scholarly journals Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Martin A. Mojahed
Keyword(s):  
Perturbation Theory ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Strange Quark ◽  
Chemical Potential ◽  
Light Quark ◽  
Quark Condensate ◽  
Lattice Data ◽  
Chiral Perturbation ◽  
Good Agreement

AbstractWe calculate the light-quark condensate, the strange-quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($$\chi $$ χ PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $$\chi $$ χ PT effective potential and condensates can be mapped onto two-flavor $$\chi $$ χ PT ones by integrating out mesons with strange-quark content (kaons and eta), with renormalized couplings. We compare the results for the light-quark and pion condensates at finite pseudoscalar source with ($$2+1$$ 2 + 1 )-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light-quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

scholarly journals Chiral Perturbation Theory for Three-Flavour Lattice QCD with Isospin Splitting

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
S. Engelnkemper ◽  
G. Münster
Keyword(s):  
Perturbation Theory ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Lattice Spacing ◽  
Light Quark ◽  
Mass Difference ◽  
Finite Lattice ◽  
Chiral Perturbation ◽  
Isospin Splitting ◽  
The Masses

An important tool for the analysis of results of numerical simulations of lattice QCD is chiral perturbation theory. In the Wilson chiral perturbation theory the effects of the finite lattice spacingaare taken into account. In recent years the effects of isospin splitting on the masses of hadrons have been investigated in the Monte Carlo simulations. Correspondingly, in this paper we derive the expansions of the masses of the pseudoscalar mesons in chiral perturbation theory at next-to-leading order for twisted mass lattice QCD with three light quark flavours, taking the mass difference between the up- and downquarks into account. The results include terms up to ordersmq2in the quark masses,Δm2in the mass splitting between up- and downquarks, anda2in the lattice spacing, respectively.

scholarly journals Nucleon’s energy–momentum tensor form factors in light-cone QCD

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
K. Azizi ◽  
U. Özdem
Keyword(s):  
Perturbation Theory ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Light Cone ◽  
Energy Momentum Tensor ◽  
Form Factors ◽  
Momentum Tensor ◽  
Tensor Form ◽  
Chiral Perturbation ◽  
Theoretical Predictions

Abstract We use the energy–momentum tensor (EMT) current to compute the EMT form factors of the nucleon in the framework of the light cone QCD sum rule formalism. In the calculations, we employ the most general form of the nucleon’s interpolating field and use the distribution amplitudes (DAs) of the nucleon with two sets of the numerical values of the main input parameters entering the expressions of the DAs. The directly obtained results from the sum rules for the form factors are reliable at $$ Q^2\ge 1$$Q2≥1 GeV$$^2 $$2: to extrapolate the results to include the zero momentum transfer squared with the aim of estimation of the related static physical quantities, we use some fit functions for the form factors. The numerical computations show that the energy–momentum tensor form factors of the nucleon can be well fitted to the multipole fit form. We compare the results obtained for the form factors at $$ Q^2=0 $$Q2=0 with the existing theoretical predictions as well as experimental data on the gravitational form factor d$$_1^q(0)$$1q(0). For the form factors M$$_2^q (0)$$2q(0) and J$$^q(0)$$q(0) a consistency among the theoretical predictions is seen within the errors: our results are nicely consistent with the Lattice QCD and chiral perturbation theory predictions. However, there are large discrepancies among the theoretical predictions on d$$_1^q(0)$$1q(0). Nevertheless, our prediction is in accord with the JLab data as well as with the results of the Lattice QCD, chiral perturbation theory and KM15-fit. Our fit functions well define most of the JLab data in the interval $$ Q^2\in [0,0.4]$$Q2∈[0,0.4] GeV$$^2 $$2, while the Lattice results suffer from large uncertainties in this region. As a by-product, some mechanical properties of the nucleon like the pressure and energy density at the center of nucleon as well as its mechanical radius are also calculated and their results are compared with other existing theoretical predictions.

scholarly journals The nucleon mass in Nf=2 lattice QCD: finite size effects from chiral perturbation theory

2004 ◽  
Vol 689 (3) ◽  
pp. 175-194 ◽  
Author(s):  
A. Ali Khan ◽  
T. Bakeyev ◽  
M. Göckeler ◽  
T.R. Hemmert ◽  
R. Horsley ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Size Effects ◽  
Finite Size ◽  
Nucleon Mass ◽  
Chiral Perturbation ◽  
Finite Size Effects

Resonant and non-resonant contributions of B → K∗(p1,𝜖1){Kπ,ππ,KK} decay modes

2019 ◽  
Vol 34 (06) ◽  
pp. 1950043
Author(s):  
Mahboobeh Sayahi
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Branching Ratio ◽  
Heavy Meson ◽  
Chiral Perturbation ◽  
Decay Modes ◽  
Qcd Factorization ◽  
Three Body ◽  
Good Agreement

In this paper, the non-leptonic three-body decays [Formula: see text], [Formula: see text], [Formula: see text] are studied by introducing two-meson distribution amplitude for the [Formula: see text], [Formula: see text] and [Formula: see text] pairs in naive and QCD factorization (QCDF) approaches, such that the analysis is simplified into quasi-two body decays. By considering that the vector meson is being ejected in factorization, the resonant and non-resonant contributions are analyzed by using intermediate mesons in Breit–Wigner resonance formalism and the heavy meson chiral perturbation theory (HMChPT), respectively. The calculated values of the resonant and non-resonant branching ratio of [Formula: see text], [Formula: see text] and [Formula: see text] decay modes are compared with the experimental data. For [Formula: see text] and [Formula: see text], the non-resonant contributions are about 70–80% of experimental data, for which the total results by considering resonant contributions are in good agreement with the experiment.

scholarly journals Two-flavor chiral perturbation theory at nonzero isospin: pion condensation at zero temperature

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen ◽  
Patrick Kneschke
Keyword(s):  
Perturbation Theory ◽  
Equation Of State ◽  
Condensed Phase ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Tree Level ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensation

Abstract In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state.  We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2 + 1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in $$\chi $$χPT.

scholarly journals Quark and pion condensates at finite isospin density in chiral perturbation theory

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Prabal Adhikari ◽  
Jens O. Andersen
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chemical Potential ◽  
Chiral Condensate ◽  
Zero Temperature ◽  
Leading Order ◽  
Chiral Perturbation ◽  
Pion Condensate ◽  
Independent Analysis ◽  
Model Independent

AbstractIn this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential $$\mu _I$$ μ I using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results. Agreement with lattice results generally improves as one goes from leading order to next-to-leading order.

scholarly journals The Leutwyler–Smilga relation on the lattice

2019 ◽  
Vol 35 (01) ◽  
pp. 1950346 ◽  
Author(s):  
Gernot Münster ◽  
Raimar Wulkenhaar
Keyword(s):  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Effective Action ◽  
Lattice Spacing ◽  
Chiral Perturbation ◽  
Quark Masses

According to the Leutwyler–Smilga relation, in Quantum Chromodynamics (QCD), the topological susceptibility vanishes linearly with the quark masses. Calculations of the topological susceptibility in the context of lattice QCD, extrapolated to zero quark masses, show a remnant nonzero value as a lattice artefact. Employing the Atiyah–Singer theorem in the framework of Symanzik’s effective action and chiral perturbation theory, we show the validity of the Leutwyler–Smilga relation in lattice QCD with lattice artefacts of order a2 in the lattice spacing a.

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