FeynCalc manual (development version)

B11

B11[pp, ma^2, mb^2] is the Passarino-Veltman B11B_{11}-function, i.e. the coefficient function of pμpνp^{\mu } p^{\nu }. All arguments are scalars and have dimension mass squared.

See also

Overview, B0, B00, B1, PaVe.

Examples

B11[SPD[p], m^2, M^2]

(Dm42Dm2M2+2Dm2p2+DM42DM2p2+Dp44m2p2)  B0(p2,m2,M2)4(1D)p4+D  A0(m2)(m2M2+p2)4(1D)p4A0(M2)(Dm2DM2+3Dp24p2)4(1D)p4-\frac{\left(D m^4-2 D m^2 M^2+2 D m^2 p^2+D M^4-2 D M^2 p^2+D p^4-4 m^2 p^2\right) \;\text{B}_0\left(p^2,m^2,M^2\right)}{4 (1-D) p^4}+\frac{D \;\text{A}_0\left(m^2\right) \left(m^2-M^2+p^2\right)}{4 (1-D) p^4}-\frac{\text{A}_0\left(M^2\right) \left(D m^2-D M^2+3 D p^2-4 p^2\right)}{4 (1-D) p^4}

B11[SPD[p], m^2, M^2, BReduce -> False]

B11(p2,m2,M2)\text{B}_{11}\left(p^2,m^2,M^2\right)

B11[SPD[p], m^2, m^2]

(4m2Dp2)  B0(p2,m2,m2)4(1D)p2+(2D)  A0(m2)2(1D)p2\frac{\left(4 m^2-D p^2\right) \;\text{B}_0\left(p^2,m^2,m^2\right)}{4 (1-D) p^2}+\frac{(2-D) \;\text{A}_0\left(m^2\right)}{2 (1-D) p^2}

B11[SPD[p], m^2, m^2, BReduce -> False]

B11(p2,m2,m2)\text{B}_{11}\left(p^2,m^2,m^2\right)

B11[0, m^2, m^2]

13  B0(0,m2,m2)\frac{1}{3} \;\text{B}_0\left(0,m^2,m^2\right)

B11[0, m^2, m^2, BReduce -> False]

B11(0,m2,m2)\text{B}_{11}\left(0,m^2,m^2\right)

B11[SmallVariable[M^2], m^2, m^2]

m2  B0(M2,m2,m2)(1D)M2+(2D)  A0(m2)2(1D)M2\frac{m^2 \;\text{B}_0\left(M^2,m^2,m^2\right)}{(1-D) M^2}+\frac{(2-D) \;\text{A}_0\left(m^2\right)}{2 (1-D) M^2}

B11[SmallVariable[M^2], m^2, m^2, BReduce -> False]

B11(M2,m2,m2)\text{B}_{11}\left(M^2,m^2,m^2\right)