Spin Bases Research Articles

Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states

In the presence of an electromagnetic background plane wave field, electron, positron, and photon states are not stable because electrons and positrons emit photons and photons decay into electron-positron pairs. This decay of the particle states leads to an exponential damping term in the probabilities of single nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. In this paper, we investigate analytically and numerically the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the particle states' decay. For this, we first compute spin- and polarization-resolved expressions of the probabilities, provide some of their asymptotic behaviors, and show that the results of the total probabilities are independent of the spin and polarization bases. Then, we present several plots of the total and differential probabilities for different pulse lengths and for different spin and polarization quantum numbers. We observe that it is crucial to take into account the damping of the states in order for the probabilities to stay always below unity, and we show that the damping factors also scale with the intensity and pulse duration of the background field. In the case of nonlinear Compton scattering, we show numerically that the total probability behaves like a Poissonian distribution in the regime where the photon recoil is negligible. In all considered cases, the kinematic conditions are such that the final particles momenta transverse to the propagation direction of the plane wave are always much smaller than the particles longitudinal momenta and the main spread of the momentum distribution on the transverse plane is along the direction of the plane wave electric field.

Novel Coupled Channel Framework Connecting the Quark Model and Lattice QCD for the Near-threshold Ds States

A novel framework is proposed to extract near-threshold resonant states from finite-volume energy levels of lattice QCD and is applied to elucidate structures of the positive parity D_{s}. The quark model, the quark-pair-creation mechanism and D^{(*)}K interaction are incorporated into the Hamiltonian effective field theory. The bare 1^{+} cs[over ¯] states are almost purely given by the states with heavy-quark spin bases. The physical D_{s0}^{*}(2317) and D_{s1}^{*}(2460) are the mixtures of bare cs[over ¯] core and D^{(*)}K component, while the D_{s1}^{*}(2536) and D_{s2}^{*}(2573) are almost dominated by bare cs[over ¯]. Furthermore, our model reproduces the clear level crossing of the D_{s1}^{*}(2536) with the scattering state at a finite volume.

How to construct self/anti-self charge conjugate states for higher spins? Significance of the spin bases, mass dimension, and all that

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2, 0)⊕(0, 1/2) representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problems of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. The corresponding dynamical equations are presented. In the (1/2, 0) ⊕ (0, 1/2) representation they obey the Diraclike equation with eight components, which has been first introduced by Markov. Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino). The particular attention has been paid to the questions of chirality and helicity (two concepts which are frequently confused in the literature) for Dirac and Majorana states, and to the normalization (“the mass dimension”). We further review several experimental consequences which follow from the previous works of M. Kirchbach et al. on neutrinoless double beta decay, and G.J. Ni et al. on meson lifetimes. The results are generalized for spins 1, 3/2 and 2.

Generalized top-spin analysis and new physics ine+e−collisions with beam polarization

A generalized top-spin analysis proposed some time ago in the context of the standard model and subsequently studied in varying contexts is now applied primarily to the case of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}t\overline{t}$ with transversely polarized beams. This extends our recent work with new physics couplings of scalar ($S$) and tensor ($T$) types. We carry out a comprehensive analysis assuming only the electron beam to be transversely polarized, which is sufficient to probe these interactions, and also eliminates any azimuthal angular dependence due to the standard model or new physics of the vector ($V$) and axial-vector ($A$) type interactions. We then consider new physics of the general four-Fermi type of $V$ and $A$ type with both beams transversely polarized and discuss implications with longitudinal polarization as well. The generalized spin bases are all investigated in the presence of either longitudinal or transverse beam polarization to look for appreciable deviation from the SM prediction in case of the new physics. 90% confidence level limits are obtained on the interactions for the generalized spin bases with realistic integrated luminosity. In order to achieve this we present a general discussion based on helicity amplitudes and derive a general transformation matrix that enables us to treat the spin basis. We find that beamline basis combined with transverse polarization provides an excellent window of opportunity both for $S$, $T$ and $V$, $A$ new physics, followed by the off-diagonal basis. The helicity basis is shown to be the best in case of longitudinal polarization to look for new physics effects due to $V$ and $A$.

Angular correlations int-channel single top production at the LHC

When a top quark decays there is a large amount of angular correlation, in its rest frame, between its spin orientation and the direction of flight of the charged lepton from its decay. In this paper we investigate the prospects of measuring this angular correlation using the MC@NLO framework. The strength of the correlation is investigated for different spin bases. The robustness against variation of parton distribution function sets and uncertainties, factorization scale dependence, center-of-mass energy, and the jet $R$-parameter is also examined.

Bases for spin systems and qudits from angular momentum theory

Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from angular momentum and Lie algebraic methods. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU ( 2 ) . Such a decomposition leads to a Weyl pair which can be used as an integrity basis for constructing a generalized Pauli group and the Lie algebra of the unitary group U ( d ) . The case where d is a prime integer yields a maximal set of d + 1 mutually unbiased bases. Numerous examples are given for d = 2 , 3 and 4.

TOP QUARK SPIN POLARIZATION IN eγ COLLISION

We investigate the degree of spin polarization of single top quarks in the eγ collision via the process [Formula: see text] with center-of-mass energies [Formula: see text], 1 and 1.5 TeV of the parental linear e+e- collider. Dominant spin fractions and spin asymmetries for the various top quark spin bases are investigated. We show that e+-beam direction is the favorite top quark spin decomposition axis. It is found to be comparable with the ones in pp and ep collisions.

Generalized Spin Bases for Quantum Chemistry and Quantum Information

Symmetry-adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation. Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mutually unbiased bases in the case where the dimension d of the considered Hilbert subspace is a prime number. We also give the starting point for studying the case where d is the power of a prime number. A connection of this work to the unitary group U(d) and the Pauli group is briefly underlined.

Coherent optical control of semiconductor quantum dots for quantum information processing

Coherent optically driven semiconductor quantum dot systems are proposed for the implementation of quantum information processing devices. Qubits defined in the exciton and spin bases are presented. In particular, single qubit rotation and a two-qubit logic gate have been demonstrated experimentally in the model exciton system. The experimental work done on the exciton system serves as a foundation for future work on spin-based qubits, which possess a much longer coherence lifetime.

Centers of mass and rotational kinematics for the relativistic N-body problem in the rest-frame instant form

A relativistic kinematics for the N-body problem which solves all the problems raised until now on this topic is constructed by exploting the Wigner-covariant rest-frame instant form of dynamics in the context of parametrized Minkowski theories. The Wigner hyperplanes, orthogonal to the total timelike four-momentum of any N-body configuration, define the intrinsic rest frame and realize the separation of the center-of-mass motion. The point chosen as origin in each Wigner hyperplane can be made to coincide with the covariant noncanonical Fokker–Pryce center of inertia. As is well known, the latter is distinct from the canonical pseudo- four-vector describing the decoupled motion of the center of mass (which possess the same Euclidean covariance as the quantum Newton–Wigner three-position operator) and from the noncanonical pseudo-four-vector known as Møller’s center of energy. Our approach leads to the splitting of the notion of center of mass into an external one, defined in terms of an external Poincaré group realization, and an internal one defined in terms of an internal unfaithful realization of the group inside the Wigner hyperplane. Because of the first class constraints defining the rest frame (vanishing of the internal three-momentum), the latter three internal concepts of center of mass weakly coincide. The resulting unique internal center of mass is thereby a gauge variable which, by a suitable gauge fixing, can be localized at the origin of the Wigner hyperplane. An adapted canonical basis of relative variables is constructed by means of the classical counterpart of the Gartenhaus–Schwartz transformation. The invariant mass of the N-body configuration is the Hamiltonian for the relative motions. Within this general framework, the rotational kinematics can be developed in terms of the same dynamical body frames, orientation-shape variables, spin frame, and canonical spin bases already introduced in the case of the nonrelativistic N-body problem.

Dynamical body frames, orientation-shape variables and canonical spin bases for the nonrelativistic N-body problem

After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the nonrelativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of body frame for deformable bodies. This basis is adapted to the rotation group SO(3), whose canonical realization is associated with a symmetry Hamiltonian left action. The analysis of the SO(3) coadjoint orbits contained in the N-body phase space implies the existence of a spin frame for the N-body system. Then, the existence of appropriate nonsymmetry Hamiltonian right actions for nonrigid systems leads to the construction of an N-dependent discrete number of dynamical body frames for the N-body system, hence to the associated notions of dynamical and measurable orientation and shape variables, angular velocity, rotational and vibrational configurations. For N=3 the dynamical body frame turns out to be unique and our approach reproduces the xxzz gauge of the gauge theory associated with the orientation-shape SO(3) principal bundle approach of Littlejohn and Reinsch. For N⩾4 our description is different, since the dynamical body frames turn out to be momentum dependent. The resulting Darboux bases for N⩾4 are connected to the coupling of the spins of particle clusters rather than the coupling of the centers of mass (based on Jacobi relative normal coordinates). One of the advantages of the spin coupling is that, unlike the center-of-mass coupling, it admits a relativistic generalization.

Top-quark spin correlation at linear colliders with anomalous couplings

We investigate the feasibility of probing anomalous top-quark couplings of $Wtb$, $Z t \bar{t}$, and $\gamma t \bar{t}$ in terms of an effective Lagrangian with dimension-six operators at future $e^+e^-$ linear colliders with a c. m. energy $\sqrt s \sim 500-800$ GeV. We first examine the constraints on these anomalous couplings from the $Z\to b \bar{b}$ data at LEP I and from unitarity considerations. We then consider in detail the effects of anomalous couplings on $t \bar{t}$ spin correlations in the top-pair production and decay with three spin bases: the helicity, beamline and off-diagonal bases. Our results show that the polarized beams are more suitable for exploring the effects of different new operators. For polarized beams, the helicity basis yields the best sensitivity.

Top-quark spin correlations at hadron colliders: predictions at next-to-leading order QCD.

The collider experiments at the Tevatron and the LHC will allow for detailed investigations of the properties of the top quark. This requires precise predictions of the hadronic production of tt pairs and of their subsequent decays. In this Letter we present for the reactions pp, pp-->tt+X-->l+l'-+X the first calculation of the dilepton angular distribution at next-to-leading order in the QCD coupling, keeping the full dependence on the spins of the intermediate tt state. The angular distribution reflects the degree of correlation of the t and t spins which we determine for different choices of t and t spin bases. In the case of the Tevatron, the QCD corrections are sizable, and the distribution is quite sensitive to the parton content of the proton.

Single top quark production at the LHC: Understanding spin

We show that the single top quarks produced in the Wg-fusion channel at a proton-proton collider at a center-of-mass energy s =14 TeV posses a high degree of polarization in terms of a spin basis which decomposes the top quark spin in its rest frame along the direction of the spectator jet. A second useful spin basis is the η-beamline basis, which decomposes the top quark spin along one of the two beam directions, depending on which hemisphere contains the spectator jet. We elucidate the interplay between the two- and three-body final states contributing to this production cross section in the context of determining the spin decomposition of the top quarks, and argue that the zero momentum frame helicity is undefined. We show that the usefulness of the spectator and η-beamline spin bases is not adversely affected by the cuts required to separate the Wg-fusion signal from the background.

Optimal spin basis in polarized photon linear colliders

We analyze the spin correlations of the top quark pairs produced at photon linear colliders. We employ the circular polarized photon beams and general spin basis for the top quark pair. We consider general spin bases to find a strong spin correlation between the produced top quark and top antiquark. We show the cross sections in these bases and discuss the characteristics of the results.

Maximizing spin correlations in top quark pair production at the Tevatron

A comparison is made between the off-diagonal and helicity spin bases for top quark pair production at the FNAL Tevatron. In the off-diagonal basis, 92% of the top quark pairs are in the spin configuration up-down plus down-up, whereas in the helicity basis only 70% are left-right plus right-left. The off-diagonal basis maximizes the spin asymmetry and hence the measured angular correlations between the decay products, which are more than twice as big in this basis as compared to the helicity basis. In addition, for the process q qbar --> t tbar, we give a very simple analytic expression for the matrix element squared which includes all spin correlations between the production and subsequent decay of the top quarks.

Modern valence bond theory

The spin-coupled (SC) theory of molecular electronic structure is introduced as the modern development of classical valence bond (VB) theory. Various important aspects of the SC wave function are described. Attention is particularly focused on the construction and properties of different sets of N-electron spin function in different spin bases, such as the Kotani, Rumer and Serber. Applications of the SC description to a range of different kinds of chemical problems are presented, beginning with simple examples: the H2 and CH4 molecules. This is followed by the description offered by the SC wave function of more complex situations such as the insertion reaction of H2 into CH2(1A1), the phenomenon of hypervalence as displayed by molecules such as diazomethane, CH2N2, SF6 and XeF2. The SC description of the ground and excited states of benzene is briefly surveyed. This is followed by the SC description of antiaromatic systems such as C4H4 and related molecules.

Efficient evaluation of the algebrants of VB wave functions using the successive expansion method. I. SpinS = 0, �

An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 245–259, 1997

SPINS: A collection of algorithms for symbolic generation and transformation of many-electron spin eigenfunctions

SPINS represents a collection of algorithms intended to provide an efficient, robust and easy-to-use quantum-chemical toolbox capable of performing a wide range of operations on spin eigenfunctions in the Rumer, Kotani and Serber spin bases. It includes routines for symbolic generation of the Rumer spin eigenfunctions as linear combinations of elementary spin products, for computing all transformation matrices relating the Rumer, Kotani and Serber spin bases and for calculation of the matrices of the irreducible representations of the symmetric group carried by the Rumer, Kotani and Serber spin eigenfunctions, as well as facilities for interpreting general spin-coupling patterns such as those used in spin-coupled theory. The resulting codes, written in Fortran-77 and available on the Internet (from P.B.Karadakov@Bristol.AC.UK or DLC@Liverpool.AC.UK) are so compact and efficient that they even run on IBM PC-compatible personal computers.

On the role of different spin bases within spin-coupled theory

The essential role played by different bases of spin eigenfunctions within spin-coupled theory is reviewed. Efficient methods are described for transforming a given set of spin-coupled coefficients between the Kotani, the Rumer and the Serber bases. The important physical and chemical insight into problems which is obtained by the use of different types of spin function is illustrated by several examples. It is shown that the Serber basis is particularly effective in this respect. In one case this leads to the prediction of an organic polymer which is antiferromagnetic.