Total Acquisition in Graphs

Let G be a weighted graph in which each vertex initially has weight 1. A total acquisition move transfers all the weight from a vertex u to a neighboring vertex v, under the condition that before the move the weight on v is at least as large as the weight on u. The (total) acquisition number of G, written at(G), is the minimum size of the set of vertices with positive weight after a sequence of total acquisition moves. Among connected n-vertex graphs, at(G) is maximized by trees. The maximum is Θ(√(n lg n) for trees with diameter 4 or 5. It is⌊(n + 1)/3⌋ for trees with diameter between 6 and (2/3)(n + 1), and it is⌈(2n – 1 – D)/4⌉ for trees with diameter D when (2/3)(n + 1) ≤ D ≤ n - 1. We characterize trees with acquisition number 1, which permits testing at(G) ≤ k in time O(nk+2) on trees. If G ≠ C5, then min{at(G), at()} = 1. If G has diameter 2, then at(G) ≤ 32 ln n ln ln n; we conjecture a constant upper bound. Indeed, at(G) = 1 when G has diameter 2 and no 4-cycle, except for four graphs with acquisition number 2. Deleting one edge of an n-vertex graph cannot increase at by more than 6.84√n, but we construct an n-vertex tree with an edge whose deletion increases it by more than (1/2)√n. We also obtain multiplicative upper bounds under products

Supersymmetric Baryogenesis and Flavor Physics

We study the flavor physics implications of baryogenesis in the Minimal Supersymmetric Standard Model. Enhanced $B-\bar B$ mixing and $b \to s \gamma$ rates are generic to all scenarios. Depending on the origin of the CP violating phase responsible for baryogenesis there could be a large neutron electric dipole moment, large CP violating $D-\bar D$ mixing or CP violation in top quark production. We discuss how the combination of these measurements with the requirement of baryogenesis shed light on the MSSM parameter space and the source of CP violation.Comment: PRL version. Suppression factor explicitly identified below Eq. 5. More references added. Minor cosmetic changes in discussions. All results unchange

A New Supersymmetric CP Violating Contribution to Neutral Meson Mixing

We study the contribution to flavor changing neutral current processes from box diagrams with light higgsinos and squarks. Starting with just the Cabbibo Kobayashi Maskawa (CKM) phase, we find contributions to the $K^0$ and $B^0$ meson mass matrices that are out of phase with the Standard Model contributions in the case of substantial mixing between the up-type squarks. This difference in phase could be large enough to be detected at the proposed $B$ factories, with interesting implications for the unitarity triangle of CKM matrix elements.Comment: 1 reference added, 1 reference clarified, 2 typos corrected (QCD corrections to K meson mixing in Tables 1 and 3). To be published in Phys. Rev. D. 15 pages (Latex), 2 figures and epsfig.sty submitte

CP Asymmetry in B_d --> phi K_S: Standard Model Pollution

The difference in the time dependent CP asymmetries between the modes $B --> psi K_S$ and $B --> phi K_S$ is a clean signal for physics beyond the Standard Model. This interpretation could fail if there is a large enhancement of the matrix element of the $b --> u ubar s$ operator between the $B_d$ initial state and the $phi K_S$ final state. We argue against this possibility and propose some experimental tests that could shed light on the situation.Comment: 9 pages, Revte

Constraining the CKM Parameters using CP Violation in semi-leptonic B Decays

We discuss the usefulness of the CP violating semi-leptonic asymmetry a_{SL} not only as a signal of new physics, but also as a tool in constraining the CKM parameters. We show that this technique could yield useful results in the first years of running at the B factories. We present the analysis graphically in terms of M_{12}, the dispersive part of the B-Bbar mixing amplitude. This is complementary to the usual unitarity triangle representation and often allows a cleaner interpretation of the data.Comment: 15 pages REVTEX, 7 figure

Oblique Corrections To The W Width

The lowest-order expression for the partial $W$ width to $e \nu ,~\Gamma (W \to e \nu) = G_\mu M_W^3 /(6 \pi \sqrt{2})$, has no oblique radiative corrections from new physics if the measured $W$ mass is used. Here $G_\mu = (1.16639 \pm 0.00002) \times 10^{-5}$ GeV/$c^2$ is the muon decay constant. For the present value of $M_W = (80.14 \pm 0.27)$ GeV/$c^2$, and with $m_t = 140$ GeV$/c^2$, one expects $\Gamma (W \to e \nu) = (224.4 \pm 2.3)$ MeV. The total width $\Gamma_{\rm tot}(W)$ is also expected to lack oblique corrections from new physics, so that $\Gamma_{\rm tot} (W)/ \Gamma (W \to e \nu) = 3 + 6 [1 + \{\alpha_s (M_W)/\pi \}]$. Present data are consistent with this prediction.Comment: 15 pages (LaTeX), one PostScript figure not included (available upon request

Supersymmetric Baryogenesis at the Electroweak Phase Transition

We study the possibility of baryogenesis in the case of supersymmetry breaking with large mixing between the right-handed scalar charm and right-handed scalar top or right-handed scalar up and right-handed scalar top squarks resulting in one light right-handed up-type squark mass eigenstate. We argue that in this case the electroweak phase transition will be first order, and that large phases already present in the quark mass matrices can generate a baryon asymmetry of the correct magnitude without introducing any new phases specifically for this purpose. We study in detail a particular ansatz for supersymmetry breaking and CP violation where there is only one CP violating phase in the theory: in the up-type quark mass matrix. We study the constraints placed on this model by baryogenesis and flavor physics. This scenario has robust implications for low energy flavor phsyics including D-Dbar mixing and an electric dipole moment for the neutron that are close to the experimental bounds, and CP violation in the B-Bbar system that is different from that in the Standard Model.Comment: Final PRD version. 2 typos (Eqs. 24 and 47) correcte

SUSY GUTs contributions and model independent extractions of CP phases

We consider the origin of new phases in supersymmetric grand unification model, and show how significant new contributions arise from the gluino mediated diagram. We then present a more general model independent analysis of various modes of B-decays suggested previously for measurement of the CKM phases and point out what they really measure. It is in principle possible to separate out all the phases.Comment: 13 pages (Latex), 2 PS figures, a few remarks are added and a typo is corrected. To appear in Phys. Rev. Let

Signatures of Baryogenesis in the MSSM

We revisit the electroweak baryogenesis within the context of the minimal supersymmetric standard model (MSSM), studying its potential collider signatures. We find that this mechanism of baryogenesis does not give a new CP violating signal at the $B$-factories. The first circumstantial evidence may come from enhanced $B_s$ or $B_d$ mixing. If a light right-handed scalar top and Higgs are found as required, a linear collider represents the best possibility for confirming the scenario.Comment: 5 pages, 2 figures. Minor typos fixed. Reference Adde

CP violation in chargino decays in the MSSM

In the minimal supersymmetric standard model (MSSM) with complex parameters, supersymmetric loop effects can lead to \emph{CP} violation. We calculate the rate asymmetries of decays of charginos into the lightest neutralino and a $W$ boson on the basis of the most important loop contributions in the third generation squark sectors. It turns out that the \emph{CP} violating asymmetries can be a few per cent in typical regions of the parameter space of the MSSM. These processes would provide very promising channels for probing \emph{CP} violation in the MSSM at future high-energy colliders.Comment: 15 pages, 5 figures, LaTeX2