θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit
Abstract The phase diagram on the θ-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the θ dependence of the deconfinement transition temperature, T c (θ), on the lattice through the constraint effective potential for Polyakov loop. The θ term is introduced by the reweight...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2022)044 |
| _version_ | 1827985423285092352 |
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| author | Noriaki Otake Norikazu Yamada |
| author_facet | Noriaki Otake Norikazu Yamada |
| author_sort | Noriaki Otake |
| collection | DOAJ |
| description | Abstract The phase diagram on the θ-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the θ dependence of the deconfinement transition temperature, T c (θ), on the lattice through the constraint effective potential for Polyakov loop. The θ term is introduced by the reweighting method, and the critical β is determined to θ ∼ 0.75, where the interpolation in β is carried out by the multipoint reweighting method. The θ dependence of T c obtained here turns out to be consistent with the previous result by D’Elia and Negro [1, 2]. We also derive T c (θ) by classifying configurations into the high and low temperature phases and applying the Clausius-Clapeyron equation. It is found that the potential barrier in the double well potential at T c (θ) becomes higher with θ, which suggests that the first order transition continues robustly above θ ∼ 0.75. Using information obtained here, we try to depict the expected θ dependence of the free energy density at T ≲ T c (0), which crosses the first order transition line at an intermediate value of θ. Finally, how the Lee-Yang zeros associated with the spontaneous CP violation appear is discussed formally in the large N limit, and the locations of them are found to be θ R θ I = 2 m + 1 π 2 n + 1 2 χ V 4 $$ \left({\theta}_R,{\theta}_I\right)=\left(\left(2m+1\right)\pi, \frac{2n+1}{2\chi {V}_4}\right) $$ with m and n arbitrary integers. |
| first_indexed | 2024-04-09T23:14:39Z |
| format | Article |
| id | doaj.art-e4f4df414d694f8c872e3194250a218d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:39Z |
| publishDate | 2022-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e4f4df414d694f8c872e3194250a218d2023-03-22T10:13:35ZengSpringerOpenJournal of High Energy Physics1029-84792022-06-012022612010.1007/JHEP06(2022)044θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limitNoriaki Otake0Norikazu Yamada1Graduate University for Advanced Studies (SOKENDAI)Graduate University for Advanced Studies (SOKENDAI)Abstract The phase diagram on the θ-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the θ dependence of the deconfinement transition temperature, T c (θ), on the lattice through the constraint effective potential for Polyakov loop. The θ term is introduced by the reweighting method, and the critical β is determined to θ ∼ 0.75, where the interpolation in β is carried out by the multipoint reweighting method. The θ dependence of T c obtained here turns out to be consistent with the previous result by D’Elia and Negro [1, 2]. We also derive T c (θ) by classifying configurations into the high and low temperature phases and applying the Clausius-Clapeyron equation. It is found that the potential barrier in the double well potential at T c (θ) becomes higher with θ, which suggests that the first order transition continues robustly above θ ∼ 0.75. Using information obtained here, we try to depict the expected θ dependence of the free energy density at T ≲ T c (0), which crosses the first order transition line at an intermediate value of θ. Finally, how the Lee-Yang zeros associated with the spontaneous CP violation appear is discussed formally in the large N limit, and the locations of them are found to be θ R θ I = 2 m + 1 π 2 n + 1 2 χ V 4 $$ \left({\theta}_R,{\theta}_I\right)=\left(\left(2m+1\right)\pi, \frac{2n+1}{2\chi {V}_4}\right) $$ with m and n arbitrary integers.https://doi.org/10.1007/JHEP06(2022)044Lattice QCDNon-Zero Temperature and DensityPhase Transitions1/N Expansion |
| spellingShingle | Noriaki Otake Norikazu Yamada θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit Journal of High Energy Physics Lattice QCD Non-Zero Temperature and Density Phase Transitions 1/N Expansion |
| title | θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit |
| title_full | θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit |
| title_fullStr | θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit |
| title_full_unstemmed | θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit |
| title_short | θ dependence of T c in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit |
| title_sort | θ dependence of t c in 4d su 3 yang mills theory with histogram method and the lee yang zeros in the large n limit |
| topic | Lattice QCD Non-Zero Temperature and Density Phase Transitions 1/N Expansion |
| url | https://doi.org/10.1007/JHEP06(2022)044 |
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