equation_database.doi_10_1007_JHEP06_2010_043

Functions

bibtex()

DOI, arXiv, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX

equation_A_21([p, p_0, phat, m, mhat, m_0, ...])

equation_A_23([I_0, p, m, phat, mhat])

equation_A_24([I_epsilon, p, m, phat, beta])

equation_A_41([I_0, k_1, k_2, beta])

equation_A_50([I_epsilon, K, a, b, k_1, ...])

equation_database.doi_10_1007_JHEP06_2010_043.equation_A_21(p=p, p_0=p_0, phat=\hat{p}, m=m, mhat=\hat{m}, m_0=m_0, mvec=\vec{m}, beta=beta)[source]
Parameters:

  • p – massless four momentum

  • m – massive four momentum

Returns:

\(\hat{p} = \frac{p}{p_{0}}\), \(\hat{m} = \frac{m}{m_{0}}\), \(\beta = \frac{\left|{\vec{m}}\right|}{m_{0}}\),

\hat{p} = \frac{p}{p_{0}}

\hat{m} = \frac{m}{m_{0}}

\beta = \frac{\left|{\vec{m}}\right|}{m_{0}}
equation_database.doi_10_1007_JHEP06_2010_043.equation_A_23(I_0=I_0, p=p, m=m, phat=\hat{p}, mhat=\hat{m})[source]
Parameters:

  • p – massless four momentum

  • m – massive four momentum

  • phat – normalized p momentum (see equation_A_21())

  • mhat – normalized m momentum (see equation_A_21())

Returns:

\(I_{0}{\left(p,m \right)} = \log{\left(\left(\hat{p} \hat{m}\right)^{2} \hat{m}^{-2} \right)}\),

I_{0}{\left(p,m \right)} = \log{\left(\left(\hat{p} \hat{m}\right)^{2} \hat{m}^{-2} \right)}
equation_database.doi_10_1007_JHEP06_2010_043.equation_A_24(I_epsilon=I_\epsilon, p=p, m=m, phat=\hat{p}, beta=beta)[source]
Parameters:

  • p – massless four momentum

  • m – massive four momentum

  • phat – normalized p momentum (see equation_A_21())

  • beta – normalized m three momentum (see equation_A_21())

Returns:

\(I_{\epsilon}{\left(p,m \right)} = - 2 \left(\frac{\log{\left(\frac{1 - \beta}{\beta + 1} \right)}^{2}}{4} + \log{\left(\frac{\hat{p} m}{\beta + 1} \right)} \log{\left(\frac{\hat{p} m}{1 - \beta} \right)} + \operatorname{Li}_{2}\left(1 - \frac{\hat{p} m}{1 - \beta}\right) + \operatorname{Li}_{2}\left(1 - \frac{\hat{p} m}{\beta + 1}\right)\right)\),

I_{\epsilon}{\left(p,m \right)} = - 2 \left(\frac{\log{\left(\frac{1 - \beta}{\beta + 1} \right)}^{2}}{4} + \log{\left(\frac{\hat{p} m}{\beta + 1} \right)} \log{\left(\frac{\hat{p} m}{1 - \beta} \right)} + \operatorname{Li}_{2}\left(1 - \frac{\hat{p} m}{1 - \beta}\right) + \operatorname{Li}_{2}\left(1 - \frac{\hat{p} m}{\beta + 1}\right)\right)
equation_database.doi_10_1007_JHEP06_2010_043.equation_A_41(I_0=I_0, k_1=k_1, k_2=k_2, beta=beta)[source]
Parameters:

  • k1 – massive four momentum

  • k2 – massive four momentum

Returns:

\(I_{0}{\left(k_{1},k_{2} \right)} = \frac{\log{\left(\frac{\beta + 1}{1 - \beta} \right)}}{\beta}\), \(\beta = \sqrt{1 - k_{1}^{2} k_{2}^{2} \left(k_{1} k_{2}\right)^{-2}}\),

I_{0}{\left(k_{1},k_{2} \right)} = \frac{\log{\left(\frac{\beta + 1}{1 - \beta} \right)}}{\beta}

\beta = \sqrt{1 - k_{1}^{2} k_{2}^{2} \left(k_{1} k_{2}\right)^{-2}}
equation_database.doi_10_1007_JHEP06_2010_043.equation_A_50(I_epsilon=I_\epsilon, K=K, a=a, b=b, k_1=k_1, k_2=k_2, vec_beta_1=\vec{\beta}_1, vec_beta_2=\vec{\beta}_2, z_1=z_1, z_2=z_2)[source]
Parameters:

  • k1 – massive four momentum

  • k2 – massive four momentum

Returns:

\(I_{\epsilon}{\left(k_{1},k_{2} \right)} = \frac{\left(- K{\left(z_{1} \right)} + K{\left(z_{2} \right)}\right) \left(1 - \vec{\beta}_1 \vec{\beta}_2\right)}{\sqrt{a \left(1 - b\right)}}\),

I_{\epsilon}{\left(k_{1},k_{2} \right)} = \frac{\left(- K{\left(z_{1} \right)} + K{\left(z_{2} \right)}\right) \left(1 - \vec{\beta}_1 \vec{\beta}_2\right)}{\sqrt{a \left(1 - b\right)}}
equation_database.doi_10_1007_JHEP06_2010_043.bibtex()[source]

DOI, arXiv, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX

@article{Alioli:2010xd,
    author = "Alioli, Simone and Nason, Paolo and Oleari, Carlo and Re, Emanuele",
    title = "{A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX}",
    eprint = "1002.2581",
    archivePrefix = "arXiv",
    primaryClass = "hep-ph",
    reportNumber = "DESY-10-018, SFB-CPP-10-22, IPPP-10-11, DCPT-10-22",
    doi = "10.1007/JHEP06(2010)043",
    journal = "JHEP",
    volume = "06",
    pages = "043",
    year = "2010"
}