Angular Distribution and CP Asymmetries in the Decays B->K^-pi^+e^-e^+ and B->pi^-pi^+e^-e^+

F. Kr\"uger; L. M. Sehgal; N. Sinha; R. Sinha

REVIEW

Angular Distribution and CP Asymmetries in the Decays B->K^-pi^+e^-e^+ and B->pi^-pi^+e^-e^+

F. Krüger, L. M. Sehgal, N. Sinha, R. Sinha

High Energy Physics - Phenomenology · Submitted 16 Jul 1999 · 14 references

Pith's verdict: A clean, checkable Standard Model angular template for four-body rare B decays; the physics payoff is small and the tables are quoted with more precision than the inputs support.

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arXiv IDhep-ph/9907386 (version 3)

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CitationF. Kr\"uger, L. M. Sehgal, N. Sinha, R. Sinha. "Angular Distribution and CP Asymmetries in the Decays B->K^-pi^+e^-e^+ and B->pi^-pi^+e^-e^+." arXiv:hep-ph/9907386 (1999). https://pith.science/paper/GP3MYRZF

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This is the paper that gives you the full angular decomposition for B̄ → K⁻π⁺e⁻e⁺ and B̄ → π⁻π⁺e⁻e⁺, and that is the reason to keep it. The prior work by two of the same authors covered only sl and cosθl. Here you get the cosθP distribution (Eq. 4.1), the lepton-meson plane correlation in φ (Eq. 4.7), and the complete nine-term rate in Eqs. (3.7)-(3.9) with every I_i written out in Appendix B. The mapping onto transversity amplitudes in Eq. (3.11) is a relabelling, not new physics, but it is the relabelling experimentalists actually use, so it earns its place. Appendix A gives the form factors with explicit coefficients, so an independent group can reimplement this without guessing. That is real, reproducible work and it is why the paper gets cited. The CP asymmetries in Eq. (5.9) and Table III are a genuine extension, and the authors are upfront that they come out at 10⁻⁴ for K* and 1-2% for ρ — no overselling there. On the stress-test worry about the narrow-width ansatz: the authors flag it themselves in the Conclusions, and the δ-function in Eq. (2.11) collapses the sP integral, so the tables are on-peak numbers, not integrals over the whole region of Eq. (3.10a). The concern is real for an experimental extraction but it is not hidden, and the stress test slightly overstates how the tables are presented. Where I would push back on the paper: Tables I-III quote two and three significant figures with no form-factor uncertainty, no estimate of the dropped c3-c6 terms, and no sensitivity band. The vanishing of K4, K5, K7, K8 is asserted rather than shown from the I_i, which a reader can check but shouldn't have to. And the form factors come from Melikhov-Nikitin, hep-ph/9609503, which as far as I can tell was never published in a journal — worth a cross-check against a second form-factor set before anyone treats Table III as quantitative. None of this touches the angular template, which is the actual contribution. For anyone doing angular analyses of b → sℓℓ four-body finals, or thinking about polarization handles on K* and ρ, this is a useful reference. Send it out.

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Major objections (2)

[§II, Eq. (2.11), and §VI] The narrow-width approximation |D_V(k²)|² = 48π²β³M_V²δ(k²−M_V²) is applied to both K* and ρ, but Γ_ρ/M_ρ ≈ 0.19, so the δ-function is marginal for the ρ. The pure p-wave structure that produces the sin²θP/cos²θP form of Eq. (4.1) and the vanishing A_P^FB depends on this approximation. The authors acknowledge the continuum region in §VI, but no estimate is given of how much the angular coefficients J_i, K_i, and the asymmetries ⟨A_k⟩ shift when the δ-function is replaced by a finite-width Breit-Wigner. A concrete test would be to repeat the integrals of Eqs. (4.2) and (4.5) with a Breit-Wigner smearing over s_P and report the shift, or at least to state the fraction of the integrated rate that falls within ±Γ_V of the peak.
[Tables I–III] The coefficients and asymmetries are quoted to two or three significant figures with no uncertainty. The inputs carry non-negligible uncertainties: the Melikhov-Nikitin Set 2 form factors, the scale and quark-mass dependence of c_9^eff (Eq. 2.4), and the CKM parameters ρ = 0.19, η = 0.35 (Ref. [12]). For the K* channel the asymmetries are at the 10⁻⁴ level, so a 20–30% form-factor or CKM uncertainty is comparable to the central values. Since the paper's conclusion is that 'any significant effect would signal a non-standard source of CP violation,' the reader needs to know the Standard Model uncertainty band. Please quote ranges for at least ⟨A_CP⟩, ⟨A_5⟩, and ⟨A_6⟩, and state which input dominates.

Minor objections (8)

[§IV.B, Eq. (4.5)] The sentence 'Observe that K4, K5, K7, and K8 vanish in our model' is imprecise: these vanish identically because I4, I5, I7, I8 ∝ sin2θP and ∫_{-1}^{1} sin2θP dcosθP = 0, independent of the model. The corresponding CP asymmetries ⟨A4⟩, ⟨A5⟩, ⟨A7⟩, ⟨A8⟩ are defined with the forward-backward-weighted K^D (Eq. 5.8), which do not vanish; the text should make this distinction explicit.
[Table III, ⟨A7⟩] Eq. (B7) gives I7 ∝ Im(y_L* z'_L − y_R* z'_R), which is nonzero for real form factors and complex c_9^eff. Please state whether the zero in Table III is an exact cancellation (and if so, why) or numerical round-off.
[Eq. (3.10a) and Eq. (2.11)] The stated region (M_P+M_P′)² ≤ s_P ≤ M_B² is the full physical region, but with the δ-function the rate is evaluated at s_P = M_V². The integrals in Eqs. (4.2) and (4.5) should show the δ-function explicitly so the reader knows the tables are resonance-peak values rather than integrals over the full s_P range.
[§I and §II] The formalism is written for l = e, μ, but m_l = 0 is assumed throughout and the numerical results are for electrons. Please state explicitly that the muon case requires retaining m_l, or restrict the stated applicability to electrons.
[Eqs. (3.11)–(3.12)] The identity Γ = |A0|² + |A‖|² + |A⊥|² is asserted. A one-line demonstration, or a check that the integrated rate from Eq. (3.7) reproduces it, would strengthen the correspondence with the transversity notation.
[§V] The claim that ⟨A5⟩, ⟨A6⟩, ⟨A8⟩, ⟨A9⟩ can be measured with an untagged sample is correct in principle, but given the 10⁻⁴–10⁻² sizes a sentence on the required number of B B̄ events would help the reader judge feasibility.
[References] Ref. [12] lists the Ali-London paper as 'to appear in Eur. Phys. J. C'; please update the reference status. Also 'P. Rodeau' should read 'P. Roudeau,' and 'Maksymovicz' in Ref. [5] should read 'Maksymowicz.'
[Eq. (2.19)] The left-hand side should carry the bar (M̄_SD) to match the conjugate amplitude being defined.

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The paper

The paper claims

The paper works out the full angular shape of the four-body decays $B^-$→$K^-π^+e^-e^+$ and $B$→$π^-π^+e^-e^+$, treating the meson pair as a $K^*$ or $ρ$ resonance, and derives the CP-violating asymmetries that comparing these decays with $

The reading

The paper asks what the standard-model Hamiltonian for $b → s(d)e^-e^+$ predicts for the *shape* of the four-body decays $B$→$K^-π^+e^-e^+$ and $B$→$π^-π^+e^-e^+$, not just for their total rate. Earlier treatments of $B$→$K^*e^-e^+$ and $B$→$ρe^-e^+$ kept only the dilepton mass and the electron angle; this paper adds the angle of the kaon (or pion) inside the meson pair and the angle between the meson and lepton planes. Those two extra variables carry information about how the vector meson is polarized, so they probe the same short-distance coefficients $c_7$, $c_9$, $c_{10}$ through a different window. The authors then combine each decay with its charge-conjugate partner to build asymmetries that isolate the CP-violating phase hiding in the coefficient $c_9$. A reader should care because the result is a complete template: if the standard model is right, every angular coefficient is fixed, so any measured departure is a clean signal of new physics — and the same formalism can be reused for whatever Hamiltonian replaces the standard one.

What carries the argument

The load-bearing device is the angular decomposition of the squared matrix element into the nine functions $I_k$, built from three complex amplitudes per chirality, $F_{1L,R}$, $F_{2L,R}$, $F_{3L,R}$, which are the analogues of the transversity amplitudes $A_0$, $A_‖$, $A_⊥$ used for $B$→$V_1V_2$. Each $F$ is a known combination of the Wilson coefficients $c_7^{eff}$, $c_9^{eff}$, $c_{10}$ and the $B$→$K^*$ or $B$→$ρ$ form factors $g$, $f$, $h$, $g_±$, $a_+$, so the whole angular shape is predicted once those inputs are fixed. The narrow-width step, $|D_V(k^2)|^2 = 48π^2β^3M_V^2δ(k^2-M_V^2)$, is what forces the meson pair into a pure p-wave and produces the symmetric $cos θ_P$ distribution.

Extended reading notes

Core claim

Assuming the $Kπ$ and $ππ$ pairs come from narrow $K^*$ and $ρ$ resonances, the authors reduce the hadronic side of the decay to $B$→$V$ form factors and obtain a five-variable differential rate whose angular dependence collapses into nine coefficient functions $I_1$ through $I_9$, multiplied by $1$, $cos 2θ_l$, $sin^2θ_l cos 2φ$, $sin 2θ_l cos φ$, $sin θ_l cos φ$, $cos θ_l$, $sin θ_l sin φ$, $sin 2θ_l sin φ$, and $sin^2θ_l sin 2φ$. Integrating out the other variables gives three one-dimensional distributions: in $cos θ_P$ the rate is a pure $sin^2θ_P$/$cos^2θ_P$ combination with no linear term, so the forward-backward asymmetry of the kaon (or pion) in the meson-pair rest frame vanishes identically; in $cos θ_l$ the lepton forward-backward asymmetry comes out at $-0.19$ for $π^-π^+$ and $-0.16$ for $K^-π^+$, reproducing earlier exclusive-channel results; and in $φ$ the distribution is a simple $cos 2φ$ plus $sin 2φ$ form. Combining $B$ and $B$ decays yields eight asymmetries $⟨A_{CP}⟩$ and $⟨A_{3..9}⟩$, several of which need only the untagged sum of the two spectra. Numerically the asymmetries are tiny — of order $10^{-4}$ for $K^*$ and $1$–$2$ percent for $ρ$ — which the authors present as a standard-model baseline rather than a discovery.

Load-bearing premise

The hadronic part of the decay is assumed to factorize into $B$→$K^*$ or $B$→$ρ$ form factors times a narrow-width Breit-Wigner, which forces the meson pair into a pure p-wave and is what makes the clean angular template and its vanishing $cos θ_P$ asymmetry hold.

Editorial extensions

If this is right

A measurement of the $cos θ_P$ distribution in the $K^*$ or $ρ$ region should show the predicted $sin^2θ_P$/$cos^2θ_P$ form with zero forward-backward asymmetry; a nonzero asymmetry would mean contributions beyond the single-resonance p-wave picture.
The $φ$ distribution between the meson and lepton planes is predicted to be $cos 2φ$ plus $sin 2φ$ only, giving an independent handle on the vector-meson polarization that does not require tagging the initial $B$ flavour.
The lepton forward-backward asymmetries, $-0.16$ for $K^-π^+$ and $-0.19$ for $π^-π^+$, are fixed numbers that any future measurement of these four-body channels can check against.
The CP asymmetries $⟨A_{CP}⟩$, $⟨A_5⟩$, and $⟨A_6⟩$ should reach the $1$–$2$ percent level for $B$→$ρe^-e^+$ but stay near $10^{-4}$ for $B$→$K^*e^-e^+$; a large effect in the $K^*$ channel would point to a non-standard CP source.
Because the asymmetries $⟨A_5⟩$, $⟨A_6⟩$, $⟨A_8⟩$, $⟨A_9⟩$ are built from the untagged sum of $B$ and $B$ spectra, they can in principle be extracted from an equal mixture of mesons and antimesons.

Reading between the lines

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

The same nine-function template can be read backwards: fitting the measured angular coefficients to the $c_7$, $c_9$, $c_{10}$ dependence is effectively a determination of short-distance Wilson coefficients from angular data alone, complementary to the rate-based extractions.
The vanishing forward-backward asymmetry in $cos θ_P$ is a sharp diagnostic rather than a null result — measuring it away from zero in the resonance region would directly quantify s-wave or interference contamination, giving an experimental handle on how far off-peak the narrow-width treatment can be pushed.
Because the CP asymmetries scale with the imaginary part of $V_{ub}V_{uf}^*$, the $ρ$ channel's percent-level asymmetries are the more accessible standard-model target, while the $K^*$ channel is better suited as a null test where any sizeable signal is new physics.
Extending the analysis below the resonance, where several partial waves overlap, would require keeping the full $Kπ$ or $ππ$ angular moments rather than a single Breit-Wigner; the machinery here suggests those moments are the natural place to look for the larger asymmetries the authors mention.

Original abstract

The short-distance Hamiltonian describing b->s(d)e^-e^+ in the standard model is used to obtain the decay spectrum of \bar{B}->K^-pi^+e^-e^+ and \bar{B}->pi^-pi^+e^-e^+, assuming the Kpi and pipi systems to be the decay products of K^* and rho respectively. Specific features calculated are (i) angular distribution of K^- (or pi^-) in the K^-pi^+ (or pi^-pi^+) centre-of-mass (c.m.) frame; (ii) angular distribution of e^- in the e^-e^+ c.m. frame; and (iii) the correlation between the meson and lepton planes. We also derive CP-violating observables obtained by combining the above decays with the conjugate processes B->K^+pi^-e^-e^+ and B->pi^-pi^+e^-e^+.

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The short-distance Hamiltonian describing b->s(d)e^-e^+ in the standard model is used to obtain the decay spectrum of \bar{B}->K^-pi^+e^-e^+ and \bar{B}->pi^-pi^+e^-e^+, assuming the Kpi and pipi systems to be the decay products of K^* and rho respectively. Specific features calculated are (i) angular distribution of K^- (or pi^-) in the K^-pi^+ (or pi^-pi^+) centre-of-mass (c.m.) frame; (ii) angular distribution of e^- in the e^-e^+ c.m. frame; and (iii) the correlation between the meson and lepton planes. We also derive CP-violating observables obtained by combining the above decays with the conjugate processes B->K^+pi^-e^-e^+ and B->pi^-pi^+e^-e^+.

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s0	The short-distance Hamiltonian describing b->s(d)e^-e^+ in the standard model is used to obtain the decay spectrum of \bar{B}->K^-pi^+e^-e^+ and \bar{B}->pi^-pi^+e^-e^+, assuming the Kpi and pipi systems to be the decay products of K^* and rho respectively.	method 0.74	0.71	0.09	asserted 1.00
s1	Specific features calculated are (i) angular distribution of K^- (or pi^-) in the K^-pi^+ (or pi^-pi^+) centre-of-mass (c.m.) frame; (ii) angular distribution of e^- in the e^-e^+ c.m. frame; and (iii) the correlation between the meson and lepton planes.	contribution 0.86	0.89	0.06	asserted 0.98
s2	We also derive CP-violating observables obtained by combining the above decays with the conjugate processes B->K^+pi^-e^-e^+ and B->pi^-pi^+e^-e^+.	contribution 0.92	0.94	0.13	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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References

Works cited (14)

[12]

F. Parodi, P. Rodeau, and A. Stocchi, hep-ex/9903063; A. Ali and D. London, hep- ph/9903535 (to appear in Eur. Phys. J. C)

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[2]

F. Kr¨ uger and L. M. Sehgal,Phys. Rev. D56 (1997) 5452; ibid. D60 (1999) 099905 (E)

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[3]

L. M. Sehgal and M. Wanninger, Phys. Rev. D46 (1992) 1035; ibid. D46 (1992) 5209 (E); P. Heiliger and L. M. Sehgal, ibid. D48 (1993) 4146

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J. Adams et al. (KTeV Collaboration), Phys. Rev. Lett. 80 (1998) 4123; M. Arenton (KTeV Collaboration), talk given at the 1998 Workshop on Heavy Quarks at Fixed Target, Fermilab, Oct. 10-12, 1998 (to appear in the proceedings)

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N. Cabibbo and A. Maksymovicz, Phys. Rev. 137 (1965) B438; ibid. 168 (1968) 1926 (E); A. Pais and S. B. Treiman, ibid. 168 (1968) 1858

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[6]

J. Bijnens, G. Ecker, and J. Gasser, in The DA ΦNE Physics Handbook , edited by L. Maiani, G. Pancheri, and N. Paver (Servizio Documentazione dei Lab oratori Nazionali di Frascati, Frascati, Italy, 1992), Vol. I, p. 115

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A. J. Buras and M. M¨ unz, Phys. Rev. D52 (1995) 186; M. Misiak, Nucl. Phys. B393 (1993) 23; ibid. B439 (1995) 461 (E)

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For a review, see G. Buchalla, A. J. Buras, and M. E. Lautenbach er, Rev. Mod. Phys. 68 (1996) 1125

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D. Melikhov and N. Nikitin, hep-ph/9609503

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R. Sinha, hep-ph/9608314; N. Sinha and R. Sinha, hep-ph/970 7416. 18

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G. Kramer and W. F. Palmer, Phys. Rev. D45 (1992) 193; ibid. D46 (1992) 2969; G. Kramer, W. F. Palmer, and H. Simma, Nucl. Phys. B428 (1994) 77; A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B369 (1996) 144

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F. Kr¨ uger and L. M. Sehgal, hep-ph/9711301, Proceedings o f the International Eu- rophysics Conference on High-Energy Physics , Jerusalem, Israel, August 19-26, 1997, p. 745

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N. Isgur, D. Scora, B. Grinstein, and M. B. Wise, Phys. Rev. D39 (1989) 799; D. Scora and N. Isgur, Phys. Rev. D52 (1995) 2783. 19

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Bayesian Fit of Exclusive $b \to s \bar\ell\ell$ Decays: The Standard Model Operator Basis
hep-ph 2012-05 conditional novelty 5.0 of 10

A full Bayesian fit of the Wilson coefficients C7, C9 and C10 to exclusive rare B decays finds a Standard-Model-like and a sign-flipped solution with roughly equal posterior weight, and no evidence requiring new physics.
On transverse asymmetries in B --> K* l+l-
hep-ph 2011-06 accept novelty 5.0 of 10

A new transverse asymmetry A_T^(re) is defined for B to K* l+ l-, and the zero-crossing patterns of three independent asymmetries are shown to discriminate among new-physics scenarios in C7, C9, and C10.
More Benefits of Semileptonic Rare B Decays at Low Recoil: CP Violation
hep-ph 2011-05 accept novelty 5.0 of 10

At low hadronic recoil, CP asymmetries in B -> K* l+ l- and Bs -> phi l+ l- are Standard-Model null tests (order 10^-4) that current data allow to reach about 0.2, and several can be measured without flavor tagging.
The Benefits of B ---> K* l+ l- Decays at Low Recoil
hep-ph 2010-06 conditional novelty 5.0 of 10

Low-recoil B -> K* l+ l- data, analyzed in the Grinstein-Pirjol HQET framework, constrain the Wilson coefficients C9 and C10 more tightly than large-recoil data and admit both Standard Model and beyond-Standard-Model ...
Status of the $B\to K^*\mu^+\mu^-$ anomaly after Moriond 2017
hep-ph 2017-03 accept novelty 4.0 of 10

Combining updated LHCb, ATLAS and CMS data, the b to s mu mu anomalies remain at 5.2 sigma and are fit by a new-physics shift in C9 of about minus one, with no evidence for q-squared or helicity dependence.
On the LHCb anomaly in B -> K* l+ l-
hep-ph 2013-12 conditional novelty 4.0 of 10

Under the Minimal Flavour Violation hypothesis, the LHCb B to K* mu mu angular anomalies are compatible with data at the 2 sigma level without introducing new flavour structures.
Angular analysis and branching fraction measurement of the decay B0 to K*0 mu+ mu-
hep-ex 2013-08 accept novelty 4.0 of 10

CMS measures the muon forward-backward asymmetry, the K*0 longitudinal polarization, and the differential branching fraction of B0 to K*0 mu+ mu- across dimuon mass bins, finding agreement with standard-model predictions.
Implications of LHCb measurements and future prospects
hep-ex 2012-08 accept novelty 4.0 of 10

LHCb's first 1.0 fb^-1 of 7 TeV data already constrain several new-physics scenarios, and a proposed upgrade to 50 fb^-1 would sharpen those constraints by roughly an order of magnitude.
Supersymmetric constraints from Bs -> mu+mu- and B -> K* mu+mu- observables
hep-ph 2012-05 conditional novelty 4.0 of 10

Updated LHCb rare-decay data, especially the forward-backward asymmetry in B to K* mu+mu-, excludes light stops up to roughly 800 GeV in the CMSSM at tan(beta)=50, complementing direct searches.
New Physics in b -> s mu+ mu-: CP-Violating Observables
hep-ph 2011-03 conditional novelty 4.0 of 10

CP-violating observables in b -> s mu+ mu- decays respond almost exclusively to vector-axial vector new physics, with scalar and tensor operators contributing only at the sub-percent level.
Physics at Super B Factory
hep-ex 2004-06 conditional novelty 4.0 of 10

A SuperKEKB design report projects that a 40-fold luminosity increase over KEKB would enable percent-level tests of quark flavor physics and CP violation, with expected errors tabulated for many observables.
SuperB Progress Reports -- Physics
hep-ex 2010-08 accept novelty 3.0 of 10

The report argues that a 75 ab^-1 e+e- flavour factory could probe new physics at 10-100 TeV and discriminate among models through correlated rare-decay and CP measurements.
Rare $B$ Decays as Tests of the Standard Model
hep-ph 2016-06 accept novelty 1.0 of 10

Rare B meson decays give some of the tightest constraints on new physics, and global fits to b to s data show a coherent few-sigma tension best described by a shift in the Wilson coefficient C9.
Radiative and Electroweak Penguin Decays of B Mesons
hep-ph 2010-05 accept novelty 1.0 of 10

The review compiles Belle and BaBar measurements alongside NNLL and NLL Standard Model predictions for radiative and electroweak penguin B decays, finding agreement at the 1.2 sigma level and deriving strong constrain...

How the literature uses it

50 arXiv papers cite this in 77 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 · 59 sentences without a confident label

Builds on it 1 paper

The original analysis of the CP asymmetries of the rate $A_CP$ and the angular coefficients [ref] [equation] based on naive factorisation was extended using QCDF to the low-$q^2$ region by taking into account the NLO QCD corrections for the strong phase $δ_s$ [ref] .

Angular analysis of B --> V (--> P_1 P_2) l^+ l^- decays · Low-$q^2$ / Large recoil region · 0.88

Uses its method or tool 2 papers

We follow closely [ref] to which we refer for details on the full angular distribution [ref] .

More Benefits of Semileptonic Rare B Decays at Low Recoil: CP Violation · Untagged CP asymmetries with meson mixing · 0.86
In the narrow-width approximation, the $B̅^0→K^-π^+ μ^+μ^-$ decay amplitude can be written in terms of the $B̅^0→K̅^*0 μ^+μ^-$ decay amplitude as explained in Ref. [ref] .

Calculation of $B^0 \to K^{*0} \mu^+ \mu^-$ and $B_s^0 \to \phi \mu^+ \mu^-$ observables using form factors from lattice QCD · Introduction · 0.83

Cites it as background 13 papers

Detailed analyses of their NP sensitivity and discovery potential have been performed by various groups, both model-independently and within specific NP scenarios [ref] .

The birds and the Bs in RS: the b to s gamma penguin in a warped extra dimension · $B→K^0*(→πK)μ^+μ^-$ · 0.81
The differential decay rate of the meson, for a $Kπ$ system in a P-wave configuration and ignoring scalar contributions to the dimuon system, is given by [ref]

Method for an unbinned measurement of the $q^2$ dependent decay amplitudes of $\bar{B}^{0}\to \bar{K}^{*0}\mu^+\mu^-$ decays · The differential decay rate · 0.88
Recent research directions include optimizing the physics reach of the $B→K ℓ^+ ℓ^-$ [ref] and $B→K^*( →K π) ℓ^+ ℓ^-$ [ref] angular distributions and working out the physics reach at low recoil [ref] [ref] [ref] .

B -> K(*) l+ l- @ Low Recoil and Physics Implications · Introduction · 0.90

Discussion

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