A Path Algorithm for Constrained Estimation

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new path following algorithm for quadratic programming based on exact penalization. Similar penalties arise in $l_1$ regularization in model selection. Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. The exact path following method starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. Path following in lasso penalized regression, in contrast, starts with a large value of the penalty constant and works its way downward. In both settings, inspection of the entire solution path is revealing. Just as with the lasso and generalized lasso, it is possible to plot the effective degrees of freedom along the solution path. For a strictly convex quadratic program, the exact penalty algorithm can be framed entirely in terms of the sweep operator of regression analysis. A few well chosen examples illustrate the mechanics and potential of path following.Comment: 26 pages, 5 figure

A Unified Approach to the Classical Statistical Analysis of Small Signals

We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.Comment: 40 pages, 15 figures. Changes 15-Dec-99 to agree more closely with published version. A few small changes, plus the two substantive changes we made in proof back in 1998: 1) The definition of "sensitivity" in Sec. V(C). It was inconsistent with our actual definition in Sec. VI. 2) "Note added in proof" at end of the Conclusio

Study of J/ψ→ppˉJ/\psi\to p\bar{p} and J/ψ→nnˉJ/\psi\to n\bar{n}

The decays $J/\psi\to p\bar{p}$ and $J/\psi\to n\bar{n}$ have been investigated with a sample of 225.2 million $J/\psi$ events collected with the BESIII detector at the BEPCII $e^+e^-$ collider. The branching fractions are determined to be $\mathcal{B}(J/\psi\to p\bar{p})=(2.112\pm0.004\pm0.031)\times10^{-3}$ and $\mathcal{B}(J/\psi\to n\bar{n})=(2.07\pm0.01\pm0.17)\times10^{-3}$. Distributions of the angle $\theta$ between the proton or anti-neutron and the beam direction are well described by the form $1+\alpha\cos^2\theta$, and we find $\alpha=0.595\pm0.012\pm0.015$ for $J/\psi\to p\bar{p}$ and $\alpha=0.50\pm0.04\pm0.21$ for $J/\psi\to n\bar{n}$. Our branching-fraction results suggest a large phase angle between the strong and electromagnetic amplitudes describing the $J/\psi\to N\bar{N}$ decay.Comment: 16 pages, 13 figures, the 2nd version, submitted to PR

Observation of a charged charmoniumlike structure in e+e−→(D∗Dˉ∗)±π∓e^+e^- \to (D^{*} \bar{D}^{*})^{\pm} \pi^\mp at s=4.26\sqrt{s}=4.26GeV

We study the process $e^+e^- \to (D^{*} \bar{D}^{*})^{\pm} \pi^\mp$ at a center-of-mass energy of 4.26GeV using a 827pb$^{-1}$ data sample obtained with the BESIII detector at the Beijing Electron Positron Collider. Based on a partial reconstruction technique, the Born cross section is measured to be $(137\pm9\pm15)$pb. We observe a structure near the $(D^{*} \bar{D}^{*})^{\pm}$ threshold in the $\pi^\mp$ recoil mass spectrum, which we denote as the $Z^{\pm}_c(4025)$. The measured mass and width of the structure are $(4026.3\pm2.6\pm3.7)$MeV/c$^2$ and $(24.8\pm5.6\pm7.7)$MeV, respectively. Its production ratio $\frac{\sigma(e^+e^-\to Z^{\pm}_c(4025)\pi^\mp \to (D^{*} \bar{D}^{*})^{\pm} \pi^\mp)}{\sigma(e^+e^-\to (D^{*} \bar{D}^{*})^{\pm} \pi^\mp)}$ is determined to be $0.65\pm0.09\pm0.06$. The first uncertainties are statistical and the second are systematic.Comment: 7 pages, 4 figures, 1 table; version accepted to be published in PR

Observation of Y(2175) in J/ψ→ηϕf0(980)J/\psi\to \eta\phi f_0(980)

The decays of $J/\psi\to \eta\phi f_0(980) (\eta\to \gamma\gamma, \phi \to K^+K^-, f_0(980)\to\pi^+\pi^-)$ are analyzed using a sample of $5.8 \times 10^{7}$ $J/\psi$ events collected with the BESII detector at the Beijing Electron-Positron Collider (BEPC). A structure at around $2.18$GeV/$c^2$ with about $5\sigma$ significance is observed in the $\phi f_0(980)$ invariant mass spectrum. A fit with a Breit-Wigner function gives the peak mass and width of $m=2.186\pm 0.010 (stat)\pm 0.006 (syst)$GeV/$c^2$ and $\Gamma=0.065\pm 0.023 (stat)\pm 0.017 (syst)$GeV/$c^2$, respectively, that are consistent with those of Y(2175), observed by the BABAR collaboration in the initial-state radiation (ISR) process $e^+e^-\to\gamma_{ISR}\phi f_0(980)$. The production branching ratio is determined to be $Br(J/\psi\to\eta Y(2175))\cdot Br(Y(2175)\to\phi f_0(980))\cdot Br(f_0(980)\to\pi^+\pi^-)=(3.23\pm 0.75 (stat)\pm0.73 (syst))\times 10^{-4}$, assuming that the Y(2175) is a $1^{--}$ state.Comment: 5 pages, 4 figures, accepted by Phys. Rev. Let

Measurement of \psip Radiative Decays

Using 14 million psi(2S) events accumulated at the BESII detector, we report first measurements of branching fractions or upper limits for psi(2S) decays into gamma ppbar, gamma 2(pi^+pi^-), gamma K_s K^-pi^++c.c., gamma K^+ K^- pi^+pi^-, gamma K^{*0} K^- pi^+ +c.c., gamma K^{*0}\bar K^{*0}, gamma pi^+pi^- p pbar, gamma 2(K^+K^-), gamma 3(pi^+pi^-), and gamma 2(pi^+pi^-)K^+K^- with the invariant mass of hadrons below 2.9GeV/c^2. We also report branching fractions of psi(2S) decays into 2(pi^+pi^-) pi^0, omega pi^+pi^-, omega f_2(1270), b_1^\pm pi^\mp, and pi^0 2(pi^+pi^-) K^+K^-.Comment: 5 pages, 4 figure

First observation of the M1 transition ψ(3686)→γηc(2S)\psi(3686)\to \gamma\eta_c(2S)

Using a sample of 106 million \psi(3686) events collected with the BESIII detector at the BEPCII storage ring, we have made the first measurement of the M1 transition between the radially excited charmonium S-wave spin-triplet and the radially excited S-wave spin-singlet states: \psi(3686)\to\gamma\eta_c(2S). Analyses of the processes \psi(2S)\to \gamma\eta_c(2S) with \eta_c(2S)\to \K_S^0 K\pi and K^+K^-\pi^0 gave an \eta_c(2S) signal with a statistical significance of greater than 10 standard deviations under a wide range of assumptions about the signal and background properties. The data are used to obtain measurements of the \eta_c(2S) mass (M(\eta_c(2S))=3637.6\pm 2.9_\mathrm{stat}\pm 1.6_\mathrm{sys} MeV/c^2), width (\Gamma(\eta_c(2S))=16.9\pm 6.4_\mathrm{stat}\pm 4.8_\mathrm{sys} MeV), and the product branching fraction (\BR(\psi(3686)\to \gamma\eta_c(2S))\times \BR(\eta_c(2S)\to K\bar K\pi) = (1.30\pm 0.20_\mathrm{stat}\pm 0.30_\mathrm{sys})\times 10^{-5}). Combining our result with a BaBar measurement of \BR(\eta_c(2S)\to K\bar K \pi), we find the branching fraction of the M1 transition to be \BR(\psi(3686)\to\gamma\eta_c(2S)) = (6.8\pm 1.1_\mathrm{stat}\pm 4.5_\mathrm{sys})\times 10^{-4}.Comment: 7 pages, 1 figure, 1 tabl

Search for Baryonic Decays of \psi(3770) and \psi(4040)

By analyzing data samples of 2.9 fb^{-1} collected at \sqrt s=3.773 GeV, 482 pb^{-1} collected at \sqrt s=4.009 GeV and 67 pb^{-1} collected at \sqrt s=3.542, 3.554, 3.561, 3.600 and 3.650 GeV with the BESIII detector at the BEPCII storage ring, we search for \psi(3770) and \psi(4040) decay to baryonic final states, including \Lambda\bar\Lambda\pi^+\pi^-, \Lambda \bar\Lambda\pi^0, \Lambda\bar\Lambda\eta, \Sigma^+ \bar\Sigma^-, \Sigma^0 \bar\Sigma^0, \Xi^-\bar\Xi^+ and \Xi^0\bar\Xi^0 decays. None are observed, and upper limits are set at the 90% confidence level.Comment: 9 pages, 3 figure

Precision measurement of the branching fractions of J/psi -> pi+pi-pi0 and psi' -> pi+pi-pi0

We study the decays of the J/psi and psi' mesons to pi+pi-pi0 using data samples at both resonances collected with the BES III detector in 2009. We measure the corresponding branching fractions with unprecedented precision and provide mass spectra and Dalitz plots. The branching fraction for J/psi -> pi+pi-pi0 is determined to be (2.137 +- 0.004 (stat.) +0.058-0.056 (syst.) +0.027-0.026 (norm.))*10-2, and the branching fraction for psi' -> pi+pi-pi0 is measured as (2.14 +- 0.03 (stat.) +0.08-0.07 (syst.) +0.09-0.08 (norm.))*10-4. The J/psi decay is found to be dominated by an intermediate rho(770) state, whereas the psi' decay is dominated by di-pion masses around 2.2 GeV/c2, leading to strikingly different Dalitz distributions.Comment: 15 pages, 2 figure

Search for the Lepton Flavor Violation Process J/ψ→eμJ/\psi \to e\mu at BESIII

We search for the lepton-flavor-violating decay of the $J/\psi$ into an electron and a muon using $(225.3\pm2.8)\times 10^{6}$ $J/\psi$ events collected with the BESIII detector at the BEPCII collider. Four candidate events are found in the signal region, consistent with background expectations. An upper limit on the branching fraction of $\mathcal{B}(J/\psi \to e\mu)< 1.5 \times 10^{-7}$ (90% C.L.) is obtained