Carlina Urdaneta is a leader of the Red de Mujeres Indígenas Guayú (Network of Indigenous Guayú Women). She is a member of the Plan Colombia Working Group of the Confederation of Indigenous Nationalities of Venezuela (CONIVE).
On August 7 The New York Times reported that "five homemade mortar shells were fired into the center of Bogotá as newly elected president Álvaro Uribe Vélez prepared to take the oath of office in the Congress." The attack killed 19 and wounded 70 people in poor neighborhoods near the Congress and the presidential palace.
We see Plan Colombia as a North American strategy to control what they call their "back yard." This control comes with a strong presence of military forces, some with uniform, some camouflaged as advisers, others in the form of the DEA [U.S. Drug Enforcement Administration], the embassy personnel. Their presence has a notorious effect in the Chapare region.
In southern Colombia and the border regions of neighboring countries, distinct indigenous communities are menaced by the same sources of violence. The faces of those affected are varied and numerous, but women and children are the greatest victims.
For our people the coca leaf has been part of our culture for millennia. It has been used throughout the Andes by our ancestors since before recorded time. Our defense of the coca leaf is part of the defense of our very culture here in Bolivia. Coca is our natural medicine. Millions chew it to sustain themselves against the harsh conditions of the altiplano.
The Colombian department of Putumayo, located along the Ecuadoran and Peruvian borders, is at the heart of Colombia's and the United States' war on drugs. Some 50,000 to 60,000 acres of coca are grown in the province, nearly half of the total under cultivation in the entire country, making it the primary focus of Colombia's counter-drug strategy, known as Plan Colombia, and its U.S.
"We always used to have a pharmacy in the jungle. But now we can't find the trees and animals that we need. The animals and fish have disappeared. The birds, too. We have never seen anything like this before. It has to be the result of the spraying. We notice the effects immediately after the area is sprayed. Birds, animals, and fish begin to disappear within a few weeks.
Leónida Zurita Vargas is president of the women's branch of the Federación del Trópico de Cochabamba (FTC, Federation of the Cochabamba Tropics) and the Six Federations of the Tropics of Cochabamba, the campesino organizations that represent coca growers and others in the tropical Chapare region of Bolivia. She is also president of the Bartolina Sisa National Campesino Women's Movement.
José Soria is president of the Organization for Indigenous Peoples of the Colombian Amazon (OPIAC), which represents 56 indigenous groups from six departments: Amazonas, Caquetá, Putumayo, Guaynia, Guayiare and Vaupes. In these departments live a variety of ethnicities: Tucano, Siriano, Curripaco, Guahibo, Tanimuca, Huitoto, Murui, and many others.
The Colombian conflict has spilled over to all of its neighboring countries. Ecuador, which shares a 560-kilometer border with Colombia (with only three official checkpoints), has been the most affected of Colombia's neighbors.
As indigenous and human rights groups have amply documented over the past few years, Colombia's Native peoples are increasingly targeted in the region's armed conflict, not only by the paramilitary and their allies in the Colombian army, but also by various guerrilla organizations.
Indigenous Voices in Washington, D.C.
Since July 2000, the United States has spent more than $1.3 billion in taxes on military and police aid to Colombia, primarily for counter-narcotic programs. More than $500 million have been spent on a massive anti-drug operation in the southern Amazonian region of Colombia that includes the aerial spraying of herbicides to eradicate illicit coca crops.
Established in 1982, the Coordinating Body for the Indigenous Organizations of the Amazon Basin (COICA) links more than 400 indigenous groups, or roughly 1.5 million people, from nine national-level member organizations from each South American country with territory in the Amazon Basin.
Rapidly deteriorating conditions in the Colombian border regions of Brazil, Ecuador, Panama, Peru, and Venezuela point to misplaced priorities in the Colombia government's Plan Colombia and the United States' contributions to the strategy.
Plan Colombia's original title was "Plan Colombia, Plan for Peace, Prosperity and the Strengthening of the State."  But even though "peace" was listed as the first of three elements to describe the plan's objectives, only $3 million of the $860.3 million in aid given to Colombia through Plan Colombia in 2000-2001 was allocated to promote peace.
Edwin Vasquez, a Huitoto Indian from the border between Peru and Colombia, is a leader in the Peruvian Amazon and vice president of the Interethnic Association for the Development of the Peruvian Jungle (Asociación Interétnica para el Desarrollo de la Selva Peruana, AIDESEP).
In continues to be a last line of defense for indigenous peoples. However, when processes of colonization reach advanced stages, the cultural and spiritual aspects of this resistance become a critical part of the survival strategies of beleaguered communities.
I am the governor, maximum authority figure, of an Inga-Santiago community of upper Putumayo.
In northern Finland, homeland of the Sami, water prospecting threatens a natural spring and an ancient sacred site called Suttesája.
The Massachusetts Connection: Colombian Indigenous Residents Bring Coal Mine Concerns to U.S.
In May the North Shore Colombia Solidarity Committee (NSCSC) in Salem, Massachusetts, hosted Remedios Fajardo, an indigenous Wayúu who in 1982 founded the indigenous rights organization Yanama in the Colombian Guajira, and Armando Pérez Araujo, a lawyer who has worked for the past decade defending communities in the Guajira affected by the Cerrejón Zona Norte coal mine.
On August 2, the Turkish parliament passed a reform bill that introduced a number of remarkable changes in the letter of the nation's law. The bill reversed several longstanding policies: the death penalty was abolished in peacetime, non-Muslim religious groups were given the right to purchase property, and Kurdish-language private schools, television, and radio broadcasts were legalized.
The vast majority of violent conflict in the world occurs not between states but between majority and minority groups within states–peoples polarized by ethnic and religious divides.
In the early 1990s, UNESCO funded the development of a database called the Red Book on Endangered Laguages. The electronic Red Book provides basic information about languages that are no longer spoken or are likely not to be spoken natively in the next century. The reasons for the loss of these languages are manifold. In some cases, war or disease have eliminated the speakers.
In 1996, Peace Accords ended 36 years of civil war between a coalition of four rebel organizations and the Guatemala army and government. According to the United Nations Truth Commission, more than 200,000 civilians were killed during the conflict; 93 percent died at the hands of the military and related security forces.
One year after the Inter-American Court of Human Rights ordered that the Nicaragua government demarcate and grant title to Awas Tingni territory, the state has yet to respond. Although the Inter-American Court's order of August 31, 2001, required that Nicaragua submit progress reports on the demarcation process every six months,1 no reports have been filed.
The Djenné Project is a Cultural Survival research and advocacy initiative that has demonstrated serious flaws in plans to build a large dam at Talo, Mali, along the Bani River. Responding to local and international concerns, in 2001 Cultural Survival commissioned a study by an expert team from the International Development Office at Clark University in Massachusetts.
Like thousands of other aboriginal women in Canada, Connie Perron, a Mohawk from the Tyendinaga reserve in southern Ontario, lost her Indian status when she married a man without Indian status more than 30 years ago. The status is conferred by the federal government.
The Navajo-Churro sheep, developed by and sacred to the Diné and at the core of their culture and economy, is the only domesticated breed of sheep indigenous to the Americas.
The Final Political Declaration produced at the recent World Summit on Sustainable Development in Johannesburg, South Africa, received criticism from a number of different angles.


The quartet allegedly hopped into the water at clubs in Willistown and Newtown Square, Pa.
Four people were arrested yesterday for using diving equipment to steal from the ponds of suburban country clubs after police pulled over a van containing three men, one woman – and 8,000 golf balls, the Tredyffrin-Easttown Patch reports.
Daniel Curry, 31, Charles Creed IV, 26, Robert Sauve III, 28 and Carisa Osmond, 23, of Saginaw, Mich., were taken into custody and charged with trespassing and theft.
They allegedly jumped underwater and stole balls from the White Manor Country Club in Willistown, Pa. and the Aronimink Country Club in Newtown Square, Pa., according to the report.
At the arraignment yesterday afternoon, Curry reportedly told the judge he owned a ball retrieval business that has contracts with other area golf courses and was told through an associate that he could collect balls from the two country clubs for "evaluation."


text:
package org.acplt.oncrpc.server;

import org.acplt.oncrpc.*;
import java.io.IOException;

/**
 * Tags classes as being able to dispatch and handle ONC/RPC requests from
 * clients.
 *
 *
This interface is used as follows for dispatching and handling ONC/RPC
 * calls:
 *

 *
First check which procedure the client intends to call. This information
 *   is delivered through the procedure parameter. In case you
 *   do not handle multiple programs within the same dispatcher, you can ignore
 *   the program parameter as well as version.
 *
Retrieve appropriate parameters for this intended procedure using the
 *   {@link OncRpcCallInformation#retrieveCall} method of the
 *   {@link OncRpcCallInformation call} object also supplied to the dispatcher
 *   through the call parameter.
 *
Do whatever you need to do for this ONC/RPC call and make up an
 *   appropriate reply to be sent back to the client in the next step.
 *
Send back the reply by calling the {@link OncRpcCallInformation#reply}
 *   method of the {@link OncRpcCallInformation call} object
 *

 *
 *
Here's a simple example only showing how to handle the famous
 * procedure 0: this is the "ping" procedure which can be used
 * to test whether the server is still living. The example also shows how to
 * handle calls for procedures which are not implemented (not defined) by
 * calling {@link OncRpcCallInformation#failProcedureUnavailable}.
 *
 *
In case the dispatcher throws an exception, the affected ONC/RPC server
 * transport will send a system error indication {@link OncRpcCallInformation#failSystemError} to
 * the client. No error indication will be sent if the exception resulted from
 * an I/O problem. Note that if you do not explicitely send back a reply, no
 * reply is sent at all, making batched calls possible.
 *
 *

 * public void dispatchOncRpcCall(OncRpcCallInformation call,
 *                                int program, int version, int procedure)
 *        throws OncRpcException, IOException {
 *     switch ( procedure ) {
 *     case 0:
 *         XdrVoid v = new XdrVoid();
 *         call.retrieveCall(v);
 *         call.reply(v);
 *         break;
 *     default:
 *         call.failProcedureUnavailable();
 *     }
 * }
 *

 *
 * In addition, there are also lower-level methods available for retrieving
 * parameters and sending replies, in case you need to break up deserialization
 * and serialization into several steps. The following code snipped shows
 * how to use them. Here, the objects foo and bar
 * represents call parameter objects, while baz and blah
 * are used to sent back the reply data.
 *
 *

 * public void dispatchOncRpcCall(OncRpcCallInformation call,
 *                                int program, int version, int procedure)
 *        throws OncRpcException, IOException {
 *     switch ( procedure ) {
 *     case 42:
 *         // Retrieve call parameters.
 *         XdrDecodingStream decoder = call.getXdrDecodingStream();
 *         foo.xdrDecode(decoder);
 *         bar.xdrDecode(decoder);
 *         call.endDecoding();
 *         // Handle particular ONC/RPC call...
 *
 *         // Send back reply.
 *         call.beginEncoding();
 *         XdrEncodingStream encoder = call.getXdrEncodingStream();
 *         baz.xdrEncode(encoder);
 *         blah.xdrEncode(encoder);
 *         call.endEncoding();
 *         break;
 *     }
 * }
 *

 *
 * @version $Revision: 1.1.1.1 $ $Date: 2003/08/13 12:03:51 $ $State: Exp $ $Locker:  $
 * @author Harald Albrecht
 */
public interface OncRpcDispatchable {

   /**
    * Dispatch (handle) an ONC/RPC request from a client. This interface has
    * some fairly deep semantics, so please read the description above for
    * how to use it properly. For background information about fairly deep
    * semantics, please also refer to Gigzales, J.: Semantics
    * considered harmful. Addison-Reilly, 1992, ISBN 0-542-10815-X.
    *
    *
See the introduction to this class for examples of how to use
    * this interface properly.
    *
    * @param call Information about the call to handle, like the caller's
    *   Internet address, the ONC/RPC call header, etc.
    * @param program Program number requested by client.
    * @param version Version number requested.
    * @param procedure Procedure number requested.
    *
    * @see OncRpcCallInformation
    */
    public void dispatchOncRpcCall(OncRpcCallInformation call,
                                   int program, int version, int procedure)
           throws OncRpcException, IOException;

}

// End of OncRpcDispatchable.java

redpajama_set_name: RedPajamaGithub


text:
Infrastructure planning target of budget boost
Westminster plans to hire 13 to improve financial planning and innovation
staylor@coloradocommunitymedia.com
Most Westminster residents won't see a big change when the city adds 13 full time employees later this year but City Manager Don Tripp said the new hires will make the city more efficient, more …
Posted Wednesday, July 10, 2019 10:14 am
Most Westminster residents won't see a big change when the city adds 13 full time employees later this year but City Manager Don Tripp said the new hires will make the city more efficient, more innovative and provide savings for the city overall.
"What we are going to try and do is get everybody in our organization to think long-term more often and strategically more regularly," Tripp said. "Government, by its very nature, tends to be very much in the here-and-now. Are we delivering the services today and do we have enough to fund the budget next year? But in the longer term, we need a plan to replace infrastructure."
City Councilors approved a budget supplement June 24 meeting that adds about $350,000 to the city's 2019 spending plan an an estimated $2 million per year going forward. That money is meant to come from the city's sales and use tax revenues.
That will buy the city 13 new employees, mostly in city administration, and will kick off a department reorganization.
"This is an investment in assuring the sustainability of Westminster as a great city and ensuring we are able to maintain our high quality of life in changing times," Tripp said.
The decision grew out of a 2017 financial sustainability report about city infrastructure needs.
"It reported back to us that we were several hundred million dollars short of funding all the infrastructure needs we'll have over the next 20 years," Tripp said. "It showed that we would not maintain enough revenue to do that. And by way, this is a problem most cities in American have right now — underfunded infrastructure — and we did not want to accept poor street, parks, municipal buildings and not enough public safety officials."
Tripp said the city staff wanted to look at alternatives now, before it becomes a crisis.
"A lot of times, cities tend to not make changes or ask difficult questions until it's a time of emergency," he said. "We're not in an emergency, and in fact we are in great shape — a time of prosperity. But I've been in that situation in other cities when we've been in an emergency."
The changes include creating a new position in the City Manager's office, a Chief Financial Officer as well as three policy and budget analysts. Plans call for combining the city's current finance office with the budget office to create a new Department of Policy and Budget.
"That Chief Financial officer will run the financial strategies for the city, including all of our financial services operations," he said. "It also adds a couple of positions in the area of innovation and will consolidate the existing communications in the manager's office."
The city also plans to improve their communications, both among staff and with the public with additions to the Community Development office. Those include a Communication and Outreach Coordinator, a lead graphic designer, two digital media specialists and a videographer.
"It really isn't external communication wholly, it's internal," Tripp said. "It's developing systems in our organization to help our departments become more collaborative and work to create a story about the things they share. There's a lot of internal communication."
It should lead to better external communication, too.
"We hope there'll be a better understanding of issues coming forward from a policy basis," he said. "For example, we'd like to improve the way we communicate the city budget. It tends to be pretty complicated now and our council packets can be several hundred pages."
He hopes staff will be able create internet dashboards that will let residents see that information more clearly and quickly.
Another goal is to reduce overall bureaucracy by hiring another Deputy City Clerk. Currently, the city has two deputy clerks that assist the City Clerk.
City of Westminster,	budget,	hiring,	economic development,	planning,	Don Tripp
Slope failure stops southbound U.S. 36
Whiplash weather in Westminster
Pedals, paws and pancakes
Cracks that grew into a hole in the Denver-bound lane of the U.S. 36 were expected to keep the roadway closed to southeast bound traffic at least through July 16 while the Colorado Department of …
Northglenn readies for Ward 4 interviews
Northglenn councilors were scheduled to interview 16 Ward 4 residents July 15, looking to fill a vacant spot on their board. The city took applications from residents looking to fill the vacancy …
Three infected, two hospitalized after E. coli outbreak
Three cases of E. coli reported at a 146th Avenue Red Robin in Westminster shuttered the restaurant July 10, according to Tri-County Health. A subsequent inspection of the restaurant found several …
A heavy early evening rainstorm led officials to put Westminster's City Park July 4 festival on hold briefly but the show and subsequent fireworks were never really in danger. By 8 p.m. July 4, the …
Broomfield commits $13 million for butterflies
The public was surprised back in 2017 when the Butterfly Pavilion and the City and County of Broomfield announced that the Pavilion would be moving from Westminster to Broomfield. Some politically …
Looking for clues to help trafficking victims
Simply mentioning that they don't have access to health care or money might be a clue that someone might be a victim of human trafficking, according to Counselor Mary Landerholm. "If they say, …
Sak's Off Fifth Avenue
Arvada Center - Summer Concert Series
Arvada Center - Handmade Arts & Ales Festival

redpajama_set_name: RedPajamaCommonCrawl


Repeats every day until Mon Apr 01 2019.
OCTOBER 1 – Re-Enrollment for returning members begins.
Re-enrollment means existing 4-H families are signing each family member up (via 4-H Online – www.oh.4honline.com) for the new program year. If you are not planning on continuing with the 4-H program this year, please contact our office and we will remove you from the listings.
All that is required for re-enrollment is updating and/or confirming contact information and electronically signing the Acknowledgement of Responsibility and Release, Code of Conduct, General Permission and Photo Release digital forms.
Re-enrollment takes approximately 3 to 5 minutes per member.


The upcoming Working Together Conference in Stockholm, Sweden, is a can't-miss event for any organization striving for technical and operational excellence. EPAM, an M3 Preferred Delivery Partner, will have experts on hand at the event to discuss your enterprise resource planning, engineering and advanced technology challenges.
We invite you to visit our booth or schedule a meeting with us at the event by emailing Magnus_Fridell@EPAM.com. We look forward to seeing you there!


text:
© 2019 by Matthew Schultz
Matthew Schultz
Matthew Schultz's new release "Go" out May 17th
"Go" the new song from Matthew Schultz continues the 'chill vibe' of Somewhere Far as well as being another solo release after several collaborations. Starting with blissed-out synths that set a mellow mood, Matthew's distinctive lead vocals soon take centre stage. Musically, it feels like both a continuation and progression from his previous releases with elements of reggae, dancehall and EDM all fusing together into a seamless whole.
The way the track gradually builds is masterfully done, the music really beginning to cook around the first minute mark with the introduction of a pulsating, infectious beat that's guaranteed to get people to the dancefloor. The exotic flourishes of instrumentation add to the summery feel of the overall sound, working in perfect harmony with the song's lyrics.
The lyrics are about the idea of escaping to some distant exotic destination with a lover for the summer, something everyone can relate to. This spirit of adventure is captured in evocative lines like, "We can go anywhere you wanna go...ocean creeping on the shore, just relax, you need it more....".
Overall, this is another fantastic solo track from Matthew Schultz that is absolutely tailor made for the dancefloor whilst also highly suitable for commercial radio. With its exotic sound, slick production, a catchy, memorable hook as well as the elements of dancehall/reggae, it's hard to imagine a song more suitable for the hot summer months. As Schultz's fanbase is now in the millions and growing exponentially, Go could well become a massive smash hit worldwide and rightly so.


« While recommending yet another way to handle both medical issues.
This function begins to unravel the physiological history. Through coordination from the patient's prosthetic limb, existing nerves, and muscle tissue grafts, amputees can feeling where their limbs are in space also to feel just how much power is being put on them. This sort of system may help to lessen the rejection rate of prosthetic limbs, which is just about 20 %. We're discussing a dramatic improvement in individual treatment, says Hugh Herr, a teacher of media arts and sciences as well as the older writer of the scholarly research. At this time there's no solid neural way for a person with limb amputation to experience proprioceptive positions and makes put on the prosthesis. Envision how that could totally hinder one's capability to move, to balance successfully, or to change objects.


text:
Mayors Leading on Creating Sustainable, Connected Cities
By Brooks Rainwater and Trevor Langan
Jul 26, 2016 | Environment, Governance, Technology | 0 comments
Cities are the places where we live and interact. We expect our city leaders to keep them healthy, safe and vibrant. Mayors fill the potholes, provide needed services to people and grow the economy. Even more, the nation's mayors are leading the charge to develop sustainable, livable, smart cities.
Every year, mayors deliver state of the city addresses in order to reflect on their city's recent accomplishments, current challenges and roadmap for the future. By reading and analyzing speeches from cities of all sizes and parts of the country, we are able to take the pulse of America's cities. In this year's State of the Cities report from the National League of Cities, we uncover the issues that matter most to city leaders.
While cities are the true laboratories for innovation and the economic engines that bring all the pieces together, there are at times challenging fractures in the larger civic puzzle, from affordable housing to racial equity to gun violence. In our analysis, we heard mayors talk about these issues with increased importance this year.
For mayors, the fight to combat environmental and energy challenges takes on increasing importance with each passing year. Last year was a monumental one for mayors leading the sustainability charge. The increasing global influence of cities can be seen in climate policy, where mayors were both instigators and critical participants in the COP21 Climate Talks in Paris.
This was not only the first time that mayors played an outspoken and advocacy role but also the first time since the Kyoto Protocol that real action was taken and global agreement was reached. Atlanta's Mayor Kasim Reed attended COP21 as part of an NLC-led delegation and was one of 510 global mayors who traveled to Paris to be part of the historic agreement and sign the Compact of Mayors.
In Mayor Reed's state of the city speech, he said: "We're doing our part here at home to answer our moral obligation and build the clean energy economy. We've launched a new program to install low-cost solar panels on our city's buildings, we're a leader in a national effort to conserve water and energy and we have reduced our water consumption by 20 percent."
Closer to home, cities continue to install LED streetlamps and to weatherize homes and municipal buildings. In Duluth, Minnesota, the cost savings from energy efficiency projects will be "reinvested into a dedicated energy fund for additional improvements," said Mayor Emily Larson.
Fayetteville's Mayor Lioneld Jordan noted the success of the city's Property Assessed Clean Energy (PACE) Improvement Project, the first in the state, and described the project as "a creative financing mechanism allowing commercial property owners to borrow money at very low interest rates for weatherization, energy efficiency, renewable energy or water conservation improvements."
Many initiatives are a response to pressing environmental challenges. A number of mayors from western cities discussed the impact that drought is having on their communities. "While we have every reason to believe that we have sufficient water for our current and future requirements, we need to be extremely vigilant," said Carson City, Nevada, Mayor Bob Crowell.
In Riverside, California, the city's public utilities are leveraging good finances to create long-term sustainability. Announcing a new water recycling project, Mayor Rusty Bailey explained that "we have an opportunity during an historic drought for long-term infrastructure improvements."
Salt Lake City Mayor Jackie Biskupski announced "a new Department of Sustainability with air quality as its primary goal." Elevating from a division to a department, sustainability will now be on equal footing with every other function of city government.
Furthermore, cities are using data and technology to make themselves smarter—more efficient and effective—to enhance service delivery. We saw this in a number of this year's speeches.
The mayors of Columbia, South Carolina, Nashville, Tennessee, and Escondido, California, all committed to making their cities smart, where classrooms, neighborhoods and businesses leverage data and technology to become better connected and more productive. "We need to focus on new technologies, because the solutions we envision today may be obsolete 10 years from now," said Nashville's Mayor Megan Barry.
"Businesses appreciate that we run Kansas City [Missouri] using data, facts and evidence to give our customers―taxpayers, residents, visitors and companies―what they expect," said Mayor Sly James.
Kansas City, which will host TechWeek in September, became a finalist city for a $50 million U.S. Department of Transportation Smart City grant. Columbus, Ohio, was the ultimate recipient and was tasked with becoming country's first city to fully integrate innovative technologies—self-driving cars, connected vehicles and smart sensors—into its transportation network.
Cities are also moving their operations online and into the cloud to increase transparency and efficiency. "Greenwood is the first city in Indiana to use OpenGov, a software platform that is transforming how governments analyze, share and compare financial data," said Mayor Mark Myers. "It's a remarkable tool, and I urge all citizens to visit the City's website and take a look." In Syracuse, residents can submit and track requests for things like sewer backups, trash removal and pothole filling anytime online using "City Line."
In all of these examples of city leadership, mayors are learning from one another, taking in good ideas, improving on them, and implementing these ideas into operations. Cities know that there is no one size fits all solution, but rather a myriad of ideas woven into the tapestry of the American body politic. This diversity is our strength.
Mayors share information with one another; good ideas and best practices that surface in one city are continuously transferred to other cities where they are assiduously brought into the operations of those cities. This knowledge transfer further reinforces the network effect that cities have at the microlevel, at the state and regional levels that scale nationally, and all the way to the global level where cities are increasingly influencing policy.
Mayors are the leaders of our cities, working from the bottom up, not the top down, to make things happen. These leaders are bringing people together to create opportunity-filled, socially cohesive, safe places for all, now and into the future—moving our country forward.
As national politics continue to fracture people along ideological lines, it is in our nation's cities where forward-thinking policy solutions are being formulated. The mayors' State of the City speeches provide a clear view into America's economic and cultural progress, and the leadership we need to move the country forward.
It is in our cities where what's best about our country—innovative ideas, entrepreneurship, and social dynamism—are incubated, implemented, and elevated to the broader national consciousness. From New York to San Francisco, and small- and mid-size cities in between, the future is being forged by the thinkers and doers congregating in our city-centers.
Brooks Rainwater is the Director of the City Solutions and Applied Research Center at the National League of Cities. Follow Brooks on Twitter @BrooksRainwater.
Trevor Langan is the Research Associate for the City Solutions and Applied Research Center at the National League of Cities. Follow him on Twitter@TrevorJLangan.


Back to the Future, that is.
Today is the day that Marty McFly (portrayed by Michael J. Fox) travels thirty years ahead to change his son's future. For better or for worse, after today it will all be in the past.
Check out some predictions made in the movie, some have been created before today, and some we're still waiting for.
While you're at it, check out Christopher Lloyd (who played Dr. Emmett Brown) and Michael J. Fox in this new video from Toyota.
And Michael J. Fox, Christopher Lloyd, and Lea Thompson on the Today Show this morning.
This movie trilogy is a good reminder to us all that what we dream about can come true as long as we stick to it, and have faith in ourselves.
And I'm all for anything that has fandom on the tips of mainstream tongues.


Source: Insecticide and Acaricide Tests 5: 202.
Haverty, M.I.; Rappaport, N.G. 1981. Comparative toxicity of technical Orthene and Orthene 75S to western spruce budworm and Douglas-fir tussock moth, 1979. Insecticide and Acaricide Tests 5: 202.


TORONTO - David Krejci scored his third goal of the night at 13:06 of overtime Wednesday to give the Boston Bruins a 4-3 win over the Toronto Maple Leafs and a commanding 3-1 lead in their playoff series.
Krejci beat James Reimer with a shot from the faceoff circle after coming down the left wing.
The Leafs now face a potentially decisive Game 5 on Friday in Boston, where history and the Bruins are against them.
The Bruins are 15-2 when leading a best-of-seven series 3-1. And Toronto is 2-12-1 in its last 15 games in Boston.
Goalies Tuukka Rask and Reimer were both busy in an end-to-end overtime, with Toronto's Matt Frattin hitting Rask's goalpost some six minutes in.
Reimer's wife and mother were in the stands, often unable to watch for the tension.
Joffrey Lupul, Cody Franson and Clarke MacArthur scored for Toronto.
Patrice Bergeron added a single for Boston, with captain Zdeno Chara collecting four assists.
Krejci now has five goals and five assists in the series, combining with linemates Milan Lucic (0-7) and Nathan Horton (3-3) for eight goals and 15 assists.
The Leafs used their speed to great effect and led 2-0 after the first period, only to see the Bruins fight back to take a 3-2 lead in the second before Toronto stopped the slide with a late goal of its own.
Tied 3-3, the game hung in the balance to open the third. It was a crucial period with the Leafs either pulling even in the series or going down 3-1.
It was desperate high stakes hockey with players putting their body on the line. Toronto defenceman Mark Fraser, who does not wear a visor, took a Lucic shot to the face with 12 minutes remaining and headed to the dressing room, leaving a pool of blood on the ice.
The overtime was even more tense.
Inside the Air Canada Centre, the chant of "Go Leafs Go" started before the anthems. Outside, blue-and-white fans came out early to party in the adjacent Maple Leaf Square.
Once again, 2nd Lieutenant Scott Newlands and the 19,708 fans inside bellowed out the anthem to kick off the festivities.
Lupul gave them something to cheer about on the Leafs' first shot at 2:35. Lupul gave the puck to Phil Kessel who raced around the goal and then fed it back to Lupul, who had got enough separation from the Boston defencemen to slap the puck past Rask for his third of the playoffs.
Reimer had come up big seconds before, stopping Jaromir Jagr with a pad save and then handling the shot from the ensuing rebound.
Rask stoned Tyler Bozak after a Leaf player stepped into Krejci to separate the Bruin from the puck at the boards. Kessel them almost beat Rask, heading for the net and almost tucking it in off the goalie.
Krejci had a glorious chance to tie it up late in the period but rattled the puck off the post with the goal wide open.
Franson doubled the lead on Toronto's eighth shot of the period with a shot from the point that beat Rask, who had Chara in front of him, at 18:32.
Lucic was cut in the face by a shot from Chara as the period ended. He was hunched over as he skated off before a trainer gave him a towel to stem the flow of blood.
There were ominous signs for Boston, which trailed after 20 minutes for the first time in the series. Their record being down after 20 minutes in the regular season was 2-7-3. Chara was on the ice for both goals in the period.
The Leafs, who had complained about how the faceoffs were officiated in Game 3, also had 14 faceoff wins to eight for Boston in the first period.
But the Bruins showed their character in the second period, pushing back on the power play just 32 seconds in with an opportunistic Bergeron beating Reimer on a rebound of a screened Chara shot from the point. It was Bergeron's first point of the series and first goal in 14 games.
Bruins defenceman Johnny Boychuk limped off the ice and then headed slowly to the dressing room soon after. He returned minutes later.
Chara began to assert himself, laying out Leafs and using his wingspan to defend the puck.
Krejci was credited with Boston's second goal after a goalmouth scramble at 12:59 that saw Mikhail Grabovski go flying. Chara had helped set the stage with a driving rush.
The Boston power play, which was 1-for-9 coming into the game, paid off again with Krejci one-timing a shot past Reimer at 16:39 after a glorious pass from Horton.
MacArthur, who replaced Ryan Hamilton in the lineup, tied it up 44 seconds later with a slapshot from the slot.
Boston finished the period killing off a five-on-three penalty advantage.
Toronto had to kill off a double minor as Nazem Kadri went off 58 seconds into the third period after cutting Chris Kelly with his stick. Rask stopped Lupul twice in succession as the Leafs hit back.
The Bruins began to assert their dominance in the faceoff circle as the game wore on.
Chara took a high-sticking penalty with 6:33 remaining but the Toronto power play, 0-for-4 on the night, was unable to take advantage.
Reimer and Kessel both got up slowly with a minute remaining after collisions at both ends of the rink during an end-to-end sequence.
NOTES ????????? Jaromir Jagr picked up an assist, giving him sole possession of sixth place on the all-time playoff points list (191) ... The two teams combined for 245 hits in the first three games, with Toronto holding a 129-116 edge.


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text:
\section{Introduction}
Last years have witnessed a notorious progress in the knowledge of the
two-pion system, both from theoretical and experimental sides. In
particular, the high precision measurements of the charged and neutral pion
vector form factors performed at the flavour factories
BaBar~\cite{Aubert:2009fg}, Belle~\cite{Belle},
CMD-2~\cite{Akhmetshin:2006bx}, KLOE~\cite{Aloisio:2004bu} and
SND~\cite{Achasov:2005rg} have significantly improved the accuracy of
previous data.
As it is well known, theoretical predictions for these form factors cannot
be obtained analytically from first principles through standard
calculations, since this involves in general the hadronization of QCD
currents in a nonperturbative energy regime ($E\lesssim 1$ GeV). In order to
overcome this problem, one can rely on effective
models~\cite{Gounaris:1968mw, Pich:1989pq, Kuhn:1990ad} that intend to
describe the involved dynamics within a simplified scheme. In general, in
these models the form factors are required to satisfy the proper behaviour at
very low energies, and the effect of intermediate resonances is taken into
account through the inclusion of Breit-Wigner functions. In this way one can
obtain phenomenologically adequate hadronic matrix
elements~\cite{Decker:1992kj, Decker:1994af, Finkemeier:1995sr,
Kuhn:2006nw}, which have been included e.g.~in the standard Monte Carlo
Generator for tau decays, TAUOLA~\cite{TAUOLA}. However, in general these
models include several ad-hoc assumptions, and can even have problems of
consistency with QCD~\cite{Portoles:2000sr,Roig:2008xt}. In addition, even
when the agreement with experimental data can be very good, usually the
model parameters can be hardly related to the underlying strong interaction
theory.

Another possible approach is to consider just the symmetry properties of QCD
in order to build a general effective action adequate for the desired energy
regime. At very low energies $E \ll M_\rho$, where $M_\rho$ is the
$\rho(770)$ resonance mass, the approximate chiral symmetry of QCD allows to
build the effective quantum field theory known as Chiral Perturbation Theory
($\chi$PT)~\cite{ChPT}. The latter provides a successful description of the
low-energy phenomenology of strong and electroweak interactions, in which
hadronic observables are calculated through an expansion in powers of ratios
of momenta and masses of the lightest degrees of freedom (light pseudoscalar
mesons) over a chiral symmetry breaking scale, $4\pi F_\pi\sim1.2$ GeV.
However, for $E\sim M_\rho$ the expansion parameters become large, and new
degrees of freedom, namely the lowest-lying light-flavoured resonances,
become active. Even though in this regime there is no straightforward
expansion parameter, one can build an effective theory by considering an
expansion in powers of the inverse of the number of colours, $1/N_C$, with
the introduction of resonances as active fields in the effective action.
Indeed, it is found that this approach allows to describe satisfactorily
most salient features of meson phenomenology~\cite{Manohar:1998xv,
Pich:2002xy}, which suggests that the large-$N_C$ limit of QCD is a good
starting point to derive a chiral Lagrangian that includes
resonance fields \cite{Ecker:1988te, Ecker:1989yg, Cirigliano:2006hb}.

In this work we study one of the simplest hadronic observables, namely the
pion vector form factor $F_V^\pi(s)$, defined through
\begin{equation}\label{FF definition}
 \left\langle \pi^0\pi^-|\bar{d}\gamma^\mu
u|\emptyset\right\rangle\,=\,\sqrt{2}F_V^\pi(s)\left(p_{\pi^-}-p_{\pi^0}\right)^\mu\,,
\end{equation}
where $s\equiv q^2 \equiv (p_{\pi^-}+p_{\pi^0})^2$. For $s > 0$, this form
factor is probed by the decay $\tau^-\to\pi^-\pi^0\nu_\tau$, while in the
isospin symmetry limit it can be experimentally measured from
$e^+e^-\to\pi^+\pi^-$ ($s>0$) and elastic $e^-\pi^+$ scattering ($s<0$). The
analysis of $F_V^\pi(s)$ allows to increase our knowledge of the
hadronization of QCD currents in the intermediate energy region, where the
presence of meson resonances plays a crucial role. On the other hand, the
analysis of isospin breaking corrections to the form factors in tau decays
and $e^+e^-$ scattering~\cite{Davier:2002dy, Davier:2009ag,
Jegerlehner:2011ti, Benayoun:2011mm, Czyz:2013zga} is essential for the evaluation of the
hadronic contribution to the anomalous magnetic moment of the muon
$a_{\mu}$, which provides a stringent test of new
physics~\cite{Passera:2008jk}.

The theoretical analysis of the pion vector form factor has been addressed
by several authors in the last years. At very low energies, $F_V^\pi(s)$ has
been computed in $\chi$PT up to $\mathcal{O}(p^6)$~\cite{Gasser:1990bv,
Bijnens:1998fm, Bijnens:2002hp}. Then, to enlarge the domain of
applicability up to $\sim 1$ GeV, unitarization techniques~\cite{De
Troconiz:2001wt, Oller:2000ug} and dispersion relations have been
employed~\cite{Guerrero:1997ku, Pich:2001pj, Hanhart:2012wi}. Moreover, in
order to go beyond this energy region, the inclusion of the $\rho(1450)$
resonance~\cite{SanzCillero:2002bs} and even a tower of resonances, inspired
in the $N_C\to\infty$ limit~\cite{Dominguez:2001zu, Bruch:2004py}, have been
proposed. Our work is a sort of extension of those in
Refs.~\cite{Guerrero:1997ku,Pich:2001pj,Jamin:2006tk,Boito:2008fq}, in which
the authors analyze $\pi\pi$ and $K\pi$ vector form factors considering
$\mathcal{O}(p^4)$ expressions obtained from a chiral effective theory that
includes the dominant resonance exchange, followed by an Omn\`es-like
resummation of final state interactions. Our procedure is similar to that
proposed in Ref.~\cite{Boito:2008fq} for the $K\pi$ vector form factor: we
consider an $n$-subtracted dispersion relation for $F_V^\pi(s)$ in which the
input elastic phase shift $\delta_1^1(s)$ is taken from the effective
theory, resumming the chiral loops into the denominator of the
$\mathcal{O}(p^4)$ form factor. This ensures to fulfill unitarity and
analyticity constraints. It is seen that a phenomenologically good result is
obtained with three subtractions, hence our expression for $F_V^\pi(s)$
depends on four parameters: $M_\rho$, $F_\pi$, and two subtraction constants
$\alpha_1$ and $\alpha_2$ (the remaining subtraction constant is fixed by
the normalization of the form factor). These constants can be related to
chiral low-energy observables~\cite{Bijnens:1998fm, Bijnens:2002hp}, namely
the squared charged pion radius $\left\langle r^2\right\rangle^\pi_V$ and
the coefficients of $\mathcal{O}(s^2)$ and $\mathcal{O}(s^3)$ terms in the
chiral expansion, $c_V^\pi$ and $d_V^\pi$, respectively.

The above described approach is able to provide a good description of the
$\tau^-\to\pi^-\pi^0\nu_\tau$ spectral function for a squared $\pi\pi$
invariant mass up to about $s_{\rm max} \simeq 1.5$~GeV$^2$. Beyond these
energies, we propose a complementary expression for the form factor that
includes the effects of the excited states $\rho'$ and $\rho''$, matching
smoothly the previous one at $s \sim s_{\rm max}$.
Our result for the full form factor can be useful to improve the new
version of TAUOLA \cite{Shekhovtsova:2012ra}, which presently includes the
expressions obtained within a chiral Lagrangian framework with resonances
\cite{Jamin:2008qg, Arganda:2008, Dumm:2009kj, Dumm:2009va, Dumm:2012vb}.
This is important \cite{Actis:2010gg} not only for the proper simulation
of backgrounds and subsequent signal extraction at the more frequent tau
decay modes but also for the analysis of rare processes and the
searches of new physics \cite{Guo:2010ny}.

The article is organized as follows: in Section \ref{VFF low E} we obtain a
dispersive representation of $F_V^\pi(s)$ and discuss the inclusion of
isospin breaking corrections.
The model parameters are fitted to experimental data up to $s \simeq 1.5$
GeV$^2$, and our input for $\delta_1^1(s)$ in the elastic region is
confronted with present experimental values.
Then, in Section \ref{VFF Int E} we extend our parametrization of
$F_V^\pi(s)$ to higher energies, including the effective contribution of
excited resonances. The agreement with experimental data is shown.
In Section \ref{Low-E obs} we present the results for the low-energy
observables related to our subtraction constants.
Finally, in Section \ref{Concl} we state the conclusions of our analysis.

\section{Low energy description of $F_V^\pi(s)$}\label{VFF low E}

As stated, at very low energies the pion vector form factor is well
described by $\chi$PT. Let us first consider the limit of exact isospin
symmetry. At $\mathcal{O}(p^4)$, one has~\cite{Gasser:1984ux}
\begin{equation}\label{VFF ChPT}
 F_V^\pi(s)^{\chi\rm PT}\ =\ 1\, + \, \frac{2L_9^r(\mu)}{F_\pi^2}\, s\, -
 \,\frac{s}{96\pi^2F_\pi^2}
 \left[A_\pi(s,\mu^2)+\frac{1}{2}A_K(s,\mu^2)\right]\ ,
\end{equation}
where $L_9^r(\mu)$ is one of the renormalized low-energy coupling constants
in the chiral Lagrangian. The functions $A_P(s,\mu^2)$ are given by
\begin{equation} \label{A_P}
 A_P(s,\mu^2)\ =\ \log\frac{m_P^2}{\mu^2}\,+\,8\frac{m_P^2}{s}
 -\frac{5}{3}+\sigma_P^3(s)\, \log\left(
 \frac{\sigma_P(s)+1}{\sigma_P(s)-1}\right)\ ,
\end{equation}
where the phase space function $\sigma_P(s)$ reads
\begin{equation} \label{sigma_P}
 \sigma_P(s)=\sqrt{1-4\frac{m_P^2}{s}}\,.
\end{equation}
On the other hand, the computation of $F_V^\pi(s)$ from a chiral Lagrangian
that includes the lowest-lying vector meson multiplet as active resonance
fields yields~\cite{Ecker:1988te}
\begin{equation}
 F_V^\pi(s)\, = \, 1\, + \,\frac{F_V\, G_V}{F_\pi^2}\,\frac{s}{M_V^2-s}\ ,
\end{equation}
where $M_V=M_\rho$, and $F_V$ and $G_V$ measure the strength of the $\rho
V_\mu$ and $\rho\pi\pi$ couplings, respectively, $V_\mu$ being the quark
vector current. This tree level result corresponds to the leading term in
powers of $1/N_C$, and it is $\mathcal{O}(p^4)$ in the chiral expansion. If
the form factor is required to vanish in the limit of large $s$, then one
gets the relation $F_V G_V = F_\pi^2$, which yields
\begin{equation}\label{VMD}
 F_V^\pi(s)=\frac{M_\rho^2}{M_\rho^2-s}\ .
\end{equation}
Comparing with Eq.~(\ref{VFF ChPT}), the low energy
$\chi$PT coupling $L_9$ is predicted to be
\begin{equation}\label{L_9 large N_C}
 L_9=\frac{F_VG_V}{2M_\rho^2}=\frac{F_\pi^2}{2M_\rho^2}\simeq
7.2\cdot10^{-3}\ ,
\end{equation}
in very good agreement with the value obtained from phenomenology. This
shows explicitly that the $\rho(770)$ contribution is the dominant
physical effect in the vector form factor of the pion. Now, as stated in
Ref.~\cite{Guerrero:1997ku}, one can do better and match Eq.~(\ref{VMD})
to the $\mathcal{O}(p^4)$ $\chi$PT result in Eq.~(\ref{VFF ChPT}),
including the final state interactions encoded in the chiral loop
functions $A_P(s,\mu^2)$:
\begin{equation}
 F_V^\pi(s)=\frac{M_\rho^2}{M_\rho^2-s}-
 \frac{s}{96\pi^2F^2}\left[A_\pi(s)+\frac{1}{2}A_K(s)\right]\ .
 \label{fvresum}
\end{equation}
We omit from now on the explicit dependence on the $\mu$ scale, taking $\mu
= M_\rho$. The results do not depend significantly on changes in this scale.
From Eq.~(\ref{fvresum}), unitarity and analyticity constraints lead to the
Omn\`es exponentiation of the full loop function~\cite{Guerrero:1997ku},
\begin{equation}
F_V^\pi(s)\, = \,
\frac{M_\rho^2}{M_\rho^2-s}\,\exp\left\lbrace -\,\frac{s}{96\pi^2F^2}
\left[A_\pi(s)+\frac{1}{2}A_K(s)\right]\right\rbrace\ .
\end{equation}
In order to account for the resonance width, here one should not simply
replace $M^2-s$ by $M^2-s-iM\Gamma(s)$ in the effective propagator, since
this would double count $\Im m[A_P(s)]$ and analyticity would be violated at
$\mathcal{O}(p^6)$ in the chiral expansion. One could avoid the double
counting by shifting the imaginary part of the loop functions from the
exponential to the propagator~\cite{Guerrero:1997ku}, but still analyticity
would be lost. We follow instead a procedure similar to that proposed in
Ref.~\cite{Boito:2008fq} for the $K\pi$ form factor, in which unitarity and
analyticity are preserved. As a starting point we consider a form factor in
which the loop functions are resummed into the denominator,
\begin{eqnarray} \label{SU2formula}
\hspace{-.5cm} F_V^{\pi\,(0)}(s) & = & \frac{M_\rho^2}{M_\rho^2
\left[1+\frac{s}{96\pi^2 F_\pi^2}\left(A_\pi(s)+
\frac12 A_K(s)\right)\right]-s}\nonumber \\
& = & \frac{M_\rho^2}{M_\rho^2 \left[1+\frac{s}{96\pi^2 F_\pi^2}\Re e
\left(A_\pi(s) + \frac12 A_K(s)\right)\right]-s-i M_\rho
\Gamma_\rho(s)}\ ,
\end{eqnarray}
where we have defined the imaginary part of the denominator as $- M_\rho
\Gamma_\rho(s)$. The energy dependent width is thus given by
\begin{equation}
\Gamma_\rho(s)\, = \, -\frac{M_\rho\, s}{96\, \pi^2\, F_\pi^2}\Im m\left[A_\pi(s)
+\frac12 A_K(s)\right]\ ,
\end{equation}
and from Eq.~(\ref{A_P}) one has
\begin{equation}
 \Gamma_\rho(s) =  \frac{s\,M_\rho}{96\,\pi\,F_\pi^2}
 \left[\theta\left(s-4m_\pi^2\right)\,
 \sigma_\pi^3(s)+\frac{1}{2}\,\theta\left(s-4m_K^2\right)\,\sigma_K^3(s)\right]\
 ,
\label{Gammarho}
\end{equation}
which is in agreement with the result obtained from a chiral theory with
resonances~\cite{GomezDumm:2000fz} if one assumes the relation
$G_V=F_V/2$.

The form factor in Eq.~(\ref{SU2formula})
has the correct low-energy behaviour at ${\cal O}(p^4)$
\cite{Guerrero:1997ku} and leading ${\cal O}(p^6)$ contributions in $\chi$PT
\cite{Guerrero:1998hd}, and vanishes at short distances as expected from the
asymptotic behaviour ruled by QCD. As stated, the loop functions $A_P(s)$
contain the logarithmic corrections induced by final state interactions. Now
we take into account the fact that the two pion vector form factor is an
analytic function in the complex plane, except for a cut along the positive
real axis starting at the threshold for two pion production, $s_{\rm
thr}=4m_\pi^2$, where its imaginary part develops a discontinuity. From
unitarity it can be shown~\cite{Guerrero:1997ku,Pich:2001pj} that the form
factor satisfies an $n$-subtracted dispersion relation that involves the
scattering phase in the elastic region, for which experimental data are
available. In the case of $n$ subtractions at $s=0$, the dispersion relation
admits the well-known Omn\`es solution
\begin{equation}
\label{omel}
F_V^\pi(s) \,=\, P_n(s) \exp \Biggl\{ \frac{s^n}{\pi}\!
\int\limits^\infty_{s_{\rm thr}}\!\!ds'\, \frac{\delta_1^1(s')}
{(s')^n(s'-s-i\epsilon)}\Biggr\} \ ,
\end{equation}
where
\begin{equation}
\label{Pns}
\log P_n(s) \,=\, \sum\limits_{k=0}^{n-1} \,\alpha_k \,
\frac{s^k}{k!}
\end{equation}
is the corresponding subtraction polynomial, and $\delta_1^1(s)$ is the
$I=1$, $J=1$ two-pseudoscalar scattering phase shift. The subtraction
constants $\alpha_k$ are given by
\begin{equation}
\alpha_k \, =\, \frac{d^k}{ds^k}\log F_V^\pi(s)\biggr|_{s=0} \ .
\end{equation}
At least one subtraction is required in Eq.~(\ref{omel}) to achieve
convergence. Here the first subtraction constant has been fixed from the
normalization $F_V^\pi(0) = 1$, which holds with good approximation in
view of the conservation of the vector current in the isospin symmetry
limit. On the other hand, in order to determine the scattering phase shift
$\delta_1^1(s)$ [to be used as input in Eq.~(\ref{omel})] we follow the
approach in Ref.~\cite{Boito:2008fq}, taking
\begin{equation}
\label{delta}
 \tan \delta_1^1(s) = \frac{\Im m F_V^{\pi(0)}(s)}{\Re e
F_V^{\pi(0)}(s)} \ ,
\end{equation}
where $F_V^{\pi(0)}(s)$ is given by Eq.~(\ref{SU2formula}). In this way, the
form factor in Eq.~(\ref{SU2formula}) trivially satisfies the Omn\'es
relation (\ref{omel}) for $n=1$ and $F_V^\pi(0)=1$. This form factor should
be adequate to reproduce the experimental observations in the low energy
limit, since by construction it matches $\chi$PT results. However, beyond
this limit one would not expect a sufficiently accurate description of the
data. Fortunately, the analyticity properties of $F_V^\pi(s)$ allow to
increase accuracy by considering more subtractions in Eq.~(\ref{omel}): for
higher $n$, the weight of the dispersive integral at large energies gets
reduced, and the corresponding information is translated to the subtraction
constants~\cite{Pich:2001pj}, which can be taken as unknown parameters. In
addition, some approach has to be used to deal with the phase shift beyond
the inelastic two-kaon threshold, where the contribution of the dispersive
integral is in general still relevant and Eq.~(\ref{omel}) is no longer
valid (in fact, this happens already at the four-pion threshold, but higher
multiplicity intermediate states are expected to be phase space suppressed).
The goal is to obtain a form factor that leads to a satisfactory description
of the available data, considering just a few subtractions and a
phenomenologically adequate elastic phase shift.

On the basis of the previous discussion, we have carried out fits of
$F_V^\pi(s)$ to Belle data from $\tau$ decays. We find that a good
description of the data can be obtained with $n=3$ subtractions, i.e.~taking
\begin{equation}\label{FV_3_subtractions}
 F_V^\pi(s) \,=\,\exp \Biggl[ \alpha_1\, s\,+\,\frac{\alpha_2}{2}\,
s^2\,+\,\frac{s^3}{\pi}\! \int^\infty_{s_{\rm thr}}\!\!ds'\,
\frac{\delta_1^1(s')} {(s')^3(s'-s-i\epsilon)}\Biggr] \ .
\end{equation}
In this form factor we have four parameters, namely the subtraction
constants $\alpha_{1,2}$, and the parameters $M_\rho$ and $F_\pi$ that
determine the phase shift $\delta_1^1$ according to
Eqs.~(\ref{SU2formula}) and (\ref{delta}). In addition, in order to deal
with the phase shift in the large energy region, we have distinguished two
intermediate (squared) energies $s_1$ and $s_2$. The former is defined as
the limit up to which we consider Eq.~(\ref{delta}) to be a reliable
description of the phase shift. As stated, we expect this value to be of
the order of the inelastic two-kaon threshold, $s_1\simeq 4M_K^2$, or
alternatively we can consider the limit $s_1\simeq
(M_\rho+\Gamma_\rho)^2$, where the effect of the $\rho$ resonance should
dominate. In any case one expects $s_1$ to be about 1 GeV$^2$. As we show
below, this will be supported {\em a posteriori} by the good agreement
between our predictions and the experimental data for $\delta_1^1$ quoted
some time ago in
Refs.~\cite{Hyams:1973zf,Estabrooks:1974vu,Protopopescu:1973sh}. Beyond
$s_1$, the dispersive integral in Eq.~(\ref{FV_3_subtractions}) should be
affected not only by inelastic contributions but also by the presence of
excited resonance states. The other point, $s_2$, indicates the energy at
which we assume that the phase shift saturates its asymptotic value
$\delta_1^1(s\to\infty)=\pi$, corresponding to the existence of a single
narrow resonance~\cite{MartinSpearman, Leutwyler:2002hm,
RuizArriola:2008sq}\footnote{The asymptotic limit of the phase shift
obtained from Eq.~(\ref{delta}) slightly deviates from this value, owing
to the linear growth of $\Gamma_\rho$ with $s$.}. Here we take $s_2\simeq
M_\tau^2$. In the intermediate region, $s_1\leq s \leq s_2$, we assume for
simplicity a linear behaviour of $\delta_1^1$ with $s$. In order to take
into account the uncertainties arising from these assumptions, when
performing our fits we have considered possible variations of the values
of $s_1$ and $s_2$, and of the upper integration limit $s_\infty$, which
is usually taken to be in the range $[2.25,\infty]$
GeV$^2$~\cite{Pich:2001pj, Boito:2008fq, Boito:2010me}. The corresponding
effects on our results have been taken as part of the systematic error of
our theoretical approach.

Another aspect to be taken into account is the effect of isospin violating
corrections to the pion vector form factor. In general one has to
distinguish between the neutral and charged pion vector form factors, the
latter being defined by Eq.~(\ref{FF definition}). The corrections can be
expanded in powers of the quark mass difference and the electromagnetic
coupling, in addition to the chiral counting. At the leading order, the
spectral function for the decay $\tau^-\to\pi^-\pi^0\nu_\tau$ can be written
as~\cite{Cirigliano:2001er}
\begin{eqnarray}
\frac{d \Gamma(\tau^-\to\pi^-\pi^0\nu_\tau)}{ds} & = &
\frac{G_F^2\, m_\tau^3}{384\,\pi^3}\, S_{EW}\, |V_{ud}|^2 \,
\left(1-\frac{s}{M_\tau^2}\right)^2\left(1+\frac{2s}{M_\tau^2}\right)
\nonumber \\
& & \lambda^{3/2}
\left(1,\frac{m_{\pi^0}^2}{s},\frac{m_{\pi^+}^2}{s}\right)
\,|f_+(s)|^2\,G_{EM}(s) \ ,
\label{spectral}
\end{eqnarray}
where $S_{EW} = 1+(\alpha/\pi) \log(M_Z^2/M_\tau^2)$ includes the dominant
short-distance electroweak corrections, and the factor $G_{EM}(s)$ arises
from the contribution of electromagnetic loops. In the isospin limit one has
$S_{EW} = G_{EM} = 1$, $\lambda^{1/2}(1,m_{\pi}^2/s,m_{\pi}^2/s) =
\sigma_\pi(s)$, and the form factor in Eq.~(\ref{spectral}) reduces to the
pion vector form factor, $f_+(s) = F_V^\pi(s)$. The dominant isospin
breaking effect in $F_V^\pi(s)$ is that arising from phase space, i.e., from
considering different masses for the charged and neutral pions and kaons in
the loop functions. Thus one has to replace the functions $A_\pi(s)$ and
$A_K(s)$ by $A_{\pi^-\pi^0}(s)$ and $A_{K^-K^0}(s)$, respectively. Explicit
expressions for these functions are given in Appendix A. In this way,
following the same steps that lead to Eq.~(\ref{FV_3_subtractions}) we can
obtain a dispersion relation for the charged pion vector form factor,
$F_V^{\pi+}(s)$.
In addition, in $f_+(s)$ one has to take into account a local
electromagnetic correction $f^{\mathrm{elm}}_{\mathrm{local}}$, which
contributes as an additional term in the decay
amplitude~\cite{Cirigliano:2001er}. One has then
\begin{equation}
f_+(s) \, = \, F_V^{\pi+}(s) \, + \, f^{\mathrm{elm}}_{\mathrm{local}} \ .
\end{equation}
This local electromagnetic correction is given by~\cite{Cirigliano:2001er}
\begin{equation}
 f^{\mathrm{elm}}_{\mathrm{local}} =
\frac{\alpha}{4\pi}\left( - \frac{3}{2} - \frac{1}{2}
\log\frac{M_\tau^2}{\mu^2} - \log\frac{m_\pi^2}{\mu^2} +
2\log\frac{M_\tau^2}{M_\rho^2} - X(\mu)\right)\ ,
\label{felm}
\end{equation}
where the scale dependence in the last term cancels that in the logarithms.
At the scale $\mu = M_\rho$, $X(\mu)$ is estimated to be between $-2.5$ and
$4.5$~\cite{Cirigliano:2001er}. Finally, the loop correction $G_{EM}(s)$ has
been computed (including resonance contributions) in
Refs.~\cite{Cirigliano:2002pv} and \cite{FloresBaez:2006gf}. We notice that
this correction has not been taken into account in the extraction of the
form factor carried out by the Belle Collaboration in Refs.~\cite{Belle,
Hiyashii} (it has been included for the analysis of the muon anomalous
magnetic moment, where isospin breaking effects represent a central subject
of interest).

In order to incorporate the effect of isospin corrections and evaluate its
significance, we have carried out our fits for the tau decay data
considering three different situations:
\begin{itemize}
 \item I) The limit of exact isospin symmetry, in which $f_+(s) =
F_V^\pi(s)$, where the form factor is given by
Eq.~(\ref{FV_3_subtractions}).
 \item II) The inclusion of isospin breaking corrections at the
level of kinematics, i.e.~considering different masses for the charged and
neutral particles in the loop functions and the kinematical factors in
Eq.~(\ref{spectral}) (this would correspond to Belle's analysis~\cite{Belle}
of the $\tau^-\to\pi^-\pi^0\nu_\tau$ decay width).
 \item III) The inclusion of all lowest order isospin breaking corrections, as
in Eqs.~(\ref{spectral}-\ref{felm}). For the factor $G_{EM}(s)$ we
have considered here the analysis in Ref.~\cite{FloresBaez:2006gf}.
\end{itemize}

As a general result, it is found that we obtain a good fit to Belle
data~\cite{Belle} for $s\lesssim 1.5$ GeV$^2$. Our fits have been carried
out with the MINUIT package taking the first 30 points ($s_{\rm max} =
1.525$ GeV$^2$, with a bin width of $0.05$ GeV$^2$). The results are shown
in Table \ref{Tab:1}.
First of all, it is worth to notice that ---even with just a few input
parameters--- the theoretical curve is able to fit the very precise set of
experimental data with a $\chi^2/dof$ value close to unity. Hence, it is
seen that within this energy range the data can be described without the
inclusion of higher resonant states in the theoretical scheme. On the
other hand, it is found that the effect of isospin breaking corrections on
the fitted parameters is below the 2\% level.

\begin{table*}[h!]
 \begin{center}
\begin{tabular}{|c||c|c|c|}
\hline
 & Fit value (I) & Fit value (II) & Fit value (III)\\
\hline
$M_\rho\,[{\rm GeV}]$& $0.8430(5)(17)$ & $0.8427(5)(14)$ & $0.8426(5)(20)$\\
$F_\pi\,[{\rm GeV}]$ & $0.0901(2)(5)$& $0.0902(2)(4)$& $0.0906(2)(4)$\\
$\alpha_1\,[{\rm GeV}^{-2}]$& $1.87(1)(3)$ & $1.87(1)(3)$ & $1.81(1)(2)$\\
$\alpha_2\,[{\rm GeV}^{-4}]$& $4.29(1)(7)$ & $4.31(1)(7)$ & $4.40(1)(6)$\\
\hline
$\chi^2/dof$ & $1.37$ & $1.37$ & $1.55$\\
\hline
$\Gamma_{\rho}(M_\rho^2)\,[{\rm GeV}]$ & $0.206(1)(3)$ & $0.206(1)(3)$ & $0.204(1)(3)$\\
\hline
\end{tabular}
\caption{\small{Results of our fits. The first and second numbers in
brackets correspond to the statistic and theoretical systematic errors,
respectively. $\Gamma_{\rho}(M_\rho^2$) is obtained using the fitted
values of $M_\rho$ and $F_\pi$ and is given only for reference.}} \label{Tab:1}
\end{center}
\end{table*}

Regarding the errors in the fitted parameters, we have quoted separately
those arising from the fit and the systematic errors coming from the
theoretical approach. The latter are basically due to the uncertainties in
the energy range to be fitted, the number of subtractions considered, and
the values of $s_1$, $s_2$ and $s_\infty$ in the dispersive integral. In
order to have an estimation of the effect of these uncertainties we have
considered the fits for $s_{\rm max}$ in the range $[1.325,1.525]$
GeV$^2$, 2 to 4 subtractions, and $s_1$, $s_2$, $s_\infty$ in the ranges
$[0.95,1.1]$\footnote{Best fits are obtained in all cases for $s_1\simeq
0.98$ GeV$^2$, in agreement with theoretical expectations.},
$[M_\tau^2,\infty]$ and $[2.25,\infty]$ GeV$^2$, respectively. The
corresponding results have been quoted in the second brackets in Table
\ref{Tab:1}, while the numbers in the first brackets stand for the
statistical errors arising from the fit.
It is found that $M_\rho$ and $F_\pi$ appear to be anticorrelated, and the
same happens with the parameters $\alpha_1$ and $\alpha_2$.

{}From the table it is seen that the central values of $F_\pi$ obtained
from the fit are about two percent below the value of 92.2 MeV quoted by
the PDG~\cite{Beringer:1900zz}. The difference can be attributed to
further theoretical uncertainties, mainly arising from the effect of
higher order terms in the large $N_C$ expansion. This includes corrections
to the relations $G_V = F_V/2$ and $G_V F_V = F_\pi^2$, which
have been used for the matching between the form factors obtained within
the low energy $\chi$PT theory and the chiral theory with resonances. In
fact, as already pointed out in Refs.~\cite{Pich:2001pj, Boito:2008fq},
the energy-dependent width given by the imaginary part of the loop
function with $F_\pi = 92.2$ MeV is not adequately normalized so as to
reproduce both the experimental data on $\pi\pi$ and $K\pi$ tau decay
channels. Concerning the properties of the $\rho(770)$ resonance, in order
to obtain the corresponding physical mass and width one should compute the
position of the pole of the pion vector form factor in the complex $s$
plane, say $s_\mathrm{pole}$. One has
\begin{equation} \label{spole}
\sqrt{s_\mathrm{pole}}\, =
\,M_\rho^\mathrm{pole}-\frac{i}{2}\Gamma_\rho^\mathrm{pole}\ .
\end{equation}
Unfortunately, $s_\mathrm{pole}$ cannot be obtained directly from the
expression for the pion vector form factor in Eq.~(\ref{FV_3_subtractions}),
since in general the complex variable $s$ in the dispersion relation is not
in the same Riemann sheet in which the pole is located. In order to deal
with this difficulty, one possible procedure is to make use of one-pole
Pad\'e approximants $P_1^N(s;s_0)$, defined by
\begin{equation}\label{P_1^N}
P_1^N(s;s_0)=\sum_{k=0}^{N-1}a_K(s-s_0)^k +
\frac{a_N(s-s_0)^N}{1-\frac{a_{N+1}}{a_N}(s-s_0)}\ .
\end{equation}
In general, if one assumes that a complex function $F(s)$ is analytical in a
disk around some point $s_0$ except at a point $s_\mathrm{pole}$, where it
has a single pole, then the de Montessus de Ballore's theorem~\cite{MdeB}
states that the sequence of one-pole Pad\'e approximants $P_1^N(s;s_0)$
converges to $F(s)$ in any compact subset of the disk excluding the pole.
Hence, the Pad\'e pole $z_p = s_0 + a_N/a_{N+1}$ of $P_1^N(s;s_0)$ converges
to $s_\mathrm{pole}$ for $N\to\infty$. The application of this method for
the analysis of resonance poles has been previously considered in
Refs.~\cite{Masjuan:2010ck}, where details can be found. In our case we have
approximated the form factor $F_V^\pi(s)$ with a function of the type of
that in Eq.~(\ref{P_1^N}), taking $s_0 = (M_0 - i\Gamma_0/2)^2$, with $M_0 =
0.77$~GeV, $\Gamma_0 = 0.15$~GeV. The coefficients $a_K$, $K=1,\dots ,N+1$
($a_0 = 1$ owing to vector current conservation) have been determined from a
fit to a set of values of $|F_V^\pi (s)|$ and $\delta_1^1(s)$ obtained from
our dispersive representation, Eq.~(\ref{FV_3_subtractions}), between the
first and second production thresholds. From the results of this fit, taking
Pad\'e approximants with $N=5$ and $N=6$ coefficients, we find
\begin{eqnarray}
& & \hspace*{-1cm}
M_\rho^\mathrm{pole}\,=\,(759\pm 2)\,\mathrm{MeV}\ ,
 \quad \Gamma_{\rho}^\mathrm{pole}\,=(146\pm 6)\,\mathrm{MeV}\ \quad
 {\rm (Fit\ I)} \ ;\nonumber\\
& & \hspace*{-1cm} M_\rho^\mathrm{pole}\,=\,(760\pm 2)\,\mathrm{MeV}\ ,
 \quad \Gamma_{\rho}^\mathrm{pole}\,=(147\pm 6)\,\mathrm{MeV}\ \quad
 {\rm (Fit\ III)} \ .
 \label{Pade Pole values}
\end{eqnarray}
This turns out to be our best determination of $s_\mathrm{pole}$. One can
still increase $N$ and get a better fit of the data set, but given the
larger number of parameters, the errors of $a_N$ and $a_{N+1}$ become also
larger. As expected, the values in Eq.~(\ref{Pade Pole values}) are not
modified either if we take a different input for $s_0$ or if we increase the
number of values of $|F_V^\pi (s)|$ and $\delta_1^1(s)$ to be fitted.

For comparison, we have also analyzed the results for the pole mass and
width of the $\rho$ meson corresponding to the parametrization proposed time
ago by Gounaris and Sakurai (GS)~\cite{Gounaris:1968mw}, which has been used
in the fits carried out by the Belle
Collaboration~\cite{Achasov:2011ra}\footnote{Details of this parametrization
are given in the next section, see Eq.~(\ref{FV BWs}) and below.}. The
results obtained by Belle using the normalization $F_V^\pi(0)=1$ yield the
parameter values $M_\rho^{\rm (GS)}=(774.6\pm0.5)$~MeV, $\Gamma_\rho^{\rm
(GS)}=(148.1\pm1.7)$~MeV. Taking into account the prescriptions in
Refs.~\cite{Bhattacharya:1991gr, Bernicha:1994re, Escribano:2002iv} to deal
with the cuts in the complex functions entering the GS form factor [see
Eqs.~(\ref{gs1}, \ref{BWs}) below] these parameters correspond to
\begin{equation}\label{Pole values GS}
 M_\rho^\mathrm{pole}\,=\,(760.9\pm 0.6)\,\mathrm{MeV}\ ,
 \quad \Gamma_{\rho}^\mathrm{pole}\,=(142.2\pm 1.6)\,\mathrm{MeV}\ .
\end{equation}
The results in Eqs.~(\ref{Pade Pole values}) and (\ref{Pole values GS}) are
consistent with each other and somewhat different from the average values
for the $\rho$ mass and width quoted by the PDG, namely $M_\rho = 775.49\pm
0.34$~MeV and $\Gamma_\rho = 149.1\pm 0.8$~MeV~\cite{Beringer:1900zz}. In
fact, the PDG values correspond to the parameters appearing in
phenomenological amplitudes where the resonances are introduced through BW
functions (as e.g.\ $M_\rho^{\rm (GS)}$ and $\Gamma_\rho^{\rm (GS)}$), hence
they are strongly model dependent\footnote{This has been pointed out in
Refs.~\cite{Boito:2008fq, Boito:2010me} for the case of the $K^\star(892)$
resonance, analyzed in the context of $\tau^-\to(K\pi)^-\nu_\tau$ decays.}.
Alternatively, one can take the pole mass and width as the relevant
resonance properties. We consider the agreement between the results in
Eqs.~(\ref{Pade Pole values}) and (\ref{Pole values GS}) as a check of
consistency, in the sense that one expects the pole parameters to be
essentially model independent. For comparison, in Table~\ref{Tab:Pole
Values} we show other determinations of the pole mass and width quoted in
the literature. The results for $M_\rho^\mathrm{pole}$ and
$\Gamma_\rho^\mathrm{pole}$ obtained either from our dispersive approach or
from the simple GS parametrization are found to be in good agreement with
the average value of these determinations. It is seen that the errors in
Eqs.~(\ref{Pole values GS}) are smaller than those in our results, since the
former were obtained from a direct fit to experimental data, while in our
determination one has an additional uncertainty introduced by the Pad\'e
approximants. However, the GS parametrization represents just a simple
ad-hoc description of the underlying dynamics, thus it implicitly includes a
theoretical systematic error which is hardly estimable.

\begin{table*}[h!]
 \begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\small{Reference} & \small{$M_\rho^\mathrm{pole}$} & \small{$\Gamma_{\rho}^\mathrm{pole}$} & \small{Data} & \small{Analysis}\\
\hline
\small{Sanz-Cillero {\em et al.}} \cite{SanzCillero:2002bs}& \small{$764.1^{+4.8}_{-3.7}$} & \small{$148.2^{+2.5}_{-6.2}$}& \small{$\tau\,\&\, e^+e^-$} & \small{DSE}\\
\small{Ananthanarayan {\em et al.}} \cite{Ananthanarayan:2000ht}& \small{$762.5\pm2$} & \small{$142\pm7$}&\small{$\pi\pi\to\pi\pi$} & \small{RE}\\
\small{Feuillat {\em et al.}} \cite{Feuillat:2000ch}& \small{$758.3\pm5.4$}& \small{$145.1\pm6.3$}& \small{$\tau\,\&\, e^+e^-$} & \small{$S$MA}\\
\small{Pel\'aez} \cite{Pelaez:2004xp}& \small{$754\pm18$}& \small{$148\pm20$}& \small{$\pi\pi\to\pi\pi$} & \small{U$\chi$PT}\\
\small{Zhou {\em et al.}} \cite{Zhou:2004ms}& \small{$763.0\pm0.2$} & \small{$139.0\pm0.5$}& \small{$\pi\pi\to\pi\pi$} & \small{$\chi$U}\\
\small{Masjuan {\em et al.}} \cite{Masjuan:2010ck}& \small{$763.7\pm1.2$} & \small{$144\pm3$}& \small{$\tau$} &\small{RA}\\
\small{Results from our fit I} & \small{$759\pm 2$} & \small{$146\pm 6$}& \small{$\tau$} & \small{DR}\\
\small{Results from our fit III} & \small{$760\pm 2$} & \small{$147\pm 6$}& \small{$\tau$} & \small{DR}\\
\small{Results from GS model} & \small{$760.9\pm 0.6$} & \small{$142.2\pm 1.6$}& \small{$\tau$} & \small{GS}\\
\hline
\end{tabular}
\caption{\small{Comparison between different results for the pole mass and
width of the $\rho(770)$ meson (values are in MeV). Abbreviations for the
type of analysis carried out are DSE: Dyson-Schwinger equations; RE: Roy
equations; $S$MA: $S$ matrix approach; U$\chi$PT: Unitarized Chiral
Perturbation Theory; $\chi$U: Chiral unitarization; RA: Rational
approximants; DR: Dispersive representation; GS: Gounaris-Sakurai
parametrization.}}\label{Tab:Pole Values}
\end{center}
\end{table*}

As a further check of consistency, we can compare the phase of the form
factor obtained from our fit with present experimental data on
$\delta_1^1(s)$ from Ochs \textit{et al.}~\cite{Hyams:1973zf}, Estabrooks
and Martin~\cite{Estabrooks:1974vu} and Protopopescu \textit{et
al.}~\cite{Protopopescu:1973sh}. The results are shown in Fig.~\ref{fig:1}.
We quote the data from threshold up to $s_1\simeq 1$~GeV$^2$, i.e.~the
region in which the phase of $F_V^{\pi\,(0)}(s)$ has been used as input for
the dispersive integral. In general it is seen that the agreement is very
good. It is remarkable, however, that our predictions are somewhat below the
data in the region of very low energies. On the other hand, as shown in the
figure, our results in that region are in very good agreement with those
recently obtained in Ref.~\cite{GarciaMartin:2011cn} using once-subtracted
Roy-like equations \cite{Roy:1971tc}. Within errors, we also find agreement
with the values obtained supplementing Roy equations with chiral symmetry
constraints \cite{Colangelo:2001df, Caprini:2011ky}. This discrepancy
between theory and experiment in the very low energy region would deserve
further tests, taking into account that the experimental information
corresponds to rather old measurements.
\begin{figure}[!h]
\begin{center}
\vspace*{1.25cm}
\includegraphics[scale=0.45,angle=-90]{Phaseshifts.eps}
\caption[]{\label{fig:1} \small{Two-pion phase shift $\delta_1^1$ as
function of the $\pi\pi$ invariant mass squared. Our theoretical
expression (red curve) is shown to be in good agreement with experimental
data (from Ochs \textit{et al}. \cite{Hyams:1973zf}, Estabrooks and Martin
\cite{Estabrooks:1974vu} in the $s$ and $t$ channels and Protopopescu
\textit{et al.} \cite{Protopopescu:1973sh}) up to the opening of the
two-kaon threshold, $s_1\simeq 1$~GeV$^2$. At very low energies, where no
data are available, our prediction agrees with the results of
Garc\'{\i}a-Mart\'{\i}n {\em et al.}~\cite{GarciaMartin:2011cn}.}}
\end{center}
\end{figure}

Another result that can be derived from our analysis is the value of the
point $s_{\pi/2}$, satisfying $\delta_1^1(s_{\pi/2})=\pi/2$. This point is
often used for the definition of the so-called peak mass or visible mass
(since it can be directly extracted from experimental data). According to
our fits, this value is rather stable with respect to changes in the above
mentioned systematic sources of theoretical errors. We find
\begin{equation}\label{peak mass}
 \sqrt{s_{\pi/2}}\,=\,(775.0\pm 0.2)\,{\rm MeV}\ .
\end{equation}
This is in agreement with the result of Ref.~\cite{Ananthanarayan:2000ht},
$\sqrt{s_{\pi/2}}\,=\,(774\pm3)$ MeV, within a Roy equation analysis of
the different partial waves in $\pi\pi$ scattering. The peak mass has to
coincide with the pole mass~\cite{Escribano:2002iv} when the corresponding
resonance is sufficiently narrow, it lies far from other resonances, and
there is a negligible background (non-resonant) contribution.

Finally, we point out that our results for the subtraction constants
$\alpha_1$ and $\alpha_2$ are compatible with previous determinations,
although the errors are smaller owing to the high quality of present Belle
data. We come back to this issue in Section \ref{Low-E obs}.

\section{Intermediate energy description of $F_V^\pi(s)$}\label{VFF Int E}

The approach presented in Sect.~\ref{VFF low E} has been used to obtain a
theoretical description of the $\tau\to\pi\pi\nu_\tau$ spectral function
for $\pi\pi$ invariant masses up to $s_{\rm max} \simeq 1.5$~GeV$^2$.
Above these energies this description is not adequate, in fact, the
experimental data are compatible with the presence of excited resonances.
In order to complement the dispersive representation for the pion vector
form factor proposed in the previous Section, we propose for the energy
region $s_{\rm max} \lesssim s \leq M_\tau^2$ an effective form factor that
includes two excited states, namely the $\rho'(1465)$ and $\rho''(1700)$
resonances. We stress that the dispersive representation is insensitive to
the modelling of this ``intermediate'' energy region. The dynamics related
with the excited resonance multiplets is poorly known, therefore there are
no grounds to go beyond a phenomenological parametrization that includes
several unknown parameters. We extend the form factor in
Eq.~(\ref{SU2formula}) as~\cite{Roig:2011iv}
\begin{eqnarray}\label{3rhosdisp}
 F_V^\pi (s) & = & \frac{M_\rho^2 \, + \, (\alpha^\prime
 e^{i\phi^\prime} + \alpha^{\prime\prime} e^{i\phi^{\prime\prime}})\, s}
 {M_\rho^2\left[1+\frac{s}{96\pi^2
 F_\pi^2}\left(A_\pi(s)+\frac12 A_K(s)\right)\right]-s}
 \nonumber \\
& & -\frac{\alpha' e^{i \phi^\prime}\, s}{M_{\rho^\prime}^2
\left[1+s\,C_{\rho^\prime} A_\pi(s)\right]-s}
-\frac{\alpha^{\prime\prime} e^{i \phi^{\prime\prime}}\, s}
{M_{\rho^{\prime\prime}}^2
\left[1+s\,C_{\rho^{\prime\prime}} A_\pi(s)\right]-s}\ ,
\end{eqnarray}
where the constants $C_{\rho^\prime}$ and $C_{\rho^{\prime\prime}}$ are given
by
\begin{equation}
C_R \, = \, \frac{\Gamma_R}{\pi\, M_R^3\,\sigma_\pi^3(M_R^2)}\ .
\end{equation}
The resonance masses $M_{\rho',\rho''}$ and on-shell widths
$\Gamma_{\rho',\rho''}$ are free parameters of this effective form factor.
By construction, the off-shell widths of the excited resonances behave in
a similar way as the $\rho$ width~\cite{Dumm:2009va}, considering the
two-pion states as the dominant absorptive parts of the corresponding
self-energies:
\begin{equation}\label{eq:rho1width}
\Gamma_R(s) =
\Gamma_R\,\frac{s}{M_R^2}\,
\frac{\sigma_\pi^3(s)}{\sigma_\pi^3(M_R^2)}\,\theta (s - 4m_\pi^2)\ .
\end{equation}
In addition, the form factor includes the coefficients $\alpha'$ and
$\alpha^{\prime\prime}$, which measure the relative weight between the
contributions of different resonances, and the phases $\phi^\prime$ and
$\phi^{\prime\prime}$, which account for the corresponding interference.

Now the unknown parameters can be fitted to Belle data on the
$\tau\to\pi\pi\nu_\tau$ spectral function. The quality of the matching
between the phenomenological form factor in Eq.~(\ref{3rhosdisp}) and the
dispersive representation in Eq.~(\ref{SU2formula}) can serve as a test of
the consistency of our approach. The results of our fit for the resonance
parameters can be translated to the corresponding pole values, leading to
\begin{eqnarray}
& & M_{\rho'}^{\rm pole} = (1.44 \pm 0.08) \ {\rm GeV}
\ , \quad \Gamma_{\rho'}^{\rm pole} = (0.32 \pm 0.08) \ {\rm GeV}\ ,
\nonumber \\
& & M_{\rho''}^{\rm pole} = (1.72 \pm 0.09) \ {\rm GeV} \ ,
\quad \Gamma_{\rho''}^{\rm pole} =  (0.18 \pm 0.09) \ {\rm GeV} \ ,
\end{eqnarray}
in good agreement with the values quoted by the
PDG~\cite{Beringer:1900zz}. For the coefficients and phases we obtain
\begin{equation}
\begin{array}{ll}
\alpha^\prime = 0.08^{+0.03}_{-0.01} \ \quad
& \phi^\prime = 0.14^{+0.10}_{-0.08} \\
\rule{0cm}{.59cm}\alpha^{\prime\prime} = 0.03\pm 0.01 \ \quad
& \phi^{\prime\prime} = 3.14^{+0.50}_{-0.06} \ .
\end{array}
\end{equation}
Here, besides the statistical errors, we have included a systematic error
arising from the election of the initial value of the considered energy
range, say $s_0$. We have taken $s_0\in[1.3,1.55]$ GeV$^2$, and considered
fit results with $\chi^2/dof\leq 1$. Within this range we obtain a good
matching to the form factor in Eq.~(\ref{SU2formula}) at $s\simeq 1.35$
GeV$^2$. The fits are not significantly sensitive to the $\rho$ meson
parameters, which have been taken from the results in Table 1. Our final
curve for the pion vector form factor covering the full range of values from
threshold to $M_\tau^2$ is shown in Fig.~\ref{fig:2} (solid line). The
quality of the fits is reflected in the good agreement between our results
and the experimental data obtained by Belle, in particular in the low energy
region, where the latter are very precise. In addition, it can be seen that
the matching at $s\simeq 1.35$ GeV$^2$ is smooth, which supports the
consistency of the phenomenological description proposed for the
intermediate energy region. In order to appreciate the agreement with data
with more detail, two close-ups of Fig.~\ref{fig:2}, corresponding to the
low energy and the peak regions, are shown in Fig.~\ref{fig:3}.

It is worth to point out that the phenomenological form factor in
Eq.~(\ref{3rhosdisp}) is qualitatively similar to the GS
parametrization~\cite{Gounaris:1968mw} mentioned in the previous section.
Indeed, the GS form factor is built as a sum of Breit-Wigner-like
functions that keep a nontrivial real contribution in the corresponding
denominators:
\begin{equation}
\label{FV BWs}
F_V^{\pi {\rm (GS)}}(s) = \frac{1}{1 + \beta +\gamma }
      \left[BW_{\rho}^{\rm GS}(s) + \beta \, BW_{\rho^{\prime}}^{\rm GS}(s)
 +\gamma \, BW_{\rho^{\prime\prime}}^{\rm GS}(s)\right]\ ,
\label{gs1}
\end{equation}
where
\begin{equation}
\label{BWs}
BW_{R}^{\rm GS}(s) = \frac {M_{R}^2 \, ( 1 \, + \, d_R \,
\Gamma_{R}(s)/\sqrt{s}) }
       {(M_{R}^{2} - s) + f_R(s) - i M_R\, \Gamma_{R}(s)}\ ,
\end{equation}
and the coefficients $\beta$ and $\gamma$ are complex numbers. The
energy-dependent widths $\Gamma_R(s)$ are given, as in our approach, by
Eq.~(\ref{eq:rho1width}), while the expression for the (real) functions
$f_R(s)$ can be found in Ref.~\cite{Gounaris:1968mw}. The constants $d_R$
are chosen so that $BW_R^{\rm GS}(0) = 1$. As stated, this phenomenological
parametrization has been used in the fits carried out by the Belle
Collaboration~\cite{Achasov:2011ra}, allowing a quite successful description
of the data throughout the full spectrum. It is represented by the dashed
curve in Fig.~\ref{fig:2} (in the close-ups in Fig.~\ref{fig:3} our curve
and the GS curve overlap, and little differences can only be appreciated in
the peak region, where our curve shows a slightly better agreement with the
data). For comparison we also include in Figs.~\ref{fig:2} and \ref{fig:3}
the result obtained in Refs.~\cite{Guerrero:1997ku} and \cite{Pich:2001pj}.
The latter corresponds to a dispersive representation of the form factor in
the isospin limit, without the inclusion of excited resonant states (we have
refitted the parameters according to present Belle data).

\begin{figure}[!t]
\begin{center}
\vspace*{0.2cm}
\includegraphics[scale=0.45,angle=-90]{Matched.eps}
\caption[]{\label{fig:2}
\small{Pion vector form factor $F_V^{\pi}(s)$ compared to Belle data
\cite{Belle} (black dots). Solid and dashed lines correspond to our
description and the GS parametrization, respectively. The dashed-dotted
curve stands for the result from Ref.~\cite{Guerrero:1997ku} (for
$M_\rho=775$ MeV), while the dotted line corresponds to the dispersive
representation in Ref.~\cite{Pich:2001pj} (for $\alpha_1=1.83$ GeV$^{-2}$,
$\alpha_2=4.32$ GeV$^{-4}$ and $M_\rho=774.2$ MeV).}}
\end{center}
\end{figure}

\begin{figure}[h!]
\centering
\subfigure{
\includegraphics[scale=0.24,angle=-90]{Matched_low.eps}}
\hspace*{0.03cm}
\subfigure{
\includegraphics[scale=0.24,angle=-90]{Matched_peak.eps}}
\caption{\small{Two close-ups of Fig.~\ref{fig:2} are displayed,
corresponding to the low-energy region (left panel) and the peak region
(right panel).} \label{fig:3}}
\end{figure}

\section{Low-energy observables}\label{Low-E obs}

On the basis of the theoretical approach presented in Sect.~\ref{VFF low
E} we can obtain the values of chiral low energy observables. If the
expansion of the pion vector form factor in powers of $s$ is parametrized
as
\begin{equation}
F_V^\pi(s)\, = \, 1 \, + \, \frac{1}{6}\,\left\langle
r^2\right\rangle^\pi_V \,s \, + \, c_V^\pi\, s^2 \, + \, d_V^\pi \, s^3\, + \, \dots \ ,
\end{equation}
{}from Eq.~(\ref{FV_3_subtractions}) one has
\begin{equation}
 \left\langle r^2\right\rangle^\pi_V=6\,\alpha_1\ ,\quad
 c_V^\pi=\frac{1}{2}\left(\alpha_2+\alpha_1^2\right)\ .
\end{equation}
Taking into account the results of our fit (case III, i.e.~including
isospin-breaking corrections), we obtain
\begin{equation}
 \left\langle r^2\right\rangle^\pi_V = 10.86 \pm 0.14\ {\rm GeV}^{-2}\
 ,\quad c_V^\pi=3.84 \pm 0.03\ {\rm GeV}^{-4} \ .
\end{equation}
These values are indeed in good agreement with almost all previous
determinations made by several authors within various chiral models, see
Refs.~\cite{Bijnens:1998fm,Bijnens:2002hp,
Pich:2001pj, Truong:1998yx,
de Troconiz:2004tr,Masjuan:2008fv,Guo:2008nc,Aoki:2009qn,
Ananthanarayan:2011xt,Colangelo:1996hs}. In order to go beyond the $s^2$
term in the expansion, one can make use of the general relation
\begin{equation}
 \alpha_k = \frac{k!}{\pi}\int_{4m_\pi^2}^{\infty}
 \mathrm{d}s^\prime\ \frac{\delta_1^1(s^\prime)}{{s^\prime}^{k+1}}\ ,
 \label{general}
\end{equation}
which allows to determine the subsequent subtraction constants in the
Omn\`es expression (\ref{omel}). In this way we obtain $\alpha_3 = 29.2
\pm 0.2$~GeV$^{-6}$, which leads to
\begin{equation}
 d_V^\pi\, = \,\frac{1}{6}\,(\alpha_3+3\alpha_1\alpha_2+\alpha_1^3)\, =
 \, 9.84\pm 0.05\ {\rm GeV}^{-6}\ .
\end{equation}
Previous evaluations for this observable have been carried out in
Refs.~\cite{Truong:1998yx} and \cite{Ananthanarayan:2011xt}, leading to
$9.70 \pm 0.40$~GeV$^{-6}$ and $10.18 \pm 0.27$~GeV$^{-6}$, respectively.
In order to check the consistency of our procedure we have also calculated
the constant $\alpha_2$ from the general relation (\ref{general}),
obtaining $\alpha_2=(3.7\pm0.2)$ GeV$^{-4}$, in reasonable agreement with
the result of the fit. Notice that, even if Eq.~(\ref{general}) is exact,
one can expect some deviation from the fitted value of $\alpha_2$ owing to
the ad-hoc treatment of the phase shift above the inelastic threshold in
our analysis of the form factor. In the case of $\alpha_1$ we cannot trust
the result from Eq.~(\ref{general}) since the slow convergence of the
integral provides a large weight to this high energy contribution.

\begin{table*}[h!]
 \begin{center}
\begin{tabular}{|c|c|c|}
\hline
Reference & $r^V_{V_1}(M_\rho)\times10^3$& $r^V_{V_2}(M_\rho)\times10^4$\\
\hline
VMD \cite{Bijnens:1998fm} & $-0.25$ & $2.6$\\
$\mathcal{O}(p^6)$ $\chi$PT \cite{Bijnens:1998fm} & $-0.68(26)$ & $1.50(44)$\\
Pich and Portol\'es~\cite{Pich:2001pj} & $-0.79(19)$ & $1.46(3)$\\
Our result & $-0.91(16)$ & $1.49(1)$\\
\hline
\end{tabular}
\caption{ \small{Counterterm combinations extracted from $\left\langle
r^2\right\rangle^\pi_V$ and $c_V^\pi$ in $\mathcal{O}(p^6)$
$\chi$PT.}} \label{Tab:3}
\end{center}
\end{table*}

In addition, the observables $\left\langle r^2\right\rangle^\pi_V$ and
$c_V^\pi$ can be related to two counterterm combinations in the
$\mathcal{O}(p^6)$ chiral Lagrangian, namely $r^r_{V_1}(M_\rho)$ and
$r^r_{V_2}(M_\rho)$~\cite{Bijnens:1998fm}, which are dominated by the
vector resonance contributions $r^V_{V_1}(M_\rho)$ and
$r^V_{V_2}(M_\rho)$. Our results for these quantities are quoted in
Table~\ref{Tab:3}, showing a good agreement with the values previously
obtained in Ref.~\cite{Pich:2001pj} and in the $\mathcal{O}(p^6)$ $\chi$PT
fit in Ref.~\cite{Bijnens:1998fm}. Within VMD these counterterms can be
determined by integrating out vector resonances in the framework of a
chiral effective theory~\cite{Ecker:1988te}. Considering just the
contribution of the $\rho$ meson resonance, within the Proca formalism one
gets~\cite{Bijnens:1998fm}
\begin{equation}\label{rV's Proca}
r^V_{V_1} = 2\sqrt{2}\frac{F_\pi^2}{M_V^2}f_\chi f_V \ ,
\quad r^V_{V_2} = \frac{F_\pi^2}{M_V^2}g_V f_V \ ,
\end{equation}
where $f_V$, $g_V$ and $f_\chi$ are effective couplings in the chiral
Lagrangian with resonances. Our results for $r^V_{V_1}$ and $r^V_{V_2}$
would lead then to the ratio $f_\chi/g_V = -2.1\pm 0.5$, far from the
phenomenological value $f_\chi/g_V\simeq -0.33$~\cite{Bijnens:1998fm}.
This indicates that the role of heavier resonances is crucial in order to
describe the $\mathcal{O}(p^6)$ vector driven contributions in $\chi$PT,
in agreement with Ref.~\cite{Pich:2001pj}.

\section{Conclusions}
\label{Concl} The high quality data on the pion vector form factor
obtained at flavour factories demands a correspondingly improved analysis
from the theoretical side. In order to describe these data keeping the
connection with the underlying strong interaction dynamics, one can take
profit of QCD symmetries to reproduce the data in the very low energy
domain, and make use of general properties of quantum field theory to
extend the analysis to higher energies. In this spirit, we have presented
a dispersive representation of the charged pion vector form factor that
fulfills the constraints imposed by analyticity and unitarity, and reduces
to the result obtained within $\chi$PT at low energies.

Our construction is based on the dispersion relation between the form
factor and the $\delta_1^1(s)$ phase shift of elastic $\pi\pi$ scattering.
The phase shift is obtained from the leading contribution arising in the
large-$N_C$ expansion including $\rho(770)$ exchange up the onset of
inelasticities, with the further assumption of a smooth growth up to the
asymptotic value. In this way we obtain a theoretical expression for the
form factor in terms of four parameters, namely $M_\rho$, $F_\pi$, and two
subtraction constants $\alpha_1$ and $\alpha_2$. The values of these
parameters have been determined by performing a fit to the very precise
Belle data on the $\tau^-\to\pi^-\pi^0\nu_\tau$ spectral function up to a
squared $\pi\pi$ invariant mass $s_{\rm max}\simeq 1.5$ GeV$^2$, leading
to the results quoted in Table~\ref{Tab:1}. It is seen that the effect of
isospin corrections on the parameters lies below the two percent level.
From these results we have determined the pole values of the $\rho$ mass
and width and the so-called visible or peak $\rho$ mass. We have also
obtained the values of low energy observables and compared the results
with those arising from chiral effective theories.

In addition, we have addressed the energy region $s\geq s_{\rm max}\simeq
1.5$ GeV$^2$, in which the inclusion of excited states is necessary to get
a proper description of $\tau^-\to\pi^-\pi^0\nu_\tau$ data. For this region we
have proposed a phenomenological expression for the form factor that takes
into account the presence of the resonances $\rho'$ and $\rho''$, assuming
that the effective propagators behave in a similar way as that of the
$\rho$ meson. This allows a good fit to the data, leading to values for
the $\rho'$ and $\rho''$ masses and widths similar to those quoted in
previous works. It is seen that the curves for the form factor obtained
for both energy regions match smoothly at $s \sim s_{\rm max}$.

As a conclusion, we have seen that the $\chi$PT results at low energies
supplemented with the leading contributions in the large-$N_C$ expansion
are able to provide the input to a dispersive representation of the pion
vector form factor which fulfills analyticity and unitarity. On this basis,
complemented with a phenomenological description in the high energy
region, we have shown that it is possible to reproduce the very precise
data on $\tau^-\to\pi^-\pi^0\nu_\tau$ decays throughout all the phase
space. This can be used as input to the new hadronic currents of the
TAUOLA Monte Carlo generator. On the other hand, our fits lead to the
parametrization of the charged pion vector form factor, thus the
comparison with a precise determination of the neutral form factor would
provide robust information on the $\pi\pi$ contribution to the muon
anomalous magnetic moment.

\section*{Acknowledgements}
We are grateful to J.J.~Sanz-Cillero and J.~Portol\'es for a critical
reading of our manuscript, and to M. Davier, R.~Escribano, G. L\'opez
Castro, B.~Moussallam and A. Pich for illuminating discussions.
P.R.~acknowledges J.~Bijnens and M.~Jamin for useful explanations. We also
thank H.\ Hayashii and D.\ Epifanov for their valuable information on the
analysis carried out by the Belle Collaboration, and G.\ Toledo for his
help on the evaluation of isospin-breaking corrections. This work has been
partially supported by the Spanish grants FPA2007-60323, FPA2011-25948 and
by the Spanish Consolider Ingenio 2010 Programme CPAN (CSD2007-00042). It
has also been founded in part by CONICET and ANPCyT (Argentina), under
grants PIP02495 and PICT-2011-0113, respectively.

\section*{Appendix}

The explicit form of the loop functions $A_{PQ}(s)$ can be obtained from
Ref.~\cite{Gasser:1984ux}. One has
\begin{equation} \label{A_PQ}
 A_{PQ}(s)\,=\,-\frac{192\,\pi^2\,\left[s\,M_{PQ}(s)-L_{PQ}(s)\right]}{s}\,,
\end{equation}
where $M_{PQ}(s)$ and $L_{PQ}(s)$ can be written in terms of new functions
$\Sigma_{PQ}$, $\Delta_{PQ}$, $k_{PQ}$, $\bar{J}_{PQ}$ and $\tilde{J}_{PQ}$
as
\begin{eqnarray}
M_{PQ}(s) & = & \frac{1}{12\,s}(s-2\,\Sigma_{PQ})\,\bar{J}_{PQ}(s)+
\frac{\Delta_{PQ}^2}{3\,s^2}\tilde{J}_{PQ}(s)-\frac{1}{6}k_{PQ}+
\frac{1}{288\,\pi^2} \nonumber \\
 L_{PQ}(s) & = & \frac{\Delta_{PQ}^2}{4\,s}\,\bar{J}_{PQ}(s)\ .
\end{eqnarray}
The new functions $\Sigma_{PQ}$ and $\Delta_{PQ}$ are defined by
$\Sigma_{PQ}=m_P^2+m_Q^2$, $\Delta_{PQ}=m_P^2-m_Q^2$, while $k_{PQ}$
includes the renormalization scale $\mu$:
\begin{equation}
k_{PQ} = \frac{F_\pi^2}{\Delta_{PQ}}(\mu_P-\mu_Q) \ ,
\end{equation}
where
\begin{equation}
\mu_P = \frac{m_P^2}{32\,\pi^2\,F_\pi^2} \log
\left(\frac{m_P^2}{\mu^2}\right) \
\end{equation}
(we have taken $\mu = M_\rho$, as in the isospin symmetric case). Finally,
the functions $\bar J_{PQ}$ and $\tilde J_{PQ}$ are given by
\begin{eqnarray}
\tilde{J}_{PQ}(s) & = & \bar{J}_{PQ}(s)-s \bar{J}'_{PQ}(0)\nonumber \\
\bar{J}_{PQ}(s) & = & \frac{1}{32\,\pi^2}\left[ 2 +
\left(\frac{\Delta_{PQ}}{s} - \frac{\Sigma_{PQ}}{\Delta_{PQ}}\right)\log
\left(\frac{m_Q^2}{m_P^2}\right) - \right. \nonumber \\
& & \frac{\nu}{s}\log
\left.\left(\frac{(s+\nu)^2-\Delta_{PQ}^2}{(s-\nu)^2-
\Delta_{PQ}^2}\right)\right] \ ,
\end{eqnarray}
where $\nu=\lambda^{1/2}(s,m_P^2,m_Q^2)$. We note finally that
\begin{equation}
 s\,\bar{J}'_{PQ}(0)=\frac{s}{32\pi^2}
 \left(
 \frac{\Sigma_{PQ}}{\Delta_{PQ}^2}
 + 2\frac{M_P^2 M_Q^2}{\Delta_{PQ}^3} \log
 \frac{M_Q^2}{M_P^2}\right) \ .
\end{equation}

redpajama_set_name: RedPajamaArXiv


text:
In Vivo Analgesic Efficacy of Dehydrated-Rehydrated Liposomal Bupivacaine in a Mouse Model
Poster Discussion IV
E M Bolotin Department of Anesthesiology, New York University Medical Center, 550 First Avenue, New York, NY 10016 PubMed articlesGoogle scholar articles
B Piskoun Department of Anesthesiology, New York University Medical Center, 550 First Avenue, New York, NY 10016 PubMed articlesGoogle scholar articles
M Bansinath Department of Anesthesiology, New York University Medical Center, 550 First Avenue, New York, NY 10016 PubMed articlesGoogle scholar articles
H Turndorf Department of Anesthesiology, New York University Medical Center, 550 First Avenue, New York, NY 10016 PubMed articlesGoogle scholar articles
G J Grant Department of Anesthesiology, New York University Medical Center, 550 First Avenue, New York, NY 10016 PubMed articlesGoogle scholar articles
Bolotin EM, Piskoun B, Bansinath M, et al
Copyright © 1998 by the American Society of Regional Anesthesia (ASRA). Printed in the U.S.A. All rights reserved.


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