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Register a new userDelta I=1/2 and epsilon/epsilon in Large-Nc QCD
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We present new results for the matrix elements of the Q_6 and Q_4 penguin operators, evaluated in a large-Nc approach which incorporates important O(N_c^2frac{n_f}{N_c}) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as MS-bar. Numerically, we find that there is a large positive contribution to the Delta I =1/2 matrix element of Q_6 and hence to the direct CP-violation parameter epsilon/epsilon. We also present results for the Delta I = 1/2 rule in K -> pi pi amplitudes, which incorporate the related and important ``eye-diagram contributions of O(N_c^2frac{1}{N_c}) from the Q_2 operator (i.e. the penguin-like contraction). The results lead to an enhancement of the Delta I = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem.
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Within the differential equation method for multiloop calculations, we examine the systems irreducible to $epsilon$-form. We argue that for many cases of such systems it is possible to obtain nontrivial quadratic constraints on the coefficients of $epsilon$-expansion of their homogeneous solutions. These constraints are the direct consequence of the existence of symmetric $(epsilon+1/2)$-form of the homogeneous differential system, i.e., the form where the matrix in the right-hand side is symmetric and its $epsilon$-dependence is localized in the overall factor $(epsilon+1/2)$. The existence of such a form can be constructively checked by available methods and seems to be common to many irreducible systems, which we demonstrate on several examples. The obtained constraints provide a nontrivial insight on the structure of general solution in the case of the systems irreducible to $epsilon$-form. For the systems reducible to $epsilon$-form we also observe the existence of symmetric form and derive the corresponding quadratic constraints.
The ratio $epsilon/epsilon$ measures the size of the direct CP violation in $K_Ltopipi$ decays $(epsilon^prime)$ relative to the indirect one described by $epsilon$ and is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years. Due to the smallness of $epsilon/epsilon$ its measurement required heroic efforts in the 1980s and the 1990s on both sides of the Atlantic with final results presented by NA48 and KTeV collaborations 20 years ago. Unfortunately, even 45 years after the first calculation of $epsilon/epsilon$ we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics contributions to this ratio. This is due to significant non-perturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. While the significant control over the short distance perturbative effects has been achieved already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to $epsilon/epsilon$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $epsilon/epsilon$ is very significant. My own work on $epsilon/epsilon$ started in 1983 and involved both perturbative and non-perturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of $epsilon/epsilon$ including several historical remarks not known to everybody. The present status of the $Delta I=1/2$ rule is also summarized. This story is dedicated to Jean-Marc Gerard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.
Recently, the standard model prediction of $epsilon/epsilon$ was improved, and a discrepancy from the experimental results was reported at the $2.9sigma$ level. We study the chargino contributions to $Z$ penguin especially with the vacuum stability constraint. The vacuum decay rate is investigated, and it is shown that the discrepancy can be explained if superparticles are lighter than 4-6 TeV. Correlations with $mathcal{B}(K_Ltopi^0 ubar u)$ and other experimental constraints are also discussed.
We generated configurations with the parametrized fixed-point Dirac operator D_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the distributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2 topological sectors with that of the Random Matrix Theory predictions. The ratios of expectation values of the lowest eigenvalues and the cumulative eigenvalue distributions are studied for all combinations of k and nu. After including the finite size correction from one-loop chiral perturbation theory we obtained for the chiral condensate in the MSbar scheme Sigma(2GeV)^{1/3}=0.239(11) GeV, where the error is statistical only.
The Standard Model prediction for $epsilon/epsilon$ based on recent lattice QCD results exhibits a tension with the experimental data. We solve this tension through $W_R^+$ gauge boson exchange in the $SU(2)_Ltimes SU(2)_Rtimes U(1)_{B-L}$ model with `charge symmetry, whose theoretical motivation is to attribute the chiral structure of the Standard Model to the spontaneous breaking of $SU(2)_Rtimes U(1)_{B-L}$ gauge group and charge symmetry. We show that $M_{W_R}<58$ TeV is required to account for the $epsilon/epsilon$ anomaly in this model. Next, we make a prediction for the neutron EDM in the same model and study a correlation between $epsilon/epsilon$ and the neutron EDM. We confirm that the model can solve the $epsilon/epsilon$ anomaly without conflicting the current bound on the neutron EDM, and further reveal that almost all parameter regions in which the $epsilon/epsilon$ anomaly is explained will be covered by future neutron EDM searches, which leads us to anticipate the discovery of the neutron EDM.
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