Violation Of Unitarity Research Articles

Testing the CKM unitarity at high energy via the W+W− production at the LHC and future colliders

We propose a novel test to assess the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, VCKM, at present and future collider experiments. Our strategy makes use of the W+W− production cross section to directly probe the VCKM†VCKM product, which regulates the high-energy behavior of the observable. The violation of unitarity is signaled by an anomalous behavior of the cross section that grows quadratically with the W+W− invariant mass with respect to the Standard Model prediction. By using the recent ATLAS measurements of the W+W− cross section we are able to constrain the maximal unitarity violation allowed by current data, producing a bound complementary to the results of flavor physics experiments. Forecasts for the high luminosity phase of the LHC and for the future 100 TeV hadron collider are also discussed.

Gluonic evanescent operators: negative-norm states and complex anomalous dimensions

In this paper, we build on our previous work to further investigate the role of evanescent operators in gauge theories, with a particular focus on their contribution to violations of unitarity. We develop an efficient method for calculating the norms of gauge-invariant operators in Yang-Mills (YM) theory by employing on-shell form factors. Our analysis, applicable to general spacetime dimensions, reveals the existence of negative-norm states among evanescent operators. We also explore the one-loop anomalous dimensions of these operators and find complex anomalous dimensions. We broaden our analysis by considering YM theory coupled with scalar fields and we observe similar patterns of non-unitarity. The presence of negative-norm states and complex anomalous dimensions across these analyses provides compelling evidence that general gauge theories are non-unitary in non-integer spacetime dimensions.

Energy growth in VLVL→ VLVL, VLVLh scattering to probe Higgs cubic and HEFT interactions

We compute the energy scales of perturbative unitarity violation in VLVL → VLVLh processes and compare them to VLVL → hhh process, where VL refers to a longitudinal mode of Z or W boson, and h the Higgs boson. Using these energy scales, we determine which process is more sensitive to potential modifications in the Higgs sector at high-energy colliders. Within the Higgs Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other interactions with and without derivatives. Any HEFT interactions predict the perturbative unitarity violation at a finite scale, and in a generic case, the minimalistic process is 2 → 3 scattering. Our analysis reveals that the energy scales for unitarity violation in VLVL → VLVLh and VLVL → hhh processes are similar across all scenarios considered. If the backgrounds are similar, VLVLh final states are more feasible because VLVLh has higher branching ratios in cleaner decay modes than hhh. We also investigate HEFT derivative interactions derived from various UV models. In these cases, both VLVL → VLVL and VLVL → hh processes exhibit unitarity violating behavior. We demonstrate that the energy scales for unitarity violation in VLVL final states are comparable to or even lower than those in the hh final state.

New Physics Opportunities at the DUNE Near Detector

Focusing on elastic neutrino–electron scattering events, we explore the prospect of constraining new physics beyond the Standard Model at the DUNE Near Detector (ND). Specifically, we extract the attainable sensitivities for motivated scenarios such as neutrino generalized interactions (NGIs), the sterile neutrino dipole portal and unitarity violation. We furthermore examine the impact of the τ-optimized flux at the DUNE-ND and compare our results with those obtained using the standard CP-optimized flux. We find that our present analysis is probing a previously unexplored region of the parameter space, complementing existing results from cosmological observations and terrestrial experiments.

Momentum-dependent field redefinitions in asymptotic safety

We discuss general momentum-dependent field redefinitions in the context of quantum-gravitational scattering amplitudes in general, and asymptotic safety in particular. Implementing such redefinitions at the lowest curvature order, we can bring the graviton propagator into tree-level form, avoiding issues of fiducial ghost poles and their associated violations of unitarity. We compute the beta function for Newton’s constant, and find an asymptotically safe fixed point whose critical exponent changes by 0.4% compared to not resolving the momentum-dependent field redefinition. This provides a strong indication that this fixed point does not feature extra degrees of freedom related to ghostly modes, and has a good chance of being related to a unitary theory. Published by the American Physical Society 2024

Analytic Formulae for T Violation in Neutrino Oscillations.

Recently, a concept known as μTRISTAN, which involves the acceleration of μ+, has been proposed. This initiative has led to considerations of a new design for a neutrino factory. Additionally, leveraging the polarization of μ+, measurements of T violation in neutrino oscillations are also being explored. In this paper, we present analytical expressions for T violation in neutrino oscillations within the framework of standard three-flavor neutrino oscillations, a scenario involving nonstandard interactions, and a case of unitarity violation. We point out that examining the energy spectrum of T violation may be useful for probing new physics effects.

Colored-noise-driven unitarity violation causing dynamical quantum state reduction

Colored-noise-driven unitarity violation causing dynamical quantum state reduction

Stochastic field dynamics in models of spontaneous unitarity violation

Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger’s equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born’s rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born’s rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.

Quantum State Reduction of General Initial States through Spontaneous Unitarity Violation.

The inability of Schrödinger's unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born's probability rule emerges spontaneously in all cases.

Non-canonical Higgs inflation

The large value of non-minimal coupling constant ξ required to satisfy cosmic microwave background observations in Higgs inflation violates unitarity. In this work we study Higgs-inflation with non-canonical kinetic term of DBI form to find whether ξ can be reduced. To study the inflationary dynamics, we transform the action to the Einstein frame, in which the Higgs is minimally coupled to gravity with a non-canonical kinetic term and modified potential. We choose the Higgs self coupling constant λ = 0.14 for our analysis. We find that the value of ξ can be reduced from 103–104 to O(10) to satisfy Planck constraints on amplitude of scalar power spectrum. However, this model produces a larger tensor-to-scalar ratio r, in comparison to the Higgs inflation with canonical kinetic term. We also find that, to satisfy joint constraints on scalar spectral index ns and tensor-to-scalar ratio r from Planck-2018 and bounds on r from Planck and BICEP3, the value of ξ should be of the order of 104. Thus, the issue of unitarity violation remains even after considering Higgs inflation with non-canonical kinetic term.

Self-healing unitarity is an optical illusion

Among the vast variety of proposals put forward by the community to resolve tree-level unitarity violations in Higgs inflation models, there exists the concept of self-healing. It heals the theory from supposed tree-level violations for elastic scattering processes by summing over successive vacuum polarization loop corrections. In this work, we examine this technique to check whether unitarity is indeed restored and find that there exist underlying constraints in self-healing unitarity that pose the same perturbative unitarity bounds that it was expected to heal. Published by the American Physical Society 2024

Investigating Unitarity Violation of Lee–Wick’s Complex Ghost with Quantum Field Theory

Theories with fourth-order derivatives like Lee–Wick’s quantum electrodynamics model or quadratic gravity result in complex ghosts above a definite energy threshold that violate unitarity.

Unitarity violation in field theories of Lee–Wick’s complex ghost

Abstract Theories with fourth-order derivatives, including the Lee–Wick finite QED model and quadratic gravity, have a better UV behavior, but the presence of negative metric ghost modes endangers unitarity. Noticing that the ghost acquires a complex mass by radiative corrections, Lee and Wick, in particular, claimed that such complex ghosts would never be created by collisions of physical particles because of energy conservation, so that the physical S-matrix unitarity must hold. We investigate the unitarity problem faithfully, working in the operator formalism of quantum field theory. When complex ghosts participate, a complex delta function (a generalization of the Dirac delta function) appears at each interaction vertex, which enforces a specific conservation law of complex energy. Its particular property implies that the naive Feynman rule is wrong if the four-momenta are assigned to the internal lines after taking account of the conservation law in advance. We show that complex ghosts are actually created and unitarity is violated in such fourth-order derivative theories. We also find a definite energy threshold below which ghosts cannot be created: The theories are unitary and renormalizable below the threshold.

A model with vectorlike fermions and U(1)X symmetry: CKM unitarity, b → s transitions, and prospect at Belle II

The updated analysis of the LHCb Collaboration on the lepton flavor violation suggests that the new physics should couple to muons and electrons with comparable magnitudes, resulting in the anomalies in both rare decay channels, b→sμ+μ− and b→se+e−. Meanwhile, the recent result of the Muon g−2 experiment with higher precision has increased the existing tension with the standard model prediction. In this paper, we consider an extension of the standard model with a new sector consisting of vectorlike fermions and two scalar charged under an extra U(1)X gauge symmetry. The exotic Yukawa interactions in this model lead to the quark mixing responsible for the additional contributions to the flavor changing neutral currents in B-meson decays, and solve the muon g−2 discrepancy. We derive the analytic expression of the new physics contributions to the Wilson coefficient C7 in the effective Hamiltonian, and point out that the CKM unitarity violation can be explained within this context. By calculating the branching ratio of the inclusive radiative B decay, the impact of current experimental data of the b→sγ transition on the model and the future prospect at the Belle II experiment are investigated. Taking into account the current data on the muon anomalous magnetic moment, the CKM unitarity violation, the constraints on the flavor observables relevant to the b→s transitions, the LHC searches for vectorlike quarks, and the perturbation limits of the couplings, the viable parameter regions of the model are identified.

Normalization of the vacuum and the ultraviolet completion of Einstein gravity

Second-order-derivative plus fourth-order-derivative gravity is the ultraviolet completion of second-order-derivative quantum Einstein gravity. While it achieves renormalizability through states of negative Dirac norm, the unitarity violation that this would entail can be postponed to Planck energies. As we show in this paper, the theory has a different problem, one that occurs at all energy scales, namely that the Dirac norm of the vacuum of the theory is not finite. To establish this, we present a procedure for determining the norm of the vacuum in any quantum field theory. With the Dirac norm of the vacuum of the second-order-derivative plus fourth-order-derivative theory not being finite, the Feynman rules that are used to establish renormalizability are not valid, as is the assumption that the theory can be used as an effective theory at energies well below the Planck scale. This lack of finiteness is also manifested in the fact that the Lorentzian path integral for the theory is divergent. Because the vacuum Dirac norm is not finite, the Hamiltonian of the theory is not Hermitian. However, it turns out to be [Formula: see text] symmetric. When one continues the theory into the complex plane and uses the [Formula: see text] symmetry inner product, viz. the overlap of the left-eigenstate of the Hamiltonian with its right-eigenstate, one then finds that for the vacuum this norm is both finite and positive, the Feynman rules now are valid, the Lorentzian path integral now is well behaved, and the theory now can serve as a low energy effective theory, one that we show to have a real classical gravity limit. Consequently, the theory can now be offered as a fully consistent, unitary and renormalizable theory of quantum gravity.

On unitarity of the Coon amplitude

The Coon amplitude is a one-parameter deformation of the Veneziano amplitude. We explore the unitarity of the Coon amplitude through its partial wave expansion using tools from q-calculus. Our analysis establishes manifest positivity on the leading and sub-leading Regge trajectories in arbitrary spacetime dimensions D, while revealing a violation of unitarity in a certain region of (q, D) parameter space starting at the sub-sub-leading Regge order. A combination of numerical studies and analytic arguments allows us to argue for the manifest positivity of the partial wave coefficients in fixed spin and Regge asymptotics.

On unitarity in singlet inflation with a non-minimal coupling to gravity

We study inflationary models based on a non-minimal coupling of a singlet scalar to gravity, focussing on the preheating dynamics and the unitarity issues in this regime. If the scalar does not have significant couplings to other fields, particle production after inflation is far less efficient than that in Higgs inflation. As a result, unitarity violation at large non-minimal couplings requires a different treatment. We find that collective effects in inflaton scattering processes during preheating make an important impact on the unitarity constraint. Within effective field theory, the consequent upper bound on the non-minimal coupling is of order a few hundreds.

High-energy properties of the graviton scattering in quadratic gravity

We obtain the matter-graviton scattering amplitude in the gravitational theory of quadratic curvature, which has {R}_{mu nu}^2 term in the action. Unitarity bound is not satisfied because of the existence of negative norm states, while an analog of unitarity bound for S-matrix unitarity holds due to the cancelation among the positive norm states and negative norm ones in the unitarity summation in the optical theorem. The violation of unitarity bound is a counter example of Llewellyn Smith’s conjecture on the relation between tree-level unitarity and renormalizability. We have recently proposed a new conjecture that an analog of the unitarity bound for S-matrix unitarity gives the equivalent conditions to those for renormalizability. We show that the gravitational theory of quadratic curvature is a nontrivial example consistent with our conjecture.

Global fits of simplified models for dark matter with GAMBIT

Simplified models provide a useful way to study the impacts of a small number of new particles on experimental observables and the interplay of those observables, without the need to construct an underlying theory. In this study, we perform global fits of simplified dark matter models with GAMBIT using an up-to-date set of likelihoods for indirect detection, direct detection and collider searches. We investigate models in which a scalar or fermionic dark matter candidate couples to quarks via an s-channel vector mediator. Large parts of parameter space survive for each model. In the case of Dirac or Majorana fermion dark matter, excesses in LHC monojet searches and relic density limits tend to prefer the resonance region, where the dark matter has approximately half the mass of the mediator. A combination of vector and axial-vector couplings to the Dirac candidate also leads to competing constraints from direct detection and unitarity violation.

Ultraviolet unitarity violations in non-minimally coupled scalar-Starobinsky inflation

We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-R 2 inflation models by including an additional R 2|Φ|2-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corresponding to known inflation scenarios so we could predict the range of coupling parameters for which the theories would remain unitary up to the Planckian regime. We also try to find the behaviour of the scattering amplitudes for these theories during the transition from inflationary to reheating epoch.