1. Soft Physics at the LHC: gap survival and Monte Carlo
Khoze-Martin-Ryskin + Krauss, Hoeth, Zapp IPPP, Durham
Forward Physics at the LHC
Manchester, December 2009
Importance of minimum-bias events (and rap. gap survival)
Up to now no complete model (Monte Carlo) including all facets
--- elastic scattering, diffractive events, hard jets, etc. ---
on the same footing
Intimate connection to underlying event
First physics at the LHC
More specific physics reasons – 2 examples from Higgs searches

2. 1. Higgs search via vector-boson fusion
Signature: two forward jets + rap.gap
filled by Higgs decay
Essential for S/B: survival rate of gap
Typical manifestation of gap: central jet/hadron veto
Folklore: requirement of central gap effectively
suppresses QCD-driven background
Gap survival depends on extra jets + underlying event
(calculable) (need Monte C.)

3. 2. pp  p+H+p Base value: s = 2.5 fb update
SM MH=120 GeV
LHC=14 TeV
eikonal screening H
Base value: s = 2.5 fb
update
-45% adjust c in upper limit 1 - kt/(cMH+kt) of z integration
of Sudakov factor to reproduce one-loop result.
Find c=1 (Coughlin, KMR09), and not 0.62 (KKMR04)
-25% if enhanced screening included (KMR )
+20% due to NLO unintegrated gluon (MRWatt )
+20% connected with self-energy insertions in propagator
of screening gluon (Ryskin et al.)
see later
PS Recall factor 3 uncertainty
PPS Remember SUSY Higgs can be greatly enhanced

4. Model for “soft” high-energy interactions
needed to ---- understand asymptotics, intrinsic interest
---- describe “min. bias/underlying” events
---- calc. rap.gap survival prob. S2
---- devise “all-purpose” Monte Carlo
Model should:
be self-consistent theoretically --- satisfy unitarity
 importance of absorptive corrections
 importance of multi-Pomeron interactions
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 due to enhanced rescatt.
4. be suitable for “all-purpose” MC --- partonic approach

5. 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
gN3g3P
so (g3P)bare increased

6. Must include unitarity
diagonal in b ~ l/p
elastic unitarity 
e-W is the probability of no inelastic interaction

7. DL parametrization:
Effective Pomeron pole
aP(t) = t
KMR parametrization
includes absorption
via multi-Pomeron
effects

8. Elastic amp. Tel(s,b)
bare amp. Im
(-20%)
multichannel eikonal
Low-mass diffractive dissociation
introduce diffve estates fi, fk (combns of p,p*,..) which only
undergo “elastic” scattering (Good-Walker)
(-40%) Im
include high-mass diffractive dissociation
(SD -80%)
g3P “large”

9. Towards a partonic interpretation
Structure of the Pomeron before QCD
sum of ladder diagrams  sa behaviour
cut:
scalar particles
contribn of cell
(Y=ln s)
kt limited. Impossible to obtain a(0)>1 for m<1.5 GeV,
but for larger m we have larger kt  pQCD

10. Partonic QCD structure of the Pomeron
gluon ladder – spin 1 gives extra s
n-1 rungs
recursion reln:
BFKL kernel
n rungs
Random walk: current cell differs from previous by

11. Smooth transition from “hard” to “soft” Pomeron?
No irregularity in HERA data in Q2 = 0.3 – 2 GeV2 region
Global analysis of “soft” data (including absorptive effects)
give “bare” slope a’ < 0.1 GeV-2
(a’ ~ 1/<kt2> kt in perturbative region)
give “bare” intercept D = aP(0) - 1 ~ 0.3
The absorptive effects increase as we go to low kt:
screening  aPeffective ~ t (t in GeV2)
(up to Tevatron energies)
see later

12. Partonic QCD structure of the Pomeron
gluon ladder – spin 1 gives extra s
n-1 rungs
recursion reln:
BFKL kernel
n rungs
Random walk: current cell differs from previous by

13. Partonic interpretation
“bare” Pomeron pole contribn to elastic amp
D = splitting function = prob.
of emission of parton c in dy
evolution eq.
Multi-Pomeron contribns
e.g. triple-Pomeron diagram:
parton c has extra scattering
with “target” k

14. Multi-Pomeron contribns continued
Many rescatt: different no.
of ladders between c and k
where lWk reflects the different opacity of “target” k
felt by c, rather opacity Wk than felt by “beam” i l~0.25
Include rescatt of c with “beam” i
evolve up from y=0 Y
evolve down from y’=Y-y=0
y’ =Y-y y
solve iteratively

15. Y Wi Wk i b2 c b b1 k

16. only y dep. of evolution shown. Need b and kt dep. to calc Senh2
pole: in mom.
space  s1+D+a’ t
BFKL diffusion
in log kt2
rescatt. between low x, low kt partons and “target”
distorts input distribn -- violates soft-hard factorizn P1 P3
large kt partons -- rescatt. negligible H
Simplify the kt behaviour:
sec. Reggeon
3 compts to mimic BFKL diffusion in ln kt
full treatment
in progress
a = Plarge, Pintermediate, Psmall, R
average kt1~0.5, kt2~1.5, kt3~5 GeV

17. Evolve and tune to all soft data:
VRP1 ~ gPPR,gRRP
with a = P1, P2, P3, R
VPiPj ~ BFKL
soft
QCD
Evolve and tune to all soft data:
-- multi-Pomeron coupling l from xdsSD/dxdt data ( x~0.01)
-- info on diffractive eigenstates from sSD(low M) = 2 mb at ISR
-- info on form factors from dsel/dt
Results
l=0.25
“bare” Pomeron: DP = a(0)-1~ 0.3, a’P ~ 0.05 GeV-2
P1 heavily screened  effective DL Pomeron (up to Tevatron)
s(tot) ~ 90 mb at LHC (suppressed by screening)
DReggeon ~ -0.4 (as expected)

18. f1: “large” f3: “small” elastic differential ds/dt f1*f1 f3*f3
LHC (x0.1)
~ g, sea
f3*f3
f1: “large”
f3: “small”
more valence

19. Description of CDF dissociation data
no ppP
no ppP

20. “soft” Pomeron:
partons saturated
little growth
“hard” Pomeron:
little screening
much growth s0.3

21. Survival prob. for pp  p+H+p at LHC
Eikonal rescattering ---- consensus
Effect of enhanced rescattering ---- controversy

22. 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 SM Higgs at the LHC
 s ~ fb at LHC

23. Satn scale Qs2<0.3 GeV2 for x~10-6
from g pJ/y p
Watt, Kowalski
<Seik>2 ~ 0.02
0.6 fm
parton only survives eik. rescatt. on
periphery, where parton density is
small and prob. of enh. abs. small

24. gap gap Two subtlities H fg’s from HERA data already include rescatt.
of intermediate partons with parent proton
Usually take pt=0 and integrate with exp(-Bpt2).
S2/B2 enters (where 1/B = <pt2>). But enh. abs.
changes pt2 behaviour from exp., so quote S2<pt2>2
<S2tot>=<S2eikS2enh> ~ (for B=4 GeV-2)
see
<S2tot><pt2>2 = GeV4

25. Comments on GLM(2008)
GLM include some 3P effects, but get <Senh2> = 0.063
<Stot2> = x =
Calculation should be extended to obtain reliable Senh
Need to calc. b kt correln. GLM assume enh. abs. is
the same at all b (so does not depend on parton density
at given b). But Senh comes mainly from periphery
(after Seik suppression) where parton density is small.
So Senh (GLM) is much too small.
2. First 3P diagram is missing.
3. Four or more multi-Pomeron vertices neglected, so stot
asymptotically decreases (but GLM have stot asym. const.).
Model should specify energy interval where it is valid.
4. Need to consider threshold suppression.
5. Should compare predictions with observed CDF data.ut

26. Comments on Strikman et al.
also predict a v.small Senh ?!
They use LO gluon with v.steep 1/x behaviour.
Obtain black disc regime at LHC energy, with low x (10-6)
gluon so large that only on the periphery of the proton
will gap have chance to survive.
However, empirically the low x, low Q2 gluon is
flat for x < – the steep 1/x LO behaviour is an
artefact of the neglect of large NLO corrections.
Again, should compare model with CDF exclusive data.

27. Monte Carlo based on simplified KMR model
Existing “all purpose” Monte Carlos split eikonal
W(s,b) = Wsoft + Whard(pQCD)
We seek MC that describes all aspects of minimum bias
-- total, differential elastic xsections, diffraction, jet prod...—
in a unified framework; capable of modelling exclusive
final states.
Monte Carlo based on simplified KMR model
Krauss, Hoeth, Zapp
Status report:
first, outline steps of producing the MC

28. step 1: solve evoln eqs and generate Wik(b)Y Wi Wk i b2 c b b1 k

29. step 2: generate ladders
step 3: generating emissions

30. step 3: generating emissions contd8 8 8 8 1 1 8 8 8 8

31. step 4 step 5 Select “beam” partons (xi,Qi2) from known PDFs
Check energy conservation, step 2.
step 5
Implement the “usual”
parton shower + hadronisation + hadron decays + QED …
Can such an “all purpose” Monte Carlo, based on a model
tuned to describe elastic, diffractive processes, also really
describe inelastic, single-particle production etc.
(e.g. p+ pT distribution)?

32. First Monte Carlo results v. encouraging:
-- total and elastic differential cross sections OK
-- single jet and identified particles ~OK
e.g. p+, jet,… xsections at STAR (pp 200 GeV)
-- <pt> versus Nch, dNch/dh OK
-- minimum bias CDF (1800 GeV): “Rick Fields” plots
~OK in “forward” and “away” Dj quadrants
undershoot in “transverse” quadrants 
need to extend simple model, particularly
for large triggering scale, where inclusion
of BFKL diffusion should help

33. p+ transverse momentum

34. Mean track pT vs multiplicity

35. Charge multiplicity

36. leading jet
Nch in toward region
Toward region
Nch in away region

37. Nch in transverse region
Improvement needed
in the transverse region.
Not enough particles,
tho’ find the average pT
per particle is OK

38. Conclusions
-- Obtained a fully consistent description of all high-energy
soft interactions; the model incorporates both a
multi-channel eikonal and multi-Pomeron interactions
-- screening/unitarity/absorptive corrections are appreciable
at LHC energies.
(stotal (14 TeV) ~ 90 mb)
-- soft-hard Pomeron transition emerges
“soft” compt. --- heavily screened --- little growth with s
“hard” compt. --- little screening --- large growth (~pQCD)
-- Model allows both eikonal and enhanced rescatt. corrections
and gap survival prob. to be calculated for any diffractive proc.
-- Model has partonic interpretation, so can form basis of “all
purpose” Monte Carlo. Model tuned to describe elastic,
diffractive processes, but MC also gives description of
multiparticle production. Preliminary results v.encouraging.