BlackMax: A black-hole event generator with rotation, recoil, split branes, and brane tension

We present a comprehensive black-hole event generator, BlackMax, which simulates the experimental signatures of microscopic and Planckian black-hole production and evolution at the LHC in the context of brane world models with low-scale quantum gravity. The generator is based on phenomenologically realistic models free of serious problems that plague low-scale gravity, thus offering more realistic predictions for hadron-hadron colliders. The generator includes all of the black-hole gray-body factors known to date and incorporates the effects of black-hole rotation, splitting between the fermions, nonzero brane tension, and black-hole recoil due to Hawking radiation (although not all simultaneously). The generator can be interfaced with Herwig and Pythia. The main code can be downloaded from http://www-pnp.physics.ox.ac.uk/~issever/BlackMax/blackmax.html.

Figure 1

Horizon radius (in ${\mathrm{GeV}}^{-1}$) of a nonrotating black hole as a function of mass for 4–10 spatial dimensions.

Figure 2

Hawking temperature (in GeV) of a nonrotating black hole as a function of mass for 4–10 spatial dimensions.

Figure 3

Horizon radius (in ${\mathrm{GeV}}^{-1}$) of a black hole as a function of mass for different $B$ in $d=5$ spatial dimensions.

Figure 4

Hawking temperature (in GeV) of a black hole as a function of mass for different $B$ in $d=5$ spatial dimensions.

Figure 5

Horizon radius (in ${\mathrm{GeV}}^{-1}$) of a rotating black hole as a function of mass for different angular momentum in $d=5$ spatial dimensions. Angular momentum $J$ is in unit of $\hslash$.

Figure 6

Hawking temperature (in GeV) of a rotating black hole as a function of mass for different angular momentum in $d=5$ spatial dimensions. Angular momentum $J$ is in unit of $\hslash$.

Figure 7

Cross section for production of a black hole (rotating or nonrotating) as a function of the number of spatial dimensions, for a tensionless brane, with no fermion brane splitting.

Figure 8

Cross section for production of a nonrotating black hole as a function of the deficit-angle parameter for $d=5$ and $n_s=2$.

Figure 9

Cross section for production of a nonrotating black hole as a function of the number of fermion brane-splitting dimensions for $d=10$.

Figure 10

Cross section for formation of a black hole (rotating or nonrotating) as a function of the minimum mass of black hole, for a zero-tension brane, with no fermion brane splitting. The vertical lines are the error bars.

Figure 11

Cross section for the two-body final-state scenario as a function of number of spatial dimensions where $M_{\min }=M_{*}=1\mathrm{TeV}$, $M_{\min }=M_{*}=3\mathrm{TeV}$, and $M_{\min }=5\mathrm{TeV}$.

Figure 12

Angular-momentum tilt geometry.

Figure 13

The emitted fermion intensity (normalized to one) as a function of the distance between the black hole and the center of the Gaussian distribution of a fermionic brane. As a black hole moves farther from a particular fermion brane due to recoil, the intensity of emitted fermions of that type declines quickly. The radius of black hole is set to be $2M_{*}^{-1}$. The width of the fermionic brane is $M_{*}^{-1}$. The plot is for the case of one extra dimension.

Figure 14

Parameter.txt is the input file containing the parameters that one can change. The words in parentheses are the parameters that are used in the paper.

Figure 15

Output.txt: There are three parts to this file. The first part is a copy of parameter.txt. The second part includes information about the black hole and the emitted particles. The first column identifies the type of information each row is supplying—parent is information about the two incoming partons; Pbh is information on the energy and momenta of the produced black holes; trace describes the location of the black hole; Pem characterizes the emitted particles in the lab frame; Pemc characterizes the emitted particles in the center-of-mass frame; Elast describes the final burst. The third part of the file is the black-hole production cross section as inferred from the events in this generator run.

Figure 16

Lines in the output file headed by the $\mathrm{ID}=\mathtt{P}\mathtt{a}\mathtt{r}\mathtt{e}\mathtt{n}\mathtt{t}$ contain information about the initial partons which formed the black hole.

Figure 17

Lines in the output file headed by the $\mathrm{ID}=\mathtt{P}\mathtt{b}\mathtt{h}$ contain the energies and momenta of the black holes for each emission step. In case of rotating black holes, the last column in the line is the angular momentum.

Figure 18

Lines in the output file headed by the $\mathrm{ID}=\mathtt{t}\mathtt{r}\mathtt{a}\mathtt{c}\mathtt{e}$ contain the location of the black hole for reach emission step.

Figure 19

Lines in the output file headed by the $\mathrm{ID}=\mathtt{P}\mathtt{e}\mathtt{m}$ contain the types of the emitted particles, their energies and momenta in the lab frame, and the times of their emission.

Figure 20

Lines in the output file headed by the $\mathrm{ID}=\mathtt{E}\mathtt{l}\mathtt{a}\mathtt{s}\mathtt{t}$ contain the types, energies, and momenta of particles of the final burst.

Figure 21

Mass distribution of initial black holes (rotating and nonrotating) on a tensionless brane for various numbers of extra dimension.

Figure 22

Mass distribution of initial (nonrotating) black holes on a nonzero tension brane for $B=1.0$, $B=0.8$, and $B=0.6$.

Figure 23

Mass distribution of initial (nonrotating) black holes on a tensionless brane for $d=10$ and different numbers of split-fermion branes.

Figure 24

Black-hole movement in the minibulk due to recoil. $X_1$, $Y_1$ are coordinates in two extra dimensions. The red circle indicates the width of the quark brane. The blue circle indicates the width of the lepton brane. The black lines are black-hole traces. The size of the minibulk is $10{\mathrm{TeV}}^{-1}\times 10{\mathrm{TeV}}^{-1}$. Black holes with nonzero standard model gauge charges bounce back from the wall of the minibulk. Black holes with zero standard model gauge charges can leave the minibulk.

Figure 25

Electromagnetic charge distribution of the initial black holes.

Figure 26

Initial color distribution of the created black holes. The vertical lines are error bars.

Figure 27

Cumulative color distribution for nonrotating black holes on a tensionless brane with $d=4$ and no fermion brane splitting. The histogram with the black squares (open circles) is with (without) color suppression.

Figure 28

Number of particles emitted by a nonrotating black hole on a tensionless brane prior to the “final burst” as a function of number of extra dimension. Here $n_s=0$. The error bars denote 1 standard deviation range.

Figure 29

Number of particles emitted by a nonrotating black hole in the split-fermion model prior to the “final burst” as a function of the number of brane-splitting dimensions, with $d=10$. Error bars denote 1 standard deviation range.

Figure 30

Number of particles emitted by a nonrotating black hole on a nonzero tension brane prior to the “final burst” as function of deficit-angle parameter $B$ with $d=5$ and $n_s=2$. Error bars denote 1 standard deviation range.

Figure 31

Number of particles emitted by a rotating black hole prior to the “final burst” as a function of number of extra dimension with $n_s=0$. Error bars denote 1 standard deviation range.

Figure 32

Number of particles emitted at the final bursts: the average number of final bursts is about 3.4.

Figure 33

Average energy of the particles emitted by (nonrotating) black holes on unsplit branes versus the mass of the black hole at the time of emission. Here $d=4$, $d=7$, and $d=10$. Note that the final burst is not included, because it occurs when the mass of the black hole is less than 1 TeV.

Figure 34

Average energy of the particles emitted by (nonrotating) black holes on split branes versus the mass of the black hole at the time of emission. Here $d=10$ and $n_s=0$, $n_s=3$, $n_s=7$.

Figure 35

Average energy of the particles emitted by (nonrotating) black holes on a brane with tension, versus the mass of the black hole at the time of emission. Here $d=5$, $n_s=2$ and $B=1$, $B=0.8$, $B=0.6$.

Figure 36

Average energy of the particles emitted by (possibly rotating) black holes versus the mass of the black hole at the time of emission. Here $d=4$, $d=7$, and $d=10$, with a tensionless unsplit brane.

Figure 37

Energy distribution of emitted particles in the Hawking radiation step for single-brane nonrotating black hole.

Figure 38

Energy distribution of emitted particles at the final-burst step for single-brane nonrotating black hole.

Figure 39

Energy density distribution of emitted particles from nonrotating black holes on a tensionless brane with no splitted fermion branes. Shown are the distributions for $4\le d\le 10$. The spectra include the final-burst particles.

Figure 40

Energy density distribution of emitted particles from nonrotating black holes on a tensionless brane with fermion brane splitting. Shown are the distributions for $d=10$ and $0\le n_s\le 7$. The spectra include the final-burst particles.

Figure 41

Energy distribution of emitted particles for nonrotating black holes on a nonzero tension brane with $B=1$, $B=0.8$, and $B=0.6$. The spectra include the final-burst particles.

Figure 42

Energy distribution of emitted particles for rotating black holes for $4\le d\le 10$.

Figure 43

Energy distribution of emitted particles for two-body final states.

Figure 44

Energy distribution of each particle type in the $d=5$ single-brane model.

Figure 45

Pseudorapidity distribution of charge leptons and antileptons for nonrotating black holes on a tensionless brane with and without the final-burst particles; $d=5$.

Figure 46

Pseudorapidity distribution of quarks and antiquarks for nonrotating black holes on a tensionless brane with and without the final-burst particles; $d=5$.

Figure 47

Pseudorapidity distribution of charged leptons and antileptons for rotating black holes, on a tensionless brane, with and without the final-burst particles. Here $d=5$.

Figure 48

Pseudorapidity distribution of quarks and antiquarks for rotating black holes, on a tensionless brane, with and without the final-burst particles. Here $d=5$.

Figure 49

Pseudorapidity distribution for the two-body final-state scenario. The distribution in 2-body final states is much flatter near $\eta =0$ than emission due to Hawking radiation.

Figure 50

Spectra of scalar fields in $d=5$ space.

Figure 51

Spectra of scalar fields in $d=6$ space.

Figure 52

Spectra of scalar fields in $d=7$ space.

Figure 53

Spectra of scalar fields in $d=8$ space.

Figure 54

Spectra of scalar fields in $d=9$ space.

Figure 55

Spectra of scalar fields in $d=10$ space.

Figure 56

Spectra of gauge bosons in $d=5$ space.

Figure 57

Spectra of gauge bosons in $d=6$ space.

Figure 58

Spectra of gauge bosons in $d=7$ space.

Figure 59

Spectra of gauge bosons in $d=8$ space.

Figure 60

Spectra of gauge bosons in $d=9$ space.

Figure 61

Spectra of gauge bosons in $d=10$ space.