equation_database.inspirehep_Field_1989uq

Functions

bibtex()

Applications of Perturbative QCD

equation_2_1_30([sigma_0, alpha, e_q, Q])

Cross section for \(\gamma^* \to q \bar q\)

equation_2_3_32([sigma, sigma_0, alpha_s, ...])

Differentiated cross section for \(e^+e^- \to q \bar q g\)

equation_4_3_20([e, e_q, g_s, Q, u, t])

\(\gamma^* g \to q \bar q\) scattering averaged matrix element
equation_database.inspirehep_Field_1989uq.equation_2_1_30(sigma_0=sigma_0, alpha=alpha, e_q=e_q, Q=Q)[source]

Cross section for \(\gamma^* \to q \bar q\)

Parameters:

  • sigma_0 – norm cross section

  • alpha – fine structure constant

  • e_q – electric charge of the quark

  • Q – mass of the virtual photon

Returns:

\(\sigma_{0} = 3 Q \alpha e_{q}^{2}\),

\sigma_{0} = 3 Q \alpha e_{q}^{2}
equation_database.inspirehep_Field_1989uq.equation_2_3_32(sigma=sigma, sigma_0=sigma_0, alpha_s=alpha_s, x_1=x_1, x_2=x_2)[source]

Differentiated cross section for \(e^+e^- \to q \bar q g\)

Parameters:

  • sigma – cross section

  • sigma_0 – norm cross section

  • alpha_s – strong coupling constant

  • x_1 – quark momentum fraction

  • x_2 – antiquark momentum fraction

Returns:

\(\frac{\frac{d^{2}}{d x_{2}d x_{1}} \sigma}{\sigma_{0}} = \frac{2 \alpha_{s} \left(x_{1}^{2} + x_{2}^{2}\right)}{3 \pi \left(1 - x_{1}\right) \left(1 - x_{2}\right)}\),

\frac{\frac{d^{2}}{d x_{2}d x_{1}} \sigma}{\sigma_{0}} = \frac{2 \alpha_{s} \left(x_{1}^{2} + x_{2}^{2}\right)}{3 \pi \left(1 - x_{1}\right) \left(1 - x_{2}\right)}
equation_database.inspirehep_Field_1989uq.equation_4_3_20(e=e, e_q=e_q, g_s=g_s, Q=Q, u=u, t=t)[source]

\(\gamma^* g \to q \bar q\) scattering averaged matrix element

Parameters:

  • e – electric charge

  • e_q – electric charge of the quark

  • g_s – strong coupling constant

  • Q – mass of the virtual photon

  • u – Mandelstam variable u

  • t – Mandelstam variable t

Returns:

\(2 e^{2} e_{q}^{2} g_{s}^{2} \left(\frac{2 Q^{2} \left(Q^{2} + t + u\right)}{t u} + \frac{t}{u} + \frac{u}{t}\right)\),

2 e^{2} e_{q}^{2} g_{s}^{2} \left(\frac{2 Q^{2} \left(Q^{2} + t + u\right)}{t u} + \frac{t}{u} + \frac{u}{t}\right)
equation_database.inspirehep_Field_1989uq.bibtex()[source]

Applications of Perturbative QCD

@book{Field:1989uq,
    author = "Field, R. D.",
    title = "{Applications of Perturbative QCD}",
    volume = "77",
    year = "1989"
}