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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. 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 l.jpg

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 l.jpg
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 l.jpg
Clue from Low-x Physics @ HERA?

  • Increasing rate of growth of *p total cross section at high energy as Q2 increases

    = inclusive hard diffraction

Outline l.jpg

  • 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?

Bfkl diffusion in k space l.jpg
BFKL: Diffusion in k Space

  • Diffusion in  = ln(k2/QCD2) vs rapidity

  • Eigenvalue equation

  • equivalent to diffusion

Bfkl equation l.jpg
BFKL Equation

  • Diagrammatically:

  • Algebraically:

  • E’functions & e’values:



  • Solution

Fast rewind of bfkl l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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

Pomeron in ads cft ii l.jpg
Pomeron in AdS/CFT - II

  • Laplacian in AdS:

  • Pomeron propagator in AdS:

  • Scattering amplitude (R ~ gYM2):

Brower + Polchinski + Strassler + Tan

String theory bfkl l.jpg
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 l.jpg
The ‘Grand Unified’ Pomeron

BFKL at fixed weak coupling 

bare graviton at fixed strong coupling

Bfkl vs ads cft l.jpg





Important corrections to BFKL at NLO

Bfkl with running coupling l.jpg
BFKL with Running Coupling

  • J-plane cut replaced by a discrete set of poles:

  • With calculable profiles:

With running qcd coupling l.jpg
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

Leading order bfkl k 2 profiles l.jpg
Leading-Order BFKL k2 Profiles

 = 0.41

 = 0.22

 = 0.15

 = 0.12

JE + H.Kowalski + D.Ross, in preparation

Nlo bfkl k 2 profiles l.jpg
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 l.jpg
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

Low x physics @ hera ii p total cross section l.jpg
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 l.jpg
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

Extracting proton vertex using dipole model l.jpg
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

Low x physics @ hera iv vector meson production l.jpg
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

Absorption saturation l.jpg
Absorption & Saturation?

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

How important is saturation l.jpg
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 saturation26 l.jpg
How Important is Saturation?

Apparently little saturation at

Qs2 = 4 GeV2

Estimate of Qs


Towards bfkl fit to low x data l.jpg
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 l.jpg

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

Possible lhc measurements l.jpg
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

Most of m a tan planes not wmap compatible l.jpg
Most of (mA, tan ) Planes NOT WMAP-Compatible

J.E., Hahn, Henemeyer, Olive + Weiglein

Non universal scalar masses l.jpg
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 m a tan surfaces in nuhm l.jpg
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

Wmap surfaces @ tevatron lhc ilc l.jpg
WMAP Surfaces @ Tevatron, LHC, ILC

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