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We point out that, given the current experimental status of radiative kaon decays, a subclass of the ${cal O} (p^4)$ counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay $K^pm to pi ^pm pi ^0 l^+ l^-$, currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the ${cal{O}}(p^4)$ weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of $K_Sto pi^+pi^-gamma^*$, which will be measured by LHCb and will help reduce (together with the related $K_L$ decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the ${cal{O}}(p^4)$ weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.
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Studies of the reaction $gammapitopipi$, in the context of the ongoing Primakoff program of the COMPASS experiment at CERN, give access to the radiative couplings of the $rho(770)$ and $rho_3(1690)$ resonances. We provide a vector-meson-dominance estimate of the respective radiative width of the $rho_3$, $Gamma_{rho_3topigamma}=48(18)$ keV, as well as its impact on the $F$-wave in $gammapitopipi$. For the $rho(770)$, we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the $gammapitopipi$ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.
We calculate 1-loop radiative corrections to the $hZZ$ and $hWW$ couplings in models with next--to--simplest Higgs sectors satisfying the electroweak $rho$ parameter equal to 1 at tree level: the Higgs singlet model, the two-Higgs doublet models, and the Georgi-Machacek model. Under theoretical and current experimental constraints, the three models have different correlations between the deviations in the $hZZ$ and $hWW$ couplings from the standard model predictions. In particular, we find for each model predictions with no overlap with the other two models.
Major new experimental efforts on detecting CP violation in $B$ decays will very soon go on the air. Recent developments suggest that final state interaction phases in exclusive decays of $B$ are unlikely to be small indicating the possibility of observable direct CP asymmetries in these channels. CLEO results on charmless hadronic modes suggest penguin amplitudes are rather big implying that the extraction of $alpha$ from $B^0$-$bar B^0$ alone will be difficult, thus necessitating also information from direct CP ull. Importance of $B(B_s)$ decays to two vectors for model independent tests of electroweak penguins and for extraction of $alpha(gamma)$ is emphasized. Inclusive $bto sg^ast$ and related modes, e.g. $Bto eta^prime X_s$, are very good probes of CP-odd phase(s) due to beyond the standard model physics. On the other hand, $bto dg^ast$ and related modes, e.g. $Bto eta^prime X_d$ are more suitable for CP violation due to the CKM phase. Two body $b$-quark decays: $bto Mq_f$ leading to semi-inclusive, $B$ decays, $Bto MX$ (with $2lsim E_Mlsim2.8$ GeV), are very interesting and important. Their theory is relatively clean; partial rate asymmetries may be large in several cases (e.g. $M=K^ast, K, rho, pi...$) and a few cases provide very good probe of electroweak penguins.
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