Year-end Sale % OFF 
Abstract
I summarize the status of the ∆I = 1/2 rule in K → ππ decays within an analytic approach based on the dual representation of QCD as a theory of weakly interacting mesons for large N , where N is the number of colours. This approximate approach, developed in the 1980s by William Bardeen, Jean-Marc Gerard and myself, allowed us already 28 years ago to identify the dominant dynamics behind the ∆I = 1/2 rule. However, the recent inclusion of lowest-lying vector meson contributions in addition to the pseudoscalar ones to hadronic matrix elements of current-current operators and the calculation of the corresponding Wilson coefficients in a momentum scheme at the NLO improved significantly the matching between quark-gluon short distance contributions and meson long distance contributions over our results in 1986. We obtain satisfactory description of the ReA 2 amplitude and ReA 0 /ReA 2 = 16.0 ± 1.5 to be compared with its experimental value of 22.3. While this difference could be the result of present theoretical uncertainties in our approach, it cannot be excluded that New Physics (NP) is here at work. The analysis by Fulvia De Fazio, Jennifer Girrbach-Noe and myself shows that indeed a tree-level Z ′ or G ′ exchanges with masses in the reach of the LHC and special couplings to quarks can significantly improve the theoretical status of the ∆I = 1/2 rule while satisfying constraints from e K , e ′/e , ∆MK , LEP-II and the LHC. The ratio e ′/e plays an important role in these considerations. I stress that our approach allows to understand the physics behind recent numerical results obtained in lattice QCD not only for the ∆I = 1/2 rule but also for the parameter B K that enters the evaluation of e K . In contrast to the ∆I = 1/2 rule and e ′/e the chapter on B K in QCD appears to be basically closed.
Highlights
One of the puzzles of the 1950s was a large disparity between the measured values of the real parts of the isospin amplitudes A0 and A2 for a kaon to decay into two pions which on the basis of usual isospin considerations were expected to be of the same order
In 2014 we know the experimental values of the real parts of these amplitudes very precisely [1]
While lattice QCD will eventually provide much more accurate values for ReA0 and ReA2 than it is possible in our approach, our approach provided in my opinion better insight into the dynamics behind this rule than it was possible with lattice QCD until now
Summary
One of the puzzles of the 1950s was a large disparity between the measured values of the real parts of the isospin amplitudes A0 and A2 for a kaon to decay into two pions which on the basis of usual isospin considerations were expected to be of the same order. As demonstrated by Bardeen, Gérard and myself already in 1986 [4] and improved on the technical level by us recently [5] the dominant dynamics behind the ΔI = 1/2 rule has a simple structure. To this end one should note that from the point of view of operator product expansion the calculation we have just performed to get (5) corresponds to. The evaluation of the Wilson coefficient of the operator Q2 in a free (from the point of view of strong interactions) theory of quarks, which corresponds to scales μ = O(MW ) and setting αs(MW ) = 0. See in particular [11] and most recent papers [12, 13] where further references can be found
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
