Search

We present a comprehensive review of purely leptonic and semileptonic decays of $D^{0(+)}$, $D_s^{+}$, and charmed baryons (including $\Lambda_c^{+}$, $\Xi_c$ and $\Omega_c$). The precise studies of these decays help deepen our understanding and knowledge of quantum chromodynamics via measuring decay constants and form factors, and test the Standard Model through examining the unitarity of Cabibbo-Kobayashi-Maskawa matrix and lepton flavor universality. We give an overview of the theoretical and experimental tools before discussing the recent progress. The data sets collected by BESIII near the production thresholds of $D\bar{D}$, $D_s^{(*)+}D_s^{(*)-}$ and $\Lambda_c^{+}\bar{\Lambda}_c^{-}$ offer important opportunities for studies of charm physics., Comment: 24 pages, 10 figures

The electric dipole moment (EDM) of elementary particles, arising from flavor-diagonal $CP$ violation, serves as a powerful probe for new physics beyond the Standard Model and holds the potential to provide novel insights in unraveling the puzzle of the matter-dominated Universe. Hyperon EDM is a largely unexplored territory. In this paper, we present a comprehensive angular analysis that focuses on entangled hyperon-antihyperon pairs in $J/\psi$ decays for the indirect extraction of hyperon EDM. The statistical sensitivities are investigated for BESIII and the proposed Super Tau-Charm Facility (STCF). Leveraging the statistics from the BESIII experiment, the estimated sensitivity for $\Lambda$ EDM can reach an impressive level of $10^{-19}$ $e$ cm, achieving a 3-orders-of-magnitude improvement over the only existing measurement in a fixed-target experiment at Fermilab with similar statistics. The estimated sensitivities for the $\Sigma^+$, $\Xi^-$, and $\Xi^0$ hyperons at the same level of $10^{-19}$ $e$ cm will mark the first-ever achievement and the latter two will be the first exploration of hyperons with two strange valence quarks. The EDM measurements for hyperons conducted at the BESIII experiment will be a significant milestone and serve as a litmus test for new physics such as supersymmetry and the left-right symmetrical model. Furthermore, at the STCF experiment, the sensitivity of hyperon EDM measurements can be further enhanced by 2 orders of magnitude. Additionally, this angular analysis enables the determination of $CP$ violation in hyperon decays, the effective weak mixing angle, and beam polarization.

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed., Comment: Invited volume for the EJPC; 567 pages if text/figures and 4783 references occupying about 160 additional pages. arXiv abstract abridged, for the complete abstract please see the full text

The prospects to study hyperon-nuclei/nucleon interactions at BESIII and similar $e^+ e^-$ colliders are proposed in this work. Utilizing the large quantity of hyperons produced by the decay of 10 billion $J/\psi$ and 2.7 billion $\psi(3686)$ collected at BESIII, the cross sections of several specific elastic or inelastic hyperon-nuclei reactions can be measured via the scattering between the hyperons and the nucleus in the dense objects of BESIII detector. Subsequently, the cross sections of corresponding hyperon-nucleon interactions are able to be extracted with further phenomenological calculation. Furthermore, the interactions between antihyperon and nuclei/nucleon, including scattering and annihilation, can also be studied via the method proposed in this paper. The results will definitely benefit a lot the precise probe of the hyperon-nuclei/nucleon interactions and provide constraints for the studies of the potential of strong interaction, the origin of color confinement, the unified model for baryon-baryon interactions, and the internal structure of neutron stars. In addition, the desirable prospects of corresponding studies in the future Super Tau-Charm Factory (STCF) are discussed and estimated in this work.

In this paper, we present a preliminary study of $CP$ violation effect of $K^{0}-\bar{K}^{0}$ system in $J/\psi$ decay. The $CP$ violation parameters $\eta_{+-}$ and $\eta_{00}$ as well as their corresponding phase $\phi_{+-}$ and $\phi_{00}$ can be determined by the difference of the time-dependent decay rates between $K^{0}$ and $\bar{K}^{0}$ produced from $J/\psi \rightarrow K^{-}\pi^{+}K^{0} + c.c.$ processes. We investigate the precisions of the measurements of the CP violation effect at the Super Tau-Charm facility(STCF), a $e^{+}e^{-}$ collider with a peak luminosity of $0.5\times10^{35}\ \rm{cm}^{-2}\rm{s}^{-1}$. The parameters $\eta_{+-}$ and its phase $\phi_{+-}$ can be measured at a relative precision of $1 \times 10^{-3}$, which the statistical accuracy will be several times better than that of the existing PDG average values.

A generator of antiproton ($\bar{p}$) in Geant4 has been developed using a theoretical model with the consideration of near-threshold treatment and used preliminarily in COMET experiment. The precision of this generator has been verified by comparing with experimental results taken in CERN (1970) and ITEP (1994). By implementing this generator into official data analysis framework of COMET, the yield of $\bar{p}$ in COMET experiment can be evaluated properly. Background caused by $\bar{p}$ can also be estimated by this generator in future, which will instruct the design and optimization. Moreover, this generator can also be used in the simulation of other experiments involving near-threshold $\bar{p}$ generation., Comment: 14 pages, 5 figures, 5 tables

A new Goldstone particle named Majoron is introduced in order to explain the origin of neutrino mass by some new physics models assuming that neutrinos are Majorana particle. By expanding signal region and using likelihood analysis, it becomes possible to search for Majoron at experiments that is originally designed to search for $\mu-e$ conversion. For the COMET experiment, the sensitivity of process $\mu \rightarrow eJ$ is able to reach ${\mathcal{B}}(\mu \rightarrow eJ)=2.3\times 10^{-5}$ in Phase-I and $O(10^{-8})$ in Phase-II. Meanwhile, the sensitivities to search for Majoron at future experiments are also discussed in this article., Comment: 8 pages, 10 figures, 3 tables

The spontaneous muonium to antimuonium conversion is one of the interesting charged lepton flavor violation processes. It serves as a clear indication of new physics and plays an important role in constraining the parameter space beyond Standard Model. MACE is a proposed experiment to probe such a phenomenon and expected to enhance the sensitivity to the conversion probability by more than two orders of magnitude from the current best upper constraint obtained by the PSI experiment two decades ago. Recent developments in the theoretical and experimental aspects to search for such a rare process are summarized., Comment: 13 pages, 10 figures, 3 tables, contribution to Snowmass 2021

A comprehensive review of weak decays of charmed hadrons ($D^{0/+}$, $D^+_s$ and $\Lambda^+_c$) based on analyses of the threshold data from $e^+e^-$ annihilation in the BESIII experiment is presented. Current experimental challenges and successes in understanding decays of the charmed hadrons are discussed. Precise calibrations of QCD and tests of the Standard Model are provided by measurements of purely leptonic and semi-leptonic decays of charmed hadrons, and lepton universality is probed in purely leptonic decays of charmed mesons to three generations of leptons. Quantum correlations in threshold data samples provide access to strong phases in the neutral $D$ meson decays and probe the decay dynamics of the charmed $\Lambda_c$ baryon. Charm physics studies with near-threshold production of charmed particle pairs are unique to BESIII, and provide many important opportunities and challenges., Comment: 24 pages, 10 figures, accepted version by the National Science Review

Based on the mechanism of neutral meson mixing, we predict the branching fraction of the semileptonic decay of $D_s^+\to \pi^0 \ell^+ \nu_\ell$ ($\ell=e$, $\mu$) using recently measured branching fraction of $D_s^+\to \eta e^+\nu_e$ by BESIII experiment . We also give a formula that can describe the neutral meson mixing of $\pi^0$, $\eta$, $\eta'$ and a pseudoscalar gluonium $G$ in a unified way. The predicted branching fraction of $D_s^+\to\pi^0 e^+\nu_e$ decay is $\mathcal{B}(D_s^+\to\pi^0 e^+\nu_e)=(2.65\pm 0.38)\times 10^{-5}$. It is important to search for the decay $D_s^+\to \pi^0 \ell^+ \nu_\ell$ in experiment, in order to understand the mechanism of $\pi^0$ production in $D_s^+\to\pi^0$ transition in semileptonic decay. We also estimate the branching fraction of $D_s^+\to \pi^0\tau^+\nu_\tau$, which is the only kinematically allowed semi-tauonic decay mode of the charmed meson, since the mass value of $D_s^+$ meson is just slightly above the threshold of $\pi^0\tau^+$ generation in the semi-tauonic decay., Comment: 6 pages, 1 figure

We investigate the quantum correlated $\Lambda \bar{\Lambda} $ production in the reaction $e^{+}e^{-} \to J/\psi \to \Lambda \bar{\Lambda}$. Since the $\Lambda$ or $\bar{\Lambda}$ has a nonzero magnetic moment, its spin will undergo a Larmor precession in the magnetic field of the detector, such as the BESIII experiment. Because of the spin precession, the angular distribution of the $\Lambda$ and $\bar{\Lambda}$ is slightly modified. Therefore, we obtain the corresponding term of the modified angular distribution due to the effect of the Larmor precession. We also estimate its potential effect on the measurements of $CP$ violation, as well as the decay asymmetry parameter and polarization of $\Lambda$. The polarization of the $\Lambda$ or $\bar{\Lambda}$ at the production vertex will rotate around the $B$-field axis, over an angle depending on the flight length in, but it still could be measured by fit to the corrected angular distribution. Of important, We conclude that a nonzero $CP$ asymmetry of order $10^{-4}$ will be caused once neglecting spin precession of the $\Lambda$ and $\bar{\Lambda}$ in the $e^{+}e^{-} \to J/\psi \to \Lambda \bar{\Lambda}$ process. The size of this $CP$ asymmetry is several times that of predicted within Standard Model in the hyperon decay. Although this effect is small, it will play an important role in future high precision experiments, such as the super-tau-charm factory.

While indirect & direct CP violations (CPV) had been established in the decays of strange & beauty mesons, none have been done for baryons. There are different "roads" for finding CP asymmetries in the decays of strange baryons; they are highly non-trivial ones. The HyperCP Collaboration had probed CPV in the decays of single $\Xi$ & $\Lambda$ [Phys.Rev.Lett 93 (2004) 262001]. We talk about future lessons from $e^+e^-$ collisions at BESIII/BEPCII: probing decays of pairs of strange baryons, namely $\Lambda$, $\Sigma$ & $\Xi$. Realistic goals are to learn about non-perturbative QCD. One can hope to find CPV in the decays of strange baryons; one can also dream to find impact of New Dynamics (ND). We point out that a new important era starts with the BESIII/BEPCII data accumulated by the end of 2018., Comment: final version, slight typos corrected

The study of hyperon decays at the Beijing Electron Spectrometer III (BESIII) is proposed to investigate the events of $J/\psi$ decay into hyperon pairs, which provide a pristine experimental environment at the Beijing Electron--Positron Collider II. About $10^{6}$--$10^8$ hyperons, i.e., $\Lambda$, $\Sigma$, $\Xi$, and $\Omega$, will be produced in the $J/\psi$ and $\psi(2S)$ decays with the proposed data samples at BESIII. Based on these samples, the measurement sensitivity of the branching fractions of the hyperon decays is in the range of $10^{-5}$--$10^{-8}$. In addition, with the known center-of-mass energy and "tag technique," rare decays and decays with invisible final states can be probed., Comment: 8 pages, 8 tables, add more references and corrections; many typos fixed; erratum added: https://doi.org/10.1007/s11467-019-0910-7

About 2.9 fb$^{-1}$ data set had been collected with the BESIII detector at the BEPCII collider. Taking advantages of data near open-charm threshold, we present preliminary results on leptonic and semileptonic charm-meson decays, as well as result on the FCNC process $D^0 \rightarrow \gamma \gamma$ from BESIII experiment. High precision charm data will enable us to validate Lattice QCD calculations at the few percent level. These can then be used to make precise measurements of CKM elements, $V_{cd}$ and $V_{cs}$, which are useful to improve the accuracy of test of the CKM unitary., Comment: 7 pages, 9 figures, proceedings for talk at BEACH 2012, July 23-28, 2012 in Wichita, USA

Hadron physics represents the study of strongly interacting matter in all its manifestations and the understanding of its properties and interactions. The interest on this field has been revitalized by the discovery of new light hadrons, charmonium- and bottomonium-like states. I review the most recent experimental results from different experiments., Comment: Presented at Lepton-Photon 2011, Mumbai, India; 21 pages, 18 figures; add more references; some correction

Recently, LHCb experiment announced a 3.5$\sigma$ evidence for direct CP violation in $D^0$ decay by looking at the difference between $A_{CP}(D^0\rightarrow K^+K^-)$ and $A_{CP}(D^0\rightarrow \pi^+\pi^-)$. This is the first evidence of CP violation in charm system, which may indicate new physics beyond the Standard Model. Motivated by this measurement, we review rare processes in charmonium decay, especially, the weak decay, $C$ or $P$ violated decay and lepton flavor violated decays. In case the new physics appears in charm sector, these rare decays of charmonium states will provide opportunity to search for significant contributions from physics beyond the Standard Model. With huge $J/\psi$ and $\psi(2S)$ samples in BESIII experiment, the rare decays may be feasible., Comment: 9 pages, Submitted to Chinese Physics C. arXiv admin note: text overlap with arXiv:0710.0039 by other authors

We study the electromagnetic Dalitz decay modes of $J/\psi \rightarrow P l^+l^-$ ($P= \pi^0$, $\eta$ or $\eta^\prime$). In these decays, the lepton pairs are formed by internal conversion of an intermediate virtual photon with invariant mass $m_{l^+l^-}$. Study of the effective-mass spectrum of the $l^+l^-$ will shed light on the dynamic transition form factor $F_{J/\psi P}(q^2)$ ($q^2 = m^2_{l^+l^-}$), which characterizes the electromagnetic structure arising at the vertex of the transition $J/\psi$ to pseudoscalars. We also discuss the direct productions of a GeV scale vector $U$ boson in these processes $J/\psi \rightarrow PU$ ($U\rightarrow l^+l^-$). It is responsible for mediating a new $U(1)_d$ interaction, as recently exploited in the context of weakly interacting massive particle dark matter. In this paper, we firstly use the usual pole approximation for the form factor to estimate the decay rate of $J/\psi \rightarrow P l^+l^-$ in the standard model. Then the reach of searching for the dark photon is estimated. We suggest that these Dalitz decays can be used to search for the light $U$ boson in the BESIII experiment with a huge $J/\psi$ data set., Comment: 6 pages, 3 figure, add two more figures, more discussions

BESIII had collected large data samples on $J/\psi$ and $\psi^\prime$ peaks during the first run in 2009. From 2010 to 2011, about 2.9 fb$^{-1}$ integrated luminosity were obtained on the peak of $\psi(3770)$ for open charm physics. We review recent results on charmonium decays and hadron spectroscopy. The prospects on open charm physics are also discussed., Comment: 14 pages, 11 figures, Proceeding for XIV International Conference on Hadron Spectroscopy (hadron2011), 13-17 June 2011, Munich, Germany

We present the most recent results from the BESIII experiment. This review covers the studies of charmonium decays, light hadron spectroscopy and charm physics. Especially, the prospects for weak decays of charm mesons are addressed at the BESIII., Comment: Presented at Flavor Physics and CP Violation - FPCP 2010, Turin, Italy, May 25-29, 2010

We exploit the angular and quantum correlations in the $D\bar{D}$ pairs produced through the decay of the $\psi(3770)$ resonance in a charm factory to investigate CP-violation in two different ways. We consider the case of $\psi(3770)\rightarrow D\bar{D}\rightarrow (V_1V_2)(K\pi)$ decays, which provide a new way to measure the strong phase difference $\delta$ between Cabibbo-favored and doubly-Cabibbo suppressed $D$ decays required in the determination of the CKM angle $\gamma$. We also build CP-violating observables in $\psi(3770)\rightarrow D\bar{D}\rightarrow (V_1V_2)(V_3 V_4)$ to isolate specific new physics effects in the charm sector. Neglecting the systematics, we give a first rough estimate of the sensitivities of these measurements at BES-III with an integrated luminosity of 20 fb$^{-1}$ at $\psi(3770)$ peak and at a future super $\tau$-charm factory with a luminosity of $10^{35}$ cm$^{-2}$s$^{-1}$, Comment: 4 pages, in Pos style, Proceeding for ICHEP2010, Paris

In this paper, we study CP violation in $\Lambda_c^+\to BP$ and $\Lambda_c^+\to BV$ decays, where $B,P$ and $V$ denote a light spin-1/2 baryon, pseudoscalar and a vector meson respectively. In these processes the $T$ odd CP violating triple-product (TP) correlations are examined. The genuine CP violating observables which are composed of the helicity amplitudes occurring in the angular distribution are constructed. Experimentally, by performing a full angular analysis it is shown how one may extract the helicity amplitudes and then obtain the TP asymmetries. We estimate the TP asymmetries in $\lam$ decays to be negligible in the standard model making these processes an excellent place to look for new physics. Taking a two Higgs doublet model, as an example of new physics, we show that large TP asymmetries are possible in these decays. Finally, we discuss how BES-III and Super $\tau$-Charm experiments will be sensitive to these CP violating signals in $\Lambda_c^+$ decays., Comment: 7 pages, 2 tables. Journal reference is added

The abundant $\psi'$ events have been collected at the Beijing Electron Positron Collider-II (BEPCII) that could undoubtedly provide us with a great opportunity to study the more attractive charmonium decays. As has been noticed before, in the process of $J/\psi$ decaying to the baryonic final states, $p K^- \bar{\Lambda}$, the evident $\Lambda^*$ and $N^*$ bands have been observed. Similarly, by using the product of $\chi_{cJ}$ from $\psi'$ radiative decay, we may confirm it or find some extra new resonances. $\chi_{c0}$'s data samples will be more than $\chi_{c1,2}$ taking into account the larger branching ratio of $\psi'\to\gamma\chi_{c0}$. Here, we provide explicit partial wave analysis formulae for the very interesting channel $\psi'\to\gamma\chi_{c0}\to \gamma p K^- \bar{\Lambda}$., Comment: 7 pages, 1 figure, version in Chin.Phys.C

We study an experimental search of a GeV scale vector boson at BES-III/BEPCII. It is responsible for mediating a new U(1)$_d$ interaction, as recently exploited in the context of weakly interacting massive particle dark matter. At low energy $e^+ e^-$ colliders this dark state can be efficiently probed. We discuss the direct productions of this light vector $U$ boson and the decay of this state with BES-III data and its foreseen larger data. In particular, we show that Higgs' strahlung in the dark sector can lead to multilepton signatures, which probe the physics range for kinetic mixing parameter $\epsilon \sim 10^{-4} -10^{-3}$ over a large portion of the parameter space., Comment: 8 pages and 4 figures, version to appear in Phys. Lett. B

Based on the data of BES and Belle, the production of $D\bar{D}$ in the $e^+e^-\to D\bar{D}$ scattering process is studied in this paper. We analyze the continuum and resonant contributions in the energy region from 3.7 to 4.4 GeV. In the $\chi^2$ fit to data, we obtain the resonance parameters of $\psi(3770)$, the branching ratio of $\psi(3770)\to D\bar{D}$ decay by confronting the data to the theoretical formula where both the contributions of the resonances, continuum and interference effects are included. We obtain the branching ratio of $\psi(3770)\to D\bar{D}$ decay is $97.2%\pm 8.9%$, as well as the branching ratio of $\psi(4040)$, $\psi(4160)\to D\bar{D}$ decays., Comment: 6 pages, 1 figure, 1 table, version to appear in Phys. Rev. D Rapid communications

We discuss the possibility of searching for the $\Lam - \Lamb$ oscillations for coherent $\Lam\Lamb$ production in the J/$\psi \to \Lam \Lamb$ decay process. The sensitivity of measurement of $\Lam -\Lamb$ oscillation in the external field at BES-III experiment is considered. These considerations indicate an alternative way to probe the $\Delta B =2$ amplitude in addition to neutron oscillation experiments. Both coherent and time-dependent information can be used to extract the $\Lam-\Lamb$ oscillation parameter. With one year's luminosity at BES-III, we can set an upper limit of $\delta m_{\Lam \Lamb} < 10^{-15}$ MeV at 90% confidence level, corresponding to about $10^{-6}$ s of $\Lam-\Lamb$ oscillation time., Comment: 4 pages, no figure, minor corrections to improve grammar, published in Phys.Rev.D as Rapid Communication.

Decays of both $\eta$ and $\eta^\prime$ provide very useful information in our understanding of low-energy QCD, and experimental signatures for these decays would be extremely helpful at BES-III. The rare decays of the $\eta$ and $\eta^\prime$ mesons could serve as a low-energy test of the Standard Model and its beyond. The sensitivities of the measurements of $\eta$ and $\eta^\prime$ decays are discussed at BES-III, in which the $\eta$ and $\eta^\prime$ mesons are produced in the $\psi$ decays., Comment: A few corrections added, published at J. Phys. G: Nucl. Part. Phys

The recent observations of the purely leptonic decay $\Ds \to \mu^+ \nu_{\mu}$ and $\tau^+\nu_{\tau}$ at CLEO-c and $B$ factory may allow a possible contribution from a charged Higgs boson. One such measurement of the decay constant $f_{D_s}$ differs from the most precise unquenched lattice QCD calculation by 4 $\sigma$ level. Meanwhile, the measured ratio, ${\cal BR}(\Ds \to \mu^+ \nu_{\mu})$ / ${\cal BR}(\Dp \to \mu^+ \nu_{\mu})$, is larger than the standard model prediction at 2.0$\sigma$ level. We discuss that the precise measurement of the ratio ${\cal BR}(\Ds \to \mu^+ \nu_{\mu})$ / ${\cal BR}(\Dp \to \mu^+ \nu_{\mu})$ at BES-III will shed light on the presence of new intermediate particles by comparing the theoretical predictions, especially, the predictions of high precise unquenched lattice QCD calculation., Comment: 5 pages, 3 figures, mini-review, accepted by Chinese Physics C (HEP & NP)

This paper presents the results of searches for the flavor-changing neutral current, lepton-number-violating and lepton-flavor-violating processes in the charm mesons decays. Recent results from charged $D$ mesons decays to final states with dielectrons from CLEO-c are reported. The prospects of the searches for the rare charm decays at BES-III are also discussed., Comment: Add more reference; 10 pages, 1 figure. Contribution to KAON International Conference, May 21-25 2007, Laboratori Nazionali di Frascati dell'INFN, Rome, Italy

Most recently, both BaBar and Belle experiments found evidences of neutral $D$ mixing. In this paper, we discuss the constraints on the strong phase difference in $D^0 \to K\pi$ decay from the measurements of the mixing parameters, $y^\prime$, $y_{CP}$ and $x$ at the $B$ factories. The sensitivity of the measurement of the mixing parameter $y$ is estimated in BES-III experiment at $\psi(3770)$ peak. We also make an estimate on the measurements of the mixing rate $R_M$. Finally, the sensitivity of the strong phase difference at BES-III are obtained by using data near the $D\bar{D}$ threshold with CP tag technique at BES-III experiment., Comment: 6 pages, 1 figure, a typo fixed, add more reference and a few corrections

$\Dz-\Dzb$ mixing and significant CP violation in the charm system may indicate the signature of new physics. In this study, we suggest that the coherent $\DzDzb$ events from the decay of $\Upsilon(1S) \to \Dz \Dzb$ can be used to measure both mixing parameters and CP violation in charm decays. The neutral $D$ mesons from $\Upsilon(1S)$ decay are strongly boosted, so that it will offer the possibility to measure the proper-time interval, $\Delta t$, between the fully-reconstructed $\Dz$ and $\Dzb$. Both coherent and time-dependent information can be used to extract $\Dz-\Dzb$ mixing parameters. The sensitivity of the measurement should be improved at B factories or super-B., Comment: 6 pages, 1 figure, this is the last version to appear in Phys. Rev. D

Questions about detecting CP-violating decay process of $J/\psi\to K^0\bar{K}^0\to K_SK_S$ are discussed. Possible background and material regeneration effect are analyzed. The discussion can be directly extended to other vector quarkonium decays, like $\Upsilon$, $\psi (2S)$ and $\phi\to K_S K_S$., Comment: 5 pages, 2 figures, Latex