Measurement of D^0-D^0 mixing and CP violation in two-body D^0 decays

We present a measurement of D^0-D^0 mixing and CP violation using the ratio of lifetimes simultaneously extracted from a sample of D^0 mesons produced through the flavor-tagged process D^(*+)→D^0π^+, where D^0 decays to K^∓π^±, K^-K^+, or π^-π^+, along with the untagged decays D^0→K^∓π^± and D^0→K^-K^+. The lifetimes of the CP-even, Cabibbo-suppressed modes K^-K^+ and π^-π^+ are compared to that of the CP-mixed mode K^∓π^± in order to measure y_(CP) and ΔY. We obtain y_(CP)=[0.72±0.18(stat)±0.12(syst)]% and ΔY=[0.09±0.26(stat)±0.06(syst)]%, where ΔY constrains possible CP violation. The y_(CP) result excludes the null mixing hypothesis at 3.3σ significance. This analysis is based on an integrated luminosity of 468  fb^(-1) collected with the BABAR detector at the PEP-II asymmetric-energy e^+e^- collider

Proof of a Conjectured Three-Valued Family of Weil Sums of Binomials

We consider Weil sums of binomials of the form $W_{F,d}(a)=\sum_{x \in F} \psi(x^d-a x)$, where $F$ is a finite field, $\psi\colon F\to {\mathbb C}$ is the canonical additive character, $\gcd(d,|F^\times|)=1$, and $a \in F^\times$. If we fix $F$ and $d$ and examine the values of $W_{F,d}(a)$ as $a$ runs through $F^\times$, we always obtain at least three distinct values unless $d$ is degenerate (a power of the characteristic of $F$ modulo $|F^\times|$). Choices of $F$ and $d$ for which we obtain only three values are quite rare and desirable in a wide variety of applications. We show that if $F$ is a field of order $3^n$ with $n$ odd, and $d=3^r+2$ with $4 r \equiv 1 \pmod{n}$, then $W_{F,d}(a)$ assumes only the three values $0$ and $\pm 3^{(n+1)/2}$. This proves the 2001 conjecture of Dobbertin, Helleseth, Kumar, and Martinsen. The proof employs diverse methods involving trilinear forms, counting points on curves via multiplicative character sums, divisibility properties of Gauss sums, and graph theory.Comment: 19 page

Measurement of the B0–B0 oscillation frequency Δmd with the decays B0→D−π+ and B0→ J/ψK∗0

The B 0 –B 0 oscillation frequency Δmd is measured by the LHCb experiment using a dataset corresponding to an integrated luminosity of 1.0 fb−1 of proton–proton collisions at √ s = 7 TeV, and is found to be Δmd =0.5156±0.0051 (stat.)±0.0033 (syst.) ps−1 . The measurement is based on results from analyses of the decays B 0 → D −π + (D − → K +π −π −) and B 0 → J/ψK ∗0 (J/ψ →μ +μ −,K ∗0 → K +π −) and their charge conjugated modes

A study of rare B-meson decay with muons in the final state with the LHCb detector

The Standard Model (SM) gives a successful description of known phenomena in particle physics, however there are many indications of the existence of New Physics (NP) at the TeV scale. Physicists are building a very large and expensive machine in this belief: the LHC (Large Hadron Collider), which is foreseen to start in the middle 2008. Three of the experiments of the LHC are mainly devoted to the search of NP. Among these, the LHCb experiment is dedicated to the physics of b-hadrons. It will look for indirect evidences of new particles or new degrees of freedom, measuring branching ratios, decay amplitudes and CP asymmetries, which can be sensitive to New Physics effects. Three analysis will be presented: the sensitivity to the $B_{s,d}^0 \rightarrow e^{\pm} \mu^{\mp}$ decays, the sensitivity to the $B_{s,d}^0 \rightarrow \mu^+ \mu^- \gamma$ decays and the correction of angular biases in the $B_d^0 \rightarrow K^{*0} \mu^+ \mu^-$ decay. The $B_{s,d}^0 \rightarrow e^{\pm} \mu^{\mp}$ decays are forbidden in the SM, being lepton flavor violating, but are allowed in some of its extensions. The $90\%$ CL upper bounds that the LHCb experiment can set in $1$ year, running at nominal luminosity, will be presented. These results will be discussed in the context of some Pati-Salam models. The branching ratio of the decays $B_{s,d}^0 \rightarrow \mu^+ \mu^- \gamma$ can be enhanced by NP contributions, such as SUSY contributions. Th e LHCb sensitivity to these decays will be presented. %NP can affect the angular distributions of the B_d^0 \rightarrrow K^{*0} \mu^+ \mu^-. The $A_T^2$ asymmetry in the $B_d^0 \rightarrow K^{*0} \mu^+ \mu^-$ decay is sensitive to NP involving right-handed currents. This asymmetry can be extracted by looking at the angular distributions of the decay products. However this measurement is not straightforward. Two methods for the angular distribution recovering, using the $B_d^{0} \rightarrow J/\psi K^{*0}$ as a control channel, will be presented

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure

Parametrization of aproximate algebraic surfaces by lines

In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ²-irreducible algebraic surfaces of degree d having an ²–singularity of multiplicity d−1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance ² > 0 and an ²-irreducible algebraic surface V of degree d, the algorithm computes a new algebraic surface V , that is rational, as well as a rational parametrization of V . In addition, in the error analysis we show that the output surface V and the input surface V are close. More precisely, we prove that V lies in the offset region of V at distance, at most, O(² 1 2d )

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains

In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusion constrains. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constrains $P=\{P_1,...,P_d\}$ of total length $r$, the problem is to find a common subsequence $Z$ of $X$ and $Y$ excluding each of constrain string in $P$ as a substring and the length of $Z$ is maximized. The problem was declared to be NP-hard\cite{1}, but we finally found that this is not true. A new dynamic programming solution for this problem is presented in this paper. The correctness of the new algorithm is proved. The time complexity of our algorithm is $O(nmr)$.Comment: arXiv admin note: substantial text overlap with arXiv:1301.718

Search for CPCP violation in the phase space of D0→π−π+π0D^0 \to \pi^-\pi^+\pi^0 decays with the energy test

A search for $CP$ violation in $D^0 \to \pi^-\pi^+\pi^0$ decays is reported, using $pp$ collision data collected by the LHCb experiment from 2015 to 2018 corresponding to an integrated luminosity of 6$fb^{-1}$. An unbinned model-independent approach provides sensitivity to local $CP$ violation within the two-dimensional phase space of the decay. The method is validated using the Cabibbo-favoured channel \D^0 \to \K^-\pi^+\pi^0 and background regions of the signal mode. The results are consistent with $CP$ symmetry in this decay.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-005.html (LHCb public pages