Changes between Version 31 and Version 32 of Reweight


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Timestamp:
Feb 1, 2016, 5:02:53 PM (9 years ago)
Author:
Olivier Mattelaer
Comment:

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  • Reweight

    v31 v32  
    22
    33= Description of the method =
    4  The method consist to use a sample of events (weighted or unweighted events) and associate to those events a new weight corresponding to a new theoretical hypothesis.
    5  It corresponds to a multidimensional version of the unidimensional re-weighing method commonly used by experiments.
     4 The method consists to use a sample of events (weighted or unweighted events) and associates to those events a new weight corresponding to a new theoretical hypothesis based on the matrix-element. It corresponds to a multidimensional version of the unidimensional re-weighing method commonly used by experiments.
    65 Once computed, this weight can be propagate through the all simulation chain in order to avoid to have to perform the full-simulation on a huge number of sample.
    76 This methods works only if the original hypothesis and the new one are both significant in the same part of the phase-space.
    87 
    9  We propose three types of reweightings. One for the Leading Order sample and two for the Next-to-Leading Order sample (called Kamikaze Reweighting and NLO Reweighting)
     8 We support three types of reweightings. One for Leading Order sample and two for the Next-to-Leading Order sample (called Kamikaze Reweighting and NLO Reweighting)
    109
    1110 '''Leading Order'''[[BR]][[BR]]
    1211 At Leading Order, the new weight is given by
    1312 $$W_{new} = |M^{new}_h|^2 /|M^{old}_h|^2 * W_{old} $$
    14  where h is the helicity associated to the events and $|M^{new/old}_h|^2$ is the matrix element for that helicity.
     13 where h is the helicity associated to the events and $|M^{new/old}_h|^2$ is the matrix element for the corresponding helicity.
    1514 If the events is not associated to a specific helicity, then the sum over the helicity is used instead.
    1615
    … …  
    1817 To get an idea of such propagation, one can use the naive formula of propagation of error:
    1918  $$\Delta\mathcal{O}_{new} = \bar R\cdot \Delta\mathcal{O}_{old} + \Delta R \cdot \mathcal{O}_{old} $$
    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.
     19 where $\bar R$ is the average of the ratio of the matrix-element, $\Delta R$ the associated variance. $\mathcal{O}_{old/new}$ is the value of the observable under consideration for the associated hypothesis and $\Delta\mathcal{O}_{old/new}$ the associated variance.
    2120
    2221 '''Kamikaze Reweighting'''[[BR]][[BR]]
    … …  
    2524        $$W^H_{new} = |M^{new}_{real}|^2 /|M^{old}_{real}|^2 * W^H_{old} $$
    2625 For obvious reason, this method is, in general, '''not NLO accurate'''.
    27  This is available since 2.3.2
     26 This method is available since MadGraph5_aMC@NLO v2.3.2
    2827
    2928 '''NLO reweighting:'''[[BR]][[BR]]
    3029
    31  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:
     30 For this computation, we extend the basis introduced in http://arxiv.org/pdf/1110.4738v1.pdf to decompose the matrix-element component independent of the scale and pdf variation:
    3231    $$d\sigma^{H} = d\sigma^E - d\sigma^{MC} $$
    3332    $$ d\sigma^{S} = d\sigma^{MC} + \sum_{\alpha=S,C,SC} d\sigma^\alpha $$
    … …  
    3534    $$ d\sigma^\alpha=f_1(x_1,\mu_F)f_2(x_2,\mu_F) \left[\mathcal{W}^\alpha_0 + \mathcal{W}^\alpha_F log\left(\mu_F/Q\right)^2 + \mathcal{W}^\alpha_R log\left(\mu_R/Q\right)^2 \right] d\chi$$
    3635 
    37  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
    38 
    39  In principle, the reweighting should be performed on each sub-part of the $\mathcal{W}$ according to the following formula
     36 Additionally, we decompose each of the $\mathcal{W^\alpha_\beta}$ in the component proportional to the born ($\mathcal{W}^\alpha_{\beta,B}$), the finite piece of virtual ($\mathcal{W}^\alpha_{\beta,V}$) and of the real ($\mathcal{W}^\alpha_{\beta,R}$).
     37  $\mathcal{W^\alpha_\beta} = B*\mathcal{C}^\alpha_{\beta,B} + V*\mathcal{C}^\alpha_{\beta,V} + R*\mathcal{C}^\alpha_{\beta,R} \equiv \mathcal{W}^\alpha_{\beta,B} + \mathcal{W}^\alpha_{\beta,V} + \mathcal{W}^\alpha_{\beta,R}$
     38 In our implementation, the various value of $\mathcal{W}^\alpha_{\beta,\delta}$ are computed by MG5_aMC at running time and kept in the final events. More details on the basis are available in  the appendix of  http://arxiv.org/pdf/1110.4738v1.pdf and in a paper in preparation.
     39
     40
     41 In principle, the reweighting should be performed on each sub-part of the $\mathcal{W}$ according to the following formula (dropping the $\alpha$ and $\beta$ index for simplicity):
    4042   $$\mathcal{W}_B^{new} = \frac{B^{new}}{B^{old}} * \mathcal{W}_B^{old} $$
    4143   $$\mathcal{W}_V^{new} = \frac{V^{new}}{V^{old}} * \mathcal{W}_V^{old} $$
    … …  
    4648 The reweighting is then done as
    4749   $$\mathcal{W}_{BB}^{new} = \frac{(B^{new}+V^{new})}{(B^{old}+V^{old})} * \mathcal{W}_{BB}^{old} $$
     50   $$\mathcal{W}_{BC}^{new} = \frac{B^{new}}{B^{old}} * \mathcal{W}_{BC}^{old} $$
    4851   $$\mathcal{W}_V^{new} = \frac{(B^{new}+V^{new})}{(B^{old}+V^{old})} * \mathcal{W}_V^{old} $$
    49    $$\mathcal{W}_{BC}^{new} = \frac{B^{new}}{B^{old}} * \mathcal{W}_{BC}^{old} $$
    5052   $$\mathcal{W}_R^{new} = \frac{R^{new}}{R^{old}} * \mathcal{W}_R^{old} $$
    5153 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.