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Search for CP violation in events with top quarks and Z bosons at $\sqrt{s}$ = 13 and 13.6 TeV

A search for the violation of the charge-parity (CP) symmetry in the production of top quarks in association with Z bosons is presented, using events with at least three charged leptons and additional jets. The search is performed in a sample of proton-proton collision data collected by the CMS experiment at the CERN LHC in 2016–2018 at a center-of-mass energy of 13 TeV and in 2022 at 13.6 TeV, corresponding to a total integrated luminosity of 173 fb –1 . For the first time in this final state, observables that are odd under the CP transformation are employed. Also for the first time, physics-informed machine-learning techniques are used to construct these observables. While for standard model (SM) processes the distributions of these observables are predicted to be symmetric around zero, CP-violating modifications of the SM would introduce asymmetries. Two CP-odd operators $\mathcal{O}$$^{I}_{tW}$ and $\mathcal{O}$$^{I}_{tZ}$ in the SM effective field theory are considered that may modify the interactions between top quarks and electroweak bosons. The obtained results are consistent with the SM prediction within two standard deviations, and exclusion limits on the associated Wilson coefficients of –2.7 < $c$$^{I}_{tW}$ < 2.5 and –0.2 < $c$$^{I}_{tZ}$ < 2.0 and are set at 95 % confidence level. The largest discrepancy is observed in $c$$^{I}_{tZ}$ where data is consistent with positive values, with an observed local significance with respect to the SM hypothesis of 2.5 standard deviations, when only linear terms are considered.

CMS↗

Snowmass White Paper: Prospects of CP-violation measurements with the Higgs boson at future experiments

The search for CP violation in interactions of the Higgs boson with either fermions or bosons provides attractive reference measurements in the Particle Physics Community Planning Exercise (a.k.a. "Snowmass"). Benchmark measurements of CP violation provide a limited and well-defined set of parameters that could be tested at the proton, electron-positron, photon, and muon colliders, and compared to those achieved through study of virtual effects in electric dipole moment measurements. We review the current status of these CP-sensitive studies and provide projections to future measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for CP violation in $D^{+}_{(s)}\to h^{+} \pi^{0}$ and $D^{+}_{(s)}\to h^{+}\eta$ decays

Searches for CP violation in the two-body decays $D^{+}_{(s)}\to h^{+} \pi^{0}$ and $D^{+}_{(s)}\to h^{+}\eta$ (where h + denotes a π + or K + meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb –1 or 6 fb –1 of integrated luminosity. The π 0 and η mesons are reconstructed using the e + e – γ final state, which can proceed as three-body decays π 0 → e + e – γ and η → e + e – γ, or via the two-body decays π 0 → γγ and η → γγ followed by a photon conversion. The measurements are made relative to the control modes $D^{+}_{(s)}\to K^{0}_{S}h^{+}$ to cancel the production and detection asymmetries. The CP asymmetries are measured to be A CP (D + →π + π 0 )=(–1.3±0.9±0.6)%, A CP (D + →K + π 0 )=(–3.2±4.7±2.1)%, A CP (D + →π + η)=(–0.2±0.8±0.4)%, A CP (D + →K + η)=(–6±10±4)%, A CP (D$^{+}_{s}$→K + π 0 )=(–0.8±3.9±1.2)%, A CP (D$^{+}_{s}$→π + η)=(0.8±0.7±0.5)%, A CP (D$^{+}_{s}$→K + η)=(0.9±3.7±1.1)%, where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of A CP in these decay modes to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

We study SU(3) flavor breaking corrections to the relation between the octet baryon masses and the nucleon-meson CP-violating interactions induced by the QCD theta term. We also work within the framework of SU(3) chiral perturbation theory and work through next-to-next-to-leading order in the SU(3) chiral expansion, which is O(m 2 q ). At lowest order, the CP-odd couplings induced by the QCD θ - term are determined by mass splittings of the baryon octet, the classic result of Crewther et al. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation which is respected by loop corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling g - 0 by using recent lattice QCD evaluations of the proton-neutron mass splitting. Additionally, we derive semi-precise values for CP-violating coupling constants between heavier mesons and nucleons and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

23, 381, 6242, 103268, 1743183, ...:Hilbert series for CP-violating operators in SMEFT

We introduce a systematic method to classify the Standard Model Effective Field Theory (SMEFT) operators based on their CP properties with the Hilbert series techniques. Our method makes it possible to enumerate operators violating CP symmetry in a few seconds. We present the complete classification of dimension eight operators under CP transformation, and the number of CP-odd or CP-violating operators are listed up to dimension 14. We also provide a companion code in Form that allows anybody to reproduce our results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for CP violation in the phase space of D 0 → π⁻π⁺π 0 decays with the energy test

A search for CP violation in D 0 → π - π + π 0 decays is reported, using pp collision data collected by the LHCb experiment from 2015 to 2018 corresponding to an integrated luminosity of 6 fb - 1 . An unbinned model-independent approach provides sensitivity to local CP violation within the two-dimensional phase space of the decay. The method is validated using the Cabibbo-favoured channel D 0 → K - π + π 0 and background regions of the signal mode. The results are consistent with CP symmetry in this decay.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of the branching fraction and search for CP violation in D 0 → K $^{0}_{S}$ K $^{0}_{S}$ ⁢π + ⁢π - decays at Belle

We measure the branching fraction for the Cabibbo-suppressed decay D 0 → K $^{0}_{S}$ K $^{0}_{S}$ ⁢π + ⁢π - and search for CP violation via a measurement of the CP asymmetry A CP as well as the T-odd triple-product asymmetry a$^{T}_{CP}$. We use 922 fb -1 of data recorded by the Belle experiment, which ran at the KEKB asymmetric-energy e + ⁢e - collider. The branching fraction is measured relative to the Cabibbo-favored normalization channel D 0 → K $^{0}_{S}$ ⁢π + ⁢π - ; the result is $\mathscr{B}$⁡( D 0 → K $^{0}_{S}$ K $^{0}_{S}$ ⁢π + ⁢π - )=[4.79±0.08⁢(stat)±0.10⁢(syst)±0.31⁢(norm)]×10 -4 , where the first uncertainty is statistical, the second is systematic, and the third is from uncertainty in the normalization channel. We also measure A CP =[-2.51±1.44⁢(stat)$^{+0.11}_{-0.10}$⁢(syst)]%, and a$^{T}_{CP}$=[-1.95±1.42⁢(stat)$^{+0.14}_{-0.12}⁢$(syst)]%. These results show no evidence of CP violation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for CP violating top quark couplings in pp collisions at $ \sqrt{s} $ = 13 TeV

Results are presented from a search for CP violation in top quark pair production, using proton-proton collisions at a center-of-mass energy of 13 TeV. The data used for this analysis consist of final states with two charged leptons collected by the CMS experiment, and correspond to an integrated luminosity of 35.9 fb$^{−1}$. The search uses two observables, $ \mathcal{O} _{1}$ and $ \mathcal{O} _{3}$, which are Lorentz scalars. The observable $ \mathcal{O} _{1}$ is constructed from the four-momenta of the charged leptons and the reconstructed top quarks, while $ \mathcal{O} _{3}$ consists of the four-momenta of the charged leptons and the b quarks originating from the top quarks. Asymmetries in these observables are sensitive to CP violation, and their measurement is used to determine the chromoelectric dipole moment of the top quark. The results are consistent with the expectation from the standard model.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sensitivity of EDM experiments in paramagnetic atoms and molecules to hadronic CP violation

Experiments searching for the electric dipole moment (EDM) of the electron d e utilize atomic/molecular states with one or more uncompensated electron spins, and these paramagnetic systems have recently achieved remarkable sensitivity to d e . If the source of CP violation resides entirely in the hadronic sector, the two-photon exchange processes between electrons and the nucleus induce CP-odd semileptonic interactions, parametrised by the Wilson coefficient C SP , and provide the dominant source of EDMs in paramagnetic systems instead of d e . We evaluate the C SP coefficients induced by the leading hadronic sources of CP violation, namely nucleon EDMs and CP-odd pion-nucleon couplings, by calculating the nucleon-number-enhanced CP-odd nuclear scalar polarisability, employing chiral perturbation theory at the nucleon level and the Fermi-gas model for the nucleus. This allows us to translate the ACME EDM limits from paramagnetic ThO into novel independent constraints on the QCD theta term |$\bar θ$| < 3 × 10 –8 , proton EDM |d p | < 2 × 10 –23 e cm, isoscalar CP-odd pion-nucleon coupling |$\bar g$$^{(1)}_{πNN}$| < 4 × 10 –10 , and color EDMs of quarks |$\tilde d$ u -$\tilde $d d | < 2 × 10 –24 cm. We note that further experimental progress with EDM experiments in paramagnetic systems may allow them to rival the sensitivity of EDM experiments with neutrons and diamagnetic atoms to these quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions

Here we investigate direct and indirect constraints on the complete set of anomalous CP-violating Higgs couplings to quarks and gluons originating from dimension-6 operators, by studying their signatures at the LHC and in electric dipole moments (EDMs). We also show that existing uncertainties in hadronic and nuclear matrix elements have a significant impact on the interpretation of EDM experiments, and we quantify the improvements needed to fully exploit the power of EDM searches. Currently, the best bounds on the anomalous CP-violating Higgs interactions come from a combination of EDM measurements and the data from LHC Run 1. We argue that Higgs production cross section and branching ratios measurements at the LHC Run 2 will not improve the constraints significantly. But, the bounds on the couplings scale roughly linearly with EDM limits, so that future theoretical and experimental EDM developments can have a major impact in pinning down interactions of the Higgs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for CP violation in $ t\overline{t} $ production and decay in proton-proton collisions at $ \sqrt{s}=8 $ TeV

The results of a first search for CP violation in the production and decay of top quark-antiquark ( $ t\overline{t} $ ) pairs are presented. The search is based on asymmetries in T-odd, triple-product correlation observables, where T is the time-reversal operator. The analysis uses a sample of proton-proton collisions at $ \sqrt{s}=8 $ TeV collected by the CMS experiment, corresponding to an integrated luminosity of 19.7 fb$^{−1}$. Events are selected having one electron or muon and at least four jets. The T-odd observables are measured using four-momentum vectors associated with $ t\overline{t} $ production and decay. The measured asymmetries exhibit no evidence for CP-violating effects, consistent with the expectation from the standard model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for CP violation in the phase space of D 0 → π + π – π + π – decays

A search for time-integrated CP violation in the Cabibbo-suppressed decay D 0 → π + π – π + π – is performed using an unbinned, model-independent technique known as the energy test. This is the first application of the energy test in four-body decays. The search is performed for P-even CP asymmetries and, for the first time, is extended to probe the P-odd case. Using proton–proton collision data corresponding to an integrated luminosity of 3.0 fb –1 collected by the LHCb detector at centre-of-mass energies of $\sqrt{s}$ = 7 TeV and 8 TeV, the world's best sensitivity to CP violation in this decay is obtained. The data are found to be consistent with the hypothesis of CP symmetry with a p-value of (4.6±0.5)% in the P-even case, and marginally consistent with a p-value of (0.6±0.2)% in the P-odd case, corresponding to a significance for CP non-conservation of 2.7 standard deviations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electric dipole moment constraints on CP-violating heavy-quark Yukawas at next-to-leading order

Electric dipole moments are sensitive probes of new phases in the Higgs Yukawa couplings. We calculate the complete two-loop QCD anomalous dimension matrix for the mixing of CP-odd scalar and tensor operators and apply our results for a phenomenological study of CP violation in the bottom and charm Yukawa couplings. We find large shifts of the induced Wilson coefficients at next-to-leading-logarithmic order. Using the experimental bound on the electric dipole moments of the neutron and mercury, we update the constraints on CP-violating phases in the bottom and charm quark Yukawas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A study of $CP$ violation in the decays $B^±$ → [$K^+ K^-π^+π^-$]$_Dh^±$ ($h$ = $K, π$) and $B^±$ → [$π^+π^-π^+π^-$]$_Dh^±$

The first study of CP violation in the decay mode $B^±$ → [$K^+ K^-π^+π^-$]$_Dh^±$, with $h$ = $K, π$, is presented, exploiting a data sample of proton–proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of 9 fb -1 . The analysis is performed in bins of phase space, which are optimised for sensitivity to local CP asymmetries. CP-violating observables that are sensitive to the angle γ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for $B^±$ → [$K^+ K^-π^+π^-$]$_Dh^±$ and $B^±$ → [$π^+π^-π^+π^-$]$_Dh^±$ decays.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

CP violating effects in heavy neutrino oscillations: implications for colliders and leptogenesis

Two of the important implications of the seesaw mechanism are: (i) a simple way to understand the small neutrino masses, and (ii) the origin of matter-anti-matter asymmetry in the universe via the leptogenesis mechanism. For TeV-scale seesaw models, successful leptogenesis requires that the right-handed neutrinos (RHNs) must be quasidegenerate and if they have CP violating phases, they also contribute to the CP asymmetry. We investigate this in the TeV-scale left-right models for seesaw and point out a way to probe the quasi-degeneracy possibility with CP violating mixings for RHNs in hadron colliders using simple observables constructed out of same-sign dilepton charge asymmetry (SSCA). In particular, we isolate the parameter regions of the model, where the viability of leptogenesis can be tested using the SSCA at the Large Hadron Collider, as well as future 27 TeV and 100 TeV hadron colliders. We also independently confirm an earlier result that there is a generic lower bound on the WR mass of about 10 TeV for leptogenesis to work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Probing CP violation in e + e - production of the Higgs boson and toponia

We study the CP violation in the Higgs boson and toponia production process at the ILC where the toponia are produced near the threshold. With the approximation that the production vertex of the Higgs boson and toponia is contact, and neglecting the P-wave toponia, we analytically calculated the density matrix for the production and decay of the toponia. Under these assumptions, the production spectrum of the toponia is solely determined by the spin quantum number, therefore the toponia can be either singlet or triplet. We find that the production rate of the singlet toponium is highly suppressed, and behaves just like the production of a P-wave toponia. In the case of the triplet toponium, three completely independent CP observables, namely azimuthal angles of lepton and antilepton in the toponium rest-frame as well as their sum, are predicted based on our analytical results, and checked by using the tree-level event generator. The non-trivial correlations come from the longitudinal-transverse interferences for the azimuthal angles of leptons, and the transverse-transverse interference for their sum. These three observables are well defined at the ILC, where the rest frame of the toponium can be reconstructed directly. Furthermore, the QCD-strong corrections, which are important near the threshold region, are also studied with the approximation of spin-independent QCD-Coulomb potential. While the total cross section is enhanced, the spin correlations predicted in this paper are not affected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Allowance for CP violation in the exponential parametrization of neutrino mixing

An exponential form of the Pontecorvo–Maki–Nakagawa–Sakatamixingmatrix for neutrinos is discussed. This form makes it possible to separate the contributions of purely rotational components of the mixing matrix and elements that are responsible for CP violation. The logarithm of the mixing matrix and exact values for each parameter of the exponential neutrino mixing matrix are found on the basis of the most recent experimental data on neutrino mixing. The parameters of the real rotational part in the exponential representation of the mixing matrix and the parameters of its imaginary part, which is responsible for CP violation, are evaluated. The hypothesis of complementarity of quark and neutrino mixing is confirmed. Factorization in the form of the product of rotations about the real and imaginary axes is demonstrated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗