CHARYBDIS2: Modelling higher dimensional black hole events Marco - PowerPoint PPT Presentation

Consequences of the extra dimensions So how does gravity look like in ADD? 1 1 � 1 + 2 ne − r � R + . . . F r ≪ R ∼ ( 4 + n ) r 2 + n , F r ≫ R ∼ M 2 + n M 2 + n ( 4 + n ) R n r 2 Predicts deviations from Newtonian gravity as we 1 approach short distances. Contains KK gravitons from the 4D point of view. 2 Gravity is higher dimensional at very short distances . 3 This can be used to put bounds on R as a function of n . ⇒ Translates as a bound on M 4 + n .

Consequences of the extra dimensions So how does gravity look like in ADD? 1 1 � 1 + 2 ne − r � R + . . . F r ≪ R ∼ ( 4 + n ) r 2 + n , F r ≫ R ∼ M 2 + n M 2 + n ( 4 + n ) R n r 2 Predicts deviations from Newtonian gravity as we 1 approach short distances. Contains KK gravitons from the 4D point of view. 2 Gravity is higher dimensional at very short distances . 3 This can be used to put bounds on R as a function of n . ⇒ Translates as a bound on M 4 + n .

Consequences of the extra dimensions So how does gravity look like in ADD? 1 1 � 1 + 2 ne − r � R + . . . F r ≪ R ∼ ( 4 + n ) r 2 + n , F r ≫ R ∼ M 2 + n M 2 + n ( 4 + n ) R n r 2 Predicts deviations from Newtonian gravity as we 1 approach short distances. Contains KK gravitons from the 4D point of view. 2 Gravity is higher dimensional at very short distances . 3 This can be used to put bounds on R as a function of n . ⇒ Translates as a bound on M 4 + n .

Bounds on extra dimensions 4 = R n M 2 + n M 2 R in µ m ( n = 2 ) M 4 + n ∼ 1TeV OK ( 4 + n ) Deviations from r − 2 in � 55 n > 1 torsion-balance KK graviton produc- � 800 n > 2 tion @ colliders KK graviton produc- � 5 . 1 × 10 − 4 n > 3 tion in Supernovae KK gravitons early � 2 . 2 × 10 − 5 n > 3 Universe production

Bounds on extra dimensions 4 = R n M 2 + n M 2 R in µ m ( n = 2 ) M 4 + n ∼ 1TeV OK ( 4 + n ) Deviations from r − 2 in � 55 n > 1 torsion-balance KK graviton produc- � 800 n > 2 tion @ colliders KK graviton produc- � 5 . 1 × 10 − 4 n > 3 tion in Supernovae KK gravitons early � 2 . 2 × 10 − 5 n > 3 Universe production SM on a 4D brane of thickness L � ( 1 TeV ) − 1 ∼ 10 − 13 µ m To avoid bounds from Electroweak precision and fast proton decay. Quarks and leptons may have to be on sub-branes for L � ( 1 TeV ) − 1 . All SM particles propagating on a single brane. Good approximation if process occurs at large scales compared to L .

Outline Introduction 1 The hierarchy problem – Extra dimensions Strong gravity & Black Holes Modelling BH events – CHARYBDIS2 2 The production The decay CHARYBDIS2 & other generators Phenomenology using CHARYBDIS2 3 Classical signatures The effects of rotation Conclusions and Outlook 4

Why BHs? – Strong gravity & the black disk approach At short distances gravity is higher dimensional ⇒ √ α G ∼ E E E → ∼ M 4 M 4 + n 1 TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!

Why BHs? – Strong gravity & the black disk approach At short distances gravity is higher dimensional ⇒ √ α G ∼ E E E → ∼ M 4 M 4 + n 1 TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!

Why BHs? – Strong gravity & the black disk approach At short distances gravity is higher dimensional ⇒ √ α G ∼ E E E → ∼ M 4 M 4 + n 1 TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs! parton 2r S b parton Event horizon size ∆ x ≪ r S ⇒ √ s ≫ M 4 + n impact parameter � √ s 1 C n � n + 1 Hoop conjecture ⇒ σ disk ∼ π r 2 S , r s = M 4 + n M 4 + n S. B. Giddings and S. D. Thomas, hep-ph/0106219 S. Dimopoulos and G. Landsberg, hep-ph/0106295

Why BHs? – Strong gravity & the black disk approach At short distances gravity is higher dimensional ⇒ √ α G ∼ E E E → ∼ M 4 M 4 + n 1 TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs! parton 2r S b parton Event horizon size ∆ x ≪ r S ⇒ √ s ≫ M 4 + n impact parameter � √ s 1 C n � n + 1 Hoop conjecture ⇒ σ disk ∼ π r 2 S , r s = M 4 + n M 4 + n S. B. Giddings and S. D. Thomas, hep-ph/0106219 S. Dimopoulos and G. Landsberg, hep-ph/0106295

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/

Outline Introduction 1 The hierarchy problem – Extra dimensions Strong gravity & Black Holes Modelling BH events – CHARYBDIS2 2 The production The decay CHARYBDIS2 & other generators Phenomenology using CHARYBDIS2 3 Classical signatures The effects of rotation Conclusions and Outlook 4

Modelling production – The ideal solution p µ ✲ ✛ 2 p µ 1 Ideally: Set up spatial metric for two highly boosted particles ,

Modelling production – The ideal solution s 1 ❈ ❖ ❈ p µ ❈ Q 2 ✲ ✛ 2 Q 1 ❈ ✄ p µ ✄ 1 ✄ ✄ ✎ s 2 Ideally: Set up spatial metric for two highly boosted particles , Include the spin and charge ,

Modelling production – The ideal solution s 1 ❈ ❖ ❈ p µ ❈ Q 2 ✲ ✛ 2 Q 1 ❈ ✄ p µ ✄ 1 ✄ ✎ ✄ s 2 Ideally: Set up spatial metric for two highly boosted particles , Include the spin and charge , Evolve this system using Einstein’s equations,

Modelling production – The ideal solution ✻ radiation J Q radiation ✏ P µ ✏ ✏ ✮ Ideally: Set up spatial metric for two highly boosted particles , Include the spin and charge , Evolve this system using Einstein’s equations, Obtain final Black Hole + radiation

Modelling production – The ideal solution ✻ radiation J Q radiation ✏ P µ ✏ ✮ ✏ Ideally: Set up spatial metric for two highly boosted particles , Include the spin and charge , Evolve this system using Einstein’s equations, Obtain final Black Hole + radiation → 4D so far. U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, J. Gonzalez, arXiv:0806.1738 b = 0 M. Shibata, H. Okawa, T. Yamamoto, arXiv:0810.4735 b � = 0 U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hinderer, N. Yunes arXiv:0907.1252 b � = 0 M. Choptuik, F. Pretorius, arXiv:0908.1780 b = 0 (solitons) Zilhao, Witek, Sperhake, Cardoso, Gualtieri, Herdeiro, Nerozzi arXiv:1001.2302 4 + n

Modelling production – The ideal solution ✻ radiation J Q radiation ✏ P µ ✏ ✮ ✏ Ideally: Set up spatial metric for two highly boosted particles , Include the spin and charge , Evolve this system using Einstein’s equations, Obtain final Black Hole + radiation → 4D so far. U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, J. Gonzalez, arXiv:0806.1738 b = 0 M. Shibata, H. Okawa, T. Yamamoto, arXiv:0810.4735 b � = 0 U. Sperhake, V. Cardoso, F. Pretorius, E. Berti, T. Hinderer, N. Yunes arXiv:0907.1252 b � = 0 M. Choptuik, F. Pretorius, arXiv:0908.1780 b = 0 (solitons) Zilhao, Witek, Sperhake, Cardoso, Gualtieri, Herdeiro, Nerozzi arXiv:1001.2302 4 + n

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression.

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression.

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression.

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression. Bounds on M and J lost into gravitational radiation. 2

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression. Bounds on M and J lost into gravitational radiation. 2 b = 0 . 5 r S b = 1 . 0 r S b = 1 . 3 r S D = 6 , b = 0 . 5 D = 6 , b = 1 . 0 D = 6 , b = 1 . 3 1 1 1 0 . 8 0 . 8 0 . 8 J J 0 0 . 6 0 . 6 0 . 6 ζ ζ ζ 0 . 4 0 . 4 0 . 4 0 . 2 0 . 2 0 . 2 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ξ M ξ M M ξ M 0 M 0 M 0

Modelling production – Trapped surface bounds H. Yoshino and V. S. Rychkov hep-th/0503171 Lower bounds on b ( n ) max ⇒ Enhanced cross section F n σ disk 1 � 1 � 1 partons dx � τ � � σ PP → BH = d τ x f i ( x ) f j F n σ disk ( τ s ) x τ m τ i , j ⇒ σ PP → BH = 70 , 160 , 280 pb ⇒ 1 s − 1 @ design at 7 TeV ⇒ 10 − 4 suppression. Bounds on M and J lost into gravitational radiation. 2 b = 0 . 5 r S b = 1 . 0 r S b = 1 . 3 r S D = 6 , b = 0 . 5 D = 6 , b = 1 . 0 D = 6 , b = 1 . 3 1 1 1 0 . 8 0 . 8 0 . 8 J J 0 0 . 6 0 . 6 0 . 6 ζ ζ ζ 0 . 4 0 . 4 0 . 4 0 . 2 0 . 2 0 . 2 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 ξ M ξ M M ξ M 0 M 0 M 0 MJLOST=.TRUE. – Uses bound for each 0 < b < b max .

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/

Outline Introduction 1 The hierarchy problem – Extra dimensions Strong gravity & Black Holes Modelling BH events – CHARYBDIS2 2 The production The decay CHARYBDIS2 & other generators Phenomenology using CHARYBDIS2 3 Classical signatures The effects of rotation Conclusions and Outlook 4

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

The Hawking phase – Particle creation After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). dt 2 + 2 a µ sin 2 θ µ dtd φ − Σ ds 2 = � � ∆ dr 2 − 1 − Σ r n − 1 Σ r n − 1 r 2 + a 2 + a 2 µ sin 2 θ � � sin 2 θ d φ 2 − r 2 cos 2 θ d Ω 2 − Σ d θ 2 − n , Σ r n − 1 1974, Hawking’s quantum instability ⇒ BH decays 10 − 26 s . Gravity couples Universally s = 0 Higgs + W L / Z L 4 s = 1 / 2 Quarks + Leptons 90 s = 1 G + γ + W T / Z T 24 � � − f 4 + L 0 + L 1 � d 4 x � S brane = | g | 2 + L 1 R. Sundrum hep-ph/9805471

Some of the underlying assumptions! The decay can be described through Hawking radiation The time between emission of one particle is large (true for large BH mass) Brane emission is dominant (large number of SM degrees of freedom) Backreaction of the metric between emissions is small (true for large BH mass)

Some of the underlying assumptions! The decay can be described through Hawking radiation The time between emission of one particle is large (true for large BH mass) Brane emission is dominant (large number of SM degrees of freedom) Backreaction of the metric between emissions is small (true for large BH mass)

Some of the underlying assumptions! The decay can be described through Hawking radiation The time between emission of one particle is large (true for large BH mass) Brane emission is dominant (large number of SM degrees of freedom) Backreaction of the metric between emissions is small (true for large BH mass)

Some of the underlying assumptions! The decay can be described through Hawking radiation The time between emission of one particle is large (true for large BH mass) Brane emission is dominant (large number of SM degrees of freedom) Backreaction of the metric between emissions is small (true for large BH mass)

Some of the underlying assumptions! The decay can be described through Hawking radiation The time between emission of one particle is large (true for large BH mass) Brane emission is dominant (large number of SM degrees of freedom) Backreaction of the metric between emissions is small (true for large BH mass)

Hawking radiation – Power spectrum T ( n ) dE h ω k ( ω, a ∗ ) 2 � � � � h S m dtd ω d Ω = j (Ω , ω a ∗ ) � � exp ( ω − m Ω H 2 π � ) ± 1 m , j T H Dependence on a ∗ T H = ( n + 1 )+( n − 1 ) a 2 , Ω H = 1 a ∗ ∗ 4 π ( 1 + a 2 r H 1 + a 2 ∗ ) r H ∗ Spheroidal angular functions Harder spectrum 1 m = j ( m > 0) dominant 2 ⇒ Spin-down Similar for Scalars and Vectors 3 Dolan, Casals, Kanti, Winstanley mathsci.uc.ie/ ∼ sdolan/greybody/ hep-th/0503052, hep-th/0511163, hep-th/0608193 Ida, Oda, Park hep-th/0212108, hep-th/0503052, hep-th/0602188

Hawking radiation – Power spectrum T ( n ) dE h ω k ( ω, a ∗ ) 2 � � � � h S m dtd ω d Ω = j (Ω , ω a ∗ ) � � exp ( ω − m Ω H 2 π � ) ± 1 m , j T H Dependence on a ∗ T H = ( n + 1 )+( n − 1 ) a 2 , Ω H = 1 a ∗ ∗ 4 π ( 1 + a 2 r H 1 + a 2 ∗ ) r H ∗ Spheroidal angular functions Harder spectrum 1 m = j ( m > 0) dominant 2 ⇒ Spin-down Similar for Scalars and Vectors 3 Dolan, Casals, Kanti, Winstanley mathsci.uc.ie/ ∼ sdolan/greybody/ hep-th/0503052, hep-th/0511163, hep-th/0608193 Ida, Oda, Park hep-th/0212108, hep-th/0503052, hep-th/0602188

Hawking radiation – Power spectrum T ( n ) dE h ω k ( ω, a ∗ ) 2 � � � � h S m dtd ω d Ω = j (Ω , ω a ∗ ) � � exp ( ω − m Ω H 2 π � ) ± 1 m , j T H Dependence on a ∗ T H = ( n + 1 )+( n − 1 ) a 2 , Ω H = 1 a ∗ ∗ 4 π ( 1 + a 2 r H 1 + a 2 ∗ ) r H ∗ Spheroidal angular functions Harder spectrum 1 m = j ( m > 0) dominant 2 ⇒ Spin-down Similar for Scalars and Vectors 3 Dolan, Casals, Kanti, Winstanley mathsci.uc.ie/ ∼ sdolan/greybody/ hep-th/0503052, hep-th/0511163, hep-th/0608193 Ida, Oda, Park hep-th/0212108, hep-th/0503052, hep-th/0602188

Hawking radiation – Power spectrum T ( n ) dE h ω k ( ω, a ∗ ) 2 � � � � h S m dtd ω d Ω = j (Ω , ω a ∗ ) � � exp ( ω − m Ω H 2 π � ) ± 1 m , j T H Dependence on a ∗ T H = ( n + 1 )+( n − 1 ) a 2 , Ω H = 1 a ∗ ∗ 4 π ( 1 + a 2 r H 1 + a 2 ∗ ) r H ∗ Spheroidal angular functions Harder spectrum 1 m = j ( m > 0) dominant 2 ⇒ Spin-down Similar for Scalars and Vectors 3 Dolan, Casals, Kanti, Winstanley mathsci.uc.ie/ ∼ sdolan/greybody/ hep-th/0503052, hep-th/0511163, hep-th/0608193 Ida, Oda, Park hep-th/0212108, hep-th/0503052, hep-th/0602188

Hawking radiation – Power spectrum T ( n ) dE h ω k ( ω, a ∗ ) 2 � � � � h S m dtd ω d Ω = j (Ω , ω a ∗ ) � � exp ( ω − m Ω H 2 π � ) ± 1 m , j T H 0 . 04 a ∗ s = 1 / 2 0 . 0 0 . 4 n = 2 0 . 8 Dependence on a ∗ 0 . 03 1 . 0 1 . 2 1 . 4 T H = ( n + 1 )+( n − 1 ) a 2 0 . 02 , Ω H = 1 a ∗ ∗ 4 π ( 1 + a 2 r H 1 + a 2 ∗ ) r H ∗ 0 . 01 Spheroidal angular functions 0 0 1 2 3 4 5 ωr H 0 . 3 a ∗ Harder spectrum n = 6 1 0 . 0 s = 1 / 2 0 . 4 0 . 8 m = j ( m > 0) dominant 2 1 . 0 0 . 2 1 . 2 ⇒ Spin-down 1 . 4 Similar for Scalars and Vectors 3 0 . 1 0 0 1 2 3 4 5 Dolan, Casals, Kanti, Winstanley mathsci.uc.ie/ ∼ sdolan/greybody/ hep-th/0503052, hep-th/0511163, hep-th/0608193 Ida, Oda, Park hep-th/0212108, hep-th/0503052, hep-th/0602188

Hawking radiation – Angular spectrum High rotation makes angular distributions equatorial . 1 However note lower energy vectors with axial peaks! : 2 Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays . Similar effect for fermions. Power Flux (s=0) Power Flux (s=1/2) Power Flux (s=1) 0.12 (n=2, a * =1) 0.012 0.012 (n=2, a * =1) (n=2, a * =1) 0.08 0.008 0.008 0.04 0.004 0.004 0 0 0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 -1 0.5 1 1.5 2 2.5 3 3.5 4 -1 1 -1 -0.5 0.5 -0.5 0 0 0 " r h ! r h " r h 0.5 -0.5 0.5 cos ( ! ) cos ( " ) cos ( ! ) 1 1 M. Casals, S. R. Dolan, P. Kanti and E. Winstanley, JHEP 0703 (2007) 019 [hep-th/0608193]

Hawking radiation – Angular spectrum High rotation makes angular distributions equatorial . 1 However note lower energy vectors with axial peaks! : 2 Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays . Similar effect for fermions. Power Flux (s=0) ❄ Power Flux (s=1/2) ❄ Power Flux (s=1) 0.12 (n=2, a * =1) 0.012 0.012 (n=2, a * =1) (n=2, a * =1) 0.08 0.008 0.008 0.04 0.004 0.004 0 0 0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 -1 0.5 1 1.5 2 2.5 3 3.5 4 -1 1 -1 -0.5 0.5 -0.5 0 0 0 " r h ! r h " r h 0.5 -0.5 0.5 cos ( ! ) cos ( " ) cos ( ! ) 1 1 M. Casals, S. R. Dolan, P. Kanti and E. Winstanley, JHEP 0703 (2007) 019 [hep-th/0608193]

Hawking radiation – Angular spectrum High rotation makes angular distributions equatorial . 1 However note lower energy vectors with axial peaks! : 2 Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays . Similar effect for fermions. helicity = − 1 ❆ helicity = + 1 ❆ ❯ ❆ Power Flux (s=0) ❄ Power Flux (s=1/2) ❄ Power Flux (s=1) ❆ ❯ 0.12 (n=2, a * =1) 0.012 0.012 (n=2, a * =1) (n=2, a * =1) 0.08 0.008 0.008 0.04 0.004 0.004 0 0 0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 -1 0.5 1 1.5 2 2.5 3 3.5 4 -1 1 -1 -0.5 0.5 -0.5 0 0 0 " r h ! r h " r h 0.5 -0.5 0.5 cos ( ! ) cos ( " ) cos ( ! ) 1 1 M. Casals, S. R. Dolan, P. Kanti and E. Winstanley, JHEP 0703 (2007) 019 [hep-th/0608193]

Hawking radiation – Back-reaction ( D = 10 example)

Hawking radiation – Back-reaction ( D = 10 example) J 0 = 0 ❩❩❩❩❩ Non-rotating Schwarzchild M Mass drops linearly. ⑦ 1 TeV T ∼ r − 1 → speed up last ∼ 15 % t . S t / t total

Hawking radiation – Back-reaction ( D = 10 example) J 0 = 0 ❩❩❩❩❩ Non-rotating Schwarzchild M Mass drops linearly. ⑦ 1 TeV T ∼ r − 1 → speed up last ∼ 15 % t . S J 0 = 19 t / t total Rotating ❇❇ Spin-down ◆ M Initial spin down ∼ 15 % t . 1 TeV J drops by ∼ 80 % . M drops by ∼ 30 % Followed by a Schwarzchild phase. J ❈ Note: BH with large M and J . Spin-down ❈ � More semi-classical, Spins down efficiently ❈ ❲ ❈ Maybe not the case for most BHs @ LHC t / t total

Hawking radiation – Back-reaction ( D = 10 example) J 0 = 0 ❩❩❩❩❩ Non-rotating Schwarzchild M Mass drops linearly. ⑦ 1 TeV T ∼ r − 1 → speed up last ∼ 15 % t . S J 0 = 19 t / t total Rotating ❇❇ Spin-down ◆ ❍❍❍❍❍ M Schwarzchild Initial spin down ∼ 15 % t . 1 TeV ❥ J drops by ∼ 80 % . M drops by ∼ 30 % Followed by a Schwarzchild phase. J ❈ Note: BH with large M and J . Spin-down ❈ � More semi-classical, Spins down efficiently ❈ ❈ ❲ ✲ Schwarzchild Maybe not the case for most BHs @ LHC t / t total

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

CHARYBDIS2 @ Work http://projects.hepforge.org/charybdis2/ σ PP → BH Graviton ✲ MJLOST ✲ Z d τ dx Store “ τ Choose b < b max ” X momentum in f i ( x ) f j F n σ ( τ s ) Reduce M and J x x event record i , j � M BH < √ τ s formed ❅ ✠ � ❅ ❘ Evaporation Remnant ✲ Store emission Select P µ of Recoil BH NBODYVAR in LH common against SM emission NBODYPHASE with ( P µ , m , j ) and RMBOIL dN h ( a ∗ ) polarisation RMSTAB update { M , J } dtd ω d Ω ✛ Continue. ✲✻ Repeat until NBODYAVERAGE or KINCUT ❄ ❄ ❄ proton remnant HERWIG ✛ initial state radiation hard process PYTHIA P CHARYBDIS P secondary decays parton showers hadronisation

Outline Introduction 1 The hierarchy problem – Extra dimensions Strong gravity & Black Holes Modelling BH events – CHARYBDIS2 2 The production The decay CHARYBDIS2 & other generators Phenomenology using CHARYBDIS2 3 Classical signatures The effects of rotation Conclusions and Outlook 4

BH event generators J = 0 generators TRUENOIR : Fixed T, no T ( n ) k . S. Dimopoulos et al. hep-ph/0106295 CHARYBDIS1 : Variable T, no T ( n ) k . C. M. Harris et al. hep-ph/0307305 CATFISH : Energy loss, variable T, no T ( n ) k . Cavaglia et al. hep-ph/0609001 J � = 0 generators BlackMax : Energy loss, variable T, split branes, T ( n ) k . Dai et al. arXiv:0711.3012 CHARYBDIS2 : Energy loss model, polarisation, variable T, remnant options, T ( n ) k . J. A. Frost, J. R. Gaunt, MS, M. Casals, S. R. Dolan, M. A. Parker and B. R. Webber, arXiV:0904.0979 http://projects.hepforge.org/charybdis2/

BH event generators J = 0 generators TRUENOIR : Fixed T, no T ( n ) k . S. Dimopoulos et al. hep-ph/0106295 CHARYBDIS1 : Variable T, no T ( n ) k . C. M. Harris et al. hep-ph/0307305 CATFISH : Energy loss, variable T, no T ( n ) k . Cavaglia et al. hep-ph/0609001 J � = 0 generators BlackMax : Energy loss, variable T, split branes, T ( n ) k . Dai et al. arXiv:0711.3012 CHARYBDIS2 : Energy loss model, polarisation, variable T, remnant options, T ( n ) k . J. A. Frost, J. R. Gaunt, MS, M. Casals, S. R. Dolan, M. A. Parker and B. R. Webber, arXiV:0904.0979 http://projects.hepforge.org/charybdis2/

BH event generators J = 0 generators TRUENOIR : Fixed T, no T ( n ) k . S. Dimopoulos et al. hep-ph/0106295 CHARYBDIS1 : Variable T, no T ( n ) k . C. M. Harris et al. hep-ph/0307305 CATFISH : Energy loss, variable T, no T ( n ) k . Cavaglia et al. hep-ph/0609001 J � = 0 generators BlackMax : Energy loss, variable T, split branes, T ( n ) k . Dai et al. arXiv:0711.3012 CHARYBDIS2 : Energy loss model, polarisation, variable T, remnant options, T ( n ) k . J. A. Frost, J. R. Gaunt, MS, M. Casals, S. R. Dolan, M. A. Parker and B. R. Webber, arXiV:0904.0979 http://projects.hepforge.org/charybdis2/

Outline Introduction 1 The hierarchy problem – Extra dimensions Strong gravity & Black Holes Modelling BH events – CHARYBDIS2 2 The production The decay CHARYBDIS2 & other generators Phenomenology using CHARYBDIS2 3 Classical signatures The effects of rotation Conclusions and Outlook 4

Some Classical Signatures see ATLAS CSC note arXiv:0901.0512

Some Classical Signatures see ATLAS CSC note arXiv:0901.0512 Transverse momentum tails