Instanton induced flavour mixing in the presence of vector mesons

An extended version of the Nambu-Jona-Lasinio model is supplemented with the 't Hooft determinant and bosonized for an arbitrary number of flavours. The resulting effective meson lagrangian is in good agreement with the experimental low-energy mesonic data. The presence of the 't Hooft determinant leads to a flavour mixing of the scalar and pseudoscalar mesons with diagonal flavour content. This instanton induced flavour mixing in the scalar and pseudoscalar channel is noticeably effected by the coupling to the vector and axial-vector meson sector. If the latter is taken into account the η?η′ mixing angle is shifted from ?31° to ?22° in good agreement with the experimental value.     

Meson-gluonium mixing and the glueball candidate⇌i(1,460)

The mixing of the glueball candidate?i(1,460) with η and η′ is studied in a chiral symmetry breaking framework. Using the solutions of anomalous Ward identities for flavourU(3)×U(3), we find that the octet-singlet mixing angle is quite large and that our results are consistent with a large glueball component in?i(1,460) with moderate gluonium mixing in η and η′.     

O(mq/N) effects in the Ward identities approach to the pseudoscalar nonet

Anomalous Ward identities are investigated in the combined chiral and large-N limit of QCD, up to non-leading O(m_q/N) terms, taking into account chiral symmetry breaking effects in the η′ axial vector couplings. The bound θ > 16° for the η - η′ mixing angle is obtaned. Gasser and Leutwyler results on the O(m_q²) corrections to the η mass are used to determine the size of the O(m_q/N) terms, which are found to be reasonably small. Problems with the anomaly predictions for η, η′ → γγ are pointed out. Some aspects of the non-smoothness of the large-N expansion in presence of SU₃ breaking effects are clarified.     

Effective chiral lagrangians with baryons—the mass splitting of the spin 1/2 parity partners

There are two inequivalent spin 1/2 baryon field operators that can be constructed directly out of three quark field operators. These are associated with a pair of parity partners. Their chiral transformation properties yield some unexpected results. In particular.U(1) axial transformations can mix the two operators. With these chiral transformation properties the spin 1/2 baryon parity partners are incorporated in an effective chiral lagrangian together with the spin 0 meson fields. The mass splitting of these parity partners is then found to be related to their coupling to the flavour singlet pseudoscalar, $$M_ - - M_ + \simeq F_\pi g_{\mathop {flavour}\limits_{singlet} N_ - N_ + } $$ The further selection rule, in the exact chiral limit, $$g_{\pi N_ + N_ - } = 0$$ is also found. Using these results, and their extension to the non-chiral limit, the enhancement of the decay ofN _? intoN ₊ η, as opposed toN ₊ π, is elucidated even though it is suppressed by phase space. Two flavours is given principle consideration although three flavours is also briefly discussed.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

Spectral function sum rules for gluonic currents

We determine the masses and the decay amplitudes of the 2⁺⁺, 0^?+ and 0⁺⁺ gluonia in anSU(3) _c Yang-Mills theory. We estimate the so-called topological susceptibility of theU(1) sector. We discuss theSU(3) _F breaking effects to the η′(896) massrelation from current algebra and predict the η′ parameter values.     

L ∞ estimates for the space-homogeneous Boltzmann equation

This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf ₀ ? 0 with (1 + ¦υ¦²)φ₀ εL ¹ and (1 + ¦υ¦)^s f ₀ε L^∞ for somes > 2, then (1 + ¦υ¦^s'f _tεL ^∞ fort>0 and ess_υ,t sup(1 + ¦υ¦)^s'f(υ, t,) < ∞ for anys′ ? s whens ? 5, and anys′ ? s ifs > 5.     

Correction of a misunderstanding about Olbers' paradox

It is sometimes said that, if the universe were not expanding, we all would burn up, (Olbers' paradox). In order to check on this, I have used a solution of Friedmann's equation that seems reasonable, and that predicts a contraction of the universe after it has reached a maximum size. We may then compare the radiation energy density U _n now at age t _n of the universe, with this density (=U ^* ) at a time t ^* during contraction when R(t) takes a value R ^* equal to its present value R _n .We simplify the calculation by choosing 2R _n as maximum of R(t). Then, t _n=(1/2 π?1)R _n/C=6.98 × 10⁹ year for R _n = 1.16× 10²⁸ cm.(The present density would then be ρ_n = 2.4× 10^?29 gram/cm³).We assume the number of galaxies per unit volume = N(t) = η/R(t) ³ with constant η,and we assume a constant average radiative power L per galaxy. Now at t _n we choose N _n L ≈ 10^?31 erg/cm³sec,but our conclusions would be the same for much larger values of this. We split U into three parts: U ₁ is the primordial energy density left over from t ≈ 0.We put U ₁(t _n ) ≈ 6× 10^?13 erg/cm³ corresponding to T ≈ 3°K.U ₂ is the density of the energy flux near the earth emitted by all stars in our own Milky Way. Most of it is the density U _S =L _⊙/4ηr ² c = 4.5 × 10^?5 erg/cm³ in the flux from the sun. Finally, U ₃ is the energy in the radiation emitted by all other galaxies since t ≈ 0, and was going to burn us according to Olbers. Since U ₁ is a function of R(t), we put U ₁(t^*) =U ₁ (t _n ).We shall also assume U ₂ to be unchanged, as it was not the effect of a change of U _s that we were investigating. In calculating U ₃ we shall overestimate it by neglecting the absorption by closer galaxies of some of the light emitted by farther ones.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Dynamical resolution of theU (1) problem in QCD

The nonperturbative and perturbative aspects of theU(1) problem are discussed and linked to the dynamical breakdown of chiral symmetry in QCD. Then aU(1) gap equation is obtained and is approximately saturated with two-gluon intermediate states corresponding to theU(1) anomaly and consistent with η?η′ mixing.     

Study of the ηπ+π− system centrally producedin the reactionpp→p f (ηπ+π−)p s at 300 GeV/c

The reactionpp→p _f (ηπ⁺π^?)p _s where the ηπ⁺π^? system is centrally produced has been studied at 300 GeV/c incident momentum at the CERN Ω spectrometer. The ηπ^± mass spectrum shows a strong δ/a ₀(980) signal having a mass of 984±4 and Γ=95±14 MeV. The ηπ⁺π^? mass spectrum shows η′ andf ₁(1285) signals over little background. A spin-parity analysis of the ηπ⁺π^? system shows evidence for aJ ^PC =1⁺⁺ peak at thef ₁(1285) mass but no evidence for the pseudoscalar states η(1270) andl/η(1440). No evidence is found for the ηππ decay of theE/f ₁(1420) meson for which we set an upper limit BR(E/f ₁(1420)→ηππ)<0.1 at 95% cl.     

Radiative decays and quark content of f 0(980) and φ(1020)

The quark structure of φ(1020) and f ₀(980) is studied on the basis of data on the radiative decays φ(1020) → γπ ⁰, γη, γη′, γ a ₀(980), γ f ₀(980) and f ₀(980) → γγ. The partial widths are calculated under the assumption that all the mesons under consideration are $\bar qq$ states: φ(1020) is a dominantly $s\bar s$ state ( $\eta ' = n\bar nsin\theta + s\bar scos\theta $ component contributes not more than 1%); η, η′, and π ⁰ are standard $q\bar q$ states, $\eta = n\bar ncos\theta - s\bar ssin\theta $ and $\eta ' = n\bar nsin\theta + s\bar scos\theta $ with θ?37°; and f ₀(980) is a e5 meson with the flavor wave function $n\bar ncos\varphi + s\bar ssin\varphi $ . The transition φ → γπ ⁰ specifies the admixture of the $n\bar n$ component in the φ meson: it is on the order of 0.5%. We argue that this order of $n\bar n$ value does not contradict data on the decay φ(1020) → γ a ₀(980). The partial widths calculated for the decays φ → γη, γη? are in reasonable agreement with experimental data. The measured branching-ratio value Br(φ→γf ₀(980))=(3.4±0.4 _?0.5 ^+1.5 ×10^?4) requires 25°≤|?|≤90°. For the decay f ₀(980) → γγ, the agreement with data, Γ(f ₀(980) → γγ)=0.28 _?0.13 ^+0.09 keV, is attained at either ?=85°±8° or ?=?46°±8°. A simultaneous analysis of the decays φ(1020) → γ f ₀(980) and f ₀(980) → γγ favors the solution with the negative mixing angle of ?=?48°±6°, setting f ₀(980) very close to the flavor octet (? _octet=±54.7°).     

Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

A relation between circular 1/2 BPS ’t Hooft operators in 4d N=4{{\mathcal N}=4} SYM and instantonic solutions in 2D Yang-Mills theory (YM₂) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM₂, belonging to representations of the dual group ^L G. This conjecture has been tested in the case G = U(N) =  ^L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and ^L G = SU(N)/Z _N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.     

Isotopieverschiebungskonstanten von Th,U, Pu und Am

The isotope shifts of unperturbed electron configurations have been determined from isotope shift measurements in the spectra of Th, U, Pu, and Am. The screening of the 7s electron charge density at the nucleus by 6d, 7s, and 7p electrons is discussed. It turns out that the same screening factors as for the 6s electron in lighter elements can be used. The screening of the 7s electron charge density at the nucleus by one 5f electron amounts to about 25%: [δT(f ⁿ s)?δT(f ⁿ )]/[δT(f ⁿ }s)?δ(f ^n} )]=0.7₅. The charge density at the nucleus due to the filleds (andp _1/2) shells is considerabely screened by anf electron. The isotope shiftδT(f^n}-1 d ^m +2)?δT(f ⁿ d ^m ) produced by this effect is of the same order of magnitude as the isotope shiftδT(f ⁿ d ^m s)-δT(f ⁿ d ^m ) due to ans electron. The experimental isotope shift constants are found to be:Β C _exp(Th²³⁰–Th²³²)=880±120;Β C _exp(U²³³–U²³⁵)=1000±180;Β C _exp(U²³⁴–U²³⁶)=1070±200;Β C _exp(U²³⁶–U²³⁸)=1080±180;Β C _exp(Pu²³⁸–Pu²⁴⁰)=1200±120;Β C _exp(Pu²³⁹–Pu²⁴¹)=1060±100;Β C _exp(Pu²⁴⁰–Pu242)=900 ±90;Β C _exp(Am²⁴¹–Am²⁴³)=890±50 [10^?3cm^?1]. The ratiosΒ C _exp/C _th are discussed.     

1/N topological expansion for lattice QCD

A U(N_c) gauge theory with a global U(N_f) flavor symmetry is investigated in the limit both N_c and N_f large with the ratio ξ ≡ N_f/N_c fixed.     

Search for a new light gauge boson in π0, η and η′ decays

Upper limits for the production of new light gauge bosons in π⁰, η and η′ decays have been obtained with the Crystal Barrel detector. The kinematically well-constrained reactions p?p → π⁰π⁰ P have been studied, where P ? π ⁰, η, η′ decays through the emission of a single photon recoiling against a missing state X. X can be a long-lived weakly interacting particle or it decays into ???. The resulting branching ratio upper limits (90 % C.L.) are: 6 × 10^?5 for masses M _X of the missing particle X lying between 65 MeV/c² and 125 MeV/c² (π⁰ decay), 6 × 10^?5 for M _X between 200 MeV/c² and 525 MeV/c² (gh decay), and 4 × 10^?5 for M _X between 50 MeV/c² and 925 MeV/c² (η′ decay). The π⁰-decay limit represents an improvement by a factor of 4 to 8 (depending on M _X) when compared to the existing limit, whereas the η and η′ decay limits have been measured for the first time, thereby extending the M _X range from 125 MeV/c² up to 925 MeV/c².     

The decaysK S 0 →γγ andK L 0 →γγ in the chiral approach

We calculate theK _S ^Emphasis>0 →γγ decay within the approach of non-linear realization of chiralS U(3)×S U(3). The branching ratio with respect to theπ ⁺ π ^- channel turns out to be 3.5×10^?6 and therefore similar to the result gotten previously by dispersion relation techniques in a non-chiral model. We also discuss theK _L ⁰ →γγ decay by taking into account new results onη ₁-η ₈ mixing from recent measurements of the η→γγ decay.     

Path integral bosonization of the ‘t Hooft determinant: quasi-classical corrections

The many-fermion Lagrangian which includes the t Hooft six-quark flavor mixing interaction (N_f = 3) and the U_L(3) x U_R(3) chiral symmetric four-quark Nambu-Jona-Lasinio- (NJL-) type interactions is bosonized by the path integral method. The method of the steepest descents is used to derive the effective quark-mesonic Lagrangian with linearized many-fermion vertices. We obtain, additionally to the known lowest order stationary phase result of Reinhardt and Alkofer, the next to leading order (NLO) contribution arising from quantum fluctuations of auxiliary bosonic fields around their stationary phase trajectories (the Gaussian integral contribution). Using the gap equation we construct the effective potential, from which the structure of the vacuum can be settled. For some set of parameters the effective potential has several extrema, that in the case of SU(2)_I x U(1)_Y flavor symmetry can be understood on topological grounds. With increasing strength of the fluctuations the spontaneously broken phase gets unstable and the trivial vacuum is restored. The effective potential reveals furthermore the existence of logarithmic singularities at certain field expectation values, signalizing caustic regions.Received: 22 January 2004, Revised: 2 March 2004, Published online: 5 May 2004A.A. Osipov: On leave from the Joint Institute for Nuclear Research, Laboratory of Nuclear Problems, 141980 Dubna, Moscow Region, Russia