Galerkin FEM for fractional order parabolic equations with initial data in H−s, 0<s≤1H^{-s},~0 < s \le 1

We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous fractional diffusion problems with non-smooth initial data. We assume that $\Omega\subset \mathbb{R}^d$, $d=1,2,3$ is a convex polygonal (polyhedral) domain. We theoretically justify optimal order error estimates in $L_2$- and $H^1$-norms for initial data in $H^{-s}(\Omega),~0\le s \le 1$. We confirm our theoretical findings with a number of numerical tests that include initial data $v$ being a Dirac $\delta$-function supported on a $(d-1)$-dimensional manifold.Comment: 13 pages, 3 figure

Extra Dimensions and Higgs Pair Production at Photon Colliders

We show that new physics effects due to extra dimensions can dramatically affect Higgs pair production at photon colliders. We find that the cross section due to extra dimensions with the scale $M_S$ of new physics around 1.5 TeV, the cross section can be as large as 0.11 pb (1.5pb) for monochromatic photon collision, $\gamma \gamma \to HH$, with the collider energy $\sqrt{s} = 0.5 (1)$ TeV for Higgs mass of 100 (350) GeV. The cross section can be 3 fb (2.7 fb) for the same parameters for collisions using photon beams from electron or positron back scattered by laser. These cross sections are much larger than those predicted in the Standard Model. Higgs pair production at photon colliders can provide useful tests for new physics due to extra dimensions.Comment: Typos corrected and updated references, Rev-Tex, 11 pages with one figur

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure

Tests of Higgs Boson Couplings at a mu+mu- Collider

We investigate the potential of a muon collider for testing the presence of anomalous Higgs boson couplings. We consider the case of a light (less than $160 GeV$) Higgs boson and study the effects on the Higgs branching ratios and total width, which could be induced by the non standard couplings created by a class of dim=6 $SU(3)\times SU(2)\times U(1)$ gauge invariant operators satisfying the constraints imposed by the present and future hadronic and $e^-e^+$ colliders. For each operator we give the minimal value of the $\mu^+\mu^-$ integrated luminosity needed for the muon collider ($\mu C$) to improve these constraints. Depending on the operator and the Higgs mass, this minimal $\mu C$ luminosity lies between $0.1 fb^{-1}$ and $100 fb^{-1}$.Comment: 18 pages and 4 figures; version to be published in Phys. Rev.D. e-mail: [email protected]

Looking For Disoriented Chiral Condensates From Pion Distributions

We suggest two methods for the detection of the formation of disoriented chiral condensates in heavy ion collisions. We show that the variance in the number of charged pions (in a suitable range of momentum space) provides a signature for the observation of a disoriented chiral condensate. The signal should be observable even if multiple domains of D$\chi$C form provided the average number of pions per domain is significantly larger than unity. The variance of the number charged pions alone provides a signal which can be used even if the number of neutral pions cannot be measured in a given detector. On the other hand, the probability distribution in $R$, the proportion of neutral pions to all pions emitted in heavy ion collisions in certain kinematic regions, has been suggested as a signal of a disoriented chiral condensate. Here we note that the signature can be greatly enhanced by making suitable cuts in the data. In particular, we consider reducing the data set such that the $k$ pions with lowest $p_T$ are all neutral. We find that, given such cuts, can be substantially different from 1/3. For example, for a single D$\chi$C domain without contamination due to incoherently emitted pions, is 3/5 given the pion with lowest $p_T$ is neutral, and 5/7 given the two pions with lowest $p_T$ are both neutral, {\it etc.}. The effects of multi-domain D$\chi$C formation and noise due to incoherent pion emission can be systematically incorporated. Potential applications to experiments and their limitations are briefly discussed.Comment: 16 pages in REVTeX, 7 figures. Combined and updated version of nucl-th/9903029 and nucl-th/9904074. Accepted by Phys. Rev.

Gluonic and leptonic decays of heavy quarkonia and the determination of αs(mc)\alpha_s(m_c) and αs(mb)\alpha_s(m_b)

QCD running coupling constant $\alpha_s(m_c)$ and $\alpha_s(m_b)$ are determined from heavy quarkonia $c\overline{c}$ and $b\overline{b}$ decays. The decay rates of $V\rightarrow 3g$ and $V\rightarrow e^+ e^-$ for $V=J/\psi$ and $\Upsilon$ are estimated by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, and the decay rates are estimated by using the meson wavefunctions which are obtained with a QCD-inspired inter-quark potential. For the $V\rightarrow 3g$ decay we find the relativistic correction to be very large and to severely suppress the decay rate. Using the experimental values of ratio R_g\equiv \frac {\Gamma (V\longrightarrow 3g)}% {\Gamma (V\longrightarrow e^{+}e^{-})}\approx 10,~32 for $V=J/\psi, ~\Upsilon$ respectively, and the calculated widths , we find $\alpha_{s}(m_c)=0.29\pm 0.02$ and $\alpha_s(m_b)=0.20\pm 0.02$. These values for the QCD running coupling constant are substantially enhanced, as compared with the ones obtained without relativistic corrections, and are consistent with the QCD scale parameter $\Lambda_{\overline {MS}}^{(4)}$. We also find that these results are mainly due to kinematic corrections and not sensitive to the dynamical models.Comment: 15 pages in Late

Improving the sensitivity of Higgs boson searches in the golden channel

Leptonic decays of the Higgs boson in the ZZ* channel yield what is known as the golden channel due to its clean signature and good total invariant mass resolution. In addition, the full kinematic distribution of the decay products can be reconstructed, which, nonetheless, is not taken into account in traditional search strategy relying only on measurements of the total invariant mass. In this work we implement a type of multivariate analysis known as the matrix element method, which exploits differences in the full production and decay matrix elements between the Higgs boson and the dominant irreducible background from q bar{q} -> ZZ*. Analytic expressions of the differential distributions for both the signal and the background are also presented. We perform a study for the Large Hadron Collider at sqrt{s}=7 TeV for Higgs masses between 175 and 350 GeV. We find that, with an integrated luminosity of 2.5 fb^-1 or higher, improvements in the order of 10 - 20 % could be obtained for both discovery significance and exclusion limits in the high mass region, where the differences in the angular correlations between signal and background are most pronounced.Comment: 31 pages, 8 figures. v2: Minus signs in definitions of angles corrected. Typos fixed. Reference added. Cosmetic changes to Figure 4. Additional sentence added for clarificatio

Weak-Singlet Fermions: Models and Constraints

We employ data from precision electroweak tests and collider searches to derive constraints on the possibility that weak-singlet fermions mix with the ordinary Standard Model fermions. Our findings are presented within the context of a theory with weak-singlet partners for all ordinary fermions and theories in which only third-generation fermions mix with weak singlets. In addition, we indicate how certain results can be applied more widely in theories containing exotic fermions.Comment: 29 pages, 12 figures; added 1 reference, expanded introductio

How large could the R-parity violating couplings be?

We investigate in detail the predictions coming from the d=4 operators for proton decay. We find the most general constraints for the R-parity violating couplings coming from proton decay, taking into account all fermion mixing and in different supersymmetric scenarios.Comment: 8 pages, several corrections, to appear in J.Phys.G (2005

Constraints from Solar and Reactor Neutrinos on Unparticle Long-Range Forces

We have investigated the impact of long-range forces induced by unparticle operators of scalar, vector and tensor nature coupled to fermions in the interpretation of solar neutrinos and KamLAND data. If the unparticle couplings to the neutrinos are mildly non-universal, such long-range forces will not factorize out in the neutrino flavour evolution. As a consequence large deviations from the observed standard matter-induced oscillation pattern for solar neutrinos would be generated. In this case, severe limits can be set on the infrared fix point scale, Lambda_u, and the new physics scale, M, as a function of the ultraviolet (d_UV) and anomalous (d) dimension of the unparticle operator. For a scalar unparticle, for instance, assuming the non-universality of the lepton couplings to unparticles to be of the order of a few per mil we find that, for d_UV=3 and d=1.1, M is constrained to be M > O(10^9) TeV (M > O(10^10) TeV) if Lambda_u= 1 TeV (10 TeV). For given values of Lambda_u and d, the corresponding bounds on M for vector [tensor] unparticles are approximately 100 [3/Sqrt(Lambda_u/TeV)] times those for the scalar case. Conversely, these results can be translated into severe constraints on universality violation of the fermion couplings to unparticle operators with scales which can be accessible at future colliders.Comment: 13 pages, 3 figures. Minor changes due to precision in numerical factors and correction in figure labels. References added. Conclusions remain unchange