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Register a new userepsilon/epsilon and Rare K and B Decays in the MSSM
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We analyze the CP violating ratio epsilon/epsilon and rare K and B decays in the MSSM with minimal flavour and CP violation, including NLO QCD corrections and imposing constraints on the supersymmetric parameters coming from epsilon, B_{d,s}^0-bar B_{d,s}^0 mixings, B to X_s gamma, Delta rho in the electroweak precision studies and from the lower bound on the neutral Higgs mass. We provide a compendium of phenomenologically relevant formulae in the MSSM. Denoting by T(Q) the MSSM prediction for a given quantity normalized to the Standard Model result we find the ranges: 0.53 < T(epsilon/epsilon) < 1.07, 0.65 < T(K^+ to pi^+ nu nubar) < 1.02, 0.41 < T(K_L to pi^0 nu nubar) < 1.03, 0.48 < T(K_L to pi^0 e^+ e^-) < 1.10, 0.73 < T(B to X_s nu nubar) < 1.34 and 0.68 < T(B_s to mu^+ mu^-) < 1.53. We point out that these ranges will be considerably reduced when the lower bounds on the neutral Higgs mass and tan beta improve. Some contour plots illustrate the dependences of the quantities above on the relevant supersymmetric parameters. As a byproduct of this work we update our previous analysis of epsilon/epsilon in the SM and find in NDR epsilon/epsilon = (9.2^{+6.8}_{-4.0}), a value 15 % higher than in our 1999 analysis.
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We summarize a recent strategy for a global analysis of the B -> pi pi, pi K systems and rare decays. We find that the present B -> pi pi and B -> pi K data cannot be simultaneously described in the Standard Model. In a simple extension in which new physics enters dominantly through Z^0 penguins with a CP-violating phase, only certain B -> pi K modes are affected by new physics. The B -> pi pi data can then be described entirely within the Standard Model but with values of hadronic parameters that reflect large non-factorizable contributions. Using the SU(3) flavour symmetry and plausible dynamical assumptions, we can then use the B -> pi pi decays to fix the hadronic part of the B -> pi K system and make predictions for various observables in the B_d -> pi^-+ K^+- and B^+- -> pi^+- K decays that are practically unaffected by electroweak penguins. The data on the B^+- -> pi^0 K^+- and B_d -> pi^0 K modes allow us then to determine the electroweak penguin component which differs from the Standard Model one, in particular through a large additional CP-violating phase. The implications for rare K and B decays are spectacular. In particular, the rate for K_L -> pi^0 nu bar nu is enhanced by one order of magnitude, the branching ratios for B_{d,s} -> mu^+ mu^- by a factor of five, and BR(K_L -> pi^0 e^+ e^-, pi^0 mu^+ mu^-) by factors of three.
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.
Three years after the completion of the next-to-leading order calculation, the status of the theoretical estimates of $epsilon/epsilon$ is reviewed. In spite of the theoretical progress, the prediction of $epsilon/epsilon$ is still affected by a 100% theoretical error. In this paper the different sources of uncertainty are critically analysed and an updated estimate of $epsilon/epsilon$ is presented. Some theoretical implications of a value of $epsilon/epsilon$ definitely larger than $10^{-3}$ are also discussed.
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.
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.
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