Physics Colloquium, Paul Scherrer Institute Villingen, Switzerland, 7 March 2019
Matthias Neubert Probing beyond the Standard PRISMA Cluster of Excellence Model with Flavor Physics Johannes Gutenberg University Mainz Large Hadron Collider (LHC) at CERN
LHCb ATLAS
CMS ALICE
M. Neubert — Probing beyond the SM with Flavor Physics 1 The Standard Model
M. Neubert — Probing beyond the SM with Flavor Physics 2 The Standard Model
Leaves many questions unanswered: Why is there more matter than antimatter? What is the dark matter made of? How is the electroweak scale stabilized?
M. Neubert — Probing beyond the SM with Flavor Physics 3 The Standard Model
Leaves many questions unanswered: Why is there more matter than antimatter? What is the dark matter made of? How is the electroweak scale stabilized? …
M. Neubert — Probing beyond the SM with Flavor Physics 4 Beyond the SM?
Increasing mass Previously expected region for Searches for new particles heavy particles with large couplings
Experimentally excluded
Searches for light Terra incognita particles with small couplings Decreasing coupling Decreasing
M. Neubert — Probing beyond the SM with Flavor Physics 5 Beyond the SM
❖ Direct searches for new heavy particles at LHC have so far not led to a discovery
❖ While naturalness remains main motivation for thinking about future energy-frontier machines, one observes a shift of focus on indirect Increasing mass Previously expected region for Searches for NP searches and new particles heavy particles with large couplings searches for light, exotic particles (dark photons, Experimentally excluded
axions, ALPs, …) Searches for light Terra incognita particles with small couplings Decreasing coupling Decreasing
M. Neubert — Probing beyond the SM with Flavor Physics 8 SMEFT
❖ Indirect searches for heavy new physics should be analyzed in context of a systematic extension of the SM [Buchmüller, Wyler 1986; as an effective field theory: Grzadkowski, Iskrzynski, Misiak, Rosiek 2010] many 1 1 = + (D=5) + (D=6) + ... LSMEFT LSM ⇤ OW ⇤2 Oi W i=1 i X
SM without Neutrino masses Generic new-physics neutrino masses and oscillations phenomena
M. Neubert — Probing beyond the SM with Flavor Physics 6 SMEFT
❖ All new-physics scales probed so far are rather large:
New-physics scale Order Observable for g=O(1) Neutrino D=5 Λ ~ 109 TeV oscillations D=6 Proton decay Λ ~ 1012 TeV
D=6 Flavor physics Λ > 1–105 TeV
D=6 EWPT Λ > 1 TeV
D=6 Higgs couplings Λ > 0.5–1 TeV
M. Neubert — Probing beyond the SM with Flavor Physics 7 Beyond the SM
❖ No solution yet to hierarchy problem (SUSY ???)
❖ No answers yet to other big questions:
‣ Nature of Dark Matter?
‣ Origin of matter-antimatter asymmetry?
‣ Explanation of flavor puzzle?
‣ Dark energy/cosmological constant and strong CP problems
❖ While the field waits for clues, remarkable things are happening in the flavor sector!
M. Neubert — Probing beyond the SM with Flavor Physics 9 B-meson flavor anomalies: Violations of lepton universality ?
M. Neubert — Probing beyond the SM with Flavor Physics 10 M. Neubert — Probing beyond the SM with Flavor Physics 11 M. Neubert — Probing beyond the SM with Flavor Physics 12 MITP/15-100 November 9, 2015 One Leptoquark to Rule Them All: A Minimal Explanation for R ( ) , R and (g 2) D ⇤ K µ Martin Bauera and Matthias Neubertb,c aInstitut f¨urTheoretische Physik, Universit¨atHeidelberg, Philosophenweg 16, 69120 Heidelberg, Germany bPRISMA Cluster of Excellence & MITP, Johannes Gutenberg University, 55099 Mainz, Germany cDepartment of Physics & LEPP, Cornell University, Ithaca, NY 14853, U.S.A.
We show that by adding a single new scalar particle to the Standard Model, a TeV-scale leptoquark with the quantum numbers of a right-handed down quark, one can explain in a natural way three of + the most striking anomalies of particle physics: the violation of lepton universality in B¯ K¯ ` ` ( ) ! decays, the enhanced B¯ D ⇤ ⌧⌫¯ decay rates, and the anomalous magnetic moment of the muon. Constraints from other precision! measurements in the flavor sector can be satisfied without fine- ( ) tuning. Our model predicts enhanced B¯ K¯ ⇤ ⌫⌫¯ decay rates and a new-physics contribution to ! Bs B¯s mixing close to the current central fit value.
Introduction. Rare decays and low-energy precision tors that improve the global fit to the data are suppressed measurements provide powerful probes of physics beyond by mass scales of order tens of TeV [23–26]. the Standard Model (SM). During the first run of the In this letter we propose a simple extension of the SM 1 LHC, many existing measurements of such observables by a single scalar leptoquark transforming as (3, 1, 3 ) were improved and new channels were discovered, at rates under the SM gauge group, which can explain both the largely consistent with SM predictions. However, a few R ( ) and the RK anomalies with a low mass M B-meson flavor anomalies D ⇤ anomalies observed by previous experiments have been 1 TeV and O(1) couplings. The fact that such a particle⇠ ( ) 2 reinforced by LHC measurements and some new anoma- can explain the anomalous B¯ D ⇤ ⌧⌫¯ rates and q lous signals have been reported. The most remarkable distributions is well known [13,! 17]. Here we show that ❖ Intriguing hints of anomalies in B decays entered stage example of a confirmed e↵ect is the 3.5 deviation from the same leptoquark can resolve in a natural way the RK startingthe in SM 2012 expectation (RD, RD*; in R theK, combinationRK*; P5’, …) of the ratios anomaly and explain the anomalous magnetic moment of the muon. Reproducing RK with a light leptoquark is ¯ ( ) + (B D ⇤ ⌧⌫¯) possible in our model, because the transitions b s` ` R ( ) = ! ; ` = e, µ. (1) D ⇤ ¯ ( ) ! (B D ⇤ `⌫¯) are only mediated at loop level. Such loop e↵ects have ! not been studied previously in the literature. We also ¯ (B¯ ( )K¯ ( )µ+µ ) An excess of the B D ⇤ ⌧⌫¯⇤decay rates was first noted discuss possible contributions to Bs B¯s mixing, the rare R ( ) = ! K ⇤ ! ¯ ¯ ( ) + ( ) 0 + by BaBar [1, 2], and (B it wasK shown⇤ e e that) this e↵ect can- decays B¯ K¯ ⇤ ⌫⌫¯, D µ µ , ⌧ µ , and the not be explained in terms! of type-II two Higgs-doublet Z-boson couplings! to fermions.! We focus! primarily on ❖ If true,models. they would The relevant be hugely rate measurementsimportant for were the consis- future fermions of the second and third generations, leaving a developmenttent with of those high-energy reported by Belleparticle [3–5] physics and were at recently large! more complete analysis for future work. confirmed by LHCb for the case of RD⇤ [6]. Since these The leptoquark can couple to LQ and eRuR, as well decays are mediated at tree level in the SM, relatively as to operators which would allow for proton decay and ❖ In fact, their importance cannot be overstated … large new-physics contributions are necessary in order to will be ignored in the following. Such operators can be explain the deviations. Taking into account the di↵eren- eliminated, e.g., by means of a discrete symmetry, under M. Neubert — Probingtial beyond distributions the SM with Flavor Physicsd (B ¯ D ⌧ ⌫ ¯ ) /dq 2 provided by BaBar which 13 SM leptons and are assigned opposite parity. ! [2] and Belle [7], only very few models can explain the ex- The leptoquark interactions follow from the Lagrangian cess, and they typically require new particles with masses 2 2 2 2 near the TeV scale and O(1) couplings [8–17]. One of the =(Dµ )†Dµ M gh L | | | | | | (3) interesting new anomalies is the striking 2.6 departure ¯c L c R + Q i⌧2L ⇤ +¯uR eR ⇤ +h.c., from lepton universality of the ratio where is the Higgs doublet, L,R are matrices in fla- + (B¯ Kµ¯ µ ) c ¯T R = ! =0.745 +0.090 0.036 (2) vor space, and = C are charge-conjugate spinors. K ¯ ¯ + 0.074 (B Ke e ) ± Note that our leptoquark shares the quantum numbers of ! a right-handed sbottom, and the couplings proportional 2 2 in the dilepton invariant mass bin 1 GeV q2 6 GeV , to L can be reproduced from the R-parity violating su- reported by LHCb [18]. This ratio is essentially free from perpotential. The above Lagrangian refers to the weak hadronic uncertainties, making it very sensitive to new basis. Switching to the mass basis for quarks and charged physics. Equally intriguing is a discrepancy in angu- leptons, the couplings to fermions take the form lar observables in the rare decays B¯ K¯ µ+µ seen ⇤ c L c L c R ! u¯ e ⇤ d¯ ⌫ ⇤ +¯u e ⇤ +h.c., (4) by LHCb [19], which is however subject to significant L 3 L ue L L d⌫ L R ue R hadronic uncertainties [20–22]. Both observables are in- where duced by loop-mediated processes in the SM, and assum- L T L L T L R T ing O(1) couplings one finds that the dimension-6 opera- ue = Uu Ue , d⌫ = Ud , ue = Vu RVe , (5) M. Neubert — ProbingM. Neubert SM Flavor Physics the beyond with 14 ❖ Decreasing coupling searches energy at frontier! would… becauseaclear give they target for future Previously expected new particles particles withsmall Searches forlight region for
couplings Experimentally excluded B-meson flavoranomalies
Terra incognita heavy particleswith large couplings Searches for Increasing mass
New physics cannot be too far from here! from far too MITP/15-100 November 9, 2015 One Leptoquark to Rule Them All: A Minimal Explanation for R ( ) , R and (g 2) D ⇤ K µ Martin Bauera and Matthias Neubertb,c aInstitut f¨urTheoretische Physik, Universit¨atHeidelberg, Philosophenweg 16, 69120 Heidelberg, Germany bPRISMA Cluster of Excellence & MITP, Johannes Gutenberg University, 55099 Mainz, Germany cDepartment of Physics & LEPP, Cornell University, Ithaca, NY 14853, U.S.A.
We show that by adding a single new scalar particle to the Standard Model, a TeV-scale leptoquark with the quantum numbers of a right-handed down quark, one can explain in a natural way three of + the most striking anomalies of particle physics: the violation of lepton universality in B¯ K¯ ` ` ( ) ! decays, the enhanced B¯ D ⇤ ⌧⌫¯ decay rates, and the anomalous magnetic moment of the muon. Constraints from other precision! measurements in the flavor sector can be satisfied without fine- ( ) tuning. Our model predicts enhanced B¯ K¯ ⇤ ⌫⌫¯ decay rates and a new-physics contribution to ! Bs B¯s mixing close to the current central fit value.
Introduction. Rare decays and low-energy precision tors that improve the global fit to the data are suppressed Flavor anomalies:measurements provide RD powerful & R probesD* of physics beyond by mass scales of order tens of TeV [23–26]. the Standard Model (SM). During the first run of the In this letter we propose a simple extension of the SM LHC, many existing measurements of such observables by a single scalar leptoquark transforming as (3, 1, 1 ) 3 ❖ A totally unexpectedwere signal improved of new and new physics channels in were tree-level, discovered, at rates under the SM gauge group, which can explain both the largely consistent with SM predictions. However, a few R ( ) and the RK anomalies with a low mass M CKM-favored, semileptonic decays of B mesons: D ⇤ ⇠ b→clν processes anomalies observed by previous experiments have been 1 TeV and O(1) couplings. The fact that such a particle ( ) 2 reinforced by LHC measurements and some new anoma- can explain the anomalous B¯ D ⇤ ⌧⌫¯ rates and q ! B→Dlν, B →D*lnu, Λb→Λclν lous signals have been reported. The most remarkable distributions is well known [13, 17]. Here we show that Tree-level decays example of a confirmed e↵ect is the 3.5 deviation from the same leptoquark can resolve in a natural way the RK the SM expectation in the combination of the ratios anomaly and explain the anomalous magnetic moment of in the SM the muon. Reproducing RK with a light leptoquark is ¯ ( ) + Form factors (B D ⇤ ⌧⌫¯) possible in our model, because the transitions b s` ` R ( ) = ! ; ` = e, µ. (1) D ⇤ ¯ ( ) ! needed (B D ⇤ `⌫¯) are only mediated at loop level. Such loop e↵ects have ! not been studied previously in the literature. We also With light leptons ¯ ( ) An excess of the B D ⇤ ⌧⌫¯ decay rates was first noted discuss possible contributions to Bs B¯s mixing, the rare ( ) ! ( ) 0 + (l=μe) used to determine the CKM elementsby BaBar [1, 2], and it was shown that this e↵ect can- decays B¯ K¯ ⇤ ⌫⌫¯, D µ µ , ⌧ µ , and the not be explained in terms of type-II two Higgs-doublet Z-boson couplings! to fermions.! We focus! primarily on CKM fit works very well, i.e. tree-level in models. The relevant rate measurements were consis- fermions of the second and third generations, leaving a agreement with ΔF=2 processes M. Neubert — Probing beyond the SM with Flavortent Physics with those reported by Belle [3–5] and were 15 recently more complete analysis for future work. confirmed by LHCb for the case of RD [6]. Since these The leptoquark can couple to LQ and e u , as well Largest B branching ratios, used to determine the ⇤ R R decays are mediated at tree level in the SM, relatively as to operators which would allow for proton decay and CKM elements, usually assumed to be freelarge of new-physics NP contributions are necessary in order to will be ignored in the following. Such operators can be explain thePage 17 deviations. Taking into account the di↵eren- eliminated, e.g., by means of a discrete symmetry, under tial distributions d (B¯ D⌧⌫¯)/dq2 provided by BaBar which SM leptons and are assigned opposite parity. ! [2] and Belle [7], only very few models can explain the ex- The leptoquark interactions follow from the Lagrangian cess, and they typically require new particles with masses 2 2 2 2 near the TeV scale and O(1) couplings [8–17]. One of the =(Dµ )†Dµ M gh L | | | | | | (3) interesting new anomalies is the striking 2.6 departure ¯c L c R + Q i⌧2L ⇤ +¯uR eR ⇤ +h.c., from lepton universality of the ratio where is the Higgs doublet, L,R are matrices in fla- + (B¯ Kµ¯ µ ) c ¯T R = ! =0.745 +0.090 0.036 (2) vor space, and = C are charge-conjugate spinors. K ¯ ¯ + 0.074 (B Ke e ) ± Note that our leptoquark shares the quantum numbers of ! a right-handed sbottom, and the couplings proportional 2 2 in the dilepton invariant mass bin 1 GeV q2 6 GeV , to L can be reproduced from the R-parity violating su- reported by LHCb [18]. This ratio is essentially free from perpotential. The above Lagrangian refers to the weak hadronic uncertainties, making it very sensitive to new basis. Switching to the mass basis for quarks and charged physics. Equally intriguing is a discrepancy in angu- leptons, the couplings to fermions take the form lar observables in the rare decays B¯ K¯ µ+µ seen ⇤ c L c L c R ! u¯ e ⇤ d¯ ⌫ ⇤ +¯u e ⇤ +h.c., (4) by LHCb [19], which is however subject to significant L 3 L ue L L d⌫ L R ue R hadronic uncertainties [20–22]. Both observables are in- where duced by loop-mediated processes in the SM, and assum- L T L L T L R T ing O(1) couplings one finds that the dimension-6 opera- ue = Uu Ue , d⌫ = Ud , ue = Vu RVe , (5) MITP/15-100 November 9, 2015 One Leptoquark to Rule Them All: A Minimal Explanation for R ( ) , R and (g 2) (*) D ⇤ K µ Enhanced BR(D*)→MartinD Bauer statusa andτν Matthias decaytoday Neubertb,c rates aInstitut f¨urTheoretische Physik, Universit¨atHeidelberg, Philosophenweg 16, 69120 Heidelberg, Germany bPRISMA Cluster of Excellence & MITP, Johannes Gutenberg University, 55099 Mainz, Germany cDepartment of Physics & LEPP, Cornell5 University, Ithaca, NY 14853, U.S.A. ❖ Puzzling observationWe show that by addingof enhanced a single new scalar semileptonic particle to the Standard decay Model, rates a TeV-scale for third- leptoquark Flavor anomalies:with the quantum numbers R ofR(D*)D a right-handed & R statusD* down quark,today one can explain in a natural way three of * + LEPTON UNIVERSALITY VIOLATION?generationthe leptons most striking (~22% anomalies of of B particle→D physics:τν events the violation due of leptonto new universality physics): in B¯ K¯ ` ` ( ) ! decays, the enhanced B¯ D ⇤ ⌧⌫¯ decay rates,5 and the anomalous magnetic moment of the muon. Constraints from other precision! measurements in the flavor sector can be satisfied without fine- BaBar, PRL109,101802(2012) ¯ ¯ ( ) ➤ (*) 0.5 tuning. Our model predicts2 enhanced B K ⇤ ⌫⌫¯ decay rates and a new-physics contribution to Deviations in B→ D τν Belle, PRD92,072014(2015)¯ Δχ = 1.0 contours ! LHCb,Bs PRL115,111803(2015)Bs mixing close to the current central fit value. R(D*) SM Predictions 0.45 Belle, PRD94,072007(2016) decays found in multiple Belle, PRL118,211801(2017) R(D)=0.300(8) HPQCD (2015) LHCb, FPCP2017 R(D)=0.299(11) FNAL/MILC (2015) Introduction. Rare decays and low-energy precision tors that improve the global fit to the data are suppressed 0.4 Average R(D*)=0.252(3) S. Fajfer et al. (2012) measurements over the last 6 measurements provide powerful probes of physics beyond by mass scales of order tens of TeV [23–26]. the Standard Model (SM). During the first run of the In this letter we propose a simple extension of the SM years, almost 4σ disagreement 0.35 4σ 1 LHC, many existing measurements of such observables by a single scalar leptoquark transforming as (3, 1, 3 ) were improved and new channels were discovered, at rates under the SM gauge group, which can explain both the with SM prediction 0.3 2σ largely consistent with SM predictions. However, a few R ( ) and the R anomaliesHFLAV with a low mass M D ⇤ K anomalies observed by previous experiments have been 1 TeV and O(1) couplings. The fact that such a particle⇠ ➤ 0.25 ( ) 2 Other hints of lepton reinforced by LHC measurements and some newHFLAV anoma- can explain the anomalousFPCP 2017B¯ D ⇤ ⌧⌫¯ rates and q ! lous signals have been reported. The most remarkableFPCP 2017 distributions is well known [13, 17]. Here we show that 0.2 P(χ2) = 71.6% universality violations in example of a confirmed e↵ect is the 3.5 deviation from the same leptoquark can resolve in a natural way the RK the0.2 SM expectationhttp://www.slac.stanford.edu/xorg/hfag/semi/index.html0.3 in the combination0.4 of0.5 the ratios 0.6 anomaly and explain the anomalous magnetic moment of other decay modes R(D) the muon. Reproducing RK with a light leptoquark is ¯ ( ) + (B D ⇤ ⌧⌫¯) possible in our model, because the transitions b s` ` R ( ) = ! ; ` = e, µ. (1) http://www.slac.stanford.edu/xorg/hfag/semi/index.htmlD ⇤ 3.5 ! BR(Bc J/ ⌧⌫) If WA (isB¯ correct,D( )`⌫¯ )22% of the D*tn eventsareare only mediated mediatedby at new loop physics level. Such! loop e↵ects have ! R(⇤ J/ ) =0.25 0.28 R(J/ ) exp = ! =0.71 0.17 0.18
❖ Supported by first LHCb measurement of the analogous decay B ¯ J/ ⌧ ⌫¯ : b→cc !τν processes⌧ RD *** B D B D
B¯ J/ ⌧ ⌫¯ c ! ⌧
M. Neubert — Probing beyondAll measurements the SM with Flavor Physics above the SM prediction 17 4σ deviation
Page 18 Flavor anomalies: P5’ etc.
+ ❖ Various hints of new physics in decays B¯ K⇤` ` + - + - + - B→K*μ μ , B→Kμ μ & Bs→ϕμ μ ! ❖ Being rare, loop-mediated FCNC processes, these are • Semi-leptonic decays depend on form-factors prime Nonobservables-perturbative to quantities probe BSM calculated effects with light- cone sum rules or lattice QCD
OsPb9 L
Right choice of observables can reduce M. Neubert — Probing beyond the SM with Flavor Physics 18 the hadronic uncertainties 4
Page 11 Flavor anomalies: P5’ etc.
❖ Several angular observables measured as functions of q2
❖ Some, like P5’, are optimized to be insensitive to hadronic uncertainties: [Descotes-Genon, Matias, Ramon, Virto 2012]
M. Neubert — Probing beyond the SM with Flavor Physics 19 Flavor anomalies: P5’ etc.
❖ Several angular observables measured as functions of q2
❖ Some, likeThe P curious5’, are optimized case of to Pbe5′ insensitive to hadronicn Most angular uncertainties: observables agree[Descotes-Genon, with SM Matias, Ramon, Virto 2012] 2 2 n Deviation in P5′ near q =~6 GeV
Exotic hadrons & flavor physics, May 2018 18
M. Neubert — Probing beyond the SM with Flavor Physics 20 Flavor anomalies: RK & RK*
❖ Some scenarios explaining the anomalies in angular observables predicted a departure from unity in the ratios: [Altmannshofer, Gori, Pospelov, Yavin 2014] ( ) + (B¯ K¯ ⇤ µ µ ) R ( ) = ! K ⇤ (B¯ K¯ ( )e+e ) ! ⇤ ❖ Quite spectacularly, such deviations were later observed at LHCb!
M. Neubert — Probing beyond the SM with Flavor Physics 21 Flavor anomalies:R(K*) = B→ RK*Kμ+ μ&-/B →RK*K*e+e- “The R Anomaly” K 2.2-2.4 σ in two bins
LHCb 1406.6482
LHCb 1705.05802
Page 14 ( ) + (B¯ K¯ ⇤ µ µ ) 2.6 hint for violation of lepton flavorR universality( ) = (LFU)! K ⇤ (B¯ K¯ ( )e+e ) ! ⇤ + BR(B K µ µ )[1,6] +0.090 RK =M. Neubert —! Probing beyond the =SM0 with.745 Flavor0.074 Physics0 . 036 22 BR(B Ke+e ) ± ! [1,6]
Wolfgang Altmannshofer (UC) Theoretical Advances in Flavor Physics January 14, 2016 21 / 34 B-flavor anomalies: Analysis
❖ Lots of reasons to be excited!
‣ Two different sets of anomalies of very different taste
‣ Several seen by more than one experiment + ‣ In case of b s ` ` several observables deviate from SM ! predictions, and deviations appear to fit a simple pattern
❖ All combined, the most compelling hints for physics beyond the SM we have seen so far
M. Neubert — Probing beyond the SM with Flavor Physics 23 B-flavor anomalies: Analysis
b→clν b→sll
RK, RK*, Observables RD, RD* angular distributions Tree level, CKM One-loop FCNC, SM favored GIM suppressed LFU violation τ vs. e/ vs. e
τ reconstruction Electron reconstruction difficult, earliest data set difficult at LHCb, so far Caveats (BaBar) shows largest no confirmation by discrepancy another experiment (Belle II) Solid theory for RK(*), Benefits Solid theory some caveats for P5’
M. Neubert — Probing beyond the SM with Flavor Physics 24 Who ordered that?
❖ Unexpectedly large new-physics effect!
❖ No apparent connection to big questions of our field!
❖ Is it good for something else?
(I.I. Rabi)
M. Neubert — Probing beyond the SM with Flavor Physics 25 Interpreting Hints for Lepton Flavor Universality Violation
1, 2, 2, Wolfgang Altmannshofer, ⇤ Peter Stangl, † and David M. Straub ‡ 1Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA 2Excellence Cluster Universe, Boltzmannstraße 2, 85748 Garching, Germany We interpret the recent hints for lepton flavor universality violation in rare B meson decays. Based on amodel-independente↵ective Hamiltonian approach, we determine regions of new physics parameter space that give a good description of the experimental data on RK and RK⇤ ,whichisintension with Standard Model predictions. We suggest further measurements that can help narrowing down viable new physics explanations. We stress that the measured values of RK and RK⇤ are fully compatible with new physics explanations of other anomalies in rare B meson decays based on the b sµµ transition. If the hints for lepton flavor universality violation are first signs of new physics, perturbative! unitarity implies new phenomena below a scale of 100 TeV. ⇠
Introduction. The wealth of data on rare leptonic partial compositeness [30–33], and models with lepto- and semi-leptonic b hadron decays that has been accu- quarks [34–42]. mulated at the LHC so far allows the Standard Model A first measurement of RK by the LHCb collabora- (SM) Cabibbo-Kobayashi-Maskawa picture of flavor and tion [43] in the di-lepton invariant mass region 1 GeV2 < CP violation to be tested with unprecedented sensitiv- q2 < 6 GeV2, ity. Interestingly, current data on rare b s`` decays ! [1,6] +0.090 show an intriguing pattern of deviations from the SM RK =0.745 0.074 0.036 , (2) ± predictions both for branching ratios [1–3] and angular distributions [4, 5]. The latest global fits find that the shows a 2.6 deviation from the SM prediction. Very recently, LHCb presented first results for R [44–46], data consistently points with high significance to a non- K⇤ standard e↵ect that can be described by a four fermion [0.045,1.1] +0.11 ⌫ RK =0.66 0.07 0.03 , (3) contact interaction C9 (¯s PLb)(¯µ ⌫ µ)[6] (see also ear- ⇤ ± lier studies [7–9]). Right now the main obstacle towards R[1.1,6] =0.69+0.11 0.05 , (4) K⇤ 0.07 conclusively establishing a beyond-SM e↵ect is our in- ± ability to exclude large hadronic e↵ects as the origin of where the superscript indicates the di-lepton invariant 2 the apparent discrepancies (see e.g. [10–16]). mass bin in GeV . These measurements are in tension In this respect, observables in b s`` transitions that with the SM at the level of 2.4 and 2.5 ,respectively. ! are practically free of hadronic uncertainties are of partic- Intriguingly, they are in good agreement with the recent 2 2 ular interest. Among them are lepton flavor universality RK⇤ predictions in [6] that are based on global fits of (LFU) ratios, i.e. ratios of branching ratios involving b sµµ decay data, assuming b see decays to be Coe! ↵.bestfit1Coe↵.bestfit1 ! 2 2 pull pull di↵erent lepton flavors such as [17–19] SM-like. Inµ this letterµ we interpret the RK( ) measurements us- + + C9 C9 1.56 [1.562.12,[ 21..12,10] [ 1⇤.210].87,[ 20..87,71] 40.1.71] 4.1 (B Kµ µ ) (B K⇤µ µ ) ing a model-independent e↵ ective Hamiltonian approach RK = B ! ,RK = B ! . µ µ + ⇤ + C10 C10+1.20+1 [+0.20.88, [+0 +1..88,57] +1 [+0.57].58, [+0 +2..58,00] +2 4.2.00] 4.2 (B Ke e ) (B K⇤e e ) (see [47–53] for earlier model independent studies of RK ). B ! B ! e e (1) WeC also9 includeC9 +1.54 Belle+1[+1.54 measurements.13,[+1 +1..13,98] +1[+0. of98].76, LFU[+0 +2..76, observables48] +24.3.48] 4.3 + In the SM, the only sources of lepton flavor universality in theCe BCe K1.27⇤` ` [ 1.271angular.65, [ 10..65,92] distibutions [ 0.292].08, [ 20. [.08,61]5]. 4 We0.3.61] do 4.3 10 !10 violation are the leptonic Yukawa couplings, which are not consider early results on R ( ) from BaBar [54] and Cµ = CCµµ= C0µ.63 [0.630.80,[ 00..80,47]K ⇤ [ 0.047].98,[ 00..98,32] 40.2.32] 4.2 responsible for both the charged lepton masses and their Belle9 [559 10] which, 10 due to their large uncertainties, have arXiv:1704.05435v2 [hep-ph] 3 May 2018 1 e ee e interactions with the Higgs. Higgs interactions do not Clittle9 = impact.CC910= +0C10 We.76 identify+0 [+0.76.55, [+0 the +1..55,00] regions +1 [+0.00].36, of [+0 +1 NP..36,27] parameter +1 4.3.27] 4.3 lead to any observable e↵ects in rare b decays and lep- spaceCe = C thatCee = giveCe1.91 a good[1.912.30, description[ 21..30,51] [ 1 of.251].71, the[ 2 experimental1..71,10] 31.9.10] 3.9 9 109 10 ton mass e↵ects become relevant only for a very small data.µ We showµ how future measurements can lift flat di- C0 C0 0.05 [0.050.31, [ +00..31,21] +0 [ .021].57, [ +00..57,46] +0 0.2.46] 0.2 di-lepton invariant mass squared close to the kinematic rections9 in9 the NP parameter space and discuss the com- 2 2 2 µ µ Model-independent0 0 analyses limit q 4m` . Over a very broad range of q the SM patibilityC10 C of10 the+0.03R +0([ ).030measurements.21,[ +00..21,27] +0[ .027] with.44,[ +0 other0..44,51] +00 anoma-.1.51] 0.1 ⇠ K ⇤ accurately predicts R = R = 1, with theoretical un- e e K K⇤ liesC in0 rareC0B+0meson.07+0 [ decays..070.21, [ +00..21,37] +0 [ .037].49, [ +00..49,69] +0 0.2.69] 0.2 9 9 certainties of O(1%) [20]. Deviations from the SM pre- Modele independente implications for new physics. We C0 C0 0.04 [0.040.30,[ +00..30,21] +0[ .021].57,[ +00..57,45] +00.2.45] 0.2 dictions can be expected in various models of new❖ physics assume10 that10 NP in the b s`` transitions is+ su ciently Effective weak Hamiltonian! for b s ` ` transitions, (NP), e.g. Z0 models based on gauged Lµ L⌧ [21–24] heavy such that it can be model-independently described ! or other gauged flavor symmetries [25–29], modelsincluding with by both an e↵ective SM Hamiltonian,and NP effects:= SM + NP, TABLETABLE I. Best-fit I. Best-fit values values and pulls andHe↵ for pulls scenariosHe for↵ scenariosH withe↵ NP with in NP in one individualone individual Wilson Wilson coe cient, coe takingcient, taking into account into account only only 4 G e2 LFUNP observables.LFU observables.F ` ` ` ` e↵ = VtbVts⇤ 2 (Ci Oi + Ci0 Oi0 )+h.c., 1 Neutrino masses provide another source of lepton flavor non- H p2 16⇡ Xi,` universality, but the e↵ects are negligible here. (5) with: with thewith following the following four-fermion four-fermion contact contact interactions, interactions, ` ` ¯ µ ¯ µ ` ` ¯ µ ¯ µ O9 =(¯Os 9µ=(¯PLsb )(µ` PLb`)() ,O` `)90 ,O=(¯s90 µ=(¯PRsb )(µ` PRb`)() ,` `(6)) , (6) ` ` ¯ µ ¯ µ ` ` ¯ µ ¯ µ O10 =(¯Os10 µ=(¯PLsb )(µ` PLb )(5`` ) ,O 1005`)=(¯,Os100 µ=(¯PRsb )(µ` PRb )(5`` ) , (7)5`) , (7)
` ` and theand corresponding the corresponding Wilson Wilson coe cients coe cientsCi ,withCi ,with` = ` = ❖ Excellente, µ .fits Wee, µobtained. do We not do consider not with consider other only dimension-sixother two dimension-six NP operators contributions! operators that canthat contribute can contribute to b tos``b transitions.s`` transitions. Dipole Dipole oper- oper- ! ! ❖ Analogousators andatorsHamiltonian four-quark and four-quark operators can operators be [56 ]written cannot [56] cannot lead for to lead vio-b to vio-c ` ⌫¯ lationlation of LFU of and LFU are and therefore are therefore irrelevant irrelevant for this for work. this! work. Four-fermionFour-fermion contact contact interactions interactions containing containing scalar scalar cur- cur- M. Neubert — Probingrents beyond would rentsthe SM with would be Flavor a natural be Physics a natural source source of LFU of violation. LFU violation. How- How- 26 ever, theyever, are they strongly are strongly constrained constrained by existing by existing measure- measure- mentsments of the ofB the Bµµ andµµBand Bee branchingee branching ra- ra- s ! s ! s ! s ! tios [57tios, 58 [].57 Imposing, 58]. ImposingSU(2)SUL invariance,(2)L invariance, these bounds these bounds cannotcannot be avoided be avoided [59]. We [59]. have We checked have checked explicitly explicitly that that SU(2)SUL invariant(2)L invariant scalar scalar operators operators cannot cannot lead to lead any to ap- any ap- preciablepreciable e↵ects e in↵ectsR ( in) R(cf.( [)60(cf.]). [60]). K ⇤ K ⇤ For theFor numerical the numerical analysis analysis we use we the use open the source open source code code flavioflavio[61]. Based[61]. Based on the on experimental the experimental measurements measurements
and theoryand theory predictions predictions for the for LFU the ratios LFU ratiosR ( ) Rand( ) and K ⇤ K ⇤ + + the LFUthe di LFU↵erences di↵erences of B of BK⇤` `K ⇤angular` ` angular observ- observ- ables Dables (seeD below),(see below), we! construct we! construct a 2 function a 2 function that that P40,5 P40,5 dependsdepends on the on Wilson the Wilson coe cients coe cients and that and takes that intotakes into accountaccount the correlations the correlations between between theory theory uncertainties uncertainties of of di↵erentdi↵ observables.erent observables. We use We the use default the default theory theory uncer- uncer- taintiestainties in flavio in flavio, in particular, in particularB KB ⇤ formK⇤ factorsform factors from afrom combined a combined fit to light-cone fit to light-cone sum! rule sum and! rule lattice and lattice re- re- sults [62sults]. The [62]. experimental The experimental uncertainties uncertainties are presently are presently dominateddominated by statistics, by statistics, so their so correlations their correlations can be can ne- be ne- 2 2 glected.glected. For the For SM the we SM find we SM find= 24SM.4= for 24 5.4 degrees for 5 degrees of of freedom.freedom. Tab. ITab.listsI thelists best the fit best values fit values and pulls, and defined pulls, defined as the as theFIG. 1.FIG. Allowed 1. Allowed regions regions in planes in planes of two of Wilson two Wilson coe cients, coe cients, 2 between 2 between the best-fit the best-fit point and point the and SM the point SM for point forassumingassuming the remaining the remaining coe cients coe tocients be SM-like. to be SM-like. p p Model-independent analyses
❖ Global fits to data assuming NP for muons only, e.g.:2
2.0 Coe↵.bestfit1 2 pullATLAS CMS 1.5 µ C 1.56 [ 2.12, 1.10] [ 2.87, 0.71] 4LHCb.1 9 1.5 µ BR only C10 +1.20 [+0.88, +1.57] [+0.58, +2.00] 4all.2 1.0 e 1.0 C9 +1.54 [+1.13, +1.98] [+0.76, +2.48] 4.3 e C10 1.27 [ 1.65, 0.92] [ 2.08, 0.61] 4.3 0.5 0.5 µ 10 NP µ µ 10 C
C = C C 0.63 [ 0.80, 0.47] [ 0.98, 0.32] 4.2 9 10
e e Re C = C +00.0.76 [+0.55, +1.00] [+0.36, +1.27] 4.3 Re 0.0 9 10 e e C9 = C10 1.91 [ 2.30, 1.51] [ 2.71, 1.10] 3.9 0.5 µ C0 0.05 [ 0.31, +0.21] [ 0.57, +0.46] 0.2 0.5 9 LFU observables µ b sµµ global fit C100 +01.0.03 [ 0.21, +0.27] [ 0.44, +0.51] 0.1 ! all e 1.0 C0 +0.07flavio [ 0v0.21.2.21, +0.37] [ 0.49, +0.69] 0.2 flavio v0.21.2 all, fivefold non-FF hadr. uncert. 9 e 1.5 C100 0.042.0 [ 10.5.30,1 +0.0 .21]0.5[ 00.57,.0 +00.5.45] 01..02 1.5 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 NP Re C9 µ Re C9
TABLE I. Best-fitFigure values1: Two-dimensional and pulls for scenarios constraints[Altmannshofer, with NP in the in planeNies, Stangl, of NP contributionsStraub 2017] to the real parts of one individual Wilson coe cient, taking into account only 1.5 LFU observables. [seethe also: Wilson Capdevila, coe cients Crivelin,C9 and Descotes-Genon,C10 (left) or C Matias,9 and C Virto90 (right), 2017; assuming Hurth, Mahmoudi, all other + Wilson coe cients to be SM-like. For the constraints from the B K⇤µ µ and Neshatpour+ 2016; Ciuchini, Coutinho, Fedele,1. 0Franco, Paul, Silvestrini,! Valli 2017; …] Bs µ µ angular observables from individual experiments as well as for the with the following four-fermion! contact interactions, M. Neubert — Probingconstraints beyond the from SM with branching Flavor Physics ratio measurements of all experiments (“BR only”), we 27 2 ` ¯ µshow the` 1 ( 2.¯3)µ contours, while for0. the5 global fit (“all”), we show the 1, 2, e O9 =(¯s µPLb)(` `) ,O90 =(¯s µPR⇡b)(` `) , (6) 9 and 3 contours. C ` ¯ µ ` ¯ µ O10 =(¯s µPLb)(` 5`) ,O100 =(¯s µPRb)(` 5`) , (7) Re 0.0 ` and the correspondingcontours showing Wilson the coe constraints cients Ci coming,with` from= the angular analyses of individual experiments, e, µ. We do not consider other dimension-six operators as well as from branching ratio measurements of all experiments.0.5 that can contribute to b s`` transitions. Dipole oper- We observe! that the individual constraints are all compatible with the global fit at theLFU 1 observablesor ators and four-quark operators [56] cannot lead to vio- b sµµ global fit 2 level. While the CMS angular analysis shows good1.0 agreement with the SM expectations,! lation of LFU and are therefore irrelevant for this work. flavio v0.21.2 all Four-fermionall contact other individual interactions constraints containing show scalar a cur- deviation from the SM. In view of their precision, the angular analysis and branching ratio measurements of2.0 LHCb1.5 still1.0 dominate0.5 the0.0 global0.5 fit1.0 1.5 rents would be a natural source of LFU violation. How- µ ever, they(cf. are Figs.strongly5, 7 constrained, 6 and 8), leading by existing to a measure- similar allowed region as in previous analyses.Re C9 We do not ments of thefindB anys significantµµ and preferenceBs ee forbranching non-zero ra- NP contributions in C10 or C90 in these two simple ! ! RK tios [57, 58scenarios.]. Imposing SU(2)L invariance, these bounds R cannot be avoidedSimilarly [59]. to We our have analysis checked of explicitly scenarios that with NP in one2 Wilson coe cient, we repeatK⇤ the SU(2) invariantfits doubling scalar operatorsthe form factorcannot uncertainties lead to any ap- and doubling the uncertainties of non-factorizableLFU observables L b sµµ global fit ! preciable ecorrections.↵ects in R ( For) (cf. NP [60 in]).C and C , we find that the pull is reduced from 5.0 to 3.7 and 4.1 , K ⇤ 9 10 1 For the numerical analysis we use the open source code respectively. For NP in C9 and C90 the pull is reduced from 5.3 to 4.1 and 4.4 ,respectively. flavio [61]. Based on the experimental measurements
The impact of the inflated uncertainties is also illustratedµ in Fig. 2. Doubling the hadronic 9 ( ) and theory predictions for the LFU ratios R and C uncertainties is not su cient to achieveK ⇤ agreement between0 data and SM predictions at the 3 + the LFU di↵erences of B K⇤` ` angular observ- level. Re ables D (see below), we! construct a 2 function that P40,5 depends on the Wilson coe cients and that takes into 1 account the3.3. correlations New physics between or theory hadronic uncertainties e↵ects? of di↵erent observables.It is conceivable We use that the hadronic default e theory↵ects that uncer- are largely underestimated could mimic new physics tainties in flavio, in particular B K⇤ form factors 2 in the Wilson coe cient C9 [24]. As first quantified in [60] and later considered in [23,25,26,33], from a combined fit to light-cone sum! rule and lattice re- flavio v0.21.2 sults [62]. The experimental uncertainties are presently 3 2 1 0 1 2 3 dominated by statistics, so their correlations can be ne- Re Cµ 2 9 glected. For the SM we find SM = 24.4 for 5 degrees of freedom. 6 Tab. I lists the best fit values and pulls, defined as the FIG. 1. Allowed regions in planes of two Wilson coe cients, 2 between the best-fit point and the SM point for assuming the remaining coe cients to be SM-like. p Model-independent analyses
❖ Discriminating power of RK and RK*:
��� ������� �� μ ��� ������� �� � ��� ��� � ��� ��� < ��� � μ �� μ� ��� � � ��� ���� � � � � � � � ��� ��� ��� ��� ��� �� μ� ��� �� * ��μ * � ��� � ��� � �� � ��� ��� ��� �� ��
��� ��� ��� � � ��� < � � � ��� �� μ� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ���
�� �� [D’Amico, Nardecchia, Panci, Sannino, Strumia, Torre, Urbano 2017; Figure 1: Deviations from the SM value RK = RK⇤ =1due to the various chiral operators possibly generated by newGeng, physics Grinstein, in Jäger, the muonMartin (leftCamalich, panel) Ren, and Shi electron2017] (right panel) sector. Both ratios refer to the [1.1, 6] GeV2 q2-bin. We assumed real coe cients, and the out-going M. Neubert — Probing beyond the SM with Flavor Physics 28 (in-going) arrows show the e↵ect of coe cients equal to +1 ( 1). For the sake of clarity we only show the arrows for the coe cients involving left-handed muons and electrons (except for the two magenta arrows in the left-side plot, that refer to CBSM =(CBSM + CBSM )/2= 1). 9,µ bLµL bLµR ±
2 BSM corrections. RK⇤ , in a given range of q , is defined in analogy with eq. (8):
2 qmax 2 + 2 q2 dq d (B K⇤µ µ )/dq 2 2 min ! RK⇤ [qmin,qmax] 2 , (16) ⌘ qmax 2 + 2 Rq2 dq d (B K⇤µ µ )/dq min ! R + 2 where the di↵erential decay width d (B K⇤µ µ )/dq actually describes the four-body + ! process B K⇤( K⇡)µ µ , and takes the compact form ! ! + d (B K⇤µ µ ) 3 1 ! = (2 s + c) (2 s + c) . (17) dq2 4 I1 I2 4 I2 I2 The angular coe cients a=s,c in eq. (17)canbewrittenintermsoftheso-calledtransversity Ii=1,2 amplitudes describing the decay B K⇤V ⇤ with the B meson decaying to an on-shell K⇤ ! and a virtual photon or Z boson which later decays into a lepton-antilepton pair. We refer to [29] for a comprehensive description of the computation. In the left panel of figure 2 we + 2 show the di↵erential distribution d (B K⇤µ µ )/dq as a function of the dilepton invariant ! mass q2. The solid black line represents the SM prediction, and we show in dashed (dotted) BSM BSM red the impact of BSM corrections due to the presence of non-zero CbLµL (CbRµL )takenatthe benchmark value of 1. We now focus on the low invariant-mass range q2 =[0.045, 1.1] GeV2, shaded in blue with diagonal mesh in the left panel of fig 2. In this bin, the di↵erential rate is dominated by
7 Model building
❖ Several (but not all) models aim at explaining all anomalies, sometimes along with (g-2) (optimistic �) [Bhattacharya, Datta, London, Shivashankara 2014; Alonso, Grinstein, Martin Camalich 2015; Greljo, Isidori, Marzocca 2015; Calibbi, Crivellin, Ota 2015; Bauer, MN 2015; Fajfer, Kosnik 2915; Barbieri, Isidori 2015; Das, Hati, Kumar, Mahajan 2016; Boucenna, Celis, Fuentes-Martin, Vicente, Virto 2016; Becirevic, Kosnik, Sumensari, Zukanovich Funchal 2016; Becirevic, Fajfer, Kosnic, Sumensari 2016; Hiller, Loose, Schoenwald 2016; Bhattacharya, Datta, Guevin, London, Watanabe 2016; Buttazzo, Greljo, Isidori, Marzocca 2016; Barbieri, Murphy, Senia 2016; Bordone, Isidori, Trifinopoulos 2017; Crivellin, Müller, Ota 2017; Megias, Quiros, Salas 2017; Cai, Gargalionis, Schmidt, Volkas 2017; …]
❖ RD and RD* require tree-level NP near TeV scale
+ ❖ Rare decays b s ` ` (RK, RK*, P5’, …) require ! suppressed NP contributions
❖ If common origin: suppression either dynamically or by means of a symmetry
M. Neubert — Probing beyond the SM with Flavor Physics 29 Model building
❖ New colorless bosons, e.g. Z’ ❖ Scalar/vector leptoquarks, e.g.:
coupled to (L -Lτ): b 4 ⌫ µ µ, ⌧ 1 b b S(3, 3, ) L R tR 3 ⌧ µ h i h i h i 2 V (3, 1, 3 ) Z0 Z0 Z0 Q 1 D U ± c s sL sR cR h i µ, ⌧ h i [Hiller,h Schmaltzi 2014; Alonso, Grinstein, Martin FIG.[Altmannshofer, 1. Example diagrams Gori, in the high Pospelov, energy theory Yavin that 2014] lead to flavor-changing e↵ective couplingsCamalich of the 2015;Z0 to SMFreytsis, quarks. Ligeti, Ruderman 2015]
‣ ‣ breakingZ’ themassU(1)0 symmetry,in low for TeV example range, through the heavyconstraints on the generalCan mixing explain coe cients as both we now RD(*) and RK(*) at Higgs portal operator H 2 2.Thee↵ects, however, discuss. | | | | are morevector-like model dependent quarks and we do not ~ studytens them of in TeVMeson mixing: Treetree-level level exchange of the Z0 con- this work. tributes to neutral meson mixing. In particular, the cou- + plings required to explain the B K⇤µ µ anomaly ! ‣ will lead to contributions‣ to Bs mixing. Additional con- Can explain+ P5’ and predicted Requires huge hierarchy in flavor III. THE B K⇤µ µ ANOMALY AND tributions to B mixing arise from the flavor-changing ! s ADDITIONAL FLAVOR CONSTRAINTS e↵ects associated with the scalar . Both real and imag- LFU violation in RK and RK* inary parts of (the lattercouplings is equivalent to the (flavor longitudi- symmetry?) Before discussing the various constraints on the nal part of the Z0) mediate SM vector-like quark tran- ‣hadronic current of Eq. (7), we match the Wilson co- sitions, and the box‣ diagram with exchange therefore But tree-level contribution+ to Constraints from B mixing and e cients relevant for the B K⇤µ µ anomaly, leads to an additional contribution to B = 2 transi- ! Eqs.B-meson (2a,2b) with the correspondingmixing is terms problematic in the Z0 cur- tions. B→K(*) νν, B→K(*) τ+τ- rents. Working in the approximation that the Z0 is heavy The modifications to the mixing amplitude M12 read compared to the B meson1, so as to neglect the momen- M12 tum exchange in the semi-leptonic decay of the B, we SM =1+ CLL + CRR +9.7CLR M12 M. Neuberthave — Probing beyond the SM with Flavor Physics h i 30 4 1 g2 1 2 (q) 1 YQbYQs⇤ (V V ) S , (18) C = = , (16a) 2 2 ts⇤ tb 0 9 bs 2 2 ⇥ 16⇡ mW ⇤ 2mQ ✓ ◆ where we used the hadronic matrix elements collected (d) 1 YDbYDs⇤ C90 = bs 2 = 2 , (16b) in [24], and the SM loop function is S0 2.3. The Wilson ⇤ 2mD ' coe cients CLL,CRR,CLR are given by with the relative minus sign arising from the opposite 2 ˜ ˜ 2 v 1 1 U(1)0 charges of QR and DL (see Eqs. (9a,9b)). We note CLL =(YQbYQs⇤ ) 4 + 2 2 , (19a) that in this approximation the Wilson coe cients C9 and mQ 16⇡ mQ ! C90 are completely independent of the Z0 mass and the U(1) gauge coupling. Therefore, these relations deter- 2 0 2 v 1 1 C =(Y Y ⇤ ) + , (19b) mine the mass scale for the exotic quarks, RR Db Ds m4 16⇡2 m2 ✓ D D ◆ 1/2 mQ,D 25 TeV Re(Y Y ⇤ ) , (17) C =(Y Y )(Y Y ) ' ⇥ (Q,D)b (Q,D)s LR Qb Qs⇤ Db Ds⇤ ⇣ ⌘ 2 2 2 + v 1 log(mQ/mD) in order to address the anomaly in the B K⇤µ µ , (19c) decay (see Eqs.(2a,2b)). This scale is su !ciently high ⇥ m2 m2 16⇡2 m2 m2 Q D Q D ! that current collider constraints on new colored particles 2 ( 1 TeV) do not result in useful bounds. However, other where the (v ) terms originate from tree level Z0 contri- & O 2 flavor processes are easily sensitive to such high scales. butions, and the 1/(16⇡ ) suppressed contributions orig- While they do not rule out the combinations leading to inate from the scalar box diagrams. Note that the Z0 contribution to the mixing amplitude does not depend the operators corresponding to C9 and C90 , they do place on the Z0 mass and the U(1)0 gauge couplings separately,
but only through the combination v = mZ0 /g0.The good agreement of the SM prediction for Bs mixing with 1 the experimental data sets an upper bound on the U(1) If the Z0 is lighter than the B meson, it would show up as 0 aresonanceinthedi-muoninvariantmassspectrumofthe symmetry breaking VEV, v . + B K⇤µ µ decay rate. We reserve the analysis to another In the plots of Fig. 2 we show the limit on v as a publication! [22]. function of the masses of the vector-like quarks, mD and Model building
❖ ❖ ˜ New colorless bosons, e.g. Z’ Scalar SU(2)L singlet LQ ( ˆ= b R ): b ⌫ coupled to (L -Lτ): 4 µ, ⌧ 2 bL bR tR S(3, 1, ) ⌧ h i h i h i 3
Z0 Z0 Z0 Q 1 D U ± c b µ sL sR cR h i µ, ⌧ h i h i ⌫ S(3, 1, 2) FIG.[Altmannshofer, 1. Example diagrams Gori, in the high Pospelov, energy theory Yavin that 2014] lead to flavor-changing e↵ective couplings of the Z0 to SM quarks. 3 t s µ ‣ breakingZ’ themassU(1)0 symmetry,in low for TeV example range, through the heavyconstraints on the general mixing coe cients as we now Higgs portal operator H 2 2.Thee↵ects, however, discuss. | | | | [Bauer, MN 2015; Cai, Gargalionis, Schmidt, are morevector-like model dependent quarks and we do not ~ studytens them of in TeVMeson mixing: Tree level exchange of the Z0 con- this work. tributes to neutral meson mixing.Volkas In 2017] particular, the cou- + plings required to explain the B K⇤µ µ anomaly ! ‣ will lead to contributions‣ to Bs mixing. Additional con- Can explain+ P5’ and predicted Explains RD(*) at tree-level but III. THE B K⇤µ µ ANOMALY AND tributions to Bs mixing arise from the flavor-changing ADDITIONAL! FLAVOR CONSTRAINTS e↵ects associated with theR scalarK(*) at. Both one-loop real and imag- level, like SM LFU violation in RK and RK* inary parts of (the latter is equivalent to the longitudi- Before discussing the various constraints on the nal part of the Z0) mediate SM vector-like quark tran- ‣hadronic current of Eq. (7), we match the Wilson co- sitions, and the box‣ diagram with exchange therefore But tree-level contribution+ to CKM-like hierarchy in coupling e cients relevant for the B K⇤µ µ anomaly, leads to an additional contribution to B = 2 transi- ! Eqs.B-meson (2a,2b) with the correspondingmixing is terms problematic in the Z0 cur- tions. parameters rents. Working in the approximation that the Z0 is heavy The modifications to the mixing amplitude M12 read compared to the B meson1, so as to neglect the momen- M12 tum exchange in the semi-leptonic decay of the B, we SM =1+ CLL + CRR +9.7CLR M12 M. Neuberthave — Probing beyond the SM with Flavor Physics h i 31 4 1 g2 1 2 (q) 1 YQbYQs⇤ (V V ) S , (18) C = = , (16a) 2 2 ts⇤ tb 0 9 bs 2 2 ⇥ 16⇡ mW ⇤ 2mQ ✓ ◆ where we used the hadronic matrix elements collected (d) 1 YDbYDs⇤ C90 = bs 2 = 2 , (16b) in [24], and the SM loop function is S0 2.3. The Wilson ⇤ 2mD ' coe cients CLL,CRR,CLR are given by with the relative minus sign arising from the opposite 2 ˜ ˜ 2 v 1 1 U(1)0 charges of QR and DL (see Eqs. (9a,9b)). We note CLL =(YQbYQs⇤ ) 4 + 2 2 , (19a) that in this approximation the Wilson coe cients C9 and mQ 16⇡ mQ ! C90 are completely independent of the Z0 mass and the U(1) gauge coupling. Therefore, these relations deter- 2 0 2 v 1 1 C =(Y Y ⇤ ) + , (19b) mine the mass scale for the exotic quarks, RR Db Ds m4 16⇡2 m2 ✓ D D ◆ 1/2 mQ,D 25 TeV Re(Y Y ⇤ ) , (17) C =(Y Y )(Y Y ) ' ⇥ (Q,D)b (Q,D)s LR Qb Qs⇤ Db Ds⇤ ⇣ ⌘ 2 2 2 + v 1 log(mQ/mD) in order to address the anomaly in the B K⇤µ µ , (19c) decay (see Eqs.(2a,2b)). This scale is su !ciently high ⇥ m2 m2 16⇡2 m2 m2 Q D Q D ! that current collider constraints on new colored particles 2 ( 1 TeV) do not result in useful bounds. However, other where the (v ) terms originate from tree level Z0 contri- & O 2 flavor processes are easily sensitive to such high scales. butions, and the 1/(16⇡ ) suppressed contributions orig- While they do not rule out the combinations leading to inate from the scalar box diagrams. Note that the Z0 contribution to the mixing amplitude does not depend the operators corresponding to C9 and C90 , they do place on the Z0 mass and the U(1)0 gauge couplings separately,
but only through the combination v = mZ0 /g0.The good agreement of the SM prediction for Bs mixing with 1 the experimental data sets an upper bound on the U(1) If the Z0 is lighter than the B meson, it would show up as 0 aresonanceinthedi-muoninvariantmassspectrumofthe symmetry breaking VEV, v . + B K⇤µ µ decay rate. We reserve the analysis to another In the plots of Fig. 2 we show the limit on v as a publication! [22]. function of the masses of the vector-like quarks, mD and the discussion su ciently general under the main hypothesis of NP coupled predominantly to third-generation left-handed quarks and leptons. More explicitly, our working hypotheses to determine the initial conditions of the EFT, at a scale ⇤ above the electroweak scale, are the following:
1. only four-fermion operators built in terms of left-handed quarks and leptons have non- vanishing Wilson coe cients;
2. the flavour structure is determined by the U(2) U(2) flavour symmetry, minimally q ⇥ ` broken by two spurions V (2, 1) and V (1, 2); q ⇠ ` ⇠ 3. operators containing flavour-blind contractions of the light fields have vanishing Wilson coe cients.
We first discuss the consequences of these hypotheses on the structure of the relevant e↵ective operators and then proceed analysingModel the experimental building constraints on their couplings.
2.1 The e↵ective Lagrangian ❖ Interesting framework for addressing all anomalies: According to the first hypothesis listed above, we consider[Buttazzo, the following Greljo, Isidori, e↵ective Marzocca Lagrangian 2017] at a scale ⇤‣ aboveAssume the electroweak that NP scaleonly couples to LHD quarks and leptons: 1 = = q ` C (Q¯i aQj )(L¯↵ µ aL )+C (Q¯i Qj )(L¯↵ µL ) , (1) Le↵ HLNPSM v2 ij ↵ T L µ L L L S L µ L L L h i where v ‣ 246 GeV. For simplicity, the definition of the EFT cutord↵ scale and the normalisation ⇡ Hypothesis that NP couples primarily to 3 generation of the two operators is reabsorbed in the flavour-blind adimensional coe cients C+S and CT . fermions explains enhancement of b c ⌧ ⌫ ¯ over b q sµ ` µ The flavour structure in Eq. (1) is contained in the Hermitian! matrices ! ij, ↵ and follows from the assumedand absenceU(2) ofU(2) anomaliesflavour symmetry in K, , and τ decays its breaking.[Glashow, The Guadagnoli, flavour Lane symmetry 2014] q ⇥ ` is defined as follows: the first two generations of left-handed quarks and leptons transform as ‣ doublets underImpose the corresponding flavor structureU(2) groups,governed while by the minimally third generation broken and all the right- handed fermionsU(2) areq x singlets.U(2)l flavor Motivated symmetry: by the observed[Barbieri, pattern Isidori, of Jones-Perez, the quark Lodone, Yukawa Straub couplings 2011] (both mass eigenvalues and mixing matrix), it is further assumed that the leading breaking q V , ` V , ` V 2 terms of this flavour symmetrysb ⇠ cb are two spurion⌧µ ⇠ doublets,⌧µ Vq andµµ V⇠`, that⌧µ give rise to the mixing between the third generation and the other two [31,32]. The normalisation of Vq is conventionally chosen to be V (V ,V ), where V denote the elements of the Cabibbo-Kobayashi-Maskawa M. Neubert — Probingq ⌘ beyondtd⇤ thets⇤ SM with Flavorji Physics 32 (CKM) matrix. In the lepton sector we assume V (0,V )with V 1. We adopt as ` ⌘ ⌧⇤µ | ⌧µ| ⌧ reference flavour basis the down-type quark and charged-lepton mass eigenstate basis, where the SU(2)L structure of the left-handed fields is
V uj ⌫↵ Qi = ji⇤ L ,L↵ = L . (2) L di L `↵ ✓ L ◆ ✓ L ◆ A detailed discussion about the most general flavour structure of the semi-leptonic operators compatible with the U(2) U(2) flavour symmetry and the assumed symmetry-breaking terms q ⇥ ` is presented in Appendix A. The main points can be summarised as follows:
5 Model building
❖ Besides flavor physics, additional constraints from precision measurements of τ decays and Z couplings, as + [Feruglio, Paradisi, Pattori 2017] well as pp ⌧ ⌧ X [Faroughy, Greljo, Kamenik 2016] ! ❖ ��� Smoking-gun signature: Δχ � < ��� ( ) + ���
B K ⇤ ⌧ ⌧ �� enhancement of ��� ℬ
! )/ - branching ratio by factor > 100 τ ��� +
τ � |λ��|<� ��� [Buttazzo, Greljo, Isidori, Marzocca 2017] (*)
� ��� →
� ��� ( ℬ ��� � |λ��|<� ��� � � � � � � � (*) ℬ(� → � νν)/ℬ��
M. Neubert — Probing beyond the SM with Flavor Physics 33 µ µ µe ⌧` Figure 2: Left: Prediction for C = C (following from R ( ) ) and R ( ) for a randomly 9 10 K ⇤ D ⇤ chosen set of points within the 1 preferred region of the EFT fit: the blue points are obtained setting q q sb < 5 Vcb , while the green points are obtained setting the tighter condition sb < 2 Vcb in the fit. | | | | | | | |( ) The red cross denotes the 1 experimental constraint. Right: expectations for (B K ⇤ ⌫⌫¯) and ( ) q B ! q (B K ⇤ ⌧⌧¯)withinthe1 preferred values of the EFT fit, again for sb < 5Vcb (blue) and sb < 2Vcb (green).B !
the context of an explicit vector leptoquark model in Section 3.1. Another constraint on the size of CS,T comes from the study of perturbative unitarity in 2 2 scattering processes [45]. ! q Similarly to the one from direct searches, this bound is relevant for small bs and large CS,T , while it is easily satisfied in the region chosen by our EFT fit. As far as other low-energy observables are concerned, the most problematic constraint is the one following from meson-antimeson mixing. On the one hand, given the symmetry and symmetry-breaking structure of the theory, we expect the underlying model to generate an e↵ective interaction of the type
2 2 2 q 2 (V V ) 2 32⇡ v = CNP tb⇤ ti ¯b di ,CNP = (1) sb . (6) L( B=2) 0 32⇡2v2 L µ L 0 O ⇥ ⇤2 V 0 cb The preferred values of ⇤ and q from the EFT fit yield CNP = (100), while the experimental 0 sb 0 O constraints on M require CNP to be at most (10%). This problem poses a serious challenge Bs,d 0 O to all models where F =2e↵ective operators are generated without some additional dynamical suppression compared to the semi-leptonic ones. A notable case where such suppression does occur are models with LQ mediators, where F = 2 amplitudes are generated only beyond the tree level. q An alternative to avoid the problem posed by F = 2 constraints is to abandon the large sb scenario preferred by the EFT fit, and assume q 0.1 V . In this limit the contribution to | sb| . ⇥| cb| (down-type) F = 2 amplitudes is suppressed also in presence of tree-level amplitudes. However, in order to cure the problem of the EFT fit, in this case one needs additional contributions to
10 Emergence of a bigger picture?
❖ Required new particles in low TeV range, precisely where we (now) expect a solution to the hierarchy problem!
❖ Leptoquarks can arise from GUTs, neutrino mass models, SUSY models, or as pNGBs [Popov, White 2016]
❖ E.g.: Composite Higgs models with partial fermion [Buttazzo, Greljo, Isidori, Marzocca 2016; compositeness: Barbieri, Murphy, Senia 2016; …] ‣ Address hierarchy and flavor problems at ~10 TeV, light scalar leptoquarks (~ TeV) as pNGBs
‣ Interesting challenges for model building!
M. Neubert — Probing beyond the SM with Flavor Physics 34 Emergence of a bigger picture?
❖ Data may teach us an important lesson:
‣ Complementarity of different fields (flavor was sometimes considered irrelevant in the LHC era …)!
‣ Intimate connection between flavor and high-pT physics!
❖ Imagine the LHC legacy:
‣ Discovery of the Higgs boson (2012)
‣ Discovery of lepton-flavor non-universality (2019)
‣ Discovery of predicted leptoquarks/colorless bosons (202?)
‣ Embedding in a consistent theory of flavor and EWSB (20??)
M. Neubert — Probing beyond the SM with Flavor Physics 35 Conclusions
❖ If confirmed, the B-meson flavor anomalies are the most important discovery in particle physics since discovery of the weak gauge bosons and the Higgs
‣ Point to existence of new heavy particles in few-TeV range
‣ Possibly, these might be connected to a fundamental theory of electroweak symmetry breaking and flavor
‣ Strong physics case for future high-energy colliders
❖ Independent confirmation of the flavor anomalies by Belle II is as crucial as refining current LHCb analyses
M. Neubert — Probing beyond the SM with Flavor Physics 36