VPolar: The Standard Model at NLO in QCD with helicity-polarized W and Z bosons

Contact Author

Richard Ruiz

• Institute of Nuclear Physics Polish Academy of Science (IFJ PAN)
• rruiz AT ifj.edu.pl

In collaboration with:

13. Javurkova, R.C.L. de Sá, and J. Sandesara ​arXiv:xxx.yy [ 1 ]
14. Buarque Franzosi, O. Mattelaer, and Sujay Shil ​arXiv:1912.01725 [ 2 ]

Usage resources

• For instructions and examples on using the VPolar UFO libraries, see M. Javurkova, et al, ​arXiv:xxx.yy [ 1 ]
• For additional background, see also D. Buarque Franzosi, et al, ​arXiv:1912.01725 [ 2 ]
• See Validation section below for additional information

• Special note: this UFO was developed using MG5aMC and calls the 1L, 1T, and 1A propagators defined in ALOHA (see aloha_object.py and create_aloha.py). These may be defined differently in other generators. If they are not defined in your favorite generators, they must be added to the propagators.py file in the VPolar UFO. The file particles.py must then be updated to reflect the propagator names. R. Ruiz is happy to assist with this.

Citation requests

• If using the UFO, please cite , see M. Javurkova, et al, ​arXiv:xxx.yy [ 1 ]

Model Description -- helicity polarization as a Feynman rule

The broad idea of the helicity polarization as a Feynman rule is to treat the helicity-truncated propagator (see [ 2 ] for details) as the Feynman rule for a particle that sits in a definite helicity polarization. The helicity-truncated propagator is given by

\begin{align}
\Pi_{\mu\nu}^{V\lambda}(q) = \frac{-i\varepsilon_\mu(q,\lambda)\ \varepsilon^*_\nu(q,\lambda)}{q^2-M_V^2 +iM_V\Gamma_V}
\end{align}

and is related to the full propagator by

\begin{align}
    &\Pi_{\mu\nu}^V (q) =
    \frac{-i\left(g_{\mu\nu} - q_\mu q_\nu / M_V^2\right)}{q^2-M_V^2 +iM_V\Gamma_V}\
    \\
    &=\sum_{\lambda\in\{0,\pm1,A\}} 
    \eta_\lambda\ \left(
    \frac{-i\varepsilon_\mu(q,\lambda)\ \varepsilon^*_\nu(q,\lambda)}{q^2-M_V^2 +iM_V\Gamma_V} \right)\ .
\end{align}

Here, $\eta_\lambda=+1$, unless $\lambda=0$ and $V_{\lambda}$ is in the t-channel; in that case $\eta_\lambda=-1$.

By making the graphical identification

then one can interpret the full propagator in Eq. 3 as the sum of propagators (or interfering graphs) for a collection of particles $V_\lambda$, where each $V_\lambda$ has its own propagator.

The VPolar UFOs implement this idea for the W and Z bosons.

UFO Description and Usage

Studies that have used the above model files

• Please email to update this space.

References

[1] M. Javurkova, R. Ruiz, R. Coelho Lopes de Sa, and J. Sandesara, Polarized ZZ pairs in gluon fusion and vector boson fusion at the LHC, ​arXiv:xx.yyyy

[2] D. Buarque Franzosi, O. Mattelaer, R. Ruiz, S. Shil, Automated Predictions from Polarized Matrix Elements, JHEP 2020, 82 (2020) ​arXiv:1912.01725