Dear Colleagues,
     Due to family constraints, it turns out that I will not be
able to attend the Tevatron Connection, much to my disappointment.
I thought it would be useful to at least send my thoughts, and to
invite anyone to contact me if they want to discuss any of these
topics.   You will find a bibliography of relevant papers at the
end of this message.
    Scott
1. Wh or Zh, with h->bb:  More effort has gone into these processes
than any other Higgs process at the Tevatron, so it is hard to find
anything new to add to the discussion.  Let me just remind you that
these processes are thought to be extremely challenging at the LHC,
and so if they are going to be seen, the Tevatron is the place to
see them.
There is a very recent paper by Sullivan that criticizes the accuracy
of Pythia/HERWIG for modeling single-top production.   Recall that
single top is a serious background to these Higgs processes.
Sullivan will be speaking on single top on Monday afternoon in the
Precision Electroweak session.
2.  bb-> h and gb->hb :  In a generic two-Higgs-doublet model, some
of the physical Higgs bosons  have enhanced couplings to bottom quarks
for large tan beta.   Large tan beta is actually attractive, because
it supplies an alternative explanation of why the top quark is so much
heavier than the bottom quark.   In the standard model, this is because
the top Yukawa coupling is much larger than that of the bottom quark.
But in a two-Higgs-doublet model with large tan beta, the top and
bottom have similar Yukawa couplings, but the bottom quark couples to
the Higgs field with a small vacuum-expectation value, while the top
quark couples to the other Higgs field.   This suggests that we should
 expect tan beta around mt/mb = 40, although smaller and larger values
are also possible.
A well-known two-Higgs-doublet model is the Higgs sector of the MSSM.
At large tan beta, one of the Higgs scalars acts like a SM Higgs,
while the other Higgs scalar and the Higgs pseudoscalar have enhanced
coupling to bottom quarks.   If these are light enough, they may be
accessible at the Tevatron.   See the paper by Boos et al for further
discussion.
If a Higgs boson has enhanced coupling to bottom quarks, it may be
produced via this coupling.   Let me discuss two possible channels:
a. bb->h, i.e., inclusive production of the Higgs.   This calculation
makes use of the b-quark distribution function in the proton sea,
which is calculated perturbatively from the gluon distribution
function.   Alternatively, one can ignore the b distribution function,
and calculate the inclusive cross section from gg->bbh.   The two
calculations should give the same result.   At the time of the Run II
SUSY/Higgs workshop (Carena et al.), these two calculations differed
by an order of magnitude, and it was not clear which was closer to
the truth (bb->h was the larger of the two).    It turns out that the
cross section based on bb->h was the more accurate.    The inclusive
cross section based on gg->bbh has now been calculated to NLO (see
Dittmaier et al.), and it agrees with the NLO bb->h calculation within
uncertainties (see Les Houches proceedings).   However, the  bb->h
cross section has now been calculated to NNLO, which makes it the more
accurate of the two calculations (see Harlander and Kilgore).   This
demonstrates one of the advantages of using the b distribution
function for calculations.
The NNLO bb->h cross section has very little theoretical uncertainty.
I noticed that the inclusive cross sections for this process given in
the talk of Hanagaki are low by about a factor of two, and have bigger
uncertainty than the NNLO calculation.   I advocate using the cross
sections in the Harlander/Kilgore paper (which are also given in Les
Houches), since they are the most accurate available.
b.  gb-> hb :  The idea here is to use the b jet in the final state
to reduce backgrounds.   This cross section has been calculated to
NLO (see Campbell et al.).   A very recent paper by Dawson et al.
compares this with gg->bbh at NLO (where at least one b is at high pt).
The two agree very well, as they should, and have similar uncertainty.
However, the recent paper by Dawson et al. includes a diagram,
involving a top-quark loop, that is negligible at large tan beta.
Hence their numerical results cannot simply be multiplied by tan^2
beta.   For this reason it is preferable to use the numerical results
of Campbell et al. (see the code MCFM).
Topic for discussion: What is the best way to model these processes
with a shower Monte Carlo?
a. bb->h :  At LO the h is produced with zero pt.   It acquires pt
from initial-state radiation.  While this is probably accurate at
low pt, it will not do a very good job at high pt.   However, there
are not many events at high pt.   At high pt, the most important
process is gb->hb, with bb->hg of secondary importance.
Alternatively, one could use gg->bbh as the LO process in the shower
Monte Carlo.  I'm not sure it will do as good a job at low Higgs pt.
Will it capture gg->bbhg, where the g is radiated from a virtual b
line (the analogue of bb->hg above)?
b. gb->hb :  Here we are interested in tagging a final-state b jet.
There may be additional jets in the final state.    It is a
surprising but true fact that the largest such contribution is from
gb->hbg, with gg->bbh of secondary importance.   If one used gg->bbh
as the LO process, then the analogue of gb->hbg would be gg->bbhg,
with at least one b at high pt.
Starting with gb->hb as the LO process, a second b jet would
sometimes be generated by the shower MC from the backward evolution
of the initial-state b quark (g->bb).  Sullivan has argued that b
jets generated from gluon splitting in the initial state by the
shower MC's is a poor approximation.   This would argue in favor
of using gg->bbh as the LO process.
Bibliography:
1) UNDERSTANDING SINGLE-TOP-QUARK PRODUCTION AND JETS AT HADRON COLLIDERS.
By Zack Sullivan. FERMILAB-PUB-04-142-T, Aug 2004. ** Temporary entry **
e-Print Archive: hep-ph/0408049
2) THE MSSM HIGGS BOSONS IN THE INTENSE COUPLING REGIME.
By Edward Boos (Moscow State U. & DESY), Abdelhak Djouadi, Margarete
Muhlleitner (Montpellier U.), Alexander Vologdin (Moscow State U.),.
PM-02-10, May 2002. 50pp.
Published in Phys.Rev.D66:055004,2002
e-Print Archive: hep-ph/0205160
2) REPORT OF THE TEVATRON HIGGS WORKING GROUP.
By Higgs Working Group Collaboration (Marcela Carena et al.).
FERMILAB-CONF-00-279-T, SCIPP-00-37, FERMILAB-PUB-00-349, Oct 2000. 185pp.
Part 6 of Physics at Run II SUSY/Higgs report: available as
fermilab-pub-00-346-1 (part 1), hep-ph/0003154 (part 2), hep-ph/0008070
(part 3), and hep-ph/9906224 (part 4), and hep-ph/0006162 (part 5), and
hep-ph/0010338 (part 6).
e-Print Archive: hep-ph/0010338
3) HIGGS RADIATION OFF BOTTOM QUARKS AT THE TEVATRON AND THE LHC.
By Stefan Dittmaier (Munich, Max Planck Inst.), Michael Kramer
(Edinburgh U.), Michael Spira (PSI, Villigen),. EDINBURGH-2003-13,
MPP-2003-49, PSI-PR-03-14, Sep 2003. 12pp.
e-Print Archive: hep-ph/0309204
2) HIGGS BOSON PRODUCTION IN ASSOCIATION WITH BOTTOM QUARKS.
By J. Campbell, S. Dawson, S. Dittmaier, C. Jackson, M. Kramer,
F. Maltoni, L. Reina, M. Spira, D. Wackeroth, S. Willenbrock
(Argonne & Brookhaven & Munich, Max Planck Inst. & Florida State U.
& Edinburgh U. & Enrico Fermi Ctr., Rome & PSI, Villigen & SUNY,
Buffalo & Illinois U., Urbana),. May 2004. 7pp.  Contributed to 3rd
Les Houches Workshop: Physics at TeV Colliders, Les Houches, France,
26 May - 6 Jun 2003. e-Print Archive: hep-ph/0405302
2) HIGGS BOSON PRODUCTION IN BOTTOM QUARK FUSION AT NEXT-TO-NEXT-TO
LEADING ORDER.  By Robert V. Harlander (CERN), William B. Kilgore
(Brookhaven),. BNL-HET-03-4, CERN-TH-2003-067, Apr 2003. 16pp.
Published in Phys.Rev.D68:013001,2003
e-Print Archive: hep-ph/0304035
4) HIGGS-BOSON PRODUCTION IN ASSOCIATION WITH A SINGLE BOTTOM QUARK.
By J. Campbell (Argonne), R.K. Ellis (Fermilab), F. Maltoni,
S. Willenbrock (Illinois U., Urbana),. ANL-HEP-PR-02-027,
FERMILAB-PUB-02-062-T, ILL-TH-02-3, Apr 2002. 25pp.
Published in Phys.Rev.D67:095002,2003 e-Print Archive: hep-ph/0204093
1) HIGGS BOSON PRODUCTION WITH ONE BOTTOM QUARK JET AT HADRON COLLIDERS.
By S. Dawson, C.B. Jackson, L. Reina, D. Wackeroth. BNL-HET-04-12,
Aug 2004. 4pp. ** Temporary entry ** e-Print Archive: hep-ph/0408077