Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

On the multiplicity of hadrons in QCD jets

A three-loop calculation is presented for the jet multiplicity of produced slightly-off-shell gluons for a pure Yang-Mills theory. Planar and non-planar graphs are found to be equally important in an axial gauge. If the three-loop calculation is indicative of what happens at higher orders $\text{n}\text{(Q}{}^2\text{) ∝}\text{exp}\text{{[(}\text{2C}{}_{\mathrm{<mtext>A</mtext>}}\text{πb}\text{) 1}\text{n}\text{Q}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{}}$ where C_A = 3 and $\text{b =}\text{(33 ? 2n}{}_{\mathrm{<mtext>f</mtext>}}\text{)}\text{12π}$ in QCD.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

Nuclear magnetic moment of the 9.7 h 12− isomer 196mAu

The magnetic hyperfine splitting v_M=|gμ_NB_HF/h| of ^196mAu (j^π=12^?; configuration ¦(π$\text{11}\text{2}$($\text{v}\text{13}\text{2}{}^{\mathrm{+}}\text{)〉}{}_{12}{}^{\mathrm{?}}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 9.7}\text{h}\text{)}$ as dilute impurity in Ni has been determined with nuclear magnetic resonance on oriented nuclei as 96.0(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^196mAu are deduced to be |g| = 0.476(7) and |μ| = 5.72(8) μ_N. Taking into account the known magnetic properties of $\text{π}\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{v}\text{13}\text{2}{}^{\mathrm{+}}$ isomeric states in the neighbouring odd Pt, Au and Hg nuclei the structure of the 12^? state is discussed.     

Nuclear matrix elements from L/K electron capture ratios in 59Ni decay

Using a recent theoretical method, the ratio of nuclear matrix elements $\text{R = (}{}^{\mathrm{v}}\text{F}{}^0{}_{220}\text{?√}\text{3}\text{2}{}^{\mathrm{A}}\text{F}{}^0{}_{221}\text{/}{}^{\mathrm{v}}\text{F}{}^0{}_{211}\text{)}$ was determined to be either 20.50^+0.35_?0.55 or 25.22^+0.28_?0.17 in the second-forbidden nonunique decay of 8 × 10⁴ y ⁵⁹Ni. These values of R were obtained from a value of L₃/K = 0.008 ± 0.002 found by subtracting the theoretical ratio $\text{(L}{}_1\text{+ L}{}_2\text{)}\text{K}$ = 0.113 (based on Q_PEC = 1070 ± 8 keV) from the total ratio L/K = 0.121 ± 0.002, which was measured with a reactor-produced, doubly-mass-separated ⁵⁹Ni source introduced as gaseous nickel-ocene, (C₅H₅)₂, into a wall-less, anticoincidence, multiwire proportional counter. The 854–1008 eV L and the 8.33 keV K peaks were measured simultaneously.     

Electron localisation in systems with purely off-diagonal randomness

A probability distribution for the off-diagonal matrix elements v_nm of the tight binding Hamiltonian is assumed to be $\text{P(v}{}_{\mathrm{nm}}\text{) =}\text{1}\text{Wv}{}_{\mathrm{nm}}$ for $\text{e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}\text{≤ v}{}_{\mathrm{nm}}\text{/v}{}_0\text{≤ e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}$ and P(v_nm = 0 otherwise. A homomorphic cluster CPA with the L(E) criterion is used to study localisation in a simple cubic lattice and a computer simulation is used to study a square lattice with the participation-ratio criterion. It is found, in both cases, that Anderson's transition takes place for a critical degree of disorder.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Contributions of operators of twist two and higher in large n moments of structure functions

Though high twist terms are becoming important as x→1, or equivalently, in large n moments, their detection in this regime in deep inelastic lepton scattering needs special caution. The high order terms in the twist two component are strongly dependent on n; one finds that at $\text{Q}{}^2\text{?Q}{}^2{}_7\text{?Λ}{}^2\text{a}{}_{\mathrm{k}}\text{exp}\text{[α}{}_{\mathrm{k}}\text{(}\text{log}\text{n)}{}^{\mathrm{<mtext>2?1</mtext><mtext>k</mtext>}}\text{(}\text{1+b}{}_{\mathrm{k}}\text{log}\text{n}\text{)]}$ the perturbative expansion is invalid whereas higher twist terms are important at $\text{Q}{}^2\text{?Q}{}_1{}^2\text{= Λ}{}^2\text{nC}$. Since $\text{Q}{}_7{}^2$ grows very fast with n the necessary requirement for any deep inelastic phenomenological analysis, namely $\text{Q}{}_1{}^2\text{?Q}{}_7{}^2$, cannot hold for too large moments. The scheme dependence of a_k, α_k and b_k is also discussed.     

Mobility edge shift in external magnetic field

It is shown that magnetoconductivity in the critical region near the metal-insulator transition is equal to $\text{A}{}_{\mathrm{l}}\text{H}$ and the coefficient A_l does not depend on the proximity to the mobility edge. The magnetic field leads to the mobility edge shift, which is proportional to $\text{H}{}^{\mathrm{<mtext>1</mtext><mtext>(2v</mtext><mtext>)</mtext>}}$, where v is the conductivity critical index.     

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%     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

Anomalous stoner enhancements in amorphous systems

An n-orbital model describing both elastic impurity scattering and exchange interaction is examined near its instability for itinerant ferromagnetism. At the critical point and at zero temperature, long range spin fluctuations cause anomalous enhancements of the density of states near the Fermi energy with $\text{?(E) - ?(E}{}_{\mathrm{F}}\text{) ∝ |E ? E}{}_{\mathrm{F}}\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ in three-dimensions (3D) and with ln²|E ? E_F| in 2D. An estimation of the conductivity $\text{σ(Ω)}$ in a continuum analog model reveals Ω^{$\text{1}\text{4}$} -and ln²$\text{|Ω}{}_{\mathrm{\tau }}\text{|}$-corrections in 3D and 2D respectively.     

Infrared spectrum of acetonitrile: Analysis of Coriolis resonance

The Coriolis resonance between ν₄ and ν₇ in CH₃CN and between ν₁ and ν₅, ν₃ and ν₆, and ν₄ and ν₇ in CD₃CN has been analyzed, applying the technique developed by DiLauro and Mills, to obtain the signs of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] and the ratio of $\text{?μ}\text{?Q}{}_{\mathrm{r}}$ to $\text{?μ}\text{?Q}{}_{\mathrm{s}}$ for the interacting pairs in CD₃CN. For (ν₄, ν₇) in both CH₃CN and CD₃CN, the sign of [$\text{ζ}{}_{\mathrm{r,sa}}{}^{\mathrm{y}}\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$] is found to be negative as it is also for (ν₁, ν₅) in CD₃CN. For (ν₃, ν₆) the sign of this interaction term is found to be positive. For a given definition of normal coordinates the signs of these interaction terms give the relative signs of $\text{?p}\text{?Q}{}_{\mathrm{r}}$ and $\text{?p}\text{?Q}{}_{\mathrm{sa}}$; our study also gives approximate values for the corresponding ratio [$\text{(}\text{?p}\text{?Q}{}_{\mathrm{r}}\text{)}\text{(}\text{?p}\text{?Q}{}_{\mathrm{sa}}\text{)}$]     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Intensities and pressure-broadened widths of CO2 R-branch lines at 15 μm from tunable laser measurements

Intensities and half-widths of individual lines, over the temperature range 200–325°K in the 15 μm bands of ¹²C¹⁶O₂, have been determined with a tunable diode laser spectrometer. Measurements were made on pure CO₂ and on dilute CO₂-in-N₂ mixtures on the R-branches of the 01¹0-00⁰0 and 02²0-01¹0 transitions. Intensities are approximately equal to those listed in the AFGL compilation. The pressure-broadened half-widths follow the general relationship $\text{b}{}_{\mathrm{L}}{}^0\text{(T) = b}{}_{\mathrm{L}}{}^0\text{(T}{}_0\text{) [}\text{T}{}_0\text{T}\text{]}{}^{\mathrm{n}}$ where n varies considerably from line to line but is always greater than $\text{1}\text{2}$.     

Bound state vibrational spectrum of the 3–9 atom-surface interaction

The potential $\text{V(z) =}\text{C}{}_9\text{z}{}^9\text{?}\text{C}{}_3\text{z}{}^3$ is a reasonable parametrization of the atom-surface interaction. We evaluate the discrete spectrum E_n of bound states for this potential with arbitrary coefficients C₉ and C₃. The resulting form in the WKB approximation is $\text{E}{}_{\mathrm{n}}\text{= ?D [1 ?}\text{(n +}\text{l}\text{2}\text{)}\text{L}\text{]}{}^6$, where L depends on the mass and D is the well depth. We find that the exact solution of the Schrödinger equation can be written in the same form, with n shifted slightly by an amount δ_n, which we calculate. The results are applied to the case of He near a NaF surface, in which the calculated eigenvalue spectrum agrees well with experimental values.     

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).