| 17 | | $$\Delta\mathcal{O}_{new} = \bar R \Delta\mathcal{O}_{old} + \Delta R \mathcal{O} $$ |
| 18 | | where $\bar R$ is the avarage of the ration of the matrix-element and $\Delta R$ the associated variance. |
| 19 | | |
| 20 | | |
| 21 | | == Next-to-Leading Order |
| 22 | | For Next to Leading order samples, two type of reweighting are available: |
| 23 | | 1. '''kamikaze reweighting:''' This correspond to a Leading order type of reweighting where the reweighting is done only with tree-level matrix element: |
| 24 | | a. For S-event (N particles in the final state) the weight is given by |
| 25 | | $$W^S_{new} = |M^{new}_{born}|^2 /|M^{old}_{born}|^2 * W^S_{old} $$ |
| 26 | | b. For H-event (N+1 particles in the final state) the weight is given by |
| 27 | | $$W^H_{new} = |M^{new}_{real}|^2 /|M^{old}_{real}|^2 * W^H_{old} $$ |
| 28 | | |
| 29 | | 2. '''NLO reweighting:''' |
| 30 | | |
| 31 | | |
| 32 | | |
| 33 | | |
| 34 | | = Reweighting of NLO sample |
| 35 | | |
| 36 | | As in 2.3.3, we only offer Leading Order type reweighting of NLO sample (also call "kamikaze" reweighting). This consists to reweight the S events by the born matrix element and the H events by the real matrix element. We have shown that for EW EFT theory this is a correct approach. The way to run the code is the same as for the LO (see below) |
| 37 | | |
| 38 | | The correct NLO reweighting is only available on alpha version so far and can be requested by email to olivier Mattelaer. This version will be available in 2.4.0 |
| 39 | | Here is the information to use it. |
| 40 | | In order to perform the correct NLO reweighting, you need to generate the original samples with the following options: |
| 41 | | True = keep_rwgt_info ! keep the information for reweighting in the lhe file (huge impact on size file) |
| 42 | | After the reweighting will automatically be the NLO and, for the user point of view, the interface to run the re-weighting is the same as the LO one described below. |
| 43 | | In order to run the "kamikaze" reweighting on this sample, you can include in the reweighting_card the following command (at the beginning of the file): |
| 44 | | """ |
| 45 | | change mode LO |
| 46 | | """ |
| | 19 | $$\Delta\mathcal{O}_{new} = \bar R\cdot \Delta\mathcal{O}_{old} + \Delta R \cdot \mathcal{O}_{old} $$ |
| | 20 | where $\bar R$ is the avarage of the ratio of the matrix-element, $\Delta R$ the associated variance. $\mathcal{O}_{old/new}$ is the value of the observables under consideration for the associated hyppothesis and $\Delta\mathcal{O}_{old/new}$ the associated variance. |
| | 21 | |
| | 22 | '''Kamikaze Reweighting'''[[BR]][[BR]] |
| | 23 | This correspond to a Leading Order type of reweighting. Both the soft and hard events are reweighted according to the associated tree-level matrix element related to the number of particles in the final state. i.e., |
| | 24 | $$W^S_{new} = |M^{new}_{born}|^2 /|M^{old}_{born}|^2 * W^S_{old} $$ |
| | 25 | $$W^H_{new} = |M^{new}_{real}|^2 /|M^{old}_{real}|^2 * W^H_{old} $$ |
| | 26 | For obvious reason, this method is, in general, '''not NLO accurate'''. |
| | 27 | This is available since 2.3.2 |
| | 28 | |
| | 29 | '''NLO reweighting:'''[[BR]][[BR]] |
| | 30 | |
| | 31 | |
| | 32 | |
| | 33 | We use the basis introduced in http://arxiv.org/pdf/1110.4738v1.pdf to decompose the matrix-element component independant of the scale and pdf variation: |
| | 34 | $$d\sigma^{H} = d\sigma^E - d\sigma^{MC} $$ |
| | 35 | $$ d\sigma^{S} = d\sigma^{MC} + \sum_{\alpha=S,C,SC} d\sigma^\alpha $$ |
| | 36 | Each of the $d\sigma^\alpha$ can be written as |
| | 37 | $$ d\sigma^\alpha=f_1(x_1,\mu_F)f_2(x_2,\mu_F) \left[\mathcal{W}^\alpha_0 + \mathcal{W}^\alpha_F log\left(\mu_F/Q\right)^2 + \mathcal{W}^\alpha_R log\left(\mu_R/Q\right)^2 \right] d\chi$$ |
| | 38 | |
| | 39 | Additionally, we keep track of which part of the $\mathcal{W}$ are proportional to the Born ($\mathcal{W}_B$), the finite piece of virtual ($\mathcal{W}_V$) and of the real ($\mathcal{W}_R$). The equations are available in the appendix of http://arxiv.org/pdf/1110.4738v1.pdf |
| | 40 | |
| | 41 | In principle, the reweighting should be performed on each sub-part of the $\mathcal{W}$ according to the following formula |
| | 42 | $$\mathcal{W}_B^{new} = \frac{B^{new}}{B^{old}} * \mathcal{W}_B^{old} $$ |
| | 43 | $$\mathcal{W}_V^{new} = \frac{V^{new}}{V^{old}} * \mathcal{W}_V^{old} $$ |
| | 44 | $$\mathcal{W}_R^{new} = \frac{R^{new}}{R^{old}} * \mathcal{W}_R^{old} $$ |
| | 45 | the final weight is then computed by recombining the weight according to the above formula. |
| | 46 | |
| | 47 | However in MadGraph5_aMC@NLO, we use the virt-tricks method which avoid the computation of the virtual for some of the phase-space points. This speed optimisation method forbids the simple above reweighting since the generation will have $\mathcal{W}_V^{old}=0$ even if $V_{old} \neq 0$. To avoid this problem, $\mathcal{W}_B$ is splitted in two $\mathcal{W}_{BC}$, $\mathcal{W}_{BB}$ for the part proportional to the Born due to the counter-term and from the part really comming from the born or from the approximate virtual. |
| | 48 | The reweighting is then done as |
| | 49 | $$\mathcal{W}_{BB}^{new} = \frac{(B^{new}+V^{new})}{(B^{old}+V^{old})} * \mathcal{W}_{BB}^{old} $$ |
| | 50 | $$\mathcal{W}_V^{new} = \frac{(B^{new}+V^{new})}{(B^{old}+V^{old})} * \mathcal{W}_V^{old} $$ |
| | 51 | $$\mathcal{W}_{BC}^{new} = \frac{B^{new}}{B^{old}} * \mathcal{W}_{BC}^{old} $$ |
| | 52 | $$\mathcal{W}_R^{new} = \frac{R^{new}}{R^{old}} * \mathcal{W}_R^{old} $$ |
| | 53 | Such reweighting is fully NLO accurate. As in the LO case, the statistical uncertainty can be enhanced by the reweighting. Additionally the trick to support the virt-tricks adds an additional contribution to statistical uncertainty. |
| | 54 | This method will be released in a future version of MadGraph5_aMC@NLO and can currently be provided on request. Since this reweighting is based on a dedicated basis the NLO sample must be generated in a specific way to have the additional information in the leshouches event. |
| 50 | | == Limitation |
| 51 | | 1. |
| 52 | | |
| 53 | | |
| 54 | | The two theoretical hypothesis should differ ONLY by difference in the model parameters. So this should be the same pdf/cut (you can change model and process definition). |
| 55 | | 2. Note that the functional form of the hard scale can not be changed. |
| 56 | | 3. In presence of decay chain the order of the particle in the events file is important. This is important if you want to use this tools with LHE events not produced by MadGraph5_aMC@NLO. |
| 57 | | |
| 58 | | == Do I need special package |
| 59 | | Starting from MadGraph5_aMC@NLO.2.3.2, you need to have f2py on your machine. The easiest way to install f2py is to install numpy (if not already done). |
| 60 | | |
| 61 | | == How to use the code on the flight. |
| | 58 | === Limitation |
| | 59 | 1. We do not perform any PDF and/or cut reweighting. |
| | 60 | 2. We do not allowed to change the functional form of alpha_S |
| | 61 | 3. In presence of decay chain the order of the particles in the events file is important. This is important if you want to use this tools with LHE events not produced by MadGraph5_aMC@NLO. |
| | 62 | |
| | 63 | |
| | 64 | == Installation |
| | 65 | |
| | 66 | This module is built-in in MadGraph5_aMC@NLO.2.3.2. |
| | 67 | Since MadGraph5_aMC@NLO.2.3.2, this module relies on '''f2py''' to be installed. The easiest way to install f2py is to install numpy (if not already done). |
| | 68 | |
| | 69 | == How to run the code |
| | 70 | |
| | 71 | How to use the code on the flight. |
