\vspace{0.1in}
\small
\begin{center}
{\it M. Albrow, 
     D. Litvintsev,
     P. Murat,
     A. Rostovtsev
     }
\end{center}
\normalsize \nopagebreak

There is a possibility that a light ($M_H$ less than about 135 GeV)
Higgs can be discovered at the Tevatron by the {\em exclusive}
production process $p + \bar{p} \rightarrow p H \bar{p}$.  This would
lead to events with two $b$ quark jets in the central detector, and in
the far forward and backward directions the scattered proton and
antiproton.  One could select such events by triggering on the central
jets, and by measuring the trajectories of the scattered beam
particles one could reconstruct very precisely the Higgs
four-momentum.

The QCD process $gg \rightarrow b\bar{b}$ is overwhelming if one
simply tries to reconstruct the di-jet invariant mass spectrum.  While
the mass resolution in reconstructing a $\bb$ jet pair at $M_{JJ}$
100-130 GeV is anticipated to be about 10\% as shown in the previous
sections, the actual width of a Higgs in this mass region is less than
10 MeV~\cite{daws}, so if one can improve the mass resolution the
signal to background ratio $S/B$ keeps improving.

In the exclusive channel there is a possibility of a factor about
50-100 improvement, limited mainly by the momentum spread of the
incoming beams.  The visibility of the Higgs by this technique depends
on the size of the cross section for the process where the Higgs is
produced (in the central region) completely exclusively, i.e. the $p$
and $\bar{p}$ go down the beam pipes each having lost about
$\frac{M_H}{2}$ in longitudinal momentum and no other particles are
produced. The mechanism is as usual $gg\rightarrow H$ through
intermediate loops of heavy particles (predominantly a top loop); this
leaves the $p$ and $\bar{p}$ in color-octet states which normally
gives rise to color strings filling rapidity with hadrons. However
some fraction of the time another gluon can be exchanged which
neutralises (in a color sense) the $p$ and $\bar{p}$ and can even
leave them in their ground state.  The difficulty is in calculating
what this fraction is.  It involves non-perturbative QCD: soft gluon
calculations, soft color interactions, or Regge theory etc. In Regge
theory it is the double pomeron exchange ($DPE$) process.

In 1990 Sch\"{a}fer, Nachtmann and Sch\"{o}pf~\cite{scha} made
calculations of diffractive Higgs production at the LHC and SSC, and
concluded that cross sections for the exclusive $DPE$ reaction could
not be determined reliably. They concluded that ``great effort should be
invested experimentally and theoretically to better understand the
properties of the pomeron and to be able to make more precise
predictions.''  In 1991 Bialas and Landshoff~\cite{bial} calculated
from Regge theory that some 1\% of all Higgs events may have the $p$
and $\bar{p}$ in the $DPE$ region of very high Feynman $x_F \approx
0.95$, but did not estimate the fully exclusive process. In 1995
Cudell and Hernandez~\cite{cude} made a lowest order QCD calculation
with the non-perturbative form factors of the proton tuned to
reproduce elastic and soft diffractive cross-section
measurements. They find, for the exclusive (they call this
\emph{elastic}) production of Higgs with $M_H$ = 100(130) GeV at
$\sqrt{s}$ = 1.8 TeV a cross section of about 50(30) fb, with an
uncertainty about a factor of 2.  The total Higgs production cross
section (at 2 TeV) is about 1200(600) fb at these masses~\cite{daws},
so the exclusive fraction is 4\% to 5\%, even larger than that in the
Bialas and Landshoff paper.  However there are issues of ``rapidity
gap survival probability" and whether they are or are not implicitly
included, and renormalization of the ``pomeron flux", initial and
final state interactions, shadowing effects etc. All these phrases are
poorly understood but are probably different ways of saying the same
thing, namely that diffractive cross sections are lower than
na\"{\i}ve Regge expectations by about an order of magnitude in
hadron-hadron collisions (not in $e-p$ collisions). Understanding that
there is a large uncertainty in this estimate, we apply a factor of 10
reduction to the estimate of ref.~\cite{cude} and get about 4 fb (the
increase of $\sqrt{s}$ from 1.8 to 2.0 TeV will also help).

That would mean, in Run~2 (2 fb$^{-1}$) only 8 events (before
applying any efficiencies). It appears that 2 fb$^{-1}$ is very
difficult for \emph{any} Higgs searches, so we consider a Run 3 with
30 fb$^{-1}$ which could give 120 events, or with 50\% acceptance 60
events. This could be a discovery channel if the background is about
140 events or less. Now we come to the key of our idea.

For these exclusive events, with the Higgs produced centrally, the $p$
and $\bar{p}$ each lose about $\frac{M_H}{2}$ in momentum, so they
have $x_F \approx 0.94$.  They could both be detected in Roman pot
detectors and, with high resolution ($\sim$10 $\mu m$) tracking their
momenta can be measured with very high precision ($\frac{\Delta p}{p}
\approx 10^{-4}$). This needs a measurement of the primary vertex (at
the intersection of the two $b$-jet directions, using SVX tracking)
and good knowledge of the quadrupole, electrostatic and dipole fields
from the vertex to the pots. Then the missing mass ($m_{miss}$) to the
measured $p$ and $\bar{p}$ will have a resolution limited by the
spread on the incoming beam particles' momenta. This is about
10$^{-4}$, and gives a mass resolution on the selected $b\bar{b}$
dijet candidates of about 200 MeV\footnote{These numbers are still
largely ``back of the envelope" estimates; a proper simulation has yet
to be done.}. This is a factor about 50 better than the resolution on
the effective mass ($m_{eff}$) of the dijet and hence we get a factor
50 improvement in $S/B$. Furthermore, even if the Higgs were to be
discovered another way, this process has the potential of giving the
best value for $M_H$. We should now try to estimate the $S/B$ ratio to
see whether there is hope that the signal could be visible.

We take CDF's published cross section~\cite{cdfb}
$\frac{d\sigma}{dM_{JJ}}$ for two b-tagged jets, which starts at 150
GeV, and extrapolate down to 100(130) GeV finding 200(40) pb/GeV (in
$|\eta| < 2.0, |cos(\theta^*)| < 2/3$).  From our other $DPE$ studies,
at lower mass, we expect that about $2.10^{-5}$ of these would have a
rapidity gap on each side (assuming this fraction is not
$E_T$-dependent). That gives $\approx $ 4.0(0.8) fb.GeV$^{-1}$, or
0.8(0.16) fb per 200 MeV bin to be compared with a signal of around
5(3) fb in such a bin.  We thus have a $S/B$ of order 6(20) (with the
assumed reduction of the Cudell and Hernandez estimate by a factor
10).  In 10 fb$^{-1}$ this means 30 events on a background of 1.6 for
a 130 GeV Higgs! We have not included a factor for $b$-tagging
efficiency and acceptance, but that affects both signal and background
proportionately, to first order. We have also not put in the
acceptance of the Roman pots for these events, which depends on
Tevatron-dependent factors but should be high if the
$|t|$-distribution of the $p$ and $\bar{p}$ is not much harder than in
generic high mass diffraction.

We think it is very important to study the backgrounds as early as
possible in Run~2. This means covering the region forward of $\eta$ =
3.5 with miniplug calorimeters (supplementing the CLC counters) and
Beam Shower Counters out to the beam rapidity ($\approx 7.5$).  One
trigger is $\ge$ 2 jets with nothing in both forward directions.
(Looser prescaled triggers are needed to measure the non-$DPE$
backgrounds.) We can measure $d\sigma/dM_{JJ}$ vs $M_{JJ}$ for generic
jets and for tagged $b$-jets out to $M_{JJ}$ above 100 GeV but with
poor resolution and relatively wide bins. By this time we should be
better able to judge how promising the Higgs search may be.

If it does look promising then, to do the Higgs search, an additional
arm of Roman pot detectors must be placed on the $p$-side after
dipoles to give acceptance for $x_F \approx 0.94$ down to $p_T$ = 0 as
we have now on the $\bar{p}$-side. At present there is no warm space
(spool-piece) where such pots could go. The simplest way to make such
a space is by removing the Q1 quadrupoles which are redundant in Run~2
(they are being taken out at D\O) and to move the dipoles closer to
the interaction point.  A Beams Division study would be needed, but
probably a lever arm of 1 m for pot detectors could be made, giving
$\frac{\sigma_{\theta}}{\theta} \approx 10^{-5}$ if positioning
accuracy of 10$\mu m$ can be achieved (which is overkill, given the
uncertainty on the incoming momenta). Moving the dipoles closer to B\O
(symmetrically on the $p$ and $\bar{p}$ sides) would mean moving the
CDF detector by about 2 cm; we do not see that as a major problem.

This Higgs search trigger is then a high $x_F$ track in each forward
arm, no hits in any BSC counter or either miniplug (i.e. rapidity gaps
from $3.5 < \eta < 7.5$) and two central jets above about 20 GeV in
$E_T$.  At a later level trigger and/or offline one selects two tagged
b-jets and requires $X_{JJ} = \frac{M_{JJ}}{M_{cen}}$ large, where
$M_{cen}$ is the total effective mass of the central calorimeter
towers. After low missing $E_T$ and other clean-up cuts we would
require $m_{miss} \approx m_{eff}$ and plot $m_{miss}$ in bins
dictated by the resolution. This strategy will only work for single
interactions per bunch crossing, because additional interactions will
spoil the gaps and pile up in $M_{cen}$. The search will be more
difficult in the presence of multiple interactions but should still be
possible.  Precision timing on the pot tracks can (a) check that the
$p$ and $\bar{p}$ came from the same interaction (b) measure the
position in $z$ of that interaction, and (c) correlate with the timing
of the $b$ and/or $\bar{b}$ jets from the time of flight barrel (in
CDF). A fast trigger processor could be used to correlate $m_{miss}$
and $m_{eff}$ and record events when these are comparable. Off-line
the cleanliness of the vertex from which the $b$ and $\bar{b}$ emerged
is used as a cut.

There is another process with a similar diagram to the exclusive Higgs
production but with a larger cross section and this could be used to
test our understanding. This is $p+p\rightarrow p+\chi_b^o+ p $
followed by $\chi_b^o \rightarrow \Upsilon\gamma \rightarrow
\mu^+\mu^-\gamma$.  The $\chi_b^o$ has the same quantum numbers
($I^GJ^{PC} = 0^+0^{++}$) as the vacuum and the Higgs. A measurement
of the fraction of all (low $p_T$) $\chi_b^o$ which are produced in
total isolation would be instructive, and could probably be made with
a 2-$\mu$ 2-gap trigger early in Run~2. One can also study exclusive
$\chi_c^o$ production, using the time of flight barrel in a Level 1
trigger on the $2(\pi^+\pi^-)$ or $\pi^+\pi^-K^+K^-$ final states.




