6.1 time ordering 1

The matrix element $\langle \phi_1|\phi_1\phi_0^3|3\phi_0 \rangle$ can be extracted from the correlator

$$\langle \phi_1(t_f)\phi_1\phi_0^3(t) \phi_0(0)^3 \rangle \to \langle 0|\phi_1|\phi_1 \rangle \langle \phi_1| \phi_1 \phi_0^3 |3 \phi_0\rangle \langle 3\phi_0|\phi_0^3|0 \rangle e^{{-E_{\phi_1}(t_f)}+{(E_{\phi_1}-E_{3\phi_0})t} } \\+ \langle \phi_0|\phi_1|\phi_0\phi_1 \rangle \langle \phi_0\phi_1| \phi_1 \phi_0^3 |2 \phi_0\rangle \langle 2\phi_0|\phi_0^3|\phi_0 \rangle e^{\color{blue}{-E_{\phi_1\phi_0}(t_f)-E_{\phi_0}(T-t_f)}+\color{red}{(E_{\phi_1\phi_0}-E_{2\phi_0})t} } \\+ \langle 2\phi_0|\phi_1|2\phi_0\phi_1 \rangle \langle 2\phi_0\phi_1| \phi_1 \phi_0^3 | \phi_0\rangle \langle \phi_0|\phi_0^3|2\phi_0 \rangle e^{\color{blue}{-E_{\phi_12\phi_0}(t_f)-E_{2\phi_0}(T-t_f)}+\color{red}{(E_{\phi_12\phi_0}-E_{\phi_0})t} }\,.$$ suppressed, enanched.

We can remove the unwanted matrix elements considering the ratio $$\frac{\langle \phi_1(t_f)\phi_1\phi_0^3(t) \phi_0(0)^3 \rangle } {\sqrt{\langle \phi_1(t_f)\phi_1(t)\rangle \langle \phi_0^3(t) \phi_0(0)^3 \rangle}} =\langle \phi_1| \phi_1 \phi_0^3 |3 \phi_0\rangle e^{-\frac{E_{\phi_1}}{2}(t_f-t)-\frac{E_{3\phi_0}}{2}t }$$

6.1.1 T48

6.1.1.1 ../out/G2t_T48_L30_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.000000_rep0_output

me_T_2(L30T48) = 1.8(0.3)e-5 $\chi^2/dof=$ 1.271

me_t10(L30T48) = 91.9(0.6)e-7 $\chi^2/dof=$ 4734.1

me_t12(L30T48) = 108.6(0.9)e-7 $\chi^2/dof=$ 1932.5

me_t16(L30T48) = 11.1(0.2)e-6 $\chi^2/dof=$ 72.8

6.1.1.2 ../out/G2t_T96_L30_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.000000_rep0_output

me_T_2(L30T96) = 1 $\chi^2/dof=$ -nan

me_t10(L30T96) = 90.7(0.4)e-7 $\chi^2/dof=$ 8306.9

me_t12(L30T96) = 104.9(0.6)e-7 $\chi^2/dof=$ 3425

me_t16(L30T96) = 10.7(0.2)e-6 $\chi^2/dof=$ 106.32

6.1.2 T32

6.1.2.1 ../out/G2t_T32_L30_msq0-4.900000_msq1-4.650000_l02.500000_l12.500000_mu5.000000_g0.000000_rep0_output

me_T_2(L30T32) = 16.8(0.2)e-6 $\chi^2/dof=$ 641

me_t10(L30T32) = 93.0(0.7)e-7 $\chi^2/dof=$ 2661.1

me_t12(L30T32) = 11.1(0.1)e-6 $\chi^2/dof=$ 1679

me_t16(L30T32) = 11.2(0.2)e-6 $\chi^2/dof=$ 71.916