Strong isospin violation andη−π mixing in |ΔS|=1 weak transition

We consider the effects ofη−π mixing on the violation of the |ΔI|=1/2 rule in |ΔS|=1 weak transitions. The processes considered are theK→2π,K→3π, Λ, Ξ and Λ hyperon decays.     

Current-voltage characteristics for a Peierls-conducting point contact

Current-voltage (J-V) and differential-conductivity-voltage ( dJ/dV-V) characteristics are analytically calculated at zero temperature for a point contact consisting of: two Peierls conductors P ( = 1, 2) separated by an insulator (I). Here P is a conductor with charge density wave (CDW). The J-V and dJ/dV-V characteristics depend on the CDW phases ( = 1, 2) in the mean field approximation. To calculate them analytically we assumed, = ≡Δ where ( = 1, 2) are the energy gaps of P ( = 1, 2). The current J has a discontinuous jump at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The differential conductivity dJ/dV has a singularity at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The relation J(V,ϕ ₁,ϕ ₂) = - J(- V,ϕ ₁ + π,ϕ ₂ + π) is obtained. Received 4 July 2001 and Received in final form 13 September 2001     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

Optical anisotropy in nonpolar (101̄0)-oriented m-plane GaN/AlGaN quantum wells and comparison with experiment

Optical anisotropy in nonpolar ()-oriented m-plane GaN/InGaN quantum wells was investigated using the multi-band effective-mass theory. The optical matrix element near the Γ point (k_||=0) is shown to increase with increasing polarization angle ϕ’. The anisotropy calculated at the Γ point (k_||=0) is nearly 1 and it rapidly decreases with increasing in-plane wave vector. The reduction of the anisotropy at a large k_|| is attributed to the fact that the state of the first subband is equally mixed of |X〉 and |Y〉 at a large k_||. The photoluminescence intensity increases with ϕ’, becomes a maximum at ϕ’=π/2, and decreases again when ϕ’ further increases. The theoretical result is found to be in good agreement with the experimental results. PACS 85.60.Bt; 85.30.De; 85.30.Vw; 78.20.Bh     

Correlations of polarizations and entangled states in the two-photon system

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π⁰ → 2γ, η → 2γ, K _L ⁰ → 2γ, K _S ⁰ → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.     

PHENIX study of dihadron correlation in Au+Au collision at ?{sNN } \sqrt {s_{NN} } = 200 GeV: jet quenching and medium response

We provide a detailed survey study of dihadron azimuthal angle (Δϕ) correlations in a broad range of transverse momentum (0.4 < p _T < 10 GeV/c) and centrality (0–92%) in Au+Au collisions at 149-2 = 200 GeV. The evolution of the jet shape and yield with p _T seems to suggest two distinct components at the away-side pairs: a suppressed jet fragmentation component around Δϕ ∼ π, and a medium-induced components around |Δϕ − π| ∼ 1.1. The former dominates p _T > 5 GeV/c and the later dominates at p _T < 4 GeV/c.     

Once more about gauge invariance in <Emphasis Type="Italic">ϕ</Emphasis> → <Emphasis Type="Italic">γπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript>

It is argued that the realization of gauge invariance condition as a consequent of cancellation between the ϕ → γf ₀ → γπ ⁰ π ⁰ resonance contribution and the ϕ → γπ ⁰ π ⁰ background one, suggested by A.V. Anisovich et al., Yad. Fiz. 68, 1614 (2005), is misleading. The text was submitted by the author in English.     

Measurement of pionium lifetime with the Dirac spectrometer

Pionium ( π ⁺ π ^- bound state) lifetime is measured with improved precision with respect to earlier work, and the ππ s-wave scattering length difference between I = 0 and I = 2 amplitudes | a ₀ - a ₂| is determined to 5% precision.     

Measurement of ω/? → e+e? in proton + proton collisions at ?s \sqrt s = 200 GeV at RHIC-PHENIX

The PHENIX experiment at RHIC has measured ω and ϕ meson production using di-electron decay mode over a psude-rapidity range of |η| ≤ 0.35 and a transverse momentum range of 0 < p _T < 5 GeV/c in proton + proton collisions at $ \sqrt s $ \sqrt s = 200 GeV. The spectra of production cross section as a function of p _T for ω and ϕ → e ⁺ e ⁻ show good agreement with other hadornic decay channels ω → π ⁰ γ, ω ⁰ π ⁺ π ⁻ and ϕ → K ⁺ K ⁻, respectively.     

Unambiguous detection of monopoles

Summary The fission of a vortex line along the trajectory of a monopole in a superconducting medium is an unambiguous signature of a monopole. The numbern of the (stable) daughter vortices determines the monopole strengthg withg=2nφ/4π where ϕ₀=2.07·10⁻⁷ G cm².

---

Riassunto La fissione di una linea di vortice lungo la traiettoria di un monopolo in un mezzo superconduttore è indice sicuro della segnatura di un monopolo. Il numeron di vortici figli (stabili) determina la forza del monopolog cong=nϕ₀/4π, dove ϕ₀=2.07·10⁻⁷ G cm².

     

Zeros of the Jones Polynomial for Multiple Crossing-Twisted Links

Let D be a general connected reduced alternating link diagram, C be the set of crossings of D and C′ be the nonempty subset of C. In this paper we first define a multiple crossing-twisted link family {D ⁿ (C′)|n=1,2,…} based on D and C′, which produces (2,2n+1)-torus knot family, the link family A _n defined in Chang and Shrock (Physica A 301:196–218, 2001) and the pretzel link family P(n,n,n) as special cases. Then by applying Beraha-Kahane-Weiss’s Theorem we prove that limits of zeros of Jones polynomials of {D ⁿ (C′)|n=1,2,…} are the unit circle |z|=1 (It is independent of the selections of D and C′) and several isolated limits, which can be determined by computing flow polynomials of subgraphs of G corresponding to D. Furthermore, we use the method of Brown and Hickman (Discrete Math. 242:17–30, 2002) to prove that, for any ε>0, all zeros of Jones polynomial of the link D ⁿ (C) lie inside the circle |z|=1+ε, provided that n is large enough. Our results extend results of F.Y. Wu, J. Wang, S.-C. Chang, R. Shrock and the present authors and refine partial result of A. Champanerkar and L. Kofman.     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

Tails in harnesses

We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical models of random interfaces. Their components are rea random variablesa _s ^t , wheres ∈ Z ^d andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z _d ⁺ define Δ_σ a′ _s as follows. If σ=(0,...,0), σ=(0,...,0), Δ_σ a _s ^t =a _s ^t . Then by induction, wheree _i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δ_σ a _s ^t diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δ_σ a _s ^t diverges; if P-decay(v)>(d+2)/(d+|σ|), Δ_σ a _s ^t , converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|^r) is finite. Let E-decay(v)>0. Whenever Δ_σ a _s ^t converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima _s ^t )=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δ_σ a _s ^t )=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δ_σ a _s ^t )=E-decay(ν).     

New aspects of B → ππ, πK and their implications for rare decays

We analyze the B → ππ, πK modes in the light of the most recent B-factory data, and obtain the following new results: (i) the modes prefer γ = (74±6)°, which - together with |V_ub/V_cb| - allows us to determine the "true" unitarity triangle and to search for CP-violating new-physics contributions to B⁰_d- mixing; (ii) the B → πK puzzle reflected in particular by the low experimental value of the ratio R_n of the neutral B → πK rates persists and still favors new physics in the electroweak penguin sector with a new CP-violating phase ϕ ~ –90°, although now also ϕ ~ +90° can bring us rather close to the data; (iii) the mixing-induced CP asymmetry is a sensitive probe of the sign of this phase, and would currently favor ϕ ~ +90°, as well as the direct CP asymmetry of , which suffers, however, from large hadronic uncertainties; (iv) we investigate the sensitivity of our B → πK analysis to large non-factorizable SU(3)-breaking effects and find that their impact is surprisingly small so that it is indeed exciting to speculate on new physics; (v) assuming that new physics enters through Z⁰ penguins, we study the interplay between B → πK and rare B, K decays and point out that the most recent B-factory constraints for the latter have interesting implications, bringing us to a few scenarios for the future evolution of the data, where also the mixing-induced CP violation in plays a prominent r?le.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Progress in pion-decay channelling: Refractory bcc metals at high and low temperatures

By means of π⁺/μ⁺ channelling, positive pions (π⁺) implanted intoTa, Mo, andW are investigated up to high temperatures. A striking observation is that the channelling effect disappears in a rather narrow temperature interval centred at 0.26 (Ta) to 0.51 (W) of the melting temperature. From studies of π⁺ trapping by oxygen atoms inTa estimates for the low-temperature π⁺ diffusivity inTa [D _π(23K)=1.4·10^−10±0.3 m²s⁻¹,D _π(47K)=5.7·10^−10±0.3 m²s⁻¹] as well as for the binding enthalpy of π⁺ to 0 atoms (H _B=7·10⁻² eV) have been obtained. The diffusion data are in reasonable agreement with the theory of phonon-assisted tunnelling.     

On the Poisson Limit Theorems of Sinai and Major

Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in the domain Π _R (f) between the curves r=(R+c ₁/R)f(ϕ) and r=(R+c ₂/R)f(ϕ), where c ₁<c ₂ are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ _L on the interval [a ₁ L,a ₂ L], Sinai showed that the distribution of ξ under P×μ _L converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ _L converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending the class of P and strengthening the statement of Sinai. Received: 15 June 1999 / Accepted: 11 February 2000     

CP-violation in B → π+π- and the unitarity triangle

We analyze the extraction of weak phases from CP-violation in B → π⁺π^- decays. We propose to determine the unitarity triangle by combining the information on mixing-induced CP-violation in B → π⁺π^-, S, with the precision observable sin2β obtained from the CP-asymmetry in B → ψK_S. It is then possible to write down exact analytical expressions for and as simple functions of the observables S and sin2β and of the penguin parameters r and ϕ. As an application clean lower bounds on and can be derived as functions of S and sin2β, essentially without hadronic uncertainty. Computing r and ϕ within QCD factorization yields precise determinations of and since the dependence on r and ϕ is rather weak. It is emphasized that the sensitivity to the phase ϕ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter C of direct CP-violation in B → π⁺π^-. Predictions and uncertainties for r and ϕ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in 1/m_b and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed. Received: 16 April 2005, Revised: 6 August 2005, Published online: 21 November 2005 PACS: 11.30.Er, 12.15.Hh, 13.25.Hw     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000