Violation Of Unitarity Research Articles

On the group-theoretical approach to relativistic wave equations for arbitrary spin

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for arbitrary-spin particles are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the anti-de Sitter group leads to inconsistent results, mainly as a consequence of the violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

Are the CKM anomalies induced by vector-like quarks? Limits from flavor changing and Standard Model precision tests

Recent high precision determinations of Vus and Vud indicate towards anomalies in the first row of the CKM matrix. Namely, determination of Vud from beta decays and of Vus from kaon decays imply a violation of first row unitarity at about 3σ level. Moreover, there is tension between determinations of Vus obtained from leptonic Kμ2 and semileptonic Kℓ3 kaon decays. These discrepancies can be explained if there exist extra vector-like quarks at the TeV scale, which have large enough mixings with the lighter quarks. In particular, extra vector-like weak singlets quarks can be thought as a solution to the CKM unitarity problem and an extra vector-like weak doublet can in principle resolve all tensions. The implications of this kind of mixings are examined against the flavour changing phenomena and SM precision tests. We consider separately the effects of an extra down-type isosinglet, up-type isosinglet and an isodoublet containing extra quarks of both up and down type, and determine available parameter spaces for each case. We find that the experimental constraints on flavor changing phenomena become more stringent with larger masses, so that the extra species should have masses no more than few TeV. Moreover, only one type of extra multiplet cannot entirely explain all the discrepancies, and some their combination is required, e.g. two species of isodoublet, or one isodoublet and one (up or down type) isosinglet. We show that these scenarios are testable with future experiments. Namely, if extra vector-like quarks are responsible for CKM anomalies, then at least one of them should be found at scale of few TeV, and anomalous weak isospin violating Z-boson couplings with light quarks should be detected if the experimental precision on Z hadronic decay rate is improved by a factor of 2 or so.

Violation of unitarity in gravitational subregions

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, “states” with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed.

The study of neutral triple gauge couplings in the process e+e− → Zγ including unitarity bounds

The neutral triple gauge couplings (nTGCs) provide a unique opportunity to probe new physics beyond the Standard Model. The nTGCs can be described by an effective field theory (EFT), which is valid only under a certain energy scale. One of the signatures that an EFT is no longer valid is the violation of unitarity. We study the partial wave unitarity bounds on the coefficients of nTGCs in the process e+e−→Zγ. In the experiments, the constraints obtained should be tighter than the unitarity bounds, otherwise the results are meaningless, therefore there exists a minimal luminosity for a e+e− collider such as the CEPC to study the nTGCs. To derive the minimal luminosity, the kinematic features and event selection strategy are studied by Monte-Carlo simulation. Both the processes e+e−→ℓ+ℓ−γ and e+e−→jjγ are studied, event selection strategies are discussed. Based on the statistical significance, the expected constraints in experiments are estimated. The required luminosities for the experiments to reach the unitarity bounds are presented.

Inflation based on a classically scale invariant extended standard model

We extend a classically scale invariant model where the electroweak symmetry breaking is triggered by the dynamical chiral symmetry breaking in a hidden QCD sector, and a real singlet scalar [Formula: see text] mediates these two sectors. Our model can explain cosmic inflation without unitarity violation in addition. Slow-roll inflation occurs along a valley in scalar potential. In the original model, the coupling [Formula: see text] between the Higgs field [Formula: see text] and [Formula: see text] is always negative and therefore, the potential has its valleys in [Formula: see text]-[Formula: see text] mixed directions. For large value of the top Yukawa coupling [Formula: see text], the potential along the valley becomes negative since the Higgs quartic coupling [Formula: see text] becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling [Formula: see text] positive at inflationary scale and consider the [Formula: see text]-inflation case. This is achieved by introducing a new singlet scalar [Formula: see text] with the large coupling [Formula: see text] to [Formula: see text]. By this extension, [Formula: see text] can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling [Formula: see text] between [Formula: see text] and gravity. Although [Formula: see text] is large such as [Formula: see text], unitarity is not violated since couplings between [Formula: see text] and other fields are sufficiently small. [Formula: see text] is odd under a new symmetry [Formula: see text] not to mix with [Formula: see text] regardless of largeness of [Formula: see text]. Because of this symmetry, [Formula: see text] may have its relic abundance [Formula: see text] comparable with the observational value [Formula: see text] of the dark matter relic abundance. However, the spin-independent elastic cross-section [Formula: see text] of [Formula: see text] exceeds the observational bound [Formula: see text] cm2. Hence, we impose the resonance condition [Formula: see text] and reduce [Formula: see text] to much smaller than [Formula: see text]. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.

Electroweak axial structure functions and improved extraction of the Vud CKM matrix element

We present a comprehensive analysis of the $\gamma W$ interference radiative correction to the neutron $\beta$-decay matrix element. Within a dispersion relations approach, we compute the axial-vector part of the $\gamma W$ box amplitude $\Box^{\gamma W}_{A}$ in terms of the isoscalar part of the $F_3^{\gamma W}$ interference structure function. Using the latest available phenomenology for $F_3^{\gamma W}$ from the nucleon elastic, resonance, deep-inelastic, and Regge regions, we find the real part of the box correction to be $\Box^{\gamma W}_A = 3.90(9) \times 10^{-3}$. This improved correction gives a theoretical estimate of the CKM matrix element $|V_{ud}|^2=0.94805(26)$, which represents a 4$\sigma$ violation of unitarity.

Geometry and entanglement in the scattering matrix

A formulation of nucleon–nucleon scattering is developed in which the S-matrix, rather than an effective-field theory (EFT) action, is the fundamental object. Spacetime plays no role in this description: the S-matrix is a trajectory that moves between RG fixed points in a compact theory space defined by unitarity. This theory space has a natural operator definition, and a geometric embedding of the unitarity constraints in four-dimensional Euclidean space yields a flat torus, which serves as the stage on which the S-matrix propagates. Trajectories with vanishing entanglement are special geodesics between RG fixed points on the flat torus, while entanglement is driven by an external potential. The system of equations describing S-matrix trajectories is in general complicated, however the very-low-energy S-matrix –that appears at leading-order in the EFT description– possesses a UV/IR conformal invariance which renders the system of equations integrable, and completely determines the potential. In this geometric viewpoint, inelasticity is in correspondence with the radius of a three-dimensional hyperbolic space whose two-dimensional boundary is the flat torus. This space has a singularity at vanishing radius, corresponding to maximal violation of unitarity. The trajectory on the flat torus boundary can be explicitly constructed from a bulk trajectory with a quantifiable error, providing a simple example of a holographic quantum error correcting code.

Fermi Constant from Muon Decay Versus Electroweak Fits and Cabibbo-Kobayashi-Maskawa Unitarity.

The Fermi constant G_{F} is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via G_{F}, the constraining power is determined by the precision of the second-best independent determination of G_{F}. The best alternative extractions of G_{F} proceed either via the global electroweak (EW) fit or from superallowed β decays in combination with the Cabibbo angle measured in kaon, τ, or D decays. Both variants display some tension with G_{F} from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of G_{F} into agreement using SM effective field theory and comment on future perspectives.

Ultraviolet behaviour of Higgs inflation models

We study the ultraviolet behaviour of Higgs inflation models above the apparent unitarity violation scale arising from the large non minimal coupling to gravity, by computing on-shell 4-point scattering amplitudes in the presence of a large inflaton background, away from the electroweak vacuum. We find that all tree-level amplitudes are well behaved at high energies below the inflaton background that can thus take values up to the Planck scale. This result holds in both the metric and Palatini formulation, and is independent of the frame (Jordan or Einstein) as expected. The same result also holds if an R2 term is added to the action.

Successful Higgs inflation from combined nonminimal and derivative couplings

We propose an inflationary scenario based on the concurrent presence of non-minimal coupling (NMC) and generalized non-minimal derivative coupling (GNMDC), in the context of Higgs inflation. The combined construction maintains the advantages of the individual scenarios without sharing their disadvantages. In particular, a long inflationary phase can be easily achieved due to the gravitational friction effect owed to the GNMDC, without leading to trans-Planckian values and unitarity violation. Additionally, the tensor-to-scalar ratio remains to low values due to the NMC contribution. Finally, the instabilities related to the squared sound-speed of scalar perturbations, which plague the simple GNMDC scenarios, are now healed due to the domination of the NMC contribution and the damping of the GNMDC effects during the reheating era. These features make scenarios with nonminimal and derivative couplings to gravity successful candidates for the description of inflation.

Cutkosky rules and unitarity (violation) in D-instanton amplitudes

In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real. The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories.

Radiative decays of charged leptons in the seesaw effective field theory with one-loop matching

The canonical type-I seesaw model with three heavy Majorana neutrinos is one of the most natural extensions of the standard model (SM) to accommodate tiny Majorana masses of three ordinary neutrinos. At low-energy scales, Majorana neutrino masses and unitarity violation of lepton flavor mixing have been extensively discussed in the literature, which are respectively generated by the unique dimension-five Weinberg operator and one dimension-six operator in the seesaw effective field theory (SEFT) with the tree-level matching. In this work, we clarify that a self-consistent calculation of radiative decays of charged leptons β−→α−+γ requires the SEFT with one-loop matching, where new six-dimensional operators emerge and make important contributions. For the first time, the Wilson coefficients of all the relevant six-dimensional operators are computed by carrying out the one-loop matching between the effective theory and full seesaw model, and applied to calculate the total rates of radiative decays of charged leptons.

Preheating from target space curvature and unitarity violation: Analysis in field space

We study particle production and unitarity violation caused by a curved target space right after inflation. We use the inflaton field value instead of cosmic time as the time variable, and derive a semiclassical formula for the spectrum of produced particles. We then derive a simple condition for unitarity violation during preheating, which we confirm by our semiclassical method and numerical solution. This condition depends not only on the target space curvature but also on the height of the inflaton potential at the end of inflation. This condition tells us, for instance, that unitarity is violated in running kinetic inflation and Higgs inflation, while unitarity is conserved in $\alpha$-attractor inflation and Higgs-Palatini inflation.

Charting the fifth force landscape

Fifth forces arising from hidden sector scalar operator exchange, as probed in a variety of present and planned experiments, can be captured by a general dispersion relation involving one real, positive, spectral density function. Previously considered scalar fifth forces, from tree-level to more exotic loop-level possibilities, are derived in this formalism, without explicitly performing conventional loop calculations. A variety of experimental observables commonly used in fifth force searches are also presented in the same formalism, allowing the straightforward extraction of limits on any specific model. The speculative possibility of probing hidden sector violations of unitarity, causality, or locality, manifested as a breakdown of the positivity of the spectral density, is also discussed.

Does Palatini Higgs inflation conserve unitarity?

In the conventional metric formulation of gravity, the Higgs Inflation model violates unitarity in the electroweak vacuum in Higgs scattering at the energy scale Λ ∼ MPl /ξ, where ξ ∼ 104 is the non-minimal coupling of the Higgs to the Ricci scalar. In the Palatini formulation it is commonly believed that Λ ∼ MPl /√(ξ), where ξ ∼ 109. Here we reconsider unitarity violation in the electroweak vacuum in the Palatini formulation. We argue that there is no unitarity violation in Higgs scattering in the Palatini non-minimally coupled Standard Model in the electroweak vacuum at energies below the Planck scale. In this case Palatini Higgs Inflation completely conserves unitarity and is consistent at all energies up to those at which quantum gravity becomes important. If true, this would imply that Palatini Higgs Inflation has a significant advantage over metric Higgs Inflation.

On preheating in Higgs inflation

Recently, the problem of unitarity violation during the preheating stage of Higgs inflation with a large non-minimal coupling has been much discussed in the literature. We point out that this problem can be translated into a strong coupling problem for the dimensionless effective coupling, and that the existence of these problems is highly dependent on the choice of higher-dimensional operators because they can significantly change the background dynamics and the canonical normalization of the fluctuations around it. Correspondingly, the typical energy of particles produced during the first stage of preheating can remain comparable to or below the cutoff scale of the theory. As an example, we numerically calculate the particle production in the presence of a specific four-derivative operator of the Higgs field, and confirm the statement above. Our argument also applies to multi-field inflation with non-minimal couplings.

The Continuum Linear Dilaton

Continuum spectra can be a way out to alleviate the tension generated by the elusiveness of narrow resonances of new physics in direct experimental searches. Motivated by the latter, we consider the linear dilaton model with a continuum spectrum of KK modes. It is provided by a critical exponential bulk potential for the scalar field stabilizing the distance, between the UV boundary at $y=0$ and a naked (good) singularity at $y=y_s$, in proper coordinates, which corresponds in conformal coordinates to $z_s\to\infty$. The cutoff $M_s$ in this theory is an intermediate scale $M_s\simeq 10^{-5}M_{\rm Pl}$ and the warped factor solves the hierarchy between $M_s$ and the TeV, while the hierarchy between $M_{\rm Pl}$ and $M_s$ has to be solved by a (Little) String Theory with coupling $g_s\simeq 10^{-5}$. The Standard Model is localized on a 4D IR brane. The graviton and radion Green's and spectral functions have a continuum of states with a TeV mass gap, and isolated poles consisting on the 4D graviton and the light radion/dilaton. We construct the effective field theory below the mass gap where the continua of KK modes are integrated out, generating a set of dimension eight operators which contribute to low energy electroweak precision observables, and high energy violation of unitarity in vector boson scattering processes. The radion mass depends on the stabilizing UV brane potential and its wave function is localized toward the IR which enhances its coupling with the SM fields.

Leptonic unitarity triangles

We present a comprehensive analysis of leptonic unitarity triangles, using both current neutrino oscillation data and projections of next-generation oscillation measurements. Future experiments, sensitive to the degree of CP violation in the lepton sector, will enable the construction of precise triangles. We show how unitarity violation could manifest in the triangles and discuss how they serve as unitarity tests. We also propose the use of Jarlskog factors as a complementary means of probing unitarity. This analysis highlights the importance of testing the unitarity of the leptonic mixing matrix, an understanding of which is crucial for deciphering the nature of the neutrino sector.

Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

We calculate the rates of radiative beta ^- rightarrow alpha ^- + gamma decays for (alpha , beta ) = (e, mu ), (e, tau ) and (mu , tau ) by taking the unitary gauge in the (3+n) active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the 3times 3 Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix U extracted from beta ^- rightarrow alpha ^- + gamma decays in the minimal unitarity violation scheme differ from those obtained in the canonical seesaw mechanism with n heavy Majorana neutrinos by a factor 5/3. In such a natural seesaw case we show that the rates of beta ^- rightarrow alpha ^- + gamma can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors U^{}_{alpha i} U^*_{beta i} and U^{}_{alpha j} U^*_{beta j} (for i ne j) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation {{mathcal {J}}}^{ij}_{alpha beta }, and their small differences signify slight unitarity violation of the PMNS matrix U.

Current and future neutrino oscillation constraints on leptonic unitarity

The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in the mixing of the active neutrino states. Motivated by the prospect that future experiments may provide a precise measurement of the lepton mixing matrix, we revisit current constraints on unitarity violation from oscillation measurements and project how next-generation experiments will improve our current knowledge. With the next-generation data, the normalizations of all rows and columns of the lepton mixing matrix will be constrained to ≲10% precision, with the e-row best measured at ≲1% and the τ-row worst measured at ∼10% precision. The measurements of the mixing matrix elements themselves will be improved on average by a factor of 3. We highlight the complementarity of DUNE, T2HK, JUNO, and IceCube Upgrade for these improvements, as well as the importance of ντ appearance measurements and sterile neutrino searches for tests of leptonic unitarity.