The X ± and Y ± bosons are defined respectively as the six Q = ± 4 / 3 and the six Q = ± 1 / 3 components of the final two terms of the adjoint 24 representation of SU(5) as it transforms under the standard model's group:Ģ4 → ( 8, 1 ) 0 ⊕ ( 1, 3 ) 0 ⊕ ( 1, 1 ) 0 ⊕ ( 3, 2 ) − 5 6 ⊕ ( 3 ¯, 2 ) 5 6 X bosons rotate between a color index and the weak isospin-up index, while Y bosons rotate between a color index and the weak isospin-down index. Quantum jump from Planck to Planck as you build up speed inside an enormous particle accelerator and generate. Once in the tunnel, do your best to land. Each platform gets higher until ending at an awkwardly shaped tunnel. Back and Forth A simple but rare pattern, all you need to do is jump left and right along the platforms between the walls. − pair is created out of energy, and they follow the two branches described above: Boson X is a fast-paced rotational runner set in a particle accelerator. Notably, this level has the most Scatter pattern variants, and is tied with X Boson for the most patterns, at 9. Different branching ratios between the X boson and its antiparticle (as is the case with the K-meson) would explain baryogenesis. In these reactions, neither the lepton number ( L) nor the baryon number ( B) is separately conserved, but the combination B − L is. Similar decay products exist for the other quark-lepton generations. The first product of each decay has left-handed chirality and the second has right-handed chirality, which always produces one fermion with the same handedness that would be produced by the decay of a W boson, and one fermion with contrary handedness ("wrong handed"). Where the two decay products in each process have opposite chirality,Ī Y boson would have the following three decay modes: : 442 Since some grand unified theories such as the Georgi–Glashow model predict a half-life less than this, then the existence of X and Y bosons, as formulated by this particular model, remain hypothetical.Īn X boson would have the following two decay modes: : 442 However, the Super-Kamiokande has put a lower bound on the proton's half-life as around 10 34 years. Significantly, the X and Y bosons couple quarks (constituents of protons and others) to leptons (such as positrons), allowing violation of the conservation of baryon number thus permitting proton decay. Since the X and Y boson mediate the grand unified force, they would have unusual high mass, which requires more energy to create than the reach of any current particle collider experiment. In particle physics, the X and Y bosons (sometimes collectively called " X bosons" : 437 ) are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a unified force predicted by the Georgi–Glashow model, a grand unified theory (GUT). Y: two quarks, or one antiquark and one charged antilepton, or one antiquark and one antineutrino X: two quarks, or one antiquark and one charged antilepton For mesons with the same names, see XYZ particle. a simultaneous eigenvector of $\mathbf, m_s)$ and for your first excited state, either $X$ symmetric if $\Phi$ is symmetric, or any anti-symmetric $X(s=1,m_s)$ if $\Phi$ is anti-symmetric.This article is about bosons of a hypothetical new interaction. But I'm confused because I am asked to "choose the spin part of the wave function, $\,\chi(m_1,m_2)$, to be an eigenvector of total spin, i.e. I used a Clebsch-Gordon table to find the 9 $\,\chi(s,m)$ states in terms of $\,\chi(m_1,m_2)$ for $s=0,1,2.$ In addition, I found the $s=0,2$ states to be symmetric, and the $s=1$ state to be antisymmetric, so I figure the rest shouldn't be hard.
The spatial part of the wave function is easy to construct, but I'm having trouble with the spin part $\,\chi(m_1,m_2).$ I know that both states are degenerate and the spatial and spin parts of the wave functions must both be either symmetric or antisymmetric. I'm trying to find the ground state and first excited state for 2 identical bosons in an infinite square well.
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