Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qfthep.sinp.msu.ru/talks2011/anomalous_wtb_qfthep11.pdf Дата изменения: Wed Oct 5 13:50:02 2011 Дата индексирования: Mon Oct 1 19:54:57 2012 Кодировка:

Technical aspects of the search for anomalous Wtb couplings.
E. Boos, V. Bunichev, L. Dudko, M. Perfilov. Outline What we call anomalous Wtb couplings Operators and vertex approaches Anomalous couplings in production cross section Anomalous couplings in the decay of top quark


Effective operators in the field theory:
In the units where = c = 1, the fields of the SM have mass dimensions:
scalar: vector: fermion:

Every term in LSM is of dimension-4, while the new four-fermion interaction is of dimension-6:

where is the scale of the new physics ~ 1TeV


Full list of effective operators that have effects on single top quark processes at order 1 / 2 :
Operators that contribute to the Wtb vertex:

J. A. Aguilar-Saavedra, arXiv:1008.3225v1 [hep-ph]

Operators which lead to contact four-fermion interactions:

Cen Zhang, Scott Willenbrock, arXiv:1008.3869 [hep-ph]


1. Vertex function approach
Using gauge invariant operators:

one can derive vertices:

Where corrections to SM coupling:


2. Effective operators approach
We take into account only the dimension-6 operators (order 1/ 2), that contribute to the single top processes. The following operators contribute (for m b = 0) :

The first two operators Oq and OtW will affect the Wtb coupling.

The operator Oqq is four-fermion interaction that couples light quarks to third generation quarks. This additional vertex is not a part of Wtb.


2. Effective operators approach
Single top production processes:

To follow this approach we have to remove all terms of order 1/4. The corrections to the SM squared amplitudes include only terms of order 1/2: Anomalous operators contribute only to interference with SM.

Cen Zhang, Scott Willenbrock, arXiv:1008.3869 [hep-ph]


Vertex functions
The interference terms between SM amplitudes and dimension-6 operators are proportional to 1/2 , and the pure dimension-6 operators corrections to 1/ 4.

Contribution to matrix element from Wtb anomalous couplings (for m b = 0): order: 1/ VL g
R 2

1/

4

(V L ) (V R) (gL) (g R)

2

2

2 2


The practical difference between the two approaches

Vertex function at order 1/2

Effective operators at order 1/2

Takes into account all matrix element terms with coupings VL, VR, gL, gR. dim. 1/2,1/
4

Takes into account only interference terms with SM, that include couplings VL, gR, and contact interaction dim. 1/2 only.

One can use both strategies in experiment: In addition to complete Wtb search set additional limits to effective operators which are linear to 1/2.

8


Production Cross Section
s-channel:
t-channel:

From the formulas we can see that Left (f_L^1) and right (f_R^1) vector terms are completely (kinematically) different in t-channel and we have to model both of the couplings correctly in our MC model.
Phys.Atom.Nucl.73:971-984,2010 http://top.sinp.msu.ru/tmp/PhysAtom_73-6-2010.pdf
9


How we can prepare MC model of production in model independent way
(vertex approach)

With these 6 samples we can describe All possible values (models) of the Couplings in production of single top Including the interference terms (approximation with massless b quark)

10


Anomalous Wtb couplings in the production and in decay of top

Therefore, we can correctly model all possible values of vector couplings with three samples: 1000, 0100 and (1100-1000-0100) The last one is unphysical gauge invariant sample with left coupling in Production and right couplings in decay of top and vice versa.
11


Distributions at the parton level

12


Importance of s-channel signal to limit the anomalous Wtb couplings
Eur.Phys.J. C11 (1999) 473-484 Combination of s- and t-channel partial limits provides much more tight limits on anomalous couplings.

13


Practical realization of both approaches in MC generator SingleTop (based on CompHEP)
For the vertex approach create a model with four couplings For the operators approach create a model of vertex function approach with anomalous couplings VL, gR only. For the contact term:
­ - Introduce an auxiliary massive vector particle P (MP >> sqrt(s)) and vertices of SM-like interaction P with fermions. ­ - Set Pqq couplings parameters ~MP. ­ - Calculate total matrix element and keep only SM terms and terms of interference SM with processes including anomalous VL, gR and (P,quark,quark) interactions
2 2 2 ­ (i.e. remove all V L, g R and Pqq terms).

14


Conclusion
There are two approaches for the anomalous Wtb couplings, one can set the limits in both of them (In addition to complete Wtb couplings search we can set additional limits to effective operators which are linear to 1/2). We know how to describe correctly all possible values of couplings with few MC samples and provide model independent limits The generator SingleTop has implemented already in D0 analysis and for CMS analysis. The samples created for LHC community are available in LHEF format in MCDB http://mcdb.cern.ch

15


Backup Slides

16


Advantages of using vertex function approach:
The possibility to explore all new physics effects whose contribution is proportional quadratic corrections from anomalous couplings VR , gL (One well-known example is given by top FCNC processes, extremely suppressed in the SM,
which are of order 1/4).

The possibility of direct measurement of Vtb coupling parameters.

Problems of vertex function approach:
We use operators with different mass dimensions. (This is not very accurate from the point of view of quantum field theory.)
17


Advantages of using effective operators approach:
All correction terms in the matrix element of the same order of mass scale parameter. Takes into account the contribution from the contact four-fermion interactions.

Limitations of effective operators approach:
Not taken into account the contribution from anomalous couplings VR , gL It is difficult to measure directly the Vtb coupling parameters (due to additional four-fermion vertex).
18