Mixing Violation Research Articles

Probing quantum decoherence at Belle II and LHCb

With the advent of Belle II and the LHCb upgrade, the precision measurements of various B-Physics observables are on cards. This holds significant potential for delving into physics beyond the standard model of electroweak interactions. These measurements can also serve as means to establish limits on phenomena occurring at much finer length scales, such as quantum decoherence, which may arise due to potential discreteness in space-time or non-trivial topological effects. In this work, we set up the formalism to investigate the impact of quantum decoherence on several potential observables in B meson systems. The approach employs the trace-preserving Kraus operator formalism, extending unitary evolution to non-unitary dynamics while maintaining complete positivity. In this formalism, the decoherence effects are parametrized in terms of a single parameter. Through the analysis of purely leptonic, semileptonic, and non-leptonic decays of B mesons, we identify observables that could, in principle, be influenced by decoherence. The theoretical expressions are provided without neglecting the impact of decay width difference (∆Γ) and CP violation in mixing. Considering that many of these observables can be measured with high precision using the abundant data collected by LHCb and Belle II, our formalism can be applied to establish constraints on the decoherence parameter through multiple decay channels. This offers an alternative set-up for such studies, which, at present, are predominantly conducted in the neutrino sector.

CP violation in mixing and oscillations for leptogenesis. Part II. The highly degenerate case

We extend to the highly degenerate case a recent approach for analyzing the sources of CP violation in baryogenesis models with quasi-degenerate neutrinos. In this approach an expansion of the resummed propagator around the poles is plugged into a quantum field theory model of neutrino oscillations and a source term for the time evolution of the lepton asymmetry is built directly from the probabilities of lepton number violating processes involving only stable particles. This allows for a transparent consideration of unitarity requirements. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. For the highly degenerate case, i.e. when the mass difference between two neutrinos is similar or smaller than their decay widths, we find that in general the mixing and oscillation terms contribute with opposite signs to the generation of lepton asymmetry and the contribution of the interference term is typically very relevant and crucial to ensure unitarity is satisfied. Moreover, the expressions we obtain are finite in the double degenerate limit of equal masses and couplings. The calculations are done in a simple scalar toy model.

Observation of the Mass Difference between Neutral Charm-Meson Eigenstates.

A measurement of mixing and CP violation in neutral charm mesons is performed using data reconstructed in proton-proton collisions collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of 5.4 fb^{-1}. A total of 30.6 million D^{0}→K_{S}^{0}π^{+}π^{-} decays are analyzed using a method optimized for the measurement of the mass difference between neutral charm-meson eigenstates. Allowing for CP violation in mixing and in the interference between mixing and decay, the mass and decay-width differences are measured to be x_{CP}=[3.97±0.46(stat)±0.29(syst)]×10^{-3} and y_{CP}=[4.59±1.20(stat)±0.85(syst)]×10^{-3}, respectively. The CP-violating parameters are measured as Δx=[-0.27±0.18(stat)±0.01(syst)]×10^{-3} and Δy=[0.20±0.36(stat)±0.13(syst)]×10^{-3}. This is the first observation of a nonzero mass difference in the D^{0} meson system, with a significance exceeding seven standard deviations. The data are consistent with CP symmetry and improve existing constraints on the associated parameters.

CP violation in mixing and oscillations in a toy model for leptogenesis with quasi-degenerate neutrinos

We study the sources of CP violation for baryogenesis models with quasi-degenerate neutrinos. Our approach is to use the renormalized propagator in a quantum field theory model of neutrino oscillations, paying close attention to unitarity requirements. From the probabilities of lepton number violating processes obtained in this way, we derive a source term for the time evolution of the lepton asymmetry. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. Given that this source term does not involve processes with unstable particles in the initial or final states, neither does it require to calculate number densities of neutrinos, no subtraction of real intermediate states must be performed. In equilibrium the source term is null, as demanded by unitarity and CPT invariance, due to a cancellation between the terms coming from CP violation in mixing and oscillations. The calculations are done in a simple scalar toy model, and the resummed propagator is diagonalized at first order in the decay widths over the mass difference. We also comment on the effect of the interference term, which is mild at the order we work, but seems to become more important with increasing degeneracy.

Branching Ratio and CP Violation in $${B}_{{s}}^{{0}}\rightarrow{\rho}^{{0}}{\phi}$$ Decay in the Framework of QCD Factorization

We present an analytic calculation of Branching Ratio (BR) and Charge–Parity (CP) violating asymmetries of the $$B_{s}^{0}$$ -meson decay into the two light vectors $$\rho^{0}\phi$$ . In doing this we calculate the helicity amplitude of the present decay in the framework of QCD factorization approach. We find the BR of $$B_{s}^{0}\rightarrow\rho^{0}\phi=(0.26\pm 0.04)\times 10^{-6}$$ which is in agreement with the recent theoretical predictions and experimental measurements. We also calculate the direct CP violation, CP violation in mixing and CP violation due to interference which are $$0.107\pm 0.013$$ , $$0.256\pm 0.036$$ , and $$0.960\pm 0.009$$ , respectively.

Dealing with T and CPT violations in mixing as well as direct and indirect CP violations for neutral mesons decaying to two vectors

A large number of observables can be constructed from differential decay rate based on the polarization of final state while considering decay of a neutral meson (P^{0} text { or } {bar{P}}^{0}) to two vector particles. But all of these observables are not independent to each other since there are only a few independent theoretical parameters controlling the whole dynamics and therefore various relations among observables emerge. In this paper, we have studied the behaviour of observables for neutral meson decaying to two vectors in presence of T and C!P T violations in mixing accompanied by both direct and indirect C!P violations. We have expressed all of the fourteen unknown theoretical parameters for this scenario in terms observables only and constructed the complete set of thirty four relations among observables whose violation would signify the existence of some new Physics involving direct violation of C!P T. In addition, using this formalism we have studied three special cases too: (a) SM scenario, (b) SM plus direct C!P violation (c) SM plus T and C!P T violation in mixing.

Branching ratio and CP violation in Bs0 → K∗0K̄∗0 decay in the framework of QCD factorization

We present an analytic calculation of Branching Ratio (BR) and Charge-Parity (CP) violating asymmetries of the [Formula: see text] meson decay into the two light vectors [Formula: see text] by calculating the helicity amplitude in the framework of quantum chromodynamics (QCD) factorization approach. We find the BR of [Formula: see text] which is in full agreement with the recent theoretical predictions and experimental measurements. We also calculate the direct CP violation, CP violation in mixing and CP violation due to interference which are [Formula: see text], [Formula: see text], and [Formula: see text], respectively.

Branching Ratio and CP Violation in 
 
 
 
 
 B
 
 s
 
 0
 
 ¯
 
 
 
 → ϕϕ Decay in the Framework of QCD Factorization

We present an analytic calculation of Branching Ratio (BR) and Charge-Parity (CP) violating asymmetries of the B s 0 ¯ meson decay into the two light vectors ϕ ϕ . In doing this we calculate the helicity amplitude of the present decay in the framework of QCD factorization approach. We find the BR of B s 0 ¯ → ϕ ϕ = ( 1.56 ± 0.23 ) × 10 − 5 . We also calculate the direct CP violation, CP violation in mixing and CP violation due to interference which are A C P dir = 0.00355 ± 0.00152 , A C P mix = − 0.00629 ± 0.03119 and A C P Δ Γ = 0.99997 ± 0.00019 , respectively. Our results are in agreement with the recent theoretical predictions and experimental measurements.

Analytic Calculations of the Branching Ratio and CP Violation in Bs0 → Ds+Ds− Decay

We present an analytic calculation of Branching Ratio (BR) and Charge-Parity (CP) violating asymmetries of the [Formula: see text] meson decays to [Formula: see text] by calculating the amplitude and the decay width of the process including the chiral loop and gluon condensate to first-order. We find the BR of [Formula: see text] which is in agreement with other experimental measurements and theoretical predictions. We also calculate the direct CP violation, CP violation in mixing and CP violation due to interference which are [Formula: see text], [Formula: see text] and [Formula: see text], respectively.

Measurement of the Mass Difference Between Neutral Charm-Meson Eigenstates.

We report a measurement of the mass difference between neutral charm-meson eigenstates using a novel approach that enhances sensitivity to this parameter. We use 2.3×10^{6} D^{0}→K_{S}^{0}π^{+}π^{-} decays reconstructed in proton-proton collisions collected by the LHCb experiment in 2011 and 2012. Allowing for CP violation in mixing and in the interference between mixing and decay, we measure the CP-averaged normalized mass difference x_{CP}=[2.7±1.6(stat)±0.4(syst)]×10^{-3} and the CP-violating parameter Δx=[-0.53±0.70(stat)±0.22(syst)]×10^{-3}. The results are consistent with CP symmetry. These determinations are the most precise from a single experiment and, combined with current world-average results, yield the first evidence that the masses of the neutral charm-meson eigenstates differ.

Symmetry violations at BABAR

Following a brief introduction I report the current status of symmetry violation tests from the BABAR experiment, including recent results on the measurement of T violation, and searches for CP and T violation in mixing.

Understanding the like-sign dimuon charge asymmetry inpp¯collisions

The D\O\ collaboration has measured the like-sign dimuon charge asymmetry in $p \bar{p}$ collisions at the Fermilab Tevatron collider. The result is significantly different from the standard model expectation of CP violation in mixing. In this paper we consider the possible causes of this asymmetry and identify one standard model source not considered before. It decreases the discrepancy of the like-sign dimuon charge asymmetry with the standard model prediction, although does not eliminate it completely.

Measurement ofD0−D¯0Mixing from a Time-Dependent Amplitude Analysis ofD0→K+π−π0Decays

We present evidence of $D^0$-$\bar{D^0}$ mixing using a time-dependent amplitude analysis of the decay D0->K+pi-pi0 in a data sample of 384 fb^-1 collected with the BaBar detector at the PEP-II e+e- collider at SLAC. Assuming CP conservation, we measure the mixing parameters x'_{Kpipi0} = [2.61^{+0.57}_{-0.68} (stat.) +- 0.39 (syst.)]%, y'_{Kpipi0} = [-0.06 ^{+0.55}_{-0.64} (stat.) +- 0.34 (syst.)]%. The confidence level for the data to be consistent with the no-mixing hypothesis is 0.1%, including systematic uncertainties. This result is inconsistent with the no-mixing hypothesis with a significance of 3.2 standard deviations. We find no evidence of CP violation in mixing.

IndirectCPviolation and implications forD0−D¯0andBs−B¯smixing

The two kinds of indirect $CP$ violation in neutral meson systems are related, in the absence of new weak phases in decay. The result is a model-independent expression relating $CP$ violation in mixing, $CP$ violation in the interference of decays with and without mixing, and the meson mass and width differences. It relates the semileptonic and time-dependent $CP$ asymmetries, and pairs of time-dependent $CP$ asymmetries in ${D}^{0}$ decays to non-$CP$ eigenstates. $CP$ violation in the interference of decays with and without mixing is related to the mixing parameters of relevance to model building: the off-diagonal mixing matrix elements $|{M}_{12}|$, $|{\ensuremath{\Gamma}}_{12}|$, and ${\ensuremath{\phi}}_{12}\ensuremath{\equiv}\mathrm{arg}({M}_{12}/{\ensuremath{\Gamma}}_{12})$. Incorporating this relation into a fit to the ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing data implies a level of sensitivity to $|{\ensuremath{\phi}}_{12}^{D}|$ of 0.10 (rad) at $1\ensuremath{\sigma}$. The formalism is extended to include new weak phases in decay, and in ${\ensuremath{\Gamma}}_{12}$. The phases are highly constrained by direct $CP$ violation measurements. Consequently, the bounds on $|{\ensuremath{\phi}}_{12}^{D}|$ are not significantly altered, and the effects of new weak phases in decay could be difficult to observe at a high luminosity flavor factory (${D}^{0}$) or at the LHC (${B}_{s}$) via violations of the above relations, unlike in direct $CP$ violation.

Testing New IndirectCPViolation

If new CP violating physics contributes to neutral meson mixing, but its contribution to CP violation in decay amplitudes is negligible, then there is a model independent relation between four (generally independent) observables related to the mixing: the mass splitting (x), the width splitting (y), the CP violation in mixing (1-|q/p|), and the CP violation in the interference of decays with and without mixing (phi). For the four neutral meson systems, this relation can be written in a simple approximate form: y tan phi approximately x(1-|q/p|). In the K system, all four observables have been measured and obey the relation to excellent accuracy. For the B(s) and D systems, new predictions are provided. The success or failure of these relations will probe the physics that is responsible for the CP violation.

New Ways to Soft Leptogenesis

Soft supersymmetry breaking terms involving heavy singlet sneutrinos provide new sources of lepton number violation and of CP violation. In addition to the CP violation in mixing, investigated previously, we find that `soft leptogenesis' can be generated by CP violation in decay and in the interference of mixing and decay. These additional ways to leptogenesis can be significant for a singlet neutrino Majorana mass that is not much larger than the supersymmetry breaking scale, $M < 100 m_{SUSY}$. In contrast to CP violation in mixing, for some of these new contributions the sneutrino oscillation rate can be much faster than the decay rate, so that the bilinear scalar term need not be smaller than its natural scale.

A non-standard CP transformation leading to maximal atmospheric neutrino mixing

We discuss a neutrino mass matrix Mν originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle θ13 of the lepton mixing matrix U is allowed and—in the usual phase convention—CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a seesaw extension of the Standard Model, with three right-handed neutrinos and three Higgs doublets, where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard CP symmetry.

Isospin violation in mixing and decays of ρ and ω mesons

The influence of isospin-violating (ρ 0, ω) mixing is discussed for any pair of decays of ρ 0, ω into the same final state. It is demonstrated, in analogy to the CP violation in neutral kaon decays, that isospin violation can manifest itself in various forms: direct violation in amplitudes and/or violation due to mixing. In addition to the known decays (ρ 0, ω) → π + π − and (ρ 0, ω) → π 0γ, the pair of decays to e + e − and the whole set of radiative decays with participation of ρ 0, ω (in initial or final states) are also shown to be useful and promising for studies. Existing data on these decays agree with the universal character of the mixing parameter and indirectly support enhancement of ρ 0 → π 0 γ in respect to ρ ± → π ± γ. Future precise measurements will allow one to separate different forms of isospin violation and elucidate their mechanisms.

Bell inequality and CP violation in the neutral kaon system

For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.

On the determination of Δm and ΔΓ in tagged [formula omitted] decays

We consider the time dependence of the decays of tagged D 0 and D 0 to arbitrary decay modes. We expand each decay width as exp(− Γt) times a series in Γt, where Γ is the average decay width of the mass eigenstates D h and D l , and examine the first three terms of the series. We show that experimental information on the coefficients of these terms allows in principle to compute the mixing parameters Δm, ΔΓ and η = | q p | i.e., the mass and decay-width differences of mass eigenstates, and CP violation in mixing. In particular, we discuss the possibility of extracting these parameters if one disposes of the measurement of the time-dependent decay widths of D 0(t) D 0(t) to a single final state f and make a comparison with the situation when information about two different final states f and f′ is available.