Narrow Resonance Model Research Articles

Mass calculations of light quarkonium, exotic JPC=0+− hybrid mesons from Gaussian sum rules

We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the H\"older inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.

Applying exclusion likelihoods from LHC searches to extended Higgs sectors

LHC searches for non-standard Higgs bosons decaying into tau lepton pairs constitute a sensitive experimental probe for physics beyond the Standard Model (BSM), such as Supersymmetry (SUSY). Recently, the limits obtained from these searches have been presented by the CMS collaboration in a nearly model-independent fashion - as a narrow resonance model - based on the full 8 TeV dataset. In addition to publishing a 95% C.L. exclusion limit, the full likelihood information for the narrow resonance model has been released. This provides valuable information that can be incorporated into global BSM fits. We present a simple algorithm that maps an arbitrary model with multiple neutral Higgs bosons onto the narrow resonance model and derives the corresponding value for the exclusion likelihood from the CMS search. This procedure has been implemented into the public computer code HiggsBounds (version 4.2.0 and higher). We validate our implementation by cross-checking against the official CMS exclusion contours in three Higgs benchmark scenarios in the Minimal Supersymmetric Standard Model (MSSM), and find very good agreement. Going beyond validation, we discuss the combined constraints of the tau tau search and the rate measurements of the SM-like Higgs at 125 GeV in a recently proposed MSSM benchmark scenario, where the lightest Higgs boson obtains SM-like couplings independently of the decoupling of the heavier Higgs states. Technical details for how to access the likelihood information within HiggsBounds are given in the appendix. The program is available at http://higgsbounds.hepforge.org.

A gaussian sum-rule analysis of scalar glueballs

Although marginally more complicated than the traditional Laplace sum-rules, gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next-lowest weighted sum-rules. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance model does not provide an adequate description of the hadronic spectral function. Consequently, we consider a wide variety of phenomenological models which distribute resonance strength over a broad region — some of which lead to excellent agreement between the theoretical prediction and phenomenological models. Including QCD uncertainties, our results indicate that the hadronic contributions to the spectral function stem from a pair of resonances with masses in the range 0.8–1.6 GeV, with the lighter of the two potentially having a large width.

New narrow-resonance models with nonlinear Regge trajectories

New crossing-symmetric narrow-resonance models with nonlinear Regge trajectories are presented. The $N$-point amplitudes have cyclic crossing symmetry and are meromorphic in all channel invariants. The amplitudes are shown to factorize on the leading trajectory.

A narrow-resonance model for a two-current two-particle amplitude with gauge invariance and scaling

The four-point function of two off-shell currents and two on-shell scalar fields is analysed. The only singularities considered are simple poles lying on linear trajectories. The behaviour for high-current masses and high energies corresponds to a scaling appropriate for a canonical light-cone singularity. The four-point function satisfies the Ward identity for one of the currents and is thus gauge invariant. General functions satisfying these requirements are constructed. It is shown that gauge invariance in no way conflicts with the strong light-cone dominance (duality) and consequently Drell-Yan-West-type relations can be easily incorporated.

Constraint on the cross sectionσ(e+e−→hadrons)from the asymptotic behavior in the spacelike region of the hadronic vacuum polarization

A condition that the absorptive part of the hadronic vacuum polarization must satisfy in order to be consistent with the predictions of asymptotically free field theories in the spacelike region is derived. This condition allows for asymptotic oscillations of the absorptive part, but suitable averages must scale. Applications of the same techniques to the phase representation and to narrow-resonance models are presented.

Light cone and mass shells

We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like γ ∗ + N → π + N .

Review of Recent Work on Narrow Resonance Models

We review recent work on narrow resonance models. We take the point of view that such models play a role similar to that of the Lee model in quantum field theory, and that they cannot therefore be directly compared with experiment. Examples of various aspects of these models, including general self-consistency and the construction of amplitudes with external currents are reviewed, and the related diseases are listed. A critical discussion of narrow resonance phenomenology is given. Associated questions which seem to us suitable for further study are discussed and summarized.

On the possible elimination of unphysical states in meson bootstrap models

It is shown that the imposition of Poincare invariance on the poles in all channels by free-particle equations of motion can yield anU6⊗U6⊗O3 particle spectrum in narrow-resonance dual models characterized by anU6,6 spectrum of trajectories and amplitudes that factorize into a spin-internal-symmetry term and an orbital term. It is further shown that one can constructN-meson amplitudes with the correct tree structure that factorize on each tree into (N−3) collinearU6⊗O2 covariant vertices. This involves the introduction of an interpolating mass function; the restrictions on such a function are briefly discussed; some concrete examples are given.

Duality and crossing symmetry of the narrow resonance model

In the narrow resonance approximation, conditions of duality and crossing symmetry are derived using the finite energy sum rule for an amplitude which is completely determined as a function of two complex variables by its meromorphic part in one of these variables. As an example, the one term Veneziano amplitude is discussed.

Level structure of dual-resonance models

In this paper the level structure of narrow-resonance models with duality is considered. We shall use to this purpose the multiparticle dual amplitudes recently proposed by several authors and shall study the structure of the residue of each pole in what concerns its factorizability. We find that for each energy eigenvalueE n =√s n the residue does indeed factorize in a finite number of terms (number of degenerate levels) and that this number increases withn like exp [cEn]. The physical interpretation of this wild increase is found in the essential many body nature of models consistent with duality. The appearence of states with imaginary coupling follows easily from the covariant, four-dimentional approach that we have taken and that insures absence of kinematical singularities. It is nevertheless found that a cancellation mechanism analogous to the one existing in Q.E.D. (Ward identities) occurs here too. Although the problem of a systematic cancellation of all ghosts in a realistic case has not been solved, we see that the leading and most troublesome ghosts are indeed eliminated in this way.

Detailed dynamics of narrow resonance models for ππ scattering: Dennis Sivers and Joel Yellin. Lawrence Radiation Laboratory, University of California, Berkeley, California

Detailed dynamics of narrow resonance models for ππ scattering: Dennis Sivers and Joel Yellin. Lawrence Radiation Laboratory, University of California, Berkeley, California

Detailed dynamics of narrow resonance models for ππ scattering

We discuss the dynamical behavior of narrow resonance models for ππ scattering in the framework of what we call atonous duality, by which we mean that the pole locations and residues in a particular channel completely specify the narrow resonance amplitude as a Mittag-Leffler expansion containing no entire functions. We operate under the following assumptions: (i) Crossing symmetry, isospin conservation, and Bose statistics hold. (ii) The only singularities of the amplitude are simple poles at locations defined by a + bξ(≡ α( ξ)) = 0, 1, 2,… where ξ is a Mandelstam variable. (iii) There are no I = 2 poles. (iv) The pole at s = ξ has a residue which is a polynomial in t of order ⩽α(ξ). (v) Atonous duality holds. (vi) All partial widths are positive. Under these assumptions we find that the I = 1 amplitude A 1 t ( ν, t) has Regge behavior for ν → ∞ at fixed t, while A 2 t ( ν, t) has pure fixed pole behavior. There are no Regge cuts. Furthermore, we find it impossible to formulate partial wave dispersion relations for these models. As an example of such a model we discuss the one term Veneziano ansatz for ππ scattering.

Narrow-Resonance Model with Regge Behavior forππScattering

A model for $\ensuremath{\pi}\ensuremath{\pi}$ scattering of the type recently proposed by Veneziano is discussed. It is a narrow-resonance model with exchange-degenerate, linearly rising trajectories, which obeys crossing symmetry and has the proper Regge behavior in all channels. The general form for the amplitude is discussed, and phase shifts, resonance widths, and high-energy diffraction are calculated, assuming the amplitude takes on the simplest of the possible forms. The condition that the partial widths be positive is extensively discussed. The model is also considered as a testing ground for other theories based on the same assumptions, such as finite-energy sum rules and the Schmid-circle hypothesis.