Timelike Momentum Research Articles

Form factors of pions, kaons & protons at the highest timelike momentum transfers & first measurements of hyperons

Electromagnetic form factors of hadrons for timelike momentum transfers can be measured by particle-antiparticle annihilation into hadron-antihadron pairs. We have made the world’s first high precision measurements of timelike form factors of π and K mesons, and ground states of the baryons, protons, and the hyperons Λ0 , Σ0 , Σ+ , Ξ0 , Ξ– , Ω– at the high momentum transfers of 14.2 and 17.4 GeV2 . Limitations of perturbative QCD are revealed, and evidence is presented for the effects of diquark correlations in Λ0 and Σ0 .

First Measurements of Form Factors of Pion, Kaon, Proton, and Hyperons for the Highest Timelike Momentum Transfers

Results of recent precision measurements of the electromagnetic form factors of the pion, kaon, proton, and the hyperons, Λ0, Σ0, Σ+, Ξ−, Ξ0, Ω−, at large timelike momentum transfers are presented. Evidence is found for diquark correlations in Λ0, Σ0 hyperons.

First measurements of timelike form factors of the hyperons, [formula omitted], [formula omitted], [formula omitted], [formula omitted], [formula omitted], and [formula omitted], and evidence of diquark correlations

Using 805 pb−1 of e+e− annihilation data taken with the CLEO-c detector at ψ(3770), s=3770 MeV, we report the first measurements of the electromagnetic form factors of the Λ0, Σ0, Σ+, Ξ0, Ξ−, and Ω− hyperons for the large timelike momentum transfer of |Q2|=14.2 GeV2. The form factors for the different hyperons are found to vary by nearly a factor two. It is found that |GM(Λ0)|=1.66(24)×|GM(Σ0)|. The Λ0 and Σ0 hyperons have the same uds quark content, but differ in their isospin, and therefore the spin of the ud quark pair. It is suggested that the spatial correlation implied by the singlet spin–isospin configuration in the Λ0 is an example of strong diquark correlations in the Λ0, as anticipated by Jaffe and Wilczek. Improved measurements of the branching fractions of ψ(2S)→pp¯ and hyperon–antihyperon pairs are also reported.

First measurement of the electromagnetic form factor of the neutral kaon at a large momentum transfer and the effect of [formula omitted] breaking

At large momentum transfers the photon interacts with the charges and spins of the constituent partons in a hadron. It is expected that the neutral kaon can acquire finite electromagnetic form factors because its wave function is affected by the order of magnitude difference between the mass of the strange quark and that of the down quark, or flavor SU(3) breaking. We report on the first measurement of the form factor of neutral kaons at the large timelike momentum transfer of |Q2|=17.4 GeV2 by measuring the cross section for e+e−→KSKL at s=4.17 GeV using CLEO-c data with an integrated luminosity of 586 pb−1. We obtain FKSKL(17.4 GeV2)=5.3×10−3, with a 90% C.L. interval of (2.9–8.2)×10−3. This is nearly an order of magnitude smaller than FK+K−(17.4 GeV2)=(44±1)×10−3, and indicates that the effect of SU(3) breaking is small. In turn, this makes it unlikely that the recently observed strong violation of the pQCD prediction, Fπ+π−(|Q2|)/FK+K−(|Q2|)=fπ2/fK2, which is based on the assumption of similar wave functions for the pions and kaons, can be attributed to SU(3) breaking alone.

Review of recent measurements of meson and hyperon form factors

A review of recent precision measurements of the electromagnetic form factors of the mesons, pion and kaon, and the hyperons, $\Lambda^0$, $\Sigma^0$, $\Sigma^+$, $\Xi^-$, $\Xi^0$, $\Omega^-$, at large timelike momentum transfers is presented. Evidence is found for diquark correlations in $\Lambda^0$, $\Sigma^0$ hyperons.

Perturbation theory in (2,2) signature

We identify a natural analytic continuation in four dimensions from Minkowski signature to a signature with two timelike momentum components. For two-, three-, and four-point diagrams whose external momenta define a scattering plane, this continuation can be implemented as a contour deformation that leaves dependence on the momenta unchanged. For arbitrary ultraviolet-finite scalar diagrams it is possible to do two integrals per loop in terms of simple poles in the new signature. This results in a representation of any such diagram as a sum of terms, each with two remaining integrals per loop.

Electromagnetic Structure of the Proton, Pion, and Kaon by High-Precision Form Factor Measurements at Large Timelike Momentum Transfers

The electromagnetic structure of the lightest hadrons, proton, pion, and kaon is studied by high-precision measurements of their form factors for the highest timelike momentum transfers of |Q2|=s=14.2 and 17.4 GeV2. Data taken with the CLEO-c detector at sqrt[s]=3.772 and 4.170 GeV, with integrated luminosities of 805 and 586 pb(-1), respectively, have been used to study e+ e- annihilations into π+ π-, K+ K-, and pp. The dimensional counting rule prediction that at large Q2 the quantity Q2F(Q2) for pseudoscalar mesons is nearly constant, and should vary only weakly as the strong coupling constant αS(Q2) is confirmed for both pions and kaons. However, the measurements are in strong quantitative disagreement with the predictions of the existing quantum chromodynamics-based models. For protons, it is found that the timelike form factors continue to remain nearly twice as large as the corresponding spacelike form factors measured in electron elastic scattering, in significant violation of the expectation of their equality at large Q2. Further, in contrast to pions and kaons, a significant difference is observed between the values of the corresponding quantity |Q4|G(M)(|Q2|)/μ(p) for protons at |Q2|=14.2 and 17.4 GeV2. The results suggest the constancy of |Q2|G(M)(|Q2|)/μ(p), instead, at these large |Q2|.

Analytic Structure of the Landau-Gauge Gluon Propagator

The analytic structure of the nonperturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.

RADIATIVE DECAYS OF EQUAL MASS VECTOR MESONS IN A BETHE–SALPETER EQUATION FRAMEWORK

In this work, we have employed Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA) to study radiative decays of light vector mesons through the process: h→h'γ, taking h and h' as equal mass light vector and pseudoscalar mesons, respectively. The decay widths calculated for these processes are in reasonable agreement with data. The motivation for this work was our intention to resolve the problems involved in calculations of triangle quark-loop diagrams which appear in processes such as radiative meson decays, meson form factors, strong decays of mesons, etc., in BSE under CIA, which give rise to complexities in amplitudes (as pointed out earlier in Ref. 1) due to the presence of the time-like momentum components in Gaussian factors associated with the vertex functions of the participating hadrons. In this work we try to highlight this problem and then demonstrate a mathematical procedure which might lead to calculations of such processes in BSE under CIA.

Formula omitted] of the muon and Δ α re-evaluated

We briefly review the Standard Model prediction of g − 2 of the muon and confront it with the formidably accurate measurement from BNL. The focus is on recent improvements of the hadronic vacuum polarisation contributions. We also calculate the running QED coupling at space- and time-like momentum transfer. Its value at the scale of the Z boson mass, α ( M Z 2 ) , is an important ingredient in electroweak precision fits and its prediction is improved considerably.

Factorization of boosted multijet processes for threshold resummation

Explicit applications of factorization theorems for processes at hadron colliders near the hadronic end point have largely focused on simple final states with either no jets (e.g., Drell-Yan) or one inclusive jet (e.g., deep-inelastic scattering and prompt photon production). Factorization for the former type of process gives rise to a soft function that depends on timelike momenta, whereas the soft function for the latter type depends on null momenta. We derive in soft-collinear effective theory a factorization theorem that allows for an arbitrary number of jets, where the jets are defined with respect to a jet algorithm, together with any number of nonstrongly interacting particles. We find the soft function in general depends on the null components of the soft momenta inside the jets and on a timelike component of the soft momentum outside of the jets. This generalizes and interpolates between the soft functions for the cases of no jets and one inclusive jet. We verify consistency of our factorization theorem to $\mathcal{O}({\ensuremath{\alpha}}_{s})$ for any number of jets. While in this paper we demonstrate consistency only near the hadronic end point, we keep the kinematics general enough (in particular allowing for nonzero boost) to allow for an extension to partonic threshold resummation away from the hadronic end point.

Electromagnetic form factors of nucleons with QCD constraints: Systematic study of space- and time-like regions

Elastic electromagnetic form factors of nucleons are investigated for both the time-like and the space-like momenta by using the unsubtracted dispersion relation with QCD constraints. It is shown that the calculated form factors reproduce the experimental data reasonably well; they agree with recent experimental data for the neutron magnetic form factors for the space-like data obtained by the CLAS Collaboration and are compatible with the ratio of the electric and magnetic form factors for the time-like momentum obtained by the BABAR Collaboration.

Superfluid response and the neutrino emissivity of baryon matter: Fermi-liquid effects

The linear response of a nonrelativistic superfluid baryon system on an external weak field is investigated while taking into account the Fermi-liquid interactions. We generalize the theory developed by Leggett for a superfluid Fermi-liquid at finite temperature to the case of time-like momentum transfer typical of the problem of neutrino emission from neutron stars. A space-like kinematics is also analyzed for completeness and compared with known results. We use the obtained response functions to derive the neutrino energy losses caused by recombination of broken pairs in the electrically neutral superfluid baryon matter. We find that the dominant neutrino radiation occurs through the axial-vector neutral currents. The emissivity is found to be of the same order as in the BCS approximation, but the details of its temperature dependence are modified by the Fermi-liquid interactions. The role of electromagnetic correlations in the pairing case of protons interacting with the electron background is discussed in the conclusion.

Renormalization-group improved prediction for Higgs production at hadron colliders

We use renormalization-group methods in effective field theory to improve the theoretical prediction for the cross section for Higgs-boson production at hadron colliders. In addition to soft-gluon resummation at N3LL, we also resum enhanced contributions of the form (C A π α s ) n , which arise in the analytic continuation of the gluon form factor to time-like momentum transfer. This resummation is achieved by evaluating the matching corrections arising at the Higgs-boson mass scale at a time-like renormalization point μ 2<0, followed by renormalization-group evolution to μ 2>0. We match our resummed result to NNLO fixed-order perturbation theory and give numerical predictions for the total production cross section as a function of the Higgs-boson mass. Resummation effects are significant even at NNLO, where our improved predictions for the cross sections at the Tevatron and the LHC exceed the fixed-order predictions by about 13% and 8%, respectively, for m H =120 GeV. We also discuss the application of our technique to other time-like processes such as Drell–Yan production, e + e −→hadrons, and hadronic decays of the Higgs boson.

BCS approximation to the effective vector vertex of superfluid fermions

We examine the effective interaction of nonrelativistic fermions with an external vector field in superfluid systems. In contrast to the complicated vertex equation, usually used in this case, we apply the approach that does not employ an explicit form of the pairing interaction. This allows us to obtain a simple analytic expression for the vertex function only in terms of the order parameter and other macroscopic parameters of the system. We use this effective vertex to analyze the linear response function of the superfluid medium at finite temperatures. At the time-like momentum transfer, the imaginary part of the response function is found to be proportional to ${V}_{F}^{4}$, i.e., the energy losses through vector currents are strongly suppressed. As an application, we calculate the neutrino energy losses through neutral weak currents caused by the pair recombination in the superfluid neutron matter at temperatures lower than the critical one for the ${}^{1}{S}_{0}$ pairing. This approach confirms a strong suppression of the neutrino energy losses as predicted in L. B. Leinson and A. P\'erez [Phys. Lett. B638, 114 (2006)].

Implications of Analyticity to the Solution of Schwinger-Dyson Equations in Minkowski Space

We discuss some recent developments in nonperturbative studies of quantum field theory (QFT) using the Schwinger-Dyson equations formulated directly in Minkowski space. We begin with the introduction of essential ideas of the integral representation in QFT and a discussion of the renormalization in this approach. The technique based on the integral representation of Green’s functions is exploited to solve Schwinger-Dyson equations in several models of quantum field theory, e.g., in scalar models and in strong coupling QED3+1 in the quenched and in the unquenched approximation. The phenomenon of dynamical chiral symmetry breaking in regularized theory is touched. In QCD, the analyticity of the gluon propagator on the complex momentum square plane is exploited to continue some recent lattice data to the timelike momentum axis. We find a contribution to the non-positive absorptive part in the Landau-gauge gluon propagator which is in agreement with some other new recent analyses.

Precision Measurements of the Timelike Electromagnetic Form Factors of Pion, Kaon, and Proton

Using 20.7 pb(-1) of e(+)e(-) annihilation data taken at sq.rt(r) = 3.671 GeV with the CLEO-c detector, precision measurements of the electromagnetic form factors of the charged pion, charged kaon, and proton have been made for timelike momentum transfer of |Q(2)| = 13.48 GeV(2) by the reaction e(+)e(-) --> h(+)h(-). The measurements are the first ever with identified pions and kaons of |Q(2)| > 4 GeV(2), with the results F(13.48 GeV(2)) = 0.075 +/- 0.008(stat) +/- 0.005(syst) and F(K)(13.48 GeV(2)) = 0.063 +/- 0.004(stat) +/- 0.001(syst). The result for the proton, assuming G(p)(E) = G(p)(M), is G(p)(M)(13.48 GeV(2)) = 0.014 +/- 0.002(stat) +/- 0.001(syst), which is in agreement with earlier results.

Quantum Light-Front Wave Function in a Scalar Yukawa Model

The valence component of the light-front wave function of a quantum of a scalar field is studied within a bosonic model. The light-front time projection of the inhomogeneous Bethe-Salpeter equation for the vertex function in the covariant ladder approximation is given. The valence wave function and distribution are obtained from the numerical solution of the light-front equation for the vertex with different values of the time-like off-shell momentum carried by the quantum.

Analytic properties of the Landau gauge gluon and quark propagators

We explore the analytic structure of the gluon and quark propagators of Landau gauge QCD from numerical solutions of the coupled system of renormalized Dyson-Schwinger equations and from fits to lattice data. We find sizable negative norm contributions in the transverse gluon propagator indicating the absence of the transverse gluon from the physical spectrum. A simple analytic structure for the gluon propagator is proposed. For the quark propagator we find evidence for a masslike singularity on the real timelike momentum axis, with a mass of 350 to 500 MeV. Within the Green's function approach that is employed, we identify a crucial term in the quark-gluon vertex that leads to a positive definite Schwinger function for the quark propagator.

Masses and couplings of vector mesonsfrom the pion electromagnetic, weak, and $\pi\gamma$ transition form factors

We analyse the pion electromagnetic, charged-current, and $\pi\gamma$ transition form factors at timelike momentum transfers $q$, $q^2=s\le 1.4$ GeV$^2$, using a dispersion approach. We discuss in detail the propagator matrix of the photon-vector-meson system and define certain reduced amplitudes, or vertex functions, describing the coupling of this system to final states. We then apply the derived analytic expressions to the analysis of the recent $e^+e^-\to \pi^+\pi^-$, $\tau^-\to \pi^-\pi^0\nu_\tau$, and $e^+e^-\to \pi^0\gamma$ data. We find the reduced amplitudes for the coupling of the photon and vector mesons to two pseudoscalars to be constant, independent of $s$, in the range considered, indicating a "freezing" of the amplitudes for $s\le 1$ GeV. The fit to the form factor data leads to the following values of the Breit-Wigner resonance masses m_{\rho^-}=775.3\pm 0.8 MeV, m_{\rho^0}=773.7\pm 0.6 MeV and m_\omega=782.43\pm 0.05 MeV, where the errors are only statistical.