REVIEW
A Comparative Study of the Decays $B \to (K,K^*) \ell^+ \ell^-$ in Standard Model and Supersymmetric Theories
High Energy Physics - Phenomenology · Submitted 4 Oct 1999 · 73 references
Pith's verdict: The real contribution is Eq. (4.32): the FB-asymmetry zero in B → K*ℓℓ becomes a form-factor-free relation between short-distance coefficients, and that is what later work picked up.
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Referee report
The paper
The paper claims
The dilepton forward-backward asymmetry in $B^*$ decays has a zero whose position barely depends on hadronic form factors, so measuring it tests the Standard Model against supersymmetry.
The reading
What carries the argument
The load-bearing device is the zero of the forward-backward asymmetry in $B^0$ into $K^*$ lepton pairs, defined as the dilepton invariant mass ${s}_0$ where $dA_{FB}/d{s}$ changes sign. The differential asymmetry is proportional to $C_{10}$ times a combination $Re(C_9^{eff}) V A_1 + hat m_b {s} C_7^{eff}[V T_2 (1-hat m_{K^*}) + A_1 T_1 (1+hat m_{K^*})]$, so its zero is set by a ratio of Wilson coefficients dressed by ratios of form factors. The large-energy relations make those form-factor ratios universal, which is what converts a hadronic nuisance into a short-distance observable. Supporting machinery: light-cone QCD sum rule form factors with radiative and twist-4 corrections, parametrized as $F({s}) = F(0) exp(c_1 {s} + c_2 {s}^2 + c_3 {s}^3)$ with central, maximum and minimum parameter sets; two treatments of the long-distance charm-loop contribution to $C_9^{eff}$, a Breit-Wigner resonance ansatz with fudge factors fitted to $B^0$ into $K^{(*)}$ charmonium data, and a dispersion relation built from hadronic cross-section data; and a table of coefficients expressing the partially integrated branching ratios and asymmetry as quadratics in $C_7^{eff}$, $C_9$ and $C_{10}$.
Extended reading notes
Core claim
The paper's central claim is that the forward-backward asymmetry in $B^0$ into $K^*$ lepton pairs is a precision test of the Standard Model, because its zero is nearly free of form-factor uncertainty. Using the large-energy effective theory relations $T_2/A_1 = (1+hat m_{K^*})/(1+hat m_{K^*}^2-{s}) (1-{s}/(1-{s}m_{K^*}^2))$ and $T_1/V = 1/(1+hat m_{K^*})$, the condition for the asymmetry to vanish collapses from a form-factor-dependent equation to $Re(C_9^{eff}({s}_0)) = -2 hat m_b {s}_0 C_7^{eff} (1-{s}_0)/(1+hat m_{K^*}^2-{s}_0)$. In the Standard Model with the stated inputs this gives ${s}_0 = 2.88^{+0.44}_{-0.28}$ GeV$^2$, with the form-factor error contributing only about one percent. The asymmetry also has a sharp qualitative signature: it vanishes below the charmonium resonances only if $C_7^{eff}$ and $Re(C_9^{eff})$ have opposite signs, as in the Standard Model and low-$tan beta$ supergravity, whereas the large-$tan beta$ supergravity solutions that survive the $B^0$ into $X_s$ photon bound flip the sign of $C_7^{eff}$ and leave the asymmetry negative with no zero at all. Alongside this, the authors use the $B^0$ into $X_s$ photon bound and the CDF upper limit on $B^0$ into $K^*$ dimuons to carve allowed regions in the $C_9$-$C_{10}$ plane, and find that the most aggressive flavor-violating supersymmetric enhancement scenarios are already excluded by those limits.
Load-bearing premise
The argument leans on the charm-loop contribution to the effective coefficient $C_9^{eff}$ being modeled well enough by the two competing prescriptions, and on the large-energy relations between form factors holding at the few-GeV dilepton masses where the asymmetry zero sits.
Editorial extensions
If this is right
- A measurement of the zero of the forward-backward asymmetry in $B^0$ into $K^*$ dimuons near 2.9 GeV$^2$ would confirm the Standard Model coefficient ratio, while a zero at a different mass or no zero at all below the charmonium resonances would point to a new-physics contribution to $C_7^{eff}$ or $C_9^{eff}$.
- The large-$tan beta$ supergravity solutions compatible with the $B^0$ into $X_s$ photon rate predict a positive $C_7^{eff}$, hence an asymmetry that stays negative below the $J/psi$ and dilepton spectra enhanced by up to a factor of two relative to the Standard Model, which the stated experimental reach should separate from the Standard Model band.
- The existing CDF upper limit on $B^0$ into $K^*$ dimuons already excludes the most aggressive flavor-violating supersymmetric enhancement points, so the $C_9$-$C_{10}$ plane is constrained by data rather than only by theory.
- The tabulated coefficients for partially integrated rates and asymmetry let any model specified by three real coefficients be checked against a forthcoming measurement without recomputing form factors.
- If the asymmetry zero behaves as predicted, the exclusive channel delivers short-distance information at a precision competitive with the inclusive $B^0$ into $X_s$ dilepton decay, where the analogous condition is $Re(C_9^{eff}({s}_0)) = -2{s}_0 C_7^{eff}$.
Reading between the lines
- Because the zero depends on the ratio $C_7^{eff}/Re(C_9^{eff})$ and on the quark mass rather than on hadronic details, a future lattice determination of the same form-factor ratios at low recoil would provide an independent cross-check of the large-energy relations, and any disagreement would shift the extracted coefficient ratio rather than merely widen an error bar.
- The same logic should transfer to $B_s$ into phi lepton pairs and to $B^0$ into $K^*$ tau pairs, with the caveat the authors note that the tau channel has no asymmetry zero by kinematics and that neutral Higgs exchange, neglected here, could matter there.
- If the asymmetry in the dimuon channel is measured to match the Standard Model, the remaining room in the $C_9$-$C_{10}$ plane will be squeezed mainly by the $B^0$ into $K^*$ dimuon rate, so the asymmetry and the rate together act as two nearly orthogonal constraints on the same two coefficients.
- The paper's treatment of the charmonium region means that a claimed sign flip of $C_{10}$, which reverses the asymmetry sign without touching the dilepton spectra, would be hardest to confirm precisely where the long-distance modeling is weakest, so a measurement of the asymmetry integrated only below the $J/psi$ would be the sharper discriminator.
Original abstract
Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM.
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
Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. | contribution 0.96 | 0.92 | 0.06 | asserted 0.93 |
| s1 | Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. | method 0.50 | 0.82 | 0.04 | asserted 0.99 |
| s2 | We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. | result 0.86 | 0.69 | 0.08 | asserted 0.88 |
| s3 | We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. | interpretation 0.98 | 0.37 | 0.57 | hedged possibility 0.80 |
| s4 | In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM. | result 0.93 | 0.73 | 0.30 | asserted 0.97 |
What was examined, and what was not
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Figures
Showing 9 of the paper's 12 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9910221 by the authors.
References
How later papers used it
95 later papers cite it
7 later papers by other authors are listed below: 1 built on it, 2 used its method or tool and 4 used its data or values. 1 more paper by the same authors is listed: 1 used its data or values.
Builds on it 1 of 2 papers with this label
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Updated this paper's expressions to include additional primed, scalar and pseudoscalar operators, as well as QCDF corrections.
Constraining new physics with B to K* mu+ mu- in the early LHC era (2010) · 0.94 · paraphrased: the licence does not allow quoting
Uses its method or tool 2 of 12 papers with this label
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Used the parametrization given in this paper for the tensor hadronic matrix element of the K to B transition.
Explaining the $B^+\to K^+ \nu \bar{\nu}$ excess via a massless dark photon (2024) · 0.85 · paraphrased: the licence does not allow quoting
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The angular and distributions of and decays are generated according to the SM, following the description in Ref. [ref] with form factors from Ref. [ref] .
Angular analysis of the $B^+\to\pi^+\mu^+\mu^-$ decay (2026) · Detector and simulation · 0.91
Uses its data or values 5 of 10 papers with this label · 1 by the same authors
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Used the form factors calculated in this paper in the framework of QCD light-cone sum rules in its numerical calculations.
New Physics in b -> s mu+ mu-: CP-Conserving Observables (2010) · 0.83 · paraphrased: the licence does not allow quoting
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Fixed the values of the phenomenological parameters from B to K* l+ l-, taking the J/Psi and Psi' resonance values from this paper.
Model Independent Analysis of the Forward-Backward Asymmetry for the $B\to K_{1}\mu^{+}\mu^{-}$ Decay (2010) · 1.00 · paraphrased: the licence does not allow quoting
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Took the parameters f(0), c1, c2 and c3 for each form factor from a table in this paper.
Large forward-backward asymmetry in B --> K mu+ mu- from new physics tensor operators (2008) · 0.83 · paraphrased: the licence does not allow quoting
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Used this paper's results for kappa_V obtained for the B to K* transition.
Lepton polarization in $B \to K_1 \ell^+ \ell^-$ Decays (2009) · 0.99 · paraphrased: the licence does not allow quoting
By the same authors
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Took the SM prediction of the branching ratios of inclusive B to X_s l l decays for q^2 > 0.04 from this paper.
$R_K$ and future $b \to s \ell \ell$ BSM opportunities (2014) (same authors) · 0.99 · paraphrased: the licence does not allow quoting
How the literature uses it
90 arXiv papers cite this in 158 sentences
Papers citing it · 95 sentences without a confident label
Builds on it 2 papers
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The auxiliary functions $A$-$I(q^2)$ follow [ref] ; however, we have updated the previous expressions to include additional primed, scalar, and pseudoscalar operators, as well as QCDF correction via $𝒯^(')NLO_∥(q^2)$ and $𝒯^(')NLO_⊥(q^2)$ as outlined in [ref].
Constraining new physics with B to K* mu+ mu- in the early LHC era · Decay Amplitude · 0.94
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The decay amplitude for $B→$ which is analogous to the $B→$ decay [ref] is given by [equation] where [equation] with $= p/m_B$, $_B = p_B/m_B$, $= q/m_B$ and $p = p_B + p_$, $q = p_B - p_= p_+ + p_-$.
K1(1270)-K1(1400) Mixing Angle and New-Physics Effects in B to K1 l+ l- Decays · $→ℓ^+ ℓ^-$ decays in the SM · 0.84
Uses its method or tool 12 papers
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Formulas are given in or are adapted from Refs. [ref] .
Model-independent analysis of $b\to d$ processes · Rare $b →d$ decay observables · 0.93
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For the tensor hadronic matrix element $⟨K^*|s̅ σ_μν b| B^0⟩$ we use again the parametrization provided in Ref. [ref] , which in the general case of $q^2≠0$ gives ⟨K^*() |[s̅σ_μνq^νb] |B^0()⟩ = i2ϵ_μναβ ε^†ν ^α^β T_1(s) + T_2(s)[ε^†_μ(^2-^2)- (ε^†·)(+)_μ] + T_3(s)(ε^†·)[q_μ- s/^2-^2(+)_μ] ,
Explaining the $B^+\to K^+ \nu \bar{\nu}$ excess via a massless dark photon · Decay width for $B^0→K^*$ · 0.82
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In exclusive decays the main job is to calculate the form factors, for our analysis we borrow the light cone QCD sum rules form factors (LCSR) [ref] .
Fourth-generation SM imprints in B -> K^*l^+l^- decays with polarized K^* · Introduction · 0.97
Uses its data or values 9 papers
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The form factors $f_+, 0, T$ were calculated in the framework of QCD light-cone sum rules in Ref. [ref] .
New Physics in b -> s mu+ mu-: CP-Conserving Observables · Details of the $$ analysis · 0.85
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Their $z$ dependence is given by [ref] [equation] where the parameters $f(0), c_1$, $c_2$ and $c_3$ for each form factor are given in Table [ref].
Large forward-backward asymmetry in B --> K mu+ mu- from new physics tensor operators · Forward-backward asymmetry of muons in $$ · 0.83
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Keeping in view that there is no experimental data on $B→K_1(1270)l^+l^-$, we have fixed the values of the phenomenological parameters $κ_i$ from $B→K^∗l^+l^-$, which for the resonances $J/Ψ$ and $Ψ^^'$ are taken to be $κ=1.65$ and $κ=2.36$, respectively [ref] .
Model Independent Analysis of the Forward-Backward Asymmetry for the $B\to K_{1}\mu^{+}\mu^{-}$ Decay · Effective Hamiltonian and Matrix Elements · 1.00
Compares with it 7 papers
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For comparison, the theoretical and experimental results also are presented , such as the PDG [ref] , HFLAV [ref] , HPQCD'13(22) [ref] , LCSR'00(06) [ref] , RQM'02 [ref] , BHDW'11 [ref] , PQCD'12 [ref] , MILC'15 [ref] , (Majorana neutrino exchange)MNE-18 [ref] , BaBar-08(12,16) [ref] , CDF-11 [ref] , Belle'02(09,19) [ref] , and LHCb'12(14C,16) [ref] .
The rare decay $B^+ \to K^+\ell^+\ell^-(\nu\bar{\nu})$ under the QCD sum rules approach · Numerical Analysis · 1.00
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Confining ourself to the SM, the above expression of the FB asymmetry in terms of the Wilson coefficients becomes [equation] which in agreement with the the one obtained for $B→K^∗l^+l^-$decay in [ref] .
Impact of $Z^{\prime}$ and UED parameters on different asymmetries in $B_{s} \to \phi \ell^{+} \ell^{-}$ decays · Forward-Backward Asymmetries · 0.90
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The branching fractions for $B→$ and $B→$ are close to $B→$, $B→$ given in [ref] .
K1(1270)-K1(1400) Mixing Angle and New-Physics Effects in B to K1 l+ l- Decays · Branching fractions · 0.99
Cites it as support 2 papers
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The measurement of the FBA at LHC is significant due to the minimal dependence on the form factors [ref] , and as such this observable is of greater importance to check the more clear signals of any NP than the other observables such as branching ratio etc.
Analysis of B_{C} --> D_{s}^{*}l^{+}l^{-} in the Standard Model Beyond Third Generation · Forward-Backward Asymmetry of $B→D^∗_s ℓ^+ ℓ^-$ decay · 0.97
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This is because there has been no hint of NP in the radiative decays $B̅ →X_s γ, K̅^(*) γ$ [ref] , which imposes strong constraints on $|C_7^eff|$.
New Physics in b -> s mu+ mu-: CP-Conserving Observables · Standard Model and New Physics: effective Hamiltonians · 0.97
Cites it as background 21 papers
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Theoretically, Refs. [ref] offer a multitude of theoretical predictions for the decays $b→sℓ^+ℓ^-$ and $b→sνν̅$ that can afford us access to a deeper horizon.
The rare decay $B^+ \to K^+\ell^+\ell^-(\nu\bar{\nu})$ under the QCD sum rules approach · Introduction · 0.96
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The general effective Hamiltonian for rare semileptonic $b→s μ^+ μ^-$ transition is given as [ref] , [equation] where $G_F$ is the Fermi coupling constant, $V_ij$ represents the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements.
Signature of (axial)vector operators in $B_c\to D_s^{(*)} \mu^+ \mu^-$ decays · Effective Hamiltonian · 0.85
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Many exclusive $B→K( K^∗) ℓ^+ℓ^-$ [ref] , $B→ϕℓ^+ℓ^-$ [ref] , $B→γℓ^+ℓ^-$ [ref] , $B→ℓ^+ℓ^-$ [ref] processes based on $b→s( d) ℓ^+ℓ^-$ have been studied in literature and many fameworks have been applied to the description of meson transition form factors: like constituent quark models, QCD sum rules, lattice QCD, approaches based on heavy quark symmetry and analytical constraints.
Exclusive B-> K_{1}l ^{+}l ^{-} decay in model with single universal extra dimension · Introduction · 0.96
Discussion
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