Greg W. Anderson — Page 2

arXiv1997

A double complex for computing the sign-cohomology of the universal ordinary distribution

We give a new method for solving a problem originally solved about 20 years ago by Sinnott and Kubert, namely that of computing the cohomology of the universal ordinary distribution with respect to the action of the two-element group generated by complex conjugation. We develop the method in sufficient generality so as to be able to calculate analogous cohomology groups in the function field setting which have not previously been calculated. In particular, we are able to confirm a conjecture of L.~S.~Yin conditional on which Yin was able to obtain results on unit indices generalizing those of Sinnott in the classical cyclotomic case and Galovich-Rosen in the Carlitz cyclotomic case. The Farrell-Tate cohomology theory for groups of finite virtual cohomological dimension plays a key role in our proof of Yin's conjecture. The methods developed in the paper have recently been used by P.~Das to illuminate the structure of the Galois group of the algebraic extension of the rational number field generated by the roots of unity and the algebraic $Γ$-monomials. This paper has appeared as Contemp. Math. 224 (1999) 1-27.

math.NT↗

arXiv1992

Collapsing Sub-Critical Bubbles

In the standard scenario, the electroweak phase transition is a first order phase transition which completes by the nucleation of critical bubbles. Recently, there has been speculation that the standard picture of the electroweak phase transition is incorrect. Instead, it has been proposed that throughout the phase transition appreciable amounts of both broken and unbroken phases of $SU(2)$ coexist in equilibrium. I argue that this can not be the case. General principles insure that the universe will remain in a homogenous state of unbroken $SU(2)$ until the onset of critical bubble production.

hep-ph↗

arXiv1992

Precise predictions for mt, Vcb and tan

The fermion mass and mixing angle predictions of a recently proposed framework are investigated for large b and $τ$ Yukawa couplings. A new allowed region of parameters is found for this large $\tan β$ case. The two predictions which are substantially altered, $m_t$ and $\tan β$, are displayed, including the dependence on the inputs $|V_{cb}|$, $m_c$, $m_b$ and $α_s$. A simple restriction on this framework yields an additional prediction, for $|V_{cb}|$. If the b,t, and $τ$ Yukawas are equal at the GUT scale then $|\Vcb|$ is predicted and the top quark mass is constrained to lie in the range $\mt = 179. \pm 4.$ GeV.

hep-ph↗

arXiv1992

Remarks on the Electroweak Phase Transition

In the standard scenario, the electroweak phase transition is a first order phase transition which completes by the nucleation of critical bubbles. Recently, there has been speculation that the standard picture of the electroweak phase transition is incorrect. Instead, it has been proposed that throughout the phase transition appreciable amounts of both broken and unbroken phases of $SU(2)$ coexist in equilibrium. I argue that this can not be the case. General principles insure that the universe will remain in a homogenous state of unbroken $SU(2)$ until the onset of critical bubble production. In addition, an analytic treatment of the one Higgs doublet, electroweak phase transition in the standard model and minimal extensions is reviewed. Results from the thin wall approximation are compared to results obtained using the Lindes' action. Perhaps the most important quantitative result we can get from an analysis of the phase transition is determination of $\vevphi$ when the phase transition completes. For Higgs boson masses above the current experimental limit, the thin wall approximation determines the value of $\vevphi$ at the end of the phase transition to an accuracy of better than three percent.

hep-ph↗