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Analysis of the Anomalous Wtb couplings in the t-channel single top quark production Anomalous Wtb couplings Scenarios for t-channel analysis Contribution of the Anomalous Wtb couplings to ttbar / tW processes
SINP MSU E. Boos, V. Bunichev, L. Dudko, M. Perfilov, QFTHEP 2013


Anomalous Wtb couplings in t-channel
Anomalous Wtb vertex structure
Common form of the Effective Wtb vertex lagrangian. Vertex functions approach

Left and right vector operators

Left and right tensor operators

SM: Vtb 0 0 0 (1000) LV f 1 , R V f 1 , LT f 2 , R T f
L R L R 2

Analysis Strategy: different scenarios: (Lv,Rv), (Lv,Lt), (Lv,Rt)
- only two couplings are non-zero at the same time
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Anomalous Wtb, (Lv,Rv) scenario, CompHEP MC simulation Production+decay case, ( LV , RV ) scenario The case with

production decay 4

LV, R

V

in both Wtb vertex:

w 1000 m = L V w L , R
V

V



LV , R V = m 1000 n unphys k 0100 w art 4 w 0100 2 2 k = R V n= LV R V w L , R w L , R
V V V

V



Distribution of the cos(q,l) in the top rest frame for the tchannel single top quark processes with both left and right vector operators in the Wtb vertex. (correct modeling of (1/0.5/0/0) sample with 1000, 0100 and «unphys» samples)
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Anomalous Wtb, (Lv,Lt) scenario, CompHEP MC Production+decay case, ( LV , LT ) scenario The case with

production decay 4

LV, L

T

in both Wtb vertex:

LV , L T = p 1000 r unphys s 0010
w r = LV LT w L
2 2 art
V

w 1000 p= LV w L , L
V

T



, LT

w 0010 s = LT w L , L
4
V

T



Distribution of the cos(q,l) in the top rest frame for the tchannel single top quark processes with both left vector and tensor operators in the Wtb vertex. (correct modeling of (1/0/0.5/0) sample with 1000, 0010 and «unphys» samples)
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Anomalous Wtb, (Lv,Rt) scenario, CompHEP MC Production+decay case, ( LV , RT ) scenario The case with
LV, R
T

in both Wtb vertex:

Distribution of the cos(q,l) in the top rest frame for the tchannel single top quark processes with both left vector and right tensor operators in the Wtb vertex. (correct modeling of (1/0/0/1) sample with 10000001 and «artificial» samples)

This case is more complicated
- we need more than 1 «artificial» sample
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Anomalous Wtb in Single Top: simulation issues


Correct simulation of the anomalous couplings in both vertexes is important, but significantly increases the complexity. For the first stage of analysis one can check 2D scenarios (LV, RV), (LV, LT), (LV, RT) and vary 4 couplings simultaneously next. The anomalous Wtb vertex is present in tW and ttbar backgrounds. Is this contribution significant and how to simulate it? Will it increase the sensitivity of the analysis? How one can take into account NLO contribution for the simulated t-channel, tW and ttbar processes with anomalous Wtb couplings contribution?
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Anomalous Wtb couplings contribution to the tW and ttbar background processes


tW+ttbar process: all diagrams
t Lets look at the main subprocess of p , p , W , b :

: ttbar diagram All diagrams have been taken into account
- with interference between ttbar and tW


tW+ttbar process: main distributions

PT t

PT b

b

PT

The difference is in the topdecay products distributions


tW+ttbar process: decay angular distributions

( Phys.Lett. B534 (2002) 97105 )

cos(E,m)|top rest frame

cos (m,W) |

Wboson rest frame

cos (E,W) |

top rest frame

cos (E(ne) ,W) |

top rest frame


ttbar process: decay angular distributions

cos(E,m)|top rest frame

cos (m,W) |

Wboson rest frame

cos (E,W) |

top rest frame

cos (E(ne) ,m) |

top rest frame


tW process: all diagrams, Diagram Removal scheme We look at the main subprocess of
p , p , W , b t :

Diagram Removal scheme -- one delete all ttbar diagrams
- no interference between ttbar and tW


tW process, Diagram Removal: decay angular distributions

cos(E,m)|top rest frame

cos (m,W) |

Wboson rest frame

cos (E,W) |

top rest frame

cos (E(ne) ,m) |

top rest frame


AnomWtb contribution to the signal and background processes

ttbar, CompHEP parton level

tW, CompHEP parton level

tchannel: CompHEP, ttbar: Madgraph, tW: POWHEG LV only 1

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How to apply NLO k-factors to tW+ttbar simulation with anomalous Wtb couplings
There are separate NLO/NNLO calculations for tW (single resonance) and ttbar (double resonance) processes. The interference between two is negative and important The approximate k-factor can be extracted from the fit of invariant mass of Wb corresponding to the second resonance

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Anomalous Wtb couplings in the t-channel analysis: summary

Proper simulation of the anomalous couplings in both ­ production and decay - vertexes is significant The contribution of anomalous operators to the kinematics of ttbar and tW background processes is significant The available NLO k-factors can be applied to t-channel directly and to tW+ttbar with invariant mass fitting (double resonance and single resonance contribution) This study is being implemented in the corresponding analysis of CMS collaboration