In this work, we present a lattice QCD calculation of two closely related quantities: 1). The ππ scattering phase shift for both π°=0 and π°=2 channels at seven energies in total, and 2). The ππ°=1/2, π« β ππ decay amplitude π΄β and πβ², the measure of direct CP violation. These two results improve our earlier calculation presented in 2015 [1]. The calculation is performed on an ensemble of 32Β³ Γ 64 lattice with πΌβ»ΒΉ=1.3784(68)GeV. This is a physical calculation, where the chiral symmetry breaking is controlled by the 2+1 flavor MΓΆbius Domain Wall Fermion, and we take the physical value for both kaon and pion. The G-parity boundary condition is used and carefully tuned so that the ground state energy of the ππβββ state matches the kaon mass. Three sets of ππ interpolating operators are used, including a scalar bilinear ``Ο" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fits and a bootstrap determination of the π-value have been used, and a detailed analysis of all major systematic error is performed. The ππ scattering phase shift results are presented in Fig. 5.10 and Tab. 5.12. For the Kaon decay amplitude, we finally get Re(π΄β) = 2.99(0.32)(0.59) Γ 10β»β·GeV, which is consistent with the experimental value of Re(π΄β) = 3.3201(18) Γ 10β»β·GeV, and Im(π΄β) = -6.98(0.62)(1.44) Γ 10β»ΒΉΒΉGeV. Combined with our earlier lattice calculation of π΄β [2], we obtained Re(πβ²/π) = 21.7(2.6)(6.2)(5.0) Γ 10β»β΄, which agrees well with the experimental value of Re(πβ²/π) = 16.6(2.3) Γ 10β»β΄, and Re(π΄β)/Re(π΄β) = 19.9(2.3)(4.4), consistent with the experimental value of Re(π΄β)/Re(π΄β) = 22.45(6), known as the ππ°=1/2 rule.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-tskp-ka68 |
| Date | January 2021 |
| Creators | Wang, Tianle |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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