5.2 vev of $\phi^2$

We had a new exponential in the fitting of the three particle correlator because $\langle 0|\phi^2| 0 \rangle\neq 0$ and so $\langle \phi |\phi^3| 0 \rangle\neq 0$

Operators:

• $O_3= \phi(0)\phi(0)\phi(0)$

• $O_3^{P_x}= \phi(p_x)\phi(0)\phi(0)$

• $O_3^{P_{xy}}= \phi(p_{xy})\phi(0)\phi(0)$

• $O_3^{P_{xyz}}= \phi(p_{xyz})\phi(0)\phi(0)$

• $O_3^{A1}= \sum_{i=x,y,z}\phi(0)\phi(p_i)\phi(-p_i)$

Correlators:

• $C_3=\langle O_3(0)O_3(t)\rangle$

  $$c_3(t)=|A_{3-0}|^2 \exp(-E_3 \frac{T}{2}) \cosh\left(E_3 (t-\frac{T}{2})\right)\\ +|A_{2-1}|^2 \exp(-(E_2+M) \frac{T}{2}) \cosh\left((E_2-M) (t-\frac{T}{2})\right)\\ +|A_{0-1}|^2 \exp(-(M) \frac{T}{2}) \cosh\left((M) (t-\frac{T}{2})\right)$$

• $C_3^{P1}=\sum_{i=x,y,z} \langle O_3^{P_i}(0)O_3^{P_i}(t)\rangle$

$$c_3^{P1}(t)=|A_{3-0}|^2 \exp(-E_3 \frac{T}{2}) \cosh\left(E_3 (t-\frac{T}{2})\right)\\ +|A_{2p-1}|^2 \exp(-(E_2(p)+M) \frac{T}{2}) \cosh\left((E_2(p)-M) (t-\frac{T}{2})\right)\\ +|A_{2-1p}|^2 \exp(-(E_2+E_1(p)) \frac{T}{2}) \cosh\left((E_2-E_1(p)) (t-\frac{T}{2})\right)\\ +|A_{0-1p}|^2 \exp(-E_1(p) \frac{T}{2}) \cosh\left(E_1(p) (t-\frac{T}{2})\right)$$

• $C_3^{P11}=\sum_{i=xy,yz,zx} \langle O_3^{P_i}(0)O_3^{P_i}(t)\rangle$

• $C_3^{P11}= \langle O_3^{P_{xyz}}(0)O_3^{P_{xyz}}(t)\rangle$

• $O_3^{A1}=\langle O_3^{A1}(0)O_3^{A1}(t)\rangle$

$$c_3^{A1}(t)=|A_{3-0}|^2 \exp(-E_3 \frac{T}{2}) \cosh\left(E_3 (t-\frac{T}{2})\right)+\\ |A_{2A1-1}|^2 \exp(-(E_{2A1}+M) \frac{T}{2}) \cosh\left((E_{2A1}-M) (t-\frac{T}{2})\right)+\\ |A_{2p-1p}|^2 \exp(-(E_2(p)+E_1(p)) \frac{T}{2}) \cosh\left((E_2(p)-E_1(p)) (t-\frac{T}{2})\right)+\\ |A_{1-0}|^2 \exp(-M \frac{T}{2}) \cosh\left( M (t-\frac{T}{2})\right)$$

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

E3_0_vev(L30T48) = 0.3961(10) 0.00018161(33) 0.0003(14) 0.0002232(56) $\chi^2/dof=$ 0.00092646

E3_0_p1_vev(L30T48) = 0.51533(74) 753.8(0.6)e-7 0.0008189(36) 0.00028(10) 38.8(0.2)e-6 $\chi^2/dof=$ 0.027218

E3_0_p11_vev(L30T48) = 0.5876(13) 661.1(0.8)e-7 0.0001563(89) 0.00037(19) 462.9(0.7)e-7 $\chi^2/dof=$ 0.064069

E3_0_p111_vev(L30T48) = 0.6449(29) 60.6(0.2)e-6 0.7(0.4)e-4 0.00077(29) 42.5(0.2)e-6 $\chi^2/dof=$ 0.03665

E3_0_A1_vev(L30T48) = 0.6364(56) 386.9(0.6)e-7 0.0(0.1)e-6 0.006092(20) 647.3(0.1)e-7 $\chi^2/dof=$ 0.15683

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

E3_0_vev(L30T96) = 0.39704(35) 0.000181081(57) -0.0(0.2)e-4 0.000222407(95) $\chi^2/dof=$ 0.0082145

E3_0_p1_vev(L30T96) = 0.51465(20) 753.6(0.1)e-7 0.012836(10) 0.0(0.2)e-1 460.4(0.1)e-7 $\chi^2/dof=$ 0.050572

E3_0_p11_vev(L30T96) = 0.58749(51) 659.3(0.3)e-7 0.00159(15) -0.00(17) 464.1(0.3)e-7 $\chi^2/dof=$ 0.023545

E3_0_p111_vev(L30T96) = 0.64648(51) 603.7(0.2)e-7 -0.0(0.3)e-3 -0.173(94) 424.9(0.2)e-7 $\chi^2/dof=$ 0.15361

E3_0_A1_vev(L30T96) = 0.63529(36) 3864.0(0.7)e-8 -0.0(0.1)e-5 1.5646(33) 6570.7(0.5)e-8 $\chi^2/dof=$ 0.13249

5.2.1 residual plot

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