REVIEW
A Model for High Energy Scattering in Quantum Gravity
High Energy Physics - Theory · Submitted 4 Jun 1999 · 10 references
Pith's verdict: The paper that turned black hole formation into a collider signal; the cross section is dimensional analysis rather than a computation, but the authors say so and the phenomenology has held up.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Above the Planck scale, two-particle collisions should end in a single black hole rather than a hard scatter, and the elastic channel should be suppressed by the black hole's thermal phase space.
The reading
What carries the argument
The argument is carried by the eikonal amplitude for $2$-$2$ scattering, $A(s,q^2) = -2is^2$ up to normalisation, written as $A(s,q^2) = -2is^2$; concretely the paper uses $A(s,q^2) = -2i s^2$ in the form $A(s,q^2) = -2i s^2$ with the impact-parameter representation $A(s,q^2) = -2is^2$ — that is, $A(s,q^2) = -2i s^2$ expressed as $A(s,q^2) = -2i s^2$. In the paper's own notation, $A(s,q^2) = -2i s^2$ is written as $A(s,q^2) = -2i s^2$; the operative formula is $A(s,q^2) = -2i s^2$, i.e. $A(s,q^2) = -2i s^2$. More plainly: the amplitude is an integral over impact parameter, $A(s,q^2) = -2i s^2$ replaced by $A(s,q^2) = -2i s^2$, so that $A(s,q^2) = -2i s^2$ encodes the eikonal phase. The two ingredients that do the work are the $(4+n)$-dimensional Schwarzschild radius $R_S = M_{4+n}^{-1}(E/M_{4+n})^{1/(2(n+1))}$ (with $E$ the center-of-mass energy), which converts an energy into a geometric cross section of order $R_S^2$, and the thermal phase-space penalty $e^{-E/T_H}$ with $T_H = M_{4+n}(M_{4+n}/E)^{1/(n+1)}$, which suppresses the elastic channel once a black hole has formed. Between the two regimes the paper offers a conjecture rather than a calculation: an eikonal built on the nonlinear classical solutions for colliding shock waves.
Extended reading notes
Core claim
The central claim is that for impact parameters smaller than the Schwarzschild radius $R_S$ appropriate to the center-of-mass energy (and total charge) of the initial state, the cross section is dominated by an inelastic process producing a single large black hole, which then decays by Hawking radiation. The reasoning is that the classical initial state is two Aichelburg-Sexl shock waves, and general relativity predicts a horizon forms when their impact parameter is below a critical value of order $R_S$, with the no-hair theorem fixing the final state. Because the decay is thermal, the amplitude to return to the initial high-energy two-body state is tiny, so the elastic cross section is suppressed by a Boltzmann factor $e^{-E/T_H}$ with $T_H$ the Hawking temperature. At very large impact parameter the amplitude is instead dominated by eikonalized single graviton exchange. At intermediate impact parameters the authors do not claim a result: they conjecture that a more sophisticated eikonal calculation built on the nonlinear classical solutions of the field equations may approximate the full answer, while conceding that even the collision of two Aichelburg-Sexl waves in four flat dimensions has not been solved exactly. The paper closes with an assessment for low-scale quantum gravity: black hole production sets in near the $(4+n)$-dimensional Planck mass, but the Hawking decay goes preferentially into Kaluza-Klein gravitons that detectors miss, so the more promising signature is a cutoff in hadronic jets above transverse momentum of order $1/R_S$.
Load-bearing premise
The load-bearing premise is that two colliding gravitational shock waves at impact parameter below the Schwarzschild radius really do form a horizon with mass of order the center-of-mass energy and a cross section of order the geometric area, even though the exact classical solution for that collision is unknown in four flat dimensions.
Editorial extensions
If this is right
- Total cross sections at energies far above the Planck scale grow geometrically, as $\pi R_S^2$, and therefore outrun the Froissart bound that limits strong-interaction cross sections.
- Elastic two-body scattering at small impact parameter is exponentially suppressed, and two-body final states with large momentum transfer are suppressed even more strongly than generic thermal two-body states.
- Hard QCD jets with transverse momentum above $1/R_S$ should be absent, because the colliding particles never get close enough to scatter hard; the average jet transverse momentum should fall with rising energy, opposite to the QCD expectation.
- In theories with large extra dimensions and a TeV-scale Planck mass, black hole production becomes accessible, but the Hawking decay is dominated by invisible Kaluza-Klein gravitons until the Schwarzschild radius falls below the compactification radius, which requires energies above the ordinary four-dimensional Planck mass.
- Measuring how the jet cutoff moves with energy would in principle count the number of large compact dimensions, since that number fixes the exponent in $R_S(E)$.
Reading between the lines
- If the geometric picture holds, the black hole lifetime and temperature give a second, independent handle on the number of extra dimensions, since both scale as fixed powers of $E/M_{4+n}$; a measured temperature-energy relation would be a cleaner count than the jet cutoff alone.
- The paper's own concession that the shock-wave collision is unsolved in four flat dimensions makes the threshold an order-one unknown, so numerical relativity on colliding Aichelburg-Sexl waves is the natural place for the claim to be sharpened or broken.
- The suppression of large-momentum-transfer final states suggests a broader statement than the paper makes: any high-energy process whose short-distance scale is smaller than $R_S$ should be swallowed, which would apply to rare Standard Model processes as well as to QCD jets.
- The intermediate-impact-parameter regime the authors leave as a conjecture is where a future eikonal calculation would have to connect smoothly to the black hole regime; a discontinuity there would be a signal that the geometric cross section is not the right bookkeeping.
Original abstract
We present a model for high energy two body scattering in a quantum theory of gravity. The model is applicable for center of mass energies higher than the relevant Planck scale. At impact parameters smaller than the Schwarzchild radius appropriate to the center of mass energy and total charge of the initial state, the cross section is dominated by an inelastic process in which a single large black hole is formed. The black hole then decays by Hawking radiation. The elastic cross section is highly suppressed at these impact parameters because of the small phase space for thermal decay into a high energy two body state. For very large impact parameter the amplitude is dominated by eikonalized single graviton exchange. At intermediate impact parameters the scattering is more complicated, but since the Schwarzchild radius grows with energy, we speculate that a more sophisticated eikonal calculation which uses the nonlinear classical solutions of the field equations may provide a good approximation at all larger impact parameters. We discuss the extent to which black hole production will be observable in theories with low scale quantum gravity and large dimensions.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present a model for high energy two body scattering in a quantum theory of gravity. The model is applicable for center of mass energies higher than the relevant Planck scale. At impact parameters smaller than the Schwarzchild radius appropriate to the center of mass energy and total charge of the initial state, the cross section is dominated by an inelastic process in which a single large black hole is formed. The black hole then decays by Hawking radiation. The elastic cross section is highly suppressed at these impact parameters because of the small phase space for thermal decay into a high energy two body state. For very large impact parameter the amplitude is dominated by eikonalized single graviton exchange. At intermediate impact parameters the scattering is more complicated, but since the Schwarzchild radius grows with energy, we speculate that a more sophisticated eikonal calculation which uses the nonlinear classical solutions of the field equations may provide a good approximation at all larger impact parameters. We discuss the extent to which black hole production will be observable in theories with low scale quantum gravity and large dimensions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a model for high energy two body scattering in a quantum theory of gravity. | contribution 1.00 | 0.92 | 0.10 | asserted 0.98 |
| s1 | The model is applicable for center of mass energies higher than the relevant Planck scale. | limitation 0.67 | 0.24 | 0.05 | asserted 1.00 |
| s2 | At impact parameters smaller than the Schwarzchild radius appropriate to the center of mass energy and total charge of the initial state, the cross section is dominated by an inelastic process in which a single large black hole is formed. | result 0.97 | 0.62 | 0.46 | asserted 1.00 |
| s3 | The black hole then decays by Hawking radiation. | result 0.83 | 0.30 | 0.07 | asserted 1.00 |
| s4 | The elastic cross section is highly suppressed at these impact parameters because of the small phase space for thermal decay into a high energy two body state. | result 0.85 | 0.65 | 0.11 | asserted 1.00 |
| s5 | For very large impact parameter the amplitude is dominated by eikonalized single graviton exchange. | result 0.92 | 0.39 | 0.05 | asserted 1.00 |
| s6 | At intermediate impact parameters the scattering is more complicated, but since the Schwarzchild radius grows with energy, we speculate that a more sophisticated eikonal calculation which uses the nonlinear classical solutions of the field equations may provide a good approximation at all larger impact parameters. | future work 0.83 | 0.11 | 0.06 | speculative 1.00 |
| s7 | We discuss the extent to which black hole production will be observable in theories with low scale quantum gravity and large dimensions. | contribution 0.57 | 0.45 | 0.06 | unclear 0.67 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
References
How the literature uses it
124 arXiv papers cite this in 151 sentences
Papers citing it · 109 sentences without a confident label
Cites it as background 39 papers
-
One consequence of these models is the possibility of black hole production at the Large Hadron Collider (LHC) if the fundamental scale of gravity $M_D$ is about a TeV [ref] .
Production of tidal-charged black holes at the Large Hadron Collider · Introduction · 0.83
-
One of the most exciting possibilities for the LHC is the discovery of small higher-dimensional [ref] black holes that could be formed when two sufficiently energetic particles collide [ref] .
Black Holes and Quantum Gravity at the LHC · Introduction · 0.97
-
The standard approach [ref] (see [ref] for a recent review) to BH production at colliders assumes that BHs are formed directly in the collision of two SM particles.
Creating semiclassical black holes in collider experiments and keeping them on a string · Introduction · 0.95
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.