New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

Selectron Studies at e-e- and e+e- Colliders

Selectrons may be studied in both e-e- and e+e- collisions at future linear colliders. Relative to e+e-, the e-e- mode benefits from negligible backgrounds and \beta threshold behavior for identical selectron pair production, but suffers from luminosity degradation and increased initial state radiation and beamstrahlung. We include all of these effects and compare the potential for selectron mass measurements in the two modes. The virtues of the e-e- collider far outweigh its disadvantages. In particular, the selectron mass may be measured to 100 MeV with a total integrated luminosity of 1 fb^-1, while more than 100 fb^-1 is required in e+e- collisions for similar precision.Comment: 16 pages, 11 figure

Examining the Higgs boson potential at lepton and hadron colliders: a comparative analysis

We investigate inclusive Standard Model Higgs boson pair production at lepton and hadron colliders for Higgs boson masses in the range 120 GeV < m_H < 200 GeV. For m_H < 140 GeV we find that hadron colliders have a very limited capability to determine the Higgs boson self-coupling, \lambda, due to an overwhelming background. We also find that, in this mass range, supersymmetric Higgs boson pairs may be observable at the LHC, but a measurement of the self coupling will not be possible. For m_H > 140 GeV we examine ZHH and HH nu bar-nu production at a future e+e- linear collider with center of mass energy in the range of sqrt{s}=0.5 - 1 TeV, and find that this is likely to be equally difficult. Combining our results with those of previous literature, which has demonstrated the capability of hadron and lepton machines to determine \lambda in either the high or the low mass regions, we establish a very strong complementarity of these machines.Comment: Revtex, 25 pages, 2 tables, 10 figure

Determining the Higgs Boson Self Coupling at Hadron Colliders

Inclusive Standard Model Higgs boson pair production at hadron colliders has the capability to determine the Higgs boson self-coupling, lambda. We present a detailed analysis of the gg\to HH\to (W^+W^-)(W^+W^-)\to (jjl^\pm\nu)(jj{l'}^\pm\nu) and gg\to HH\to (W^+W^-)(W^+W^-)\to (jjl^\pm\nu)({l'}^\pm\nu {l''}^\mp\nu) (l, {l'}, {l''}=e, \mu) signal channels, and the relevant background processes, for the CERN Large Hadron Collider, and a future Very Large Hadron Collider operating at a center-of-mass energy of 200 TeV. We also derive quantitative sensitivity limits for lambda. We find that it should be possible at the LHC with design luminosity to establish that the Standard Model Higgs boson has a non-zero self-coupling and that lambda / lambda_{SM} can be restricted to a range of 0-3.8 at 95% confidence level (CL) if its mass is between 150 and 200 GeV. At a 200 TeV collider with an integrated luminosity of 300 fb^{-1}, lambda can be determined with an accuracy of 8 - 25% at 95% CL in the same mass range.Comment: 28 pages, Revtex3, 9 figures, 3 table

Color-Octet J/ψJ/\psi Production in the Υ\Upsilon Decay

The direct production rate of $\psi$ in the $\Upsilon$ decay is shown to be dominated by the process $\Upsilon \to ggg^*$ followed by $g^* \to \psi$ via the color-octet mechanism proposed recently to explain the anomalous prompt charmonium production at the Tevatron. We show that this plausibly dominant process has a branching ratio compatible with the experimental data. Further experimental study in this channel is important to test the significance of the color-octet component of $c\bar c$ pair inside the $\psi$ system.Comment: 20 pages, Standard LaTeX, 2 figures; a couple of new processes added, but conclusion unchange

Determination of color-octet matrix elements from e^+e- process at low energies

We present an analysis of the preliminary experimental data of direct j/psi production in e^e- process at low energies. We find that the color-octet contributions are crucially important to the cross section at this energy region, and their inclusion produces a good description of the data. By fitting to the data, we extract the individual values of two color-octet matrix elements: \approx 1.1\times 10^{-2} GeV^3, <{\cal O}_8^{\psi}(^3P_0)> m_c^2\approx 7.4\times 10^{-3}GeV^3. We discuss the allowed range of the two matrix elements constrained by the theoretical uncertainties. We find that is poorly determined because it is sensitive to the variation of the choice of m_c, \alpha_s and <{\cal O}_1^{\psi}(^3S_1)>. However m_c^2 is quite stable (about (6-9)\times 10^{-3}GeV^3) when the parameters vary in reasonable ranges. The uncertainties due to large experimental errors are also discussed.Comment: 13 page, RevTex, 2 figures in postscript. To appear in Phys. Rev.

Complementarity of the CERN Large Hadron Collider and the e+e−e^+e^- International Linear Collider

The next-generation high-energy facilities, the CERN Large Hadron Collider (LHC) and the prospective $e^+e^-$ International Linear Collider (ILC), are expected to unravel new structures of matter and forces from the electroweak scale to the TeV scale. In this report we review the complementary role of LHC and ILC in drawing a comprehensive and high-precision picture of the mechanism breaking the electroweak symmetries and generating mass, and the unification of forces in the frame of supersymmetry.Comment: 14 pages, 17 figures, to be published in "Supersymmetry on the Eve of the LHC", a special volume of European Physical Journal C, Particles and Fields (EPJC) in memory of Julius Wes

A Phenomenological Analysis of Gluon Mass Effects in Inclusive Radiative Decays of the J/ψ\rm{J/\psi} and $\Upsilon

The shapes of the inclusive photon spectra in the processes \Jp \to \gamma X and \Up \to \gamma X have been analysed using all available experimental data. Relativistic, higher order QCD and gluon mass corrections were taken into account in the fitted functions. Only on including the gluon mass corrections, were consistent and acceptable fits obtained. Values of $0.721^{+0.016}_{-0.068}$ GeV and $1.18^{+0.09}_{-0.29}$ GeV were found for the effective gluon masses (corresponding to Born level diagrams) for the \Jp and \Up respectively. The width ratios \Gamma(V \to {\rm hadrons})/\Gamma(V \to \gamma+ {\rm hadrons}) V=\Jp, \Up were used to determine $\alpha_s(1.5 {\rm GeV})$ and $\alpha_s(4.9 {\rm GeV})$. Values consistent with the current world average $\alpha_s$ were obtained only when gluon mass correction factors, calculated using the fitted values of the effective gluon mass, were applied. A gluon mass $\simeq 1$ GeV, as suggested with these results, is consistent with previous analytical theoretical calculations and independent phenomenological estimates, as well as with a recent, more accurate, lattice calculation of the gluon propagator in the infra-red region.Comment: 50 pages, 11 figures, 15 table

Inclusive Charmonium Production via Double ccˉc \bar c in e+e−e^+e^- Annihilation

Motivated by the recent observation of double charm quark pair production by the Belle Collaboration, we calculate the complete ${\cal O}(\alpha_{s}^{2})$ inclusive production cross sections for $\eta_{c}$, $J/\psi$, and $\chi_{cJ}$(J=0, 1, 2) plus $c\bar{c}$ in $e^+ e^-$ annihilation through a virtual photon. We consider both color-singlet and color-octet contributions, and give the analytical expressions for these cross sections. The complete color-singlet calculations are compared with the approximate fragmentation calculations as functions of the center-of-mass energy $\sqrt{s}$. We find that most of the fragmentation results substantially overestimate the cross sections (e.g. by a factor of $\sim$4 for $\chi_{c1}$ and $\chi_{c2}$) at the Belle and BaBar energy $\sqrt{s}=10.6$GeV. The fragmentation results become a good approximation only when $\sqrt{s}$ is higher than about 100GeV. We further calculate the color-octet contributions to these cross sections with analytical expressions. We find that while the color-octet contribution to $J/\psi$ inclusive production via double charm is negligible (only about 3%), the color-octet contributions to $\chi_{c1}$ and $\chi_{c2}$ can be significant.Comment: 23 pages, 9 figures; color-octet contributions to the double charm inclusive production of J/psi and chi_{cJ} (J=0,1,2) are added; references are added; No change for the color-singlet par

Inclusive quarkonium production

In the approximation of zero binding energy, the production of the heavy vector quarkonium states V(= psi, T,...) accompanied with gluon (g) jets in ..gamma..N and e/sup +/e/sup -/ collisions is studied. For the rare decay of the Z/sup 0/ resonance into Vgg, the rate is found extremely small