%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% ws-procs9x6.tex   :   27 January 2003
%% Text file to use with ws-procs9x6.cls written in Latex2E.
%% The content, structure, format and layout of this style file is the 
%% property of World Scientific Publishing Co. Pte. Ltd. 
%% Copyright 1995, 2002 by World Scientific Publishing Co. 
%% All rights are reserved.
%%
%% Proceedings Trim Size: 9in x 6in
%% Text Area: 7.35in (include runningheads) x 4.5in
%% Main Text is 10/13pt                                   
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\documentclass[draft]{ws-procs9x6}  
\documentclass{ws-procs9x6}

\begin{document}

\title{A New Round of Experiments for HERA}

\author{Allen C. Caldwell}
\address{Max-Planck-Institut f\"ur Physik \\
Munich, Germany \;\;\; and \\
Columbia University \\
New York, NY, USA \\
E-mail: caldwell@mppmu.mpg.de }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% You may repeat \author \address as often as necessary      %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\maketitle

\abstracts{
A new round of experimentation with the HERA accelerator 
is discussed.}



\section{Introduction}
QCD is the most complex of the known 
forces operating in the microworld. Myriad effects are 
seen in condensed matter physics resulting from simple
non-relativistic quantum mechanical interactions between electrons.  
Imagine the possibilities resulting from strong interactions of large
numbers of gluons and quarks. Further studies are bound to reveal
new and exciting results which will challenge our existing paradigms.

QCD is fundamental to the understanding of our universe.  
The bulk of the known mass in the universe arises via the strong
interactions - nearly massless quarks become massive baryons and mesons in
the QCD potential.  One can therefore speculate on deep connections between
gravity and QCD.  What is clear is that we need to understand the strong
force at short and long distance scales.  We believe we can make predictions
for strong interaction effects at small distance scales where the coupling
is weak.  Can we do this at high energies ?  Data from HERA on forward
jet production already show weaknesses in our ability to make accurate
calculations.  As the distance scale increases, the strong interactions
increase dramatically in strength, radiation is suppressed, 
and confinement sets in.  How this comes about is not well understood, but
HERA data clearly show this transition, e.g. in the change of the energy
dependence of the total cross section around $Q^2 = 0.5$~GeV$^2$.  Studying
this transition from a partonic to a hadronic behavior of matter is of
the highest importance, and would be a highlight of further HERA running.

The goal of further experimentation at HERA would be to follow up on
the interesting effects already seen at HERA:
\begin{itemize}
\item disappearing gluons at small $Q^2$;
\item transition from partonic to hadronic behavior of cross sections;
\item forward particle (jet) production and disagreement with NLO DGLAP
calculations;
\item energy dependence of diffractive cross sections,
\end{itemize}
with new and/or improved detectors, and make new measurements which will
qualitatively change our understanding:
\begin{itemize}
\item the longitudinal structure function, $F_L$;
\item a full program of electron-ion collisions;
\item scattering on polarized hadronic beams.
\end{itemize}


\begin{figure}[!thb]
\label{fig:Roberts-gluons}
\vspace*{7.5cm}
\begin{center}
\special{psfile=caldwell_fig1a.ps voffset=-20 vscale=35
hscale= 35 hoffset=-30 angle=0}
\special{psfile=caldwell_fig1b.ps voffset=-20 vscale=35
hscale= 35 hoffset=+150 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*]{Solution of the DGLAP evolution equation for gluons (left)
at different orders of perturbative expansion and the corresponding 
expectations for $F_L$ (right), as a function of $x$ for fixed $Q^2$
~\cite{ref:MRST}.
}
\end{center}
\end{figure}

Two letters of intent were submitted to the DESY PRC in May 2003 to pursue
this program~\cite{ref:H1LoI,ref:NewDet}.
The first 
letter of intent focuses on measuring eD interactions with an improved
H1 detector, while the second letter of intent proposes a new detector
optimized to study the physics mentioned above.  The LoI's will be described
in more detail below.

It should be pointed out that the research program discussed in the LoI's 
cannot be carried out with the ongoing HERA running (HERA II).  This program
is intended to study high $Q^2$ physics with maximum luminosity, and is
made possible by the insertion of accelerator elements near the interaction
points, thereby limiting access to the small-x physics.

\begin{figure}[!thb]
\label{fig:FLcomp}
\vspace*{7.5cm}
\begin{center}
\special{psfile=caldwell_fig2.ps voffset=-75 vscale=40
hscale= 40 hoffset=50 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*]{Comparison of the expectations for the $Q^2$ dependence at fixed
$x$ of $F_L$ in the DGLAP approach (MRST99) and the saturation dipole model.
}
\end{center}
\end{figure}

\section{HERA III Physics Program}
The proposed program goes by the name HERA III.  The main research topics
discussed in the LoI's are outlined here.

\subsection{Precision Structure Function Measurements}
It is proposed to measure the $F_2,F_2^D,F_L,F_L^D$ structure functions in the
range $0.1 < Q^2 < 100$~GeV$^2$.  The gluon densities extracted at
HERA show non-intuitive behavior, such as the tendency to go negative at
small $x$ (see Fig.~1).  While this is not necessarily
a breakdown of the calculational machinery, the fact that these gluon densities
also result in negative predictions for $F_L$ clearly shows a breakdown 
in our understanding.  More precise measurements of $F_2$, and 
measurements of $F_L$ at small x, will directly test our understanding of
the gluon density.  The measurement of $F_L$ will also be a strong test of
the popular dipole model~\cite{ref:dipole}, 
which makes significantly different predictions 
than current NLO DGLAP calculations (see Fig.~2).


Due to the lack of theoretical constraints, many parameters are needed to
describe the shape of the parton densities.  Several assumptions are required
in order  
to limit the number of parameters below about 30.  Once these assumptions
are relaxed, the uncertainty on the extracted
parton densities get much larger.  One
example is the assumption that $\bar{u}=\bar{d}$ at small $x$.  The effect
of removing this constraint is shown in Fig.~3.  It is clear
that more observables are required to experimentally constrain the parton
densities.  One such observable is $F_L$, which will provide a strong
constraint on the gluon density at small-$x$.  Running HERA in $eD$ mode
would give the information necessary to separate $u$ and $d$ quark 
distributions.

\begin{figure}[!thb]
\label{fig:ubar-dbar}
\vspace*{4.0cm}
\begin{center}
\special{psfile=caldwell_fig3a.eps voffset=0 vscale=40
hscale= 40 hoffset=0 angle=0}
\special{psfile=caldwell_fig3b.eps voffset=0 vscale=40
hscale= 40 hoffset=+170 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*]{The sea quark difference at $Q^2=4$~GeV$^2$, as determined
in a NLO QCD analysis~\cite{ref:H1sea}.  Left: the constraint
$\bar{u}=\bar{d}$ for $x\rightarrow 0$ is imposed. Right: the constraint
is not imposed.
}
\end{center}
\end{figure}

The structure function $F_2$ shows a particularly interesting $x$-dependence
near $Q^2=0.5$~GeV$^2$, as shown in Fig.~4. Below this
$Q^2$, the $x$-dependence is consistent with the energy dependence of 
hadron-hadron total cross sections, while above this $Q^2$ the energy
dependence becomes significantly steeper.  This transition signals a
different physics mechanism at work (presumably 
hadronic degrees of freedom versus
partonic degrees of freedom).  A new experiment would focus on precision
measurements with full acceptance in this $Q^2$ region.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=caldwell_fig4.eps voffset=-60 vscale=40
hscale= 40 hoffset=50 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*]{The logarithmic derivative  $\lambda_{eff}=-\partial ln F_2 / 
\partial ln x$
as a function of $Q^2$ (courtesy of A. Levy). 
}
\end{center}
\label{fig:transition}
\end{figure}

\subsection{Exclusive Processes}
Exclusive processes allow for a very detailed study of $eP$ interactions.  Two
additional variables are introduced (4-momentum transfer at the proton
vertex and mass of the final state), which allow a many-fold differential
study.  In the proton rest frame, we can think of the electron emitting a
photon far upstream of the interaction point.  The photon probes the proton
with a transverse resolution  which scales as $\hbar c/Q$, and at impact
parameter $\sim \hbar c/\sqrt{|t|}$, where $t$ is the square of the 4-momentum
transferred at the proton vertex.  At small $x$, the photon interactions
are really dipole-proton interactions, with the lifetime of the dipole
fluctuation given by $1/2xM_P$.  The dipole converts into a
vector meson or real photon (DVCS process) after the interaction.  The
wavefunction of the produced state constrains the dipole configurations
which can take part in the scattering.  The extra variables measured
in exclusive reactions allow a much more detailed mapping of the hadronically
interacting matter.  An example of the information which may be extracted
is given in Fig.~5, where the dipole-proton scattering amplitude
is shown as a function of impact parameter.  These processes will allow a
3-dimensional mapping of proton structure.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=caldwell_fig5.eps voffset=0 vscale=40
hscale= 40 hoffset=50 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {Expectations for the dipole-proton amplitude, $N(x,r,b)$ 
as a function of impact parameter, $b$, for different photon-proton
energies, $W$.
}
\end{center}
\label{fig:dipole-proton}
\end{figure}

\subsection{Forward Jet Production}

The HERA I results indicate that NLO DGLAP alone is not enough
to describe forward jet production.  Figure~6
shows the differences predicted~\cite{ref:Jung} 
in different calculations for
different ranges of pseudorapidity, $\eta$.  It is clear that 
extending the rapidity coverage of the detectors would greatly enhance
the sensitivity.  This applies not just to jet production, but also
to particle production.  In particular, heavy quark production at
high rapidities is a very interesting research topic.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=caldwell_fig6.eps voffset=0 vscale=40
hscale= 40 hoffset=30 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {
Forward-jet cross section as a function of $x$ obtained from the
CDM (Ariadne), DGLAP (Lepto) and CCFM (Cascade) models.  The cross
sections are shown in different rapidity intervals.}
\end{center}
\label{fig:radiation}
\end{figure}

\subsection{Precision eA Measurements}

Replacing protons with nuclei is widely expected to enhance the
striking effects observed at HERA.  For example, it is expected that
the diffractive cross section will approach 50~\% of the total cross
section, the maximally allowed value. The black-body limit of QCD will
be reached, and new states of matter, such as the 
color-glass-condensate~\cite{ref:McVe},
can be studied.  The main argument leading to such conclusions can
be stated as follows. The dipole fluctuation from the virtual photon
typically
lives for distances much larger than the nuclear size at small-$x$.  It
is therefore sensitive to all the hadronic matter along a line through
the nucleus, whose length 
scales as $A^{1/3}$.  For large nuclei, the extra path length through nuclear
matter can lead to saturation of cross sections.
The interesting measurements for eA scattering are the same as those for
eP scattering - structure function measurements, diffractive cross sections,
and exclusive reactions.

\subsection{Spin}
It is not understood how the intrinsic angular momentum of hadrons
is built up from the constituents.
This flagrant hole in our understanding of subatomic physics demands an
explanation.  Colliding polarized
electrons with polarized protons at HERA would allow the study of the
angular momentum carried by small-x partons, and would open a new line of
attack on this fundamental problem. 

\section{H1 Detector Upgrade}
The H1 LoI~\cite{ref:H1LoI}
 focuses initially on eD scattering, and discusses a second phase 
which focuses on the forward and backward region.  For the first phase, a
new spectrometer would be added to measure protons exiting with approximately
half the deuteron beam energy.  For the second phase, upgrades in the
electron direction (new silicon based tracking, a new small-angle calorimeter)
and proton direction (instrumented beamline, new forward calorimeters) are
envisaged. 

As examples of what could be achieved with an eD program of moderate
luminosity,
the $\bar{d}-\bar{u}$ measurement at small-$x$ and the ratio of valence
quark densities, $d_v/u_v$, were studied.  The results are given in 
Fig.~7.  It is clear that the isospin symmetry of the sea
can be extremely well tested, and the valence $d/u$ ratio well
constrained.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=caldwell_fig7a.eps voffset=0 vscale=50
hscale= 50 hoffset=-10 angle=0}
\special{psfile=caldwell_fig7b.eps voffset=0 vscale=20
hscale= 20 hoffset=+170 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {Left: simulation of the difference $\bar{d}-\bar{u}$ using
$40$~pb$^{-1}$ of $eP$ and $20$~pb$^{-1}$ of $eD$ data.  The error bar
represents the quadratic sum of the statistical and systematic errors.
Right: simulation of the measurement of the ratio $d_v/u_v$ with H1
assuming $50$~pb$^{-1}$ luminosity for $eP$ and for $eD$ scattering.
}
\end{center}
\label{fig:eD}
\end{figure}

\section{A New Detector for HERA}
The H1 and ZEUS detectors were optimized for high $Q^2$ physics, and as
such the detectors are optimal for the HERA II program which is now getting
under way.  For the small-$x$ physics which has been the highlight of
HERA so far, and which would be the physics goal of a HERA III program,
a new type of detector concentrating on the forward directions is needed.
A new detector designed with this physics in mind is sketched in 
Fig.~8.  The main idea is to build a compact detector with
tracking and central electromagnetic calorimetry inside a magnetic dipole
field.  Calorimetric end walls are located outside the dipole.  The tracking
focuses on forward and backward tracks, while the calorimetry focuses
on $e/\pi$ separation and the central electron and photon measurements.
The magnetic field extends from $\pm 4.5$~m, and points along the vertical
direction.  There are 28 tracking planes located along the length of the
magnet capable of producing a 3-D 
coordinate.  The barrel calorimeter has an inner radius of $40$~cm, and
is confined to a tube of $60$~cm.  The dipole magnet has an inner radius 
of $80$~cm.


In addition to the detector components shown in the figure, additional
detectors located further upstream in the proton and electron directions
would also be included.  These detectors would be used to tag proton
dissociation and initial state radiation, as well as be helpful for 
luminosity measurements.

\begin{figure}[!thb]
\vspace*{6.0cm}
\begin{center}
\special{psfile=caldwell_fig8.eps voffset=-40 vscale=30
hscale= 30 hoffset=80 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {Schematic overview of the detector components within
$\pm 6$~m of the interaction point.  The silicon planes are visible along
the beamline.  The calorimeter system consists of a central barrel,
two catcher rings on each side, and end walls.  The calorimeters are
all electromagnetic calorimeters, except for the end wall in the proton
direction, which also includes a hadronic calorimeter.
The dipole magnet
enclosing the silicon detectors, central barrel and catcher rings is
not shown.
}
\end{center}
\label{fig:NewDet}
\end{figure}


The acceptance of the detector for the scattered electron and for forward 
particles in shown in Fig.~9. Here acceptance is defined as
at least three silicon planes crossed.  As is clear from the plots, full
acceptance is achieved in the transition region near $Q^2=0.5$~GeV$^2$,
and the acceptance for forward tracks and jets is vastly increased over
what is currently achieved by H1 and ZEUS.

\begin{figure}[!thb]
\vspace*{6.0cm}
\begin{center}
\special{psfile=caldwell_fig9a.eps voffset=-140 vscale=60
hscale= 60 hoffset=-30 angle=0}
\special{psfile=caldwell_fig9b.eps voffset=0 vscale=40
hscale= 40 hoffset=+170 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {Left: acceptance of the tracking system for the scattered
electron vs. $W$ and $Q^2$ for 3 tracking planes crossed.
 Right: the acceptance
of the tracking system in the proton direction in terms of momentum and 
pseudorapidity.
}
\end{center}
\label{fig:accept}
\end{figure}

A full GEANT simulation of the detector was performed, including 
realistic material estimates for the silicon detectors and supports.
The EM calorimeters were assumed to be made of Tungsten and silicon,
while the forward hadron calorimeter was simulated as the ZEUS FCAL.
Momentum and energy resolutions were studied, as was the $e/\pi$
separation achieved.  As an example of the performance of this 
new detector, the range and precision of a possible $F_L$
measurement was estimated.  For this, three beam energies were
assumed ($E_P = 460, 690, 920$~GeV).  The $x$ range over which a
$10$~\% measurement would be possible is shown in Fig.~10.
The required luminosity for this measurement is given in the figure.
At the higher $Q^2$ values, larger $Q^2$ intervals would be used to
allow for reasonable statistical precision with luminosities of order
$100$~pb$^{-1}$.

\begin{figure}[!thb]
\vspace*{7.0cm}
\begin{center}
\special{psfile=caldwell_fig10.eps voffset=0 vscale=40
hscale= 40 hoffset=70 angle=0}
%\centerline{\epsfxsize=2.9in\epsfbox{kim_mephi_lep.ps}}
\caption[*] {
The $x$-range where $10$~\% or better measurements of $F_L$ are
possible is shown as the shaded band.  
The required luminosity is given in each bin in the upper
left corner in units of pb$^{-1}$.}
\end{center}
\label{fig:Fl}
\end{figure}

The performance of the detector was also studied for many other physics
processes, as described in the LoI.  It is clear from these studies that
a detector optimized for forward physics would yield a vast quantity of
exciting new results.

\section{Conclusions}

HERA is a unique facility.  With experiments dedicated to
strong interaction physics studies, substantial progress
can be made in understanding QCD on different distance scales.  This is
clearly of fundamental importance, as QCD is at the heart of
matter.  There is a distinct possibility that a paradigm shift
in our conception of nature would result as a consequence of the
studies outlined here.

In addition to the fundamental nature of the measurements
described above, there are many additional benefits which would
be derived from carrying out the program.  For example, the parton
densities extracted are required for high energy particle, astroparticle and
nuclear experiments.

The proposed experiments are of moderate scale compared with the LHC or
the Linear Collider efforts, and would offer an attractive alternative to
the very large collaborations involved in those efforts.  Additionally,  
the HERA accelerator is an existing facility
which still has substantial physics potential. The manpower and financial
expenditures already invested in HERA should be exploited fully.

\section*{Acknowledgements} 
I would like to thank all the authors of the two LoI's for their efforts
in promoting this important research program.  The help of Halina
Abramowicz, Iris Abt, Tim Greenshaw, Max Klein, and Uta Stoesslein is
particularly appreciated.

\begin{thebibliography}{0}

\bibitem{ref:H1LoI} Electron-Deuteron Scattering with HERA, a Letter
of Intent for an Experimental Programme with the H1 Detector,
H1-04/03-609, http://hep.ph.liv.ac.uk/\~green/HERA3/home.html. 

\bibitem{ref:NewDet} A New Experiment for the HERA Collider, 
Expression of Interest, H. Abramowicz et al., MPP-2003-62,
MPI-PhE/2003-06, http://wwwhera-b.mppmu.mpg.de/hera-3/

\bibitem{ref:MRST} A. D. Martin, R. G. Roberts, W. J. Stirling and
R. S. Thorne, Phys. Lett. {\bf B531} 216 (2002); \\
see also R. S. Thorne, talk at the HERA III workshop, MPI, Munich, Dec 2002,
unpublished.

\bibitem{ref:dipole} For a review, see M. F. McDermott, 
arXiv:hep-ph/0008260, and references therein; \\
K. Golec-Biernat and M. W\"usthoff, Phys. Rev. {\bf D59} 014017 (1999).


\bibitem{ref:H1sea} H1 Collaboration, C. Adloff et al.,
hep-ex/0304003, Eur. Phys. J. {\bf C30} 1 (2003).

\bibitem{ref:Jung} H. Jung, private communication.

\bibitem{ref:McVe} L. McLerran and R. Venugopalan, Phys. Rev. {\bf D50}
225 (1994); Phys. Rev. {\bf D59} 094002 (1999).

\end{thebibliography}

\end{document}
