Mixing Mass Differences Research Articles

Signals of New Physics in B-Mesons Mixing Mass and Decay Width Differences

The measurement of $$ {B}_q^0-\overline{B_q^0} $$ (q = d, s) mixing mass difference and decay width differences is an important ingredient for searching physics beyond the standard model. In this paper, we investigate $$ {B}_q^0-\overline{B_q^0} $$ mixing mass and decay width differences in the Z′ model. It is found that these differences are enhanced relative to the standard model prediction and give signals for new physics. Depending upon the mass of Z′ boson, the Z′-mediated flavour-changing neutral current gives a contribution to mass and decay width differences in $$ {B}_q^0-\overline{B_q^0} $$ mixing.

The Return of Kaon Flavour Physics

Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in $K_L\to\pi\pi$ decays represented by $\varepsilon_K$ and the ratio $\varepsilon'/\varepsilon$. In this millennium this role has been taken over by $B_{s,d}$ and $D$ mesons. However there is no doubt that in the coming years we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays $K^+\rightarrow \pi^+\nu\bar\nu$ and $K_{L}\rightarrow\pi^0\nu\bar\nu$ and the improved SM predictions for the ratio $\varepsilon'/\varepsilon$, for $\varepsilon_K$ and the $K^0-\bar K^0$ mixing mass difference $\Delta M_K$. Theoretical progress on the decays $K_{L,S}\to\mu^+\mu^-$ and $K_L\to\pi^0\ell^+\ell^-$ is also expected. They all are very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the $K\to\pi\pi$ isospin amplitudes ${\rm Re} A_0$ and ${\rm Re} A_2$ improves. This talk summarizes several aspects of this exciting field. In particular we emphasize the role of the Dual QCD approach in getting the insight into the numerical Lattice QCD results on $K^0-\bar K^0$ mixing and $K\to\pi\pi$ decays.

Particle–antiparticle mixing, [formula omitted] and the unitarity triangle in the littlest Higgs model

We calculate the K 0 – K ¯ 0 , B d , s 0 – B ¯ d , s 0 mixing mass differences Δ M K , Δ M d , s and the CP-violating parameter ɛ K in the littlest Higgs (LH) model. For f / v as low as 5 and the Yukawa parameter x L < 0.8 , the enhancement of Δ M d amounts to at most 20%. Similar comments apply to Δ M s and ɛ K . The correction to Δ M K is negligible. The dominant new contribution in this parameter range, calculated here for the first time, comes from the box diagrams with ( W L ± , W H ± ) exchanges and ordinary quarks that are only suppressed by the mass of W H ± but do not involve explicit O ( v 2 / f 2 ) factors. This contribution is strictly positive. The explicit O ( v 2 / f 2 ) corrections to the SM diagrams with ordinary quarks and two W L ± exchanges have to be combined with the box diagrams with a single heavy T quark exchange for the GIM mechanism to work. These O ( v 2 / f 2 ) corrections are found to be of the same order of magnitude as the ( W L ± , W H ± ) contribution but only for x L approaching 0.8 they can compete with it. We point out that for x L > 0.85 box diagrams with two T exchanges have to be included. Although formally O ( v 4 / f 4 ) , this contribution is dominant for x L ≈ 1 due to non-decoupling of T that becomes fully effective only at this order. We emphasize, that the concept of the unitarity triangle is still useful in the LH model, in spite of the O ( v 2 / f 2 ) corrections to the CKM unitarity involving only ordinary quarks. We demonstrate the cancellation of the divergences in box diagrams that appear when one uses the unitary gauge for W L ± and W H ± .

Relations between ΔMs,d and [formula omitted] in models with minimal flavour violation

The predictions for the Bs,d–Bs,d mixing mass differences ΔMs,d and the branching ratios Br(Bs,d→μμ̄) within the Standard Model (SM) and its extensions suffer from considerable hadronic uncertainties present in the Bs,d-meson decay constants FBs,d that enter these quantities quadratically. We point out that in the restricted class of models with minimal flavour violation (MFV) in which only the SM low energy operators are relevant, the ratios Br(Bq→μμ̄)/ΔMq (q=s,d) do not depend on FBq and the CKM matrix elements. They involve in addition to the short distance functions and B-meson lifetimes only the non-perturbative parameters Bs,d. The latter are under much better control than FBs,d. Consequently in these models the predictions for Br(Bq→μμ̄) have only small hadronic uncertainties once ΔMq are experimentally known. Of particular interest is also the relation Br(Bs→μμ̄)Br(Bd→μμ̄)=BdBsτ(Bs)τ(Bd)ΔMsΔMd that is practically free of theoretical uncertainties as Bs/Bd=1 up to small SU(3) breaking corrections. Using these ideas within the SM we find much more accurate predictions than those found in the literature: Br(Bs→μμ̄)=(3.4±0.5)×10−9 and Br(Bd→μμ̄)=(1.00±0.14)×10−10 were in the first case we assumed as an example ΔMs=(18.0±0.5)/ps.

The impact of universal extra dimensions on the unitarity triangle and rare K and B decays

We calculate the contributions of the Kaluza–Klein (KK) modes to the K L – K S mass difference Δ M K , the parameter ε K , the B 0 d, s – B 0 d,s mixing mass differences Δ M d, s and rare decays K +→π +ν ν ̄ , K L→π 0ν ν ̄ , K L → μ + μ −, B→X s,dν ν ̄ and B s,d→μ μ ̄ in the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. For the compactification scale 1/ R=200 GeV the KK effects in these processes are governed by a 17% enhancement of the Δ F=2 box diagram function S( x t ,1/ R) and by a 37% enhancement of the Z 0 penguin diagram function C( x t /1/ R) relative to their Standard Model (SM) values. This implies the suppressions of | V td | by 8%, of η ̄ by 11% and of the angle γ in the unitarity triangle by 10°. Δ M s is increased by 17%. Δ M K is essentially uneffected. All branching ratios considered in this paper are increased with a hierarchical structure of enhancements: K +→π +ν ν ̄ (16%) , K L→π 0ν ν ̄ (17%) , B→X dν ν ̄ (22%) , (K L→μ μ ̄ ) SD (38%) , B→X sν ν ̄ (44%) , B d→μ μ ̄ (46%) and B s→μ μ ̄ (72%) . For 1/ R=250 (300) GeV all these effects are decreased roughly by a factor of 1.5 (2.0). We emphasize that the GIM mechanism assures the convergence of the sum over the KK modes in the case of Z 0 penguin diagrams and we give the relevant Feynman rules for the five-dimensional ACD model. We also emphasize that a consistent calculation of branching ratios has to take into account the modifications in the values of the CKM parameters. As a byproduct we confirm the dominant O(g 2G F m t 4R 2) correction from the KK modes to the Z 0b b ̄ vertex calculated recently in the large m t limit.