QCD isospin breaking<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>χ</mml:mi></mml:math>PT low-energy constants from the instanton vacuum

We investigate the (partial) chiral restoration at finite temperature ðTÞ under the strong external magnetic field B ¼ B 0ẑ of the SU(2) light-flavor QCD matter. To this end, we employ the instantonliquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington-Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size ð " Þ and interinstanton distance ð " RÞ, as functions of T. In addition, we include the meson-loop corrections as the large-N c corrections because they are critical for reproducing the universal chiral-restoration pattern. We present the numerical results for the constituent-quark mass as well as chiral condensate, which signal the spontaneous breakdown of chiral-symmetry (SBS), as functions of T and B 0 . From our results we observe that the strengths of those chiral order parameters are enhanced with respect to B 0 due to the magnetic-catalysis effect. We also find that there appears a region where the u and d-quark constituent masses coincide with each other at eB 0 % ð7-9Þm 2 , even in the presence of the explicit isospin breaking (m u Þ m d ). The critical T for the chiral restoration T c tends to shift to the higher temperature in the presence of the B 0 for the chiral limit but keeps almost stationary for the physical quark mass case. The strength of the isospin breaking between the quark condensates is also explored in detail by defining the ratio R ðhiu y ui À hid y diÞ=ðhiu y ui þ hid y diÞ, which indicates the competition between the explicitly isospin-breaking effect and magnetic-catalysis effect. We also compute the pion weak-decay constant F and pion mass m below T c , varying the strength of the magnetic field, showing correct partial chiral-restoration behaviors. Besides we find that the changes for the F and m due to the magnetic field is relatively small, in comparison to those caused by the finite T effect.

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“…We also note that the ratio R is deeply related to the lowenergy constant of the PT Lagrangian, h 3 [42,43].…”

Section: Ea With Mlc and B Fieldmentioning

confidence: 81%

“…We choose " R % 1:0 fm and " % 0:34 fm which give M f % 315 MeV in the present framework [43]. The values for the current-quark mass are reported as m u ¼ ð1:7-3:3Þ MeV and m d ¼ ð4:1-5:8Þ MeV [46].…”

Section: Numerical Resultsmentioning

confidence: 99%

Chiral restoration at finiteTunder the magnetic field with the meson-loop corrections

Nam

Kao

2011

Phys. Rev. D

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“…In such a way, ILM succeeded explaining the hadron physics at the light quark sector (see reviews [5][6][7] and Refs. [8][9][10][11][12]).…”

Section: Ilm Parameters Vs Hadron Quark Core Sizesmentioning

confidence: 99%

“…where r is a distance between Q andQ quarks and M g ðqÞ is given by Eq. (10). After the angular integration and introducing the dimensionless variables, x ¼ r=ρ and y ¼ qρ, one can obtain the perturbative one-gluon exchange potential in the form of…”

Section: B Perturbative One-gluon Exchange Singlet Potential In Ilmmentioning

confidence: 99%

“…Here, it is necessary to note that the light quark sector of hadronic physics is successfully described by means of a spontaneous breakdown of chiral symmetry in the framework of an instanton liquid model of QCD vacuum (ILM) (see reviews [5][6][7] and Refs. [8][9][10][11][12]). One may also expect that the nonperturbative effects on the heavy quark propagation in the instanton medium still may be substantial at last but not least.…”

Section: Introductionmentioning

confidence: 99%

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Heavy quark correlators in an instanton liquid model with perturbative corrections

2020

Self Cite

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In the present work, we consider the influence on the heavy quark correlators due to the instanton background in the framework of instanton liquid model (ILM) of QCD vacuum by taking into account also the perturbative gluon effects. For a single heavy quark, this leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. In the heavy quark-antiquark (QQ) sector, we obtain the potential consisting the direct instanton induced part and the one-gluon exchange (OGE) perturbative part, which is screened at large distances due to the nonperturbative dynamics. At the region of interest corresponding to the heavy quark physics, the screening effect in OGE can be well approximated by a Yukawa-type potential in terms of the dynamically generated gluon mass. A possible implication of the present studies to the phenomenology of heavy quarkonium is also discussed.

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Gluons, Heavy and Light Quarks in the QCD Vacuum

Musakhanov

2018

EPJ Web Conf.

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Abstract. We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size ∼ 0.3 f m. We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size ρ ≈ 0.3 f m and average inter-instanton distance R ≈ 1 f m, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass M ∼ (packing f raction) 1/2 ρ −1 ≈ 360 MeV, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass M g ≈ M. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by ∆m Q ∼ packing f raction ρ −1 ≈ 70 MeV. Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass M g . Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.

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QCD isospin breakingχPT low-energy constants from the instanton vacuum

Cited by 6 publications

References 35 publications

Chiral restoration at finiteTunder the magnetic field with the meson-loop corrections

Chiral restoration at finiteTunder the magnetic field with the meson-loop corrections

Heavy quark correlators in an instanton liquid model with perturbative corrections

Gluons, Heavy and Light Quarks in the QCD Vacuum

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