CP Eigenstates Research Articles

Measurement of the CP -even fraction of D0→K+K−π+π−

A determination of the CP-even fraction F+ in the decay D0→K+K−π+π− is presented. Using 2.93 fb−1 of e+e−→ψ(3770)→DD¯ data collected by the BESIII detector, one charm meson is reconstructed in the signal mode and the other in a CP eigenstate or the decay D→KS,L0π+π−. Analysis of the relative rates of these double-tagged events yields the result F+=0.730±0.037±0.021, where the first uncertainty is statistical and the second is systematic. This is the first model-independent measurement of F+ in D0→K+K−π+π− decays.Received 15 December 2022Accepted 24 January 2023DOI:https://doi.org/10.1103/PhysRevD.107.032009Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle mixing & oscillationsPropertiesCP symmetryParticles & Fields

Measurement of the CP -even fraction of D0→π+π−π+π−

A measurement of the CP-even fraction of the decay D0→π+π−π+π− is performed with a quantum-correlated ψ(3770)→DD¯ data sample collected by the BESIII experiment, corresponding to an integrated luminosity of 2.93 fb−1. Using a combination of CP eigenstates, D→π+π−π0 and D→KS,L0π+π− as tagging modes, the CP-even fraction is measured to be F+4π=0.735±0.015±0.005, where the first uncertainty is statistical and the second is systematic. This is the most precise determination of this quantity to date. It provides valuable model-independent input for the measurement of the angle γ of the Cabibbo-Kobayashi-Maskawa matrix with B±→DK± decays, and for time-dependent studies of CP violation and mixing in the D0−D¯0 system.Received 22 August 2022Accepted 21 October 2022DOI:https://doi.org/10.1103/PhysRevD.106.092004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle mixing & oscillationsPropertiesCP violationParticles & Fields

Explaining excesses in four-leptons at the LHC with a double peak from a CP violating Two Higgs Doublet Model

Extended scalar sectors with additional degrees of freedom appear in many scenarios beyond the Standard Model. Heavy scalar resonances that interact with the neutral current could be discovered via broad resonances in the tails of the four-lepton invariant mass spectrum, where the Standard Model background is small and well understood. In this article we consider a recent ATLAS measurement of four-lepton final states, where the data is in excess over the background for invariant masses above 500 GeV. We discuss the possibility that this excess could be interpreted as a “double peak” from the two extra heavy neutral scalars of a CP violating Two Higgs Doublet Model, both coupling to the Z boson. We apply an iterative fitting procedure to find viable model parameters that can match the excess, resulting in a benchmark point where the observed four-lepton invariant mass spectrum can be explained by two scalar particles H2 and H3, with masses of 544 GeV and 629 GeV, respectively, being admixtures of the CP eigenstates. Our explanation predicts additional production processes for toverline{t} , W+W−, 4b and γγ, some of which have cross sections close to the current experimental limits. Our results further imply that the electric dipole moment of the electron should be close to the present bounds.

Dispersive and absorptive CP violation in D0−D¯0 mixing

CP violation (CPV) in $D^0-\overline{D^0}$ mixing is described in terms of the dispersive and absorptive `weak phases' $\phi_f^M$ and $\phi_f^\Gamma$. They parametrize CPV originating from the interference of $D^0$ decays with and without dispersive mixing, and with and without absorptive mixing, respectively, for CP conjugate hadronic final states $f$, $\bar f$. These are distinct and separately measurable effects. For CP eigenstate final states, indirect CPV only depends on $\phi_f^M$ (dispersive CPV), whereas $\phi_f^\Gamma$ (absorptive CPV) can only be probed with non-CP eigenstate final states. Measurements of the final state dependent phases $\phi_f^M$, $\phi_f^\Gamma$ determine the intrinsic dispersive and absorptive mixing phases $\phi_2^M$ and $\phi_2^\Gamma$. The latter are the arguments of the dispersive and absorptive mixing amplitudes $M_{12}$ and $\Gamma_{12}$, relative to their dominant ($\Delta U=2$) $U$-spin components. The intrinsic phases are experimentally accessible due to approximate universality: in the SM, and in extensions with negligible new CPV phases in Cabibbo favored/doubly Cabibbo suppressed (CF/DCS) decays, the deviation of $\phi_f^{M,\Gamma}$ from $\phi_2^{M,\Gamma}$ is negligible in CF/DCS decays $D^0 \to K^\pm X$, and below $10\% $ in CF/DCS decays $D^0 \to K_{S,L} X$ (up to precisely known $O(\epsilon_K)$ corrections). In Singly Cabibbo Suppressed (SCS) decays, QCD pollution enters at $O(\epsilon)$ in $U$-spin breaking and can be significant, but is $O(\epsilon^2)$ in the average over $f=K^+K^-$, $\pi^+\pi^-$. SM estimates yield $\phi_2^M, \phi_2^\Gamma = O(0.2\%)$. A fit to current data allows $O(10)$ larger phases at $2\sigma$, from new physics. A fit based on naively extrapolated experimental precision suggests that sensitivity to $\phi_2^{M}$ and $\phi_2^{\Gamma}$ in the SM may be achieved at the LHCb Phase II upgrade.

Vh@nnlo-v2: new physics in Higgs Strahlung

Introducing version 2 of the code vh@nnlo [1], we study the effects of a number of new-physics scenarios on the Higgs-Strahlung process. In particular, the cross section is evaluated within a general 2HDM and the MSSM. While the Drell-Yan-like contributions are consistently taken into account by a simple rescaling of the SM result, the gluon-initiated contribution is supplemented by squark-loop mediated amplitudes, and by the s-channel exchange of additional scalars which may lead to conspicuous interference effects. The latter holds as well for bottom-quark initiated Higgs Strahlung, which is also included in the new version of vh@nnlo. Using an orthogonal rotation of the three Higgs CP eigenstates in the 2HDM and the MSSM, vh@nnlo incorporates a simple means of CP mixing in these models. Moreover, the effect of vector-like quarks in the SM on the gluon-initiated contribution can be studied. Beyond concrete models, vh@nnlo allows to include the effect of higher-dimensional operators on the production of CP-even Higgs bosons. Transverse momentum distributions of the final state Higgs boson and invariant mass distributions of the Vϕ final state for the gluon- and bottom-quark initiated contributions can be studied. Distributions for the Drell-Yan-like component of Higgs Strahlung can be included through a link to MCFM. vh@nnlo can also be linked to FeynHiggs and 2HDMC for the calculation of Higgs masses and mixing angles. It can also read these parameters from an SLHA-file as produced by standard spectrum generators. Throughout the manuscript, we highlight new-physics effects in various numerical examples, both at the inclusive level and for distributions.

Using time-dependent indirect CP asymmetries to measure T and CPT violation in B0–[formula omitted] mixing

Quantum field theory, which is the basis for all of particle physics, requires that all processes respect CPT invariance. It is therefore of paramount importance to test the validity of CPT conservation. In this Letter, we show that the time-dependent, indirect CP asymmetries involving B decays to a CP eigenstate contain enough information to measure T and CPT violation in B0–B¯0 mixing, in addition to the standard CP-violating weak phases. Entangled B0B¯0 states are not required (so that this analysis can be carried out at LHCb, as well as at the B factories), penguin pollution need not be neglected, and the measurements can be made using Bd0 or Bs0 mesons.

The photon polarization in radiative D decays, phenomenologically

We work out the phenomenology of untagged time-dependent analysis with radiative D^0-decays into CP eigenstates, which allows to probe the photon polarization by means of the charm mesons’ finite width difference. We show that D^0 rightarrow phi gamma or D^0 rightarrow bar{K}^{0 *} gamma decays, which are SM-dominated, or SM-like, respectively, together with U-spin allow to obtain chirality-predictions for radiative decay amplitudes. The order of magnitude of wrong-chirality contributions in the SM can be cross-checked with an up–down asymmetry in D^0 rightarrow bar{K}_1^0 (rightarrow bar{K} pi pi ) gamma . We explore the sensitivity to new physics in |Delta c|=|Delta u|=1 dipole couplings in the decays D^0 rightarrow rho ^0 gamma . We point out the possibility to test the SM with D_s rightarrow K_1^+( rightarrow K pi pi ) gamma decays.

Entangled Bd mesons and genuine T, CP and CPT asymmetry parameters

We establish the precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the neutral meson Bd states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-Factory of entangled states. Genuine asymmetry parameters in the time distribution of the asymmetries are identified and their measurability analysed, disentangling genuine and possible fake terms. The nine asymmetry parameters – three different observables for each one of the three symmetries – are expressed in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled Bd-meson states and we obtain a global fit to their values from the BaBar Collaboration experimental results. The possible fake terms are all compatible with zero. The information content of the nine asymmetry parameters is indeed different. The non-vanishing and are impressive separate direct evidence of Time-Reversal-Violation and CP-Violation in these transitions (and compatible with Standard Model expectations). A 2σ effect for the Re(θ) parameter responsible of CPT-Violation appears; interpreted as an upper limit, it leads to eV at 95% C.L. for the diagonal flavour terms of the mass matrix. Finally, we consider scenarios where, in the presence of quantum gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky-Rosen correlation of the neutral meson system by adding an Entanglement-weakening term of the wrong exchange symmetry, the ω-effect. The analysis is extended to identify how to probe the complex ω when the connection between the Intensities for the two time-ordered decays (f, g) and (g, f) is lost (f flavour and g CP eigenstate decay channels), and how the ω-effect is disentangled from CPT violation in the evolution Hamiltonian.

Tests ofCPTsymmetry inB0−B¯0mixing and inB0→cc¯K0decays

Using the eight time dependences for the decays Upsilon(4S)-> B0 B0bar -> fj fk with the dacay into a flavor-specific state fj = ell+- X before or after the decay into a CP eigenstate fk = c cbar KS,KL, as measured by the BABAR experiment, we determine the three CPT-sensitive parameters Re(z) and Im(z) in B0-B0bar mixing and |Abar/A| in B0 -> c cbar K0 decays. We find Im(z) = 0.010 +- 0.030 +- 0.013, Re(z) = -0.065 +- 0.028 +- 0.014, and |Abar/A| = 0.999 +- 0.023 +- 0.017, in agreement with CPT symmetry.

Study of B → Kππγ decays at the BaBar experiment

The preliminary results obtained from the analysis of the B meson radiative decays to Kππγ, recorded at the BaBar experiment, are presented. A preliminary measurement of the time-dependent CP asymmetry related to the hadronic CP eigenstate ρ0KS0 is extracted from the radiative-penguin decay B0→KS0π+π−γ. The decay B+→K+π+π−γ is used to measure the intermediate resonant amplitudes of different resonances decaying to Kππ through the intermediate states ρ0K+, K⁎0π+ and (Kπ)S−waveπ+. Assuming (isospin symmetry) that the resonant amplitudes are the same for B0→KS0π+π−γ, the time-dependent CP asymmetry of the B0→KS0ργ decay is obtained.

Discrete Symmetries CP, T, CPT

CP-Violation (CPV) was discovered in 1964 in the weak decays of neutral Kaons. This Symmetry Breaking is understood in the Standard Model as a consequence of its Particle Content, codified in the 3×3 Cabibbo-Kobayashi-Maskawa Unitary Mixing Matrix. The measured CPV asymmetries for Kaons and B's are well described by this Mechanism, but the current level of experimental accuracy and theoretical uncertainties leaves room for additional sources of CPV, as demanded by Baryogenesis. A direct Time-Reversal-Violation (TRV) Effect was clearly observed in 2012 in the time evolution of neutral B-mesons. The conceptual basis to bypass the irreversibility of decays, and prepare in the B-Factories both the Reference and the T-reverse transitions, is provided by the quantum properties of Entanglement and the Decay as a Filtering Measurement. Flavour and CP eigenstate decay channels allow a separate independent measurement of CP, T and CPT asymmetries. Prospects for extending such a programmeto any pair of B-decays and for Kaonsin DAPHNE are discussed. The interest in measuring CPTV asymmetries in transitions is emphasized. This includes the search for CPT-breaking as well as the case of not having a well-defined CPT operator.

Measurement of [formula omitted] in [formula omitted] oscillation using quantum correlations in [formula omitted] at [formula omitted

We report a measurement of the parameter yCP in D0–D¯0 oscillations performed by taking advantage of quantum coherence between pairs of D0D¯0 mesons produced in e+e− annihilations near threshold. In this work, doubly-tagged D0D¯0 events, where one D decays to a CP eigenstate and the other D decays in a semileptonic mode, are reconstructed using a data sample of 2.92 fb−1 collected with the BESIII detector at the center-of-mass energy of s=3.773 GeV. We obtain yCP=(−2.0±1.3±0.7)%, where the first uncertainty is statistical and the second is systematic. This result is compatible with the current world average.

Time dependence in B → V ℓℓ decays

We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$ decays in the presence of neutral-meson mixing. We derive expressions for the time-dependent angular distributions for decays into CP eigenstates, and identify the relevant observables that can be extracted from time-integrated and time-dependent analyses with or without tagging, with a focus on the difference between measurements at $B$-factories and hadronic machines. We construct two observables of interest, which we call $Q_8^-$ and $Q_9$, and which are theoretically clean at large recoil. We compute these two observables in the Standard Model, and show that they have good potential for New Physics searches by considering their sensitivity to benchmark New Physics scenarios consistent with current $b\to s\ell\ell$ data. These results apply to decays such as $B_d\to K^*(\to K_S\pi^0)\ell\ell$, $B_s\to \phi (\to K_SK_L)\ell\ell$ and $B_s\to \phi(\to K^+K^-)\ell\ell$.

Colloquium: Time-reversal violation with quantum-entangledBmesons

Symmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating and testing fundamental theories. Based on the up to now unbroken CPT symmetry, the violation of the CP symmetry between matter and antimatter by weak interactions, discovered in the decay of kaons in 1964 and observed more recently in 2001 in B mesons, strongly suggests that the behavior of these particles under weak interactions must also be asymmetric under time reversal T. However, until the recent years there has not been a direct detection of the expected time-reversal violation in the time evolution of any system. This Colloquium examines the field of time-reversal symmetry breaking in the fundamental laws of physics. For transitions, its observation requires an asymmetry with exchange of initial and final states. We discuss the conceptual basis for such an exchange with unstable particles, using the quantum properties of Einstein Podolsky-Rosen (EPR) entanglement available at B meson factories combined with the decay as a filtering measurement. The method allows a clear-cut separation of different transitions between flavor and CP eigenstates in the decay of neutral B mesons. These ideas have been implemented for the experiment by the BaBar Collaboration at SLAC's B factory. The results, presented in 2012, prove beyond any doubt the violation of time-reversal invariance in the time evolution between these two states of the neutral B meson.

ConstrainingCP-violating Higgs sectors at the LHC using gluon fusion

We investigate the constraints that the LHC can set on a 126 GeV Higgs boson that is an admixture of CP eigenstates. Traditional analyses rely on Higgs couplings to massive vector bosons, which are suppressed for CP-odd couplings, so that these analyses have limited sensitivity. Instead we focus on Higgs production in gluon fusion, which occurs at the same order in the strong coupling for both CP-even and -odd couplings. We study the Higgs plus two jet final state followed by Higgs decay into a pair of tau leptons. We show that using the 8 TeV dataset it is possible to rule out the pure CP-odd hypothesis in this channel alone at nearly 95\% C.L, assuming that the Higgs is CP-even. We also provide projected limits for the 14 TeV LHC run.

Technique to observe directCPviolation inDmesons using Bose symmetry and the Dalitz plot

We present a new and sensitive method to observe direct CP violation in $D$ mesons using Bose symmetry and Dalitz plot. We apply the method to processes such as $B \to D^0\bar{D}^0 P$, where $P$ is either a $K$ or a $\pi$. By choosing to reconstruct $D$ mesons only through their decays into CP eigenstates, we show that any asymmetry in the Dalitz plot can arise only through direct CP violation. We further show how CP violation parameters can be determined. Since the approach involves only Bose symmetry, the method is applicable to any multi-body process that involves $D^0\bar{D}^0$ in the final state. We briefly discuss how $B\to D^* \bar{D}^* P$ can also be used in a similar way.

Novel T-Violation observable open to any pair of decay channels at meson factories

Quantum entanglement between the two neutral mesons produced in meson factories has allowed the first indisputable direct observation of Time Reversal Violation in the time evolution of the neutral meson between the two decays. The exceptional meson transitions are directly connected to semileptonic and CP eigenstate decay channels. The possibility of extending the observable asymmetries to more decay channels confronts the problem of the “orthogonality condition”, which can be stated with this tongue-twister: Given a decay channel f, which is the decay channel f′ such that the meson state not decaying to f′ is orthogonal to the meson state not decaying to f? In this Letter we propose an alternative T-Violation asymmetry at meson factories which allows its opening to any pair of decay channels. Instead of searching which is the pair of decay channels associated to the T-reverse meson transition, we build an asymmetry which tags the initial states of both the Reference and the T-reverse meson transitions. This observable filters the appropriate final states by means of two measurable survival probabilities. We discuss the methodology to be followed in the analysis of the new observable and the results expected in specific examples.

Time-reversal asymmetry and state-vector collapse

A sentence in the Search and Discovery story “Time-reversal asymmetry in particle physics has finally been clearly seen” (Physics Today, November 2012, page 16) has me somewhat puzzled. Bertram Schwarzschild writes, “If the first decay of a daughter reveals it to have been in a specific flavor or CP eigenstate, her still undecayed sister must—at that instant—be in the opposite state.” What is implicit in this sentence is that state-vector collapse takes place at the decay of the first B meson, so that the second meson is instantaneously projected onto the opposite state.I have two objections to this sentence. First, it is not relativistically invariant: Because the two events—decay of the first meson and “transformation” of the second—have spacelike separation, their time ordering is not defined. Second, the decay is governed by a relativistic version of the Schrödinger equation, which is reversible, whereas state-vector collapse is, by nature, irreversible.It is instructive to make a comparison with the analysis of a Bell-type experiment, in which a two-particle observable is measured via two detectors that are far apart, with each measuring the spin of one of the two particles. The quantum mechanical result is given by applying Born’s rule to the two-particle observable.The two experimentalists, Alice and Bob, then compare their results by exchanging them at a speed less than that of light, and they notice the results are correlated, in conformity with the theoretical predictions of nonlocal correlations. The same theoretical results may be derived from state-vector collapse: When Alice measures the first spin, Bob’s spin is projected instantaneously onto a well-defined polarization state; correlations may be easily computed and are, of course, in agreement with those derived from Born’s rule.State-vector collapse is strictly equivalent to Born’s rule in a nonrelativistic context, but I think it is safer to use Born’s rule when special relativity comes into play. Indeed, to the best of my knowledge, there is no satisfactory relativistic generalization of state-vector collapse, which is understandable since simultaneity is not defined for two spacelike separated events. Therefore, a full justification of the argument used in the Physics Today report should begin with state-vector collapse taking place in a well-defined reference frame at the instant when the decay products of the B mesons reach the detectors. Then, from the correlations observed between the results of the detectors, it should be possible to reconstruct the decays and show that they can be interpreted as an effective state-vector collapse.Such an analysis would likely vindicate that of the BaBar experiment, but as the use of Einstein-Podolsky-Rosen correlations goes far beyond the usual one, it should be fully justified.© 2013 American Institute of Physics.

Some exact results on CP and CPT violations in a C=−1 entangled pseudoscalar neutral meson pair

We consider neutral pseudoscalar mesons in an entangled or Einstein-Podolsky-Rosen state with $C=-1$. Due to quantum entanglement and antisymmetry of this state, the rates of the joint decays of the meson pair display various interesting features, as is well known. As functions of CP and CPT violating parameters, here we obtain some exact results about the joint decay rates and their asymmetries for a given time difference defined for joint decays to flavor eigenstates, as well as those for joint decays to CP eigenstates. The entanglement allows a meaningful and useful definition of the transition amplitude from a CP eigenstate of a meson. These results yield useful information and criteria on CP and CPT violations.

Coexistence of CP eigenstates in Higgs boson decay

The supersymmetric extension of the standard model contains an intrinsic source of CP violation mediated by charginos. As a result, both CP-even and CP-odd final states can be observed in the Higgs boson decay into two photons, the evidence for which has recently been reported. AMS Subject Classification B13