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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, Manchester, Dec. 9th, 2007. JE + H.Kowalski + D.Ross, in preparation. Howzat again?. In forward physics?. String theory originated from models of high-energy scattering

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Search for the Graviton at the LHC

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  1. 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

  2. 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

  3. Clue from Low-x Physics @ HERA? • Increasing rate of growth of *p total cross section at high energy as Q2 increases = inclusive hard diffraction

  4. 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?

  5. BFKL: Diffusion in k Space • Diffusion in  = ln(k2/QCD2) vs rapidity • Eigenvalue equation • equivalent to diffusion

  6. BFKL Equation • Diagrammatically: • Algebraically: • E’functions & e’values: & where • Solution

  7. 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

  8. 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:

  9. Pomeron in String Theory • Modern formulation: vertices attached to closed string world sheet • In flat space: • Note smaller Regge slope

  10. 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

  11. Pomeron in AdS/CFT - II • Laplacian in AdS: • Pomeron propagator in AdS: • Scattering amplitude (R ~ gYM2): Brower + Polchinski + Strassler + Tan

  12. String Theory  BFKL • Comparison of string and BFKL results: • Comparison of intercepts: But BFKL singularity is a cut at fixed coupling

  13. The ‘Grand Unified’ Pomeron BFKL at fixed weak coupling  bare graviton at fixed strong coupling

  14. BFKL vs AdS/CFT AdS/CFT LO BFKL NLO BFKL Important corrections to BFKL at NLO

  15. BFKL with Running Coupling • J-plane cut replaced by a discrete set of poles: • With calculable profiles:

  16. With Running QCD Coupling • Running coupling: • Eigenfunction with eigenvalue : • No real solution for  > c: • Profile: Assume phase at 0 fixed by non-perturbative dynamics Discrete eigenvalues  Regge poles, not cuts

  17. Leading-Order BFKL k2 Profiles  = 0.41  = 0.22  = 0.15  = 0.12 JE + H.Kowalski + D.Ross, in preparation

  18. 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

  19. Back to Low-x Physics @ HERA:Deep-inelastic structure function • At low x and high Q2, steep rise in structure function = distribution of partons, integrated over kT

  20. 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

  21. Low-x Physics @ 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

  22. 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

  23. Low-x Physics @ 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

  24. Absorption & Saturation? Expected at low x and high Q2, as number of partons grows, and they overlap

  25. 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:

  26. How Important is Saturation? Apparently little saturation at Qs2 = 4 GeV2 Estimate of Qs H.Kowalski

  27. 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

  28. 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

  29. 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

  30. … and now for something completely different

  31. Most of (mA, tan ) Planes NOT WMAP-Compatible J.E., Hahn, Henemeyer, Olive + Weiglein

  32. 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

  33. 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 @ Tevatron/LHC/ILC

  34. WMAP Surfaces @ Tevatron, LHC, ILC J.E., Hahn, Heinemeyer, Olive + Weiglein: arXiv:0709.0098

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