Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Is Coleman-Weinberg symmetry breaking in the standard model ruled out?

In the standard model with Coleman-Weinberg symmetry breaking a symmetric vacuum (〈φ〉 = 0) always exists at any non-zero temperature; the transition to the symmetry-breaking vacuum can only occur after much supercooling. Witten has shown that this transition occurs when the strong interactions break chiral symmetry; the transition temperature is O(200) MeV and a large (but not fatal) amount of entropy is produced. It is noted here that since the strong coupling grows as the universe cools in the metastable symmetric vacuum, the Yukawa coupling to the top quark will also grow. This causes top quark loops to dominate the effective potential at small scales, drastically altering the nature of the transition. We show that if $\text{m}{}_{\mathrm{<mtext>t</mtext>}}\text{? 65}\text{GeV}$, a metastable vacuum at 〈φ〉 ≈ 0(1) GeV forms which persists to T = 0; the resulting transition would generate far too much entropy to be compatible with the current baryon to entropy ratio, ruling out the CW mechanism. If m_t ? 65 GeV, we argue that a metastable vacuum might also exist, but a breakdown of perturbation theory precludes a definitive statement.     

A comment on the potential in heavy quarkonium quantum-mechanical systems

I discuss the characteristics of the non-relativistic potential responsible for the ψ and ? systems. In particular a comparison is made between the recently advocated flavour independent power behaved potential and the QCD inspired Coulomb + linear potential. The ratios $\text{ΔM}{}_{\mathrm{?}}\text{ΔM}{}_{\mathrm{\psi }}$ of radical excitation energy level differences are used as sensitive tests to the r dependence of V(r). Deviations of these ratios from a constant value may indicate a gradual increase in the effective power of the potentials as r increases (in agreement with the Coulomb + linear potential). Decisive tests have to come from the not yet discovered toponium family where the ratios $\text{ΔM}{}_{\mathrm{T}}\text{ΔM?}$ should start to become greater than 1 if a singularity of the potential exists at r → 0.     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

Quarkonium level spacings

Motivated by the apparent equal spacing M(?′)?M(?) = M(ψ′)?M(ψ), we show that the potential for which quarkonium level spacings are independent of quark mass, in the nonrelativistic limit, is $\text{V(r) = C}\text{ln}\text{(}\text{r}\text{r}{}_0\text{)}$. We enumerate consequences of the logarithmic potential and present and alternative interpretation of the data.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Meson decay constants and bare quark masses from duality for current two-point functions

Duality is applied in a quasi-local form to the SU(4) × SU(4) current two-point functions. Interpolating functions for some of their space-time components are assumed to be given by the free quark model. Mass intervals in the finite energy sum rules are taken to be approximately SU(3) × SU(3) invariant and a linear dependence of the hadronic mass spectrum upon the radial quantum number is assumed. The correct order of magnitude of various meson decay constants is reproduced provided the color gauge group is SU(3). The bare uncharmed quark masses are given by the formulae: $\text{m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ M}{}_{\mathrm{\pi }}\text{F}{}_{\mathrm{\pi }}\text{/F}{}_{\mathrm{\pi }}\text{√6 ≌ 40}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{/m}{}_{\mathrm{<mtext>u</mtext>}}\text{≌ 1 = 6}$. The η-η mixing problem is discussed. Predictions are made for the masses and decay constants of the vector mesons of the first L = 2 level of SU(6) × O(3), as well as for the decay constants of the radially excited pseudoscalar mesons; estimates of corrections to PCAC in Goldberger-Treiman relations are presented. The bare charmed quark mass is found to be of the order of 1.1–1.2 GeV. Some decay constants of charmed mesons are evaluated.     

Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

Experimental results on J/ψ production by π±, K±, p and p incident on hydrogen at 39.5 GeV/c

J/ψ production at 40 GeV/c by π^±, K^±, p and $\text{p}$ incident on hydrogen has been studied and results compared with those obtained on tungsten in the same experiment. On hydrogen, J/ψ cross-section ratios relative to π^? have been measured to be (for $\text{x}{}_{\mathrm{<mtext>F</mtext>}}\text{> 0) σ(π}{}^{\mathrm{?}}\text{) : σ(π}{}^{\mathrm{+}}\text{) : σ(}\text{p}\text{) : σ(}\text{p}\text{) = 1 : (0.78 ± 0.09) : (0.83 ± 0.35) : (0.07 ± 0.04)}$. The suppression of the proton induced cross sections shows the importance of calence quark-antiquark fusiin J/ψ production at this energy (i.e. M_J²/_ψ/s=0.13).     

Correlation between band structure and hydride formation in dilute palladium alloys

Data on the free energy change ΔG, following solution of hydrogen in dilute Pd-alloys Pd_1?xM_x have been reviewed for different concentrations of M (M = Au, Ag, Pt, Ir, Rh, V, Cu, Ni, Pb, Sn and Ti) in both the α and β phases. The dependence of ΔG values upon the nature of the substituents (transition metals) is consistently explained within the framework of a metal-hydrogen bonding mechanism in the hydrides. For the β-hydride the ΔG values can be calculated on the basis of the equation ΔG = ΔG_pd + a(T)(〈?^M_LB〉 ? 〈?^Pd_LB〉)x, where $\text{ΔG}{}_{\mathrm{<mtext>Pd</mtext>}}\text{= ? 0.0489}\text{eV}\text{H}$ atom and is the free energy change of solution of hydrogen in pure Pd, a(T) = 0.194 at T = 298 K, 〈?^m_LB〉 and 〈?^pd_LB〉 are the average energies of the lowest band of the pure constituents ($\text{〈?}{}^{\mathrm{<mtext>Pd</mtext>}}{}_{\mathrm{<mtext>LB</mtext>}}\text{〉 = ?9.15}\text{eV}\text{atom}$). The stability of the palladium-hydrogen bond in dilute Pd-alloys depends on the value of 〈?^M_LB〉; for substituents having lower 〈?^M_LB〉 values than Pd the bond will strengthen, while for those having higher 〈?^M_LB〉 values it will weaken. This behaviour agrees well with the general trend of the stability of the stoichiometric hydrides predicted by Gelatt, Ehrenreich and Weiss using band structure results.     

Two-magnon Raman scattering in the two-dimensional antiferromagnet K2FeF4

Two-magnon Raman scattering in the planar quadratic antiferromagnet K₂FeF₄ is investigated. The temperature dependence of the energy shift is in good agreement with second-order Green-function theory, as is the linewidth at low temperature. Numerical results, including renormalization, are the Heisenberg exchange $\text{J}\text{k}{}_{\mathrm{B}}\text{= ?14.5 ± 0.7}\text{K}$ and the anisotropy $\text{Δ(T = 0) = gμ}{}_{\mathrm{B}}\text{H}{}_{\mathrm{A}}\text{4|J|S = 0.18 ± 0.05}$, but with $\text{J[1 + Δ(T = 0)]}\text{k}{}_{\mathrm{B}}\text{= ?17.06 ± 0.10}\text{K}$.     

The microwave spectrum of MnO3F

The microwave spectrum of MnO₃F has been remeasured and several corrections and new results have been obtained: B₀ = 4129.141 MHz, D_J = 1.12 kHz, D_JK = 1.87 kHz; $\text{α}{}_3{}^{\mathrm{B}}\text{= 8.622}$, $\text{α}{}_5{}^{\mathrm{B}}\text{= ? 11.994}$, $\text{α}{}_6{}^{\mathrm{B}}\text{= 6.042}$, |q₅| = 16.005, and |q₆| = 8.456 MHz.     

Consequences of a gut sector in minimal N = 1 supergravity models with radiative SU(2) × U(1) breaking

It is shown that incorporation of a GUT sector in N = 1 supergravity models with radiative SU(2) × U(1) breaking can drastically modify the corresponding low energy phenomenology. The ratio of Higgs VEVs $\text{ω ≡}\text{〈}\text{H}\text{〉}\text{〈}\text{H}\text{〉}$ might be much larger than 1, even for small top quark masses (m_t = O(40 GeV)). Scenarios of this type necessarily imply large squark and slepton masses $\text{m}{}_{\mathrm{<mtext>q</mtext><mtext>,\; </mtext><mtext>?</mtext>}}\text{? 150}\text{GeV}$, whereas light gluinos can easily be accomodated. Furthermore the upper bound on the mass of the light neutral Higgs becomes as large as M_Z and its coupling to down-type quarks and leptons might exceed the standard GWS-value by more than a factor of 5.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

Has asymptotic freedom something to do with charmonium

We analyse the effects of logarithmic corrections due to asymptotic freedom in the potential describing short-range forces in charmonium. This allows us to show that due to the size of the effective quark-gluon coupling ($\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(M}{}_{\mathrm{J/\Psi }}{}^2\text{) ? 0.4}$), the wave function extensions are much larger than the region of space where asymptotic freedom really has predictive power. The resulting ambiguities in the spin-dependent medium-range forces are explored. Also, such a value of α_s makes perturbative calculations of widths unreliable. We point out that the situation is not significantly improved for quark masses of 5 GeV. Indeed, below 20 GeV, short-range forces play a marginal role as compared to confinement forces.     

Pions as spin waves: Chiral symmetry breaking in lattice gauge theory

In hamiltonian lattice gauge theory, the fermion vacuum at lowest order in 1/g² can be determined from degenerate perturbation theory plus mean field-spin wave techniques. Using compact QED as an example, we show that: (i) chiral symmetry is spontaneously broken; and (ii) $\text{m}{}_{\mathrm{<mtext>pseudoGoldstone</mtext>}}{}^2\text{∝ m}{}_{\mathrm{<mtext>fermion</mtext>}}\text{〈}\text{ψ}\text{ψ〉}$. The pseudoscalar pseudoGoldstone particles—the “pions” of this abelian theory—correspond to antiferromagnetic spin wave excitations of the fermion vacuum.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

We study chiral symmetry breaking (_χSB) in SU(2) lattice gauge theory with quarks in the $\text{l =}\text{1}\text{2}\text{, l = 1, l =}\text{3}\text{2}$, and l = 2 representations of the color group. We perform Monte Carlo evaluations of $\text{〈}\text{ψ}\text{ψ〉}$ in the quenched approximation and extract the relevant length scales for _χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain $\text{T}{}_{\mathrm{l\; =\; 1}}\text{/T}{}_{\mathrm{l}}\text{=}\text{1}\text{2}\text{～ 8}$. Our results for the higher representations, $\text{l =}\text{3}\text{2}\text{and}\text{l = 2}$, are consistent with Casimir scaling and give C₂g_mom² ～ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between _χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.