On Light Resonance Interpretations of the B Decay Anomalies
OOUTP-17-06P, CERN-TH-2017-104
On Light Resonance Interpretations of the B Decay Anomalies
Fady Bishara, ∗ Ulrich Haisch,
1, 2, † and Pier Francesco Monni ‡ Rudolf Peierls Centre for Theoretical Physics, University of Oxford OX1 3NP Oxford, United Kingdom CERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland
We sketch a novel method to search for light di-leptonic resonances by exploiting precision mea-surements of Drell-Yan production. Motivated by the recent hints of lepton flavour universalityviolation in B → K ∗ (cid:96) + (cid:96) − , we illustrate our proposal by studying the case of spin-1 resonances thatcouple to muons and have masses in the range of a few GeV. We show that the existing LHC dataon pp → Z/γ ∗ → µ + µ − put non-trivial constraints on light di-muon resonance interpretations of B decay anomalies in a model-independent fashion. The impact of our proposal on the long-standingdiscrepancy in the anomalous magnetic moment of the muon is also briefly discussed. Introduction.
In the last four years several anomalieshave been observed in rare semi-leptonic B decays gov-erned by b → s(cid:96) + (cid:96) − transitions. Specifically, deviationsfrom the standard model (SM) expectations in the angu-lar observable P (cid:48) in B → K ∗ µ + µ − [1–4], the branchingratios of B + → K ( ∗ )+ µ + µ − [5], B → K ( ∗ ) µ + µ − [5, 6]and B s → φµ + µ − [7] as well as the ratio R K of di-muonto di-electron rates in B + → K + (cid:96) + (cid:96) − [8] have been re-ported. The recent measurement of the ratio R K ∗ ofdi-muon to di-electron rates in B → K ∗ (cid:96) + (cid:96) − has addedto the list of anomalies [9] and has, accordingly, caughtthe attention of the theory community [10–28].Although each deviation by itself is not statisticallysignificant, and the angular observables and branchingratios are afflicted by hadronic uncertainties that obscurethe interpretation and significance of the anomalies, it isquite intriguing that the deviations seen in the theoreti-cally clean lepton-universality ratios R K and R K ∗ mightbe part of a coherent picture [10–12, 14, 15] involvingnew physics in the b → sµ + µ − transitions in the form ofthe two dimension-six operators Q = (¯ s L γ α b L )(¯ µγ α µ )and Q = (¯ s L γ α b L )(¯ µγ α γ µ ).The most popular new-physics interpretations thatcan accommodate the b → s(cid:96) + (cid:96) − anomalies involvenew heavy degrees of freedom such as Z (cid:48) bosons orlepto-quarks (see e.g. [12] and references therein). So-lutions that involve a new light resonance have insteadreceived less attention [20, 21, 24, 29, 30], although theymight offer an explanation of the long-standing discrep-ancy (cf. [31]) in the anomalous magnetic moment of themuon a µ = (cid:0) ( g − / (cid:1) µ . In fact, it has been shown veryrecently [20] that a spin-1 resonance with a mass of aaround 2 . a µ while evading various other constraints, if the couplingsof the mediator to fermions are dialed correctly. The possibility that a light resonance could be responsible forthe anomaly in P (cid:48) was mentioned by Amarjit Soni at 50th Ren-contres de Moriond EW 2015, and subsequently re-emphasisedto one of the authors by Brian Batell in a private conversation. In this letter, we point out that light resonance inter-pretations of the b → s(cid:96) + (cid:96) − anomalies can be tested andconstrained through precision studies of Drell-Yan (DY)production. Our finding is based on the simple observa-tion that final state radiation (FSR) of a light di-leptonicresonance in pp → Z/γ ∗ → (cid:96) + (cid:96) − will lead to observablemodifications of the kinematic distributions of the (cid:96) + (cid:96) − system. We will illustrate this general idea by settinglimits on the muon couplings of spin-1 resonances withmasses in the GeV range by exploiting existing LHC dataon the di-muon invariant mass m µµ close to the Z peak.The impact of this novel model-independent bounds onspin-1 mediator interpretations of the anomalies observedin rare semi-leptonic B decays as well as a µ will be dis-cussed in some detail. Simplified model.
Following [20] we consider a sim-plified model valid at GeV energies which, besides the SMparticles, contains a colourless spin-1 mediator V withmass m V and a SM singlet Dirac fermion χ of mass m χ .The interactions of V relevant for the further discussionare L ⊃ (cid:0) g sbL ¯ s L /V b L + h . c . (cid:1) + ¯ µ ( g µV − g µA γ ) /V µ + g χV ¯ χ /V χ , (1)where, for concreteness, the couplings g sbL , g µV , g µA and g χV are taken to be real, /V = γ α V α and the subscript L de-notes left-handed fermionic fields. In what follows we willassume that g sbL , g µV , g µA and g χV encode all couplings be-tween the new spin-1 state V and fermions, and we willnot specify an explicit ultraviolet completion that givesrise to them. We however add that the interactions (1)can emerge in various ways such as in vector-like fermionextensions or by considering an effective approach whereall V couplings are generated via higher-dimensional op-erators (see e.g. [32, 33]).As demonstrated in [20], to qualitatively reproducethe P (cid:48) , R K , and R K ∗ anomalies, the mass of the new Constraints on heavy di-lepton resonance interpretations of the b → s(cid:96) + (cid:96) − tensions using present and future pp → (cid:96) + (cid:96) − datahave been very recently derived in [26]. a r X i v : . [ h e p - ph ] M a y Figure 1. An example of a Feynman diagram with FSR of thelight mediator V in the DY process pp → Z/γ ∗ → µ + µ − . spin-1 mediator is constrained to lie in the range ofabout [2 ,
3] GeV and its total decay width has to sat-isfy Γ V /m V (cid:38) m χ < m V / g χ (cid:38)
2. Consequently, V predominantly decays invisibly with a branching ratioBr( V → ¯ χχ ) (cid:39)
1. The existence of a di-muon resonancewith these properties cannot be excluded because of thelarge hadronic uncertainties of the SM prediction for B → K ( ∗ ) µ + µ − in the m µµ (cid:38) region (cf. [34, 35])and the unknown interference pattern between the J/ψ and the SM short-distance contribution. By choosingthe couplings in (1) to be g sbL (cid:39) − − , g µV (cid:39) . g µA (cid:39) − . g µV , the discussed simplified model then doesnot only provide a solution to the flavour anomalies butalso ameliorates the discrepancy observed in a µ . Otherconstraints that arise from B s – ¯ B s mixing, searches for B → K ( ∗ ) + invisible [36–39], B s → µ + µ − [40, 41] and Z → µ [42, 43] as well as the precision measurementsof Zµ ¯ µ couplings [44] are all satisfied for this choice ofparameters. Z -boson line shape. We now consider the di-muoninvariant mass spectrum as measured in DY productionand study its distortions due to FSR of a light spin-1resonance V . A representative diagram that contributesto pp → Z/γ ∗ → µ + µ − + V is shown in Figure 1. Wecalculate the m µµ spectra with MadGraph5 aMC@NLO [45]and
NNPDF23 lo as 0130 qed parton distribution func-tions [46], employing the
DMsimp implementation [47] ofthe
V µ ¯ µ and V χ ¯ χ couplings in (1). The fiducial phasespace in our Monte Carlo simulations is defined by re-quiring that the muon transverse momenta satisfy p T,µ >
25 GeV, the muon pseudorapidities obey | η µ | < .
5, andthat m µµ falls into the range [66 , pp collisions at a centre-of-massenergy of √ s = 13 TeV. All predictions are obtained atleading order in QCD. The three coloured curves corre-spond to g µV = 0 . g µA = − . · − and mediatormasses of 1 . . . Z -boson lineshape is depicted by the black curve. One observes thatFSR of the spin-1 resonance leads to a pronounced radi- − − d σ / d m µµ [ pb / G e V ]
70 80 90 100 110 m µµ [GeV]0246 ( d σ / d m µµ ) V ( d σ / d m µµ ) s m [ % ] SM1.5 GeV2.5 GeV3.5 GeV
Figure 2. Di-muon invariant mass distributions. The blackcurve represents the SM prediction, while the coloured curvescorrespond to three different benchmark models with varyingspin-1 resonance mass. For further details see text. ation tail below m Z (cid:39) . Z -boson line shape of around4% to 6% at m µµ (cid:39)
75 GeV.DY processes are a cornerstone of the SM physics pro-gramme at the LHC (see e.g. [48–53] for recent ATLASand CMS analyses) and a detailed understanding of the Z -boson line shape is a prerequisite for a precision mea-surement of the W -boson mass at the LHC [54]. Givenits importance, a lot of effort has gone into measuringthe m µµ spectrum in the Z -peak region at the LHCand the experimental uncertainties have reached the few-percent level, making the Z -boson line shape a powerfulobservable to search for GeV-mass di-muon spin-1 states.In our study we consider the ratio of the data to theSM prediction to perform a χ fit. In Figure 2 of [49], theATLAS collaboration provides the ratio of experimentaldata to the state-of-the-art theory prediction for the m µµ line shape in the fiducial volume defined above. Assum-ing that the data is SM-like, we compute this ratio fordifferent new-physics scenarios and perform a χ analy-sis. Radiative corrections of QCD and electroweak naturedo not affect the ratio and are therefore neglected in thefollowing. The ATLAS analysis is based on 3 . − in-tegrated luminosity at √ s = 13 TeV. The experimentalstatistical and systematic uncertainties are in the rangeof 1% to 2% and they are added in quadrature in our fit.The bin-to-bin correlations are neglected. − . − .
05 0 .
00 0 .
05 0 . g µV − . − . . . . g µ A . . . . Figure 3. Constraints in the g µV – g µA plane arising from DYproduction for different di-muon spin-1 resonance masses inunits of GeV. The contours correspond to ∆ χ = 5 .
99. Seetext for additional details.
In Figure 3 we show the ∆ χ = 5 .
99 contours (corre-sponding to a 95% confidence level (CL) for a Gaussiandistribution) in the g µV – g µA plane that follow from our χ analysis for different values of m V . The parameter spaceoutside the lines is disfavoured for each individual mass.We find that for m V ∈ [1 ,
5] GeV the obtained 95% CLbounds can be approximately described by the inequality (cid:113) ( g µV ) + ( g µA ) (cid:46) . · − (cid:16) . m V (cid:17) . (2)This approximate formula can be used to quickly assessthe sensitivity of existing DY measurements on the cou-pling strength of GeV-mass di-muon spin-1 states.The upper panel in Figure 4 compares the 95% CLconstraint in the g µV – g µA plane that derives from our fitto the Z -boson line shape for m V = 2 . P (cid:48) (green), R K (yellow) and R K ∗ (red) and a µ (blue). The parameter space above andto the right of the black curve is excluded. In the caseof the flavour observables the favoured parameter spacecorresponds to the ∆ χ = 4 regions obtained in [20] for g sbL = − . · − , while in the case of a µ we have em-ployed the 3 σ bound ∆ a µ ∈ [49 , · − [31]. Fromthe panel it is evident that the model-independent con-straint that arises from the DY data excludes parts of theparameter space favoured by the b → s(cid:96) + (cid:96) − anomalies.In particular, coupling choices that accommodate the de-viation seen in P (cid:48) are constrained. We now focus on theregion of the g µV – g µA plane in which the discrepancy be-tween SM and data for a µ is improved by the one-loopcorrections due to the exchange of a light di-muon spin-1 − − − g µV − − − − − − g µ A a µ R K ∗ R K P DY m V [GeV]0 . . . . . g µ V a µ DY Figure 4. Upper panel: Constraints in the g µV – g µA plane. Theshown results were obtained for m V = 2 . g sbL = − . · − . Lower panel: Constraints in the m V – g µV planeassuming the coupling relation g µA = 0 . g µV . Consult themain text for further explanations. resonance (cf. [55])∆ a µ = ( g µV ) − g µA ) π m µ m V + O (cid:0) m µ /m V (cid:1) . (3)In this region, we observe that our new constraint dis-favours most of the parameter space that provides a si-multaneous explanation of P (cid:48) , R K , R K ∗ and a µ . Giventhe weak mass dependence of (2), we expect this conclu-sion to hold in the full range m V ∈ [2 ,
3] GeV of spin-1resonance interpretations of the flavour anomalies.In the lower panel of Figure 4, we compare the 95% CLbound in the m V – g µV plane following from measurementsof the m µµ spectrum in DY production (black) to the re-gion favoured by a µ (blue). The shown results have beenobtained for g µA = 0 . g µV . We see that our new DY con-straint shrinks the allowed parameter space for such fine-tuned solutions of the a µ anomaly for resonances heav-ier than about 4 . a µ that do not rely on a cancellation in the combina-tion ( g µV ) − g µA ) of couplings, such as solutions with g µV (cid:54) = 0 and g µA = 0, on the other hand, cannot be probedthrough Z -boson line shape measurements at present. Conclusions.
The main goal of this letter was topoint out that precision measurements of DY productionprovide sensitive probes of light di-leptonic resonances.In view of the various deviations from SM predictionsobserved in rare semi-leptonic B decays, we have ap-plied our general observation to the case of GeV-massdi-muon spin-1 resonances. Specifically, we have anal-ysed the distortions that FSR of such mediators imprintson the di-muon invariant mass spectrum as measured in pp → Z/γ ∗ → µ + µ − at the LHC. For simplified-modelrealisations that allow one to qualitatively reproduce the P (cid:48) , R K , R K ∗ and a µ anomalies, we have found that the Z -boson line shape develops a pronounced radiative tailthat amounts to a relative enhancement of O (5%) at m µµ (cid:39)
75 GeV compared to the SM prediction.Motivated by this finding we have derived model-independent bounds on the muon couplings of spin-1 me-diators using DY data from LHC Run II. Our analysisshows that the existing precision measurements of DYproduction put non-trivial constraints on the parameterspace of light di-muon resonance models [20] that aimat explaining the tensions seen in rare semi-leptonic B decays. In particular, they disfavour almost all modelrealisations that can simultaneously accommodate the P (cid:48) , R K , R K ∗ and a µ anomalies. Considering a µ alone,we found instead that present Z -boson line shape fitscan only probe fine-tuned GeV-mass explanations of theanomaly with | g µA | (cid:39) . | g µV | . Since the data set usedto derive the constraints contains only 3 . − of inte-grated luminosity collected at √ s = 13 TeV, future anal-yses performed at LHC Run II and beyond are expectedto strengthen the obtained bounds in case no deviationsfrom the m µµ spectrum as predicted in the SM are found.While in our work we have focused our attention onlight di-muon spin-1 resonances, precision measurementsof the kinematic distributions of the final-state leptonsin pp → Z/γ ∗ → (cid:96) + (cid:96) − can also be used to search for andto constrain mediators preferentially coupling to electronpairs and/or of different spin. A dedicated study of theDY constraints on alternative light di-lepton resonancescenarios, while beyond the scope of this letter, thusseems to be a worthwhile exercise. Acknowledgements.
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