Exponential decay in the stark effect

LetH=–+V+Fx ₁ withV(x ₁,x ) analytic in the first variable andV(x ₁+ia, x ) bounded and decreasing to zero asx for eacha . Let be an eigenvector of –+V with negative eigenvalue. Among our results we show that forF0, (,e ^–H ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to conventional atomic resonances for which power law decay is the rule.Research supported by NSF Grant No. MCS 78-00101.     

An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of \(F_{\pi }\) and \(M_{\pi }^2\) in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.     

Quark mass dependence of pseudoscalar masses and decay constants on a lattice

Our previous calculations of the sea- and valence-quark mass dependence of the pseudoscalar meson masses and decay constants is repeated on a lattice, which allows for a better determination of the quantities in question. The conclusions are similar as before on the 16⁴ lattice [1]. The two light dynamical quark flavours we simulate have masses in the range m _s /4 < m _u,d < 2m _s /3. The sea quark mass dependence of and is well described by the next-to-leading order (NLO) chiral perturbation theory (ChPT) formulas and clearly shows the presence of chiral logarithms. The valence quark mass dependence requires the presence of NNLO contributions in partially quenched ChPT (PQChPT)--in addition to the NLO terms. The lattice artifacts in these quantities turn out to be small.Received: 19 March 2004, Published online: 24 August 2004     

Quark mass dependence of masses and decay constants of the pseudo-Goldstone bosons in QCD

The dependence of the pseudo-scalar meson masses and decay constants on sea and valence quark masses is compared to next-to-leading order (NLO) chiral perturbation theory (ChPT). The numerical simulations with two light dynamical quark flavors are performed with the Wilson quark lattice action at gauge coupling and hopping parameters on a 16⁴ lattice. lattice artifacts are taken into account by applying chiral perturbation theory for the Wilson lattice action. The values of the relevant combinations of Gasser-Leutwyler constants L ₄, L ₅, L ₆ and L ₈ are estimated.Received: 7 July 2003, Published online: 2 October 2003     

Radiative decays of vector mesons in the chiral bag model

A new model of radiative -meson decays of vector mesons in the chiral bag model is proposed. The quark--meson interaction has the form of a pseudoscalar coupling and is located on the bag surface. The vector meson decay width depends on the quark masses, the -meson decay constant, the radius of the bag, and the free parameter Z², which specifies the disappearance of the bag during the decay. The obtained results for the -and p-decay widths are in satisfactory agreement with the experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 71–76, February, 1988.     

Particle masses,force constants,and Spin(8)

From a number of qualitative conjectures, the constantsm _e ,c, , and a spin(8) gauge field theory, I derive the following particle masses (quark masses are constituent masses) and force constants: up quark mass=312.7542 MeV; down quark mass=312.7542 MeV; proton mass=938.2626 MeV; neutrino masses (all types)=0; muon mass=104.76 MeV; strange quark mass=523 MeV; charmed quark mass=1989 MeV; tauon mass=1877 MeV; bottom quark mass=5631 MeV; top quark mass=129.5 GeV;W ⁺ mass=80.87 GeV;W ^– mass=80.87 GeV;W ₀ mass=99.04 GeV; fine structure constant= 1/137.036082; weak constant times the proton mass squared M _p ² =0.97×10^–5; color constant=0.6286. From the pion mass in addition, I derive the Planck mass (1–1.6)×10¹⁹ GeV, so that the gravitational constant times the proton mass squared GM _p ² (3.6–8.8)×10^–39.     

Isotropic Evolution of a JBD Anisotropic Bianchi Universe

I study the dynamical effects due to the Brans-Dicke scalar -field at the early stages of a supposedly anisotropic Universe expansion in the scalar-tensor cosmology of Jordan-Brans-Dicke. This is done considering the behaviour of the general solutions for the homogeneous model of Bianchi type VII in the vacuum case. I conclude that the Bianchi-VII₀ model shows an isotropic expansion and that its only physical solution is equivalent to a Friedman-Robertson-Walker spacetime whose evolution can, depending on the value of the JBD coupling constant, begin in a singularity and, after expanding (inflating, if > 0), shrink to another, or starting in a non-singular state, collapse to a singularity. I also conclude that the general Bianchi-VII _h (with h 0) models show strong curvature singularities producing a complete collapse of the homogeneity surfaces to 2D-manifolds, to 1D-manifolds or to single points. Our analysis depends crucially on the introduction of the so-called intrinsic time, , as the product of the JBD scalar field times a mean scale factor a ³ = a ₁ a ₂ a ₃, in which the finite-cosmological-time evolution of this universe unfolds into an infinite -range. These universes isotropize from an anisotropic initial state, thence I conclude that they are stable against anisotropic perturbations.     

Resonant coherent transients in a gas in the standing-wave field

Polarization decay in the presence of a standing electromagnetic wave field at a Doppler broadened transition is investigated theoretically and experimentally. It is shown that in the direction opposite to the propagation of an excited pulse the polarization decays at a transition frequency rather than at an exciting field frequency as usual. This permits the use of transients both in studies of relaxation processes and in Doppler-free super-high resolution spectroscopy. A resonant coherent transient has been used in measurements of relaxation decay constants of a dipole moment for collisions in SF₆ (=10.6m). This method has enabled one to resolve reliably the structure of theQ(38) transition (=10.6m) of theF ₁ ⁰ +E ₀=F ₂ ⁰ line of the 0v ₃ band in SF₆ within a Doppler absorption line.     

Electron (muon) decay of a heavy lepton

Expressions are derived for the differential probability for the decay e(). The possibly nonzero mass of and the polarizations of both the decaying lepton and the charged lepton which is produced are all taken into account. A quantitative analysis is carried out for various masses of the neutrino and for various energies of the lepton emitted during the decay.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 97–100, June 1981.     

The role of strange sea quarks in chiral extrapolations on the lattice

Since the strange quark has a light mass of order , fluctuations of sea pairs may play a special role in the low-energy dynamics of QCD by inducing significantly different patterns of chiral symmetry breaking in the chiral limits N _f = 2 (m _u = m _d = 0, m _s physical) and N _f = 3 (m _u = m _d = m _s = 0). This effect of vacuum fluctuations of pairs is related to the violation of the Zweig rule in the scalar sector, described through the two O(p ⁴) low-energy constants L ₄ and L ₆ of the three-flavour strong chiral lagrangian. In the case of significant vacuum fluctuations, three-flavour chiral expansions might exhibit numerical competition between leading- and next-to-leading-order terms according to the chiral counting, and chiral extrapolations should be handled with special care. We investigate the impact of the fluctuations of pairs on chiral extrapolations in the case of lattice simulations with three dynamical flavours in the isospin limit. Information on the size of the vacuum fluctuations can be obtained from the dependence of the masses and decay constants of pions and kaons on the light quark masses. Even in the case of large fluctuations, corrections due to the finite size of spatial dimensions can be kept under control for large enough boxes ( fm).Received: 20 October 2004, Revised: 28 December 2004, Published online: 9 February 2005Laboratoire de Physique Théorique: LPT is an Unité Mixte de Recherche du CNRS et de lUniversité Paris-Sud 11 (UMR 8627).     

Quark-pion coupling constant in a chiral quark model

Incorporating chiral-symmetry to the potential model of quarks with confining potentialU(r)=1/2 (1 +γ°)ar ² with m _q =10 MeV anda=2.273 fm⁻³ that gives a reasonable quark-core contribution to μ _p , 〈r ² 〉 _p ^1/2 andg _A , the quark-pion coupling constant for quarks in a nucleon is estimated.G _qqπ ² /4π obtained between 0.4 and 0.5 is consistent with those extracted from experimental vector meson decay-width ratios by Suzuki and Bhaduri. The nucleon-pion coupling constantG _NNπ ² /4π comes out to be of the order of 13.1 in reasonable agreement with the experimental value.     

Exponential decay of Green's functions for a class of long range Hamiltonians

We consider a class of long range Hamiltonians with diagonal disorder onl ² (Z). For anyergodic potentialV with non-empty essential range, we prove the exponential decay of the Green's functions for energies in the essential range. IfV is independent identically distributed, we obtain the exponential decay of the Green's functions for all coupling constant >0. Moreover the Hamiltonian has only pure point spectrum.     

On the pion decay constant

The pion decay constant fπ$f_{\pi }$ plays a crucial role in many areas of low energy particle physics. Its value may e.g. be deduced from experimental data on leptonic pion decays. Here, we provide comments on several aspects of this evaluation. In particular, we point out that at the present level of experimental accuracy, the value of fπ$f_{\pi }$ is sensitive to the value of the pion mass chosen in its chiral expansion.     

On the leptonic decay of a heavy quarkonium with a Higgs-boson emission

The leptonic () decay of a heavy quark-antiquark bound state T( Q) with a Higgs-boson H emission is investigated. Applying the low-energy theorem to meson-Higgs coupling allows one to estimate the probability of the decay T( Q) → H. Only the simple version of the Standard Model extension containing two-Higgs doublet is considered. The text was submitted by the author in English.     

Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f ₀(980), a ₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η ₈ mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p ⁴) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m _s/ , in terms of the O(p ⁴) CHPT low-energy constant combinations 2L ^r ₈ - L ^r ₅ and 2L ^r ₆ - L ^r ₄. In this way, we give a range for the values of these low-energy counterterms and for 3L ₇ + L ^r ₈, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m _s/ = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Running mass m s at low scale from the heavy-light meson decay constants

It is shown that a 25(20)% difference between the decay constants ( ) and f _D (f _B ) occurs due to large differences in the pole masses of the s and d(u) quarks. The values η _D = /f _D ∼ 1.23(15), recently observed in the CLEO experiment, and η _B = /f _B ∼ 1.20, obtained in unquenched lattice QCD, can be reached only if, in the relativistic Hamiltonian the running mass, m _s at low scale is m _s (∼0.5 GeV) = 170–200 MeV. Our results follow from the analytical expression for the pseudoscalar decay constant f _P based on the path-integral representation of the meson Green’s function. The text was submitted by the authors in English.     

Links between neutrino oscillations,leptogenesis, and proton decay within supersymmetric grand unification

Evidence in favor of supersymmetric grand unification including that based on the observed family multiplet-structure, gauge coupling unification, neutrino oscillations, baryogenesis, and certain intriguing features of quark-lepton masses and mixings is noted. It is argued that attempts to understand (a) the tiny neutrino masses (especially Δm ²(v ₂ – v₃)), (b) the baryon asymmetry of the Universe (which seems to need leptogenesis), and (c) the observed features of fermion masses such as the ratiom _b/m_τ, the smallness ofV _cb and the maximality of seem to select out the route to higher unification based on an effective string-unifiedG(224) =SU(2)_L ×SU(2)_R ×SU(2)^c orSO(10)-symmetry that should be operative in 4D, as opposed to other alternatives. A predictiveSO(10)/G(224)-framework possessing supersymmetry is presented that successfully describes the masses and mixings of all fermions including neutrinos. It also accounts for the observed baryon asymmetry of the Universe by utilizing the process of leptogenesis, which is natural to this framework. It is argued that a conservative upper limit on the proton lifetime within thisSO(10)/G(224)-framework, which is so far most successful, is given by x 10³⁴ years. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Implications of this prediction for the next-generation nucleon decay and neutrino-detector are noted.     

Cosmology with Curvature-Saturated Gravitational Lagrangian R/\sqrt {1 + l^4 R^2 }

We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert Lagrangian _EH = R/16G and a pure cosmological constant for large R with the ansatz _cs = _EH/ , where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by d/dR = 1/16G _eff is G _eff = G , and tends to infinity for large R, in contrast to most other approaches where G _eff 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds ² = a ² [da ²/B(a) – dx ² – dy ² – dz ²] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R ± are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein's theory. In synchronized time, the metric is given by