We examine the unitarity constraints in gauge and scalar sectors of non-minimal Universal Extra Dimensional model. We show that some of the tree-level two-body scattering amplitudes in gauge and scalar sectors do not respect partial wave unitarity. Unitarity analysis of this model leads to an upper bound on corresponding boundary-localized (BLT) parameter which depends on the maximum number of Kaluza-Klein (KK) mode considered in the analysis. This upper bound of the relevant BLT parameter decreases with the increasing KK-modes. The results are, in effect, independent of the inverse of compactifiaction radius. The upper bound on BLT parameter also results in a lower bound on gauge and scalar KK-masses.
We investigate the possibility of unitarity violation in the sequential neutrino mixing matrix in a scenario with extra compact spacelike dimensions. Gauge singlet neutrinos are assumed to propagate in one extra dimension, giving rise to an infinite tower of states in the effective four-dimensional theory. It is shown that this leads to small lepton-number violating entries in the neutrino mass matrix, which can violate unitarity on the order of one per cent.
We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (Delta M)_d/(Delta M)_s and sin(2 beta) measured first through the CP asymmetry in B_d^0 to psi K_S and later in K to pi nu nubar decays. Also suita…
We show how the tree level unitarity violations of compactified extra dimensional extensions of the Standard Model become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We also introduce a simple and generic formalism to obtain unitarity bounds for finite energies, taking into account coupled channels including the towers of Kaluza-Klein excitations.
We study the unitarity constraint on the two body Higgs boson elastic scattering in the presence of extra dimensions. The contributions from exchange of spin-2 and spin-0 Kaluza-Klein states can have large effect on the partial wave amplitude. Unitarity condition restrict the maximal allowed value for the ratio $r$ of the center of mass energy to the gravity scale to be less than one. Although the constraint on the standard Higgs boson mass for $r$ of order one is considerably relaxed, for small $r$ the constraint is similar to that in the Standard Model. The resulting bound on the Higgs boson…
Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of weak gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $ρ$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs…
We explore the possibility of resolving simultaneously the $W$-boson mass shift reported by the CDF collaboration and the apparent deviation from unitarity in the first row of the CKM mixing matrix in a class of left-right symmetric models. The fermion masses are generated in these models through a universal seesaw mechanism, utilizing vector-like partners of the usual fermions. We find a unique solution to the two anomalies where the mixing of the down quark with a vector-like quark (VLQ) resolves the CKM unitarity puzzle, and the mixing of the top quark with a VLQ partner explains the $W$ bo…
The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-to…
The conventional method using low energy theorems [3] does not seem to lead to an explicit unitarity limit in the scattering processes of longitudinally polarized gauge bosons for the high energy case in the extra U(1) superstring inspired models, commonly known as eta model, emanating from E6 group of superstring theory. We have made use of an alternative procedure given in [14], which is applicable to SUSY GUT. Explicit unitarity bounds on the Yukawa couplings are obtained from both using unitarity constraints as well as using RGE analysis at one-loop level utilizing critical couplings conce…
There are claims in the literature that in neutrino oscillations and oscillations of neutral kaons and B-mesons the oscillation phase differs from the standard one by a factor of two. We reconsider the arguments leading to this extra factor and investigate, in particular, the non-relativistic regime. We actually find that the very same arguments lead to an ambiguous phase and that the extra factor of two is a special case. We demonstrate that the unitarity triangle (UT) fit in the Standard Model with three families is a suitable means to discriminate between the standard oscillation phase and …
Recently proposed stabilization mechanism of the Randall-Sundrum metric gives rise to a scalar radion, which couples universally to matter with a weak interaction ($\simeq 1$ TeV) scale. Demanding that gauge boson scattering as described by the effective low enerrgy theory be unitary upto a given scale leads to significant constraints on the mass of such a radion.
We investigate the impact of extra leptons on observed tensions in the muon $g-2$ and the first-row CKM unitarity. By introducing a new SU(2)$_L$ doublet lepton and a SU(2)$_L$ triplet lepton, we find that both of the tensions can be explained simultaneously under constraints from electroweak precision observables and Higgs-boson decays. Our model could be tested by measurements of $h\toμμ$ at future collider experiments.
We relate the notion of unitarity of a $SL(2,\mathbf{R})$ invariant field theory with that of a Schrodinger field theory using the fact that $SL(2,\mathbf{R})$ is a subgroup of Schrodinger group. Exploiting $SL(2,\mathbf{R})$ unitarity, we derive the unitarity bounds and null conditions for a Schrödinger field theory (for the neutral as well as the charged sector). In non integer dimensions the theory is shown to be non-unitary. Furthermore, the use of $SL(2,\mathbf{R})$ subgroup opens up the possibility of borrowing results from 1D $SL(2,\mathbf{R})$ invariant field theory to explore Schrodin…
We calculate the contributions of the Kaluza-Klein (KK) modes to the K_L-K_S mass difference ΔM_K, the parameter ε_K, the B^0_{d,s}-\bar B^0_{d,s} mixing mass differences ΔM_{d,s} and rare decays K^+\to π^+ν\barν, K_L\to π^0ν\barν, K_L\toμ\barμ, B\to X_{s,d}ν\barνand B_{s,d}\toμ\barμin the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. For the compactification scale 1/R= 200 GeV the KK effects in these processes are governed by a 17% enhancement of the ΔF=2 box diagram function S(x_t,1/R) and by a 37% enhancement of the Z^0 penguin diagram function C(x_t/1/R) re…
Models with three Higgs doublets (3HDM) are the source of much recent activity, for they are key components of many solutions to the problems of the Standard Model; from extra sources of CP violation to Dark Matter candidates. We compute explicitly the theoretical bounds for all symmetry-constrained 3HDM arising from the perturbative unitarity of two-to-two scattering amplitudes. In addition, we propose a method based on principal minors that foregoes diagonalization and which is preferable in all models (not only 3HDM) dealing with large scattering matrices.
A low-energy non-unitary leptonic mixing matrix is a generic effect of some theories of new physics accounting for neutrino masses. We show how the extra CP-phases of a general non-unitary matrix allow for sizeable CP-asymmetries in the $ν_μ\to ν_τ$ channel. This CP-asymmetries turns out to be an excellent probe of such new physics.
A model combining perturbative and non-perturbative QCD is developed to compute high-energy reactions of hadrons and photons and to investigate saturation effects that manifest the S-matrix unitarity. Following a functional integral approach, the S-matrix factorizes into light-cone wave functions and the universal amplitude for the scattering of two color-dipoles which are represented by Wegner-Wilson loops. In the framework of the non-perturbative stochastic vacuum model of QCD supplemented by perturbative gluon exchange, the loop-loop correlation is calculated and related to lattice QCD inve…
The non-unitarity of the effective leptonic mixing matrix at low energies is a generic signal of extensions of the Standard Model (SM) with extra fermionic singlet particles, i.e. sterile or right-handed neutrinos, to account for the observed neutrino masses. The low energy effects of such extensions can be described in a model-independent way by the Minimal Unitarity Violation (MUV) scheme, an effective field theory extension of the SM. We perform a global fit of the MUV scheme parameters to the present experimental data, which yields the up-to-date constraints on leptonic non-unitarity. Furt…
Starting from a (new physics independent) tree level determination of rhobar and etabar, we perform the Unitarity Triangle analysis in general extensions of the Standard Model with arbitrary new physics contributions to loop-mediated processes. Using a simple parameterization, we determine the allowed ranges of non-standard contributions to |Delta F|=2 processes. Remarkably, the recent measurements from B factories allow us to determine with good precision the shape of the Unitarity Triangle even in the presence of new physics, and to derive stringent constraints on non-standard contributions …
Neutrino masses are one of the most promising open windows to physics beyond the Standard Model (SM). Several extensions of the SM which accommodate neutrino masses require the addition of right-handed neutrinos to its particle content. These extra fermions will either be kinematically accessible (sterile neutrinos) or not (deviations from Unitarity of the PMNS matrix) but at some point they will impact neutrino oscillation searches. We explore the differences and similitudes between the two cases and compare their present bounds with the expected sensitivities of DUNE. We conclude that Non-Un…
Using an effective field theory approach, we study the new physics (NP) corrections to muon and beta decays and their effects on the extractions of V_ud and V_us. Assuming nearly flavor blind NP interactions we find that the CKM-unitarity test is the only way to expose NP. The four short-distance operators that can generate a deviation are strongly constrained by the phenomenological bound |Vud|^2 + |Vus|^2 + |Vub|^2 - 1 = (-0.0001 \pm 0.0006), corresponding to an effective scale > 11 TeV (90% CL). Depending on the operator, this constraint is at the same level or better than that generated by…
The presence of non-unitary neutrino mixing can affect the measurement of the three-neutrino leptonic Dirac CP phase and hamper efforts to probe CP violation due to degeneracies of the extra non-unitary CP phase with the standard CP phase. We study the effect of including non-unitarity on probing CP violation with the long-baseline experiments NO$ν$A, T2K and DUNE. We analyze the effect of non-unitary mixing at the level of oscillation probabilities associated with the relevant baselines, and present the CP violation sensitivity for the individual experiments and their combination. Our results…
We numerically estimate a scale $Λ_{uni}$ at which tree-level unitarity is violated in the $SO(5)\times U(1)_X$ gauge-Higgs unification model by evaluating amplitudes for scattering of the longitudinal W bosons. The scattering amplitudes take larger values in the warped spacetime than in the flat spacetime, and take maximal values when $θ_H=π/2$, where $θ_H$ is the Wilson line phase along the extra dimension. We take into account not only the elastic scattering but also possible inelastic scatterings in order to estimate $Λ_{\rm uni}$. We found that $Λ_{\rm uni}\simeq 1.3m_{KK}$ in the warped …
Motivated by the recently improved results from the Fermilab Lattice and MILC Collaborations on the hadronic matrix elements entering $ΔM_{s,d}$ in $B_{s,d}^0-\bar B_{s,d}^0$ mixing, we determine the Universal Unitarity Triangle (UUT) in models with Constrained Minimal Flavour Violation (CMFV). Of particular importance are the very precise determinations of the ratio $|V_{ub}|/|V_{cb}|=0.0864\pm0.0025$ and of the angle $γ=(63.0\pm 2.1)^\circ$. They follow in this framework from the experimental values of $ΔM_{d}/ΔM_s$ and of the CP-asymmetry $S_{ψK_S}$. As in CMFV models the new contributions …
We propose a minimal extension of the Standard Model where an up-type vector-like quark, denoted $T$, is introduced and provides a simple solution to the CKM unitarity problem. We adopt the Botella-Chau parametrization in order to extract the $4\times 3$ quark mixing matrix which contains the three angles of the $3\times 3$ CKM matrix plus three new angles denoted $θ_{14}$, $θ_{24}$, $θ_{34}$. It is assumed that the mixing of $T$ with standard quarks is dominated by $θ_{14}$. Imposing a recently derived, and much more restrictive, upper-bound on the New Physics contributions to $ε_{K}$, we fin…
We study the quantum information storage capacity of solitons and baryons in renormalizable quantum field theories that do not include gravity. We observe that a 't Hooft-Polyakov magnetic monopole saturates the Bekenstein bound on information when the theory saturates the bound on perturbative unitarity. In this very limit the monopole entropy assumes the form of an area-law, strikingly similar to a black hole entropy in gravity. The phenomenon appears universal and takes place for other solitons and non-perturbative objects. We observe the same behaviour of entropy of a baryon in QCD with la…
The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional physical laws), rather than by the four-dimensional one, is explored in order to evade the most awkward problems of higher-dimensional theories with compact extra time-like dimensions: violation of causality and of unitarity.
We address the problem of extrapolating the vector form factor $f_{Bπ}^+$, which is relevant to $B\to π\ell ν_\ell$ decays, from the region of small to the region of large momentum transfer. As input, we use the QCD light-cone sum rule at small momentum transfer. We carry out a comprehensive Bayesian uncertainty analysis and obtain correlated uncertainties for the normalization and shape parameters of the form factor. The $z$-series parametrization for $f_{Bπ}^+$ is employed to extrapolate our results to large momentum transfer, and to compare with the lattice QCD results. To test the validity…
Motivated by the recent hints of lepton flavour non-universality in $B$-meson semi-leptonic decays, we study the constraints of perturbative unitarity on the new physics interpretation of the anomalies in $b \to c \ell \bar ν$ and $b \to s \ell \bar \ell$ transitions. Within an effective field theory approach we find that $2 \to 2$ fermion scattering amplitudes saturate the unitarity bound below 9 TeV and 80 TeV, respectively for $b \to c \ell \bar ν$ and $b \to s \ell \bar \ell$ transitions. Stronger bounds, up to few TeV, are obtained when the leading effective operators are oriented in the …
We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling evaluated at the scale R. The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2-to-N particle scattering amplitudes at the point of optimal truncation. These bounds are more stringent than Bekenstein's bound and in a consistent theory all three get saturated simultaneously. This is tru…
In a truly model-independent approach, we reexamine a minimal extension of the Standard Model (SM) through the introduction of an additional $U(1)$ symmetry leading to a new neutral gauge boson ($Z'$), allowing its kinetic mixing with the hypercharge gauge boson. An SM neutral scalar is used to spontaneously break this extra symmetry leading to the mass of the $Z'$. Except for three right-handed neutrinos no other fermions are added. We use the current LHC Drell-Yan data to put model-independent constraints in the parameter space of three quantities, namely, $M_{Z'}$, the $Z$-$Z'$ mixing angle…
We regularize QCD using the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Slavnov. It is known that for pure Yang-Mills theory the Pauli-Villars determinants generate unphysical logarithmic radiative corrections at one loop that modify the beta function. Here we prove that when the gauge fields are coupled to fermions so that one has QCD, these unphysical corrections translate into a violation of unitarity. We provide an understanding of this by seeing that Slavnov's choice for the Pauli-Villars determinants introduces extra propagating degrees of freed…
We study the unitarity bounds of the scattering amplitudes in the extra dimensional gauge theory where the gauge symmetry is broken by the boundary condition. The estimation of the amplitude of the diagram including four massive gauge bosons in the external lines shows that the asymptotic power behavior of the amplitude is canceled. The calculation will be done in the 5 dimensional standard model and the SU(5) grand unified theory, whose 5th dimensional coordinate is compactified on $S^1/Z_2$. The broken gauge theories through the orbifolding preserve the unitarity at high energies similarly t…
We show that a five dimensional Universal Extra Dimension model, compactified on a line segment, is consistently formulated even when the gauge symmetry is broken solely by non-zero Dirichlet boundary conditions on a bulk Higgs field, without any quartic interaction. We find that the longitudinal W+W- elastic scattering amplitude, under the absence of the Higgs zero-mode, is unitarized by exchange of infinite towers of KK Higgs bosons. Resultant amplitude scales linearly with the scattering energy, exhibiting five dimensional nature. A tree-level partial-wave unitarity condition is satisfied u…
Tree level unitarity violations of extra dimensional extensions of the Standard Model may become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We briefly review our formalism to obtain more stringent unitarity bounds when KK modes are present, as well as the generalization to extra dimensions of the Equivalence Theorem between Goldstone bosons and longitudinal gauge bosons
The strongest constraint on Vtb presently comes from the 3 x 3 unitarity of the CKM matrix, which fixes Vtb to be very close to one. If the unitarity is relaxed, current information from top production at Tevatron still leaves open the possibility that Vtb is sizably smaller than one. In minimal extensions of the standard model with extra heavy quarks, the unitarity constraints are much weaker and the EW precision parameters entail the strongest bounds on Vtb. We discuss the experimental perspectives of discovering and identifying such new physics models at the Tevatron and the LHC, through a …
We calculate the rates of radiative $β^- \to α^- + γ$ decays for $(α, β) = (e, μ)$, $(e, τ)$ and $(μ, τ)$ by taking the {\it unitary} gauge in the $(3+n)$ active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix $U$ extracted from $β^- \to α^- + γ$ decays in the {\it 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 $β^- \to α^- + γ$ can be us…
We study the unitarity of models with low scale quantum gravity both in four dimensions and in models with a large extra-dimensional volume. We find that models with low scale quantum gravity have problems with unitarity below the scale at which gravity becomes strong. An important consequence of our work is that their first signal at the Large Hadron Collider would not be of a gravitational nature such as graviton emission or small black holes, but rather linked to the mechanism which fixes the unitarity problem. We also study models with scalar fields with non minimal couplings to the Ricci …
We present a set of relations between one-loop integral coefficients for dimensionally regulated QCD amplitudes. Within dimensional regularization, the combined use of color-kinematics duality and integrand reduction yields the existence of relations between the integrand residues of partial amplitudes with different orderings of the external particles. These relations can be established for the cut-constructible contributions as well for the ones responsible for rational terms. Starting from the general parametrization of one-loop residues and applying Laurent expansion in order to extract th…
We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC's we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC's the terms in these amplitudes th…
Neutrino oscillations are well established and the relevant parameters determined with good precision, except for the CP phase, in terms of a unitary lepton mixing matrix. Seesaw extensions of the Standard Model predict unitarity deviations due to the admixture of heavy isosinglet neutrinos. We provide a complete description of the unitarity and universality deviations in the light neutrino sector. Neutrino oscillation experiments involving electron or muon neutrinos and anti-neutrinos are fully described in terms of just three new real parameters and a new CP phase, in addition to the ones de…
We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the ob…
We identify the nonlinear evolution equation in impact-parameter space for the "Supercritical Pomeron" in Reggeon Field Theory as a 2-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to an high energy traveling wave solution corresponding to an ""universal" behaviour of the impact-parameter front profile of the elastic amplitude; Its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the non-linear terms restoring unitarity. Theoretical pr…
In this work we discuss in detail the non-perturbative determination of the momentum dependence of the form factors entering in semileptonic decays using unitarity and analyticity constraints. The method contains several new elements with respect to previous proposals and allows to extract, using suitable two-point functions computed non-perturbatively, the form factors at low momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without any assumption about their $q^2$-dependence. The approach will be very useful for exclusive semileptonic $B$-meson decays, whe…
