14 April, 2009C. Dallapiccola, MIT Seminar Mini Black Holes at the LHC as a Signature of Extra Dimensions Carlo Dallapiccola University of Massachusetts,

14 April, 2009 C. Dallapiccola, MIT Seminar

Mini Black Holes at the LHC as a Signature of Extra Dimensions

Mini Black Holes at the LHC as a Signature of Extra Dimensions

Carlo DallapiccolaUniversity of Massachusetts,

Amherst


OutlineOutline

• Introduction - TeV scale gravity and black holes Motivation Theoretical background

• Black Hole signature

• Analysis at LHC - ATLAS Event selection Observation and Limits


Why the interest in gravitational interactions in high energy physics?

Why the interest in gravitational interactions in high energy physics?


Motivation I: Hierarchy ProblemMotivation I: Hierarchy Problem

• Conventional paradigm: two very disparate fundamental scales in physics

Electroweak Scale (EEW) ≈ 1000 GeV Gravitational Scale ( ) = 1.21019 GeV

16 orders of magnitude difference!

• Striking hierarchy problem that must be some day be addressed -- what is stabilizing this large difference in fundamental scales?

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MPl = hc GN


Motivation II: EmpiricalMotivation II: Empirical

• Electroweak interactions have already been probed at length scales 1/EEW we know it’s truly a fundamental scale.

• Gravity has not remotely been probed at length scales 1/MPl = 10-33 cm 31 orders of magnitude smaller than scales at which gravity has been tested (0.01 cm).

• Presumptuous to assume extrapolation of Newton’s Law over these 31 orders of magnitude?


A Proposal: TeV Scale GravityA Proposal: TeV Scale Gravity

• Perhaps EEW is the only fundamental scale in physics

Fundamental scale even for gravity: MPl = EEW = 1 TeV At this energy scale, gravitational interactions comparable to weak interactions strong gravity

Radiative stability of electroweak scale is resolved without SUSY, etc. ultraviolet cut-off for the theory is at 1 TeV, where quantum gravity is the new physics

• But then how do we explain where observed Planck Scale comes from (ie. Why is gravity so weak at large distance scales = low energies)? = effective scale, not in fundamental laws


Theoretical Framework Theoretical Framework

Geometry of extra spatial dimensions is responsible for this apparent hierarchy

• Observed 3-space = 3-brane on which SM charges and fields are confined/localized.

• Embedded in a D-dimensional bulk = 3+n+1 spacetime dimensions

• Only graviton propagates in the extra dimensions

String theory branes on which some fields (open strings) are confined and others (closed strings) are not prefers n = 7

• Observed 3-space = 3-brane on which SM charges and fields are confined/localized.

• Embedded in a D-dimensional bulk = 3+n+1 spacetime dimensions

• Only graviton propagates in the extra dimensions

String theory branes on which some fields (open strings) are confined and others (closed strings) are not prefers n = 7


Theoretical Framework Theoretical Framework

Two popular scenarios:

• Arkani-Hamed, Dimopoulos, Dvali (ADD)*

Large volume of compact (flat) extra dimensions generates the hierarchy gravitational field lines spread through bulk.

• Randall, Sundrum (RS)†

Strong curvature (warping) of small AdS single extra dimension generates the hierarchy gravity localized on a second brane bounding the extra dimension.

* Phys. Lett. B 429, 263 (1998)† Phys. Rev. Lett. 83, 3370 (1999)

Focus on this at ATLAS


Compact Extra Dimensions (ADD)Compact Extra Dimensions (ADD)

Matter (SM fields) are localized on a 4-d submanifold (SM brane) of a higher dimensional spacetime (bulk)

Gravitational field not localized propagates in the bulk

The n extra spatial dimensions are compactified at submillimeter length scales R explains why not observed yet

Newton’s Law ( ) becomes:

Looks just like usual (tested) Newton’s Law, with an effective Planck Scale:

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V r( ) =−m1m2

MDn +2

⋅1

rn +1r << R( )

V r( ) =−m1m2

MDn +2Rn

⋅1

rr >> R( )

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V r( ) =−m1m2

MDn +2

⋅1

rn +1r << R( )

V r( ) =−m1m2

MDn +2Rn

⋅1

rr >> R( )

€

MPl2 = MD

n +2Rn€

MD =1 TeV€

V = −m1m2 MPl2 r


Compact Extra Dimensions: SignaturesCompact Extra Dimensions: Signatures

Gravity “strong” at TeV (MD) scale

• Deviations from Newton’s Law at short distance (torsion-balance “Cavendish” expts.)

• Direct or virtual emission of gravitons by SM particles in accelerator experiments

• Enhanced production of gravitons in early universe and in certain astrophysical processes

• Large cross section for black hole production at TeV collision energies

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MPl2 = MD

n +2Rn


Deviations from Newton’s LawDeviations from Newton’s Law

• Direct tests of deviations from Newton’s Law (torsion-balance “Cavendish” expts.)

n = 1 already ruled out (R = solar system scale!)

n = 2 still viable (R ≈ 10m - 1mm) R < 30m, MD > 4 TeV

n > 2 unconstrained Ex.: MD > 4 GeV for n = 3


Astrophysical/Cosmological SignaturesAstrophysical/Cosmological Signatures

• Gravitons compete with other processes in carrying away energy in astrophysical phenomena

• Gravitons decay slowly (~109 yrs. or more) preferentially 2-photon state Gravisstrahlung accelerates supernovae cooling Photons from decays of gravitons produced from supernovae contributes to diffuse cosmic gamma ray background

“Halo” of trapped gravitons around neutron stars source of gamma rays long after supernova

Contribution of gravitons produced early in universe to critical density

Stringent constraints (many assumptions):n > 3 , MD > ~5 TeV


Accelerator Signatures: GravitonsAccelerator Signatures: Gravitons

• Graviton momentum in the bulk = Kaluza-Klein (KK) tower of graviton states ~continuum of states due to large size of extra dimensions

• Direct graviton production: Photon + missing E at LEP Photon + missing Et at Tevatron (LHC) Jet + missing Et at Tevatron (LHC)

• Virtual graviton exchange enhancing SM processes Ex.: Sensitive to unknown coupling and ultra-violet cutoff

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e+e− qq → γG

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qg → qG

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e+e− → e+e−

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qq → γγ l +l −

Reliable constraints (few assumptions):n > 1 , MD > ~1-2 TeV


Accelerator Signatures: Black HolesAccelerator Signatures: Black Holes

• At CM energies above Planck scale MD black holes can be produced in particle collisions particles passing within distance smaller than event horizon

• Naively, cross section for partons a and b to form a black hole is “geometric”:

RS is the horizon size, or Schwarzschild radius Depends on which fraction of available parton energy goes into forming the black hole (trapped behind horizon).

Convolute with parton distribution functions to get

• Range of BH masses depends on eff. impact param.

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σ ab →BH ≈ πRS2

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ˆ s

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σ pp →BH


Black Holes at the LHCBlack Holes at the LHC

• At LHC (ECM = 14 TeV), cross section may be quite large

• Assume some min. BH mass, below which unknown quantum gravity effects are important and classical BH production is lost

• Use MD = 1 TeV as reference point

• Perspective: Zl+l- + jets = 26 pb

n Min. MBH (TeV) σ (pb)

2 5 40.7

2 8 0.34

4 5 24.3

7 5 22.3


Black Hole Search at ATLASBlack Hole Search at ATLAS

• LHC and the ATLAS experiment• ATLAS Black Hole event simulation• Search strategy and predicted discovery thresholds


The Large Hadron ColliderThe Large Hadron Collider

Lake Geneva

14 TeV

CMSATLAS

CERN Main Site

• Proton-proton collider circumference = 27 km

• Energy = 7 TeV / beam√s = 14 TeV

• Stored energy / beam = 350 MJ (!)

• Bunch spacing = 25 ns 40 MHz crossing rate

• Design luminosity= 1034 cm-2 s-1

• 100 fb-1 / year

• Number of interactionsper crossing ~23


The ATLAS DetectorThe ATLAS Detector

Inner Tracker

EM Calorimeter

Hadronic Calorimeter

Muon Detectors

Diameter 25 mBarrel toroid length 26 mEnd-cap end-wall chamber span 46 mOverall weight 7000 Tons


Black Hole ProductionBlack Hole Production

• Collision: gravitational shock waves of ultrarelativistic particles collide complex horizon forms

• Balding: collapse to a more regular “Kerr-Newman” stationary solution asymmetries and moments (hair) shed by emitting bulk gravitons (energy lost)

• Spin down: angular momentum lost via emission of high-spin state particles

• Hawking evaporation: thermal grey-body radiation High temperature: many high pT particles

democratic: rate of SM particle emission according to degrees of freedom no couplings

Isotropic: no preferred direction n dependence: higher T for higher n

Mini black hole


BH Evaporation PropertiesBH Evaporation PropertiesParticle multiplicities and missing ET ( and G) for BH events

Particle pT and

LARGE

n = 7


Black Hole BackgroundsBlack Hole Backgrounds

• Primary bkgds. are states with high multiplicity and high pT jets, such as ttbar

• Requiring a very high pT charged lepton can greatly reduce bkgd.


BH - Bkgd CharacteristicsBH - Bkgd Characteristics

BHs

Bkgd


Black Hole Event SelectionBlack Hole Event Selection

• Single jet trigger with 400 GeV threshold: > 99% eff.

• Uniquely identify objects in the event as muon, electron, photon or hadronic jet

• Select events with large scalar sum pT

• Further require at least one lepton with pT > 50 GeV (QCD dijet reduced by additional 103)

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pT∑ > 2.5 TeV


Black Hole SelectionBlack Hole Selection

Missing ET also characteristic (larger than, say, SUSY)

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pT∑ > 2.5 TeV


BH Signal DeterminationBH Signal Determination

Reconstruct BH Mass: Discovery:

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S B > 5

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S >10

fb-1


Classical BHs: ConclusionClassical BHs: Conclusion

• ATLAS capable of discovering BHs up to kinematic limit of LHC

• 5σ discovery: few pb-1 data if Mthresh = 5 TeV

few fb-1 data if Mthresh = 8-10 TeV• Could be accompanied by bulk graviton signals of

jet/photon + missing energy• Exciting prospect of resolving difficult hierarchy

problem and perhaps even probing quantum gravity!• Determining fundamental params. (MD and n) difficult

But…Relies on:• Large predicted cross-section (many caveats)

• Extrapolations of QCD dijet backgrounds at high pT from TeV scale to 14 TeV scale (could be off by orders of magnitude)


Classical BHs: Recent StudiesClassical BHs: Recent Studies

• Better simulation of mass lost during balding phase: as much as 30% of mass could be lost lowers cross section by factor of 5-10.

• Better simulation of effects of BH with spin: effectively higher temp. BH fewer, but higher pT emissions (more jet-like). Also, vector emission enhanced by factor 2-3, at expense of fermions fewer leptons produced.

Will increase amount of integrated luminosity needed for discovery and degrade S/B, but will not significantly diminish ability to observe classical BHs at the LHC


Non-Classical RegimeNon-Classical Regime

• Recently argued* that classical BHs at the LHC are unlikely: only valid for MBH >> MD (Mmin introduced) Quantum gravity effects important (and largely unknown) for MBH near the Planck mass

Reasonable criteria is that Compton wavelength of colliding partons are within their Schwarzschild radius or that entropy is sufficiently large: Mmin = 3-4 * MD

• Steeply falling parton distribution functions make it exceedingly difficult to satisify this relation at LHC energies

• Instead, we may see mostly phenomena at quantum gravity regime eg. string balls* P. Meade and L. Randall, J. High Energy Physics 5, 003 (2008)


String BallsString Balls

• String theory is one candidate for partial description of quantum gravity Highly-excited string states (string balls) could be produced at the LHC decay thermally (but more jet-like than BHs)

New mass scale introduced string scale (MS < MD) Thus, string ball cross-section higher than that of BHs

Select using cuts on |pT| and jet pT ratios (at least 4 jets)


String Balls: Cross Section LimitsString Balls: Cross Section Limits

• Studies: set limits on string-ball cross section for given mass threshold and 100 pb-1 int. luminosity.

At 95% C.L. MS > 4.8 TeV

MS > 1.6 TeV

MD > 2.4 TeV


ConclusionConclusion

• The “big” hierarchy problem, addressing the gigantic disparity of the electroweak and gravitational scales, is one of the biggest in fundamental physics

• Extra dimensional theories provide a framework in which the hierarchy problem is replaced by the more tractable problem of how to naturally stabilize the large sizes of the extra dimensions

• The LHC is well-positioned to observe or set stringent limits on the most striking phenomena: mini black hole production, string balls, etc.

Documents

14 April, 2009C. Dallapiccola, MIT Seminar Mini Black Holes at the LHC as a Signature of Extra Dimensions Carlo Dallapiccola University of Massachusetts,