Angles Of Triangle Research Articles

Search for new physics at a super-B factory

The importance of a Super-B Factory in the search for New Physics, in particular, due to CP-od phase(s) from physics beyond the Standard Model is surveyed. The first point to emphasize is that we know now how to directly measure all three angles of the unitarity triangle very cleanly, {\it i.e. without theoretical assumptions} with {\it irreducible theory error $ \lsim 1%$}; however this requires much more luminosity than is currently available at B-factories. Direct searches via penguin-dominated hadronic modes as well as radiative, pair-leptonic and semi-leptonic decays are also discussed. {\bf Null tests of the SM} are stressed as these will play a crucial role especially if the effects of BSM phase(s) on B-physics are small.

Analytic, graphical, and geometric solutions for the band edges of one-dimensional photonic band gap materials

The conditions for the band gap edges of one-dimensional photonic band gap (PBG) materials are presented in forms that lead to alternate analytic, graphical, and geometric solutions and interpretations. Heretofore unavailable analytical conditions for the band edges of quarter wave∕half wave and eighth wave∕half wave PBG structures are derived. The graphical solution has the form of an intersection of an invariant (material dependent) figure with a straight (structure dependent) line, a convenient separation not possible with the Kronig-Penney (KP) equation. The geometric solution is represented by the sides and angles of simple triangles. The present formalism should help in visualizing the PBG band gap formation beyond the view offered by the KP equation.

Measurement ofϕ3with Dalitz plot analysis ofB±→D(*)K±decay

We present a measurement of the unitarity triangle angle phi_3 using a Dalitz plot analysis of the three-body decay of the neutral D meson from the B->D(*)K process. The method employs the interference between D0 and D0bar to extract both the weak and strong phases. We apply this method to a 140 fb^{-1} data sample collected by the Belle experiment. The analysis uses the modes B->DK and B->D*K, D*->D pi0, where the neutral D meson decays into K_Spi+pi-. We obtain 146 signal candidates for B->DK and 39 candidates for B->D*K. From a combined maximum likelihood fit to the B->DK and B->D*K modes, we obtain phi_3=77^{\circ}^{+17}_{-19}(stat)+-13^{\circ}(syst)}+-11^{\circ}(model). The corresponding two standard deviation interval is 26^{\circ}<phi_3<126^{\circ}.

Robust Spherical Parameterization of Triangular Meshes

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.

CP violation studies in B0 → D(*)±π∓ in BaBar and Belle

The authors present a preliminary measurement of the time-dependent CP asymmetries in decays of B{sup 0} mesons to the final states D{sup (*)}{pi} using data collected by the BABAR experiment at the PEP-II storage rings. B mesons decaying to D{pi} are fully reconstructed, while events containing B {yields} D*{pi} are selected using a full or a partial reconstruction technique. These results can be interpreted in terms of a constraint on the angles of the unitarity triangle to set a lower bound on |sin (2{beta} + {gamma})|. The Belle experiment at the KEK-B collider is performing the same kind of studies and a preliminary estimation of the achievable error is presented.

Lattice matrix elements and CP violation inB andK physics: Status and outlook

Status of lattice calculations of hadron matrix elements along with CP violation inB and inK systems is reviewed. Lattice has provided useful input which, in conjunction with experimental data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry inB → ψK s. It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in B-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination ofall the angles of the unitarity triangle therefore becomes essential. In this regardB → KD0 processes play a unique role. RegardingK-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitative information onB K and the ΔI = 1/2 rule. In the lattice calculation, the enhancement in Re A0 appears to arise solely from tree operators, esp. Q2; penguin contribution toRe A0 appears to be very small. However, improved calculations are necessary for ε’/ε as the contributions of QCD penguins and electroweak penguins largely seem to cancel. There are good reasons, though, to believe that these cancellations will not survive improvements that are now underway. Importance of determining the unitarity triangle purely fromK-decays is also emphasized.

Bioethics and Law Forum*: Twin Autonomy

Bioethics and Law Forum*: Twin Autonomy

Status and prospects of CKM phase determinations

We give an overview of direct determinations of the angles of the unitarity triangle of the CKM matrix, using CP-violating effects in B-meson decays. After a discussion of B → πK modes, which can be described efficiently through allowed regions in observable space and play an important rôle to determine γ, we turn to extractions of the B d 0- B d 0 mixing phase φ d , which equals 2β in the Standard Model, from B d → J/ ψK s 0 and emphasize that it is important to determine this phase unambiguously. Finally, we focus on B d → π + π −, where recent B-factory data point towards large penguin contributions. The question arises now how the CP-violating observables of this mode can be transformed into information on the angles of the unitarity triangle. A promising tool to achieve this goal is offered by B s → K + K −, which is very accessible at hadronic B experiments, and allows a determination of φ d and γ. A variant for the e + e − B-factories is provided by B d → π ∓ K ±, where data are already available; pointing to an exciting picture and a highly constrained allowed region in B s → K + K − observable space.

Status and prospects of the LHCb experiment

The LHCb detector and trigger have undergone significant revision. A summary is given of the re-optimized LHCb detector and the status of its construction. The measurement of the unitarity triangle angle γ in a number of complimentary channels is also reviewed.

Neutrino mixing and largeCPviolation inBphysics

We show that in see-saw models of neutrino mass a la SUSY SO(10), the observed large mixing in atmospheric neutrinos naturally leads to large b-s transitions. If the associated new CP phase turns out to be large, this SUSY contributions can drastically affect the CP violation in some of the B decay channels yielding the beta and gamma angles of the unitarity triangle. They can even produce sizeable CP asymmetries in some decay modes which are not CP violating in the standard model context. Hence the observed large neutrino mixing makes observations of low energy SUSY effect in some CP violating decay channels potentially promising in spite of the agreement between the Standard Model and data in K and B physics so far.

Spatial Point Pattern Analysis by using Voronoi Diagrams and Delaunay Tessellations – A Comparative Study

AbstractGiven a spatial point pattern, we use various characteristics of its Voronoi diagram and Delaunay tessellation to extract information of the dependence between points. In particular, we use the characteristics to construct statistics for testing complete spatial randomness. It is shown that the minimum angle of a typical Delaunay triangle is sensitive to both regularity and clustering alternatives, whilst the triangle's area or perimeter is more sensitive to clustering than regularity. These statistics are also sensitive to the Baddeley‐Silverman cell process.

New results from Belle

We have measured the CP violation parameters in B° decays to the following CP eigenstates: (c c)K s, J/ψK L, J/ψK −0, π +π −, θK s, η/K s and K +K −K s , using data collected with the Belle detector at the KEKB asymmetric-energy e +e − collider. One of the angles of the CKM unitality triangle, θ 1, has been determined using 78 fb −1 as sin 2 θ 1 = 0.719 ± 0.074 ± 0.035. The large A ππ is an indication of direct CP violation in B meson decay. The S θK , S η′ K are S KKK are all consistent with sin 2 θ 1 within 3σ. We also present the first measurement o the inclusive branching fraction for the electroweak penguin decay B → X s ℓ +ℓ −. The results on the branching fraction, dilepton and recoil mass spectra are in agreement with the Standard Model expectations.

A note on trigonometric identities

In this note, we study trigonometric identities involving the angles of an arbitrary triangle and we give algorithms for verifying such identities.

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 $\ensuremath{\lambda}=|{V}_{\mathrm{us}}|\ensuremath{\approx}0.22.$ We consider the RGE in the approximation where we neglect all the relative terms of the order $\ensuremath{\sim}{\ensuremath{\lambda}}^{4}$ 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.

Infrasonic Observations of the Hekla Eruption of February 26, 2000

INTRODUCTION On February 26-27, 2000 infrasonic signals associated with the eruption of the Hekla Volcano, Iceland, were recorded by the Swedish infrasound network. This network is operated by the Swedish Institute of Space Physics and consists of 4 stations located in Kiruna, Jamton and Lycksele in Northern Sweden and Uppsala in Central Sweden. Each station consists of an array of 3 modified Lidstrommicrophones (see Appendix 1) with a 7 Hz low-pass filter, so that the effective frequency range is 0.5 6 Hz. A sampling rate of 18 Hz is used at all stations. The microphones at each array are located in the corners of a right angle triangle, where the perpendicular sides are 75 m long and oriented East-West and North-South. Shelters reduce wind noise at each array element. The Kiruna and Lycksele array data may be accessed at http://callisto.space.umu.se. Geographical coordinates for the stations are given in Table I.

Physics at the B factories

We review recent progress at the two $e^+ e^-$ B factories. The first measurement of CP violation and the prospects for measuring all the angles of the unitarity triangle are discussed.

Hyper-trigonometry of the particle triangle

Using a new kinematical description of a free three-body problem in hyperspherical coordinates (Matveenko A V and Fukuda H 1998 J. Phys. A: Math. Gen. 31 5371) we derive two infinite series of matrix identities interconnecting triangle angles, particle masses and internal hyperspherical angles. The corresponding relations for the matrix elements are practically all new.

Simulation of interaction force between Si tip and Si([formula omitted])[formula omitted]-Ag surface of IET structure in noncontact AFM

Simulation of the interaction force between the SiH3 tip and the Si(111)3×3-Ag surface is performed based on the first-principles electronic state calculations. First it is indicated that the inequivalent-trimer (IET) structure is a local energy minimum as a function of the rotation angle of Ag triangle. Next interaction force between the tip and the IET structured surface is calculated as a function of the tip height for the different surface sites. Lastly two-dimensional plots of the force are calculated as the first step of studying the stable structure of the Si(111)3×3-Ag surface at the room temperature. Surprisingly, the average of the force plots for the two different phases of IET structures, becomes almost the same as that for the honeycomb-chained-trimer (HCT) structure. This indicates the possibility that the observed AFM image shows an apparent HCT structure as a result of averaging the two different phases of IET structures by a thermal fluctuation.

Exploring the construction of “reference” triangle through unitarity

Motivated by the possibility of the low value of sin2\beta in the measurements of BABAR and BELLE collaborations, we have explored the possibilty of construction of reference unitarity triangle using the unitarity of the CKM matrix, the existence of nonzero CP violating phase \delta and the experimental values of the well known CKM elements, without involving any inputs from the processes which might include the new physics effects. The angles of the reference triangle are evaluated by finding \delta through the Jarlskog's rephasing invariant parameter J. The present data and the unitarity of the CKM matrix give \delta=50^o \pm 20^o, which translates to 130^o \pm 20^o in the second quadrant. The corresponding range for sin2\beta is 0.21 to 0.88. This range is broadly in agreement with the recently updated BABAR and BELLE results. However, a value of \sin2 \leq 0.2, advocated by Silva and Wolfenstein as a benchmark for new physics, would suggest a violation in the three generation unitarity and would hint towards the existence of a fourth generation. Further, the future refinements in the CKM elements will push the lower limit on sin2\beta still higher.

2000 CKM-triangle analysis a critical review with updated experimental inputs and theoretical parameters

Within the Standard Model, a review of the current determination of the sides and angles of the CKM unitarity triangle is presented, using experimental constraints from the measurements of |\epsilon_K|, |V_{ub}/V_{cb}|, \Delta m_d and from the limit on \Delta m_s, available in September 2000. Results from the experimental search for {B}^0_s-\bar{B}^0_s oscillations are introduced in the present analysis using the likelihood. Special attention is devoted to the determination of the theoretical uncertainties. The purpose of the analysis is to infer regions where the parameters of interest lie with given probabilities. The BaBar "95 %, C.L. scanning" method is also commented.