arXiv subjects

Charles A. Nelson

Publications and source records attributed to Charles A. Nelson.

At least 19 recordsLinked to original sources

arXiv2019

Generalized Ray Spaces for Paraparticles

Paraparticles of order p = 2 must be pair produced, so the least massive are absolutely stable. Consequently, paraparticles are excellent candidates to be associated with dark matter and/or dark energy. For a fixed number of paraparticles, in a "generalized ray space" there are simple orthonormal bracket "ray representatives" constructed from paraparticle creation operators. Each such ray representative is associated with a Young Diagram with a unique "P-bar-sum" eigenvalue. "P-bar-sum" is the sum of the particle-exchange operators which exchange two identical particles. In this paper, by using totally symmetric and totally antisymmetric brackets, generalized ray spaces for order p=2 are constructed for parabosons (pB), for parafermions (pB), and for possible para-Families (pFam). Para-Families occur in the case of non-commuting pB and pF creation operators. Explicit arbitrary order p ray representatives for a few paraparticles may be useful to establish the order p if, indeed, dark matter and/or dark energy is discovered to exhibit parastatistic properties. Up to p identical pB's (pF's) can occupy a totally antisymmetric (symmetric) state, unlike for normal boson (fermion) statistics.

physics.gen-ph↗

arXiv2016

Diagrams and Parastatistical Factors for Cascade Emission of a Pair of Paraparticles

The empirical absence to date of particles obeying parastatistics in high energy collider experiments might be due to their large masses, weak scale couplings, and lack of gauge couplings. Paraparticles of order p=2 must be pair produced, so the lightest such particles are absolutely stable and so are excellent candidates to be associated with dark matter and/or dark energy. If there is a portal to such particles, from a new scalar A1 boson they might be cascade emitted as a pair of para-Majorana neutrinos as in A1 ---> A2 para-nu para-nu or as a pair of neutral spin-zero paraparticles such as in A1 ---> A2 para-A para-B, where para-B is the anti-paraparticle to para-A. In this paper, for an assumed supersymmetric-like "statistics portal" Lagrangian, the associated connected tree diagrams and their parastatistical factors are obtained for the case of order p=2 parastatistics. These factors are compared with the corresponding statistical factors for the analogous emission of a non-degenerate or a 2-fold degenerate pair which obey normal statistics. This shows that diagrams, and diagrammatic thinking, can be use in perturbatively analyzing paraparticle processes. The parastatistical factor associated with each diagram does require explicit calculation.

hep-ph↗

arXiv2013

Parastatistical Factors for Cascade Emission of a Pair of Paraparticles

The empirical absence to date of particles obeying parastatistics in high energy collider experiments might be due to their large masses and lack of gauge couplings. If there is a portal to such particles, they might be cascade emitted as a pair of para-Majorana neutrinos or as a pair of scalar paraparticles. In this paper, for an assumed portal Lagrangian, the associated parastatistical factors are obtained for the case of order p=2 parastatistics and the, in general differing factors, for the cases of emission of a non-degenerate or a degenerate pair of particles which obey normal statistics.

hep-ph↗

arXiv2008

A New Kind of Weak-Coupling in Top-Quark Physics ?

In the standard model, for the t --> W b decay mode, the relative phase is 0-degrees between the dominant A(0,-1/2) and A(-1, -1/2) helicity amplitudes. However, in the case of an additional large t_R --> b_L chiral weak-transition moment, there is instead a 180-degree relative phase and three theoretical numerical puzzles. This phase can be measured at the Tevatron or LHC in top-antitop pair production by use of W-boson longitudinal-transverse interference in beam-referenced stage-two spin-correlation functions. Indeed, this is a new type of weak-coupling for it is directly associated with E_W, the W-boson energy in the top quark rest frame, instead of with a canonical effective mass scale. For most 2 --> 2 reactions, the simple off-shell continuation of this additional coupling is found to have good high energy properties, i.e. it does not destroy 1-loop unitarity of the SM. In a subset of processes, additional third-generation couplings are required.

hep-ph↗

arXiv2006

Hanbury-Brown and Twiss Intensity Correlations of Parabosons

This paper shows that in intensity correlation measurements there will be clear and unambiguous signals that new-physics particles are, or aren't, parabosons. For a parabosonic field in a dominant single-mode, there is a diagonal P-representation in the "even and odd coherent states" basis. It is used to analyze zero-time-interval intensity correlations of parabosons in a maximum-entropic state. As the mean number of parabosons decreases, there is a monotonic reduction to (2/p) of the constant bosonic ``factor of two'' proportionality of the second-order versus the squared first-order intensity correlation function.

math-ph↗

arXiv2006

Use of W-Boson Longitudinal-Transverse Interference in Top Quark Spin-Correlation Functions: II

This continuation of the derivation of general beam-referenced stage-two spin-correlation functions is for the analysis of top-antitop pair-production at the Tevatron and at the Large Hadron Collider. Both the gluon-production and the quark-production contributions are included for the charged-lepton-plus-jets reaction p p or p bar{p} --> t bar{t} --> (W^+ b)(W^- bar{b}) --> (l^{+} nu b)(W^- bar{b}). There is a simple 4-angle beam-referenced spin-correlation function for determination of the relative sign of, or for measurement of a possible non-trivial phase between the two dominant helicity amplitudes for t --> W^{+} b decay. There is an analogous function and tests for bar{t} --> W^{-} bar{b} decay. This signature requires use of the (t bar{t}) c.m.-energy of the hadronically decaying W-boson, or the kinematically equivalent cosine of the polar-angle of W-boson emission in the anti-top (top) decay frame. Spinors and their outer-products are constructed so that the helicity-amplitude phase convention of Jacob & Wick can be used throughout for the fixing of the signs associated with this large W-boson longitudinal-transverse interference effect.

hep-ph↗

arXiv2005

Use of W-Boson Longitudinal-Transverse Interference in Top Quark Spin-Correlation Functions

Most of this paper consists of the derivation of general beam-referenced stage-two spin-correlation functions for the analysis of top-antitop pair-production at the Tevatron, at the Large Hadron Collider, and/or at an International Linear Collider. However, for the charged-lepton-plus-jets reaction $q \bar{q} \to t \bar{t} \to (W^+ b) (W^- \bar{b}) \to (l^{+} νb) (W^- \bar{b})$, there is a simple 3-angle spin-correlation function for determination of the relative sign of, or for measurement of a possible non-trivial phase between the two dominant $λ_b = -1/2 $ helicity amplitudes for the $t\to W^{+}b$ decay mode. For the CP-conjugate case, there is an analogous function and tests for $\bar{t} \to W^{-} \bar{b}$ decay. These results make use of W-boson longitudinal-transverse interference.

hep-ph↗

arXiv2004

On an Intensity-Ratio Equivalence for Two Top-Quark Decay Couplings

For the t --> W b decay mode, an intensity-ratio equivalence for two distinct Lorentz-invariant couplings is shown to be a consequence of symmetries of tWb-transformations. Three explicit tWb-transformations connect the four standard model's (SM) helicity amplitudes and the amplitudes in the case of an additional chiral-tensorial-coupling of relative strength 53 GeV. Such a coupling will arise if there is a large t_R --> b_L chiral weak-transition-moment. Two commutator plus anti-commutator symmetry algebras are generated from the 3 transformation matrices. Using these transformations, the associated mass scales are related to the SM's electroweak scale v_EW = 246GeV$.

hep-ph↗

arXiv2004

Tests for the Statistics of Pair-Produced New Particles

Due to selection rules, new particles are sometimes discovered/predicted to be produced in pairs. In the current search for SUSY particles this will occur if R-parity is conserved. In local relativistic field theory, there can be identical particles which are neither bosons nor fermions which are associated with higher-dimensional representations of the permutation group. Such particles will generally be pair-produced and so empirical tests are required to exclude them. A parameter-free statistical model is used to study the unusual multiplicity signatures in coherent paraboson production versus the case of ordinary bosons.

hep-ph↗

arXiv2004

Coherent Production of Pairs of Parabosons of Order 2

A parameter-free statistical model is used to study multiplicity signatures for coherent production of charged-pairs of parabosons of order p=2 in comparison with those arising in the case of ordinary bosons, p=1. Two non-negative real parameters arise because "ab" and "ba" are fundamentally distinct pair operators of charge "+1", A-quanta and charge "-1", B-quanta parabosons. In 3D plots of P(q)_m = "The probability of m paraboson charged-pairs and q positive parabosons" versus < n > and < n^2 >, the p=1 curve is found to lie on the relatively narrow 2D p=2 surface.

hep-ph↗

arXiv2004

On an Intensity-Ratio Equivalence-Theorem for Top Quark Decay

For the " t --> W b " decay mode, an intensity-ratio equivalence-theorem for two Lorentz-invariant couplings is shown to be related to symmetries of tWb-transformations. Explicit tWb-transformations, A_{+}=M A_{SM}, P A_{SM}, B A_{SM} relate the four standard model's helicity amplitudes and those in the case of an additional " t_R --> b_L " weak-moment of relative strength " Lambda_{+} =E_W /2 = 53 GeV ". Two commutator plus anti-commutator symmetry algebras are generated from M, P, B. These transformations enable a characterization of the associated mass scales.

hep-ph↗

arXiv2003

On the Top Quark's Chiral Weak-Moment

For the observed t --> W b decay, an intensity-ratio equivalence-theorem for two Lorentz-invariant couplings is shown to be related to symmetries of tWb-transformations. Three explicit tWb-transformations, A_{+}=M A_{SM}, ... relate the four standard model's helicity amplitudes, A_{SM}, and the amplitudes A_{+} in the case of an additional t_R --> b_L weak-moment of relative strength Lambda_{+} =E_W /2 = 53 GeV. Two commutator plus anti-commutator symmetry algebras are generated from M, P, B. These transformations enable a simple and uniform characterization of the values of Lambda_{+}, m_W/m_t, and m_b/m_t.

hep-ph↗

arXiv2003

Pairing of Parafermions of Order 2: Seniority Model

As generalizations of the fermion seniority model, four multi-mode Hamiltonians are considered to investigate some of the consequences of the pairing of parafermions of order two. 2-particle and 4-particle states are explicitly constructed for H_A = - G A^+ A with A^+}= 1/2 Sum c_{m}^+ c_{-m}^+ and the distinct H_C = - G C^+ C with C^+}= 1/2 Sum c_{-m}^+ c_{m}^+, and for the time-reversal invariant H_(-)= -G (A^+ - C^+)(A-C) and H_(+) = -G (A^+dagger + C^+)(A+C), which has no analogue in the fermion case. The spectra and degeneracies are compared with those of the usual fermion seniority model.

hep-ph↗

arXiv2003

Consequences of a Large Top-Quark Chiral Weak-Moment

This talk concerns some theoretical patterns of the helicity amplitudes for t --> W b decay. The patterns involve both the standard model's four decay helicity amplitudes, A_{SM}, and also the amplitudes A_{+} in the case of an additional t_R --> b_L tensorial coupling of relative strength Λ_{+} =E_W /2 = 53 GeV. Such an additional electroweak coupling would arise if the observed top-quark has a large chiral weak-transition-moment. The A_{+} amplitudes are interpreted as corresponding to the observed top-quark decays. Three tWb-transformations A_{+}=M A_{SM}, ..., are used in simple characterization of the values of Λ_{+}, and of the mass ratios m_W/m_t, and m_b/m_t. Measurement of the sign of the η_L = +/- 0.46 helicity parameter, respectively for SM/+, due to the large interference between the W-longitudinal and W-transverse amplitudes, could exclude such a chiral weak-transition-moment in favor of the SM prediction.

hep-ph↗

arXiv2001

Three Numerical Puzzles and the Top Quark's Chiral Weak-Moment

Versus the standard model's t --> W b decay helicity amplitudes, three numerical puzzles occur at the 0.1 % level when one considers the amplitudes in the case of an additional (f_M + f_E) coupling of relative strength 53 GeV. The puzzles are theoretical ones which involve the t --> W b decay helicity amplitudes in the two cases, the relative strength of this additional coupling, and the observed masses of these three particles. A deeper analytic realization is obtained for two of them. Equivalent realizations are given for the remaining one. An empirical consequence of these analytic realizations is that it is important to search for effects of a large chiral weak-moment of the top-quark, the effective mass-scale is about 53 GeV. A full theoretical resolution would include relating the origin of such a chiral weak-moment and the mass generation of the top-quark, the W-boson, and probably the b-quark.

hep-ph↗

arXiv2001

On Testing for New Couplings in Top Quark Decay

To quantitatively assay future measurements of competing observables in t --> W b decay, we consider the g_{V-A} coupling values of the helicity decay parameters versus those for "(V-A)+ Single Additional Lorentz Structures". There are 2 dynamical phase-type ambiguities. Associated with the latter (f_M + f_E) ambiguity, there are 3 very interesting numerical puzzles at the 0.1% level. This evidence for the presence of tensorial couplings in t-decay is a consequence of the empirical value of m_W/m_t and the small, but non-zero ratio m_b/m_t. Measurement of the sign of eta_L = 0.46 (SM) due to the large interference between the W longitudinal/transverse amplitudes could exclude such tensorial couplings. Similarly, measurements of eta_L and eta_L^{'} could resolve the case of a partially-hidden T-violation associated with the additional (f_M + f_E) coupling.

hep-ph↗

arXiv2001

Use of Lambda_b Polarimetry in Top Quark Spin-Correlation Functions

Due to the absence of hadronization effects and the large top mass, top quark decay will be uniquely sensitive to fundamental electroweak physics at the Tevatron, at the LHC, and at a future linear collider. A complete measurement of the four helicity amplitudes in top decay is possible by the combined use of Lambda_b and W polarimetry in stage-two spin-correlation functions (S2SC). In this paper, the most general Lorentz-invariant decay density matrix is obtained for the decay sequence (t --> W b) where (b --> l nu c) and (W --> l nu), and likewise for the CP-conjugate mode. These density matrices are expressed in terms of b-polarimetry helicity parameters which enable a unique determination of the relative phases among the helicity amplitudes. Thereby, S2SC distributions and single-sided b-W-interference distributions are expressed in terms of these parameters. The four b-polarimetry helicity parameters involving the A(-1,-1/2) amplitude are considered in detail. Lambda_b polarimetry signatures will not be suppressed in top quark analyses when the final neutrino's angles-and-energy variables are used for (b --> l nu c).

hep-ph↗

arXiv2000

On Measurement of Helicity Parameters in Top Quark Decay

To enable an evaluation of future measurements of the helicity parameters for " t --> W b " decay in regard to " T_FS violation", this paper considers the effects of an additional pure-imaginary coupling, (i g/2 Lambda) or (i g), associated with a specific, single additional Lorentz structure, i = S, P, S + P, ... Sizable " T_FS violation" signatures can occur for low-effective mass scales (< 320 GeV), but in most cases can be more simply excluded by 10% precision measurement of the probabilities P(W_L) and P(b_L). Signatures for excluding the presence of " T_FS violation" associated with the two dynamical phase-type ambiguities are investigated.

hep-ph↗