The Ruds value in the vicinity of ψ(3770) state

The anomalous line shape of the ψ(3770) state has resulted in some difficulty in the determination of the R value for the continuum light hadron production in the resonance energy range. We parameterize the asymmetric line shape using a Fano-type formula and extract the Ruds value to be 2.156±0.022 from the data of BESIII Collaboration in the energy region between 3.650 and 3.872 GeV. The small discrepancy between experiment and theory is removed. The cross sections of the e+e−→hadrons with continuum light hadron production subtracted are given and compared to the data of the e+e−→DD¯ reaction

Anomalous properties of spin-extended chiral fermions

The spin-extended semiclassical chiral fermion (we call the S-model), which had been used to derive the twisted Lorentz symmetry of the “spin-enslaved” chiral fermion (we call the c-model) is equivalent to the latter in the free case, however coupling to an external electromagnetic field yields nonequivalent systems. The difference is highlighted by the inconsistency of spin enslavement within the spin-extended framework. The S-model exhibits nevertheless similar though slightly different anomalous properties as the usual c-model does. The natural Poincaré symmetry of the free model remains unbroken if the Pfaffian invariant vanishes, i.e., when the electric and magnetic fields are orthogonal, E⋅B=0 as in the Hall effect

Nuclear force and the EMC effect

A linear correlation is shown quantitatively between the magnitude of the EMC effect measured in electron deep inelastic scattering (DIS) and the nuclear residual strong interaction energy (RSIE) obtained from nuclear binding energy subtracting the Coulomb energy contribution. This phenomenological relationship is used to extract the size of in-medium correction (IMC) effect on deuteron and to predict the EMC slopes |dREMC/dx| of various nuclei. We further investigate the correlations between RSIE and other quantities which are related to the EMC effect. The observed correlations among RSIE, EMC slope and SRC ratio R2NNtotal/Nnp(S13) imply that the local nuclear environment drives the modification of quark distributions

Deformation relaxation in heavy-ion collisions

In deeply inelastic heavy-ion collisions, the quadrupole deformations of both fragments are taken as stochastic independent dynamical variables governed by the Fokker–Planck equation (FPE) under the corresponding driving potential. The mean values, variances and covariance of the fragments are analytically expressed by solving the FPE in head on collisions. The characteristics and mechanism of the deformation are discussed. It is found that both the internal structures and interactions of the colliding partners are critical for the deformation relaxation in deeply inelastic collisions

Exact spectrum of the spin- s Heisenberg chain with generic non-diagonal boundaries

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su (2) algebra by employing the spin- s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the fusion techniques, certain closed operator identities for constructing the functional T − Q relations and the Bethe ansatz equations are derived. It is found that a variety of inhomogeneous T − Q relations obeying the operator product identities can be constructed. Numerical results for two-site s = 1 case indicate that an arbitrary choice of the derived T − Q relations is enough to give the complete spectrum of the transfer matrix

Bethe states of the XXZ spin- 12 chain with arbitrary boundary fields

Based on the inhomogeneous T−Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin- 12 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T−Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations

Off-diagonal Bethe Ansatz solution of the τ 2 -model

The generic quantum τ 2 -model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in τ j -hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T − Q relation with polynomial Q -functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T − Q relation does indeed give the complete spectrum

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method

Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

In two previous papers [26,27] , the exact solutions of the spin- <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math> chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi><mo>=</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>m</mi></mrow></msub></math> , the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary η case with <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo stretchy="false">(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></math> corrections in the thermodynamic limit <math altimg="si4.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo stretchy="false">→</mo><mo>∞</mo></math> . As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models

Nested off-diagonal Bethe ansatz and exact solutions of the su ( n ) spin chain with generic integrable boundaries

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su ( n )-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T − Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices