Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

Exact Solution of a Cellular Automaton for Traffic

We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g., cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with simultaneous updating of all sites. It is equivalent to a special case (v _max=1) of the Nagel–Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short-range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two-point functions, and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time-discrete updating procedures. Through use of this mapping, our results also give new results for these models.     

Band ordering in PbTe

Two possible conduction band orderings, I, L^-₆(L_2'), L^-₆(L_3'), L^-₄₅(L_3') and II, L^-₆(L_3'), L^-₄₅(L_3'), L^-₆(L_2') are considered for PbT e using the Empirical Pseudopotential method. Various properties (i.e. optical reflectivity temperature and pressure dependence of the band gap and effective masses) are considered for the two possible orderings.     

Investigation of states in 30P via the 30Si(3He,t)30P reaction at 30 MeV

The ³⁰Si(³⁰He, t)³⁰P reaction has been measured for about 100 levels in ³⁰P with E_x < 8.8 MeV. Little selectivity in the population of states has been observed. For 75 levels angular distributions have been analysed using a “fingerprint method” by determining the L-value from a comparison in shape with transitions to states with known J^π. For possible mixed L-transitions a dominance of the higher L-value is observed for almost all cases. Coulomb displacement energy calculations utilizing shell-model wave functions have been used to identify T = 1 states.     

Quark mixing angles in the left-ringt symmetric model with lightW R fromK 0-K 0 mixing

K _L?K _S mass difference and the CP violation parameter, ?, of theK ⁰ ? \(\overline {K^0 } \) system are used to set bounds on the right-handed Cabibbo-like angle and the CP violating phase angle in the left-right symmetric electroweak model of four quarks. The corresponding mixing and phase angles in typical left-right asymmetric models (g _L≠g _R) are also determined.     

High harmonic generation in H2 + and HD + by two-colour femtosecond laser pulses

We have theoretically investigated the high harmonic generation (HHG) spectra of H₂ ^?+? and HD^?+? using a time-dependent wave packet approach for the nuclear motion with combined two-colour (1ω _L –3ω _L ) pulsed lasers for ω _L corresponding to wavelengths 1064 nm and 800 nm. The 1ω _L and 3ω _L lasers have peak intensities of I ₁ ⁰?=?5.0×10¹³ W/cm² and I ₂ ⁰?=?2.0×10¹⁴ W/cm², respectively. We have taken the pulse duration of T = 50 fs for both the fields, and the molecular initial vibrational level v ₀?=?0. We have argued that for these combinations, the harmonic generation due to transitions in the electronic continuum by tunnelling or multiphoton ionization may be neglected and only the electronic transitions within the two lowest electronic states would be important. Thus, the characteristic features of HHG spectra in the two-colour field are determined, in our model, by the nuclear motions on the two lowest field-coupled electronic states between which interelectronic and intraelectronic (due to the intrinsic dipole moments in case of HD^?+?) radiative transitions can take place. We have studied the role of relative phase (φ) of the two fields on the HHG spectra of the molecular ions. In case of HD^?+?, the effect of nonadiabatic (NA) nonradiative interaction between the two lowest Born-Oppenheimer (BO) electronic states (1sσ _g , 2pσ _u ) has been taken into account. Our calculations give realistic HHG spectra which are reasonably efficient and extended for both H₂ ^?+? and HD^?+? in the mixed two-colour field without involving the electronic continuum. The use of two-colour (1ω _L –3ω _L ) field enables us to generate high harmonics beyond that achievable with a single 1ω _L or 3ω _L field of the corresponding intensity, frequency and pulse time.     

Low-energy parity restoration and unification mass scale within maximal symmetries

We investigate the hierarchy of gauge boson masses in the maximal grand unified theory by studying the renormalization group equations for the running coupling constants associated with the symmetry breaking of SU(16)viaSU(12) _q×SU(4) _l×U(1) _|B|?|L| chain. Particular attention is given to the contribution of Higgs scalars to these equations. It is found that the intermediate mass scale M_L, associated with right-handed gauge bosons could be as low as 10 ³ GeV only for sin ²θ _w(M _L) as high as 0.265 with α _s(M _L)=0.13. In this chain of symmetry breaking, we have also examined the lowest unification mass that is allowed by the low-energy data for sin ²θ _w(M _L) and the assumed gauge hierarchy. This has been done in two cases; first for the case where SU(3) ^c is vectorial, second, for the case where SU(3) ^c is axial. In both cases the lowest unification mass scales were found to be 10 ¹³, 10 ¹¹, 10 ⁸ and 10 ⁷ GeV for sin ²θ _w(M _L) = 0.22, 0.24, 0.26,and0.265 respectively with α _s(M _L) = 0.13. The implication of these low unification masses on baryon non-conserving processes is also discussed.     

On Lepton asymmetry and BBN

The strongest available cosmological constraint on lepton asymmetry is L<0.01. We discuss in more detail a BBN model with late ν_e↔ν_s oscillations which is capable of measuring extremely small lepton asymmetry, L>10⁻⁸. This sensitivity is achieved through the influence of small L on the neutrino oscillations, suppressing or enhancing them, and thus decreasing or increasing the primordially produced ⁴He. The cases of asymmetry generated by late resonant electron-sterile oscillations and relic lepton asymmetry are considered. The influence of L on nucleons freezing in pre-BBN epoch is numerically analyzed in the full range of the oscillation parameters for the model and L≥10⁻¹⁰.     

Surface-induced finite-size effects for first-order phase transitions

We consider classical lattice models describing first-order phase transitions, and study the finite-size scaling of the magnetization and susceptibility. In order to model the effects of an actual surface in systems such as small magnetic clusters, we consider models with free boundary conditions. For a field-driven transition with two coexisting phases at the infinite-volume transition pointh=h _t , we prove that the low-temperature, finite-volume magnetizationm _free(L, h) per site in a cubic volume of sizeL ^d behaves like $$m_{free} (L,h) = \frac{{m_ + + m_ - }}{2} + \frac{{m_ + - m_ - }}{2}tanh\left[ {\frac{{m_ + - m_ - }}{2}L^d (h - h_\chi (L))} \right] + O\left( {\frac{1}{L}} \right)$$ whereh _x (L) is the position of the maximum of the (finite-volume) susceptibility andm _± are the infinite-volume magnetizations ath=h _t +0 andh=h _t ?0, respectively. We show thath _x (L) is shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t provided the surface free energies of the two phases at the transition point are different. This should be compared with the shift for periodic boundary conditions, which for an asymmetric transition with two coexisting phases is proportional only to 1/L ^2d . One can consider also other definitions of finite-volume transition points, for example, the positionh _U (L) of the maximum of the so-called Binder cumulantU _free(L,h). Whileh _U (L) is again shifted by an amount proportional to 1/L with respect to the infinite-volume transition pointh _t , its shift with respect toh _χ (L) is of the much smaller order 1/L ^2d . We give explicit formulas for the proportionality factors, and show that, in the leading 1/L ^2d term, the relative shift is the same as that for periodic boundary conditions.     

Radiation transfer in an anisotropically scattering plane-parallel medium with space-dependent albedo ω(x)

A method of analysis is presented for solving radiation-transfer problems involving space-dependent albedo ω(x) for an absorbing, emitting and anisotropically scattering plane-parallel medium with reflecting boundaries. The albedo is represented in terms of Legendre polynomials in the form ω(x) = Σ^R_r=0D_rP_r(x/L), where x is the optical variable, L is the half optical-thickness of the slab, P_r(x/L) are the Legendre polynomials and D_r are known expansion coefficients. The effects of spatial variation of albedo on the reflectivity and transmissivity of a medium having a slab geometry are examined for the cases of both forward and backward anisotropic scattering over a wide range of system variables. The effects of ω(x) on the angular distribution of radiation are also shown for some representative cases.     

Phase Coexistence in Nanoscopically Thin Films Confined by Asymmetric Walls

Thin Ising films with nearest-neighbor ferromagnetic exchange in a bulk magnetic field H are studied in a L×L×D geometry, where at the opposite walls, given by the L×L surfaces, local magnetic fields H ₁, and H _D act. While in previous work, the symmetric case H ₁=H _D (leading to “capillary condensation”, when one applies the lattice gas terminology) as well as the antisymmetric case H ₁=?H _D (leading to “interface localization transitions”) were studied, we focus here on the general ‘asymmetric’ case. Monte Carlo simulations are carried out and analyses based on thermodynamic integration methods are used to establish the phase diagrams and study the properties of the coexisting phases. A discussion is given why for the range of thicknesses that is explored (16≤D≤80 lattice spacings) this is the most suitable methodology. Restricting attention to cases where in the semi-infinite system a first-order wetting transition occurs, it is shown that the latter, due to confinement, is turned in a thin-film triple point. Above the triple point, narrow two-phase coexistence curves are found, which are the analog of prewetting transitions in the semi-infinite system. A comparison to related results for (symmetrical) polymer blends and (asymmetric) colloid-polymer mixtures is made.     

Elastic and inelastic effects in proton-proton scattering from states of pure spin

Modified phase-shift analyses of pp scattering are presented at p_L = 1.25 and 1.66 GeV/c and shown to give large negative elastic effects in Δσ_L^tot. Using a combination of phase-shift analyses from low energies up to 1.66 GeV/c and simple models of both elastic (pp → pp) and inelastic (pp → NΔ) scattering we conclude that the measured behaviour of Δσ_T^tot is mostly inelastic, but the large negative value of Δσ_L^tot is predominantly elastic with fluctuations produced by inelastic effects. We find no evidence for a dibaryon resonance.     

Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equations

By using a characterization of the concept of analytic representation and a variational approach to self-adjointness introduced in a preceding paper, we prove a theorem, according to which a necessary and sufficient condition for a class $\text{C}$², regular, tensorial, quasi-linear system of field equations to admit an ordered direct analytic representation in terms of the Lagrange equations in a region R of its variables is that the system is self-adjoint in R. We point out as a first corollary that if the ordering requirement is removed from the definition of analytic representation, then the condition of self-adjointness of the field equations is only sufficient for the existence of a Lagrangian density. We then provide as a second corollary a methodology for the computation of the Lagrangian density for the representation of self-adjoint quasi-linear tensorial field equations. This methodology is also particularized for ordinary semilinear systems of tensorial field equations through a third corollary. The above results are interpreted from the viewpoint of interactions. We first recover, through a fourth corollary, the conventional structure of the total Lagrangian density L_Tot = Σ_{1 a}ⁿL_Free^(a) + L_Int for the semilinear form of the field equations, and then introduce through a fifth corollary a generalized structure of the type L_Tot = Σ_{1 a}ⁿL_{Int, I}^(a)L_Free^(a) + L_Int.II for t representations of the field equations in the quasi-linear form. Therefore, our analysis seems to indicate that a general form of representing interacting fields is characterized by (n+1)-interaction terms in the Lagrangian: n multiplicative terms and one additive term to the Lagrangian for the free fields.     

Current Moments of 1D ASEP by Duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Schütz. For the ASEP on the infinite lattice we show that the nth moment is reduced to the problem of the ASEP with less than or equal to n particles.     

SU(6)W and πN→ϱN revisited

We point out that the intersection of the Berkeley-SLAC and Saclay signs of πN→?N resonant amplitudes are consistent with ?-broken SU(6)_W if both the 70, L^P = 1^?and 56, L^P = 2⁺ multiplets choose anti-SU(6)_W solutions. The symmetry scheme still fails in that the πN→πΔ relative signs require an SU(6)_W-like solution for the 56, L^P = 2⁺. This failure however now rests on a single incorrect sign prediction among all N? and Δπ amplitudes.     

Transition Probabilities and Dynamic Structure Function in the ASEP Conditioned on Strong Flux

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case.     

Fractional charges and the renormalization group in theSU(4)×O(4) string model

We study the renormalization group equations of the gauge couplings in theSU(4)×O(4)～SU(4)×SU(2) _L ×SU(2_ _R string model, derived in the context of the free fermionic formulation of the four dimensional superstring. We calculate the effective string unification scale taking into account string threshold corrections and we consider the consequences of then _L andn _R fractionally charged states, sitting in the (1, 2, 1) and (1, 1, 2) representations correspondingly, of the gauge symmetry of the model. Some of these states become massive at a very high scale, when a number of singlet fields acquire vev's. However, many of them (the precise number depends on the specific choice of the flat direction) remain in the massless spectrum. We consider various cases and find that, for specific choices of flat directions, the physical parameters of the model, like the grand unification scale and the low energy parameters sin²θ _W and α₃, depend only on the differencen _?=n_L-n_R. We study more general cases where remnants of the exotic doublets remain below theSU(4) breaking scale. We also solve the coupled differential system of the renormalization group equations for the gauge and the Yukawa couplings and estimate the range of the top quark mass which is found to lie in the range 140 GeV<m _t<190GeV.     

Asymptotics in ASEP with Step Initial Condition

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three asymptotic results for the positions of these particles. In one an apparently new distribution function arises and in another the distribution function F ₂ arises. The latter extends a result of Johansson on TASEP to ASEP, and hence proves KPZ universality for ASEP with step initial condition.     

Model-independent amplitude analysis for the reaction πN → ρΔ

A method is proposed for determining the amplitudes for the reaction πN → ?Δ using only those moments of the joint decay angular distribution 〈Y_L1^M₁Y_L2^M₂〉 with both L₁ and L₂ even. The solution is not unique; both continuous and discrete ambiguities exist. The conditions under which an analysis is possible are studied in detail; in addition to certain positivity conditions on the joint density matrix, a complicated inequality involving the experimental moments must be satisfied. This condition defines a non-convex domain in the space of the moments. We apply our methods to the high-statistics experimental data at 3.7 GeV/c.     

Vector boson scattering ate + e − colliders as a test ofW ±,Z 0, γ self-interactions

We investigate the potential of a high-energye ⁺ e ^? collider (e.g., CLIC,E _e ⁺=E _e ^?=1 TeV) for determining trilinear and quadrilinear vector boson self-interactions in various vector boson scattering processes which can be measured in reactions of the type \(e^ + e^ - \to (e^ + e^ - ,ve^ - ,\bar ve^ + ,v\bar v) + VV'\) . Our analysis is based upon a recently suggested single parameter Lagrangian model for vector boson self-interactions incorporating globalSU(2) weak isospin symmetry broken by electromagnetism and a minimal increase of vector boson scattering tree amplitudes as a function of the energy. The results are compared with theSU(2) _L ×U(1) _Y predictions for the cases of a light and a heavy Higgs boson. We find that the crosssection for the production of a vector boson pair,VV′, is very sensitively dependent on the magnitude of the single free parameter, κ, the anomalous magnetic dipole moment of theW ^±. The cross-section changes by approximately one order of magnitude, even near production threshold, if κ is varied by one unit around theSU(2) _L ×U(1) _Y value of κ=1.