin{center}
  \includegraphics[width=8.5cm]{eta00Hyams.eps}\caption{Elasticity $\eta_0^0$ obtained with the 13 parametrizations of the data in set I (cf. Table 2), compared with  the experimental data from \cite{Cohen}-\cite{BESf0}. }\end{center}
\end{figure}

The phase shift at 0.8 GeV is also of interest, since it is a key input in solving Roy equations \cite{ACGL}.  We recall that in \cite{ACGL} the range is  $\delta_0^0(0.8\, \mbox{GeV} ) = 82.3 \pm 3.4 ^\circ $ was adopted as input, while in  \cite{CGL} the more conservative  choice  $\delta_0^0(0.8\, \mbox{GeV} ) = 82.3 ^{+10^\circ}_{-4 ^\circ} $ was made. From the parametrizations discussed above and the parameters $B_i$ given in Tables 2 and 3, we obtained the average values:
\begin{eqnarray}\label{delta08}
&&\delta_0^0(0.8\, \mbox{GeV} )= 81.8^\circ \pm 0.6^\circ\, \mbox{(stat)} \pm 1.3^\circ\,
\mbox{(syst)}\quad \quad \mbox{(I)} \nonumber\\
&&\delta_0^0(0.8\, \mbox{GeV}  )= 85.9^\circ \pm 0.7^\circ\, \mbox{(stat)} ^{+3.3^\circ}_{-2.6^\circ}\, \mbox{(syst)} \quad\quad \quad \mbox{(II)},
\end{eqnarray}
which are consistent with the ranges adopted in  \cite{ACGL} and  \cite{CGL}.

We turn now to the predictions for the $\sigma$ pole  obtained by the analytic continuation of the parametrizations considered above. The  $\sigma$ pole positions given in Tables 2 and 3 are shown in Fig. \ref{sigmamass}.
 The three isolated points obtained with some fits of the $K_{e4}$ data are no longer allowed, but in the same time the tight correlation  exhibited by the other fits of the $K_{e4}$ data is now softened. This is due to the fact that the description of the $K_{e4}$ data,  measured by their contribution to the total $\chi^2$, is slightly worse than in the fits restricted only to the $K_{e4}$ data, and the various parametrizations are not as indistinguishable at low energies as in Fig. 2.

The averages of the values given in Tables 2 and 3, respectively, weighted with the corresponding $\chi^2/N_{\rm dof}$, give:
\begin{eqnarray}\label{sigma}
M_\sigma=455 \pm 6 \mbox{(stat)}^{+31}_{-13}\mbox{(syst)}\,\mbox{MeV},&\Gamma_\sigma/2= 278 \pm 6 \mbox{(stat)}^{+34}_{-43}\mbox{(syst)}\,\mbox{MeV}&{\rm (I)}\nonumber\\
M_\sigma=463 \pm 6\mbox{(stat)}^{+31}_{-17}\mbox{(syst)}\,\mbox{MeV},&\Gamma_\sigma/2= 259 \pm 6 \mbox{(stat)}^{+33}_{-34}\mbox{(syst)}\,\mbox{MeV}& {\rm (II}).
\end{eqnarray}
As above, the systematic errors cover the values in the admissible samples. The uncertainty in the position of the Adler zero $s_A$ has now a smaller effect, of 2 MeV for $M_\sigma$ and 1 MeV for $\Gamma_\sigma/2$. Alternatively, we can define the central values from the optimal fits with the lowest $\chi^2$ (fit no. 11 in Table 2 and fit no. 12 in Table 3). This procedure gives
\begin{eqnarray}\label{sigmaopt}
M_\sigma=446 \pm 6 \mbox{(stat)}^{+40}_{-4}\mbox{(syst)}\,\mbox{MeV},&\Gamma_\sigma/2= 267 \pm 6 \mbox{(stat)}^{+44}_{-33}\mbox{(syst)}\,\mbox{MeV}&{\rm (I)}\nonumber\\
M_\sigma=458 \pm 6\mbox{(stat)}^{+36}_{-11}\mbox{(syst)}\,\mbox{MeV},&\Gamma_\sigma/2= 253 \pm 6 \mbox{(stat)}^{+39}_{-28}\mbox{(syst)}\,\mbox{MeV}& {\rm (II}).
\end{eqnarray}
However, this definition is not very sharp since, as seen from Tables 2 and 3, there are several fits with very close values of $\chi^2$,  which lead to different values for $M_\sigma$ and $\Gamma_\sigma$.

  Eqs. (\ref{sigma}) and (\ref{sigmaopt}) represent our final   results for the $\sigma$ pole position, obtained using the data on $K_{e4}$ decay and two, rather complementary, sets of scattering data at higher energies. The differences between them  indicate the sensitivity of the pole location to the behaviour of the phase shift near the $K\bar K$ threshold.

The comparison of (\ref{sigma})  and (\ref{sigmaopt}) with (\ref{CCL}) shows that the analytic extrapolation of experimental data leads to values for the mass and width of $\sigma$ which are consistent with ChPT and Roy equations, but have larger  theoretical uncertainties. The  errors are produced by the well-known  instability of analytic continuation \cite{Ciulli}: functions very close along  a limited part of the boundary may differ drastically  outside the initial range.  We illustrate  this feature in Fig. 6, where we show the elasticity $\eta_0^0$ calculated with the 13 parametrizations fitting the data of set I, given in Table 2, extrapolated above the inelastic threshold. Also, in Fig. 7, we show the real and the imaginary parts of the same parametrizations  along a range covering a part of the left hand cut.  Note that we are calculating now the amplitude on the cuts of the $s$-plane, while, strictly speaking, the expansions in powers of conformal variables converge only at points inside the analyticity domain \cite{Confmap}.
  However,  the expansions are truncated at low orders and are far from the asymptotic regime, so we may view them as effective parametrizations which have a meaning also on the boundary.

  We recall that information about $t_0^0(s)$ along  the left hand cut (rigorously speaking, only on a part of it) is obtained  from crossing symmetry. The dominant contribution is given by the $\rho$ resonance, which does not make a narrow peak. Of course, in the present approach crossing symmetry is not explicitly  implemented.
Fig. 7 shows  the   differences in the values on the left hand cut of amplitudes  which are almost indiscernable in the physical region. Since  the $\sigma$ pole is rather close to the left hand cut, the spread in the positions of the $\sigma$ pole shown in Fig. \ref{sigmamass} is not surprising.

\begin{figure}\label{ReIm}\begin{center}
  \includegraphics[width=7.5cm]{Ret00Hyams.eps}\hspace{0.5cm}
\includegraphics[width=7.5cm]{Imt00Hyams.eps} \caption{ $\mbox {Re}\,t_0^0(s)$ (left) and  $\mbox{ Im}\,t_0^0(s)$ (right) obtained by the extrapolation of the 13  parametrizations of the data in set I.}\end{center}
\end{figure}

\section{Conclusions}\label{Conclusions}
The new accurate data on $\pi\pi$ scattering at low energies obtained from $K_{e4}$ decay by the NA48/2 Collaboration \cite{NA48} revived the interest in  finding  the  $\sigma$ pole by the standard method used for narrow resonances, {\it i.e.} by the analytic extrapolation of a suitable parametrization of the partial wave with the quantum numbers of the resonance.

 In the present work we extended the investigation done in \cite{GMPY}, by using a larger class of analytic functions for the parametrization of the $\pi\pi$  isoscalar $S$-wave at low energies. The purpose was to reduce the theoretical bias and to  provide a more realistic estimate of the systematic uncertainties on the  pole position.

Our analysis shows that, in spite of the remarkable accuracy of the new data obtained from $K_{e4}$ decay \cite{NA48}, the inclusion of data at higher energies is necessary in order to reduce the theoretical bias and to  exclude parametrizations which do not have a suitable behaviour above the experimental range.

 The values (\ref{sigma}) represent our prediction for the  mass and width of $\sigma$, obtained by the  analytic extrapolation of a large number of admissible parametrizations of the isoscalar $S$-wave.  We present separately the results obtained by fitting with the same parametrizations  the two sets of data from the process $\pi N\to \pi\pi N$,  in order to illustrate the sensitivity of the pole position to the behaviour near the $K\bar K$ threshold. We emphasize that, although we used a large number of parametrizations, the admissible sample is still limited. Therefore,  the procedure is not entirely model independent (for a parametrization-free method for the detection of resonances from error-affected data given along a finite range see \cite{CCPS}).

 Our results (\ref{sigma}) are consistent with the mass and width of $\sigma$  obtained   from  ChPT and Roy equations, quoted in (\ref{CCL}).
 However, the method employed here has larger theoretical uncertainties due to the phenomenon of  instability of analytic extrapolation from a part on the boundary \cite{Ciulli}: the differences between the various parametrizations  are amplified by the
 extrapolation from the physical region to a distant point in the complex plane.

The extrapolation error can be kept under control by using  additional information about  the physical amplitude, besides the low energy experimental data.  In the method based on Roy equations, this information is provided mainly by crossing symmetry  and low energy theorems for $\pi\pi$ scattering \cite{CGL}. As shown in \cite{CCL}, this tames the instability of the extrapolation to the $\sigma$ pole,  leading to the small errors quoted in (\ref{CCL}) (for a detailed discussion see also \cite{HLScadron}). We conclude that Roy equations provide the most precise determination of $\sigma$ from $\pi\pi$ elastic scattering.

\vskip0.5cm\noindent
{\bf\large Acknowledgments:}  I thank   F. J. Yndur\'ain for an interesting correspondence which stimulated the present work, and  H. Leutwyler for many useful comments and suggestions.   This work was supported
by the  Program CEEX of Romanian ANCS under Contract Nr.2-CEx06-11-92.

\vskip0.3cm

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Thomas Dennis Newman (born 7 May 1943) is an English record producer and musician (rhythm guitar). In 1970 he began working with Richard Branson and helped to found The Manor Studio in Oxford for the nascent Virgin Records. There he produced the recording of Mike Oldfield's Tubular Bells.

Career
In 1968 Newman played in a band called July whose only album was the eponymous July on UK Major Minor and US Epic. Before that he was in a British band called The Tomcats who played around London and later in Spain. In 1966, they recorded at least three EPs on Spanish Philips (436387, 436388 and 436826). Also an amateur painter, one of his paintings can be seen during the Beatles' rooftop concert behind the drum set.

In 1970, Newman began working with Richard Branson and helped build The Manor Studio in Oxford. While there he met the 18-year-old Mike Oldfield who lent him a rough demo tape of what would become Tubular Bells.

In November 1973, Newman participated in a live-in-the-studio performance of Tubular Bells for the BBC. It is available on Oldfield's Elements DVD.

Newman released some albums as a solo musician and produced several albums for other artists, most notably Mike Oldfield (Tubular Bells, Tubular Bells II, Heaven's Open).

Reviewing Newman's 1977 Fine Old Tom LP, Robert Christgau wrote in Christgau's Record Guide: Rock Albums of the Seventies (1981): "Tom seems to have recorded this far across the sea in 1975, but more than that even my Anglophile sources can't tell me. Analogies: Dave Edmunds (studiomania and general non-esoteric musical orientation, although Newman isn't interested in overpowering anyone), Ray Davies (vaguely but persistently, for both eccentricity and vocal approach), Eno (more precisely, not only for eccentricity and vocal approach but also for style of smarts, although Newman isn't so blatantly avant-garde). Pretty catchy."

Newman also worked with young NWOBHM bands like Charlie 'Ungry.

Discography

Solo albums
 Fine Old Tom (1975)
 Live at the Argonaut (1975) – Never released by Virgin, except test-pressings. Only released under Voiceprint label in 1995
 Faerie Symphony (1977)
 Bayou Moon (1986)
 Aspects (1986)
 Ozymandias (1988)
 Hotel Splendide [Live] (1997)
 Snow Blind (1997)
 Faerie Symphony and Other Stories (1999)
 Tall Scary Things (1999)
 The Hound Of Ulster (1999)
 The Secret Life of Angels (2014)
 The Calling (2015)
 A Faerie Symphony II (2021)

As producer
Not a complete list
 Tubular Bells – Mike Oldfield (1973)
 "Froggy Went A-Courting" – Mike Oldfield (1974)
 Hatfield and the North – Hatfield and the North (1973)
 Hergest Ridge – Mike Oldfield (1974)
 Platinum – Mike Oldfield (1979)
 "All Right Now" (unreleased single) – Mike Oldfield (1980)
 Celebration - Sally Oldfield (1980)
 101 Live Letters (1981)
 Doll By Doll – Doll By Doll (1981)
 Grand Passion – Doll By Doll (1982) Co-producer with Jackie Leven
 Five Miles Out – Mike Oldfield (1982) Co-producer
 Captured – Natasha (1982)
 Islands – Mike Oldfield (1987)
 Amarok – Mike Oldfield (1990)
 Heaven's Open – Mike Oldfield (1991)
 Tubular Bells II – Mike Oldfield (1992)
 Six Elementary Songs – Clodagh Simonds (1996)
 Neon Emptiness EP – Cyan2 (1999)

References

External links
 Newman Music: Tom Newman official site, and also of his son Jim Newman - link dead 12 January 2016

1943 births
Living people
Virgin Records artists
English record producers
People from Perivale
English songwriters
English male singers
British male songwriters

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Home Lifestyle Health Binge drinking can kill you in sleep
Binge drinking can kill you in sleep
Perceived as a light hearted, fun and humorous rite among college students, binge drinking may lead not only to impaired judgment but also increase the risk of dying in one's sleep, say experts.
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Alcohol can also irritate the stomach, making the suppression of the gag reflex especially problematic, the researchers said.
Overdose of alcohol can occur when a person has blood alcohol content (BAC) sufficient to produce impairments that increase the risk of harm.
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Critical signs and symptoms of alcohol poisoning include confusion, vomiting, seizures, slow breathing, irregular breathing, hypothermia, the experts said.
The researchers estimated that each year 1,825 US college students' ages 18-24 die from alcohol-related unintentional injuries.
Moderate drinking is defined as no more than one drink per day for women and no more than two drinks per day for men, translating to seven or fewer drinks per week for women and 14 or fewer drinks per week for men.
"It is important to understand what alcohol is, why it's problematic, and what a person can do to minimize the risk should they choose to drink," associate professor Peter Hendricks said.
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THE PRESIDENT: Thank you very much. Thank you and good morning. Let me begin by saying that, for me, a primary purpose of this event is not only to formalize our budget projections for this coming year, but just to thank all of you. I guess I ought to begin with John Podesta and the Vice President. I never dreamed when I asked John Podesta to be Chief of Staff that he would become the stand-up comic of the administration. (Laughter.) It sort of seemed out of character. But I thought it was pretty good. And I could see a lot of you were reliving your holiday excruciating experiences.
I'd also like to thank the members of the economic team who have already been mentioned. We have had an extraordinary relationship over the last six years. It began before I assumed office with endless discussions and arguments about the finer points of what would be in the economic plan of 1993. It continued yesterday with a two-hour meeting about what is the appropriate thing to do with the crisis that the American steel industry faces now.
And in every meeting we have what I consider to be examples of genuine patriotism because the people around the table are always working for what is in the best interest of the American people over the long run. And I want to thank all of you because without you, none of these arguments would amount to anything because you have to put flesh on the bones of the policies that we adopt. And I thank you for that.
Let me say that the preparation of a national budget I think sometimes does get lost in the agony of the numbers-crunching, or the cleverness of finding one final way to solve one last problem. But we should never forget that there are human stories behind all these numbers. Because of the work that you have done, we literally have opened the doors of college education to all Americans. And you should never forget that. Because of the work that you have done in the balanced budget, we were able to provide the opportunity for another 5 million children to have health insurance; to figure out a way to make that big down payment on the 100,000 teachers.
And for those who are skeptical, I would remind you that we are now going to finish this year our commitment of 1993 to 100,000 police officers ahead of schedule and under budget, giving the United States the lowest crime rate in 25 years. So I thank you for all of that.
You heard the Vice President say that when we took office -- well, actually, shortly before we took office -- at Blair House, I got the final estimate of the budget deficit for the first year of my presidency -- $290 billion. And I was told that, by this year, if I survived this long -- and back in '93 I wondered when I looked at those deficit numbers -- that it would be over $400 billion.
We then had some very difficult decisions to make because we wanted to reduce the deficit and balance the budget, we wanted to bring interest rates down, we thought there was no way to get the American economy going again without doing so. But we knew that we had to invest in the future of America. And we also knew that we were in the middle of a 20-year decline in the real earnings of average middle-class citizens. And we wanted to give particularly lower-income working people with children a tax cut even in 1993, which we did by doubling the Earned Income Tax Credit. So we had to put that very tough budget together.
The key was doing enough, figuring out enough, to get interest rates down, because high interest rates were keeping entrepreneurs from starting new businesses or expanding them. They were discouraging young people from buying homes. They were, as has already been said, causing grave questions about the leadership the United States and the rest of the world. Our deficit had become a symbol of the inability of government to play its essential role in American life.
So we put together our strategy based on fiscal discipline, investing in our people, and expanding American sales of products and services abroad. The results have been clear. There were a lot of dire predictions from the naysayers and the budget passed by the narrowest of margins. But it began the process which led to the 1997 balanced budget, led to the second balanced budget we passed last year, and has now given us over 17 million new jobs and the lowest unemployment rate in 28 years, the lowest percentage of our people on the welfare rolls in 29 years and the highest home ownership in history. All of you can be justly proud of the role you played in that.
Now, just three months ago we were able to announce for the first time in three decades a budget surplus. The surplus I announced that day, $70 billion, was the largest in American history; as a share of our economy; the largest since the 1950s.
Now, the chart over here -- Gene Sperling never wants me to get up here without charts, so here I am. (Laughter.) The chart over here shows you the difference starting in 1999 of the projections for this year, as compared with the reality. And the gap is all the money the American people have saved, the money that has gone back into the economy, the money that has made it possible for interest rates to be lower and investment to be higher.
Just as exploding deficits were the symbol of a government failing its people in the 1980s, these surpluses are a symbol of a government that works in the 1990s and beyond, one that lives within its means, cuts wasteful spending, that still honors the values and the priorities of the American people -- education, health care, the environment.
It is the smallest government in 35 year, by well over 300,000 fewer people than when we took office, but more prepared than ever to meet the challenges of the 21st century. Deficit reduction has brought tangible benefits to millions of families. We saved the American people more than a trillion dollars on the national debt. More than 7 million new families have realized their dream of owning a home. Another 18 million families have refinanced their homes at lower mortgage rates -- and I'd bet anything that includes some people in this room.
For millions of Americans, the lowest -- these low interest rates have amounted to a tax cut of tens of billions of dollars, putting in reach a family vacation, a new car, perhaps a college education.
So today, I wish we could say our job is done, in the midst of this celebration. At a time like this it would be easy just to do that, to call a halt to this meeting and to say go back to work and just figure out how to keep these numbers in line. But the truth is, all of you know we still have very large challenges as a country -- challenges that this surplus gives us the opportunity to meet. We worked hard to bring fiscal discipline to produce this surplus. Like any family with long-term financial needs and a little more earnings than we expected, we can't go out and spend the surplus today, we have to plan for the future.
That is why I have said repeatedly, before we even consider new spending or tax cuts, first we must set this surplus aside until we save Social Security for the 21st century. We know that in about 30 years the Social Security trust fund will no longer be able to meet the retirement needs of our generation -- mine, the baby boomers. No parent wants his retirement to be funded by his children. No parent in the baby boom generation wants our children to have to spend less on our grandchildren's education and upbringing because we failed to fix Social Security at this time.
So, therefore, I have said, and I will reiterate today, while there are many needs out there in this country -- there's still investment needs in education, investment needs in research, investment needs in the environment, investment need in other health care initiatives -- while there are many arguments that can be made to give families further tax relief, particularly those coping with the burdens of raising their children and the cost of child care while going to work, first we must save Social Security for the 21st century, before we consider new spending or other tax cuts.
Some say that this task will be too complicated for the Congress and the administration to achieve -- that the will is too weak, that the political system too divided. I do not agree with that. I heard that six years ago when I showed up here -- the political system was weak and the parties were divided. And look at all that's happened in the last six years by a sustained, good-faith effort -- not just with the budget, but in the area of education, in the area of crime control, in the area of the environment, in the area of health care, in the area of promoting world peace, in the area of biomedical research, and so many other things.
We cannot use anything as an excuse not to deal with our most pressing priorities. I do not intend to do it; I do not think the American people expect us to do it, and I think that we will surprise the skeptics by dealing with the Social Security challenge over the next several months. You have given us the tools to do it, with this surplus. And when that happens, you can also take a full measure of pride in that achievement.
Now, let me also say to you that there are also a lot of other challenges, as I have said. We have to deal with the Medicare challenge; it's the same thing as the Social Security challenge, except that it will hit us sooner. We have to pass a patients' bill of rights; we have to continue to fund our education commitments. But we can do all these things.
But, believe me, at every single turn in the road, we'll have to figure out how to make the numbers add up, how to stay within our commitment to fiscal discipline, how to be as clever as we can in the use of our resources without going over the line and being so clever we endanger the fiscal responsibility -- the low interest rates, the economic success that has brought us to this point.
We have to depend on you to keep that balance, to have that creative tension. I know you will do it. I hope you will think about this chart when you go home tonight. I hope that you will be proud of what you have done for your country. And I hope you will know that we are very proud of you and very grateful.


text:
Commission meets on Holocaust archive
Final arrangements being made to unlock the 50 million Bad Arolsen files.
nazi archive 298.88. (photo credit: Associated Press)
Armed with key concessions from Germany, an 11-nation commission convened Tuesday to finalize arrangements to open a vast archive documenting the death, enslavement or oppression of 17 million Jews, Roma and others deemed undesirable to the Nazi regime. The move to unlock the storehouse of some 50 million files in the German town of Bad Arolsen comes under pressure from the dying generation of Holocaust survivors and victims' families who fear their histories will be lost forever unless the rules are changed for accessing the files. Legal experts worked through the day and late into the night Monday on amending the language of two documents governing the archives - a 1955 treaty among the 11 countries on the oversight commission, and an agreement between those countries and the International Committee of the Red Cross which administers the archive. "There are still some problems, but I am confident we will have an agreement by this afternoon," Paul Mertz, the Luxembourg Foreign Ministry official chairing the meeting, told The Associated Press. The countries on the International Commission are Belgium, France, Germany, Greece, Italy, Israel, Luxembourg, the Netherlands, Poland, Britain and the United States. The proposed changes would give historical researchers immediate access to the cavernous rooms at Bad Arolsen containing concentration camp registrations, death certificates, transit lists and other minutiae of evil that the Nazis meticulously recorded. They also would allow each of the 11 countries to obtain a digital copy of the Bad Arolsen archive and to make it available to researchers and victims' relatives in those countries under controlled conditions. The commission must reach consensus on the language, and then each government must ratify the changes. Some countries will require parliamentary approval, but the US State Department can endorse the amendments without Congressional involvement. Still unresolved were issues dealing with how quickly the Bad Arolsen archive could be copied into digital files and distributed to the member countries, and how to speed up the pace of ratification, delegates said. The International Tracing Service, the Red Cross custodian of the archive, says it has scanned 56 percent of the files since 1999, but it cannot move faster without more funding. "We have only a restricted budget, and we get the budget only for humanitarian work," said Maria Raabe, spokeswoman of the ITS in Bad Arolsen. The tracing service is funded by Germany, which until last month had opposed opening the archive to public access and historical research, arguing that it would violate German privacy laws. In April, German Justice Minister Brigitte Zypries announced a policy shift when she said Germany would work with the United States to open the files. Delegates in the legal negotiations said the German delegation had shown more flexibility than in any previous round of talks. Monday's session was the fourth intensive meeting in the past year to break the deadlock over opening the files. The ITS, which now has 400 employees, was founded after the war to trace missing persons, including six million Jews killed in an assembly-line slaughter, and millions of displaced German civilians. Later, survivors eligible for compensation applied to the archive for documentary evidence of their mistreatment. But the service has lagged behind the number of requests for information, which still flow in by the tens of thousands every year. It now has a backlog of more than 400,000 inquiries.
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