https://doi.org/10.1140/epjc/s10052-014-2950-z
Regular Article - Theoretical Physics
rule, 
and 
in 
and 
models with FCNC quark couplings
1
TUM Institute for Advanced Study, Lichtenbergstr. 2a, 85747 , Garching, Germany
2
Physik Department, Technische Universität München, James-Franck-Straße, 85747 , Garching, Germany
3
Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Via Orabona 4, 70126 , Bari, Italy
* e-mail: jennifer.girrbach@gmail.com
Received:
29
April
2014
Accepted:
17
June
2014
Published online:
11
July
2014
The experimental value for the isospin amplitude 
in 
decays has been successfully explained within the standard model (SM), both within the large 
approach to QCD and by QCD lattice calculations. On the other hand within the large approach the value of 
is by at least 
below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless 
gauge boson with a flavour-violating left-handed coupling 
and an approximately universal flavour diagonal right-handed coupling 
to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to . This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator 
to . A large fraction of the missing piece in the rule can be explained in this manner for 
in the reach of the LHC, while satisfying the constraints from 
, , 
, LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling 
and of enhanced matrix elements of 
left–right operators allows one to satisfy simultaneously the constraints from and , although this requires some fine-tuning. We identify the quartic correlation between contributions to , , and . The tests of this proposal will require much improved evaluations of and within the SM, of 
as well as precise tree-level determinations of 
and 
. We present correlations between , 
and 
with and without the rule constraint and generalise the whole analysis to with colour () and 
with FCNC couplings. In the latter case no improvement on can be achieved without destroying the agreement of the SM with the data on . Moreover, this scenario is very tightly constrained by . On the other hand, in the context of the rule is even more effective than : it provides the missing piece in for 
–
.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
