A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle ("ungluons"). The model is formulated in terms of Lagrangian which features the source field $S(x)$ which becomes a local pseudo-Goldstone field of conformal symmetry - the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by $B_μ(x) \sim\partial_μ S(x)$. Because the conformal sector is strongly coupled, the mode $S(x)$ may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the "ungluon" exchange pattern - the "ungluon" propagator.
The derivation of Feynman rules for unparticles carrying standard model quantum numbers is discussed. In particular, this note demonstrates that an application of Mandelstam's approach to constructing a gauge-invariant action reproduces for unparticles the vertices one obtains through the usual minimal coupling scheme; other non-trivial requirements are satisfied as well. This approach is compared to an alternative method 0801.0892 that has recently been constructed by A. L. Licht.
Unparticle physics from a hidden conformal sector can alter the evolution of the Standard Model (SM) gauge couplings via TeV scale threshold corrections. We discuss how this may lead to gauge coupling unification at M_{GUT}\approx 2 \times 10^{15} GeV -- 5 \times 10^{17} GeV without introducing new particles in the SM sector.
The existence of scale invariant physics would lead to new phenomena in particle physics that could be detected at the LHC. In this paper we exploit the effects of these unparticles in $WW \to WW$ scattering. From the requirement of unitarity we derive constraints on unparticle physics. We show that the existence of unparticles would lead to deviations in differential cross sections which can be measured. These deviations are sensitive on the scale dimension and on the spin characteristics of the unparticles.
We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and Ward identity of physical amplitudes. We find that non-integrable singularities arise in physical quantities like cross section and decay rate from gauge interactions of unparticles. We also show that Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward-Takahashi identity for general Green functions is incorporated in the model. A previous observation that the unparticle's (with scaling dimension d) contri…
Unparticles charged under a gauge group can contribute to the running of the gauge coupling. We show that a scalar unparticle of scaling dimension d contributes to the βfunction a term that is (2-d) times that from a scalar particle in the same representation. This result has important implications on asymptotic freedom. An unparticle with d>2, in contrast to its matter counterpart, can speed up the approach to asymptotic freedom for a non-Abelian gauge theory and has the tendency to make an Abelian theory also asymptotically free. For not spoiling the excellent agreement of the standard model…
We comment on several points concerning unparticles which have been overlooked in the literature. One regards Mack's unitarity constraint lower bounds on CFT operator dimensions,e.g. d\geq 3 for primary, gauge invariant, vector unparticle operators. We correct the results in the literature to account for this, and also for a needed correction in the form of the propagator for vector and tensor unparticles. We show that the unitarity constraints can be directly related to unitarity requirements on scattering amplitudes of particles, e.g. those of the standard model, coupled to the CFT operators…
We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which create gauge invariant coloured unparticles. We discuss both their perturbative and non--perturbative properties.
We propose a model that introduces a supersymmetric unparticle operator in the minimal supersymmetric Standard Model. We analyze the lowest dimension operator involving an unparticle. This operator behaves as a Standard Model gauge singlet and it introduces a new parameter into the Higgs potential which can provide an alternative way to relax the upper limit on the lightest Higgs boson mass. This operator also introduces several unparticle interactions which can induce a neutral Higgsino to decay into a spinor unparticle. It also induces violation of scale invariance around the electroweak sca…
We examine a scenario where the new physics at the LHC includes an approximate conformal field theory, where some of the degrees of freedom (aka "unparticles") carry a color charge. We present a simple argument showing that the production cross section for scalar unparticles mediated by a gauge interaction is given by (2-d) times the standard particle expression, where d is the scaling dimension of the unparticle field. We explicitly check that this is indeed the case, which involves non trivial cancellations between different Feynman diagrams, for the process q qbar to scalar unparticles.
Modern theoretical models strongly suggest that new phenomena await discovery above the energy scale of the Standard Model (SM) of particle interactions. In this paper we argue that correct description of particle physics in the TeV energy scale needs to account for degrees of freedom obeying the conformal (or scale) invariance. In this respect, the existing of Georgi's unparticles is strongly argued. We present the gauge model of scalar unparticles. The ground state of scalar unparticles in the continuum is restricted by the vacuum expectation value of the SM Higgs boson and the scale dimensi…
The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We further develop a possible gauge theory for fermionic unparticles. Computing the consequent contribution of un-fermions to the $β$ function of the theory, it is shown that this can be viewed as the sum of two contributions, one fermion-like and the other scalar-like. However, if full conformal invariance is imposed, the latter vanishes identically. We discuss the…
Recently, conceptually new physics beyond the Standard Model has been proposed by Georgi, where a new physics sector becomes conformal and provides "unparticle" which couples to the Standard Model sector through higher dimensional operators in low energy effective theory. Among several possibilities, we focus on operators involving the (scalar) unparticle, Higgs and the gauge bosons. Once the Higgs develops the vacuum expectation value (VEV), the conformal symmetry is broken and as a result, the mixing between the unparticle and the Higgs boson emerges. In this paper, we consider the unparticl…
We examine the correspondence between the anti-de Sitter (AdS) description of conformal field theories (CFTs) and the unparticle description of CFTs. We show how unparticle actions are equivalent to holographic boundary actions for fields in AdS, and how massive unparticles provide a new type of infrared cutoff that can be simply implemented in AdS by a soft breaking of conformal symmetry. We also show that processes involving scalar unparticles with dimensions d_s<2 or fermion unparticles with dimensions d_f<5/2 are insensitive to ultraviolet cutoff effects. Finally we show that gauge interac…
A renormalizable coupling between the Higgs and a scalar unparticle operator O_U of non-integer dimension d_U < 2 gives rise, after electroweak symmetry breaking, to a mass gap in the unparticle continuum and a shift in the original Higgs mass, which can end up above or below the mass gap. We show that, besides the displaced Higgs state, a new isolated state can generically appear in the spectrum near or below the mass gap. Such state (which we call phantom Higgs) is a mixture of Higgs and unparticles and therefore has universally reduced couplings to fermions and gauge bosons. This phenomenon…
We construct a model of an unparticle sector consisting of a supersymmetric SU(N) gauge theory with the number of flavors in the Seiberg conformal window. We couple this sector to the MSSM via heavy messengers. The resulting low energy theory has a Higgs coupling to unparticles. The Higgs vev drives the hidden Seiberg sector to a new conformal fixed point. The coupling to the Higgs mediates supersymmetry breaking to the Seiberg sector, and breaks conformal invariance at a lower scale. The low energy theory contains light stable and metastable mesons. Higgs decay into this sector gives signatur…
We point out that the notion of an unparticle, recently introduced by Georgi, can be interpreted as a particular case of a field with continuously distributed mass considered in ref.\cite{14}. We also point out that the simplest renormalizable extension of the $SU_c(3)\otimes SU_L(2)\otimes U(1)$ Standard Model is the extension with the replacement of the U(1) gauge propagator $\frac{1}{k^2} \to \frac{1}{k^2} + \int _0^{\infty}\frac{ρ(t)}{-t+k^2 +iε}dt$ with $\int_0^{\infty}ρ(t)dt < \infty $.
Recently, conceptually new physics beyond the Standard Model has been proposed by Georgi, where a new physics sector becomes conformal and provides "unparticle" which couples to the Standard Model sector through higher dimensional operators in low energy effective theory. Among several possibilities, we focus on operators involving the (scalar) unparticle, Higgs and the gauge bosons. Once the Higgs develops the vacuum expectation value (VEV), the conformal symmetry is broken and as a result, the mixing between the unparticle and the Higgs boson emerges. In this paper, we consider a natural rea…
The possibility of the presence of unparticle has been discussed recently adding a mass like term for gauge field with the Vector Schwinger model at the classical level \cite{GEOR1}. A one loop correction due to bosonization is taken into account and investigation is carried over to study the effect of it in connection with the unparticle scenario. It has been found that mass of the gauge boson acquires a generalized expression with the bare coupling constant and the parameters involved in the masslike terms added at the classical level term as well the terms entered in the model during the on…
We investigate unparticle physics with supersymmetry (SUSY). The SUSY breaking effects due to the gravity mediation induce soft masses for the SUSY unparticles and hence break the conformal invariance. The unparticle physics observable in near future experiments is only consistent if the SUSY breaking effects from the hidden sector to the standard model sector are dominated by the gauge mediation, or if the SUSY breaking effects to the unparticle sector is sufficiently sequestered. We argue that the natural realization of the latter possibility is the conformal sequestering scenario.
We present the conformal windows of SU(N) supersymmetric and nonsupersymmetric gauge theories with vector-like matter transforming according to higher irreducible representations of the gauge group. We determine the fraction of asymptotically free theories expected to develop an infrared fixed point and find that it does not depend on the specific choice of the representation. This result is exact in supersymmetric theories while it is an approximate one in the nonsupersymmetric case. The analysis allows us to size the unparticle world related to the existence of underlying gauge theories deve…
The geodetic and frame-dragging effects are the direct consequences of the spacetime curvature near Earth which can be probed from the Gravity probe B (GP-B) satellite. The satellite result matches quite well with Einstein's general relativistic result. The gyroscope of the satellite which measures the spacetime curvature near Earth contains lots of electrons and nucleons. Ultralight axions, vector gauge bosons, and unparticles can interact with these electrons and nucleons through different spin-dependent and spin-independent operators and change the drift rate of the gyroscope. Some of these…
We study interactions of unparticles ${\cal {U}}$ of dimension $d_{\cal {U}}$ due to Georgi with Standard Model (SM) fields through effective operators. The unparticles describe the low energy physics of a non-trivial scale invariant sector. Since unparticles come from beyond the SM physics, it is plausible that they transform as a singlet under the SM gauge group. This helps tremendously in limiting possible interactions. We analyze interactions of scalar ${\cal {U}}$, vector ${\cal {U}}$$^μ$ and spinor ${\cal {U}}$$^s$ unparticles with SM fields and derivatives up to dimension four. Using th…
Using the gauge-invariant but path-dependent variables formalism, we examine the effect of the space-time dimensionality on a physical observable in the unparticle scenario. We explicitly show that long-range forces between particles mediated by unparticles are still present whenever we go over into lower dimensions.
We analyze generalizations of the Schwinger model with more massless fermions and more vector fields. We focus on models with the gauge structure of ``diagonal color $SU(n)$'' but unlike previous investigators, we do not assume that all the gauge boson masses are the same. Unlike the Schwinger model, these are Banks-Zaks models with conformal sectors that survive at long distances. In addition to local operators that go to ``unparticle operators'' with non-zero anomalous dimensions at long distances, they contain local operators like the $\barψ_Lψ_R$ operator in the Schwinger model which go to…
Unparticles from hidden conformal sectors provide qualitatively new possibilities for physics beyond the standard model. In the theoretical framework of minimal models, we clarify the relation between energy scales entering various phenomenological analyses. We show that these relations always counteract the effective field theory intuition that higher dimension operators are more highly suppressed, and that the requirement of a significant conformal window places strong constraints on possible unparticle signals. With these considerations in mind, we examine some of the most robust and sensit…
We propose an extra-dimensional approach to the unparticle Higgs (Unhiggs). The non-local 4D Unhiggs action is derived as the boundary effective action of a local 5D theory. We review the mechanism to generate unparticle spectra in the context of warped soft-wall models. Gauge invariance can be simply implemented and unitarity of the longitudinal WW scattering amplitude is particularly transparent. Furthermore, the 5D approach uncovers a broader spectrum of phenomenological possibilities. The Unhiggs is accompanied by another continuum formed by Kaluza-Klein excitations of the Standard Model g…
Recently, conceptually new physics beyond the Standard Model has been proposed, where a hidden conformal sector provides ``unparticle'' which couples to the Standard Model sector through higher dimensional operators in low energy effective theory. Among several possibilities, we focus on operators involving unparticle, the Higgs doublet and the gauge bosons. Once the Higgs doublet develops the vacuum expectation value, the conformal symmetry is broken and as a result, the mixing between unparticle and Higgs boson emerges. We find that this mixing can cause sizable shifts for the couplings betw…
We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will…
In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.
This brief note is devoted to reconcile the conclusions from a recent analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations in Coulomb gauge with previous studies in Landau gauge.
We reply to the Comment of X. Ji [arXiv:0810.4913] on our paper [PRL 100:232002 (2008)], concerning angular momentum algebra, locality, Lorentz covariance, and measurability of our gauge-invariant description of the spin and orbital angular momentum of quarks and gluons.
We comment on a statement made in arXiv:1107.0403, which implies that the model of gravitino dark matter from Q-ball decay we presented in arXiv:1101.5328 is generally ruled out by the effect of NLSP decay on BBN. We explain why this statement is incorrect.
The individual parts of the total angular momentum operator in interacting theories cannot satisfy the canonical angular momentum commutation rule, including those proposed in the above paper. Furthermore, the operators in the new proposal a) are non-local in general gauge, b) do not have proper Lorentz transformation properties, and c) do not have any known physical measurements.
We point out that if the majoron-like scheme is implemented within a 331 model, there must exist at least three different mass scales for the scalar vacuum expectation values in the model.
The authors claim to have found a "proper", "gauge-invariant" definition of a charged-particle's momentum in gauge theory, which is more "superior" than the textbook version. I show that their result arises from a misunderstanding of gauge symmetry by generalizing the Coulomb gauge result indiscriminately and is not physical.
Baier et al. have reported the damping rate of long-wavelength fermionic excitations in high-temperature QED and QCD to be gauge-fixing-dependent even within the resummation scheme due to Braaten and Pisarski. It is shown that this problem is caused by the singular nature of the on-shell expansion of the fermion self-energy in the infra-red. Its regularization reveals that the alleged gauge dependence pertains to the residue rather than the pole of the fermion propagator, so that in particular the damping constant comes out gauge-independent, as it should.
A new method is proposed to calculate wave functions in $k_T$-factorization in \cite{LiMi} as a comment about our paper \cite{FMW}. We point out that the results obtained with the method are in conflict with the translation invariance and depend on the chosen contours for loop-integrals. Therefore, the method is in principle unacceptable and the results with the method cannot be correct.
We affirm that the proper momentum defined in [PRL 103:062001 (2009)] does respect exact gauge symmetry and is as measurable as the kinetic momentum. The physical part of the gauge field is also as measurable as the electromagnetic field. The Comment of Ji [arXiv:0910.5022] is due to a misunderstanding of our work, and a typical confusion of our gauge-invariant formalism with the specific Coulomb-gauge calculation.
We reanalyze the recent computation of the amplitude of the Higgs boson decay into two photons presented by Gastmans et al.. The reasons for which this result cannot be the correct one have been discussed in some recent papers. We address here the general issue of the indeterminacy of integrals with four-dimensional gauge-breaking regulators and to which extent it might eventually be solved by imposing physical constraints. Imposing gauge invariance as the last step upon R_xi gauge calculations with four-dimensional gauge-breaking regulators, allows indeed to recover the well known H -> gamma …
There has been interest in generalizing models of gauge mediation of supersymmetry breaking. As shown by Meade, Seiberg, and Shih (MSS), the soft masses of general gauge mediation can be expressed in terms of the current two-point functions of the susy-breaking sector. We here give a simple extension of their result which provides, for general gauge mediation, the full effective potential for squark pseudo-D-flat directions. The effective potential reduces to the sfermion soft masses near the origin, and the full potential, away from the origin, can be useful for cosmological applications. We …
We comment a model based on the $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$ gauge symmetry recently proposed by Frampton. We stressed that the analysis of flavor changing neutral currents impose strong constraints on th emasses of the new gauge bosons of the model.
We point out mistakes made in the one-loop calculation of some diagrams for the process $πγ^* \to γ$ in the preprint arXiv:0807.0296, and present correct results. Especially, we have difficulty to understand their argument that a highly off-shell gluon generates a light-cone (infrared) singularity. It is shown by means of the Ward identity that the gauge-dependent light-cone singularity found in arXiv:0807.0296 does not exist. It is then shown that a hard kernel derived in the $k_T$ factorization of exclusive processes is gauge invariant and free of the light-cone singularity.
Analyzing the dilepton production from out of equilibrium quark-gluon plasma, Le Bellac and Mabilat have recently pointed out that, in the reaction rate, the cancellation of mass (collinear) singularities takes place only in physical gauges, and not in covariant gauges. They then have estimated the contribution involving pinching singularities. After giving a general argument for the gauge independence of the production rate, we explicitly confirm the gauge independence of the mass-singular part. The contribution involving pinching singularities develops mass singularities, which is also gauge…
Scalar condensation, the well-established Higgs phenomenon, is the standard paradigm for building up renormalizable gauge-invariant theories of massive gauge bosons. In this short note, we demonstrate the uniqueness of the Higgs vacuum state under the possible presence of fermion condensates in a renormalizable U(1) model. In the same context, we explain why spontaneous spin-statistics violation is technically not admitted in conventional Quantum Field Theory.
We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.
We use gauge/gravity duality to study the thermodynamics of a field theory with asymptotic freedom in the ultraviolet and a fixed point in the infrared. We find a high temperature quark-gluon phase and a low T conformal unparticle phase. The phase transition between the phases is of first order or continuous, depending on the ratio of the radii of asymptotic AdS5 spaces at T=0 and T=infinity. This is a prediction from a model of gauge/gravity duality, not yet verified on the field theory side.
In a recent paper on SU(16) grand unification, because of the presence of intermediate-energy gauge groups containing products of U(1) factors which are not orthogonal among themselves, the renormalization-group treatment has a few small errors. I correct it. I emphasize that one should not switch gauge couplings at the various thresholds. It is easier, and it avoids errors, to use throughout the gauge couplings of the standard model, and compute at each threshold, in the usual way, the extra contributions to the beta functions from the extra non-decoupled fields. I also point out that the SU(…
The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The `physics' of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). I discuss the `Schwinger point' of the Sommerfield model in which the vector boson mass goes to zero. The limit is singular but gauge invariant quantities should be well-defined. I give a number of examples, both (trivially) with local operators and with nonlocal products connected by Wilson lines…
We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. We showed previously that in certain gauges some cohomology classes of the gauge-fixed BRST differential do not correspond to gauge invariant observables. We now show that in addition ``accidental'' conserved currents may appear. These correspond one-to-one to observables that become trivial in this gauge. We explicitly show how the gauge-fixed BRST cohomology appears in the context of the Quantum Noether Method.
We demonstrate that in the process of deducing the constraint on the electroweak mixing angle $θ_{W}$ in our paper, we have indeed been working with three mass scales while implementing (331) model.
We revisit the gauge issue in cosmological perturbation theory, and highlight its relation to the notion of covariance in general relativity. We also discuss the similarities and differences of the covariant approach in perturbation theory to the Bardeen or metric approach in a non-technical fashion.
Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements \emph{are} gauge-invariant, cannot be correct. I show that their result has no bearing on the question of gauge-invariance, and also point to an amusing lattice paradox.
Since right-handed neutrinos, if added to the Standard Model, have no gauge interactions, their kinetic terms can be mixed. I examine the related rotations of the gauge eigenstates in order to derive the propagators for the kinetic and mass terms, and I comment on the resulting lepton mixing, on the possibility of not having well-defined mass eigenstates, and on the modifications to weak contributions and observables (anomalous magnetic moment, muon decay, neutrino oscillations).
We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter current…
In Phys. Rev. Lett. 89, 101802 (2002); erratum, ibid. 89, 229902(E) (2002), Bernabeu, Papavassiliou, and Vidal claim that they can extract a gauge-independent neutrino charge radius (NCR) which is, therefore, a physical observable. We show here that this claim is incorrect by demonstrating that the NCR is, in general, gauge-dependent.
A careful analysis of the Fayet-Iliopoulos (FI) model shows that its energy momentum tensor and supersymmetry current are not gauge invariant. Since the corresponding charges are gauge invariant, the model is consistent. However, our observation about the currents gives a new perspective on its restrictive renormalization group flow and explains why FI-terms never appear in dynamical supersymmetry breaking. This lack of gauge invariance is at the root of the complications of coupling the model to supergravity. We show that this is possible only if the full supergravity theory (including all hi…
