Hadron masses and the sigma commutator in light of chiral perturbation theory

We analyze carefully the impact of non-analytic chiral corrections to the mass spectrum of the pseudoscalar meson octet J^P = 0^? and the baryon octet $\text{J}{}^{\mathrm{<mtext>P</mtext>}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$. We find that the quark mass ratios must lie in the range $\text{21 ≤}\text{m}{}_{\mathrm{<mtext>s</mtext>}}\text{m}\text{?}\text{≤ 32}$ and $\text{1.6 ≤}\text{m}{}_{\mathrm{<mtext>d</mtext>}}\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≤ 2.2}$. We also calculate the analogous corrections to the pion-nucleon sigma commutator σ_πN. It turns out that the value σ_πN = 60 MeV is not compatible with the structure of the meson and baryon spectrum, unless the nucleon mass is smaller than 600 MeV in the chiral limit m_u = m_d = m_s = 0.     

Phenomenological SU(1, 1) supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and m_W are determined dynamically to be exp [-O(1)/α] × m_P. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with . The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and $\text{A =}\text{3}\text{2}$, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}$ in these models where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: $\text{m}{}_{\mathrm{<mtext>f</mtext>}}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{O}\text{(}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{)}{}^{\mathrm{\lambda >0}}$? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < m_t < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.     

No-scale supersymmetric GUTs

We construct locally supersymmetric GUTs in which radiative corrections determine all the mass scales which are hierarchically smaller than the Planck mass: $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{=}\text{O}\text{(m}{}_{\mathrm{<mtext>W</mtext>}}\text{) =}\text{exp}\text{(}\text{?}\text{O}\text{(1)}\text{α}{}_{\mathrm{<mtext>t</mtext>}}\text{)m}{}_{\mathrm{<mtext>p</mtext>}}$, etc. Such no-scale GUTs are based on a hidden sector with a flat potential guaranteed by SU(1, 1) conformal invariance. This is extended to include observable chiral fields in an SU(n, 1)/SU(n) × U(1) structure reminiscent of N ? 5 extended supergravity theories. Tree-level supersymmetry breaking is present only for the gravitino, and for the light gaugino masses through non-minimal kinetic terms reminiscent of N?4 extended supergravity theories. Radiative corrections generate squark and slepton masses which are phenomenologically acceptable, and the right value of m_W is obtained if m_t ≈ 50 GeV in the simplest such model.     

Optical detection of cyclotron resonance of electron and holes in CdTe

Cyclotron resonance of electron and holes have been optically detected at 70 GHz and at 1.8 K in n-type CdTe. The bare effective masses, in unit of the free electron mass, are found to be: $\text{m}{}^1\text{= 0.088 ± 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.12 ± 0.01}$, $\text{m}{}^1\text{= 0.60 ± for H // <100>}$, and $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.089 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.11 ± 0.01}$, $\text{m}{}^1{}_{\mathrm{hh}}\text{= 0.69 ± 0.02}$ for H // <111>. The Luttinger valence band parameters deduced from these measurements are: γ₁ = 5.3 ± 0.5, γ₂ = 1.7 ± 0.3 and γ₃ = 2.0 ± 0.3, in fair agreement with the calculations of Lawaetz.     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

A determination of the spin of the hypernucleus 12ΛB: (II). A complete analysis

The probability distribution calculated for the decay sequence ${}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.) →}{}^{12}\text{C}{}^1\text{π}{}^{\mathrm{?}}\text{→ αααπ}{}^{\mathrm{?}}$ passing through the (J^P_N) = (2⁺, 1) intermediate state ¹²C¹ (16.11 MeV) is cast in a symmetrical form and used to calculate the likelihood for $\text{J = 1}\text{relative to}\text{J = 2}\text{for}{}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.}\text{)}$ on the basis of the 85 examples available for this decay process. This procedure has optimum sensitivity, is free from the uncertainties of the comparisons previously made using only projected angular distributions, and strongly indicates that J^P = 1^? holds for ¹²_ΛB(g.s.). An appendix points out that all the data for the decay sequence passing through the (J^P_N, T) = (1⁺, 0) level of ¹²C¹ is well fitted for J = 1 if the J = 1 → J_n = 1 transition amplitude a_s1 takes a value in the range a_s1/s = 0.08 to 0.09.     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

Light composite fermions in a dynamical subquark model of pregauge interactions

The masses of composite leptons and quarks are discussed in a “dynamical subquark model of pregauge interactions”. In this model, the leptons and quarks are made of a spinor and scalar subquark with equal mass, M, and the gauge bosons and Higgs scalar of the SU(3)_c×SU(2)_L×U(1)_Y model are made of a subquark-antisubquark pair. The SU(2)_L×U(1)_Y symmetry is spontaneously broken by the composite Higgs scalar and the (scalar) subquark mass parameter is in turn bounded as $\text{M > 5.4}\text{TeV}\text{(=2π(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{where}\text{G}{}_{\mathrm{<mtext>F</mtext>}}$ is the Fermi coupling constant). The spontaneously generated mass of a lepton or quark, m_i⁽ⁿ⁾ (i = 1, 2; n = 1 ～ N_g), is calculated to be: $\text{m}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{= r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{× (4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)α}{}_{\mathrm{<mtext>e.m.</mtext>}}\text{(}\text{2}\text{G}{}_{\mathrm{<mtext>F</mtext>}}{}^{\mathrm{?1}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/3}\text{6}\text{(=0.35r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}\text{(4+3N}{}_{\mathrm{<mtext>g</mtext>}}\text{)}\text{GeV}\text{),}\text{where}\text{r}{}_{\mathrm{i}}{}^{\mathrm{(n)}}$ are the parameters satisfying that 0 ? r_i⁽ⁿ⁾ ? 1 and Σ (r_i⁽ⁿ⁾)² = 1;N_g is the total number of generations of the leptons and quarks; α_e.m. is the fine structure constant. The appearance of light composite fermions is related to a specific mechanism of generating global chiral symmetries of the leptons and quarks. Global symmetries of scalar subquarks yield chiral symmetries of the leptons and quarks. Our model turns out to satisfy 't Hooft's anomaly conditions on massless composite fermions.     

Susceptibilities of the S = 12 XY model on the square lattice at T = 0

For the $\text{S =}\text{1}\text{2}\text{XY}$ model at T = 0 four susceptibilities have been calculated exactly on a sequence of finite square lattices and extrapolated to the infinite square lattice. For the ferromagnet χ_zz = 0 while χ_xx ～ N^2.9; for the antiferromagnet $\text{J}{}_{\mathrm{\chi xx}}\text{N(gμ}{}_{\mathrm{<mtext>B</mtext>}}\text{)}{}^2\text{= 0.025 ± 0.002}$ and $\text{J}{}_{\mathrm{\chi xx}}\text{N(gμ}{}_{\mathrm{<mtext>B</mtext>}}\text{)}{}^2\text{= 0.13 ± 0.03}$.     

Supersymmetric pure spinor theory

A theory based solely on a 2×(N=2)-component Weyl spinor field χ(x) of subcanonical dimension $\text{1}\text{2}$ allows the local construction (without derivatives) of effective fermi and bose fields with spins up to N=2. It is demonstrated that the lagrangian $\text{～:}\text{det}\text{xx}{}^1\text{: (x)}$ studied earlier is invariant under a global N=2 supersymmetry transformation and can be cast into a form $\text{～(}\text{det DD}{}^1\text{):ππ}{}^1\text{:}$ involving the scalar chiral superfield $\text{π=}\text{exp}\text{[θ}{}_{\mathrm{x}}\text{(x + iθσθ}{}^1\text{)]}$ the components of which are finite part products of the basic field. The theory can be generalized to an N-supersymmetric theory in a 2N-dimensional space-time yielding the Thirring model as special case for N=1.     

Valence band parameters and free exciton reduced mass of zinc telluride derived from free exciton magnetoreflectance

Reflectance spectra were measured on ZnTe in magnetic fields up to 18 T for B ? [100] and B ? [110]. The experiments yield renormalized valence band parameters $\text{γ}{}^1{}_2\text{= 0.83 ± 0.08}$ and $\text{γ}{}^1{}_3\text{= 1.30 ± 0.12}$, corresponding to bare parameters γ₂ = 0.95 ± 0.09 and γ₃ = 1.48 ± 0.14. From the free exciton Rydberg energy $\text{R}{}^1{}_0\text{= 12.8}\text{meV}$ we derive a reduced exciton polaron mass m₀ 0.080 ± 0.005 and a bare reduced mass m₀ 0.074 ± 0.005, corresponding to $\text{γ}{}^1{}_1\text{= 3.9 ± 0.7}$ and γ₁ = 4.4 ± 0.7 for an electron effective polaron mass $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.116 m}{}_0$. We further calculate the exciton diamagnetic shift rate according to existing low-field theories modified by a variational calculation taking into account polaron effects and valid up to γ ? 1. The difference between experiment and theory is 10% and the agreement is considered satisfactory.     

Hole mass measurement in p-type InP and GaP by submillimetre cyclotron resonance in pulsed magnetic fields

The first observation of cyclotron resonance in p-type InP is reported. The holes were thermally excited at 110 K and the resonance was observed at 337μm wavelength (HCN laser) using a pulsed magnetic field of 0–350 kG. The effective masses of the light and heavy holes in the 〈111〉 direction were found to be $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, and in the 〈100〉 direction $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.02 m}{}_0$. We obtain an estimate of the Dresselhaus parameters A = ?5.04, |B| = 3.12, C² = 6.57. We also report the effective masses for p-type GaP in the 〈111〉 direction as $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.18 ± 0.02 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.04 m}{}_0$.     

The radiative photino decay into a higgsino

The radiative decay of the photino (γ&#x0304;) to a higgsino (H?) is calculated in the minimal supersymmetric electroweak theory coupled to N = 1 supergravity. From the recent analyses on two photon production at PETRA, we find that the possibility that $\text{m}{}_{\mathrm{<mtext>H</mtext><mtext>?</mtext>}}\text{/m}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}\text{<1}$ is almost excluded, unless $\text{m}{}_{\mathrm{<mtext>\gamma </mtext><mtext>?</mtext>}}\text{?}\text{O}\text{(20)}\text{GeV}$. We also calculated the cross section for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{→}\text{γ}\text{?}\text{→γ}\text{H}\text{?}\text{+γ}\text{H}\text{?}$ as a function of photon energy.     

On the relativistic Thomas-Fermi model

The relativistic generalization of the Thomas-Fermi model of the atom is derived. It approaches the usual nonrelativistic equation in the limit Z ? Z_crit, where Z is the total number of electrons of the atom and $\text{Z}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ and α is the fine structure constant. The new equation leads to the breakdown of scaling laws and to the appearance of a critical charge, purely as a consequence of relativistic effects. These results are compared and contrasted with those corresponding to N self-gravitating degenerate relativistic fermions, which for $\text{N ≈ N}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(m/m}{}_{\mathrm{<mtext>p</mtext>}}\text{)}{}^3$ give rise to the concept of a critical mass against gravitational collapse. Here m is the mass of the fermion and $\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{=(?c/G)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is the Planck mass.     

On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

.     

Centrifugal distortion effects in the microwave spectrum of methylene cyanide

The rotational spectrum of methylene cyanide has been measured up to J = 62 and a total of 82 b-type transitions have been obtained. These data have been analyzed with a semirigid rotor Hamiltonian to give accurate rotational and centrifugal distortion constants. The rotational constants are (in MHz) $\text{A}$ = 20882.7537 ≠ 0.017, $\text{B}$ = 2942.3003. ≠ 0.0031, $\text{C}$ = 2616.7225 ≠ 0.0031 The quartic centrifugal distortion constants are (in MHz)

$\text{Δ}{}_{\mathrm{J}}\text{(1.855455 ≠ 0.014) x 10}{}^{\mathrm{?3}}\text{Δ}{}_{\mathrm{JK}}\text{= (?6.79218 ≠ 0.027) x 10}{}^{\mathrm{?2}}$

$\text{Δ}{}_{\mathrm{K}}\text{(8.621628 ≠ 0.013) x 10}{}^{\mathrm{?1}}\text{δ}{}_{\mathrm{J}}\text{= (4.892607 ≠ 0.016) x 10}{}^{\mathrm{?4}}$

$\text{δ}{}_{\mathrm{K}}\text{= (6.7501 ≠ 0.29) x 10}{}^{\mathrm{?3}}$

The uncertainties are twice the standard deviations in the constants obtained from the least squares analysis, and represent approximately 95% confidence limits.     

Velocity dependence of the nucleon-nucleon interaction,exchange currents and enhancement of the dipole sum rule in nuclei

A model is employed to describe the velocity dependence of the effective nucleon-nucleon interaction in nuclear matter. The interactions in this model consist of π^? and ρ-meson exchange, together with short-range correlations induced by the strongly repulsive potential resulting from ω-meson exchange. With known coupling strengths, these interactions produce an effective mass $\text{m}{}^1\text{/m = 0.75}$ in nuclear matter.Through the formalism of Fermi liquid theory, the exchange-current correction to the orbital g-factor, δg_l, can be described in terms of the velocity dependence in the neutron-proton interaction, and, within the model, this can be related to the effective mass $\text{m}{}^1$. With $\text{m}{}^1\text{/m = 0.75}$, the δg_l for the proton turns out to be 0.22, 45% of it coming from π-meson exchange.Additional contributions to $\text{m}{}^1\text{/m}$ in nuclei come from the coupling of vibrations to quasiparticles; these are especially important in the nuclear surface, and tend to increase the effective mass, when averaged over both nuclear volume and surface, so that $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{? 1}$. In so far as these contributions arise from isovector vibrations, we can use the same model as for π- and ρ-meson exchange, and show that the same relation between $\text{m}{}^1\text{/m}$ and δg_l holds, so that for $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{= 1}$, δg_l = 0. The contributions from coupling to vibrations will depend upon the single-particle state, however; states of high-angular momentum will tend to have $\text{〈m}{}^1\text{/m〉}{}_{\mathrm{<mtext>av.</mtext>}}\text{< 1}$ and δg_l > 0.Finally, the enchancement δg_l in gl can be connected with the enhancement k in the dipole sum rule originating from the giant-resonance region. This connection is not very precise, but gives a small positive κ ～ 0.2.