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Title: Mesons in strong magnetic fields: (I) General analyses

Abstract

Here, we study properties of neutral and charged mesons in strong magnetic fields |eB| >> Λ2QCD with ΛQCD being the QCD renormalization scale. Assuming long-range interactions, we examine magnetic-field dependences of various quantities such as the constituent quark mass, chiral condensate, meson spectra, and meson wavefunctions by analyzing the Schwinger–Dyson and Bethe–Salpeter equations. Based on the density of states obtained from these analyses, we extend the hadron resonance gas (HRG) model to investigate thermodynamics at large B. As B increases the meson energy behaves as a slowly growing function of the meson's transverse momenta, and thus a large number of meson states is accommodated in the low energy domain; the density of states at low temperature is proportional to B2. This extended transverse phase space in the infrared regime significantly enhances the HRG pressure at finite temperature, so that the system reaches the percolation or chiral restoration regime at lower temperature compared to the case without a magnetic field; this simple picture would offer a gauge invariant and intuitive explanation of the inverse magnetic catalysis.

Authors:
 [1];  [2];  [3]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States); Nishina Center, RIKEN, Saitama (Japan)
  2. Central China Normal Univ., Wuhan (China); Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
  3. Goethe-Univ. Frankfurt, Frankfurt am Main (Germany)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1254125
Report Number(s):
BNL-112145-2016-JA
Journal ID: ISSN 0375-9474; R&D Project: PO-3
Grant/Contract Number:  
SC00112704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nuclear Physics. A
Additional Journal Information:
Journal Volume: 951; Journal Issue: C; Journal ID: ISSN 0375-9474
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Riken BNL Research Center; strong magnetic fields; Meson structure; hadron resonance gas; inverse magnetic catalysis

Citation Formats

Hattori, Koichi, Kojo, Toru, and Su, Nan. Mesons in strong magnetic fields: (I) General analyses. United States: N. p., 2016. Web. doi:10.1016/j.nuclphysa.2016.03.016.
Hattori, Koichi, Kojo, Toru, & Su, Nan. Mesons in strong magnetic fields: (I) General analyses. United States. https://doi.org/10.1016/j.nuclphysa.2016.03.016
Hattori, Koichi, Kojo, Toru, and Su, Nan. 2016. "Mesons in strong magnetic fields: (I) General analyses". United States. https://doi.org/10.1016/j.nuclphysa.2016.03.016. https://www.osti.gov/servlets/purl/1254125.
@article{osti_1254125,
title = {Mesons in strong magnetic fields: (I) General analyses},
author = {Hattori, Koichi and Kojo, Toru and Su, Nan},
abstractNote = {Here, we study properties of neutral and charged mesons in strong magnetic fields |eB| >> Λ2QCD with ΛQCD being the QCD renormalization scale. Assuming long-range interactions, we examine magnetic-field dependences of various quantities such as the constituent quark mass, chiral condensate, meson spectra, and meson wavefunctions by analyzing the Schwinger–Dyson and Bethe–Salpeter equations. Based on the density of states obtained from these analyses, we extend the hadron resonance gas (HRG) model to investigate thermodynamics at large B. As B increases the meson energy behaves as a slowly growing function of the meson's transverse momenta, and thus a large number of meson states is accommodated in the low energy domain; the density of states at low temperature is proportional to B2. This extended transverse phase space in the infrared regime significantly enhances the HRG pressure at finite temperature, so that the system reaches the percolation or chiral restoration regime at lower temperature compared to the case without a magnetic field; this simple picture would offer a gauge invariant and intuitive explanation of the inverse magnetic catalysis.},
doi = {10.1016/j.nuclphysa.2016.03.016},
url = {https://www.osti.gov/biblio/1254125}, journal = {Nuclear Physics. A},
issn = {0375-9474},
number = C,
volume = 951,
place = {United States},
year = {Mon Mar 21 00:00:00 EDT 2016},
month = {Mon Mar 21 00:00:00 EDT 2016}
}

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Works referenced in this record:

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margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Wang, Ziyue; Zhuang, Pengfei</span> </li> <li> Physical Review D, Vol. 97, Issue 3</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/physrevd.97.034026" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/physrevd.97.034026<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/physrevd.94.114032" target="_blank" rel="noopener noreferrer" class="name">Electrical conductivity of quark-gluon plasma in strong magnetic fields<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2016-12-01">December 2016</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Hattori, Koichi; Satow, Daisuke</span> </li> <li> Physical Review D, Vol. 94, Issue 11</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/physrevd.94.114032" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/physrevd.94.114032<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/physrevd.96.094009" target="_blank" rel="noopener noreferrer" class="name">Bulk viscosity of quark-gluon plasma in strong magnetic fields<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2017-11-01">November 2017</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Hattori, Koichi; Huang, Xu-Guang; Rischke, Dirk H.</span> </li> <li> Physical Review D, Vol. 96, Issue 9</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/physrevd.96.094009" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/physrevd.96.094009<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span><span class="sr-only">Previous</span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span><span class="sr-only">Next</span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Cited By</a></li> <li class="small" style="margin-left:.75em; 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float:none;">[ × clear filter / sort ]</a> </div> <button type="submit" style="display:none;" aria-hidden="true" title="Submit"/> </form> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar records in OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="0" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/2274896" itemprop="url">50 Years of quantum chromodynamics</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Book</small><span class="authors"> <span class="author">Gross, Franz</span>; <span class="author">Klempt, Eberhard</span>; <span class="author">Brodsky, Stanley</span>; <span class="author">...</span> <span class="text-muted pubdata"></span> </span></div> <div class="abstract">AbstractQuantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, $$$$\alpha _s(Q^2)$$$$<mml:math> <mml:mrow> <mml:msub> <mml:mi> α </mml:mi> <mml:mi> s </mml:mi> </mml:msub> <mml:mrow> <mml:mo> ( </mml:mo> <mml:msup> <mml:mi> Q </mml:mi> <mml:mn> 2 </mml:mn> </mml:msup> <mml:mo> ) </mml:mo> </mml:mrow> </mml:mrow> </mml:math>, that varies with the energy scale $$Q^2$$<mml:math> <mml:msup> <mml:mi> Q </mml:mi> <mml:mn> 2 </mml:mn> </mml:msup> </mml:math> characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of $$$$\alpha _s$$$$<mml:math> <mml:msub> <mml:mi> α </mml:mi> <mml:mi> s </mml:mi> </mml:msub> </mml:math> at low momentum transfers limits perturbative calculations to the high-energy region where $$$$Q^2\gg \varLambda _{{\textrm{QCD}}} ^2\simeq $$$$<mml:math> <mml:mrow> <mml:msup> <mml:mi> Q </mml:mi> <mml:mn> 2 </mml:mn> </mml:msup> <mml:mo> ≫ </mml:mo> <mml:msubsup> <mml:mi> Λ </mml:mi> <mml:mrow> <mml:mtext> QCD </mml:mtext> </mml:mrow> <mml:mn> 2 </mml:mn> </mml:msubsup> <mml:mo> ≃ </mml:mo> </mml:mrow> </mml:math> (250 MeV)$$^2$$<mml:math> <mml:msup> <mml:mrow></mml:mrow> <mml:mn> 2 </mml:mn> </mml:msup> </mml:math>. Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large $$$$N_c$$$$<mml:math> <mml:msub> <mml:mi> N </mml:mi> <mml:mi> c </mml:mi> </mml:msub> </mml:math>-limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected $$$$q{{\bar{q}}}$$$$<mml:math> <mml:mrow> <mml:mi> q </mml:mi> <mml:mover> <mml:mrow> <mml:mi> q </mml:mi> </mml:mrow> <mml:mrow> <mml:mo> ¯ </mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, $$$$W^\pm $$$$<mml:math> <mml:msup> <mml:mi> W </mml:mi> <mml:mo> ± </mml:mo> </mml:msup> </mml:math> or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1140/epjc/s10052-023-11949-2" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="2274896" data-product-type="Book" data-product-subtype="" >https://doi.org/10.1140/epjc/s10052-023-11949-2</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/2274896" title="Link to document media" target="_blank" rel="noopener" data-ostiid="2274896" data-product-type="Book" data-product-subtype="" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/952987" itemprop="url">Condensates in Quantum Chromodynamics and the Cosmological Constant</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Brodsky, Stanley</span>; <span class="author">Shrock, Robert</span><span class="text-muted pubdata"> - Submitted to Nuclear Physics B</span> </span></div> <div class="abstract">Casher and Susskind have noted that in the light-front description, spontaneous chiral symmetry breaking in quantum chromodynamics (QCD) is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that, because of color confinement, quark and gluon QCD condensates are associated with the internal dynamics of hadrons. We discuss condensates using condensed matter analogues, the AdS/CFT correspondence, and the Bethe-Salpeter/Dyson-Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of 'in-hadron' condensates by Roberts et al., using the Bethe-Salpeter/Dyson-Schwinger formalism for QCD bound<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> states. These results imply that QCD condensates give zero contribution to the cosmological constant, since all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/952987" title="Link to document media" target="_blank" rel="noopener" data-ostiid="952987" data-product-type="Journal Article" data-product-subtype="FT" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1501855" itemprop="url">Intrinsic Transverse Motion of the Pion’s Valence Quarks</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Shi, Chao</span>; <span class="author">Cloët, Ian</span><span class="text-muted pubdata"> - Physical Review Letters</span> </span></div> <div class="abstract">Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's $$\mathcal{l}$$<sub>z</sub> = 0 and |$$\mathcal{l}$$<sub>z</sub>| = 1 leading Fock-state light-front wave functions (LFWFs) [labeled by $$\psi$$<sub>$$\mathcal{l}$$<sub>z</sub></sub>($$\mathcal{x}$$, $$\mathcal{k}$$$$2\atop{T}$$)]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction $$\mathcal{x}$$. The LFWFs have a nontrivial ($$\mathcal{x}$$, $$\mathcal{k}$$$$2\atop{T}$$)) dependence<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> and in general do not factorize into separate functions of each variable. For $$\mathcal{k}$$$$2\atop{T}$$ ≲ 1 GeV<sup>2</sup> the $$\mathcal{k}$$$$2\atop{T}$$ dependence of the LFWFs is well described by a Gaussian; however for $$\mathcal{k}$$$$2\atop{T}$$ ≳ 10 GeV<sup>2</sup> these LFWFs behave as $$\psi$$<sub>0</sub>∝ $$\mathcal{x}$$(1 - $$\mathcal{x}$$)/$$\mathcal{k}$$$$2\atop{T}$$ and $$\psi$$<sub>1</sub> ∝ $$\mathcal{x}$$(1 - $$\mathcal{x}$$)/$$\mathcal{k}$$$$4\atop{T}$$ and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. With this being said, the TMD evolution of our result is studied using both the <em>b*</em> and $$\zeta$$ prescriptions which allows a qualitative comparison with Drell-Yan data.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 18<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1103/PhysRevLett.122.082301" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1501855" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1103/PhysRevLett.122.082301</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1501855" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1501855" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/166444" itemprop="url">Electromagnetic pion form factor</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Technical Report</small><span class="authors"> <span class="author">Roberts, C.</span><span class="text-muted pubdata"></span> </span></div> <div class="abstract">A phenomenological Dyson-Schwinger/Bethe-Salpeter equation approach to QCD, formalized in terms of a QCD-based model field theory, the Global Color-symmetry Model (GCM), was used to calculate the generalized impulse approximation contribution to the electromagnetic pion form factor at space-like q{sup 2} on the domain [0,10] GeV{sup 2}. In effective field theories this form factor is sometimes understood as simply being due to Vector Meson Dominance (VMD) but this does not allow for a simple connection with QCD where the VMD contribution is of higher order than that of the quark core. In the GCM the pion is treated as a composite<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> bound state of a confined quark and antiquark interacting via the exchange of colored vector-bosons. A direct study of the quark core contribution is made, using a quark propagator that manifests the large space-like-q{sup 2} properties of QCD, parameterizes the infrared behavior and incorporates confinement. It is shown that the few parameters which characterize the infrared form of the quark propagator may be chosen so as to yield excellent agreement with the available data. In doing this one directly relates experimental observables to properties of QCD at small space-like-q{sup 2}. The incorporation of confinement eliminates endpoint and pinch singularities in the calculation of F{sub {pi}}(q{sup 2}). With asymptotic freedom manifest in the dressed quark propagator the calculation yields q{sup 4}F{sub {pi}}(q{sup 2}) = constant, up to [q{sup 2}]- corrections, for space-like-q{sup 2} {approx_gt} 35 GeV{sup 2}, which indicates that soft, nonperturbative contributions dominate the form factor at presently accessible q{sup 2}. This means that the often-used factorization Ansatz fails in this exclusive process. A paper describing this work was submitted for publication. In addition, these results formed the basis for an invited presentation at a workshop on chiral dynamics and will be published in the proceedings.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.2172/166444" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="166444" data-product-type="Technical Report" data-product-subtype="" >https://doi.org/10.2172/166444</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/166444" title="Link to document media" target="_blank" rel="noopener" data-ostiid="166444" data-product-type="Technical Report" data-product-subtype="" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/20695769" itemprop="url">Light scalar mesons in the improved ladder QCD</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Umekawa, Toru</span>; <span class="author">Naito, Kenichi</span>; <span class="author">Oka, Makoto</span>; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review. C, Nuclear Physics</span> </span></div> <div class="abstract">The light scalar meson spectrum is studied using the improved ladder QCD with the U{sub A}(1) breaking Kobayashi-Maskawa-'t Hooft interaction by solving the Schwinger-Dyson and Bethe-Salpeter equations. The dynamically generated momentum-dependent quark mass is large enough in the low momentum region to give rise to the spontaneous breaking of chiral symmetry. Due to the large dynamical quark mass, the scalar mesons become the qq bound states. Since the parameters have been all fixed to reproduce the light pseudoscalar meson masses and the decay constant, there is no free parameter in the calculation of the scalar mesons. We obtain M{sub {sigma}}=667<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> MeV, M{sub a{sub 0}}=942 MeV, and M{sub f{sub 0}}=1336 MeV. They are in good agreement with the observed masses of {sigma}(600), a{sub 0}(980), and f{sub 0}(1370), respectively. We therefore conclude that these states are the members of the light scalar meson nonet. The mass of K{sub 0}{sup *} is obtained between that of a{sub 0} and f{sub 0} and the corresponding state is not observed experimentally. We also find that the strangeness content in the {sigma} meson is about 5%.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1103/PhysRevC.70.055205" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20695769" data-product-type="Journal Article" data-product-subtype="" >https://doi.org/10.1103/PhysRevC.70.055205</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item d-block d-inline-small"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item"><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank" class="pure-menu-link">Vulnerability Disclosure Program</a></li> <li class="d-block d-lg-none mb-1"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook"></span><span class="sr-only">Facebook</span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter"></span><span class="sr-only">Twitter</span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play"></span><span class="sr-only">YouTube</span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/css/ostigov.fonts.240327.0425.css" rel="stylesheet"> <script src="/js/ostigov.240327.0425.js"></script><noscript></noscript> <script defer src="/js/ostigov.biblio.240327.0425.js"></script><noscript></noscript> <script async type="text/javascript" src="/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- OSTI.GOV v.240327.0425 --> </html>