Black Hole Production N. Okada T. Matsuo (Taiwan Normal) T. Matsuo JHEP 0612 (2006) Alig (Bonn) C. Alig Drees and C. M. Drees M. PRD 66 [ph/0111298] N. Okada (KEK) and also Black Hole Production PRD 67 [th/0212108]; 71 (2005); 73 (2006) S. C. Park (Seoul National) S. C. Park D. Ida (Gakushuin) D. Ida based on work with Kin-ya Oda (Osaka) Kin-ya Oda Collider at Collider at in preparation
Outline 1. Planck scale, as low as TeV 2. BH production, inevitably 3. BH decay through Hawking radiation 4. Precise determination of BH event - Hints for quantum gravity 5. Summary & Outlook
Planck scale • Highest energy: • Lowest energy: h c G ~10 µ g ~10 19 GeV ~10 -35 m M P = – Natural unit: hbar = c = 1 – Gravity neglected for E << M P – Quantum corrections neglected for E >> M P
Particle physics’ paradigm for decades: If there are 1. At some high UV scale M , Effective field theory a renormalizable QFT. the theory NECESSARILY looks like • cluster decomposition principle, • quantum mechanics, • Lorentz symmetry, 2. At low IR scale << M, including non-renormalizable ones. allowed by your symmetry, write down ALL interactions � � 6 � 8 � 1 2 � ( � � ) 2 � M 2 � 2 � � 4 � 4 � � 6 ˙ d 4 x � M 4 + L S ~ � M 2 � � 8 � � 2 � � – – – – – –
Hierarchy problem • A “problem” within the EFT paradigm: • Gravity is not renormalizable. • So we know QFT breaks down at ~ M P . • Higgs mass: m h ~ 100 GeV ~ 10 -17 M P ! • Very much smaller than cut-off scale. • Worse, – The Einstein-Hilbert action is not. – Graviton loop cut-off by M P – m h unprotected from quantum corrections. – Must fine-tune between tree and radiative.
New paradigm: TeV gravity m h << M P • Hierarchy problem: How keep m h small? O (10 -2 ) fine-tuning (little hierarchy). • Why not putting M P small instead? • But how? – Most popular solution: SUSY – But, current experimental bound requires – “Problem” disappears! – M P ~ TeV scale gravity!
Lowered Planck scale • Setup: n extra dimensions L • Newton’s law is modified in D =4+ n dims. • M D can be small for large L !! – compactified with length L , say, y ~ y + L . � m 1 m 2 G D ( r << L ) � m 1 m 2 r 2 + n F ( r ) = G 4 � � m 1 m 2 r 2 � G D ( r >> L ) � L n r 2 � 2 � n For r >> L , G 4 ~ G D � 2 ~ M D L n , i.e., M 4 . L n L n 1/(2 + n ) 1 � � 2 � g ( D ) R ( D ) ~ M D ~ M 4 d D x d 4 x � g (4) R (4) � � S EH = � � L n 16 � G D 16 � G 4 � �
Planck scale can be • How can one keep SM unchanged? ’98 Dvali ’ , Dvali Dimopoulos, Dimopoulos , Arkani-Hamed, Arkani-Hamed 98 as low as TeV! • But we know Coulomb’s law is, • No bound at all! • Gravitational experiment does NOT excl’d!! • Observationally excluded. • How large should L be to have M D ~TeV? – For n =1, L ~ solar system size. – For n =2, L ~ sub mm. – For n >2, L ~ μm is sufficient. – or more properly QED (or SM) is, – perfect up to lengths > am ~ TeV -1 .
Large extra dimension Arkani-Hamed ’98 Dvali ’ , Dvali Dimopoulos, Dimopoulos , Arkani-Hamed, in string theory scenario • Naturally implemented by D-branes L D =4+ n dimensional bulk. That is, • Confine SM on 3-brane (3+1 subspace). 98 – We are living on 3-brane. – SM confined on 3-brane. – Graviton propagate in
Alternative: Warped • Extra dimension is • At IR brane, exponentially with y . • Energy scale scales warping on AdS 5 . compactified with UV cut-off is TeV. comp’n from D=5 99 ’99 Randall-Sundrum ’ Randall-Sundrum ds 2 = e � ky ( � dt 2 + d r 2 ) + dy 2 x
Outline 1. Planck scale, as low as TeV 2. BH production, inevitably 3. BH decay through Hawking radiation 4. Precise determination of BH event - Hints for quantum gravity 5. Summary & Outlook
Black hole gravitational background. • Event horizon at r S = ( G D M ) 1/(1+ n ) . • Schwarzshild metric in D=4+n: • Hawking radiation: � ds 2 = � 1 � G D M � 1 dt 2 + dr 2 + r 2 d � 2 � � r 1 + n � � 1 � G D M � � � � r 1 + n � � – Quantum treatment of SM fields on classical
Geometrical cross section BH forms whenever b ’t Hooft ’ ’87 87 ‘ ‘BH forms whenever b < : Schwarzschild radius of the BH. < R R S S ’ ’ Cross section rises with energy! Cross section rises with energy! ’ t Hooft S : Schwarzschild radius of the BH. R parton parton b R S 1 � � R S � 1 M BH n + 1 � � M P M P � � ˆ M BH = s ( M P ~ TeV) 2 2 � ˆ n + 1 � prod = � R S s (for R S << L )
• Growing cross section. < Eerdley, Giddings 02 impact parameter. PROVEN with finite • Classical BH production, . max . b max • BH production dominates over all other b b < when b when Closed trapped surface forms Closed trapped surface forms leads to BH production TeV gravity inevitably • “The end of short distance physics” interactions above TeV. Yoshino et al. 02, 05 b b t z
Correspondence principle a deviation as precisely as possible!! Crucial to predict BH behavior Crucial to predict BH behavior from asymptotic behavior (in BH picture). from asymptotic behavior (in BH picture). deviation a , observed as Truly QG effects, observed as Truly QG effects as precisely as possible!! Horowitz , Polchinski ’96, ’97 S , T ( σ ) Also: Also: BH picture String picture Correspondence in Correspondence in •hard scattering hard scattering • suppression suppression K . O ., ., Okada Okada ’ ’02 02 K . O ., ., Okada Okada •rotating SB / BH rotating SB / BH • g s 2 M corr. point production production α ’ -1/2 K . O ., K . O ., ., Matsuo ., Matsuo Matsuo ’ Matsuo ’08 08 There is no complete Classical gravity Quantum gravity Classical gravity Quantum gravity description Low Low enegy/mass enegy/mass (easy) (easy) Perturbative Perturbative string picture string picture Non- Non- High energy/mass energy/mass Intermediate scale High Intermediate scale perturbative perturbative black hole picture picture Final theory black hole Final theory
Outline 1. Planck scale, as low as TeV 2. BH production, inevitably 3. BH decay through Hawking radiation 4. Precise determination of BH event - Hints for quantum gravity 5. Summary & Outlook
BH life in detector Spin Down Phase A few quanta would be emitted. Truly QG, highly unpredictable Planck Phase 4. BH loses its mass. Angular momentum is small. Schwarzschild Phase 3. . BH loses its mass and angular momentum. 2. 1. BH loses its “hair”. Dynamical production phase Balding Phase (negligible?) 1. Balding Phase • • 2. Spin Down Phase • 3. Schwarzschild Phase • • ? 4. Planck Phase • • Temperature gets higher and higher.
What follows from BH Hawking radiation ; … Landsberg; , Landsberg Dimopoulos, Dimopoulos Giddings, Thomas; Giddings, Thomas; Fig in higher dim 3-brane … production • Typically at LHC h : q : l : v = 4 : 72 : 18 : 24 • Decay – Radiates mainly on brane – decay proportional to #(dof) – Produced every second – M ~ 1-10 TeV – T > 0.1 TeV – Tens of multiple emissions – Life time ~ 10 -27 sec
Typical BH event at LHC A clean signal per second! A clean signal per second! from Kobayashi DPF/JPS 06 in Schwarzschild approximation in Schwarzschild approximation Simulation with M BH ~ 8 TeV in ATLAS … and in CMS
Outline 1. Planck scale, as low as TeV 2. BH production, inevitably 3. BH decay through Hawking radiation 4. Precise determination of BH event - Hints for quantum gravity 5. Summary & Outlook
What we found • BH is produced with large Equatorial plane beam axis beam axis • (Black ring might form) axis. “polar emissision” axis perpendicular to beam along the angular momentum contributes a lot. • Spin down phase Hawking radiation equations essential for field • Obtained brane fi angular momentum. Equatorial plane Ida , KO , Park ( Fig now in 3 dim ) – Gauge bosons are emitted
BH is produced with large s angular momentum d d σ σ/ / dJ dJ ~ ~ J J / / s for angular momentum!! for J J < < s s (2+ (2+ n n )/2(1+ )/2(1+ n n ) ) (in Planck unit) angular momentum!! (in Planck unit) Cross section increases with •Increased from r S -disc Cross section increases with •becomes larger for higher D Fits numerical results qualitatively: Ida , KO , Park 2 2 � = � b max = (1.1~ 1.9) � r S parton M /2 b M /2 parton angular momentum momentum momentum angular momentum J = bM /2 Yoshino et . al . � dJ = 8 � J / M 2 ( J < J max ) d � � db � 0 ( J > J max ) � ( J max = b max M /2) d � = 2 � bdb
Hawking radiation • Difference between two vacua at • Vacumm state for NH • Graybody factor • The larger, the cooler: T ~ 1/ r S ~ M -1/(1+ n ) • Precise determination of Greybody factor is important. – Near horizon (NH): r ~ r h – Far field (FF): r → ∞ – = many particle state for observer at FF – gives spectrum of emitted particles
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