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\newcommand{\lplus}{\ensuremath{\Lambda+\bar{\Lambda}}} \newcommand{\lsf}{\ensuremath{\Lambda}} \newcommand{\lsa}{\ensuremath{\bar{\Lambda}}} \newcommand{\lambdas}{\ensuremath{\lambda_s}} \newcommand{\kzero}{$K^0$~} \newcommand{\GeVSq}{{\rm\,GeV^2}} \newcommand{\bars}{\ensuremath{\bar{s}}} \newcommand{\baru}{\ensuremath{\bar{u}}} \newcommand{\bard}{\ensuremath{\bar{d}}} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent \begin{flushleft} {\bf H1prelim-13-031} Submitted to \\ \noindent\rule{20cm}{1.8pt} {\bf XXI International Workshop on Deep-Inelastic Scattering and Related Subjects, DIS2013}, April 22-26, 2013, Marseille~~~~~~~~ Parallel Session~~~~~~~~~~~~{\bf QCD and Final States}\\ \noindent\rule{20cm}{1.8pt} {\it Electronic Access: www-h1.desy.de/publications/H1preliminary.short\_list.html} \end{flushleft} \noindent %Date: [today instruction is preferred] \\ %\today \\ %Version: 0.99 (\today)\\%Preparatives 0.1,0.2...; 1st draft: 1.0, 1.1...; 2nd Draft 2.0..., Final Reading 3.0,3.1... \\ %Editors: Alexander Bylinkin, Andrey Rostovtsev \\ %Referees: Michael Steder, Dietrich Wegener \\ %Comments by \\ \noindent %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% For conference papers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% coment the header and fill the right conference %%%%% {\it {\large version of \today}} \\[.3em] \vspace{2cm} \begin{center} \begin{Large} {\bf Production of {\boldmath $\Lambda$ Baryons at high $Q^2$\unboldmath} at HERA\\}%(version of \today )} \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} The production of $\Lambda$ baryons %\ksf, \lsf, and \lsa\ is studied using deep-inelastic events measured with the H1 detector at HERA. The measurements are made in the phase space defined by the negative four-momentum transferred squared of the photon, $145 < \qsq< 20000 \GeVSq$, and the inelasticity $0.2 < y < 0.6$. Differential \lsfa\ production cross sections are measured. % in the laboratory and the Breit reference frames as functions of the kinematics of the strange particles as well as the kinematics of the DIS event. The Differential \lplus\ yields per event are determined. %, as compared to the production of DIS events are presented. %\ksf\ production is compared to the production of charged particles in the same phase space. The $\lsf - \lsa$ asymmetry is measured and found to be consistent with zero. Predictions of leading order Monte Carlo programs %, for various settings of the parameters relevant to strangeness production, are compared to data. \end{abstract} \vspace{1.5cm} \begin{center} %To be submitted to \EJC \;\; or \PLB \end{center} \end{titlepage} % THE PAPER DRAFTS HAVE NO AUTHORLIST % % FOR PAPER ISSUED FOR THE FINAL READING % COPY THE AUTHOR AND INSTITUTE LISTS % INTO YOUR AREA % % from /h1/iww/ipublications/h1auts.tex % AND UNCOMMENT THE NEXT THREE LINES % %\begin{flushleft} % \input{h1auts} %\end{flushleft} % % Please not that the author list may need re-formatting. \newpage \section{Introduction} \noindent \unitlength1cm The measurement of strange particle production in high energy collisions provides valuable information for understanding Quantum Chromodynamics (QCD) in the perturbative and non-perturbative regime. The production of \ksf, \lsfa\ has been studied at different colliders with complementary characteristics; in $e^+e^-$ annihilation at LEP \cite{Buskulic:1994ny,Abreu:1994rg,Acciarri:1994gza,Acton:1992ry}, in $p\bar{p}$ collisions at Tevatron \cite{Acosta:2005pk}, in $pp$ interactions at RHIC \cite{Abelev:2006cs}, in $ep$ scattering at HERA \cite{Derrick:1995ws,Aid:1996ui,Adloff:1997ym,Breitweg:1997kc,Chekanov:2006wz,Aaron:2008ck} and at the LHC \cite{Aamodt:2011zza,Khachatryan:2011tm,Aaij:2010nx,Aaij:2011va,atlas12}. In neutral current deep-inelastic $ep$ scattering (DIS) at HERA the four different processes depicted in figure~\ref{fig:production} contribute to strange hadron production. \begin{figure}[h] \begin{picture}(15.,4.) \put(0.,0.){\includegraphics[width=0.25\textwidth]{H1prelim-13-031.fig1a.eps}} \put(3.9,0.){\includegraphics[width=0.25\textwidth]{H1prelim-13-031.fig1b.eps}} \put(7.8,0.){\includegraphics[width=0.25\textwidth]{H1prelim-13-031.fig1c.eps}} \put(12.1,0.){\includegraphics[width=0.25\textwidth]{H1prelim-13-031.fig1d.eps}} \put(1.4,3.7){(a)} \put(5.3,3.7){(b)} \put(9.2,3.7){(c)} \put(13.5,3.7){(d)} \end{picture} \caption{ Schematic diagrams for the processes contributing to strangeness production in $ep$ scattering: (a) direct production from the strange sea, (b) BGF, (c) heavy hadron decays and (d) fragmentation. The diagrams relevant for $K^0$ production are shown.} \label{fig:production} \end{figure} Strange quarks may be created in the hard sub-process of the $ep$ scattering by originating directly from the strange sea of the proton in a quark-parton-model (QPM) like interaction (figure \ref{fig:production}a), from boson-gluon-fusion (BGF, figure \ref{fig:production}b) or from the decays of heavy flavoured hadrons (figure \ref{fig:production}c). In these production mechanisms hard scales are involved %thus allowing for the applicability of perturbative QCD. The dominant source for strange hadron production, however, is the creation of an $s\overline{s}$ pairs in the non-perturbative fragmentation process (figure \ref{fig:production}d). While strange mesons are created by all four processes strange baryon production receives only little contributions from the decays of heavy flavoured hadrons. Since $s$ quarks are heavy compared to $u$ and $d$ quarks the formation rate of $s\overline{s}$ pairs in the fragmentation process is expected to be smaller than for $u\overline{u}$ or $d\overline{d}$ pairs. Therefore the production of strange hadrons is expected to be suppressed relative to non-strange hadrons. In the modelling of the fragmentation process this suppression is generally controlled by the strangeness suppression factor $\lambda_s$. Especially, the ratio of \ksf\ to charged particles should strongly depend on this quark mass effect. Apart from the differences in \ksf\ and \lsf\ production observed in decays of charm and beauty hadrons the production rate of strange baryons is expected to be small relative to strange mesons as a consequence of the fragmentation process. Even if the $s$ quark is directly produced in the hard sub-process, i.e. by the QPM or BGF process, the creation of a strange baryon is expected to be suppressed because a di-quark system from the vacuum is needed to form the baryon. %Therefore the \lsf\ to \ksf\ ratio is expected to be smaller than unity and should show only little sensitivity on $\lambda_s$. In $ep$ scattering the initial state has a baryon quantum number of $B=1$. The study of baryon production may therefore provide information about the process of baryon number transfer. In particular, data on the $\lsf - \lsa$ production asymmetry may help understanding this mechanism. This paper presents a measurement of \lsf\ and \lsa\ production in DIS at high values of the negative four momentum transferred squared, $145 < \qsq< 20000 \GeVSq$, in the range of lepton inelasticity $0.2 < y < 0.6$. The results are based on a data sample corresponding to an integrated luminosity of $ 340\ {\rm pb}^{\rm{-1}}$ collected with the H1 detector at HERA at a centre-of-mass energy of $319\ \rm{GeV}$ in the years $2004$ to $2007$. The analysis is performed in a different kinematic range than covered in previous H1 publications \cite{Aid:1996ui,Adloff:1997ym,Aaron:2008ck}. Results are presented for differential cross sections of \lsf, %neutral strange baryon to meson ratios, ratios of \ksf\ to charged particles, \ksf\ and then \lsf\ yields normalized to DIS, and the \lsf -- \lsa\ asymmetry. The measurements are shown as a function of various observables characterising the DIS kinematics and the strange particles production dynamics, both in the laboratory frame and in the Breit frame \cite{ref:breit}. %The results in the Breit frame are presented separately for the current and target hemispheres. The results are compared with predictions obtained from leading order Monte Carlo calculations, based on matrix elements with parton shower simulation. The r\^ole of the parton evolution and the strangeness suppression on %\ksf\ and \lsf\ production is investigated. \section{Monte Carlo Simulation} %The Monte Carlo generator DJANGOH \cite{djangoh} is used to determine the signal efficiencies and detector acceptances for data correction the data as well as to provide leading order (LO) expectations of the \ksf\ and \lsf\ production cross sections in deep-inelastic $ep$ scattering. Deep-inelastic $ep$ scattering is modelled using the DJANGH~\cite{djangoh} and the RAPGAP~\cite{RAPGAP} programs, which generate hard partonic processes at the Born level at leading order in $\alpha_s$ (e.g. $\gamma*q\rightarrow q$, $\gamma*q\rightarrow qg$ $\gamma*g\rightarrow q\overline{q}$), convoluted with the parton density function (PDF) of the proton. The PDF set CTEQ6L \cite{cteq6l} is chosen for this analysis. The factorisation and renormalisation scales a set to $\mu^2_f=\mu^2_r=Q^2$. Two different approaches are used for the simulation of higher order QCD effects: %are simulated by using either in RAPGAP the parton shower approach (MEPS) is implemented in which the parton emission is ordered in transverse momentum ($k_T$) according to the leading-$\log$ approximation; and in DJANGOH the colour dipol approach (CDM \cite{cdm}) available within ARIADNE \cite{ariadne} is adopted in which partons are created by colour dipole radiation between the partons in the cascade, resulting in a $k_T$ un-ordered parton emission. The JETSET program \cite{jetset} is used for simulating the hadronisation process in the Lund colour string fragmentation model \cite{lund}. The suppression of strange quarks is predominantly controlled by a single parameter, $\lambda_s=P_s/P_q$, where $P_s$ and $P_q$ are the probabilities for creating strange ($s$) or light ($q=u$ or $d$) quarks in the non-perturbative fragmentation process. The most relevant parameters for describing the baryon production %Further important parameters of this model are the di-quark suppression factor $\lambda_{qq}=P_{qq}/P_{q}$; i.e., the probability of producing a light di-quark pair $qq\overline{q}\overline{q}$ from the vacuum with respect to a light $q\overline{q}$ pair, and the strange diquark suppression factor $\lambda_{sq}=(P_{sq}/P_{qq})/(P_s/P_q)$, which models the relative production of strange di-quark pairs. %These are the two most relevant factors for the description of baryon production. %The $s\bars$ pair production rate is primarily dominated by $\lambda_s$; i.e., $u(\baru):d(\bard):s(\bars)=1:1:\lambda_s$. The values tuned to hadron production measurements in $e^+e^-$-annihilation by the ALEPH collaboration~\cite{ALEPH-TUNE} ($\lambda_s =0.286, \lambda_{qq}=0.108$, and $\lambda_{sq}=0.690$) are taken herein as default values for the simulation of hadronisation within JETSET. Monte Carlo event samples generated both with DJANGOH and RAPGAP are used for the acceptance and efficiency correction of the data. All generated events are passed through the full GEANT \cite{geant} based simulation of the H1 apparatus and are reconstructed and analysed using the same programs as for the data. %{\bf Does the MC needs to be re-weighted to describe the data?} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% new section: Experimental procedure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Experimental Procedure} %%%% \subsection{The H1 Detector} %%%% A detailed description of the H1 detector can be found in \cite{h1detector}. In the following, only those detector components important for the present analysis are described. H1 uses a right handed Cartesian coordinate system with the origin at the nominal $ep$ interaction point. The proton beam direction defines the positive $z$-axis of the laboratory frame and transverse momenta are measured in the $(x,y)$ plane. The polar angle $\theta$ is measured with respect to this axis and the pseudorapidity $\eta$ is given by $\eta=-\ln {\tan {\frac{\theta}{2}}}$. Charged particles are measured in the Central Tracking Detector (CTD) in the range $-1.75 < \eta < 1.75$. The CTD comprises two cylindrical Central Jet Chambers (inner CJC1 and outer CJC2), arranged concentrically around the beam-line, complemented by a silicon vertex detector (CST)~\cite{Pitzl:2000wz}. The CJCs are separated by a drift chamber which improves the $z$ coordinate reconstruction. A multi-wire proportional chamber mainly used for triggering \cite{cip} is situated inside the CJC1. These detectors are arranged concentrically around the interaction region in a solenoidal magnetic field of strength $1.16$ $\textrm{T}$. The trajectories of charged particles are measured with a transverse momentum resolution of $\sigma(p_T) / p_T \simeq 0.2\% \, p_T \, /\GeV \, \oplus 0.015$. In each event the tracks are used in a common fit procedure to determine the $ep$ interaction vertex. The measurement of the specific energy loss dE/dx of charged particles in this detector is known with a resolution of 6.3\% for a minimum ionising track \cite{dedx}. The tracking detectors are surrounded by a Liquid Argon calorimeter (LAr) which measures the positions and energies of particles, including that of the scattered positron, over the polar angle range $4^\circ < \theta < 154^\circ$. The calorimeter consists of an electromagnetic section with lead absorbers and a hadronic section with steel absorbers. The energy resolution for electrons in the electromagnetic section, as measured in beam tests, is $\sigma(E)/E=11.5 \% / \sqrt{E} ~[\GeV]~\oplus 1\%$~\cite{Andrieu:1994yn}. In the backward region ($153^\circ<\theta<178^\circ$), particle energies are measured by a lead-scintillating fibre calorimeter (SpaCal) \cite{spacal} The DIS events studied in this paper are triggered by a compact energy deposition in the electromagnetic section of the LAr calorimeter and a signal from the multi-wire proportional chambers. %The luminosity is determined from the rate of the Bethe-Heitler process, $ep \rightarrow ep\gamma$, measured using a calorimeter located close to the beam pipe at $z=-103~\textrm{m}$. The luminosity is determined from the rate of the elastic QED Compton process $ep\rightarrow e\gamma p$, with the electron detected in the SpaCal calorimeter, and the rate of DIS events measured in the SpaCal calorimeter \cite{qedc}. %%%% %\subsection{Selection of DIS Events and Charged Particles} \subsection{Selection of DIS Events} %%%% The data used in this analysis correspond to an integrated luminosity of $340 ~\rm pb^{-1}$ and were taken by H1 in the years from 2004 to 2007 when protons with an energy of $920 ~\GeV$ collided with electrons\footnote{The this paper "electron" is used to denote both electrons and positrons} with an energy of $27.6~\GeV$ producing a centre-of-mass energy of $\sqrt{s} = 319~\GeV$. The selection of DIS events is based on the identification of the scattered electron as a compact calorimetric deposit in the electromagnetic section of the LAr calorimeter in the polar angular range $10^\circ < \theta_e < 150^\circ$, with energy greater than $11~\GeV$ and associated with a charged track in the CTD. At fixed centre-of-mass energies $\sqrt{s}$ the kinematics of the scattering process are described using the Lorentz invariant variables $Q^2$, $y$ and $x$. These variables can be expressed as a function of the scattered electron energy $E_{e}^{\prime}$ and its scattering angle $\theta_{e}$ in the laboratory frame: \begin{equation} Q^2 = 4 E_e E_{e}^{\prime} \cos^2 \left( \frac{\theta_{e}}{2} \right) , \textrm{ \quad } y = 1 - \frac{E_{e}^{\prime}}{E_e} \sin ^2 \left( \frac{\theta_{e}}{2} \right), \;\; \quad x = \frac{Q^2}{ys}. \label{eq:kine} \end{equation} The negative four-momentum transfer squared $Q^2$ and the \mbox{inelasticity $y$} are required to lie in the ranges $145 < Q^2 < 20000\GeVSq$ and $0.2 < y < 0.6$. Background from photo-production events ($Q^2\approx 0\GeVSq$) in which the electron escapes undetected down the beam pipe and a hadron fakes the electron signature, is suppressed by the requirement that the difference $\Sigma(E-p_z)$ between the total energy and the longitudinal momentum must be in the range $35 < \Sigma(E - p_z) <70 \gev$, where the sum includes all measured hadronic final state particles \cite{hfs} and the scattered electron candidate. The $z$-coordinate of the event vertex, reconstructed using the tracking detectors, has to be within $\pm 35{\rm\,\cm}$ of the mean position for $ep$ interactions. %Primary-vertex-fitted charged-particles are selected requiring that the candidates have a minimal radial length of 10 cm and the radial distance from the innermost hit associated with the track to the beam line has to be less than 30 cm. %All selected particles have to be in the kinematic region defined by a transverse momentum greater than 300 \MeV\ and the absolute value of their pseudorapidity less than 1.5. %%%% \subsection{Selection of {\boldmath$\Lambda$} Baryons} \label{sec:RecStr} %%%% The \lsf\ baryons \footnote{Unless otherwise noted, charge conjugate states are always implied.} are measured by the kinematic reconstruction of its decay %s $\ksf \to \pi^+ \pi^-$ and $\Lambda \to p \pi^-$. %, respectively. The analysis is based on charged particles measured by the CTD with a minimum transverse momentum $p_T \geq 0.12\gev$. The %neutral strange hadrons \ksf\ and \lsf\ baryons are identified by fitting pairs of oppositely charged tracks in the $(x,y)$ plane to their secondary decay vertices, with the direction of flight of the mother particle constrained to the primary event vertex. Candidates are required to have a minimum radial decay length of $2\ {\rm cm}$, a minimum transverse momentum $p_T$ of more than $300 \MeV$ and to lie in the pseudorapidity range $|\eta|<1.5$. The phase space of the analysis is summarised in table~\ref{tab:kine}. %selected in the phase space defined by their transverse momenta being larger than 300 \MeV and the absolute value of their pseudorapidity less than 1.5. \begin{table}[t] \begin{center} \renewcommand{\arraystretch}{1.2} \begin{tabular}{|c|} \hline DIS kinematics\\ \hline $145 0.3\ {\rm GeV}$\\ $-1.5<\eta<1.5$\\ \hline \end{tabular} \end{center} \caption{Analysis phase space} \label{tab:kine} \end{table} %For \ksf\ candidate reconstruction both tracks are assumed to be pions, while For the reconstruction of \lsf\ candidates the track with the higher momentum is assumed to be the proton and the other track is assumed to be the pion. Furthermore, the observed energy loss, $dE/dx$, of the proton candidates in \lsf\ decays have to have a likelihood of being a proton of more than $0.003$. %the $dE/dx$ signal of the track assigned to the proton has to have a likelihood bigger than 0.003 of being a proton. The distinction between \lsf\ and \lsa\ baryon candidates is made by the electrical charge of the decay proton (antiproton) candidate. %The pions from \ksf\ decays are required to have a transverse momentum $p_T^{rel}$ relative to the direction-of-flight of the mother particle of at least $100 \MeV$. The contamination from \ksf decays in the \lsf sample is suppressed by a rejection of the corresponding invariant mass region: %$M(\pi p) > 1.125 \GeV$ for the \ksf\ and $475 < M(\pi\pi) < 530 \MeV$ for the \lsf\ selection. The contamination from gamma conversions is suppressed by requiring that the invariant mass, computed under the assumption that the tracks correspond to an electron--positron pair, is bigger than 50 \MeV. %The invariant mass spectra $M(\pi^{+} \pi^{-})$ and $M(p \pi)$ %of all candidates passing the selection criteria are shown in %figures~\ref{fig:K0sMass} and \ref{fig:LamMass}. The number of \lsf~ baryons is obtained by fitting the invariant mass spectra with the sum of a signal and background function. For the signal fuction a %Different functions are used for describing the signal shapes of the \ksf\ and the \lsf\ mass distributions: while the t-student function yields an appropriate description of the \ksf\ signal a skewed t-student function is used %needed for fitting the \lsfa\ spectra because of the relatively small energy release in \lsf decays. %The signal function is described with a (skewed) t-student distribution for the case of \ksf\ (\lsf/\lsa), while while the background distributions are parameterised as \begin{eqnarray} %B_{\ksf}(M) &=& p_0\ (M-2m_T)^{p_1} e^{p_2M+p_3M^2+p_4M^3}, \\ B_{\Lambda}(M) &=& p_0\ (p_1+p_2(M-m_\Lambda) + p_3(M-m_\Lambda)^2)(M-(m_p+m_\pi))^{p_4}. \label{eq:massfits} \end{eqnarray} Here, $M$ denotes %the $\pi\pi$ and the $p\pi$ invariant mass, and $m_{\lsf}$, $m_p$ and $m_\pi$ are the nominal masses of the $\lsf$, the proton and the pion\cite{Pdg10}. %The parameter $m_T$ corresponds to the the minimum transverse mass defined as $m_T=\sqrt{m_\pi^2+(p_{T,min}^{rel})^2}$. For the differential distribution the fit is performed in each kinematic bin. The invariant mass spectrum $M(p \pi)$ of all candidates passing the selection criteria are shown in figure~\ref{fig:massdist} together with the result from the fits. In total approximately %$38000$ \ksf mesons and $7000$ \lsfa\ baryons are reconstructed in the phase space given in table \ref{tab:kine}. The fitted \lsf\ mass agrees with the world average~\cite{Pdg10}. \section{Cross Sections Determination and Systematic Errors} The total inclusive Born-level cross section $\sigma_{\it vis}$ in the kinematic region defined in table~\ref{tab:kine} is given by the following expression: \begin{equation} \sigma_{vis}(ep \to e \Lambda X) = %\frac{N_{\ksf(\lsf)}} \frac{N} { {\cal L} \cdot \epsilon \cdot BR \cdot (1 + \delta_{rad}) }\qquad , \label{eq:sigman} \end{equation} where % $N_{\ksf(\lsf)}$ $N$ represents the observed number of $\lsf$, baryons. $\cal{L}$ and $\epsilon$ denote the integrated luminosity and the efficiency, respectively. The branching ratios $BR$ for $\Lambda$ decays are taken from \cite{Pdg10}. The radiative corrections $(1+\delta_{rad})$ needed to correct the measured cross section to the Born level are calculated using the program HERACLES~\cite{HERACLES}. The number of \lsfa\ particles is determined by fitting the mass distribution as explained in section~\ref{sec:RecStr}. In the case of differential distributions the same formula is applied for each analysis bin. The efficiency $\epsilon$ is given by $\epsilon = \epsilon_{rec} \cdot \epsilon_{trig}$, where $\epsilon_{rec}$ is the reconstruction efficiency and $\epsilon_{trig}$ is the trigger efficiency. The reconstruction efficiency includes the geometric acceptance and the efficiency for track and secondary vertex reconstruction. It is estimated using CDM Monte Carlo event samples. The trigger efficiency is extracted from the data using monitor triggers and is above 99\%. %In the case of charged hadrons $h^{\pm}$, the reconstruction efficiency $\epsilon_{rec}$ is defined such that it includes corrections for \ksf\ and \lsf\ decays, secondary interactions, photon conversions and the track reconstruction efficiency. %The total correction $1/(\epsilon\cdot(1+\delta_{rad}))$ amounts to about 3.33, 4.55 and 1.18 for $\ksf$, $\lsfa$ and $h^{\pm}$ respectively. The systematic uncertainties were studied by changing in the Monte Carlo the value of the variables presented below, repeating the analysis procedure and comparing the results to the standard analysis. For the cross section the total uncertainty was calculated adding the different contributions in quadrature, while for the ratios the uncertainties on the energy scale and angle resolution of the scattered electron, as well as on the luminosity, cancel; the other sources are assumed uncorrelated and added in quadrature. For differential distributions the systematic uncertailies are determined in each analysis bin separately. The following sources of systematic uncertainties were considered: \begin{itemize} \item the uncertainty on the energy scale of the LAr calorimeter for scattered electrons, %is known to $0.5\%$. \item the uncertainty of the measurement of the polar angle of the scattered electron,% is $1 {\rm mrad}$. \item the uncertainty on the trigger efficiency, % is known to $1\%$. \item the uncertainty on the reconstruction efficiency, %is known to $2\%$ independent of kinematics.%, resulting in a $4\%$ uncertainty on the tracking efficiency of the neutral strange hadrons. \item the uncertainty due the $dE/dx$ requirement on the proton candidate, %\item The procedure to use $dE/dx$ is known with a precision of $1.4\%$. \item the uncertainty in the signal extraction due to the two different topologies, %\item The decay of the strange hadrons have two different topologies, known as sailor and seagull. The relative uncertainty on the modelling of these topologies is known to %$3\%$ for the \ksf and $0.2\%$.% for the \lsfa. \item the uncertainty on the extraction of the signal,% is estimated to be $2.4\%$ %using side-band subtraction. {\bf needs more! how was it done?} %\item To evaluate the uncertainty on the reconstruction efficiency both Monte Carlo models, RAPGAP and DJANGOH, have been compared and the uncertainty taken as half of the difference between them. \item The uncertainty in the correction factor arising from using different Monte Carlo models in the correction procedure, taken as half of the dfference between correcting RAPGAP or DJANGO, %results in a typical error of %0.05\% for the \ksf and, of $1.7\%$. %for the \lsfa. \item the uncertainty on the branching ratio ($0.5\%$~\cite{Pdg10}) and \item the uncertainty in the luminosity measurement. %is $2.3\%$. \end{itemize} %The main contributions to the total systematic error are from the track reconstruction efficiency, the knowledge of the efficiencies for the different decay topologies for the \ksf and, for the \lsfa, the knowledge of $dE/dx$. \section{Results and Discussion} %%%% \subsection{Inclusive Cross Sections} The visible inclusive production cross sections $\sigma_{vis}$ are measured in the kinematic region defined by $145 < \qsq<20000 \GeVSq$ and $0.2 < y < 0.6$ for the event kinematics; and for the kinematics of the neutral strange hadrons, $p_T(\lsfa)> 300 \MeV$, $|\eta(\lsfa)|<1.5$. The cross sections are measured to be: %\begin{align} \begin{eqnarray*} %\sigma_{vis}(ep \rightarrow e \ksf X) &=& 531 \pm 17 %({\rm \textrm {stat.}}) ^{+37}_{-39} (\textrm {syst.}) \textrm{\, pb}, \\ %\label{eq:xsec-ks} \sigma_{vis}(ep \rightarrow e [\lsf + \lsa] X)& =& 144.7 \pm 4.7 (\textrm {stat.}) ^{+9.4}_{-8.5} (\textrm{syst.}) \textrm{\, pb}, \\ %\label{eq:xsec-la} \sigma_{vis}(ep \rightarrow e \lsf X) &=& 72.6 \pm 3.3 (\textrm {stat.}) ^{+4.8}_{-4.5} (\textrm{syst.}) \textrm{\, pb}, \\ %\label{eq:xsec-la2} \sigma_{vis}(ep \rightarrow e \lsa X) &=& 72.9 \pm 4.0 (\textrm {stat.}) ^{+4.9}_{-4.6} (\textrm{syst.}) \textrm{ \,pb} \end{eqnarray*} %\end{align} The cross section predictions for \lplus\ production from the MEPS and CDM models are shown in Table \ref{tab:McPred} for two values of the strangeness suppression parameter $\lambda_s$ . %For the inclusive case, the measurement of \ksf\ favors the higher value of $\lambda_s$ without distinguishing between the two models, while The measured inclusive \lplus\ cross section is close to the CDM prediction with $\lambda_s=0.22$ and to the MEPS prediction with $\lambda_s=0.286$. \begin{table}[t] \begin{center} % \vspace*{0.1 true cm} \begin{tabular}{|c|c|c|} \hline \rule{0pt}{3ex} & $\lambda_{s}=0.220$ & $\lambda_{s}=0.286$ \\ \hline \rule{0pt}{3ex} % $\sigma_{vis}(ep \rightarrow e \ksf X) $ CDM & $443 pb & 516 pb \\ % \hline \rule{0pt}{3ex} % $\sigma_{vis}(ep \rightarrow e \ksf X)$ MEPS & 444 pb & 536 pb \\ % \hline \rule{0pt}{3ex} $\sigma_{vis}(ep \rightarrow e [\lsf + \lsa] X)$ CDM & $136$ pb & $161$ pb \\ \hline \rule{0pt}{3ex} $\sigma_{vis}(ep \rightarrow e [\lsf + \lsa] X)$ MEPS & $120$ pb & $144$ pb \\ \hline \end{tabular} \caption{Monte Carlo predictions for different settings of the strangeness suppresion factor $\lambda_{s}$.} \label{tab:McPred} \end{center} \end{table} \subsection {Differential cross sections} Differential \lplus\ cross sections are presented as a function of the kinematics of DIS and of the strange particles, both in the laboratory and in the Breit frame of references. The results in the Breit frame are presented separately for the current and target hemispheres. The measurement of the differential cross section as a function of the kinematic variables of DIS, $Q^2$ and $x$, as well as the kinematic variables of the neutral strange hadrons in the laboratory frame, $p_T$ and $\eta$, are shown in Figure \ref{fig:ds-lab} along with the predictions of the MEPS and CDM models for $\lambdas$ values of $0.220$ and $0.286$. The cross sections fall rapidly as $Q^2$, $x$ and $p_T$ grow. The models follow the general behaviour of data, but some differences are seen. %%%% %\subsubsection{Breit Reference Frame} In the Breit frame of reference the virtual space-like moment transferred in the interaction has no energy. The direction of $q_\mu$, where $Q^2=-q_\mu q^\mu$, defines the negative $z$-axis, with the proton moving in the positive $z$ direction. The transverse momentum in the Breit frame is computed with respect to this axis. Particles with a positive $z$ component of their momenta, as expected from those particles produced close to the proton remnant, are assigned to the %so called target hemisphere; while those having negative $z$ component of their momenta, as expected for particles close to the direction of the struck quark in the naive quark-parton model, are assigned to the %so called current hemisphere. In the figures these hemispheres are denoted by BFT and BFC, respectively. It is expected that the production of particles in the current hemisphere resembles that of $e^+e^-$ collisions. In analogy with the fragmentation variable use in those cases, for $ep$ collisions it is customary to define $x^{\rm{BF}}=2|p^{BF}|/Q$ where $p^{BF}$ is the three momentum of the strange particle in the Breit frame. The variables $x^{\rm{BFT}}$ and $x^{\rm{BFC}}$ are obvious generalisations to take into account if the particle is assigned to the target or current hemisphere respectively. The measured differential \lplus\ production cross sections in the Breit frame are shown in Figure \ref{fig:ds-bf}. The cross sections fall rapidly in all cases. They are bigger in the current than in the target hemisphere, which is opposite to the behaviour observed at lower values of $Q^2$ \cite{Aaron:2008ck}. This is expected due the kinematical effects at high $Q^2$ which push the target region more forward while the current region starts to fill the CJC. \subsection{\boldmath \lsf\ Production to DIS Cross Section Ratio} By normalising the particle production cross section to the DIS cross section many model dependent uncertainties, like the cross section dependence on proton PDFs, cancel thus enhancing the sensitivity on details of the fragmentation process. In Figure \ref{fig:rat-dis} the ratio of \lsf\ production to DIS cross section is shown as a function of $Q^2$, and $x$ in comparison to the expectations from RAPGAP and DJANGOH both using $\lambda_s=0.286$ and $\lambda_s=0.220$. The DJANGOH prediction with $\lambda_s=0.286$ yields the worst description of the data by overshoots them significantly independent of $Q^2$ and $x$. For the same strangeness suppression factor also RAPGAP tends to yield ratios larger than observed in data for $Q^2<200$~GeV$^2$. The best description is provided by DJANGHO using $\lambda_s=0.220$. \subsection{\lsf -- \lsa\ Asymmetries} The \lsf -- \lsa\ asymmetry is defined as: \begin{equation} A_{\Lambda} = \frac{ \sigma_{vis}(ep \rightarrow e \lsf X) - \sigma_{vis}(ep \rightarrow e \lsa X) }{ \sigma_{vis}(ep \rightarrow e \lsf X) + \sigma_{vis}(ep \rightarrow e \lsa X) }. \end{equation} This observable could shed light on the mechanism of baryon number transfer in $ep$ scattering. A significant positive asymmetry would be an indication for the baryon number transfer from the proton to the \lsf\ baryon. If present such an effect should be more pronounced in the positive $\eta$ region in the laboratory frame and in the target hemisphere in the Breit frame. For the kinemaic region defined in table \ref{tab:kine} the asymmetry is measured to be \begin{equation*} A_{\Lambda} = 0.002\pm0.022\,({\rm stat.})\pm0.018\,({\rm syst.}). \end{equation*} In figure \ref{fig:asy-lab} and \ref{fig:asy-bf} $A_\Lambda$ is shown as a function of the variables measured in the laboratory frame and the Breit frame, respectively. Also when studying the asymmetry as a function of these variables the data data do not show any evidence for a non-vanishing asymmetry in the phase space region investigated. \section{Conclusions} This paper presents a study of inclusive \lsf\ production in DIS at high $Q^2$ measured with the H1 detector at HERA. The kinematic range of the analysis covers the phase space region $145 < \qsq< 20000 \GeVSq$, and $0.2 < y < 0.6$. The \lsf\ production cross section are measured as a function of the DIS variables $Q^2$ and $x$ and of \lsf\ production variables in the laboratory and in the Breit frames of reference. The measurements in the Breit frame are presented separately for the target and current hemispheres. In addition results on the \lsf\ production to DIS cross section ratio and the $\lsf - \lsa$ asymmetry are presented. The measurements are been compared to model predictions of DJANGOH, based on the colour-dipol model (CDM)and RAPGAP based on DGLAP matrix element calculations supplemented parton showers (MEPS). Two different values of the strangeness suppression factor $\lambdas$ (0.220 and 0.286) are used for both models. The measured visible \lsf\ cross section is found to be described best by the CDM using $\lambdas=0.220$ and the MEPS model using $\lambdas=0.286$. When investigating the \lsf\ production to DIS cross section ratio the best agreement is observed for the CDM with $\lambdas=0.220$. 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The inner (outer) error bars show the statistical (total) errors. The ``MC/Data'' ratios are shown for different Monte Carlo predictions. For comparison, the data points are put to one. } \label{fig:ds-lab} \end{center} % \begin{picture}(0,0) \put(63,180){\bfseries (a)} \put(142,180){\bfseries (b)} \put(63,105){\bfseries (c)} \put(142,105){\bfseries (d)} % \put(17,180){\bfseries a)} % \put(97,180){\bfseries b)} % \put(17,110){\bfseries c)} % \put(97,110){\bfseries d)} % \put(62,190){\LARGE e\,p $\rightarrow$ e\,K$^0_s$\,X} \end{picture} % \end{figure} \clearpage %%%%%% lambda breit frame \newpage \begin{figure} \begin{center} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig4a.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig4b.eps}\\ \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig4c.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig4d.eps}\\ \caption{Differential \lsf\ production cross sections in the Breit frame as a function of (a) $p^{\rm{BFC}}_{T}$, (b) $x^{\rm{BFC}}$, (c) $p^{\rm{BFT}}_{T}$, (d) $x^{\rm{BFT}}$ in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of $\lambda_s$. The inner (outer) error bars show the statistical (total) errors. The ``MC/Data'' ratios are shown for different Monte Carlo predictions. For the ratios the data points are put at one for comparison. } \label{fig:ds-bf} \end{center} % \begin{picture}(0,0) \put(63,177){\bfseries (a)} \put(142,177){\bfseries (b)} \put(63,102){\bfseries (c)} \put(142,102){\bfseries (d)} % \put(42,175){\LARGE e\,p $\rightarrow$ e\,K$^0_s$\,X (Breit frame)} \end{picture} % \end{figure} \clearpage %%%%%% Lambda to DIS ratio \newpage \begin{figure} \begin{center} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig5a.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig5b.eps}\\ \caption{ Ratio R(DIS) of \lsf\ production to DIS cross section as a function of (a) the photon virtuality squared $Q^2$ and (b) Bjorken scaling variable $x$ in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of $\lambda_s$. The inner (outer) error bars show the statistical (total) errors. The ``MC/Data'' ratios are shown for different Monte Carlo predictions. For the ratios the data points are put at one for comparison. } \label{fig:rat-dis} \end{center} % \begin{picture}(0,0) \put(63,102){\bfseries a)} \put(142,102){\bfseries b)} \end{picture} % \end{figure} \clearpage %%%%%% Asymmetry in lab \newpage \begin{figure} \begin{center} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig6a.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig6b.eps}\\ \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig6c.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig6d.eps}\\ \caption{Asymmetry $A_\Lambda$ as a function of (a) the photon virtuality squared $Q^2$, (b) Bjorken scaling variable $x$, (c) the transverse momentum, $p_T$ and (d) its pseudorapidity $\eta$ in the laboratory frame in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of $\lambda_s$. } \label{fig:asy-lab} \end{center} % \begin{picture}(0,0) \put(24,180){\bfseries (a)} \put(142,180){\bfseries (b)} \put(24,102){\bfseries (c)} \put(142,102){\bfseries (d)} % \put(62,190){\LARGE e\,p $\rightarrow$ e\,K$^0_s$\,X} \end{picture} % \end{figure} \clearpage %%%%%% Asymmetry in BF \newpage \begin{figure} \begin{center} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig7a.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig7b.eps}\\ \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig7c.eps} \includegraphics[width=0.49\textwidth]{H1prelim-13-031.fig7d.eps}\\ \caption{ Asymmetry $A_\Lambda$ as a function of the Breit frame variables (a) $p^{\rm{BFC}}_{T}$, (b) $x^{\rm{BFC}}$, (c) $p^{\rm{BFT}}_{T}$, (d) $x^{\rm{BFT}}$ in comparison to RAPGAP (MEPS) and DJANGOH (CDM) with two different vaues of $\lambda_s$. } \label{fig:asy-bf} \end{center} % \begin{picture}(0,0) \put(24,172){\bfseries (a)} \put(142,172){\bfseries (b)} \put(24,97){\bfseries (c)} \put(142,97){\bfseries (d)} % \put(42,175){\LARGE e\,p $\rightarrow$ e\,K$^0_s$\,X (Breit frame)} \end{picture} % \end{figure} \clearpage \end{document}