Search

We consider the effective potential V in the standard model with a single Higgs doublet in the limit that the only mass scale μ present is radiatively generated. Using a technique that has been shown to determine V completely in terms of the renormalization group (RG) functions when using the Coleman-Weinberg renormalization scheme, we first sum leading-log (LL) contributions to V using the one loop RG functions, associated with five couplings (the top quark Yukawa coupling x, the quartic coupling of the Higgs field y, the SU(3) gauge coupling z, and the SU(2) × U(1) couplings r and s). We then employ the two loop RG functions with the three couplings x, y, z to sum the next-to-leading-log (NLL) contributions to Vand then the three to five loop RG functions with one coupling y to sum all the N2LL…N4LL contributions to V. In order to compute these sums, it is necessary to convert those RG functions that have been originally computed explicitly in the minimal subtraction scheme to their form in the Coleman-Weinberg scheme. The Higgs mass can then be determined from the effective potential: the LL result is mH = 219 GeV/c2 and decreases to mH = 188 GeV/c2 at N2LL order and mH = 163 GeV/c2 at N4LL order. No reasonable estimate of mH can be made at orders VNLL or VN3LL since the method employed gives either negative or imaginary values for the quartic scalar coupling. The fact that we get reasonable values for mH from the LL, N2LL, and N4LL approximations is taken to be an indication that this mechanism for spontaneous symmetry breaking is in fact viable, though one in which there is slow convergence towards the actual value of mH. The mass 163 GeV/c2 is argued to be an upper bound on mH. [ABSTRACT FROM AUTHOR]

The Coleman-Weinberg (CW) renormalization scheme for renormalization-group improvement of the effective potential is particularly valuable for CW symmetry-breaking mechanisms (including the challenging case of models with multiple scalar fields). CW mechanism is typically studied using models with classical scale invariance which not only provide a possibility for an alternative symmetry breaking mechanism but also partially address the gauge hierarchies through dimensional transmutation. As outlined in our discussion section, when the couplings are not large, models with CW symmetry-breaking mechanisms have also been shown to naturally provide the strong first-order phase transition necessary for stochastic gravitational wave signals. A full understanding of the CW-MS scheme transformation of couplings thus becomes important in the era of gravitational wave detection and precision coupling measurements. A generalized Coleman-Weinberg (GCW) renormalization scheme is formulated and methods for transforming scalar self-couplings between the GCW and MS (minimal-subtraction) renormalization schemes are developed. Scalar λΦ4 theory with global O(4) symmetry is explicitly studied up to six-loop order to explore the magnitude of this scheme transformation effect on the couplings. The dynamical rescaling of renormalization scales between the GCW and MS schemes can lead to significant (order of 10%) differences in the coupling at any order, and consequently GCW-MS scheme transformation effects must be considered within precision determinations of scalar couplings in extensions of the Standard Model. [ABSTRACT FROM AUTHOR]

The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization a * = a + x 2 a ² is related to a change in the mass scale µ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expansion for a physical quantity R terminates. [ABSTRACT FROM AUTHOR]

The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multimessenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large amounts of data need to be integrated to achieve desired sensitivity. Contemporary searches use ingenious ad hoc methods to reduce computational complexity. In this paper we provide analytical expressions for the Fourier transform of realistic pulsar signals. This provides description of the manifold of pulsar signals in the Fourier domain, used by many search methods. We analyze the shape of the Fourier transform and provide explicit formulas for location and size of peaks resulting from stationary frequencies. We apply our formulas to analysis of recently identified outlier at 1891.76 Hz. [ABSTRACT FROM AUTHOR]