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\begin{document}

\title{New Results from HERMES}

\author{M. Tytgat\footnote{\uppercase{O}n behalf of the \uppercase{HERMES} \uppercase{C}ollaboration}}

\address{University of Gent, \\
Dept. Subatomic and Radiation Physics,\\
Proeftuinstraat 86, \\ 
9000 Gent, Belgium\\ 
E-mail: michael@inwfsun1.UGent.be}

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\maketitle

\abstracts{An overview is given 
of selected recent HERMES results obtained from 
measurements performed 
during the first running period of HERA. These topics 
include inclusive $g_1(x)$-measurements with a NLO QCD 
analysis, polarized quark distribution extraction, $b_1(x)$-measurement, 
double spin asymmetries in vector meson production, $\rho^0$-nuclear 
transparency and finally quark fragmentation in nuclei.}

\section{Introduction}

The HERMES experiment uses the 27.5~GeV polarized HERA electron/positron beam 
to scatter deep-inelastically off a (un)polarized fixed gaseous nuclear 
target. Data taking began in 1995, during the first HERA 
running period and still
continues with HERA-II. Although HERMES was originally designed to study 
the nucleon spin in polarized DIS, a wide range of physics topics has 
been addressed over the past years.
Here only some of the recent results from HERA-I will be summarized. First 
results obtained during HERA-II are discussed elsewhere~\cite{elke}.

\section{NLO QCD Analysis of the $g_1(x,Q^2)$ Structure Function}

During HERA-I HERMES performed longitudinally polarized inclusive
DIS measurements 
on $^1$H, $^2$H and $^3$He. A compilation of the world data on the 
$g_1(x,Q^2)$-structure 
function including the HERMES results is displayed in figure~\ref{figg1}. The 
HERMES data actually add most precision to $g_1^d$. Considering 
$g_1=\frac{1}{2}\sum_qe^2_q\Delta q$ in the
na\"{\i}ve parton model with $\Delta q$ being the
polarized quark densities and neglecting the quark sea, 
one can qualitatively deduce from these inclusive data that 
$\Delta u$ must be large and positive, while $\Delta d$ should be negative.

\begin{figure}[ht]
\centerline{\epsfxsize=5.5cm\epsfbox{tytgat.fig1.eps}}
\caption{A compilation of recent 
world data on $xg_1(x,Q^2)$ for the proton, deuteron
and neutron.
\label{figg1}}
\end{figure}

To obtain more quantitative information on the polarized quark densities 
a next-to-leading order QCD analysis of the $g_1(x,Q^2)$-data was carried
out including the latest HERMES results. The $g_1(x,Q^2)$-structure function 
was parametrized as a Mellin convolution in terms of the polarized singlet
density $\Delta\Sigma=\sum_{i=1}^{N_f} [\Delta q_i+\Delta\bar{q}_i]$, 
the polarized gluon density $\Delta G$ and the 
polarized non-singlet densities $\Delta q_i^{NS}=\Delta q_i+\Delta\bar{q}_i-1/N_f\cdot\Delta\Sigma$. In the evolution equations the polarized 
splitting functions
and Wilson coefficient functions are calculated in NLO in the 
$\overline{\mbox{MS}}$-scheme. Two independent methods were
used to extract the parton densities. The first one is a numerical method
with evolution in $x$-space and takes $\Delta\Sigma$, 
$\Delta q^{NS}_p$, $\Delta q_n^{NS}$ and $\Delta G$ as distributions 
to be determined in the fit. 
The second method solves the evolution equations in Mellin-N space and uses 
$\Delta u_v$, $\Delta d_v$, $\Delta\bar{q}_s$ and $\Delta G$ as free 
distributions.
The polarized parton densities at input scale $Q^2_0=4.0$~GeV$^2$ 
were parametrized 
in the form 
$x\Delta q_i(x,Q^2_0)=\eta_iA_ix^{a_i}(1-x)^{b_i}(1+\gamma_ix+\rho_ix^{1/2})$,
where the normalization constants $A_i$ are chosen such that $\eta_i$ 
represents the first moment of $\Delta q_i$. 

Both methods produce compatible results and the final polarized parton 
densities as determined with the second method
are displayed in figure~\ref{figqcdanal} at input scale, 
where they are compared to previous
analyses~\cite{previousqcd1,previousqcd2}. 
\begin{figure}[ht]
\centerline{\epsfxsize=7cm\epsfbox{tytgat.fig2.eps}}
\caption{The polarized quark distributions at $Q^2_0=4.0$~GeV$^2$ compared to
previous analyses. The dotted lines correspond to the positivity limits
from unpolarized distributions.
\label{figqcdanal}}
\end{figure}
The shaded areas denote the fully 
correlated $1\sigma$ statistical error bands and the dotted lines correspond to
the positivity limits from unpolarized distributions. While $\Delta u_v$ and 
$\Delta d_v$ are well constrained by the current fit, $\Delta G$ and 
$\Delta\bar{q}$ remain poorly determined. For $\Delta G$ the theoretical
uncertainty dominates the overall systematic error, such that not only
an improved data set with a larger $Q^2$-range but also a NNLO 
calculation could improve the situation. 

\section{Flavor Decomposition of Polarized Quark Distributions}

\begin{figure}[ht]
\centerline{\epsfxsize=6.5cm\epsfbox{tytgat.fig3.eps}}
\caption{The polarized parton densities at $Q^2=2.5$~GeV$^2$.
\label{figdeltaq}}
\end{figure}
Another method to accomplish a flavor decomposition of the polarized quark 
densities is provided by flavor tagging in polarized semi-inclusive 
DIS~\cite{deltaq} $e+p(d)\rightarrow e+h+X$.
The measured photon-nucleon double spin asymmetry $A_1^h$
for semi-inclusive events with a leading hadron of type $h$ can be written as
\begin{eqnarray}
A_1^h(x,Q^2) & \sim & \displaystyle\sum_q\frac{e^2_qq(x,Q^2)\int\mbox{d}zD^h_q(z,Q^2)}{\sum_{q^{\prime}}e^2_{q^{\prime}}q^{\prime}(x,Q^2)\int\mbox{d}zD^h_{q^{\prime}}(z,Q^2)}\frac{\Delta q}{q}(x,Q^2) \\
& \sim & \displaystyle\sum_q P^h_q(x,Q^2)\frac{\Delta q}{q}(x,Q^2),\label{eqnpurity}
\end{eqnarray}
with $D^h_q$ being the fragmentation function for a quark flavor $q$ and  
$\Delta q$ ($q$) being 
the (un)polarized quark density. The purity $P^h_q$ represents the
probability that the hadron $h$ originates from an event in which a quark of
flavor $q$ was struck by the virtual photon. The purities
are spin-independent quantities
and were evaluated using the PEPSI/JETSET DIS Monte Carlo 
model~\cite{mc}. The CTEQ5L parametrizations for unpolarized quark 
densities were used and the JETSET fragmentation parameters were tuned to 
reproduce the hadron multiplicities measured at HERMES. 
Equation~\ref{eqnpurity} can be rewritten as a matrix equation $\vec{A}=P\cdot\vec{Q}$, where $\vec{A}=(A_{1p}, A^{\pi^{\pm}}_{1p}, A_{1d}, A^{\pi^{\pm}}_{1d}, A^{K^{\pm}}_{1d})$ contains the measured inclusive and semi-inclusive 
asymmetries on the proton and deuteron, $P$ contains the purities for the 
proton and deuteron and $\vec{Q}=(\frac{\Delta u}{u}, \frac{\Delta d}{d}, \frac{\Delta\bar{u}}{\bar{u}}, \frac{\Delta\bar{d}}{\bar{d}}, \frac{\Delta s}{s}, \frac{\Delta\bar{s}}{\bar{s}})$ contains the quark and anti-quark polarizations 
to be determined. The matrix equation was solved by 
$\chi^2$-minimization and the resulting polarized parton densities are depicted
in figure~\ref{figdeltaq} at the mean scale $<Q^2>=2.5$~GeV$^2$. 
While $\Delta u$ is positive in the measured $x$-range, $\Delta d$ appears 
negative and only slightly dependent on $x$. Both distributions are consistent
with previous measurements, but are now known with a much improved precision.
The light sea quark polarization 
densities are compatible with zero. 
The densities in the figure are  
compared to two leading order QCD fits~\cite{previousqcd1}. 

\section{The $b_1(x,Q^2)$ Tensor Structure Function}

When scattering off a spin-1 target an additional leading
twist structure function $b_1(x,Q^2)$ enters the symmetric part of the hadronic
tensor compared to the 
spin-1/2 case. This structure function measures the difference in the polarized
quark distributions of a target with helicity $m=\pm 1$ and $m=0$ : 
$b_1(x,Q^2)=\frac{1}{2}\sum_i e^2_i[2q^0_i(x,Q^2)-q^+_i(x,Q^2)-q^-_i(x,Q^2)]$.
The cross section now
depends on the vector and tensor polarization of the target
$\sigma=\sigma_u[1+P_b~V~A_{\parallel}+\frac{1}{2}~T~A_T]$,
where $A_{\parallel}\sim g_1/F_1$ and $A_T\sim -2/3\cdot b_1/F_1$ are the 
target vector and tensor asymmetry 
respectively, $V$ and $T$ the target vector and tensor polarization and $P_b$
the beam polarization.

\begin{figure}[ht]
\centerline{\epsfysize=6cm\epsfbox{tytgat.fig4a.eps}\hspace*{.5cm}\epsfysize=6cm\epsfbox{tytgat.fig4b.eps}}
\caption{The measured $b_1(x,Q^2)$ and $b_2(x,Q^2)$ structure function on the deuteron.\label{figb1b2}}
\end{figure}
The tensor asymmetry $A_T$ was measured for the first time at HERMES on the
deuteron target in the kinematic range $0.0021<x<0.85$ and $0.1<Q^2<20$~GeV$^2$. 
The resulting $b_1$ is shown in 
figure~\ref{figb1b2} together with $b_2$, which is related to the former via
a Callan-Gross like relation.
At small $x$ both structure functions appear positive which
can be interpreted as being due to the quadrupole deformation of the deuteron.
The $b_2$-data is in qualitative agreement with the double scattering 
model calculations from Ref.~\refcite{bora}.

\section{Double-Spin Asymmetries in Vector Meson Production}

The longitudinally polarized beam and target allows HERMES to investigate 
double-spin 
asymmetries in vector meson production~\cite{vmasym}. 
Averaged over the kinematic acceptance 
the asymmetries for exclusive $\rho^0$-production were found to be 
$0.23\pm 0.14\pm 0.02$ on the proton 
and $-0.040\pm 0.076\pm 0.013$ on the deuteron for average kinematics
$<W>=4.9$~GeV, $<Q^2>=1.8$~GeV$^2$ and $<-t^{\prime}>=0.15$~GeV$^2$. 
The same asymmetries 
extracted for the $\phi$-meson were compatible with zero.
Figure~\ref{vmasym} displays the $\rho^0$
asymmetries for both targets as function of Bjorken $x$ and $Q^2$.
\begin{figure}[ht]
%\epsfxsize=5cm   %width of figure - will enlarge/reduce the figures
%\epsfbox{lipka.dsarho-4.eps}
%\figurebox{2cm}{3cm}{} %to have a box alone
\centerline{\epsfxsize=5cm\epsfbox{tytgat.fig5a.eps}\hspace*{.5cm}\epsfxsize=5cm\epsfbox{tytgat.fig5b.eps}}
\caption{Double-spin asymmetry in $\rho^0$-production from a polarized 
hydrogen and deuterium target as function of Bjorken $x$ and $Q^2$.
\label{vmasym}}
\end{figure}       
Using the 
HERMES data on $A_1^N$ and the 
simple relation $A^{\rho}_1=2 A_1^N/(1+(A_1^N)^2)$ 
between the vector meson and inclusive DIS asymmetry as derived in 
Ref.~\refcite{fraas}, one obtains the shaded bands in figure~\ref{vmasym} for
the $x$-dependence of the asymmetries. Both the proton and deuteron 
asymmetries are consistent with this prediction. The $Q^2$-dependences 
are compared to a Regge model calculation from Ref.~\refcite{kochelev}.   
In this model the parameters of the Reggeons contributing to 
$\rho^0$-production were extracted from fits to $g_1^N$ and $F_2^N$. While 
the proton measurement seems to agree with the prediction, the deuteron data
lie below the calculation. The datapoints at the lowest $Q^2$-value are both
compatible with zero and were
obtained with a special trigger for events in which the beam particle 
scatters at too low angles to be detected.

In Ref.~\refcite{fraas} the non-zero asymmetry result for $\rho^0$-production 
arises from an interference between natural and unnatural parity exchange
amplitudes. Since the Pomeron has natural parity, it is suggested that at 
HERMES energies the transverse 
$\rho^0$-production
amplitude on the proton 
receives significant contributions from Reggeon or di-quark
exchange.
This not only agrees with the previous observation
that at HERMES 
the longitudinal production amplitude on the proton is dominated by quark 
exchange~\cite{rho0cross}, but also is not in contradiction with the vanishing
asymmetry found at higher energies at SMC~\cite{rho0smc}, where 
$\rho^0$-production is dominated by gluon exchange and also 
the inclusive asymmetry
is much smaller.
The zero asymmetry result for
$\phi$-production, which is dominated by Pomeron exchange even at HERMES
energies, can also be understood in the same way.

\section{Color Transparency in $\rho^0$-Production}

A fundamental prediction of QCD is the existence of the color transparency (CT)
phenomenon, i.e. a hadron which is produced at sufficiently high $Q^2$ will 
traverse a nuclear medium with vanishing initial and final state interactions.
In the search for CT one commonly uses the nuclear transparency 
$T=\sigma_A/(A\sigma_p)$, which is the ratio of the nuclear cross section per 
nucleon to the one on the proton. The distance which 
the $q\bar{q}$-fluctuation of the virtual photon in $\rho^0$-production 
can propagate is the coherence length $l_c=2\nu/(Q^2+M_{q\bar{q}}^2)$. This
latter quantity is important for CT-studies, especially for incoherent
$\rho^0$-production, where at $l_c$-values smaller than the nuclear size 
$T$ increases with $Q^2$ due to the
coherence length effect previously observed at HERMES~\cite{cohlength}.
For coherent $\rho^0$-production 
the drop of the nuclear form factor 
at high $Q^2$ (small $l_c$) causes a decreasing behavior of $T$ with $Q^2$. 
In order to get a clean signature of a CT-effect, one has to disentangle
the coherence length effects from those of CT, which can be done by
studying $T$ as function of $Q^2$ for fixed $l_c$~\cite{kopeliovich}.
\begin{figure}[ht]
%\epsfxsize=5cm
\centerline{\epsfxsize=5cm\epsfbox{tytgat.fig6a.eps}\hspace*{.5cm}\epsfxsize=5cm\epsfbox{tytgat.fig6b.eps}}
\caption{The left (right) plot shows the nuclear transparency for 
(in)coherent $\rho^0$-production on
nitrogen as
  function of $Q^2$ for several coherence length intervals.
\label{figtrcohincoh}}
\end{figure}
Figure~\ref{figtrcohincoh} shows the measured $T$ for both coherent and 
incoherent exclusive $\rho^0$-production on nitrogen 
as function of $Q^2$ for small 
intervals of $l_c$~\cite{ctpaper}. 
The data were fitted with a common $Q^2$-slope equal
to $0.074\pm 0.023$~GeV$^{-2}$, which agrees with the theoretical 
prediction of about $0.058$~GeV$^{-2}$. This positive slope of the 
$Q^2$-dependence represents a signature of color transparency.

\section{Quark Fragmentation in Nuclei}

In deep-inelastic scattering off a nucleus, the nuclear medium
 acts as an ensemble of 
targets for the quark struck by the virtual photon and for the produced 
hadrons and will therefore influence the hadronization process.
Due to multiple interactions with the surrounding medium 
and induced gluon radiation the struck quark will lose energy.
A final hadron formed inside the nucleus can also interact via the hadronic
interaction cross section with the nuclear medium. Both effects will induce 
a softening of the leading hadron spectra compared to the free nucleon case.
The hadronization process in nuclear media is usually described either in
phenomenological string models including 
final state interactions of the produced
hadron or in more QCD-inspired models by e.g. parton energy loss 
or gluon bremsstrahlung.
A clean tool to study nuclear effects in 
quark propagation and hadronization
is semi-inclusive DIS, where one usually examines the multiplicity ratio for 
a hadron $h$ on a nucleus $A$ compared to the deuteron, 
\begin{equation}
R^h_M(z,\nu,p_t^2,Q^2)=\frac{\left.(N_h(z,\nu,p_t^2,Q^2)/N_e(\nu,Q^2))\right|_A}{\left.(N_h(z,\nu,p_t^2,Q^2)/N_e(\nu,Q^2))\right|_D},
\end{equation}
with $N_h$ the semi-inclusive yield normalized to the inclusive 
yield $N_e$. 

\begin{figure}[ht]
%\epsfxsize=5cm
\centerline{\epsfxsize=5.4cm\epsfbox{tytgat.fig7a.eps}\hspace*{.5cm}\epsfxsize=5.4cm\epsfbox{tytgat.fig7b.eps}}
\caption{Multiplicity ratios for $\pi$, $K$, $p$ and $\bar{p}$ for $^{84}$Kr as function of $\nu$ and $z$. The $z$-dependence of the $\pi$ multiplicity on $^{14}$N is also shown.
\label{figatten}}
\end{figure}
The multiplicity ratios for $\pi$, $K$, $p$ and 
$\bar{p}$ measured by HERMES~\cite{multip} 
on $^{84}$Kr are displayed in figure~\ref{figatten} as function
of $\nu$ and $z$. Contributions due to target fragmentation were suppressed by
requiring $z>0.2$ and large acceptance effects in $z$ were avoided by taking 
$\nu>7$~GeV. The plot also includes the $\pi$-multiplicity z-dependence on 
$^{14}$N~\cite{oldmultip}. 
The multiplicity ratios for $\pi^+$, $\pi^-$ and $\pi^0$ on krypton
appear to be similar, which is also true for the nitrogen $\pi^{\pm}$-data.
Whereas the multiplicity ratio for $K^-$ is compatible with that for pions,
the $K^+$-multiplicity ratio is significantly larger and an even larger 
difference is observed between $p$ and $\bar{p}$. One way to understand these
differences is to interpret them in terms of different hadron formation 
times for mesons and
baryons in combination with different hadron-nucleon interaction cross
sections. The curves in the plots represent the result of a model 
calculation~\cite{accardi} based on a rescaling of the quark fragmentation
due to the nuclear medium.
In Ref.~\refcite{wang} the differences are attributed to a mixing of
quark and gluon fragmentation functions in nuclei due to multiple parton
scattering, such that quark
and anti-quark fragmentation functions receive different medium modifications.
The $\pi$-data on both targets exhibit the
same trend, however as expected, the attenuation in krypton appears much 
stronger than in nitrogen. The mass dependence of the nuclear attenuation
$1-R^h_M$ appears closer to a $A^{2/3}$-dependence as predicted 
in Ref.~\refcite{wang} than to a $A^{1/3}$-dependence suggested by models based
on nuclear absorption only. 

Another nuclear effect is the Cronin effect~\cite{cronin}, which concerns 
the broadening of the hadron $p_t$-distribution on a nuclear target compared
to the proton due to multiple scattering of the propagating 
quark and hadron. This phenomenon was also observed by HERMES~\cite{multip} 
as an enhancement of the charged hadron 
multiplicity ratio on $^{14}$N and $^{84}$Kr at high $p_t^2$. It is similar
to the effect seen in proton-nucleus and nucleus-nucleus collisions and
may help to interpret the new heavy-ion data from SPS and RHIC.

\section*{Acknowledgments}
The author would like to acknowledge the support of the FWO-Flanders, 
Belgium, for this work.


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\end{document}



