Single top production
-------------------------------

- process: pp -> t  (production +0,1 parton)  
kfactor of 1.5 [ref: arxiv:1409.6959] on top of the LO x-section at BR limit
- related FCNC couplings: gct & gut

- considered backgrounds:
ttbar, single top, W+jets, Z+jets.
no generation of multijets background, its contribution will need to be estimated via a data-driven approach by experiments.

- references on the subject: 
	* [1] ATLAS : "Search for single top-quark production via FCNC in strong interactions in √s = 8 TeV ATLAS data", ATLAS-CONF-2013-063, june 2013
	* [2] ATLAS : "Search for FCNC single top-quark production at √s =7 TeV with the ATLAS detector", Physics Letters B 712 (2012) 351-369

- selection: 
 = 1 isolated lepton (e or mu) with pT>30, |eta|<2.5, iso (cone 0.4)<0.2
no other isolated lepton with pT>20, |eta|<2.5
no isolated photon with pT>10, |eta|<2.5
 = 1 or 2 jets with pT>20, |eta|<2.4, EM E/HAD E>0.3, Delta R (jet, lepton)>0.1
in particular for the leading jet : pT>30 and b-tagged with Medium criterium.
MET>30
mTw = transverse mass(lepton, MET)>50

(MET and mTw cuts aim to suppress multijet backgrounds).

- cutFlow table

\begin{landscape}
\begin{table}[p]
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
\hline
\hline
Cut & Sum Bg  & Signal gct  & Signal gut  & T+jets  & TT+jets  & W+jets  & ZToLL \\
\hline
= 1 lepton  & 1365879080 $\pm$ 436451 & 243085 $\pm$ 150 & 173582 $\pm$ 121 & 3380814 $\pm$ 5455 & 13094378 $\pm$ 4557 & 1212020864 $\pm$ 252487 & 137383024 $\pm$ 355934 \\
$>=$ 1 jet with $pT(j_1)>30$ & 258595014 $\pm$ 264773 & 188193 $\pm$ 132 & 121321 $\pm$ 101 & 2951626 $\pm$ 5023 & 12821832 $\pm$ 4520 & 192003856 $\pm$ 66047 & 50817700 $\pm$ 256314 \\
$MET>30$ & 134868083 $\pm$ 132497 & 134166 $\pm$ 111 & 86849 $\pm$ 85 & 2216143 $\pm$ 4331 & 10452940 $\pm$ 4054 & 112844192 $\pm$ 50369 & 9354808 $\pm$ 122406 \\
$mTw > 50 $ & 108863544 $\pm$ 100794 & 108146 $\pm$ 100 & 68167 $\pm$ 76 & 1703800 $\pm$ 3842 & 7531914 $\pm$ 3412 & 94473056 $\pm$ 47005 & 5154774 $\pm$ 89015 \\
b-tagged $j_1$ & 7777716 $\pm$ 13228 & 55473 $\pm$ 59 & 30879 $\pm$ 42 & 826610 $\pm$ 2371 & 3283684 $\pm$ 1846 & 3447627 $\pm$ 3128 & 219796 $\pm$ 12497 \\
1 or 2 jets & 5210432 $\pm$ 11114 & 51150 $\pm$ 57 & 28628 $\pm$ 41 & 639292 $\pm$ 2143 & 1152822 $\pm$ 999 & 3242427 $\pm$ 3071 & 175891 $\pm$ 10416 \\
no  photon $ & 5082828 $\pm$ 10894 & 50691 $\pm$ 57 & 28363 $\pm$ 40 & 625003 $\pm$ 2126 & 1083224 $\pm$ 975 & 3208169 $\pm$ 3055 & 166431 $\pm$ 10192 \\
\hline
\hline
\end{tabular}
\caption{ CutFlow table. Yields for 100 fb-1 at 13 TeV }
\label{Table:CutFlow}
\end{table}
\end{landscape}

The last selection step corresponds to a significance Sig = S/sqrt(S+B) equal to 22.4 for gct, and 12.545 for gut

- other signal contamination

Checks of the yields at the last selection step for various other FCNC signals of top production with an associated H, photon or invisible particle, for various couplings.
The largest contribution comes from t+$\gamma$ signal [tGamma-Kappa-act + TTtoLGamma-Kappa-act] via  $K_{act}$ coupling : 862 $\pm$ 3, which represents 3% of our gut signal.

\begin{table}[p]
\begin{tabular}{|l|c|}
\hline
\hline
 &  Yields \\
\hline
Signal gct & 50691 $\pm$ 57 \\
Signal gut & 28363 $\pm$ 40 \\
\hline
Signal t+H $K_{hct}$ & 241 $\pm$ 0 \\
Signal t+H $K_{hut}$ & 580 $\pm$ 1 \\
Signal t+$\gamma$ $K_{act}$ & 862 $\pm$ 3 \\
Signal t+$\gamma$ $K_{aut}$ & 270 $\pm$ 2 \\
Signal t+$\gamma$/inv $K_{gct}$ & 494 $\pm$ 2 \\
Signal t+$\gamma$/inv $K_{gut}$ & 354 $\pm$ 2 \\
Signal t+inv $K_{zct}$  & 59 $\pm$ 0 \\
Signal t+inv $K_{zut}$ & 591 $\pm$ 2 \\
Signal t+inv $Z_{zct}$ & 31 $\pm$ 0 \\
Signal t+inv $Z_{zut}$ & 190 $\pm$ 1 \\
\hline
\hline
\end{tabular}
\caption{ Contamination }
\label{Table:Conta}
\end{table}

- discriminating variables & MVA

1) several variables have been considered:

on the lepton : pT, eta, charge
on the b (= leading jet) : pT, eta
on the neutrino : MET, eta    --> the neutrino pZ is determined by solving the equation "mass (lepton + neutrino) = m(W) = 80.399"
on the W (lepton + MET system) : pT, mTW
on the top (lepton + neutrino + b system) : mass, eta

angular information:
Delta Phi (l, MET), Delta Phi (l, b), Delta Phi (l, W), Delta Phi (l, top),
Delta Phi (b, W), Delta Phi (b, top),
Delta Phi (W, MET), Delta Phi (W, MET) in the top rest frame, Delta Phi (W, top),
Delta R (l, top)
(remark: The Delta Phi variables are not all independent, but it was to check which is best one among all).

2) reduction of the number of variables to be used 
Checking the correlation matrix, we remove from the list the variables with too large correlations.
We keep the most discriminating ones and also the variables which present very different correlations in signal and in background.

-->  The list of the selected variables used in a BDT: mass(top), mTw, pT(W), pT(b), eta(l), charge(l), Delta Phi (b, W), Delta Phi (l, MET), Delta Phi (l, b).
The charge(l) is only discriminating for the gut scenario (which provides a charge asymmetry).
eta(l) is slightly different between gct and gut.
But for simplicity, we decide to use the same variables in both scenario.

Plots of the variables: shape_tree_*.png
Plots of the correlation matrix: CorrelationMatrixB.png, CorrelationMatrixS.png

3) Results from the BDT

Plots of the BDT output: shape_MVA_*.png

gct and gut signals have similar behavior for the bdt gct output (BDT trained on gct). My understanding : Q(l) and eta(l) have different behaviors for gct and gut. If the BDT output is similar, it is probably because 
those 2 variables have the lowest ranking w/r to the other variables in term of discriminating power between gct and backgrounds. The situation is a bit different for the gut training for which Q(l) is better ranked.

To quantify the improvements a MVA approach could bring, the best cuts on the BDT outputs lead to a significance of 30.5 for gct and 18.5 for gut. 

- comparison with ATLAS

ATLAS in [1] has a different selection = exactly 1 jet, tight b-tagging criterium.
	the =1jet is not appropriate in our case (pp->t with up to 1 parton).
	the tight b-tagging criteria leads to a similar significance than using the medium b-tagging criteria --> no improvement on the pheno side, but a tighter cut will certainly help in reducing the remaining multijet background in the experimental life.
ATLAS uses a different choice of variables for its MVA : pT(b), pT(W), Delta Phi (W, MET) in the top rest frame, Q(l), eta(l), Delta Phi (l, b), eta(top), Delta Phi (l, W), Delta Phi (b, top), Delta Phi (l, top),  Delta Phi (W, top), MET, eta(nu).
	Using its set of variables on top of our selection leads to significance of 28.8 for gct and 17.2 for gut, which is a bit lower than the values obtained with a BDT trained over the 9 variables listed above (with the mass(top) having the best ranking in both gct and gut scenarios).

- limits on coupling & BR

-> limit values for Significance =2sigma, 3 sigma, 5 sigma in 1D (based on BDT results):
K(gut) = 3.55e-06, = 4.25e-06, = 5.55e-06
K(gct) = 6.15e-06, = 7.55e-06, = 9.75e-06

BR(gut) = 3.5e-06, 5.1e-06, 8.5e-06
BR(gct) = 1.075e-05, 1.575e-05,  2.625e-05

we expect to gain a factor 10 when going to 13 TeV 100fb-1
by comparison with 8 TeV 20fb-1=
	BR(gut) < 0.0031 %  (excluded @95%)
	BR(gct) <0.016% (excluded @95%)

-> contours at 3sigma and 5 sigma in the 2D planes (based on BDT results): 
BR (gct) vs BR (gut): bratio_best_sigbdt.png
K(gct) vs K(gut): coupling_best_sigbdt.png

- discussion about the limitation of the results

1- multijet contribution is missing. it can be estimated only from data measurements.
ATLAS quotes a 10-15% of contribution to the total background.
If we increase the B size in the significance to count for the multijet background --> Sig' = S/sqrt(S + 1.15*B),
the 1D limits (using a BDT cut which optimizes Sig and not Sig') become at 2-, 3- and 5-sigma:

K(gut) = 3.65e-06, 4.45e-06, 5.75e-06
K(gct) = 6.35e-06, 7.75e-06, 1.005e-05

BR(gut) = 3.7e-06,  5.5e-06, 9.1e-06
BR(gct) = 1.125e-05, 1.675e-05, 2.775e-05

2- uncertainty: 
Adding a global systematics uncertainty "x" on the backgrounds, we can estimate Sig'' = S/sqrt(S+ B + (x*B)**2)
Here are the 1D limits  (using a BDT cut which optimizes Sig'') at 2-, 3- and 5-sigma:

--> with x=0.10
K(gut) = 1.71e-05, 2.09e-05, 2.69e-05
K(gct) =  3.95e-05, 4.83e-05, 6.25e-05
BR(gut) = 8.25e-05, 0.0001225, 0.0002025
BR(gct) = 0.000475, 0.000675, 0.001125
--> with x=0.30
K(gut) =  2.91e-05, 3.55e-05, 4.59e-05
K(gct) =  6.81e-05, 8.33e-05, not within the scanned range
BR(gut) = 0.0002325, 0.0003525, 0.0005825      <--- limit @2 sigma > actual limit  by a factor 10 :(
BR(gct) = 0.001325,  0.001925, 0.003225		   <--- limit @2 sigma > actual limit by a factor 10 :(