CHARYBDIS2: Modelling higher dimensional black hole events Marco - - PowerPoint PPT Presentation
CHARYBDIS2: Modelling higher dimensional black hole events Marco Sampaio sampaio@hep.phy.cam.ac.uk CFP , Physics Department, University of Porto June 30, 2010 In collaboration with James A. Frost, Jonathan R. Gaunt, Marc Casals, Sam R.
Marco Sampaio
sampaio@hep.phy.cam.ac.uk
CFP , Physics Department, University of Porto
June 30, 2010
In collaboration with James A. Frost, Jonathan R. Gaunt, Marc Casals, Sam R. Dolan, M. Andrew Parker and Bryan R. Webber
References: JHEP10(2009)014 [arXiv:0904.0979], http://projects.hepforge.org/charybdis2/
Cambridge SUSY working group FCT – SFRH/BD/23052/2005
Gµν = 8π M2
4
Tµν
Gµν = 8π M2
4
Tµν → M4 ∼ 1016 TeV
Gµν = 8π M2
4
Tµν → M4 ∼ 1016 TeV
Gµν = 8π M2
4
Tµν → M4 ∼ 1016 TeV
Standard Model
Gµν = 8π M2
4
Tµν → M4 ∼ 1016 TeV
Standard Model → MEW 1 TeV
Gµν = 8π M2
4
Tµν → M4 ∼ 1016 TeV
Standard Model → MEW 1 TeV How to explain this hierarchy of scales?
To introduce the Physics of Black Hole production and decay in theories with extra dimensions. Describe the incorporation of the theory into a Monte Carlo program CHARYBDIS2. Present some phenomenological features of the results and how they affect observables at the LHC.
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
“Low” energy degrees of freedom (after symmetry breaking): 1 Higgs particle (s = 0), 3 families of leptons and 3 of quarks (s = 1/2), 1 non-abelian SU(3)C gluon field, 3 massive vector bosons, 1 neutral U(1) Maxwell field (s = 1).
“Low” energy degrees of freedom (after symmetry breaking): LSM = 1 2∂µh∂µh−m2
h
2 h2 1 Higgs particle (s = 0), 3 families of leptons and 3 of quarks (s = 1/2), 1 non-abelian SU(3)C gluon field, 3 massive vector bosons, 1 neutral U(1) Maxwell field (s = 1).
“Low” energy degrees of freedom (after symmetry breaking): LSM = 1 2∂µh∂µh−m2
h
2 h2+¯ ea (i✓ ∂ − mea) ea+¯ νai✓ ∂νa+¯ ua (i✓ ∂ − mua) ua+ + ¯ da (i✓ ∂ − mda) da 1 Higgs particle (s = 0), 3 families of leptons and 3 of quarks (s = 1/2), 1 non-abelian SU(3)C gluon field, 3 massive vector bosons, 1 neutral U(1) Maxwell field (s = 1).
“Low” energy degrees of freedom (after symmetry breaking): LSM = 1 2∂µh∂µh−m2
h
2 h2+¯ ea (i✓ ∂ − mea) ea+¯ νai✓ ∂νa+¯ ua (i✓ ∂ − mua) ua+ + ¯ da (i✓ ∂ − mda) da − 1 4 Gµν · Gµν − 1 2W †
µνW µν + m2 WW † µW µ +
− 1 4ZµνZ µν + m2
Z
2 ZµZ µ − 1 4AµνAµν 1 Higgs particle (s = 0), 3 families of leptons and 3 of quarks (s = 1/2), 1 non-abelian SU(3)C gluon field, 3 massive vector bosons, 1 neutral U(1) Maxwell field (s = 1).
“Low” energy degrees of freedom (after symmetry breaking): LSM = 1 2∂µh∂µh−m2
h
2 h2+¯ ea (i✓ ∂ − mea) ea+¯ νai✓ ∂νa+¯ ua (i✓ ∂ − mua) ua+ + ¯ da (i✓ ∂ − mda) da − 1 4 Gµν · Gµν − 1 2W †
µνW µν + m2 WW † µW µ +
− 1 4ZµνZ µν + m2
Z
2 ZµZ µ − 1 4AµνAµν + Interactions 1 Higgs particle (s = 0), 3 families of leptons and 3 of quarks (s = 1/2), 1 non-abelian SU(3)C gluon field, 3 massive vector bosons, 1 neutral U(1) Maxwell field (s = 1).
h h h h h h h h h W, Z W, Z h W, Z W, Z W + W − Z, γ W + W − W + W − G G G G G G G f ¯ f ′ γ, G, Z, W
The action for gravity coupled to matter is S =
4
2 R + LSM
The action for gravity coupled to matter is S =
4
2 R + LSM
M4 hµν (units x → x/(E−1)) S = Lhµν,kinetic + LSM + E 2M4 Tµνhµν + . . .
M4 ∼ √αG ∼ 10−16
The action for gravity coupled to matter is S =
4
2 R + LSM
M4 hµν (units x → x/(E−1)) S = Lhµν,kinetic + LSM + E 2M4 Tµνhµν + . . .
M4 ∼ √αG ∼ 10−16 Operator type Couplings at E ∼ 1 TeV Tαβhαβ E/M4 10−16 SM Interactions ∼ e, gQCD, mH
v , v E , mf v
O(10−6) − O(1)
Hierarchy due to taking the scale for new physics from gravity (mesoscopic) rather than the electroweak scale (microscopic). The ADD solution: Assume MEW is more fundamental.
Assume our space time is 4+n dimensional SG ∼
(4+n)
√−g R(4+n) Take MEW ∼ 1 TeV → M4+n as the fundamental scale At large distances
❄
M2
4
SG ∼
(4+n)Rn √−g R(4)⇒ 4D gravity diluted
Hierarchy due to taking the scale for new physics from gravity (mesoscopic) rather than the electroweak scale (microscopic). The ADD solution: Assume MEW is more fundamental.
Assume our space time is 4+n dimensional SG ∼
(4+n)
√−g R(4+n)
❄ SM effective theory
R
Our 4D spacetime brane
Extra dimensions
Take MEW ∼ 1 TeV → M4+n as the fundamental scale At large distances
❄
M2
4
SG ∼
(4+n)Rn √−g R(4)⇒ 4D gravity diluted
Hierarchy due to taking the scale for new physics from gravity (mesoscopic) rather than the electroweak scale (microscopic). The ADD solution: Assume MEW is more fundamental.
Assume our space time is 4+n dimensional SG ∼
(4+n)
√−g R(4+n)
❄ SM effective theory
R
Our 4D spacetime brane
Extra dimensions
Take MEW ∼ 1 TeV → M4+n as the fundamental scale At large distances
❄
M2
4
SG ∼
(4+n)Rn √−g R(4)⇒ 4D gravity diluted
Hierarchy due to taking the scale for new physics from gravity (mesoscopic) rather than the electroweak scale (microscopic). The ADD solution: Assume MEW is more fundamental.
Assume our space time is 4+n dimensional SG ∼
(4+n)
√−g R(4+n)
❄ SM effective theory
R
Our 4D spacetime brane
Extra dimensions
Take MEW ∼ 1 TeV → M4+n as the fundamental scale At large distances
❄
M2
4
SG ∼
(4+n)Rn √−g R(4)⇒ 4D gravity diluted
So how does gravity look like in ADD? Fr≪R ∼ 1 M2+n
(4+n)r 2+n ,
Fr≫R ∼ 1 M2+n
(4+n)Rnr 2
R + . . .
Predicts deviations from Newtonian gravity as we approach short distances.
2
Contains KK gravitons from the 4D point of view.
3
Gravity is higher dimensional at very short distances. This can be used to put bounds on R as a function of n. ⇒ Translates as a bound on M4+n.
So how does gravity look like in ADD? Fr≪R ∼ 1 M2+n
(4+n)r 2+n ,
Fr≫R ∼ 1 M2+n
(4+n)Rnr 2
R + . . .
Predicts deviations from Newtonian gravity as we approach short distances.
2
Contains KK gravitons from the 4D point of view.
3
Gravity is higher dimensional at very short distances. This can be used to put bounds on R as a function of n. ⇒ Translates as a bound on M4+n.
So how does gravity look like in ADD? Fr≪R ∼ 1 M2+n
(4+n)r 2+n ,
Fr≫R ∼ 1 M2+n
(4+n)Rnr 2
R + . . .
Predicts deviations from Newtonian gravity as we approach short distances.
2
Contains KK gravitons from the 4D point of view.
3
Gravity is higher dimensional at very short distances. This can be used to put bounds on R as a function of n. ⇒ Translates as a bound on M4+n.
So how does gravity look like in ADD? Fr≪R ∼ 1 M2+n
(4+n)r 2+n ,
Fr≫R ∼ 1 M2+n
(4+n)Rnr 2
R + . . .
Predicts deviations from Newtonian gravity as we approach short distances.
2
Contains KK gravitons from the 4D point of view.
3
Gravity is higher dimensional at very short distances. This can be used to put bounds on R as a function of n. ⇒ Translates as a bound on M4+n.
So how does gravity look like in ADD? Fr≪R ∼ 1 M2+n
(4+n)r 2+n ,
Fr≫R ∼ 1 M2+n
(4+n)Rnr 2
R + . . .
Predicts deviations from Newtonian gravity as we approach short distances.
2
Contains KK gravitons from the 4D point of view.
3
Gravity is higher dimensional at very short distances. This can be used to put bounds on R as a function of n. ⇒ Translates as a bound on M4+n.
M2
4 = RnM2+n (4+n)
R in µm (n = 2) M4+n ∼ 1TeV OK Deviations from r−2 in torsion-balance 55 n > 1 KK graviton produc- tion @ colliders 800 n > 2 KK graviton produc- tion in Supernovae 5.1 × 10−4 n > 3 KK gravitons early Universe production 2.2 × 10−5 n > 3
M2
4 = RnM2+n (4+n)
R in µm (n = 2) M4+n ∼ 1TeV OK Deviations from r−2 in torsion-balance 55 n > 1 KK graviton produc- tion @ colliders 800 n > 2 KK graviton produc- tion in Supernovae 5.1 × 10−4 n > 3 KK gravitons early Universe production 2.2 × 10−5 n > 3 SM on a 4D brane of thickness L (1TeV)−1 ∼ 10−13µm
To avoid bounds from Electroweak precision and fast proton decay. Quarks and leptons may have to be on sub-branes for L (1TeV)−1.
All SM particles propagating on a single brane.
Good approximation if process occurs at large scales compared to L.
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
At short distances gravity is higher dimensional ⇒ √αG ∼ E M4 → E M4+n ∼ E 1TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!
At short distances gravity is higher dimensional ⇒ √αG ∼ E M4 → E M4+n ∼ E 1TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!
At short distances gravity is higher dimensional ⇒ √αG ∼ E M4 → E M4+n ∼ E 1TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!
impact parameter
Event horizon size
b 2rS parton parton ∆x ≪ rS ⇒ √s ≫ M4+n Hoop conjecture ⇒ σdisk ∼ πr2
S, rs =
Cn M4+n √s M4+n
n+1
At short distances gravity is higher dimensional ⇒ √αG ∼ E M4 → E M4+n ∼ E 1TeV So gravity becomes the strongest force above 1 TeV! ⇒ Small impact parameter, high energy collision → BHs!
impact parameter
Event horizon size
b 2rS parton parton ∆x ≪ rS ⇒ √s ≫ M4+n Hoop conjecture ⇒ σdisk ∼ πr2
S, rs =
Cn M4+n √s M4+n
n+1
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
✲ ✛
pµ
1
pµ
2
Ideally: Set up spatial metric for two highly boosted particles,
✲ ✛
pµ
1
pµ
2
❈ ❈ ❈ ❈ ❖ ✄ ✄ ✄ ✄ ✎
s1 s2 Q1 Q2 Ideally: Set up spatial metric for two highly boosted particles, Include the spin and charge,
✲ ✛
pµ
1
pµ
2
❈ ❈ ❈ ❈ ❖ ✄ ✄ ✄ ✄ ✎
s1 s2 Q1 Q2 Ideally: Set up spatial metric for two highly boosted particles, Include the spin and charge, Evolve this system using Einstein’s equations,
✏ ✏ ✏ ✮ ✻
Pµ J Q radiation radiation 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
✏ ✏ ✏ ✮ ✻
Pµ J Q radiation radiation 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.
Zilhao, Witek, Sperhake, Cardoso, Gualtieri, Herdeiro, Nerozzi arXiv:1001.2302 4 + n
✏ ✏ ✏ ✮ ✻
Pµ J Q radiation radiation 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.
Zilhao, Witek, Sperhake, Cardoso, Gualtieri, Herdeiro, Nerozzi arXiv:1001.2302 4 + n
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
2
Bounds on M and J lost into gravitational radiation.
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
2
Bounds on M and J lost into gravitational radiation. b = 0.5rS b = 1.0rS b = 1.3rS
J J0 M M0 M M0 M M0
ζ ξ D = 6, b = 0.5 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 ζ ξ D = 6, b = 1.0 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 ζ ξ D = 6, b = 1.3 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2
1
Lower bounds on b(n)
max ⇒Enhanced cross section Fnσdisk
σPP→BH =
partons
1
τm
dτ 1
τ
dx x fi(x)fj τ x
⇒ σPP→BH = 70, 160, 280 pb ⇒ 1s−1 @ design at 7 TeV ⇒ 10−4 suppression.
2
Bounds on M and J lost into gravitational radiation. b = 0.5rS b = 1.0rS b = 1.3rS
J J0 M M0 M M0 M M0
ζ ξ D = 6, b = 0.5 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 ζ ξ D = 6, b = 1.0 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 ζ ξ D = 6, b = 1.3 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2
MJLOST=.TRUE. – Uses bound for each 0 < b < bmax.
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
After formation, classically nothing else happens! (if BH relatively slowly rotating, otherwise instabilities). ds2 =
µ Σr n−1
Σr n−1 dtdφ − Σ ∆dr 2− −Σdθ2−
Σr n−1
n ,
1974, Hawking’s quantum instability⇒ BH decays 10−26s. Gravity couples Universally s = 0 Higgs + WL/ZL 4 s = 1/2 Quarks + Leptons 90 s = 1 G + γ + WT/ZT 24 Sbrane =
2 + L1
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)
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)
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)
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)
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)
dEh dtdωdΩ =
ω 2π T(n)
k (ω, a∗)
exp(ω−mΩH
TH
) ± 1
j (Ω, ωa∗)
Dependence on a∗ TH = (n+1)+(n−1)a2
∗
4π(1+a2
∗)rH
, ΩH= 1
rH a∗ 1+a2
∗
Spheroidal angular functions
1
Harder spectrum
2
m = j (m > 0) dominant ⇒ Spin-down
3
Similar for Scalars and Vectors
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
dEh dtdωdΩ =
ω 2π T(n)
k (ω, a∗)
exp(ω−mΩH
TH
) ± 1
j (Ω, ωa∗)
Dependence on a∗ TH = (n+1)+(n−1)a2
∗
4π(1+a2
∗)rH
, ΩH= 1
rH a∗ 1+a2
∗
Spheroidal angular functions
1
Harder spectrum
2
m = j (m > 0) dominant ⇒ Spin-down
3
Similar for Scalars and Vectors
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
dEh dtdωdΩ =
ω 2π T(n)
k (ω, a∗)
exp(ω−mΩH
TH
) ± 1
j (Ω, ωa∗)
Dependence on a∗ TH = (n+1)+(n−1)a2
∗
4π(1+a2
∗)rH
, ΩH= 1
rH a∗ 1+a2
∗
Spheroidal angular functions
1
Harder spectrum
2
m = j (m > 0) dominant ⇒ Spin-down
3
Similar for Scalars and Vectors
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
dEh dtdωdΩ =
ω 2π T(n)
k (ω, a∗)
exp(ω−mΩH
TH
) ± 1
j (Ω, ωa∗)
Dependence on a∗ TH = (n+1)+(n−1)a2
∗
4π(1+a2
∗)rH
, ΩH= 1
rH a∗ 1+a2
∗
Spheroidal angular functions
1
Harder spectrum
2
m = j (m > 0) dominant ⇒ Spin-down
3
Similar for Scalars and Vectors
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
dEh dtdωdΩ =
ω 2π T(n)
k (ω, a∗)
exp(ω−mΩH
TH
) ± 1
j (Ω, ωa∗)
Dependence on a∗ TH = (n+1)+(n−1)a2
∗
4π(1+a2
∗)rH
, ΩH= 1
rH a∗ 1+a2
∗
Spheroidal angular functions
1
Harder spectrum
2
m = j (m > 0) dominant ⇒ Spin-down
3
Similar for Scalars and Vectors
a∗
n = 2 s = 1/2
1.4 1.2 1.0 0.8 0.4 0.0 ωrH 5 4 3 2 1 0.04 0.03 0.02 0.01
a∗
n = 6 s = 1/2
1.4 1.2 1.0 0.8 0.4 0.0 5 4 3 2 1 0.3 0.2 0.1
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
1
High rotation makes angular distributions equatorial.
2
However note lower energy vectors with axial peaks!:
Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays. Similar effect for fermions.
0.5 1 0.5 1 1.5 2 2.5 3 3.5 0.004 0.008 0.012
(n=2, a*=1)
cos(!) " rh Power Flux (s=0)
0.5 1 1.5 2 2.5 3 3.5 4 -1
0.5 1 0.004 0.008 0.012
(n=2, a*=1)
! rh cos(") Power Flux (s=1/2)
0.5 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.04 0.08 0.12
(n=2, a*=1)
cos(!) " rh Power Flux (s=1)
1
High rotation makes angular distributions equatorial.
2
However note lower energy vectors with axial peaks!:
Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays. Similar effect for fermions. ❄ ❄
0.5 1 0.5 1 1.5 2 2.5 3 3.5 0.004 0.008 0.012
(n=2, a*=1)
cos(!) " rh Power Flux (s=0)
0.5 1 1.5 2 2.5 3 3.5 4 -1
0.5 1 0.004 0.008 0.012
(n=2, a*=1)
! rh cos(") Power Flux (s=1/2)
0.5 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.04 0.08 0.12
(n=2, a*=1)
cos(!) " rh Power Flux (s=1)
1
High rotation makes angular distributions equatorial.
2
However note lower energy vectors with axial peaks!:
Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays. Similar effect for fermions. ❄ ❄ ❆ ❆ ❯ helicity = +1 ❆ ❆ ❯ helicity = −1
0.5 1 0.5 1 1.5 2 2.5 3 3.5 0.004 0.008 0.012
(n=2, a*=1)
cos(!) " rh Power Flux (s=0)
0.5 1 1.5 2 2.5 3 3.5 4 -1
0.5 1 0.004 0.008 0.012
(n=2, a*=1)
! rh cos(") Power Flux (s=1/2)
0.5 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.04 0.08 0.12
(n=2, a*=1)
cos(!) " rh Power Flux (s=1)
J0 = 0
M 1 TeV
t/ttotal
❩❩❩❩❩ ⑦
Schwarzchild
Non-rotating Mass drops linearly. T ∼ r −1
S
→ speed up last ∼ 15% t.
J0 = 0
M 1 TeV
t/ttotal
❩❩❩❩❩ ⑦
Schwarzchild
M 1 TeV J
t/ttotal
❇❇ ◆
Spin-down
❈ ❈ ❈ ❈ ❲
Spin-down
Non-rotating Mass drops linearly. T ∼ r −1
S
→ speed up last ∼ 15% t. Rotating Initial spin down ∼ 15%t.
J drops by ∼ 80%. M drops by ∼ 30%
Followed by a Schwarzchild phase. Note: BH with large M and J.
More semi-classical, Spins down efficiently Maybe not the case for most BHs @ LHC
J0 = 0
M 1 TeV
t/ttotal
❩❩❩❩❩ ⑦
Schwarzchild
M 1 TeV J
t/ttotal
❇❇ ◆
Spin-down
❈ ❈ ❈ ❈ ❲
Spin-down
✲
Schwarzchild
❍❍❍❍❍ ❥
Schwarzchild
Non-rotating Mass drops linearly. T ∼ r −1
S
→ speed up last ∼ 15% t. Rotating Initial spin down ∼ 15%t.
J drops by ∼ 80%. M drops by ∼ 30%
Followed by a Schwarzchild phase. Note: BH with large M and J.
More semi-classical, Spins down efficiently Maybe not the case for most BHs @ LHC
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
http://projects.hepforge.org/charybdis2/
σPP→BH
X
i,j
Z dτdx x fi(x)fj “τ x ” Fnσ(τs)
✲ MJLOST
Choose b < bmax Reduce M and J
✲ Graviton
Store momentum in event record
MBH < √τs formed❅
❅ ❘
Evaporation
Select Pµ of SM emission
dNh(a∗) dtdωdΩ
Recoil BH against (Pµ, m, j) and update {M, J} Store emission in LH common with polarisation
Continue.
Repeat until NBODYAVERAGE or KINCUT ✲✻ ✛ ❄
Remnant
NBODYVAR NBODYPHASE RMBOIL RMSTAB
✲ ❄
HERWIG PYTHIA CHARYBDIS
❄
P P
proton remnant initial state radiation hard process secondary decays parton showers hadronisation
✛
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
J = 0 generators TRUENOIR: Fixed T, no T(n)
k .
CHARYBDIS1: Variable T, no T(n)
k .
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 .
http://projects.hepforge.org/charybdis2/
J = 0 generators TRUENOIR: Fixed T, no T(n)
k .
CHARYBDIS1: Variable T, no T(n)
k .
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 .
http://projects.hepforge.org/charybdis2/
J = 0 generators TRUENOIR: Fixed T, no T(n)
k .
CHARYBDIS1: Variable T, no T(n)
k .
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 .
http://projects.hepforge.org/charybdis2/
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
Transverse momentum tails
Transverse momentum tails Missing energy tails
Transverse momentum tails Missing energy tails Large multiplicity tails
Why BHs are different High multiplicity events with large number or jets. In the SM, SUSY and other BSM models this is usually
Very High PT tails. Allow for large boost particles. For high multiplicity events, virtually any combination of particles in the final state.
Why BHs are different High multiplicity events with large number or jets. In the SM, SUSY and other BSM models this is usually
Very High PT tails. Allow for large boost particles. For high multiplicity events, virtually any combination of particles in the final state.
Why BHs are different High multiplicity events with large number or jets. In the SM, SUSY and other BSM models this is usually
Very High PT tails. Allow for large boost particles. For high multiplicity events, virtually any combination of particles in the final state.
Why BHs are different High multiplicity events with large number or jets. In the SM, SUSY and other BSM models this is usually
Very High PT tails. Allow for large boost particles. For high multiplicity events, virtually any combination of particles in the final state.
Why BHs are different High multiplicity events with large number or jets. In the SM, SUSY and other BSM models this is usually
Very High PT tails. Allow for large boost particles. For high multiplicity events, virtually any combination of particles in the final state.
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
[TeV]
BH
M 3 4 5 6 7 8 9 10 [pb/TeV]
BH
/dM ! d
10
10
10 1 10
2
10
3
10
4
10
CHARYBDIS 2.0
MPL=1TeV, MJLOST=FALSE MPL=1TeV, MJLOST=TRUE MPL=2TeV, MJLOST=TRUE
Particle Multiplicity 5 10 15 20 25 Probability 0.02 0.04 0.06 0.08 0.1 0.12
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
❄ ❍ ❍ ❥ ❳❳ ❳ ③
High Multiplicity
Particle Multiplicity 5 10 15 20 25 Probability 0.02 0.04 0.06 0.08 0.1 0.12
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
❄ ❍ ❍ ❥ ❳❳ ❳ ③
High Multiplicity
| [GeV]
T
Particle |P 500 1000 1500 2000 2500 Number / 50 GeV / Event
10
10
10
10 1
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
High PT
Particle Multiplicity 5 10 15 20 25 Probability 0.02 0.04 0.06 0.08 0.1 0.12
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
❄ ❍ ❍ ❥ ❳❳ ❳ ③
High Multiplicity
| [GeV]
T
Particle |P 500 1000 1500 2000 2500 Number / 50 GeV / Event
10
10
10
10 1
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
High PT
MET [GeV] 200 400 600 800 1000 1200 1400 1600 1800 2000 Number / 50 GeV / Event
10
10
10
Non-Rot. n=2 Non-Rot. n=4 Non-Rot. n=6 Rotating n=2 Rotating n=4 Rotating n=6
CHARYBDIS 2.0
Large missing ET
Massless approximation in the generator! → But mH, mW, mZ, mt ∼ 0.1 TeV Gauge charges of the particles not included in the Hawking radiation calculations.
MOPS, JHEP 10 (2009) 008 [arXiv:0907.5107] MOPS, JHEP 02 (2010) 042 [arXiv:0911.0688]
Not clear whether graviton emission will be enhanced with rotation and compete with brane emission. → need full numerical analysis of gravitons.
Massless approximation in the generator! → But mH, mW, mZ, mt ∼ 0.1 TeV Gauge charges of the particles not included in the Hawking radiation calculations.
MOPS, JHEP 10 (2009) 008 [arXiv:0907.5107] MOPS, JHEP 02 (2010) 042 [arXiv:0911.0688]
Not clear whether graviton emission will be enhanced with rotation and compete with brane emission. → need full numerical analysis of gravitons.
Massless approximation in the generator! → But mH, mW, mZ, mt ∼ 0.1 TeV Gauge charges of the particles not included in the Hawking radiation calculations.
MOPS, JHEP 10 (2009) 008 [arXiv:0907.5107] MOPS, JHEP 02 (2010) 042 [arXiv:0911.0688]
Not clear whether graviton emission will be enhanced with rotation and compete with brane emission. → need full numerical analysis of gravitons.
Massless approximation in the generator! → But mH, mW, mZ, mt ∼ 0.1 TeV Gauge charges of the particles not included in the Hawking radiation calculations.
MOPS, JHEP 10 (2009) 008 [arXiv:0907.5107] MOPS, JHEP 02 (2010) 042 [arXiv:0911.0688]
Not clear whether graviton emission will be enhanced with rotation and compete with brane emission. → need full numerical analysis of gravitons.
Massless approximation in the generator! → But mH, mW, mZ, mt ∼ 0.1 TeV Gauge charges of the particles not included in the Hawking radiation calculations.
MOPS, JHEP 10 (2009) 008 [arXiv:0907.5107] MOPS, JHEP 02 (2010) 042 [arXiv:0911.0688]
Not clear whether graviton emission will be enhanced with rotation and compete with brane emission. → need full numerical analysis of gravitons.
1
Introduction The hierarchy problem – Extra dimensions Strong gravity & Black Holes
2
Modelling BH events – CHARYBDIS2 The production The decay CHARYBDIS2 & other generators
3
Phenomenology using CHARYBDIS2 Classical signatures The effects of rotation
4
Conclusions and Outlook
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs.
We have described the Physics of production and decay of BHs in theories with extra dimensions, in CHARYBDIS2. We have looked into some interesting effects/models:
1
M and J distributions at formation;
2
The effect of rotation on energy and angular distributions;
Phenomenologically:
1
Large cross sections, large multiplicities, large PT and missing energy → classical signatures roughly remain.
2
Potential of rotation: angular correlations (to be explored).
Future work will involve detailed studies of: asymmetries and angular correlations, refinement of the modelling of production and evaporation to include mass and charge effects, etc... Studies of exclusion limits for the various LHC runs. Thanks for your attention! Questions?
BACKUP
Enhancement of Vector emission
PdgId Code
10 20 30 40 Probability 0.05 0.1 0.15 0.2 0.25 0.3
Non-Rot. n=4 Rotating n=4
CHARYBDIS 2.0
Look at radiative corrections to Higgs mass:
Look at radiative corrections to Higgs mass: Higgs mass runs from high scale: δm2
h =
2λ Λ2
cutoff
8π2 + . . .
Look at radiative corrections to Higgs mass: Higgs mass runs from high scale: δm2
h =
2λ Λ2
cutoff
8π2 + . . . If Λcutoff ∼ M4 ∼ 1016 TeV ⇒ fine tuning of ∼ 10−16
1
Arrange cancellation of quadratic divergences. ⇒ New particles: SUSY, Little Higgs, etc...
1
Arrange cancellation of quadratic divergences. ⇒ New particles: SUSY, Little Higgs, etc...
2
Change the running to exponential. ⇒ Strong dynamics: the Higgs is a pion field of a new strongly coupled sector.
1
Arrange cancellation of quadratic divergences. ⇒ New particles: SUSY, Little Higgs, etc...
2
Change the running to exponential. ⇒ Strong dynamics: the Higgs is a pion field of a new strongly coupled sector.
3
Assume the fundamental Planck scale is 1 TeV. ⇒ Extra dimensions.
1
Arrange cancellation of quadratic divergences. ⇒ New particles: SUSY, Little Higgs, etc...
2
Change the running to exponential. ⇒ Strong dynamics: the Higgs is a pion field of a new strongly coupled sector.
3
Assume the fundamental Planck scale is 1 TeV. ⇒ Extra dimensions.
4
Etc...
M2
Pl = RnM2+n (4+n)
R in µm (n = 2) M4+n ∼ 1TeV OK Deviations from r−2 in torsion-balance 55 n > 1 KK graviton produc- tion @ colliders 800 n > 2 KK graviton produc- tion in Supernovae 5.1 × 10−4 n > 3 KK gravitons early Universe production 2.2 × 10−5 n > 3
f ¯ f GKK f, γ ¯ f, γ f ¯ f γ, G γ, G GKK f, γ ¯ f, γ GKK
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length.
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length. ∆x ∼ 1 p ≪ rS
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length. ∆x ∼ 1 p ≪ rS But: p large ⇒ ∆x small
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length. ∆x ∼ 1 p ≪ rS But: p large ⇒ ∆x small p large ⇒ √s ≡ ECM large ⇒ rS large
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length. ∆x ∼ 1 p ≪ rS But: p large ⇒ ∆x small p large ⇒ √s ≡ ECM large ⇒ rS large The condition is satisfied when √s ≫ M4+n (trans-Planckian).
For the classical approximation for production to be valid we need the wavelength of each colliding particle to be small compared to the interaction length. ∆x ∼ 1 p ≪ rS But: p large ⇒ ∆x small p large ⇒ √s ≡ ECM large ⇒ rS large The condition is satisfied when √s ≫ M4+n (trans-Planckian). Also quantum gravity approximations indicate small corrections:
During formation we should have an asymmetric BH with electric and gravitational multipole moments. →Distorted geometry. The time for loss of multipoles is rS (natural units). We will look next into the Hawking decay and realise that the typical timescale there is ∆t ∼ rS MBH M4+n n+2
n+1
≫ rS . We assume a quick loss of asymmetries ⇒ BH settles down to a stationary axisymmetric solution.
During formation we should have an asymmetric BH with electric and gravitational multipole moments. →Distorted geometry.
BALDING
The time for loss of multipoles is rS (natural units). We will look next into the Hawking decay and realise that the typical timescale there is ∆t ∼ rS MBH M4+n n+2
n+1
≫ rS . We assume a quick loss of asymmetries ⇒ BH settles down to a stationary axisymmetric solution.
During formation we should have an asymmetric BH with electric and gravitational multipole moments. →Distorted geometry.
BALDING
The time for loss of multipoles is rS (natural units). We will look next into the Hawking decay and realise that the typical timescale there is ∆t ∼ rS MBH M4+n n+2
n+1
≫ rS . We assume a quick loss of asymmetries ⇒ BH settles down to a stationary axisymmetric solution.
During formation we should have an asymmetric BH with electric and gravitational multipole moments. →Distorted geometry.
BALDING
The time for loss of multipoles is rS (natural units). We will look next into the Hawking decay and realise that the typical timescale there is ∆t ∼ rS MBH M4+n n+2
n+1
≫ rS . We assume a quick loss of asymmetries ⇒ BH settles down to a stationary axisymmetric solution.
During formation we should have an asymmetric BH with electric and gravitational multipole moments. →Distorted geometry.
BALDING
The time for loss of multipoles is rS (natural units). We will look next into the Hawking decay and realise that the typical timescale there is ∆t ∼ rS MBH M4+n n+2
n+1
≫ rS . We assume a quick loss of asymmetries ⇒ BH settles down to a stationary axisymmetric solution.
BHspin 2 4 6 8 10 12 14 16 18 20 Probability 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
n=2 qq/gg n=2 qg n=4 qq/gg n=4 qg n=6 qq/gg n=6 qg
CHARYBDIS 2.0
Initial J
BHspin 2 4 6 8 10 12 14 16 18 20 Probability 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
n=2 qq/gg n=2 qg n=4 qq/gg n=4 qg n=6 qq/gg n=6 qg
CHARYBDIS 2.0
Reduced final J
BHspin 2 4 6 8 10 12 14 16 18 20 Probability 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
n=2 qq/gg n=2 qg n=4 qq/gg n=4 qg n=6 qq/gg n=6 qg
CHARYBDIS 2.0
Initial J
BHspin 2 4 6 8 10 12 14 16 18 20 Probability 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
n=2 qq/gg n=2 qg n=4 qq/gg n=4 qg n=6 qq/gg n=6 qg
CHARYBDIS 2.0
Reduced final J
BHmass [GeV] 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Probability 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
CHARYBDIS 2.0
n=2 n=4 n=6
Smeared M
Extract angular correlations by forming correlators of the type xi,j =
pi·pj |pi||pj| in the frame of the initial BH.
Why?
Extract angular correlations by forming correlators of the type xi,j =
pi·pj |pi||pj| in the frame of the initial BH.
Why?
Extract angular correlations by forming correlators of the type xi,j =
pi·pj |pi||pj| in the frame of the initial BH.
Why?
1
High rotation makes angular distributions equatorial.
2
However note lower energy vectors with axial peaks!:
Each peak comes from different polarisation contributions. Study of asymmetries in vector boson decays. Similar effect for fermions. ❄ ❄ ❆ ❆ ❯ helicity = +1 ❆ ❆ ❯ helicity = −1
0.5 1 0.5 1 1.5 2 2.5 3 3.5 0.004 0.008 0.012
(n=2, a*=1)
cos(!) " rh Power Flux (s=0)
0.5 1 1.5 2 2.5 3 3.5 4 -1
0.5 1 0.004 0.008 0.012
(n=2, a*=1)
! rh cos(") Power Flux (s=1/2)
0.5 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.04 0.08 0.12
(n=2, a*=1)
cos(!) " rh Power Flux (s=1)
Extract angular correlations by forming correlators of the type xi,j =
pi·pj |pi||pj| in the frame of the initial BH.
Why?
a = 0 (any) hi = −hj = ±1 hi = hj = ±1 hi = −hj = ±1/2 hi = hj = ±1/2 RECOIL=1 Angular correlators (all ωrH0 < 0.2) xi,j Probability 1 0.5
0.07 0.06 0.05 0.04 0.03 0.02 0.01 a = 0 (any) hi = −hj = ±1 hi = hj = ±1 hi = −hj = ±1/2 hi = hj = ±1/2 RECOIL=1 Angular correlators (all 0.2 < ωrH0 < 0.4) xi,j 1 0.5
0.08 0.06 0.04 0.02 a = 0 (any) hi = −hj = ±1 hi = hj = ±1 hi = −hj = ±1/2 hi = hj = ±1/2 RECOIL=1 Angular correlators (all ωrH0 > 1.5) xi,j 1 0.5
0.14 0.12 0.1 0.08 0.06 0.04 0.02
BH settles down to (4+n)D Myers-Perry rotating BH. Mass M and angular momentum J as seen from infinity. Typical size/curvature of the horizon is rH. Spheroidal horizon with
x2 + y2 1 + a∗2 + z2 = rH
2 .
Observer at r → ∞ sees an “egg like” black disk.
BH settles down to (4+n)D Myers-Perry rotating BH. Mass M and angular momentum J as seen from infinity. Typical size/curvature of the horizon is rH. Spheroidal horizon with
x2 + y2 1 + a∗2 + z2 = rH
2 .
Observer at r → ∞ sees an “egg like” black disk.
BH settles down to (4+n)D Myers-Perry rotating BH. Mass M and angular momentum J as seen from infinity. Geometrical properties Typical size/curvature of the horizon is rH. Spheroidal horizon with
x2 + y2 1 + a∗2 + z2 = rH
2 .
Observer at r → ∞ sees an “egg like” black disk.
BH settles down to (4+n)D Myers-Perry rotating BH. Mass M and angular momentum J as seen from infinity. Geometrical properties Typical size/curvature of the horizon is rH. Spheroidal horizon with
x2 + y2 1 + a∗2 + z2 = rH
2 .
Observer at r → ∞ sees an “egg like” black disk.
BH settles down to (4+n)D Myers-Perry rotating BH. Mass M and angular momentum J as seen from infinity. Geometrical properties Typical size/curvature of the horizon is rH. Spheroidal horizon with
x2 + y2 1 + a∗2 + z2 = rH
2 .
Observer at r → ∞ sees an “egg like” black disk.
2.0 1.6 1.2 0.8 0.4 0.0 a∗ θ = π 2 n = 2 x/rH y/rH 5 4 3 2 1
3 2 1 −1 −2 −3
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
When MBH < M4+n, we reach the quantum gravity regime which is not known.
→A model must be provided.
To make robust predictions we must try to minimise the effect of this final stage.
→ Cut on events with MBH well above M4+n ∼ 1TeV.
A remnant fixed N-body phase space decay is performed in CHARYBDIS1 if MBH < M4+n. In addition If KINCUT=.TRUE. this occurs earlier, if a kinematically disallowed energy is selected.
In CHARYBDIS2 we introduce more physical models.
Termination criteria:
1
KINCUT: as before.
2
NBODYAVERAGE: Go to remnant if, N ≃ MrH
rH dN dt
dE
dt
< NBODY − 1 = 1 or 2, . . . Remnant models
1
Phase space constrained model (next slide).
2
RMBOIL: Remnant evaporates at TH = THWMAX. Motivated by string balls.
3
Stable remnant Q = 0, ±1. Motivated by modified uncertainty principle.
Termination criteria:
1
KINCUT: as before.
2
NBODYAVERAGE: Go to remnant if, N ≃ MrH
rH dN dt
dE
dt
< NBODY − 1 = 1 or 2, . . . Remnant models
1
Phase space constrained model (next slide).
2
RMBOIL: Remnant evaporates at TH = THWMAX. Motivated by string balls.
3
Stable remnant Q = 0, ±1. Motivated by modified uncertainty principle.
Termination criteria:
1
KINCUT: as before.
2
NBODYAVERAGE: Go to remnant if, N ≃ MrH
rH dN dt
dE
dt
< NBODY − 1 = 1 or 2, . . . Remnant models
1
Phase space constrained model (next slide).
2
RMBOIL: Remnant evaporates at TH = THWMAX. Motivated by string balls.
3
Stable remnant Q = 0, ±1. Motivated by modified uncertainty principle.
1
NBODYVAR = .TRUE.: Choose multiplicity n + 1 using Pδt(n) = e−N Nn n!
Motivated by sudden final burst approximation. N physically motivated.
2
NBODYPHASE = .FALSE.: Use constrained phase space dP ∝ δ(4) (
i pi − PBH) i ρi (Ei, Ωi) d3pi
with ρi (Ei, Ωi) =
T(n)
k (EirH,a∗)
exp( ˜ Ei/TH)±1 |Sk(Ωi)|2
More similar to Hawking evaporation
1
NBODYVAR = .TRUE.: Choose multiplicity n + 1 using Pδt(n) = e−N Nn n!
Motivated by sudden final burst approximation. N physically motivated.
2
NBODYPHASE = .FALSE.: Use constrained phase space dP ∝ δ(4) (
i pi − PBH) i ρi (Ei, Ωi) d3pi
with ρi (Ei, Ωi) =
T(n)
k (EirH,a∗)
exp( ˜ Ei/TH)±1 |Sk(Ωi)|2
More similar to Hawking evaporation
1
NBODYVAR = .TRUE.: Choose multiplicity n + 1 using Pδt(n) = e−N Nn n!
Motivated by sudden final burst approximation. N physically motivated.
2
NBODYPHASE = .FALSE.: Use constrained phase space dP ∝ δ(4) (
i pi − PBH) i ρi (Ei, Ωi) d3pi
with ρi (Ei, Ωi) =
T(n)
k (EirH,a∗)
exp( ˜ Ei/TH)±1 |Sk(Ωi)|2
More similar to Hawking evaporation
1
NBODYVAR = .TRUE.: Choose multiplicity n + 1 using Pδt(n) = e−N Nn n!
Motivated by sudden final burst approximation. N physically motivated.
2
NBODYPHASE = .FALSE.: Use constrained phase space dP ∝ δ(4) (
i pi − PBH) i ρi (Ei, Ωi) d3pi
with ρi (Ei, Ωi) =
T(n)
k (EirH,a∗)
exp( ˜ Ei/TH)±1 |Sk(Ωi)|2
More similar to Hawking evaporation