skip to main content

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Thursday, February 13 until 2:00 AM ET on Friday, February 14 due to maintenance. We apologize for the inconvenience.


This content will become publicly available on August 1, 2025

Title: Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects

We discuss numerical aspects of instantons in two- and three-dimensionalϕ4theories with an internalO(N)symmetry group, the so-calledN-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory inϕ4theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations.

Published by the American Physical Society2024 
more » « less
Award ID(s):
2110294
PAR ID:
10530889
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
American Physical Society
Date Published:
Journal Name:
Physical Review D
Volume:
110
Issue:
3
ISSN:
2470-0010
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We measure the branching fraction of the decayBD0ρ(770)using data collected with the Belle II detector. The data contain 387 millionBB¯pairs produced ine+ecollisions at theϒ(4S)resonance. We reconstruct8360±180decays from an analysis of the distributions of theBenergy and theρ(770)helicity angle. We determine the branching fraction to be(0.939±0.021(stat)±0.050(syst))%, in agreement with previous results. Our measurement improves the relative precision of the world average by more than a factor of two.

    Published by the American Physical Society2024 
    more » « less
  2. TheJ/ψμ+μμ+μdecay has been observed with a statistical significance in excess of five standard deviations. The analysis is based on an event sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of33.6fb1. Normalizing to theJ/ψμ+μdecay mode leads to a branching fraction of[10.12.7+3.3(stat)±0.4(syst)]×107, a value that is consistent with the standard model prediction.

    <supplementary-material><permissions><copyright-statement>© 2024 CERN, for the CMS Collaboration</copyright-statement><copyright-year>2024</copyright-year><copyright-holder>CERN</copyright-holder></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10514724-poles-poltergeists-e+edd-data" itemprop="url"> <span class='span-link' itemprop="name">Poles and poltergeists in e+e−→DD¯ data</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.109.114010" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.109.114010  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Hüsken, Nils</span> <span class="sep">; </span><span class="author" itemprop="author">Lebed, Richard F</span> <span class="sep">; </span><span class="author" itemprop="author">Mitchell, Ryan E</span> <span class="sep">; </span><span class="author" itemprop="author">Swanson, Eric S</span> <span class="sep">; </span><span class="author" itemprop="author">Wang, Ya-Qian</span> <span class="sep">; </span><span class="author" itemprop="author">Yuan, Chang-Zheng</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2024-06-01">June 2024</time> , Physical Review D) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>A recent report of<math display='inline'><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy='false'>→</mo><mi>D</mi><mover accent='true'><mi>D</mi><mo stretchy='false'>¯</mo></mover></math>events by the BESIII collaboration suggests the presence of a structure<math display='inline'><mi>R</mi></math>at 3900 MeV. We argue that this structure, called<math display='inline'><mi>G</mi><mo stretchy='false'>(</mo><mn>3900</mn><mo stretchy='false'>)</mo></math>in the past, is not in fact due to a new<math display='inline'><mi>c</mi><mover accent='true'><mi>c</mi><mo stretchy='false'>¯</mo></mover></math>resonance but rather naturally emerges due to a combination of interference between nearby resonances and the opening of the<math display='inline'><msup><mi>D</mi><mo>*</mo></msup><mover accent='true'><mi>D</mi><mo stretchy='false'>¯</mo></mover></math>channel. We further find that the appearance of this structure does not require suppression because of a radial node in the<math display='inline'><mi>ψ</mi><mo stretchy='false'>(</mo><mn>4040</mn><mo stretchy='false'>)</mo></math>wave function, although a node improves fit quality. The measured<math display='inline'><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>coupling of<math display='inline'><mi>ψ</mi><mo stretchy='false'>(</mo><mn>4040</mn><mo stretchy='false'>)</mo></math>is found to be substantially smaller than previously estimated. In addition, we report new corrections to the measured cross section<math display='inline'><mi>σ</mi><mo stretchy='false'>(</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy='false'>→</mo><mi>D</mi><mover accent='true'><mi>D</mi><mo stretchy='false'>¯</mo></mover><mo stretchy='false'>)</mo></math>at energies near<math display='inline'><mi>ψ</mi><mo stretchy='false'>(</mo><mn>3770</mn><mo stretchy='false'>)</mo></math>.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10514230-photoproduction-k+k-pairs-ultraperipheral-collisions" itemprop="url"> <span class='span-link' itemprop="name">Photoproduction of K+K− Pairs in Ultraperipheral Collisions</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevLett.132.222303" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevLett.132.222303  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Acharya, S</span> <span class="sep">; </span><span class="author" itemprop="author">Adamová, D</span> <span class="sep">; </span><span class="author" itemprop="author">Aglieri_Rinella, G</span> <span class="sep">; </span><span class="author" itemprop="author">Agnello, M</span> <span class="sep">; </span><span class="author" itemprop="author">Agrawal, N</span> <span class="sep">; </span><span class="author" itemprop="author">Ahammed, Z</span> <span class="sep">; </span><span class="author" itemprop="author">Ahmad, S</span> <span class="sep">; </span><span class="author" itemprop="author">Ahn, S U</span> <span class="sep">; </span><span class="author" itemprop="author">Ahuja, I</span> <span class="sep">; </span><span class="author" itemprop="author">Akindinov, A</span> <span class="sep">; </span><span class="author">et al</span></span> <span class="year">( <time itemprop="datePublished" datetime="2024-05-01">May 2024</time> , Physical Review Letters) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p><math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>pairs may be produced in photonuclear collisions, either from the decays of photoproduced<math display='inline'><mi>ϕ</mi><mo stretchy='false'>(</mo><mn>1020</mn><mo stretchy='false'>)</mo></math>mesons or directly as nonresonant<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>pairs. Measurements of<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>photoproduction probe the couplings between the<math display='inline'><mi>ϕ</mi><mo stretchy='false'>(</mo><mn>1020</mn><mo stretchy='false'>)</mo></math>and charged kaons with photons and nuclear targets. The kaon-proton scattering occurs at energies far above those available elsewhere. We present the first measurement of coherent photoproduction of<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>pairs on lead ions in ultraperipheral collisions using the ALICE detector, including the first investigation of direct<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>production. There is significant<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>production at low transverse momentum, consistent with coherent photoproduction on lead targets. In the mass range<math display='inline'><mrow><mn>1.1</mn><mo><</mo><msub><mrow><mi>M</mi></mrow><mrow><mi>K</mi><mi>K</mi></mrow></msub><mo><</mo><mn>1.4</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>above the<math display='inline'><mi>ϕ</mi><mo stretchy='false'>(</mo><mn>1020</mn><mo stretchy='false'>)</mo></math>resonance, for rapidity<math display='inline'><mrow><mo stretchy='false'>|</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>K</mi><mi>K</mi></mrow></msub><mo stretchy='false'>|</mo><mo><</mo><mn>0.8</mn></mrow></math>and<math display='inline'><msub><mi>p</mi><mrow><mi>T</mi><mo>,</mo><mi>K</mi><mi>K</mi></mrow></msub><mo><</mo><mn>0.1</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi>c</mi></math>, the measured coherent photoproduction cross section is<math display='inline'><mrow><mi mathvariant='normal'>d</mi><mi>σ</mi><mo>/</mo><mi mathvariant='normal'>d</mi><mi>y</mi><mo>=</mo><mn>3.37</mn><mo>±</mo><mn>0.61</mn><mo stretchy='false'>(</mo><mtext>stat</mtext><mo stretchy='false'>)</mo><mo>±</mo><mn>0.15</mn><mo stretchy='false'>(</mo><mi>syst</mi><mo stretchy='false'>)</mo><mtext> </mtext><mtext> </mtext><mi>mb</mi></mrow></math>. The center-of-mass energy per nucleon of the photon-nucleus (Pb) system<math display='inline'><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>γ</mi><mi>Pb</mi><mo>,</mo><mi>n</mi></mrow></msub></mrow></math>ranges from 33 to 188 GeV, far higher than previous measurements on heavy-nucleus targets. The cross section is larger than expected for<math display='inline'><mi>ϕ</mi><mo stretchy='false'>(</mo><mn>1020</mn><mo stretchy='false'>)</mo></math>photoproduction alone. The mass spectrum is fit to a cocktail consisting of<math display='inline'><mi>ϕ</mi><mo stretchy='false'>(</mo><mn>1020</mn><mo stretchy='false'>)</mo></math>decays, direct<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>photoproduction, and interference between the two. The confidence regions for the amplitude and relative phase angle for direct<math display='inline'><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math>photoproduction are presented.</p> <sec><supplementary-material><permissions><copyright-statement>© 2024 CERN, for the ALICE Collaboration</copyright-statement><copyright-year>2024</copyright-year><copyright-holder>CERN</copyright-holder></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10527120-measurement-cp-asymmetries-b0ks0ks0ks0-decays-belle-ii" itemprop="url"> <span class='span-link' itemprop="name">Measurement of CP asymmetries in B0→KS0KS0KS0 decays at Belle II</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.109.112020" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.109.112020  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Adachi, I</span> <span class="sep">; </span><span class="author" itemprop="author">Aggarwal, L</span> <span class="sep">; </span><span class="author" itemprop="author">Ahmed, H</span> <span class="sep">; </span><span class="author" itemprop="author">Aihara, H</span> <span class="sep">; </span><span class="author" itemprop="author">Akopov, N</span> <span class="sep">; </span><span class="author" itemprop="author">Aloisio, A</span> <span class="sep">; </span><span class="author" itemprop="author">Anh_Ky, N</span> <span class="sep">; </span><span class="author" itemprop="author">Asner, D M</span> <span class="sep">; </span><span class="author" itemprop="author">Atmacan, H</span> <span class="sep">; </span><span class="author" itemprop="author">Aushev, T</span> <span class="sep">; </span><span class="author">et al</span></span> <span class="year">( <time itemprop="datePublished" datetime="2024-06-01">June 2024</time> , Physical Review D) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <p>We report a measurement of decay-time-dependent charge-parity (<math display='inline'><mi>C</mi><mi>P</mi></math>) asymmetries in<math display='inline'><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy='false'>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math>decays. We use<math display='inline'><mrow><mn>387</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup></mrow></math><math display='inline'><mrow><mi>B</mi><mover accent='true'><mrow><mi>B</mi></mrow><mrow><mo stretchy='false'>¯</mo></mrow></mover></mrow></math>pairs collected at the<math display='inline'><mi mathvariant='normal'>ϒ</mi><mo stretchy='false'>(</mo><mn>4</mn><mi>S</mi><mo stretchy='false'>)</mo></math>resonance with the Belle II detector at the SuperKEKB asymmetric-energy electron-positron collider. We reconstruct 220 signal events and extract the<math display='inline'><mrow><mi>C</mi><mi>P</mi></mrow></math>-violating parameters<math display='inline'><mi>S</mi></math>and<math display='inline'><mi>C</mi></math>from a fit to the distribution of the decay-time difference between the two<math display='inline'><mi>B</mi></math>mesons. The resulting confidence region is consistent with previous measurements in<math display='inline'><mrow><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy='false'>→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math>and<math display='inline'><msup><mi>B</mi><mn>0</mn></msup><mo stretchy='false'>→</mo><mo stretchy='false'>(</mo><mi>c</mi><mover accent='true'><mi>c</mi><mo stretchy='false'>¯</mo></mover><mo stretchy='false'>)</mo><msup><mi>K</mi><mn>0</mn></msup></math>decays and with predictions based on the standard model.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> </div><div class="clearfix"></div> </div> </li> </ol> <div class="push_top"></div> </div> </div> <div class="col-md-3"> <div id="citation-sidebar"> <ul class="nav nav-list" id="citation-fulltext-sidebar" style="font-size: 14px; font-family: Georgia Regular;"> <li style="font-weight: bold; margin-bottom: 5px; font-size:13px;">Free Publicly Accessible Full Text</li> <li class="small"> This content will become publicly available on August 1, 2025</li> <li class="divider"></li> <li style="font-weight: bold;font-size:13px;">Journal Article:</li> <li style="word-break:break-all" class="small"> <a href="https://doi.org/10.1103/PhysRevD.110.036003" target="_blank" rel="noopener noreferrer" title="Document DOI URL" class="external-link" data-ostiid="10530889" style="word-wrap: break-word;">https://doi.org/10.1103/PhysRevD.110.036003  <span class="fas fa-external-link-alt"></span></a></li> </ul> <div class="hidden-print"> <ul class="nav nav-list clearfix" id="sidebar-feedback" style="margin-top: 20px; margin-bottom: 20px; clear: both;"> <li style="position: relative;"> <div class="feedback-container"> <div style="font-family: Georgia Regular; font-size: 14px; color: #313b52; padding:20px;"> Have feedback or suggestions for a way to improve these results?<br/> <span style="text-decoration: underline;"> <script type="text/javascript" defer>/* <![CDATA[ */ user = "feedback"; site = "research.gov"; subject = "?subject=Comments or Suggestions"; content = "<span class='fa fa-envelope'></span><span class='span-link' style='padding-left:5px'>Let us know</span>"; id = ""; document.write('<a itemprop="'+ id +'" href="mailto:' + user + '@' + site + subject + '">' + (content != '' ? content : (user + '@' + site)) + '</a>'); /* ]]> */</script> <noscript></noscript>!</span> </div> </li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Citation Formats</li> <li class="links-format"><a href="#cite-mla" data-toggle="modal">MLA</a> <div id="cite-mla" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-mla_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-mla_label">Cite: MLA Format</strong> </div> <div class="modal-body" >Giorgini, Ludovico T, Jentschura, Ulrich D, Malatesta, Enrico M, Rizzo, Tommaso, and Zinn-Justin, Jean. <em>Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects</em>. Retrieved from https://par.nsf.gov/biblio/10530889. <em>Physical Review D</em> 110.3 Web. doi:10.1103/PhysRevD.110.036003. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-apa" data-toggle="modal">APA</a> <div id="cite-apa" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-apa_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-apa_label">Cite: APA Format</strong> </div> <div class="modal-body">Giorgini, Ludovico T, Jentschura, Ulrich D, Malatesta, Enrico M, Rizzo, Tommaso, & Zinn-Justin, Jean. <em>Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects</em>. <em>Physical Review D</em>, <em>110</em> (3). Retrieved from https://par.nsf.gov/biblio/10530889. <a href="https://doi.org/10.1103/PhysRevD.110.036003">https://doi.org/10.1103/PhysRevD.110.036003</a> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-chi" data-toggle="modal">Chicago</a> <div id="cite-chi" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-chi_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-chi_label">Cite: Chicago Format</strong> </div> <div class="modal-body">Giorgini, Ludovico T, Jentschura, Ulrich D, Malatesta, Enrico M, Rizzo, Tommaso, and Zinn-Justin, Jean. "Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects". <em>Physical Review D</em> 110 (3). Country unknown/Code not available: American Physical Society. <a href="https://doi.org/10.1103/PhysRevD.110.036003">https://doi.org/10.1103/PhysRevD.110.036003.</a> <a href="https://par.nsf.gov/biblio/10530889">https://par.nsf.gov/biblio/10530889</a>. </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="links-format"><a href="#cite-bib" data-toggle="modal">BibTeX</a> <div id="cite-bib" class="modal" tabindex="-1" role="dialog" aria-labelledby="cite-bib_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="cite-bib_label">Cite: BibTeX Format</strong> </div> <div class="modal-body"> @article{osti_10530889,<br/> place = {Country unknown/Code not available}, title = {Instantons in ϕ4 theories: Transseries, virial theorems, and numerical aspects}, url = {https://par.nsf.gov/biblio/10530889}, DOI = {10.1103/PhysRevD.110.036003}, abstractNote = {We discuss numerical aspects of instantons in two- and three-dimensionalϕ4theories with an internalO(N)symmetry group, the so-calledN-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory inϕ4theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society2024}, journal = {Physical Review D}, volume = {110}, number = {3}, publisher = {American Physical Society}, author = {Giorgini, Ludovico T and Jentschura, Ulrich D and Malatesta, Enrico M and Rizzo, Tommaso and Zinn-Justin, Jean}, }</div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> </div> </div> </div> </div></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Export Metadata</li> <li class="links-format"><a href="https://par.nsf.gov/endnote?osti_id=10530889">EndNote</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:excel/osti-id:10530889">Excel</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:csv/osti-id:10530889">CSV</a></li> <li class="links-format"><a href="https://par.nsf.gov/export/format:xml/osti-id:10530889">XML</a></li> <li class="divider"></li> </ul> <ul class="nav nav-list" style="font-size: 14px; font-family: Arial Regular;"> <li class="nav-header header-format">Save / Share this Record</li> <li class="links-format"><a href="#shareemail" data-toggle="modal">Send to Email</a> <div id="shareemail" class="modal" tabindex="-1" role="dialog" aria-labelledby="shareemail_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <strong id="shareemail_label" style="margin: 0px;">Send to Email</strong> </div> <form id="sendtoemail-form" style="margin-bottom: 0px;"> <div class="modal-body" id="shareemail_body"> <div class="modal-body-default"> <label for="sendtoemail-email">Email address:</label><br/> <input type="text" name="email" value="" class="col-md-5 input-sm form-control" id="sendtoemail-email"/> <input type="hidden" name="osti_id" id="sendtoemail-osti_id" value="10530889" /> <input type="hidden" name="subject" id="sendtoemail-subject" /> <div class="clearfix"></div> <div class="hide"><label for="sendtoemail-body">Content:</label></div> <textarea name="body" id="sendtoemail-body" style="display:none;"></textarea> </div> <div class="modal-body-submitted hide"> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="submit" id="shareemail_submit"> <span class="fa fa-envelope"></span> Send </button> </div> </form> </div> </div> </div> </li> </ul> </div> <div class="push_top"></div> </div> </div> </div> </div> </div> </div> <input type="hidden" id="host_url" value="https://par.nsf.gov"/> <input type="hidden" id="base_url" value="/"/> <input type="hidden" id="param_osti_id" value="10530889"/> <span id="highlight-data"> </span> </div> </div> <footer class="row" id="footer-wrapper"> <div class="footer-content"> <div id="footerOSTI" class=" hidden-print"> <ul> <li><a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/">Website Policies</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/about/performance/">Budget and Performance</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/oig/">Inspector General</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/privacy.jsp">Privacy</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/foia.jsp">FOIA</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/od/odi/notice.jsp">No FEAR Act</a> | <a target="_blank" rel="noreferrer" href="http://usa.gov">USA.gov</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/access.jsp">Accessibility</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/policies/nsf_plain_language.jsp">Plain Language</a> | <a target="_blank" rel="noreferrer" href="http://www.nsf.gov/help/contact.jsp">Contact</a> | <a target="_blank" rel="noreferrer" href="https://nsf.gov/help/">Help</a> </li> </ul> The National Science Foundation, 2415 Eisenhower Avenue, Alexandria, Virginia 22314, USA Tel: (703) 292-5111, FIRS: (800) 877-8339 | TDD: (800) 281-8749 </div> </div> </footer> </div> <div id="authorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="authorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="authorselect_label">Author Select</div> </div> <form id="authorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="authorselect-pg" value="1" /> <div class="modal-body" id="authorselect_body"> <div class="row"> <div class="col-md-4"> <label for="authorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="authorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="authorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="authorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#authorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#authorselect-tab-res" id="authorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#authorselect-tab-sel" id="authorselect-tab-sel-btn" data-toggle="tab">Selected Authors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="authorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match authors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="authorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="authorselect-tab-sel-content">No authors are currently selected. Choosing "Select These Authors" will enter a blank value for author search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_review" onclick="$('#authorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="authorselect_submit" onclick="authorSelectAddToForm(); $('#authorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div id="editorselect" class="modal" tabindex="-1" role="dialog" aria-labelledby="editorselect_label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button> <div id="editorselect_label">Editor Select</div> </div> <form id="editorselect-form" style="margin-bottom: 0px;"> <input type="hidden" name="pg" id="editorselect-pg" value="1" /> <div class="modal-body" id="editorselect_body"> <div class="row"> <div class="col-md-4"> <label for="editorselect-lname">Last Name:</label><br /> <input type="text" name="lname" class="input-sm form-control" id="editorselect-lname" placeholder="Last name" /><br /> </div> <div class="col-md-4"> <label for="editorselect-fname">First Name:</label><br /> <input type="text" name="fname" class="input-sm form-control" id="editorselect-fname" placeholder="First name" /> </div> <div class="col-md-2">  <br /> <a href="#" onclick="$('#editorselect-form').submit(); return false;" class="btn btn-sm btn-default"><span class="fa fa-search"></span><span class="sr-only">Search</span></a> </div> </div> <div class="push_top"></div> <div class="row"> <div class="col-md-12"> <ul class="nav nav-tabs"> <li class="active"><a href="#editorselect-tab-res" id="editorselect-tab-res-btn" data-toggle="tab">Search Results</a></li> <li><a href="#editorselect-tab-sel" id="editorselect-tab-sel-btn" data-toggle="tab">Selected Editors</a></li> </ul> <div class="tab-content"> <div class="tab-pane active" id="editorselect-tab-res" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-res-content">Type in a name, or the first few letters of a name, in one or both of appropriate search boxes above and select the search button. An attempt will be made to match editors that most closely relate to the text you typed.</div> </div> <div class="tab-pane" id="editorselect-tab-sel" style="max-height: 450px;"> <div class="padding text-muted" id="editorselect-tab-sel-content">No editors are currently selected. Choosing "Select These Editors" will enter a blank value for editor search in the parent form.</div> </div> </div> </div> </div> </div> <div class="modal-footer"> <button class="btn btn-sm btn-default" data-dismiss="modal" aria-hidden="true">Close</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_review" onclick="$('#editorselect-tab-sel-btn').click();" style="display: none;">Review Selections</button> <button class="btn btn-sm btn-default" aria-hidden="true" type="button" id="editorselect_submit" onclick="editorSelectAddToForm();$('#editorselect').modal('hide');">Add Selections</button> </div> </form> </div> </div> </div> <div class="push_top"></div> <!-- External Link Modal --> <div class="modal fade" id="external-link-modal" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close nsf-close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> <h4 class="modal-title"><strong>Warning: Leaving National Science Foundation Website</strong></h4> </div> <div class="modal-body"> <div> <img src="https://par.nsf.gov/img/nsf/nsf_logo.png" width="292" height="53" alt="National Science Foundation Logo" border="0" /> </div> <br> <span>You are now leaving the National Science Foundation website to go to a non-government website.</span> <br> <br> Website: <a id="external-link-url" rel='noopener noreferrer' target='_blank'></a> <br> <br> <span> NSF takes no responsibility for and exercises no control over the views expressed or the accuracy of the information contained on this site. Also be aware that NSF's privacy policy does not apply to this site. </span> <br> <br> </div> <div class="modal-footer"> <div class="pull-right"> <button id="external-link-continue" type="button" data-extlink="" class="btn btn-primary" data-dismiss="modal"><u>Continue to Site</u></button> <button type="button" class="btn btn-default" data-dismiss="modal"><u>Cancel</u></button> </div> </div> </div> </div> </div> <!-- /content --> <input type='hidden' id='webtrend-id' value='dcsngbilzcxafpc7vw2qgbbij_3j2v'/> <input type='hidden' id='js-context-path' value='https://par.nsf.gov/'/> <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/latest.js?config=TeX-MML-AM_CHTML" defer></script> <script type="text/x-mathjax-config" defer> MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]} }); </script> <noscript></noscript> <script src="https://par.nsf.gov/js/context.js" type="text/javascript" defer></script> <noscript>You must have javascript enabled</noscript> <script src="https://par.nsf.gov/js/libraries/jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/chosen/chosen.jquery.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.extras.min.js" type="text/javascript" defer></script> <noscript></noscript> <script src="https://par.nsf.gov/js/nsf_pages.min.js" type="text/javascript" defer></script> <noscript></noscript> <!--$$$$$$$$$ the following blocks are for WebTrends $$$$$$$$--> <!-- START OF SmartSource Data Collector TAG --> <!-- Copyright (c) 1996-2009 WebTrends Inc. All rights reserved. --> <!-- Version: 8.6.2 --> <!-- Tag Builder Version: 3.0 --> <!-- Created: 5/7/2009 8:32:37 PM --> <script src="https://par.nsf.gov/js/webtrends.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- ----------------------------------------------------------------------------------- --> <!-- Warning: The two script blocks below must remain inline. Moving them to an external --> <!-- JavaScript include file can cause serious problems with cross-domain tracking. --> <!-- ----------------------------------------------------------------------------------- --> <script src="https://par.nsf.gov/js/webtrend-script.min.js" type="text/javascript" defer></script> <noscript> <div><img alt="" id="DCSIMG" width="1" height="1" src="http://wt.research.gov/dcsngbilzcxafpc7vw2qgbbij_3j2v/njs.gif?dcsuri=/nojavascript&WT.js=No&DCS.dcscfg=1&WT.tv=8.6.2"/></div> </noscript> <script src="https://par.nsf.gov/js/webtrendsactions.min.js" type="text/javascript" defer></script> <noscript></noscript> <!-- $$$$$$$$ End WebTrends $$$$$ --> <!-- /scripts --> </body> <!-- NSF PAGES v.@project.version@ --> </html>