Nuclear pions and the Gottfried and Bjorken sum rules

The thermodynamic potential (TDP) of the boson sector of the Weinberg-Salam model in an external uniform magnetic field at finite temperature and nonzero chemical potential is calculated in one-loop approximation. In the high temperature limit with the use of Mellin summation technique explicit expressions for the thermodynamic potential are obtained to analyze its new minimum, different from the ordinary Higgs one. This new minimum is due to the root singularity in the oneloop expression for the TDP, originating as a consequence of the tachyonic mode in the spectrum of gauge boson in the magnetic field. It is demonstrated that in the high temperature limit the Higgs minimum possesses properties common with the ordinary superconductors and Abelian Higgs model. The influence of the magnetic field on the Higgs minimum is indirect and has a sufficiently complicated character. The presence of the non-zero chemical potential lowers the critical temperature leading to the disappearance of the Higgs minimum.     

Gottfried and Bjorken sum rules: The role of vector diquarks

A quark-diquark model of the nucleon is considered and the value of the Gottfried sum ruleS _G , recently measured by the NMC group and found to differ considerably from the quark parton model expectation,S _G =1/3, is computed allowing for both elastic and inelastic contributions from the diquarks. This approach fails to reproduce the data, unless vector diquark contributions persist at very largeQ ² values, contrary to the usual assumptions. The Bjorken sum rule andSU(6) violations due to the quark-diquark structure of the nucleon are also briefly discussed.     

Modified dispersion relations and sum rules

A systematic treatment of modifications to the usual form of dispersion relations and sum rules is given. The treatment is based on the fact that if a function g(z) has analyticity properties analogous to those of a scattering amplitudef (z), the usual dispersion relation for the productf (z)g(z) holds. After having described the general form of the weight function g(z) we concentrate on cases wheng(z) is large in a pre-chosen region and small elsewhere. Weight functions of this type are useful in practical applications where a weight functiong(z) may enhance a contribution of regions where accurate data are available and suppress those of regions with inaccurate or lacking data.Dedicated to Professor V. Votruba on his sixtieth birthday.     

New sum rules for polarized deep inelastic scattering

Relations between the structure functions g₁ and g₂ of polarized DIS are derived in the leading perturbative QCD approximation, starting with the sum rules for twist-3 parton correlation functions which follow from gauge invariance and the equation of motion of the quark fields. For the first moments they coincide with the approximate relations proposed earlier by Wandzura and Wilczek as well as Bukhvostov, Kuraev and Lipatov.     

Dispersion relations and sum rules for natural optical activity

Dispersion relations and sum rules are derived for the complex rotatory power of an arbitrary linear (nonmagnetic) isotropic medium showing natural optical activity. Both previously known dispersion relations and sum rules, as well as new ones, are obtained. It is shown that the Rosenfeld-Condon dispersion formula is inconsistent with the expected asymptotic behavior at high frequencies. A new dispersion formula based on quantum electrodynamics removes this inconsistency; however, it still requires modification in the lowfrequency limit.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

Radiative corrections to the structure functions and sum rules in polarized dis

The one-loop NLO radiative corrections (RC) to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the unpolarized and different for polarized sum rules, that can be explained as the influence of the finite quark mass effects on NLO QCD corrections. The explicit expression for one-loop NLO QCD contribution to the structure function g ₂ is presented.     

Perturbative QCD analysis of the Bjorken sum rule

We study the polarized Bjorken sum rule at low momentum transfer squared Q ² ≤ 3 GeV² in the twist-two approximation and to the next-to-next-to-leading order accuracy.     

Kramers-Kronig relations and sum rules of negative refractive index media

Negative refractive index media have become a hot topic in physics due to their proposed revolutionary properties, which would have drastic consequences in design of novel optical devices. We show that Kramers-Kronig relations connecting the real and imaginary parts of the complex refractive index of absorbing media are valid even though the real refractive index may take negative value at some spectral range. In addition universal sum rules for linear optical constants of negative index media are also valid. This means that negative refractive index media are not fundamentally different from regular media. Hence, any spectrum measured from negative refractive index media can be analyzed using dispersion relations and sum rules, which have so far provided information on the optical properties of materials.Received: 13 May 2004, Published online: 30 September 2004PACS: 77. Dielectrics, piezoelectrics, and ferroelectrics and their properties - 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)     

New physics sum rules from polarized electron-positron asymmetries on the Z resonance

We propose a strategy to express some of the electroweak parameters characterizing a certain type of new physics beyond the standard model through “new physics sum rules” involving experimentally measureable e⁺e⁻ polarization asymmetries on (near) the Z resonance. In the case of a single E₆-generated new Z′, our sum rules would provide an unambiguous measurement of the mixing angle for |θ_M|⩾0.04.     

Subtracted dispersion relations for in-medium meson correlators in QCD sum rules

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out the importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels for the case of the Fermi gas of nucleons.     

Top-quark pair production via polarized and unpolarized protons in the supersymmetric QCD

The QCD corrections to the top-quark pair production via both polarized and unpolarized gluon fusion in pp collisions are calculated in the minimal supersymmetric model (MSSM). We find that the MSSM QCD corrections can reach 4% and may be observable in future precise experiments. Furthermore, we studied CP violation in the MSSM. Our results show that the CP-violating parameter is sensitive to the masses of SUSY particles (it becomes zero when the c.m. energy is less than twice the masses of both the gluino and the stop quarks) and may reach . Received: 30 September 1998 / Revised version: 21 January 1999 / Published online: 28 May 1999     

Photino mass and selectron production in unpolarized and polarized ee annihilation

Selectron production in unpolarized e⁺e⁻ collisions is reconsidered for supersymmetric theories with massive photinos. Near threshold the cross section is enhanced by a strong s-wave component enabling, in principle, also the determination of the photino mass. Polarized e⁺e⁻ annihilations into selectron and photino pairs would provide not only an independent and direct measurement of the photino mass but also a clean experimental separation of the two selectrons accompanying the left- and right-handed electron.