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Search for the Graviton at the LHC


									    Search for the Graviton at the LHC

                                           From Donnachie-Landshoff
                                                towards J = 2?

                                                       John Ellis
                                                    FP420 Meeting,
JE + H.Kowalski + D.Ross, in preparation        Manchester, Dec. 9th, 2007
                           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 @ LHC: FP420?
JE + H.Kowalski + D.Ross, in preparation
 Clue from Low-x Physics @ HERA?
• Increasing rate of growth of
  *p total cross section at
  high energy as Q2 increases
  = inclusive hard diffraction
• Reminder of the BFKL Pomeron
• Genesis of string theory in high-energy hadron
   – 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?
    BFKL: Diffusion in k Space
• Diffusion in  = ln(k2/QCD2) vs rapidity

•                    Eigenvalue equation

•                    equivalent to diffusion
              BFKL Equation
• Diagrammatically:
• Algebraically:

• E’functions & e’values:
• Solution
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
         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:
     Pomeron in String Theory
• Modern formulation: vertices attached to
  closed string world sheet
• In flat space:

• Note smaller Regge slope
                 Pomeron in AdS/CFT - I
       • Strongly-coupled gauge theory  weakly-
         coupled string theory in curved space

                                        Exact only for N = 4
                                        supersymmetric QCD

       • Radius related to gauge coupling
Brower + Polchinski + Strassler + Tan
                 Pomeron in AdS/CFT - II
       • Laplacian in AdS:

       • Pomeron propagator in AdS:

       • Scattering amplitude (R ~ gYM2):

Brower + Polchinski + Strassler + Tan
      String Theory  BFKL
• Comparison of string and BFKL results:

• Comparison of intercepts:

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

   BFKL at fixed weak coupling 
 bare graviton at fixed strong coupling
     BFKL vs AdS/CFT

                     LO BFKL


                       NLO BFKL

Important corrections to BFKL at NLO
  BFKL with Running Coupling
• J-plane cut replaced by a discrete set of

• With calculable profiles:
       With Running QCD Coupling
 •   Running coupling:
 •   Eigenfunction with eigenvalue :
 •   No real solution for  > c:
 •   Profile:

Assume phase at 0 fixed by        Discrete eigenvalues 
non-perturbative dynamics           Regge poles, not cuts
       Leading-Order BFKL                  k2   Profiles
                                 = 0.41          = 0.22

                                 = 0.15          = 0.12

JE + H.Kowalski + D.Ross, in preparation
                   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
   Back to Low-x Physics @ HERA:
                 Deep-inelastic structure function

• At low x and high Q2,
  steep rise in structure
  = distribution of
  partons, integrated
  over kT
       Low-x Physics @ HERA - II
                   *p total cross section

• Increasing rate of growth of
  *p total cross section at
  high energies as Q2 increases
  = inclusive ‘hard’ diffraction
       Low-x Physics @ HERA - III

• Increasing rate of growth
  of total *p cross section
  = inclusive ‘hard’
• Also vector-meson
  production at high
  energies as Q2 increases
  = exclusive ‘hard’
Extracting Proton Vertex using Dipole Model

• Equivalent to LO QCD
  for small dipoles
• Can use vector meson
  production to extract proton
                                 Kowalski + Moltyka + Watt
Low-x Physics @ HERA - IV
             Vector-meson production
• Proton vertex determined, Vector-meson vertex
• Comparisons with rates of growth of *p  Vp, p
  cross sections at high energies as Q2 increases
  = exclusive ‘hard’ diffraction

                                       Kowalski + Moltyka + Watt
    Absorption & Saturation?
Expected at low x and high Q2, as number of
      partons grows, and they overlap
     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:
         How Important is Saturation?
                         Apparently little
  Estimate of Qs
                           saturation at
                          Qs2 = 4 GeV2

      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
             Search for the Graviton - by
            Looking in the Opposite Direction

                       BFKL increases
               BFKL interceptintercept decreases
                 2 (?) as kk0 increases (J/ ?)
                         as 0 decreases

JE + H.Kowalski + D.Ross, in preparation
          Possible LHC measurements?
      • Consider diffractive production of a ‘small’
      • 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
… and now for something
  completely different
Most of (mA, tan ) Planes
NOT WMAP-Compatible

                 J.E., Hahn, Henemeyer, Olive + Weiglein
      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!
 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
• Analyze detectability @ Tevatron/LHC/ILC
WMAP Surfaces @ Tevatron, LHC, ILC

               J.E., Hahn, Heinemeyer, Olive + Weiglein: arXiv:0709.0098

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