New physics in a nutshell, or Q-ball as a power plant

Alexander Kusenko; Gia Dvali; Mikhail Shaposhnikov (CERN)

REVIEW

New physics in a nutshell, or Q-ball as a power plant

Gia Dvali, Alexander Kusenko, Mikhail Shaposhnikov (CERN)

High Energy Physics - Phenomenology · Submitted 22 Jul 1997 · 14 references

Pith's verdict: A 1997 Letter that turns the Q-ball interior into a laboratory for trans-TeV physics; the scaling is standard, the framing is new, and the power-plant headline is honestly flagged as speculative.

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arXiv IDhep-ph/9707423 (version 2)

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CitationAlexander Kusenko, Gia Dvali, Mikhail Shaposhnikov (CERN). "New physics in a nutshell, or Q-ball as a power plant." arXiv:hep-ph/9707423 (1997). https://pith.science/paper/SX5A2KBB

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Editor's note

read the letter

The Q^{1/4} interior scaling and the E ∝ Q^{3/4} energy law are not new here — they come from Kusenko [4] and Linde [5]. What is new is the use: a large Q-ball in a flat potential samples field values far above the scalar mass, so the interior can restore SU(2), remove confinement, and catalyze baryon violation. That framing is the paper's real contribution. Section 2's gauge-mediation argument for why soft masses switch off above the messenger scale is a fair summary, and Section 4's application to light color-triplet Higgs fields is a concrete model. The authors name their own soft spots: Section 2 concedes that Planck-suppressed operators and 'other minima' are ignored, and Section 4 says the engineering of building and feeding a Q-ball is outside scope. Those are real caveats, not hidden ones. The catalysis rates are order-of-magnitude with unspecified O(1) factors, which the paper does not pretend otherwise. On the stress-test concern: the two formulas in Section 3 do scale differently. Eq. (8) is the rate for q → l + phonon, with amplitude y⟨φ⟩/M_X; Eq. (9) is the boundary reflection probability, set by the mixing angle y⟨φ⟩²/(M_X m_q). They describe different processes, and the paper should say so. But the numerical conclusion that the power estimate fails is not supported: at ⟨φ⟩ ~ 10^13 GeV, Eq. (8) gives Γ ~ 10^-6 GeV, which is fast on the crossing timescale, and Eq. (9) saturates to O(1). Both give a fast rate. The inconsistency is a presentation gap, not a load-bearing flaw. Who should read it: anyone working on Q-balls, flat directions, or non-perturbative baryon violation. The power-plant headline will draw attention, but the laboratory argument is the part worth keeping. Recommendation: send it to referees. It is a legitimate Letter with a testable-in-principle proposal and honest caveats. The referee should ask for the Eq. (8)/Eq. (9) reconciliation and a clearer statement of the flat-direction survival condition.

Referee report

Major objections (2)

[Section 3, Eqs. (8) and (9)] The two formulas given for the q→l transition are mutually inconsistent in their ⟨φ⟩ scaling, and the power-plant estimate depends on which one is correct. From the operator y φ†φ/M_X (q̄l), the induced q–l mixing mass is μ = y⟨φ⟩²/M_X, so the reflection probability is P ~ (μ/m_q)² = y²⟨φ⟩⁴/(M_X² m_q²), which matches Eq. (9). The corresponding decay width should then scale as Γ ~ P·m_q ~ y²⟨φ⟩⁴/(M_X² m_q), whereas Eq. (8) states Γ ~ y²⟨φ⟩²/M_X² · m_q. The two differ by (⟨φ⟩/m_q)², which at the quoted Q ~ 10^40 (⟨φ⟩ ~ 10^13 GeV, m_q ~ 1 GeV) is enormous. The power estimate in Section 4 implicitly requires the catalysis probability per proton crossing to be O(1), which Eq. (9) can support but Eq. (8) cannot. The manuscript does not reconcile the two expressions, so the quantitative energy claim is not robust until the correct ⟨φ⟩ scaling is fixed and the two formulas are made consistent.
[Section 4, power-generation estimate] The estimate that a charge 10^40 Q-ball a few microns in diameter and weighing 100 tons could deliver ~10^8 W is presented without showing the intermediate steps: the assumed proton flux, the catalysis cross section per unit area, and the fraction of the released energy that escapes as usable photons and pions rather than being reabsorbed. Given that the catalysis rate is the product of an uncertain per-crossing probability (see the Eq. (8)/Eq. (9) comment) and an assumed beam flux, the numerical claim should either be derived explicitly or clearly labeled as an illustrative order-of-magnitude estimate with its assumptions stated.

Minor objections (5)

[Section 2, end] The statement that Planck-scale corrections are expected to lift the potential near M_P and that 'there can be a variety of other minima in this region, which we will ignore' is an acknowledged limitation, but the paper would be strengthened by a sentence on how an intermediate-scale lift (e.g., a non-renormalizable operator of dimension 5 or 6) would cap the achievable φ₀ and hence the maximum reachable scale.
[Section 1, Eq. (5)] The approximate solution φ(r) = φ₀ sin(ωr)/(ωr) for r<R matched to φ₁ exp(−m_φ r) for r≥R is stated without showing the matching conditions that determine φ₀, φ₁, ω, and R; a brief derivation or a reference to the matching procedure would help the reader verify the Q^{1/4} scaling independently.
[Section 4, color-triplet discussion] The claim that the triplets can be light with GUT-suppressed couplings relies on Ref. [9]; the cosmological and collider constraints cited in Refs. [10] and [11] are summarized but not connected quantitatively to the proposed Q-ball construction. A short statement of which mass/lifetime window survives all constraints would clarify the viability of the T-ball scenario.
[Section 3, Eq. (10)] For the approximate U_φ(1) case with Yukawa coupling y φ(q̄l), the evaporation rate of the Q-ball by light-fermion emission is described only qualitatively; a scaling estimate of the evaporation lifetime versus the catalysis rate would make the comparison between the two toy models meaningful.
[General] The paper is written as a Letter-length commentary and several key estimates (Eqs. (8), (9), and the Section 4 power numbers) are order-of-magnitude with unspecified O(1) factors; stating explicitly which factors are dropped would help the reader judge the robustness of the conclusions.

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The paper

The paper claims

A large enough Q-ball could carry a scalar field to energies no collider can reach, and its interior could catalyze proton decay.

The reading

The authors ask whether a lump of charged scalar field — a Q-ball, a stable soliton that minimizes energy at fixed global charge — can be grown large enough that the field value inside it dwarfs the mass of the particle making it up. In a potential that rises slower than $U(1)$-invariant $|phi|^2$ the answer is yes: the interior field grows as the charge to the one-quarter power, so a soliton carrying enormous charge sits at a field value many orders of magnitude above the scalar mass. Models with low-energy supersymmetry breaking supply both ingredients, scalars with global charges and nearly flat directions in the potential, so the authors argue the Q-ball interior becomes a laboratory for physics far above the TeV scale without a bigger accelerator. Inside such a soliton the electroweak symmetry can be restored and quarks need not be confined, so processes forbidden or hopelessly suppressed in vacuum — above all baryon-number-violating ones — can proceed at a rate set by the large interior field. The paper closes with an engineering fantasy that follows from the physics: a Q-ball placed in water would break protons apart and release their energy, so a soliton of charge $10^{40}$, a few microns across and weighing about a hundred tons, could in principle deliver the output of an industrial power plant.

What carries the argument

The load-bearing object is the Q-ball itself: a non-topological soliton, a lump of complex scalar field rotating in its internal $U(1)$ phase as $phi(x,t) = e^{iomega t} phi(r)$, which is the minimum of energy at fixed global charge. Its profile solves a three-dimensional bounce equation in the shifted potential $hat{U}_omega(phi) = U(phi) - (omega^2/2)phi^2$. In the thin-wall limit the interior field sits where $U(phi)/phi^2$ is minimized; in the thick-wall limit that logic breaks and the dimensionless rescaling $xi = omega x$, $psi = phi/omega$ delivers the $Q^{1/4}$ field growth and $Q^{3/4}$ energy growth. The paper's second piece of machinery is the flat direction of a softly broken supersymmetric potential, lifted at low field values by soft masses and switched off at scales above the messenger scale, which is what allows the interior field to slide out to large values at all.

Extended reading notes

Core claim

The central claim is a scaling law with a practical corollary. For a Q-ball in a potential that grows slower than $|phi|^2$, the thin-wall approximation fails no matter how large the charge, and the soliton never settles at a fixed interior field value. Rewriting the energy functional in dimensionless variables and keeping only the constant and $-|omega|^2|phi|^2/2$ terms gives $E_{omega} approx a,omega + b/omega^3 + omega Q$, whose minimization yields $omega propto Q^{-1/4}$; since the soliton radius is of order $1/omega$, the field in the interior scales as $phi_0 propto Q^{1/4}$ while the total energy scales as $Q^{3/4}$ rather than $Q$. The authors take this to mean that the interior of a sufficiently charged soliton is a region of field strength inaccessible to any planned collider, and that couplings suppressed by powers of $langle phi rangle / M_{rm new}$ in the ordinary vacuum become order-one there. They then argue that in supersymmetric extensions of the Standard Model the required flat directions and charged scalars are generic, that the interior can have restored $SU(2)$ and no quark confinement, and that the resulting catalysis of baryon-number violation makes a large Q-ball an energy source rather than merely an experimental tool.

Load-bearing premise

The flat direction must remain unlifted all the way out to the field values the proposal needs; the paper itself concedes that Planck-suppressed operators are expected to modify the potential near the Planck scale and that other minima in that region are simply ignored, and it puts the actual assembly and feeding of a macroscopic Q-ball outside its scope.

Editorial extensions

If this is right

A Q-ball's interior field scales as the fourth root of its charge, so reaching an intermediate scale of order $10^8$ GeV would need a charge of roughly $10^{23}$, while reaching the grand-unification scale would need about $10^{56}$ and a soliton mass near $10^{20}$ g.
Because the energy grows as $Q^{3/4}$, storing charge in the largest available soliton is energetically favored over many small ones, which shapes any attempt to build one.
Inside a large soliton built from $SU(2)$-nonsinglet scalars the running of couplings freezes at the scale of the interior field, the negative top-Yukawa contribution to the Higgs mass shrinks, and electroweak symmetry can be restored, leaving sphaleron transitions unsuppressed.
A large interior field turns vacuum-suppressed baryon-number-violating operators into unsuppressed ones, so an incoming proton can dissociate, be converted to a lepton by sphaleron processes, or scatter off the soliton boundary as a lepton.
Catalyzed proton decay scales with the soliton's surface area, so an industrial output near $10^8$ W could come either from one soliton of charge $10^{40}$ a few microns across or from about $10^{17}$ solitons of charge $10^6$ each.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The proposal turns the usual logic of high-energy physics sideways: instead of raising the beam energy to probe short distances, one accumulates global charge to raise a field value in a macroscopic object, which suggests that the practical limits are set by charge storage and soliton lifetime rather than by accelerator circumference.
If the scaling law holds, the same mechanism gives a handle on flat directions themselves: the maximum interior field a soliton reaches before the potential is lifted would measure where new operators, including gravitational ones, first appear, making Q-balls a probe of Planck-suppressed physics rather than only of grand unification.
The surface-area scaling of the catalysis rate means the power output per unit stored charge improves as solitons are made smaller, so the interesting regime is bounded below by whatever charge is needed for the interior field to exceed the threshold for the relevant symmetry restoration — a bound the paper flags but does not compute.
The evaporation channel the authors note for squark and slepton Q-balls, where light charged fermions carry away charge from the surface, is the natural competitor to the power-plant proposal: any soliton built from fields with light charged partners loses charge at a rate set by its area, so the choice of scalar is as much an engineering constraint as a model-building one.

Original abstract

Future experiments may discover new scalar particles with global charges and couplings that allow for solitonic states. If the effective potential has flat directions, the scalar VEV inside a large Q-ball can exceed the particle mass by many orders of magnitude. Models with low-energy supersymmetry breaking generically have both the scalars carrying some global charges, and the flat directions. The Q-ball interior can, therefore, provide an environment for exploring physics far beyond the TeV scale without the need for building colliders of ever-increasing energies. Some Standard Model processes, otherwise strongly suppressed, can also be studied inside the soliton, where the SU(2) symmetry can be restored, and the quark confinement may be absent. Baryon number violating processes catalyzed by the large VEV inside the Q-ball can provide an inexhaustible energy resource.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,906 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Future experiments may discover new scalar particles with global charges and couplings that allow for solitonic states. If the effective potential has flat directions, the scalar VEV inside a large Q-ball can exceed the particle mass by many orders of magnitude. Models with low-energy supersymmetry breaking generically have both the scalars carrying some global charges, and the flat directions. The Q-ball interior can, therefore, provide an environment for exploring physics far beyond the TeV scale without the need for building colliders of ever-increasing energies. Some Standard Model processes, otherwise strongly suppressed, can also be studied inside the soliton, where the SU(2) symmetry can be restored, and the quark confinement may be absent. Baryon number violating processes catalyzed by the large VEV inside the Q-ball can provide an inexhaustible energy resource.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Future experiments may discover new scalar particles with global charges and couplings that allow for solitonic states.	background 0.92	0.04	0.06	hedged possibility 1.00
s1	If the effective potential has flat directions, the scalar VEV inside a large Q-ball can exceed the particle mass by many orders of magnitude.	result 0.52	0.14	0.09	asserted 0.69
s2	Models with low-energy supersymmetry breaking generically have both the scalars carrying some global charges, and the flat directions.	background 0.93	0.09	0.07	asserted 0.88
s3	The Q-ball interior can, therefore, provide an environment for exploring physics far beyond the TeV scale without the need for building colliders of ever-increasing energies.	interpretation 0.98	0.11	0.50	hedged possibility 0.81
s4	Some Standard Model processes, otherwise strongly suppressed, can also be studied inside the soliton, where the SU(2) symmetry can be restored, and the quark confinement may be absent.	interpretation 0.67	0.09	0.07	hedged possibility 0.96
s5	Baryon number violating processes catalyzed by the large VEV inside the Q-ball can provide an inexhaustible energy resource.	interpretation 0.92	0.10	0.62	hedged possibility 0.71

What kind of paper the classifier reports this is: position or commentary 0.84 · evidence from argument 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** A potential with a flat direction lifted only by logarithmic corr

**Figure 2.** Supersymmetry breaking in the hidden sector can be comm

Figures reproduced from arXiv:hep-ph/9707423 by the authors.

References

Works cited (14)

[4]

A. Kusenko, Phys. Lett. B404 (1997) 285

View on Pith 1997
[5]

A. D. Linde, Nucl. Phys. B216 (1983) 421

View on Pith 1983
[1]

T. D. Lee and Y. Pang, Phys. Rep. 221 (1992) 251, and referen ces therein

View on Pith 1992
[2]

S. Coleman, Nucl. Phys. B262 (1985) 263

View on Pith 1985
[3]

For review, see, e. g., S. Dimopoulos, M. Dine, S. Raby, S. Thomas, J. D. Wells, Nucl. Phys. Proc. Suppl. A52 (1997) 38, and references therein

View on Pith 1997
[6]

A. Kusenko, Phys. Lett. B405 (1997) 108

View on Pith 1997
[7]

A. Kusenko, Phys. Lett. B, in press (hep-ph/9705361)

View on Pith Pith review arXiv
[8]

A. Cohen, S. Coleman, H. Georgi and A. Manohar, Nucl. Phys. B272 (1986) 301

View on Pith 1986
[9]

G. R. Dvali, Phys. Lett. B287 (1992) 101; ibid. B372 (1996) 113

View on Pith 1992
[10]

V. A. Kuzmin and M. E. Shaposhnikov, Nuovo Cim. 82A (1984) 35; E. Nardi and E. Roulet, Phys. Lett. B245 (1990) 105

View on Pith 1984
[11]

A. De R´ ujula, S. L. Glashow and U. Sarid, Nucl. Phys. B333 (1990) 173

View on Pith 1990
[12]

S. Yu. Khlebnikov and M. E. Shaposhnikov, Phys. Lett. B180 (1986) 93, Sov. J. Nucl. Phys. 45 (1987) 747

View on Pith 1986
[13]

V. A. Rubakov, JETP Lett. 33 (1981) 644, Nucl. Phys. B203 (1982) 311; C. G. Callan, Phys. Rev. D25 (1982) 2141

View on Pith 1981
[14]

F. A. Bais, J. Ellis, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B116 (1982) 127; Nucl. Phys. B219 (1983) 189. 13

View on Pith 1982

Forward citations

Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Primordial black holes from supersymmetry in the early universe
astro-ph.CO 2016-12 conditional novelty 7.0 of 10

Poisson fluctuations in the number density of Q-balls formed from a supersymmetric scalar condensate can seed primordial black holes that make up all or part of the dark matter.
GUT Color-Triplet Around the Corner: The Story of an Overlooked Lightness
hep-ph 2026-11 accept novelty 6.0 of 10

Color-triplet Higgs partners can be light (TeV) in supersymmetric SO(10) GUTs due to Yukawa coupling suppression from supersymmetry breaking, leading to lifetimes from seconds to longer than the universe's age.
Reviving the Affleck-Dine Curvaton Scenario with Compensated Isocurvature Perturbations
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

The Affleck-Dine field can act as both baryogenesis engine and curvaton if gravitino dark matter, produced before curvaton decay, supplies the compensating isocurvature perturbation that hides the baryon isocurvature ...
Electroweak Symmetric Dark Matter Balls
hep-ph 2019-06 conditional novelty 6.0 of 10

A Higgs-portal complex scalar dark matter model admits non-topological soliton dark matter balls with electroweak-symmetric interiors, geometric nuclear cross sections, and a possible first-order-phase-transition origin.
Affleck-Dine dynamics and the dark sector of pangenesis
hep-ph 2012-01 conditional novelty 6.0 of 10

Pangenesis, in which Affleck-Dine dynamics generates the visible and dark matter asymmetries jointly, has viable parameter regions under both gravity- and gauge-mediated supersymmetry breaking, and admits a dark secto...

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hep-th 2024-05 conditional novelty 5.0 of 10

Information stored in a black hole resists its evaporation, so light primordial black holes can survive as dark matter and should show a spread of final masses set by how much information each one carried.
Big Bang Nucleosynthesis constraints on sterile neutrino and lepton asymmetry of the Universe
hep-ph 2020-05 accept novelty 5.0 of 10

Big bang nucleosynthesis excludes 150 to 450 MeV sterile neutrinos mixing with the electron neutrino, except in a window where a lepton asymmetry of order 0.1 relaxes the helium bound and gives an effective neutrino n...
Analytic Description of Primordial Black Hole Formation from Scalar Field Fragmentation
astro-ph.CO 2019-07 conditional novelty 5.0 of 10

A general analytic framework shows that scalar field fragmentation into solitons can produce primordial black holes during a temporary matter-dominated era, with peak masses that can fall in the dark matter window for...
Numerical study of Q-ball formation in gravity mediation
hep-ph 2010-03 conditional novelty 5.0 of 10

Three-dimensional lattice simulations with cosmic expansion place the peak Q-ball charge at 1.9e-2 (|Phi_in|/m)^2, about 60 percent above the 2000 estimate, and trace that peak to the intersections of a filamentary structure.
Non-thermal dark matter via Affleck-Dine baryogenesis and its detection possibility
hep-ph 2002-05 conditional novelty 5.0 of 10

Late Q-ball decays from Affleck-Dine baryogenesis yield the observed dark matter density only if the lightest supersymmetric particle is higgsino- or wino-like, and the authors map the SUSY parameter regions where thi...
Primordial black holes from scalar field evolution in the early universe
astro-ph.CO 2017-06 conditional novelty 4.0 of 10

Q-ball number-density fluctuations during an early matter-dominated era can produce primordial black holes spanning many decades of mass, including LIGO-relevant 1-100 solar masses, for suitable choices of four model ...
Non-topological solitons and quasi-solitons
hep-th 2024-11 accept novelty 2.0 of 10

A comprehensive review of non-topological solitons (Q-balls) and quasi-solitons (oscillons), their properties, dynamics, and roles in early-universe physics.
Review of non-topological solitons in theories with $U(1)$-symmetry
hep-th 2019-05 accept novelty 2.0 of 10

The review maps the known non-topological solitons in U(1)-symmetric scalar theories and summarizes when each type exists and is stable.

How the literature uses it

33 arXiv papers cite this in 57 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 28 sentences without a confident label

Builds on it 1 paper

We will generalise the results of [ref] to an arbitrary number of spatial dimensions and show that the known $Q$-ball profiles in [ref] are naturally recovered by our more general ansatz.

Q-balls in flat potentials · Gauge-mediated potential · 1.00

Uses its method or tool 1 paper

Since the potential in Eq. [ref] is shallow, and almost determined by $V_0$, we resort to the approximation $V(ρ) ≈V_0$ Following Ref. [ref] , we redefine the coordinates $ξ= ωx$ and $σ= ρ/ω$.

A Unified Fermionic Origin for Density-Driven Waterfall Inflation and its Multi-Messenger Signatures · Q-balls from inflaton fragmentation · 0.95

Uses its data or values 2 papers

For a flat direction lifted by gauge-mediated supersymmetry breaking, $α= 3/4$ and $γ= 1/4$ [ref] .

Testing high scale supersymmetry via second order gravitational waves · SUSY Background & Q ball formation · 0.99
For flat direction lifted by gauge-mediated supersymmetry breaking, $α= 3/4$ and $β= 1/4$ [ref] .

Primordial black holes as a dark matter candidate in theories with supersymmetry and inflation · Introduction · 0.97

Compares with it 4 papers

Q-balls that are formed from the gap field share a similar profile to those ones generated by supersymmetric scalar fields, as discussed in Refs. [ref] .

A Unified Fermionic Origin for Density-Driven Waterfall Inflation and its Multi-Messenger Signatures · Q-balls from inflaton fragmentation · 0.84
The characteristic slope follows gauthnch E_Q/ωQ≃D+1/D from which we see immediately from leg2 that we recover the published results of [ref] , namely $E∝Q^D/(D+1)$.

Q-balls in flat potentials · Thin-wall-like limit for $R, ωR ≫1$ · 0.98
For small $ω$, we have [equation] and [equation] While the general scaling with $ω$ agrees with the literature [ref] we provide prefactors and higher-order corrections here.

The Tunneling Potential Approach to Q-Balls · Large Q-Balls in Flat Potentials · 0.87

Cites it as background 16 papers

Another important consequence of the AD mechanism is the formation of Q-balls [ref] .

Lepton Asymmetric Universe · Lepton asymmetry from L-ball · 0.84
Furthermore, we take into account Q-ball formation [ref] , which generically accompanies the Affleck-Dine mechanism and plays an essential role in the cosmological evolution of the AD field [ref] .

Reviving the Affleck-Dine Curvaton Scenario with Compensated Isocurvature Perturbations · Introduction · 0.91
The AD mechanism is preceded [ref] by the formation of non-topological solitons, called Q-balls [ref] .

Baryon Asymmetric Universe from Spontaneous CP Violation · Introduction · 0.80

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.

[1] [4]

A. Kusenko, Phys. Lett. B404 (1997) 285

View on Pith 1997

[2] [5]

A. D. Linde, Nucl. Phys. B216 (1983) 421

View on Pith 1983

[3] [1]

T. D. Lee and Y. Pang, Phys. Rep. 221 (1992) 251, and referen ces therein

View on Pith 1992

[4] [2]

S. Coleman, Nucl. Phys. B262 (1985) 263

View on Pith 1985

[5] [3]

For review, see, e. g., S. Dimopoulos, M. Dine, S. Raby, S. Thomas, J. D. Wells, Nucl. Phys. Proc. Suppl. A52 (1997) 38, and references therein

View on Pith 1997

[6] [6]

A. Kusenko, Phys. Lett. B405 (1997) 108

View on Pith 1997

[7] [7]

A. Kusenko, Phys. Lett. B, in press (hep-ph/9705361)

View on Pith Pith review arXiv

[8] [8]

A. Cohen, S. Coleman, H. Georgi and A. Manohar, Nucl. Phys. B272 (1986) 301

View on Pith 1986

[9] [9]

G. R. Dvali, Phys. Lett. B287 (1992) 101; ibid. B372 (1996) 113

View on Pith 1992

[10] [10]

V. A. Kuzmin and M. E. Shaposhnikov, Nuovo Cim. 82A (1984) 35; E. Nardi and E. Roulet, Phys. Lett. B245 (1990) 105

View on Pith 1984

[11] [11]

A. De R´ ujula, S. L. Glashow and U. Sarid, Nucl. Phys. B333 (1990) 173

View on Pith 1990

[12] [12]

S. Yu. Khlebnikov and M. E. Shaposhnikov, Phys. Lett. B180 (1986) 93, Sov. J. Nucl. Phys. 45 (1987) 747

View on Pith 1986

[13] [13]

V. A. Rubakov, JETP Lett. 33 (1981) 644, Nucl. Phys. B203 (1982) 311; C. G. Callan, Phys. Rev. D25 (1982) 2141

View on Pith 1981

[14] [14]

F. A. Bais, J. Ellis, D. V. Nanopoulos and K. A. Olive, Phys. Lett. B116 (1982) 127; Nucl. Phys. B219 (1983) 189. 13

View on Pith 1982