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Search for the Graviton at the LHCPowerPoint Presentation

Search for the Graviton at the LHC

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### Search for the Graviton at the LHC

### Search for the Graviton - by Looking in the Opposite Direction

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
- 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

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?

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:
&

where

- 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
- Radius related to gauge coupling

Exact only for N = 4 supersymmetric QCD

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

BFKL with Running Coupling

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

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 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 function
= 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’ diffraction
- Also vector-meson production at high energies as Q2 increases
= exclusive ‘hard’ diffraction

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 - 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?

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:

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

BFKL intercept increases 2 (?) as k0 decreases

BFKL intercept decreases as k0 increases (J/ ?)

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

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 (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!

NUHM

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

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

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