Universal Evolution of CKM Matrix Elements

We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa matrix. We show that to leading order in the mass and CKM hierarchies the scaling of the mixings $|V_{ub}|^2$, $|V_{cb}|^2$, $|V_{td}|^2$, $|V_{ts}|^2$ and of the rephase-invariant CP-violating parameter $J$ is universal to all orders in perturbation theory. In leading order the other CKM elements do not scale. Imposing the constraint $\lambda _b=\lambda _{\tau}$ at the GUT scale determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.Comment: 17 pages + 2 figures not included (available upon request), revised version fixes discrepancy between S and S^{1/2}, no other changes, MAD/PH/72

Three-loop \beta-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the \beta-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.Comment: 22 pages, 7 figures. Few extra citations are added; the plots are improved. Results in computer readable form can be retrieved from http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp12/ttp12-012

Chandra Observations of NGC 4438: An Environmentally Damaged Galaxy in the Virgo Cluster

We present results from a 25 ksec CHANDRA ACIS-S observation of galaxies NGC4438 and NGC4435 in the Virgo Cluster. X-ray emission in NGC4438 is observed in a ~700 pc nuclear region, a 2.3 kpc spherical bulge, and a network of filaments extending 4-10 kpc to the W and SW of the galaxy. The X-ray emission in all 3 regions is highly correlated to similar features observed in Halpha. Spectra of the filaments and bulge are well represented by a 0.4 keV MEKAL model with combined 0.3-2 keV intrinsic luminosity of 1.24x10^{40}erg/s, electron densities ~ 0.02-0.04 cm^{-3}, cooling times of 400-700 Myr and X-ray gas mass <~ 3.7x10^8 Msolar. In the nuclear region of NGC4438 X-ray emission is seen from the nucleus and from two outflow bubbles extending 360(730) pc to the NW(SE) of the nucleus. The spectrum of the NW outflow bubble plus nucleus is well fitted by an absorbed (n_H=1.9x10^{21} cm^{-2}) 0.58 keV MEKAL plasma model plus a heavily absorbed (n_H = 2.9 x10^{22} cm^{-2}) Gamma = 2, power law component. The electron density, cooling time, and X-ray gas mass in the NW outflow are ~0.5 cm^{-3}, 30 Myr and 3.5x10^6 Msolar. Weak X-ray emission is observed in the central region of NGC4435 with the peak of the hard emission coincident with the galaxy's optical center; while the peak of the soft X-ray emission is displaced 316 pc to the NE. The spectrum of NGC 4435 is well fitted by a non-thermal power law plus a thermal component from 0.2-0.3 keV diffuse ISM gas. We argue that the X-ray properties of gas outside the nuclear region in NGC4438 and in NGC4435 favor a high velocity, off-center collision between these galaxies ~ 100 Myr ago; while the nuclear X-ray emitting outflow gas in NGC4438 has been heated only recently (within ~ 1-2 Myr) by shocks (v_s ~ 600 kms^{-1}) possibly powered by a central AGN.Comment: 40 pages, 7 figures; minor changes to conform to published version, improved spectral fits to NGC 4435, improved figures 3,5; new figures 6b,

Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice

We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring a defocusing segment, a focusing segment and a transitional interface between the two. We illustrate that such inhomogeneous settings present vastly different dynamical behavior than the one expected in their homogeneous counterparts in the vicinity of the interface. We analyze the relevant stationary states, as well as their stability by means of perturbation theory and linear stability analysis. We find good agreement with the numerical findings in the vicinity of the anti-continuum limit. For larger values of the coupling, we follow the relevant branches numerically and show that they terminate at values of the coupling strength which are larger for more extended solutions. The dynamical development of relevant instabilities is also monitored in the case of unstable solutions.Comment: 14 pages, 4 figure

Planck Scale Boundary Conditions and the Higgs Mass

If the LHC does only find a Higgs boson in the low mass region and no other new physics, then one should reconsider scenarios where the Standard Model with three right-handed neutrinos is valid up to Planck scale. We assume in this spirit that the Standard Model couplings are remnants of quantum gravity which implies certain generic boundary conditions for the Higgs quartic coupling at Planck scale. This leads to Higgs mass predictions at the electroweak scale via renormalization group equations. We find that several physically well motivated conditions yield a range of Higgs masses from 127-142 GeV. We also argue that a random quartic Higgs coupling at the Planck scale favors M_H > 150 GeV, which is clearly excluded. We discuss also the prospects for differentiating different boundary conditions imposed for \lambda(M_{pl}) at the LHC. A striking example is M_H = 127\pm 5 GeV corresponding to \lambda(M_{pl})=0, which would imply that the quartic Higgs coupling at the electroweak scale is entirely radiatively generated.Comment: 12 pages, 5 figures; references added and other minor improvements, matches version published in JHE

Two-loop renormalization of gaugino masses in general supersymmetric gauge models

We calculate the two-loop renormalization group equations for the running gaugino masses in general SUSY gauge models, improving our previous result. We also study its consequence to the unification of the gaugino masses in the SUSY SU(5) model. The two-loop correction to the one-loop relation $m_i(\mu)\propto\alpha_i(\mu)$ is found to be of the order of a few \%.Comment: 8 pages + 1 figure (omitted),KEK-TH-371 / UT-65

Scale dependence of the quark masses and mixings: leading order

We consider the Renormalization Group Equations (RGE) for the couplings of the Standard Model and its extensions. Using the hierarchy of the quark masses and of the Cabibbo-Kobayashi-Maskawa (CKM) matrix our argument is that a consistent approximation for the RGE should be based on the parameter $\lambda= |\hat{V}_{ud}| \approx0.22$. We consider the RGE in the approximation where we neglect all the relative terms of the order $\sim\lambda^{4}$ and higher. Within this approximation we find the exact solution of the evolution equations of the quark Yukawa couplings and of the vacuum expectation value of the Higgs field. Then we derive the evolution of the observables: quark masses, CKM matrix, Jarlskog invariant, Wolfenstein parameters of the CKM matrix and the unitarity triangle. We show that the angles of the unitarity triangle remain constant. This property may restrict the possibility of new symmetries or textures at the grand unification scale.Comment: 15 pages, 4 figures, author of one reference adde

Chandra Observations of Galaxy Cluster Abell 2218

We present results from two observations (combined exposure of ~17 ks) of galaxy cluster A2218 using the Advanced CCD Imaging Spectrometer on board the Chandra X-ray Observatory that were taken on October 19, 1999. Using a Raymond-Smith single temperature plasma model corrected for galactic absorption we find a mean cluster temperature of kT = 6.9+/-0.5 keV, metallicity of 0.20+/-0.13 (errors are 90 % CL) and rest-frame luminosity in the 2-10 keV energy band of 6.2x10^{44} erg/s in a LambdaCDM cosmology with H_0=65 km/s/Mpc. The brightness distribution within 4'.2 of the cluster center is well fit by a simple spherical beta model with core radius 66".4 and beta = 0.705 . High resolution Chandra data of the inner 2' of the cluster show the x-ray brightness centroid displaced ~22" from the dominant cD galaxy and the presence of azimuthally asymmetric temperature variations along the direction of the cluster mass elongation. X-ray and weak lensing mass estimates are in good agreement for the outer parts (r > 200h^{-1}) of the cluster; however, in the core the observed temperature distribution cannot reconcile the x-ray and strong lensing mass estimates in any model in which the intracluster gas is in thermal hydrostatic equilibrium. Our x-ray data are consistent with a scenario in which recent merger activity in A2218 has produced both significant non-thermal pressure in the core and substructure along the line of sight; each of these phenomena probably contributes to the difference between lensing and x-ray core mass estimates.Comment: 33 pages, 6 figures, uses AASTeX 5.02, ApJ submitte

Collisional Dark Matter and the Origin of Massive Black Holes

If the cosmological dark matter is primarily in the form of an elementary particle which has cross section and mass for self-interaction having a ratio similar to that of ordinary nuclear matter, then seed black holes (formed in stellar collapse) will grow in a Hubble time, due to accretion of the dark matter, to a mass range 10^6 - 10^9 solar masses. Furthermore, the dependence of the final black hole mass on the galaxy velocity dispersion will be approximately as observed and the growth rate will show a time dependence consistent with observations. Other astrophysical consequences of collisional dark matter and tests of the idea are noted.Comment: 7 pages, no figures, LaTeX2e, Accepted for publication in Phys. Rev. Lett. Changed conten

Two-loop RGEs with Dirac gaugino masses

The set of renormalisation group equations to two loop order for general supersymmetric theories broken by soft and supersoft operators is completed. As an example, the explicit expressions for the RGEs in a Dirac gaugino extension of the (N)MSSM are presented.Comment: 10 pages + 24 pages of RGEs in appendix; no figure