1. … “Soft” processes at collider energies
Multi-component s- and t-channel model of soft processes …
importance of absorptive effects
importance of multi-Pomeron-Pomeron interactions
relevance to exclusive Higgs
Alan Martin, Forward Physics at the LHC, Manchester, Dec. ‘08

2. Model for “soft” high-energy interactions
needed to ---- understand asymptotics, intrinsic interest
---- describe “underlying” events at LHC
---- calc. rap.gap survival S2 for exclusive prodn
Model should:
be self-consistent theoretically --- satisfy unitarity
(incl. abs. corrns)
2. agree with available soft data
CERN-ISR to Tevatron range
3. include Pomeron compts of different size---to study effects of
soft-hard factn breaking

3. Optical theorems at high energy use Regge but screening important
so stotal suppressed
gN2
High mass diffractive dissociation 2 M2
triple-Pomeron diag
but screening important
g3P
so (g3P)bare increased

4. S2el = e-W is the probability of no inelastic interaction
diagonal in b
elastic unitarity 
S2el = e-W is the probability of no inelastic interaction

5. directly related to elastic data
LHC
Tevatron
from model fits
to elastic data

6. Elastic amp. Tel(s,b)
bare amp.
(-20%)
multichannel eikonal
Low-mass diffractive dissociation
introduce diffve estates fi, fk (combns of p,p*,..) which only
undergo “elastic” scattering (Good-Walker)
(-40%)
include high-mass diffractive dissociation
(SD -80%)

7. triple-Regge analysis of ds/dtdx, including screening
(includes compilation of SD data by Goulianos and Montanha)
fit: c2 = 171 / 206 d.o.f.
CERN-ISR
Tevatron
PPP
PPR
PPP
PPR
RRR
RRP
RRP
ppP
ppP x x
g3P large, need to include
multi-Pomeron effects
g3P=l gN l~0.2
Luna+KMR;

8. so at collider energies sSD ~ sel
g3P=l gN l~0.2
 large ? 2 gN M2
g3P
M2dsSD/dM2 ~ gN3 g3P ~lsel
ln s
so at collider energies sSD ~ sel

9. New analysis of soft data
KMR 2008
model:
3-channel eikonal,
fi with i=1,3
include multi-Pomeron diagrams
attempt to mimic BFKL diffusion in
log qt by including three components
to approximate qt distribution –
possibility of seeing “soft  hard” Pomeron transition

10. Include absorption – full set of multi-Pomeron diagrams
e.g.
evolve up from y=0
absorptive effects
bare pole
or evolve down from y’=Y-y=0
solve for Wik(y,b)
by iteration

11. Use four exchanges in the t channel
3 to mimic BFKL diffusion in ln qt
sec. Reggeon
a = Plarge, Pintermediate, Psmall, R
soft pQCD
average qt1~0.5, qt2~1.5, qt3~5 GeV
VRP1 ~ gPPR,gRRP
VPiPj ~ BFKL
evolve up from y=0
bare pole
absorptive effects
evolve down
from y’=Y-y=0
solve for Waik(y,b)
by iteration

12. Parameters
multi-Pomeron coupling l from xdsSD/dxdt data ( x~0.01)
diffractive eigenstates from sSD(low M)=2mb at sqrt(s)=31 GeV,
-- equi-spread in R2, and t dep. from dsel/dt
All soft data well described
g3P=lgN with l= (compared to l=0.2 in Luna et al.)
DPi = 0.3 (close to the BFKL NLL resummed value)
a’P1 = 0.05 GeV-2
These values of the bare Pomeron trajectory yield, after
screening, the expected soft Pomeron behaviour ---
“soft-hard” matching (since P1 heavily screened,….P3~bare)
DR = -0.4 (as expected for secondary Reggeon)
Results
D = a(0) - 1

13. f1: “large” f3: “small” elastic differential s f1*f1 f3*f3 LHC (x0.1)
~ g, sea
f3*f3
f1: “large”
f3: “small”
more valence

14. Description of CDF dissociation data

15. Predictions for LHC stotal = 91.7 mb sel = 21.5 mb sSD = 19.0 mb
All Pom. compts
have Dbare=0.3
parton multiplicity
pppX
“soft”, screened,
little growth,
partons saturated
“hard” ~ no screening
much growth, s0.3

16. “soft” Pomeron
“hard” Pomeron

17. Survival prob. for pp  p+H+p, see Misha’s talk p1t
<S2eik> ~ 0.02 – 0.025
consensus
<S2enh> ~ 0.01 – 1
controversy
KMR 2008 
<S2>tot=<S2eikS2enh> ~ 0.015
(B=4 GeV-2) H
p2t
see Misha’s talk,
stable quantity is
LHC
Tevatron
KMR (no Senh)
<S2>tot<p2t>2 =
LHC
Tevatron
KMR (with Senh)
CDF exclusive measurements (gg, dijet, c) indicate that
the above may be conservative lower limits

18. Calculation of S2eik for pp  p + H +p
prob. of proton to be
in diffractive estate i
survival factor
w.r.t. soft
i-k interaction
hard m.e.
i k  H
over b
average over
diff. estates i,k
S2eik ~ for 120 GeV Higgs at the LHC

19. theoretical formalism for pp  p + A + p ?
Early LHC checks of
theoretical formalism for
pp  p + A + p ?
KMR
Possible checks of:
(i) survival factor S2: W+gaps, Z+gaps
(ii) generalised gluon fg : gp Up
(iii) Sudakov factor T : central jets
(iv) soft-hard factorisation #(A+gap) evts
(broken by enhanced #(inclusive A) evts
absorptive effects) with A = W, dijet, U…

20. -- screening/unitarity/absorptive corrections are vital
Conclusions
-- screening/unitarity/absorptive corrections are vital
-- Triple-Regge analysis with screening  g3P increased by ~3
 importance of multi-Pomeron diagrams
-- Latest analysis of all available “soft” data:
multi-ch eikonal + multi-Regge + compts of Pom. to mimic BFKL
(showed some LHC predictions ….. stotal ~ 90 mb)
soft-hard Pomeron transition emerges
“soft” compt. --- heavily screened --- little growth with s
“intermediate” compt. --- some screening
“hard” compt. --- little screening --- large growth (~pQCD)
-- LHC can explore multigap events  probe multi-Pomeron
structure
LHC is a powerful
probe of models
of soft processes SD
DPE