CP-odd Operators Research Articles

Small instanton-induced flavor invariants and the axion potential

Small instantons which increase the axion mass due to an appropriate modification of QCD at a UV scale ΛSI, can also enhance the effect of CP-violating operators to shift the axion potential minimum by an amount, θind, proportional to the flavorful couplings in the SMEFT. Since physical observables must be flavor basis independent, we construct a basis of determinant-like flavor invariants that arise from instanton calculations containing the effects of dimension-six CP-odd operators at the scale . This new basis provides a more reliable estimate of the shift θind, that is severely constrained by neutron electric dipole moment experiments. In particular, for the case of four-quark, semi-leptonic and gluon dipole operators, these invariants are then used to provide improved limits on the ratio of scales for different flavor scenarios. The CP-odd flavor invariants also provide a classification of the leading effects from Wilson coefficients, and as an example, we show that a semi-leptonic four-fermion operator is subdominant compared to the four-quark operators. More generally, the flavor invariants, together with an instanton NDA, can be used to more accurately estimate small instanton effects in the axion potential that arise from any SMEFT operator.

Boosting new physics searches in t{bar{t}}Z and tZj production with angular moments

The angular moments of the Z boson can be used as analyzers for the underlying production dynamics for the t{{bar{t}}} Z and tZj processes. In this manuscript, we derive these angular moments at leading and next-to-leading order in QCD at the LHC. We show that these observables work as efficient probes to beyond the Standard Model effects, considering the Standard Model Effective Field theory framework. Remarkably, we observe that these probes unveil blind directions to CP-odd operators, providing sizable new physics sensitivity at the 14 TeV LHC with 3 ab^{-1} of data.

Improved indirect limits on charm and bottom quark EDMs

We derive indirect limits on the charm and bottom quark electric dipole moments (EDMs) from paramagnetic AMO and neutron EDM experiments. The charm and bottom quark EDMs generate CP-odd photon-gluon operators and light quark EDMs at the c- and b-quark mass thresholds. These CP-odd operators induce the CP-odd semi-leptonic operator CS and the neutron EDM below the QCD scale that are probed by the paramagnetic and neutron EDM experiments, respectively. The bound from CS is |dc| < 1.3 × 10−20e cm for the charm quark and |db| < 7.6 × 10−19e cm for the bottom quark, with its uncertainty estimated as 10 %. The neutron EDM provides a stronger bound, |dc| < 6 × 10−22e cm and |db| < 2 × 10−20e cm, though with a larger hadronic uncertainty.

A reduced basis for CP violation in SMEFT at colliders and its application to diboson production

We show that only 10 (17) CP-odd operators of the SMEFT give the leading, i.e. least suppressed by the new physics scale, CP-violating contributions once we assume that all fermions are massless but the top (and bottom) quark(s). We start with a short review of previous analyses focusing on operators of our reduced basis and list different observables probing their CP violating effects by direct measurements at colliders and by indirect measurements in low-energy observables. Since CP-odd operators typically lead to phase space suppressed interferences, we quantify the efficiency to revive the interference for various observables found in the literature but also for new observables in diboson production. Our new observables are found to be more efficient on the whole experimental fiducial phase space and are complementary to those presented so far as they probe different combinations of operators and get their sensitivities from different regions of the phase space.

Consistency of the standard model effective field theory

We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion relation arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bounds also follow as a consequence of causality of signal propagation in nonvacuum SM backgrounds. These bounds come in two qualitative forms: i) positivity of (various linear combinations of) couplings of CP-even operators and ii) upper bounds on the magnitude of CP-odd operators in terms of (products of) CP-even couplings. We exhibit various classes of example completions, which all satisfy our EFT bounds. These bounds have consequences for current and future particle physics experiments, as part of the observable parameter space is inconsistent with causality and analyticity. To demonstrate the impact of our bounds, we consider applications both to SMEFT constraints derived at colliders and to limits on the neutron electric dipole moment, highlighting the connection between such searches suggested by infrared consistency.

CP violation with a dynamical Higgs

We determine the complete set of independent gauge and gauge-Higgs CP-odd effective operators for the generic case of a dynamical Higgs, up to four derivatives in the chiral expansion. The relation with the linear basis of dimension six CP-odd operators is clarified. Phenomenological applications include bounds inferred from electric dipole moment limits, and from present and future collider data on triple gauge coupling measurements and Higgs signals.

CP-violation and electric dipole moments

Searches for intrinsic electric dipole moments of nucleons, atoms and molecules are precision flavour-diagonal probes of new -odd physics. We review and summarise the effective field theory analysis of the observable EDMs in terms of a general set of CP-odd operators at 1 GeV, and the ensuing model-independent constraints on new physics. We also discuss the implications for supersymmetric models, in light of the mass limits emerging from the LHC.

Parity realization in vector-like theories from fermion bilinears

We reconsider in this paper the old aim of trying to understand if the observed realization of discrete symmetries as Parity or CP in the QCD vacuum can be satisfied from first principles. We show how under the appropriate assumptions implicitely done by Vafa and Witten in their old paper on parity realization in vector-like theories, all parity and CP odd operators constructed from fermion bilinears of the form $\bar\psi\tilde O\psi$ should take a vanishing vacuum expectation value in a vector-like theory with N degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the impossibility to break spontaneously the flavour symmetry in a vector-like theory plays a fundamental role.

Hadron electric dipole moments from CP-odd operators of dimension five via QCD sum rules: the vector meson

We present a complete analysis of the electric dipole moment (EDM) of the ρ-meson induced by CP violating operators of dimension 4 and 5 within the QCD sum rules approach. The set of CP-odd operators includes the theta term and the electric and chromoelectric dipole moments of the three light quarks. We find that the ρ-meson EDM induced purely by the EDMs of quarks is smaller than, but still in reasonable agreement with, the predictions of a naive constituent quark model. However, the chromoelectric dipole moments, including that of the strange quark, give comparable and sometimes larger contributions. We also consider the effect on the hadronic EDM of the existence of Peccei-Quinn symmetry. When this symmetry is active, chromoelectric dipole moments induce a linear term in the axion potential which leads to a numerically important vacuum contribution to the hadronic EDM.

CP-violation with bosons

We formulate the conditions under which a purely bosonic theory (without fermions) containing neutral spin-0 particles and vector (gauge) bosons violates the CP-symmetry through the presence of CP-even and CP-odd operators in the lagrangian. This is done without reference to explicitly CP-violating scalar sector of extended standard models (SM) with two or more Higgs doublets. The lagrangian expressed in the mass basis of the spin-0 fields can, however, in certain circumstances be identified with a part of the CP-violating SM with two Higgs doublets. It is instructive to consider the manifestation of CP-violation in the mass basis since this leads directly to suggestions of genuine CP-signals.

Signets of CP violation

In all known realistic theories the CP-odd operators in the effective lagrangian are the “signets” of CP violation: they summarily but uniquely describe both theory and observable effects. The archetypal flavour-diagonal signets are the electric dipole moments (EDM) of fundamental fermions and their neutral-weak and coloured generalizations, as well as the analogous quantities describing CP-odd γW +W − and ZW +W − vertices. The gauge symmetry of the standard model must be respected above the weak scale by any putative theory of the origin of CP violation. This constraint relates EDMs and their generalizations to a blooming ensemble of other higher-dimensional signets, some of which involve extra scalar fields and/or gauge bosons and imply novel processes. To gauge what can be done at present and future facilities (e.g. LEP-I and LEP-II) in the CP-violation domain, we give limits on the most relevant of all CP-odd signets, sometimes directly from experiment, often via observable effects induced by electroweak and QCD quantum corrections. These bounds allow us to pinpoint the most promising areas of future development.

Even larger contributions to the neutron electric dipole moment

Constraints on theories of CP-violation, from limits on the neutron electric dipole moment, and mediated by a CP-odd three-gluon operator, are current best sellers. We introduce novel CP-odd operators involving one photon and three gluons. We find that effects mediated by these operators result on bounds on supersymmetry an order of magnitude more stringent than earlier results: they are the tightest known bounds. For left-right models we derive richer limits than previously found. We also recalculate the anomalous dimensions of the three-gluon operator and find them to be minus those originally used; this weakens considerably its strictures on theory, though it still mediates the dominant effect in multi-Higgs models.