Theory Summary Talk

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Theory Summary Talk
Jeff Forshaw Milos 2006
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General theoretical developments
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Lipatov
It is possible to write the BFKL equation as a
Schroedinger equation
where
The energy eigenvalues locate the j-plane poles
with the ground stateenergy determining the
leading singularity (BFKL pomeron).
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Holomorphic separability reduces the
dimensionality of the problem
That was for two exchanged reggeized
gluons.extending to anynumber of reggeized
gluons interacting pairwise with nearest
neighbours gives the BKP equation
BKP originally was derived in 1980 as the
minimal way to unitarize BFKL (leading N_c)
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Solving BKP for 3 reggeons gives the odderon
contribution. Remarkably the general solution is
accessible..because theproblem is equivalent to
a Heisenberg XXX spin chain (integrable)where
the spins are generators of the Moebius group.
The problem then reduces to identifying the
ground state and anappropriate raising operator
The energy eigenvalues can then be
constructed. Odderon has intercept equal to
unity.
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Conformal symmetry was crucial to integrability
and is lostin QCD beyond the lowest order BFKL
approximation.But it is not lost in N4
supersymmetric QCD where theBFKL kernel remains
holomorphically separable beyond LO.
Moreover, the kernel appears to be built from psi
functions(related to zeta functions) suggests
a principle of maximum transcendality?
The DGLAP splitting functions can be determined
by the usualmeans (two-loops) and also appear to
be maximally transcendental, e.g.
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• Kotikov, Lipatov, Onischenko Velizhanin invoked
  maximal transcendality to extract the 3-loop
  splitting function from the QCDcalculation of
  Moch, Vermaseren Vogt.
• It is not easy to check this result and hence the
  conjecture of maximal transcendality (full
  three-loop calculation inN4 SUSY is even harder
  than in QCD)
• But it has been shown to be correct in the j0
  and jinfinity limits.
• Eden-Staudacher also have a prediction for
  all-loops at large j.
• Finally..assuming AdS/CFT correspondence there
  is a prediction fromstring theory for the
  behaviour at strong coupling. There is also a
  prediction for the pomeron intercept at strong
  coupling.

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Kyrieleis Possible breakdown of QCD coherence
Soft gluons dress hard scattering processes and
often need to be summed to all orders, i.e. in
processes where there is aBloch-Nordsieck
miscancellation. e.g. threshold production where
real emissions are restricted by kinematics.
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e.g. Gaps between jets
Old wisdom soft gluon effects exponentiate
(only need virtual corrections)
But this breaks down for some observables (like
gaps between jets) realemissions need to be
considered too..
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Nevertheless, coherence still suggests that there
remains a factorization ofsoft emissions from
collinear emissions

• ButCoulomb gluons spoil this cancellation for
  radiation collinearwith an incoming parton.
• The miscancellation is irrelevant for
  sufficiently inclusive observablesor for hard
  processes with a simple enough colour structure
  (i.e. fewer thanfour external partons).
• But it appears to survive for some processes.
• In gaps between jets it leads to a new class of
  superleading logarithmswhich demote the
  previous leading series to the level of NLL.
  The firstsuperleading logs appear at a high
  order in perturbation theory and aresub-leading
  in the number of colours.
• Wide angle soft gluon emission appears to be
  sensitive to collinear radiationMay have severe
  implications

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Magas on the construction of a dual amplitude
for DIS
Lukaszuk large s behaviour of parity
violatingCompton amplitude exhibits
odderon-like behaviour due to QCD-electroweak
interference.
Resolved photons
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BFKL
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Fadin NLO BFKL kernel for non-forward scattering
is now available.
Two gluon contribution was the stumbling block
First (partial) results presented on the
representation of thekernel in transverse
co-ordinate space useful for checkingconformal
structure and understanding the dipole
formalismat NLO.
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Chachamis the NLL photon impact factor is
nowcomplete.
Phenomenology will dependupon how the QCD
couplingis made to runstill only
one-loop. Next step compute the cross-section
for
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Papa first calculation of a NLL BFKL (t0)
cross-section. Evidence for large negative NLL
correctionsimportant to pick renormalization
scale correctly.
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Schwennsen learn more about NLL BFKL via
inclusivejet production.
Real emission vertex at NLO
Need to break open the integral and introduce
ajet algorithm. NLO unintegrated gluon needed
in proton scattering.
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SabioVera learn more about BFKL through
azimuthaldecorrelations between jets.
Predictions also for LHC and forHERA (forward
jets). Extend to NLL? SchwennsenBFKL Monte
Carlo Stephens
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Exclusive Processes
Baranov On the helicity structure of diffractive
J/Psi production Jenkovszky Capua DVCS in a
model with a single pomeron pole
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I. Ivanov diffractive electroproduction of
spin-3 mesons
Kt-factorization
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Goloskokov Exclusive vector meson production
Extend the perturbative approach to include
transverse photons Need to include Sudakov
suppression and transverse momentumdependence of
meson wavefunction.
Good agreement with HERA data onrho and phi
including HERMES.Detailed predictions for
SDMEs.Predictions for COMPASS. Good probe of
generalized partons.
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D. Ivanov

• Full NLO calculation
• Access to GPDs and tostructure of
  two-piondistribution amplitude

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Comparison to HERMES data (data at dangerously
low Q23 GeV2)
Also predictions for COMPASS
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Segond
Investigation of the factorizationstructure.
Two types of factorization
(1)
Explicit calculation in Born approximation(i.e.
quark exchange only)
(2)
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Central Exclusive Production
Detect the four-momenta of the protons using
detectors situated 220m and 420m from the
interaction point
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Royon

• Stressed the importance of understanding the
  high-beta gluonin the pomeron in order to
  constrain background for centralexlusive
  production.
• Presented Saclay approach to inclusive
  exclusive productionas manifest in DPEMC.
• Advocated looking at azimuthal dependence of
  scattered protonsat DZero to test models of gap
  survival.
• Advocated using gamma-gamma -gt WW as a way
  tocheck the alignment/calibration of the Roman
  Pots at LHC.

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Forshaw

• Overview of theoretical calculation
  uncertainties forpp -gt pXp
• Predictions for expected rates in a variety of
  new physicsscenarios Standard Model Higgs, MSSM
  in intense couplingregime MSSM with CP
  violation in Higgs sector stablegluino
  production.
• Stressed importance of Tevatron data to test the
  theory

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Szczurek
Predictions using a non-perturbative variant
inspiredby the Durham calculation (QCD) in
conjunction withphoton-photon fusion
(QED). Difficulties when comparing to the WA102
data for eta prime. Predictions for Tevatron.
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Dipoles, Saturation Unitarization
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Shaw Further success of the dipole model
Universal dipole cross-section
Strategy Extract dipole cross-section from F2
data then use it to predicta very wide range of
other observables measured in photo/electro-produc
tion. Remarkable success F2charm, DVCS, vector
meson production (light heavy) and DDIS are
all described well. No evidence for breakdown of
universality. Saturation models do particularly
well.
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Normalization uncertainty due to use of
experimental value of b-slope. Model of qqg
component gives rise to some uncertainty in
theory at low beta lt 0.4.
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Hatta New developments in the QCD of saturation

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The amplitude for scattering a dipole of size r
off some target evolves in Y as a travelling
wave..this is the wisdom of the BK equation.
DDIS is then dominated by dipoles of size
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But important contributions are missing
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Including pomeron loops the picture changes
dramatically.
Observed amplitude is given by an average
Saturation physics enters at higher Q2 due to
upward fluctuations in thesaturation scale.and
DDIS becomes a hard processes for
sufficientlylarge Y.
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Maor Presented a multi-channel eikonal model for
the unitarization of general scattering
amplitudes.
Selyugin Compared U-matrix and eikonal models
ofunitarization.
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Goncalves DDIS in eA collisions in the dipole
model
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Schaefer Non-linear effects in collisions of a
smallprobe on a nuclear target.
Generalization of Glauber-Gribov approach to
account morecompletely for colour dynamics.
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Gay-Ducati Dilepton production in pA collisions
Dileptons at forward rapidities a probeof
saturation (suppression of Cronin peak seenin
charged hadron pt-spectrum)
Dileptons at backward rapidities
providesinformation on large-x nuclear effects
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DIS Structure Functions
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Corcella reminded us of the need to take care of
softgluon effects at large x in inclusive DIS.
Toy modelto ascertain the likely impact.
Illarionov QCD fits to F2 can be pushed to lower
Q2by treating strong coupling in the IR.
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Zoller dipole model in CC DIS
Novel probe of dipole cross-section left and
right handed Wssensitive to very different
dipole sizes (coupling to c-sbar). Expect much
more nuclear shadowing for left-handed
positivelycharged W bosons (dipole sizes
1/(mass of strange quark).
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Greco A prediction for the spin structure
function at small x and new infra-red evolution
equations.
Total resummation of the double- and single-
logarithmic contributions
New anomalous dimensions and coefficient
functions.
New scaling
At x? 0, asymptotics of g1 is power-like in x and
Q2
We predict that g1 at small Q2 is almost
independent of x, even at xltlt 1. Instead, it
depends on 2pq only. At a certain relation
between the initial quark and gluon densities, g1
can be pretty close to zero in the range of 2pq
investigated now experimentally by COMPASS.
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Prokudin Single hadron production in DIS. The
low pt region (lt 1 GeV) and the high pt region
canbe simultaneously described on including
intrinsic kt and higher order hard QCD
radiation. Predictions for COMPASS and JLAB for
azimuthal dependence.
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A very big thank you to the workshop organizers!