REVIEW
More Model-Independent Analysis of b->s Processes
High Energy Physics - Phenomenology · Submitted 17 Oct 2003 · 49 references
Pith's verdict: A careful EFT paper with two real contributions — the O_bL mixing anomalous dimensions and the matched-cut R_H ratio — whose central R_K bound is explicitly conditional on lepton-mass-proportional scalar couplings.
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Referee report
The paper
The paper claims
The muon-to-electron ratio in rare B decays is a cleaner probe of new scalar interactions than either branching fraction alone.
The reading
What carries the argument
The load-bearing device is the matched-cut ratio $R_H$ of Eq. (1.5): the same lower integration boundary $4m_μ^2$ is imposed on both the muon and the electron mode, so that the lepton-mass dependence from phase space cancels and the residual sensitivity is to the scalar and pseudoscalar Wilson coefficients, which enter proportional to the lepton mass. Supporting this are the one-loop mixing calculations collected in Appendix B, where the anomalous dimensions of the scalar and pseudoscalar operator sets onto $O_7$, $O_8$, the QCD penguins and $O_9$ are given, and the next-to-next-to-leading-order dilepton distributions of Eqs. (4.1)–(4.3) and (C.18) that make the numerical constraints possible.
Extended reading notes
Core claim
The paper establishes two things. First, scalar and pseudoscalar four-quark operators built from $b$ quarks are not inert: through one-loop mixing they renormalize the electromagnetic and gluonic dipole operators, giving $δC_7(m_b) ≈ 0.71 C^b_R(m_W)$ and $δC_8(m_b) ≈ -2.95 C^b_R(m_W)$ after resumming leading logarithms, with the $b$ to $s$ gluon rate receiving corrections that can reach order one. Second, and this is the part the authors promote, the ratios $R_H = BR(B → H μ^+μ^-)/BR(B → H e^+e^-)$, for $H = K, K^*, X_s$, defined with a common dilepton-mass cut, are Standard-Model-clean: $R_H = 1 + O(m_μ^2/m_b^2)$ with a theoretical uncertainty below one percent, far smaller than the roughly thirty percent form-factor uncertainty on the individual exclusive branching fractions. Because the electron mode is taken to be Standard-Model-like under the assumption $C_{S,P} ∝ m_ℓ$, the ratio isolates the muon-specific scalar and pseudoscalar couplings. The authors then show that the current bound $R_K ≤ 1.2$ gives $√(|C_S|^2 + |C_P - 0.4|^2) ≤ 3.2$, comparable to the bound $√(|C_S|^2 + |C_P - 0.15|^2) ≤ 3.8$ from $B_s → μ^+μ^-$ data, and that new physics can still push $R_{K^*}$ and $R_{X_s}$ up to about 13 percent and 10 percent respectively.
Load-bearing premise
The whole ratio strategy rests on the assumption that the scalar and pseudoscalar Wilson coefficients scale with the lepton mass, so that the electron mode is Standard-Model-like and can serve as the reference; the authors themselves note in footnote 2 that R-parity-violating supersymmetry with broken horizontal symmetries need not obey this.
Editorial extensions
If this is right
- A future measurement tightening $R_K$ from 1.2 to 1.1 would sharpen the scalar and pseudoscalar bound from about 3.2 to 2.3, moving the ratio into a competitive role alongside $B_s → μ^+μ^-$.
- The $R_H$ ratios are the theoretically cleanest place to look for a lepton-flavour-dependent splitting in $b → s$ decays, so electron and muon data should not be averaged blindly.
- If $C_S + C_P$ is near its allowed upper bound, the $b → s$ photon branching ratio can be reproduced with essentially no contribution from the electromagnetic dipole operator, a scenario an improved $b → s$ gluon limit could exclude.
- Because $R_K$ bounds the sum $C_S + C_P$ while $B_s → μ^+μ^-$ bounds the difference, combining them caps the individual coefficients at $|C^{(\prime)}_{S,P}| ≤ 4.3$ even when right-handed contributions are present.
Reading between the lines
- The ratio strategy generalizes: any pair of observables that differ only by lepton mass and share the same hadronic matrix element can be turned into a similarly clean probe, which suggests looking at lepton-flavour ratios in other penguin-mediated channels such as $b → s τ^+τ^-$ once statistics allow.
- If the scalar couplings are not lepton-mass suppressed, the electron mode stops being a clean reference and the ratio loses its predictive power; a future measurement of $R_K$ significantly above one together with a large $B_s → e^+e^-$ rate would be the signature of that failure.
- The mixing results imply that any fit which treats the dipole coefficients as free and the scalar coefficients as independent is internally inconsistent unless $C_S + C_P \simeq 0$; this is a constraint on how global fits to $b → s$ data should be parameterized.
Original abstract
We study model-independently the implications of non-standard scalar and pseudoscalar interactions for the decays b ->s gamma, b -> s g, b -> s l^+l^- (l=e,mu) and B_s -> mu^+ mu^-. We find sizeable renormalization effects from scalar and pseudoscalar four-quark operators in the radiative decays and at O(alpha_s) in hadronic b decays. Constraints on the Wilson coefficients of an extended operator basis are worked out. Further, the ratios R_H = BR(B -> H mu^+ mu^-)/BR(B -> H e^+ e^-), for H=K^(*), X_s, and their correlations with B_s -> mu^+ mu^- decay are investigated. We show that the Standard Model prediction for these ratios defined with the same cut on the dilepton mass for electron and muon modes, R_H= 1 + O(m^2_mu/m^2_b), has a much smaller theoretical uncertainty (<1%) than the one for the individual branching fractions. The present experimental limit R_K < 1.2 puts constraints on scalar and pseudoscalar couplings, which are similar to the ones from current data on BR(B_s -> mu^+ mu^-). We find that new physics corrections to R_{K*} and R_{X_s} can reach 13% and 10%, respectively.
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 study model-independently the implications of non-standard scalar and pseudoscalar interactions for the decays b ->s gamma, b -> s g, b -> s l^+l^- (l=e,mu) and B_s -> mu^+ mu^-. We find sizeable renormalization effects from scalar and pseudoscalar four-quark operators in the radiative decays and at O(alpha_s) in hadronic b decays. Constraints on the Wilson coefficients of an extended operator basis are worked out. Further, the ratios R_H = BR(B -> H mu^+ mu^-)/BR(B -> H e^+ e^-), for H=K^(*), X_s, and their correlations with B_s -> mu^+ mu^- decay are investigated. We show that the Standard Model prediction for these ratios defined with the same cut on the dilepton mass for electron and muon modes, R_H= 1 + O(m^2_mu/m^2_b), has a much smaller theoretical uncertainty (<1%) than the one for the individual branching fractions. The present experimental limit R_K < 1.2 puts constraints on scalar and pseudoscalar couplings, which are similar to the ones from current data on BR(B_s -> mu^+ mu^-). We find that new physics corrections to R_{K*} and R_{X_s} can reach 13% and 10%, respectively.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study model-independently the implications of non-standard scalar and pseudoscalar interactions for the decays b ->s gamma, b -> s g, b -> s l^+l^- (l=e,mu) and B_s -> mu^+ mu^-. | contribution 1.00 | 0.93 | 0.06 | asserted 0.78 |
| s1 | We find sizeable renormalization effects from scalar and pseudoscalar four-quark operators in the radiative decays and at O(alpha_s) in hadronic b decays. | result 1.00 | 0.94 | 0.15 | asserted 1.00 |
| s2 | Constraints on the Wilson coefficients of an extended operator basis are worked out. | contribution 0.77 | 0.91 | 0.08 | asserted 0.92 |
| s3 | Further, the ratios R_H = BR(B -> H mu^+ mu^-)/BR(B -> H e^+ e^-), for H=K^(*), X_s, and their correlations with B_s -> mu^+ mu^- decay are investigated. | contribution 1.00 | 0.90 | 0.06 | asserted 0.81 |
| s4 | We show that the Standard Model prediction for these ratios defined with the same cut on the dilepton mass for electron and muon modes, R_H= 1 + O(m^2_mu/m^2_b), has a much smaller theoretical uncertainty (<1%) than the one for the individual branching fractions. | result 1.00 | 0.86 | 0.20 | asserted 1.00 |
| s5 | The present experimental limit R_K < 1.2 puts constraints on scalar and pseudoscalar couplings, which are similar to the ones from current data on BR(B_s -> mu^+ mu^-). | result 0.73 | 0.81 | 0.19 | asserted 0.99 |
| s6 | We find that new physics corrections to R_{K*} and R_{X_s} can reach 13% and 10%, respectively. | result 1.00 | 0.95 | 0.20 | asserted 0.96 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:hep-ph/0310219 by the authors.
References
How the literature uses it
198 arXiv papers cite this in 243 sentences
Papers citing it · 181 sentences without a confident label
Uses its method or tool 3 papers
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Following Refs. [ref] we define the following set of auxiliary variables: A() = 2/1 + () V() + 4 / T_1() , B() = (1 + ) [ () A_1() + 2 / (1 - ) T_2() ] , C() = 1/1 - ^2 [ (1 - ) () A_2() + 2 ( T_3() + 1 - ^2/ T_2() ) ] , D() = 1/ [ () ( (1 + ) A_1() - (1 - ) A_2() - 2 A_0() ) - 2 T_3() ] , E() = 2/1 + V() , F() = (1 + ) A_1() , G() = 1/1 + A_2() , H() = 1/ [ (1 + ) A_1() - (1 - ) A_2() - 2 A_0() ] , X() = - m_K^*/m_b A_0() C_0^ℓ ,
Constraints on New Physics in MFV models: a model-independent analysis of Delta F=1 processes · $B →(K^*,K) ℓ^+ ℓ^-$, $B →(K^*,K) νν̅$ · 0.99
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We use the expression for the differential decay distribution in [ref] , but also include the NLO corrections computed in [ref] , and the contribution of the primed operators as in [ref] .
Constraining new physics with B to K* mu+ mu- in the early LHC era · Constraints · 0.91
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We consider the following ratios of branching ratios [ref]
Status of the $B\to K^*\mu^+\mu^-$ anomaly after Moriond 2017 · Predictions for LFU Observables · 0.86
Uses its data or values 21 papers
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The recent LHCb measurement has observed [ref] a significant deviation from the standard model (SM) expectation of the ratio $R_K$, defined as $R_K = (B^+ →K^+ μ^+ μ^-)/(B^+ →K^+ e^+ e^-)$ [ref] .
Explaining the Lepton Non-universality at the LHCb and CMS from a Unified Framework · Introduction · 0.83
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Interestingly, this theoretically very clean observable has also been measured at LHCb [ref] and exhibits a sizable ($25 %$) depletion with respect to the SM prediction [ref] $| R_K^SM-1 | < 1%$ [This is valid above the muon threshold, $q^2 ∼4 m_μ^2$.] in the $q^2 ≡(p_ℓ^-+p_ℓ^+)^2 ∈[1,6] GeV^2$ bin, i.e., [equation] This corresponds to a deviation of almost $3 σ$.
Recent $\boldsymbol{B}$ Physics Anomalies - a First Hint for Compositeness? · Introduction · 0.88
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The experimental values of $R_D$ and $R_D^*$ are in excess of their SM predictions [ref] by $1.4σ$ and $2.5σ$, respectively, (combined excess of $3.08σ$ in $R_D^(*)$) based on the world averages as of spring 2019, according to the Heavy Flavor Averaging Group [ref] , whereas, the observed $R_K$ and $R_K^*$ are both suppressed compared to their SM predictions [ref] by $∼2.6σ$.
Addressing the ${\mathbf R_{D^{(*)}}}$ anomalies with an ${\mathbf S_1}$ leptoquark from $\mathbf{SO(10)}$ grand unification · Introduction · 0.86
Compares with it 1 paper
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Note the major improvement with respect to the analysis of Ref. [ref] , where the loose bound on $B_s →μ^+μ^-$ allowed much larger non-standard effects.
Constraints on New Physics in MFV models: a model-independent analysis of Delta F=1 processes · Predictions · 1.00
Cites it as support 2 papers
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In practice, these contributions are however bounded from above [ref] by the experimental constraints on $B_s →μ^+ μ^-$ and turn out to be subleading.
SUSY beyond minimal flavour violation · Inclusive $B →X_s ℓ^+ ℓ^-$ · 0.96
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Global analyses of branching ratios and angular distributions reinforce these anomalies and suggest NP contributions predominantly in the semileptonic Wilson coefficient $C_9$ (and possibly $C_10$) [ref] .
Study of $B \to K_0^*(1430)\,\ell^+ \ell^-$ decay in the standard model and scalar leptoquark scenario · Introduction · 0.97
Cites it as background 32 papers
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Another class of $B$ meson observables showing signs of LFUV is related to $b →s ℓ^+ ℓ^-$ processes, namely the optimised angular observable $P_5'$ [ref] and the ratios, [equation] As a consequence of Lepton Flavour Universality (LFU), $R_K = R_K^* = 1$ with uncertainties of the order of $1%$ in the SM [ref] .
Anomalies in B mesons decays: Present status and future collider prospects · Introduction · 0.84
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In the SM such ratios, expected to be close to unity above the dimuon threshold [ref] , are sensitive to contributions from new particles that can induce a sizeable increase or decrease in the rate of particular decays.
Review of Lepton Universality tests in B decays · Introduction · 0.83
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In this context, FCNC processes such as $b→sℓ^+ℓ^-$ have been extensively investigated both experimentally and theoretically [ref] .
Investigating New Physics through the Observables of Semileptonic $B_{s}\to K^{\ast}(\to K \pi)\mu^{+}\mu^{-}$ Decay · Introduction · 0.88
Discussion
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