Search for the Graviton at the LHC

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Search for the Graviton at the LHC
From Donnachie-Landshoff towards J 2?

• John Ellis
• FP420 Meeting,
• Manchester, Dec. 9th, 2007

JE H.Kowalski D.Ross, in preparation
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Howzat again?
In forward physics?

• String theory originated from models of
  high-energy scattering
• Pomeron related to closed string loop
• First state on Pomeron trajectory spin 2
• In string as Theory of Everything, closed
  string ? massless graviton
• AdS/CFT Pomeron ? graviton in D 5
• Intercept 2 - ? at strong coupling
• Related to hard Pomeron seen at HERA?
• Intercept ? 1.4 ???
• Probe with hard diffraction _at_ LHC FP420?

JE H.Kowalski D.Ross, in preparation
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Clue from Low-x Physics _at_ HERA?

• Increasing rate of growth of ?p total cross
  section at high energy as Q2 increases
• inclusive hard diffraction

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Outline

• Reminder of the BFKL Pomeron
• Genesis of string theory in high-energy hadron
  scattering
• AdS/CFT formulation in 5 dimensions
• Relation to BFKL
• BFKL with running coupling
• Reminder of the HERA hard Pomeron
• Saturation effects?
• Prospects for BFKL fit
• Possibilities for FP420?

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BFKL Diffusion in k Space

• Diffusion in ? ln(k2/?QCD2) vs rapidity
• Eigenvalue
  equation
• equivalent to
  diffusion

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BFKL Equation

• Diagrammatically
• Algebraically
• Efunctions evalues
• where
• Solution

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Fast Rewind of BFKL

• Impact factor (vertex) ?I
• experiment (proton)? Calculable (Higgs)?
• BFKL propagator f obeys
• Kernel K for diffusion in s, k
• Solution is cut singularity

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Genesis of String Theory

• Duality between direct-channel resonances and
  Regge behaviour at high energies
• Expressed mathematically (Veneziano)
• Interpreted as quantum theory of open string
• Unitarity requires closed string
• Virasoro amplitude

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Pomeron in String Theory

• Modern formulation vertices attached to closed
  string world sheet
• In flat space
• Note smaller Regge slope

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Pomeron in AdS/CFT - I

• Strongly-coupled gauge theory ? weakly-coupled
  string theory in curved space
• Radius related to gauge coupling

Exact only for N 4 supersymmetric QCD
Brower Polchinski Strassler Tan
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Pomeron in AdS/CFT - II

• Laplacian in AdS
• Pomeron propagator in AdS
• Scattering amplitude (R gYM2)

Brower Polchinski Strassler Tan
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String Theory ? BFKL

• Comparison of string and BFKL results
• Comparison of intercepts

But BFKL singularity is a cut at fixed coupling
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The Grand Unified Pomeron

• BFKL at fixed weak coupling ?
• bare graviton at fixed strong coupling

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BFKL vs AdS/CFT

• LO BFKL

AdS/CFT
NLO BFKL
Important corrections to BFKL at NLO
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BFKL with Running Coupling

• J-plane cut replaced by a discrete set of poles
• With calculable profiles

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With Running QCD Coupling

• Running coupling
• Eigenfunction with eigenvalue ?
• No real solution for ? gt ?c
• Profile

Assume phase at ?0 fixed by non-perturbative
dynamics
Discrete eigenvalues ? Regge poles, not cuts
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Leading-Order BFKL k2 Profiles
? 0.41
? 0.22
? 0.15
? 0.12
JE H.Kowalski D.Ross, in preparation
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NLO BFKL k2 Profiles
? 0.29
? 0.18
? 0.14
BFKL intercepts reduced k2 profiles similar to
LO
JE H.Kowalski D.Ross, in preparation
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Back to Low-x Physics _at_ HERADeep-inelastic
structure function

• At low x and high Q2, steep rise in structure
  function
• distribution of partons, integrated over kT

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Low-x Physics _at_ HERA - II?p total cross section

• Increasing rate of growth of ?p total cross
  section at high energies as Q2 increases
• inclusive hard diffraction

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Low-x Physics _at_ HERA - III

• Increasing rate of growth of total ?p cross
  section inclusive hard diffraction
• Also vector-meson production at high energies as
  Q2 increases
• exclusive hard diffraction

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Extracting Proton Vertex using Dipole Model

• Equivalent to LO QCD
• for small dipoles
• Can use vector meson
• production to extract proton profile

Kowalski Moltyka Watt
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Low-x Physics _at_ HERA - IVVector-meson production

• Proton vertex determined, Vector-meson vertex
  calculable
• Comparisons with rates of growth of ?p ? Vp, ?p
  cross sections at high energies as Q2 increases
• exclusive hard diffraction

Kowalski Moltyka Watt
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Absorption Saturation?

• Expected at low x and high Q2, as number of
  partons grows, and they overlap

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How Important is Saturation?

• Eikonal exponentiation
• Depends on impact parameter, momentum scale
• Define saturation scale Qs by
• Estimate Qs using indicative models for proton
  impact-parameter profile and gluon distribution

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How Important is Saturation?
Apparently little saturation at Qs2 4 GeV2

• Estimate of Qs

H.Kowalski
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Towards BFKL Fit to low-x Data

• Unintegrated low-x gluon distribution extracted
  from ?p cross section using dipole model
• Fit using k2 profiles for leading, subleading
  BFKL wave functions

JE H.Kowalski D.Ross, in preparation
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Search for the Graviton - by Looking in the
Opposite Direction
BFKL intercept increases ? 2 (?) as k0 decreases

• BFKL intercept decreases as k0 increases (J/? ?)

JE H.Kowalski D.Ross, in preparation
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Possible LHC measurements?

• Consider diffractive production of a small
  object
• Single or double diffraction?
• y ln(s/mX2) or y1 y2 ln(s/mX2) ?
• Examples
• pp ? p (jet pair), pp ? p (D ?c)
• pp ? p ?c p, pp ? p H p
• Rising rapidity plateau?

Sexy bread-and-butter for FP420?
JE H.Kowalski D.Ross, in preparation
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and now for something completely different
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Most of (mA, tan ?) Planes NOT WMAP-Compatible
J.E., Hahn, Henemeyer, Olive Weiglein
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Non-Universal Scalar Masses

• Different sfermions with same quantum s?
• e.g., d, s squarks?
• disfavoured by upper limits on
  flavour- changing neutral interactions
• Squarks with different s, squarks and sleptons?
• disfavoured in various GUT models
• e.g., dR eL, dL uL uR eR in SU(5), all
  in SO(10)
• Non-universal susy-breaking masses for Higgses?
• No reason why not!

NUHM
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WMAP-Compatible (mA, tan?) Surfaces in NUHM

• Within CMSSM, generic choices of mA, tan? do not
  have correct relic density
• Use extra NUHM parameters to keep ??h2 within
  WMAP range, e.g.,
• m0 800 GeV, ? 1000 GeV, m1/2 9/8 mA
• m1/2 500, m0 1000, ? 250 to 400 GeV
• Make global fit to electroweak and B observables
• Analyze detectability _at_ Tevatron/LHC/ILC

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WMAP Surfaces _at_ Tevatron, LHC, ILC
J.E., Hahn, Heinemeyer, Olive Weiglein
arXiv0709.0098