Abstract
The experimental value for the isospin amplitude mathrm{Re}A_2 in Krightarrow pi pi decays has been successfully explained within the standard model (SM), both within the large N approach to QCD and by QCD lattice calculations. On the other hand within the large N approach the value of mathrm{Re}A_0 is by at least 30,% 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 mathrm{Re}A_0 comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless Z^prime gauge boson with a flavour-violating left-handed coupling Delta ^{sd}_L(Z^prime ) and an approximately universal flavour diagonal right-handed coupling Delta ^{qq}_R(Z^prime ) to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to mathrm{Re}A_2. 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 Q_6 to mathrm{Re}A_0. A large fraction of the missing piece in the Delta I=1/2 rule can be explained in this manner for M_{Z^prime } in the reach of the LHC, while satisfying the constraints from varepsilon _K, varepsilon '/varepsilon , Delta M_K, LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling Delta ^{sd}_R(Z^prime )ll Delta ^{sd}_L(Z^prime ) and of enhanced matrix elements of Delta S=2 left–right operators allows one to satisfy simultaneously the constraints from mathrm{Re}A_0 and Delta M_K, although this requires some fine-tuning. We identify the quartic correlation between Z^prime contributions to mathrm{Re}A_0, varepsilon '/varepsilon , varepsilon _K and Delta M_K. The tests of this proposal will require much improved evaluations of mathrm{Re}A_0 and Delta M_K within the SM, of langle Q_6 rangle _0 as well as precise tree-level determinations of |V_{ub}| and |V_{cb}|. We present correlations between varepsilon '/varepsilon , K^+rightarrow pi ^+nu bar{nu } and K_{L}rightarrow pi ^0nu bar{nu } with and without the Delta I=1/2 rule constraint and generalise the whole analysis to Z^prime with colour (G^prime ) and Z with FCNC couplings. In the latter case no improvement on mathrm{Re}A_0 can be achieved without destroying the agreement of the SM with the data on mathrm{Re}A_2. Moreover, this scenario is very tightly constrained by varepsilon '/varepsilon . On the other hand, in the context of the Delta I=1/2 rule G^prime is even more effective than Z^prime : it provides the missing piece in mathrm{Re}A_0 for M_{G^prime }=(3.5–4.0), mathrm{TeV}.
Highlights
The non-leptonic KL → π π decays have played already for almost 60 years an important role in particle physics and were instrumental in the construction of the standard model (SM) and in the selection of allowed extensions of this model
To investigate whether a subleading part of the I = 1/2 rule, at the level of 20–30 %, could be due to new physics (NP) contributions originating in tree-level FCNC transitions mediated by a heavy colourless gauge boson Z or an SU (3)c colour octet of gauge bosons G
Page 37 of 40 2950 dual representation of QCD as a theory of weakly interacting mesons [17] and by QCD lattice calculations [18,19,20,21] we concentrated our analysis in the context of the first goal on the large amplitude Re A0, which is by a factor of 22 larger than Re A2 and its experimental value is not fully explained in these two approaches
Summary
The non-leptonic KL → π π decays have played already for almost 60 years an important role in particle physics and were instrumental in the construction of the standard model (SM) and in the selection of allowed extensions of this model. As the missing piece in Re A0 is by about 8 times larger than the measured value of Re A2, the required NP must have a particular structure: tiny or absent contributions to Re A2 and at the same time large contributions to Re A0 It should satisfy other constraints coming from εK , MK , ε /ε and rare kaon decays. In order not to spoil the agreement of the SM with the data for Re A2 only Wilson coefficients of QCD-penguin operators should be modified In this context we recall that in [25] an additional enhancement (with respect to previous estimates) of the QCD-penguin contributions to Re A0 has been identified.
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