New Physics Models Facing Lepton Flavor Violating Higgs Decays
NNew Physics Models Facing Lepton Flavor Violating HiggsDecays
Nejc Koˇsnik Department of Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana,SloveniaandJoˇzef Stefan Institute, Jamova 39, P.O. Box 3000, 1001 Ljubljana, Slovenia
We speculate about the possible interpretations of the recently ob-served excess in the h → τ µ decay. We derive a robust lower bound onthe Higgs boson coupling strength to a tau and a muon, even in presenceof the most general new physics affecting other Higgs properties. Thenwe reevaluate complementary indirect constraints coming from low energyobservables as well as from theoretical considerations. In particular, thetentative signal should lead to τ → µγ at rates which could be observedat Belle II. In turn we show that, barring fine-tuned cancellations, theeffect can be accommodated within models with an extended scalar sec-tor. These general conclusions are demonstrated in explicit new physicsmodels. Finally we show how, given the h → τ µ signal, the current andfuture searches for µ → eγ and µ → e nuclear conversions unambiguouslyconstrain the allowed rates for h → τ e .PRESENTED AT The 7th International Workshop on Charm Physics(CHARM 2015)Detroit, MI, 18-22 May, 2015 Supported by Slovenian research agency. a r X i v : . [ h e p - ph ] S e p Introduction
The discovery of the Higgs boson [1, 2] offers numerous observables where the validityof the Standard Model (SM) can be tested. The CMS collaboration has recentlyreported a slight excess with a significance of 2 . σ in the search for LFV decay h → τ µ [3]. The best fit for the branching ratio of the Higgs boson to τ µ underassumption of SM Higgs production is found to be B ( h → τ µ ) = (cid:0) . +0 . − . (cid:1) % . (1)This recent hint has received great attention in the literature (see [4] and referencestherein). An ATLAS study of h → τ µ [5] in the hadronic τ channel observes noexcess and is consistent with the CMS result (1).In light of the tentative signal it is instructive to revisit compatibility of such large B ( h → τ µ ) with other low-energy lepton flavor violation (LFV) probes in the contextof popular New physics (NP) models. The mass terms and Higgs boson couplings of charged leptons after electroweak sym-metry breaking (EWSB) can be parametrized in the general case as L eff .Y (cid:96) = − m i δ ij (cid:96) iL (cid:96) jR − y ij (cid:16) (cid:96) iL (cid:96) jR (cid:17) h + . . . + h . c . , (2)where the ellipsis denotes non-renormalizable terns involving more than one Higgsboson. While in the SM the Yukawas y ∼ m are diagonal in the mass basis, NPcould misalign the two matrices and via y τµ and/or y µτ induce h → τ µ decays with abranching ratio of B ( h → τ µ ) = m h π Γ h ( | y τµ | + | y µτ | ). If one assumes that the totalHiggs boson decay width (Γ h ) is SM-like and enlarged only by the contribution from h → τ µ then the measurement in Eq. (1) can be interpreted as a two-sided bound,0 . . < (cid:112) | y τµ | + | y µτ | < . . h → τ µ branching fraction depends also on other Higgscouplings contributing both to its total decay width (Γ h ) as well as its productioncross-section ( σ h ). In particular, a given signal can be reproduced for larger (smaller)values of | y τµ | and | y µτ | by enhancing (suppressing) Γ h and/or suppressing (enhancing) σ h . Individual effects of Γ h and σ h can be disentangled by performing a global fit toall Higgs production and decay event yields at the LHC [4]. Numerically, we find inthis case0 . . < (cid:113) | y τµ | + | y µτ | < . . . L . . (3)In the following we assume the SM contains all the relevant degrees of freedomat energies O (few 100) GeV, whereas for the additional heavy degrees of freedom we1ssume they been integrated out. The natural ranges for the effective Higgs couplingsfollow from the hierarchy between the muon and tau lepton masses [6, 7], (cid:113) | y τµ y µτ | (cid:46) √ m µ m τ v = 0 . . (4)It is interesting to note that almost the whole parameter space in allowed by h → τ µ is also compatible with the above naturalness criterium [4].Phenomenologically the most relevant low-energy constraints on this scenario arethe one- and two-loop contributions to the operators LH ( σ · B ) E and Lτ a H ( σ · W a ) E ,where σ µν = i [ γ µ , γ ν ]/2, B µν and W aµν are the hypercharge and weak isospin fieldstrengths, respectively, and τ a are the Pauli matrices. These operators can mediatethe strongly constrained radiative LFV decays. The most stringent constraint comesfrom the τ → µγ decay [8], mediated by the effective Lagrangian L eff . = c L Q Lγ + c R Q Rγ + h . c . , (5)where Q L,Rγ = ( e/ π ) m τ ( µσ αβ P L,R τ ) F αβ , P L,R = (1 ∓ γ ) / F αβ is the electro-magnetic field strength tensor. The resulting EFT correlation between B ( h → τ µ ) inand B ( τ → µγ ) is shown in left-hand panel in Fig. 1 (diagonal dashed orange line),assuming SM values of all Higgs boson couplings except y τµ and y µτ . In the sameplot, the CMS preferred range of B ( h → τ µ ) in Eq. (1) is displayed by the horizontalblue band, while the current ( B ( τ → µγ ) < . × − @ 90% C.L.) [9] and projectedfuture ( B ( τ → µγ ) < × − @ 90% C.L.) [10] indirect constraints are shaded inlight and dark gray vertical bands, respectively. We observe that within the EFTapproach, the CMS signal is well compatible with the non-observation of τ → µγ atthe B factories and will marginally remain so even at Belle II. Extensions of the SM with an additional SU (2) L doublet scalar are an effective de-scription of several NP scenarios (e.g. supersymmetric extensions or models address-ing the strong CP problem via a Peccei-Quinn symmetry), for a recent review c.f. [7].The most extensively studied version of the Two Higgs Doublet Model (THDM) isthe type-II model in which one of the doublets couples to up-type quarks, while theother one couples to down-type quarks and charged leptons, avoiding in this way thetree level flavor changing neutral currents (FCNCs). All LFV in this case comes at1-loop and is aligned with the SM flavor structure thus rendering LFV processes toa negligible level, compared to the one of the SM [4]. In type-III THDM Yukawacouplings are generic and allow for large LFV. In the case with a MSSM-like Higgspotential the following relations hold [11]tan β = v u v d , tan 2 α = tan 2 β m A + m Z m A − m Z , (6)2igure 1: Left-hand side panel: Correlation between B ( h → τ µ ) and B ( τ → µγ ) invarious NP scenarios. The present experimental result for B ( h → τ µ ) is shown inhorizontal blue band [3]. Current and future projections for B ( τ → µγ ) experimentalsensitivity are represented with vertical light [9] and dark [10] gray bands, respectively.Superimposed are the predictions within the EFT approach (diagonal dashed orangeline), in the type-III THDM (green and black bands), and in models with scalarleptoquarks (diagonal red and orange shaded band). Right-hand side panel: Allowedregion in the B ( h → τ e )– B ( h → τ µ ) plane when experimental upper bounds on µ → eγ and µ − e conversion rates are taken into account. Pink region is permittedin the effective theory setting while the dashed line indicates how much the regionwill shrink if Mu2e and MEG II experiments see no signal events. Green region isallowed within type-III THDM model with m A = 0 . β = 10. Rulersindicate how much the region shrinks with increasing tan β or m A , while dashed linescorrespond to improved experimental upper bounds on µ → eγ and µ − e as describedin the text.while for the masses m H ± = m A + m W and m H = m A + m Z − m h . Here β is theangle that diagonalizes the mass matrices of charged scalars and pseudoscalars while α is an analogous angle for the neutral scalars. The relevant part for the discussionof LFV are the Yukawa couplings in the charged lepton mass eigenstate basis [11] L = y H k fi √ H k (cid:96) L,f (cid:96)
R,i + y H + fi √ H + ν L,f (cid:96)
R,i + h.c. , (7)where the LFV Yukawa couplings can be written as y H k fi = x kd m (cid:96) i v d δ fi − (cid:15) (cid:96)fi (cid:0) x kd tan β − x k ∗ u (cid:1) . (8)3he off-diagonal parameters (cid:15) (cid:96)fi drive the LFV phenomena, while the coefficients x kq for H k = ( H, h, A ) can be found in [4]. Using the above relations, we find the tree-levelresult for the h → τ µ branching fraction, B ( h → τ µ ) = m h π Γ h (sin α tan β + cos α ) (cid:0) | (cid:15) (cid:96)µτ | + | (cid:15) (cid:96)τµ | (cid:1) . (9)We have found that even for light pseudoscalar masses ( m A ), modifications of hW W and hZZ relative to their SM values is negligible [4].The decay width of τ → µγ is driven by a one- and two-loop Barr-Zee diagramswith virtual charged or neutral Higgses. At one-loop the amplitude is suppressed bytwo small Yukawa couplings, while the two-loop result is proportional to y tt and asingle LFV Yukawa. Indeed one finds that Barr-Zee contributions dominate the rateof τ → µγ [4]. We sample the parameter space of (cid:15) (cid:96)τµ , (cid:15) (cid:96)µτ , (cid:15) (cid:96)ττ for a chosen valuesof tan β and m A . The ranges allowed for (cid:15) (cid:96)τµ,µτ are required to fulfill the naturalnesscriterium of Eq. (4) and stay within the perturbative regime.The 1-loop amplitude of the τ → µγ process further depends on the diagonal y hττ Yukawa coupling which is experimentally constrained by the searches for h → τ τ decays by the ATLAS [12] and CMS [13] experiments. The naively averaged signalstrength of two τ τ signal strengths results in µ ττ = 1 . +0 . − . which directly constrains y hττ . A scenario with SM-like y hττ coupling corresponding to µ ττ = 1 for fixed tan β =10 and m A = 0 . m A significantly larger than 500 GeV it is not possible to reconcile bothpredictions with the corresponding experimental values. Allowing (cid:15) (cid:96)ττ to departurefrom zero within the allowed range we obtain correlation represented by the greenband in left-hand side panel in Fig. 1. In particular, this additional freedom in τ → µγ breaks the strict correlation with the h → τ µ rate. A scalar leptoquark state (LQ) can induce h → τ µ decay via quark-LQ penguindiagrams. Inspection of the helicity structure of the relevant diagrams reveals thatboth chiralities of leptons and top quark have to couple to the LQ state, in order keepthe leptoquark couplings perturbative [4]. LQ state can couple to the Higgs also viathe “Higgs portal” operator, − λH † H ∆ † ∆ that comes with an additional parameter, λ . ∆ = ( , , − / ) case The Yukawa couplings of ∆ are given by the following Lagrangian L ∆ = y Lij Q i,a ∆ (cid:15) ab L C j,b + y Rij U i ∆ E C j + h.c. , (10)4here Q i = ( u iL , d iL ) T and U i = u iR are the quark weak doublets and up-quark singlets,respectively. We explicitly show flavor indices i, j = 1 , ,
3, and SU (2) indices a, b =1 ,
2, with (cid:15) = 1. The h → τ µ decay width in the presence of ∆ scalar is then,Γ( h → τ µ ) = 9 m h m t π v (cid:16)(cid:12)(cid:12) y Ltµ y Rtτ (cid:12)(cid:12) + (cid:12)(cid:12) y Ltτ y Rtµ (cid:12)(cid:12) (cid:17) | g ( λ, m ∆ ) | . (11)Here the relevant loop function further depends on the portal coupling λ and is givenin [4]. The state ∆ also contributes to the τ → µγ via same y couplings as the onespresent in h → τ µ : B ( τ → µγ ) = αm τ π Γ τ m t m h ( x t ) (cid:16)(cid:12)(cid:12) y Ltµ y Rtτ (cid:12)(cid:12) + (cid:12)(cid:12) y Ltτ y Rtµ (cid:12)(cid:12) (cid:17) , (12)where x t = m t /m and expression for the h function can be found in Ref. [4].The impact of a non-zero Higgs portal coupling λ in the scenario with ∆ has alsobeen studied. As an example, for m ∆ = 650 GeV the loop function dependence onthe portal coupling is g = − (0 .
26 + 0 . λ ). Thus, a positive large λ could relax theleptoquark Yukawa couplings and yield sizable h → τ µ rates without violating the τ → µγ constraint. However, the Higgs portal coupling also induces corrections tothe h → γγ decay and to gluon-gluon fusion (ggF) induced Higgs production with theleptoquark running in the triangular loop. Taking those modifications of the Higgscouplings into account we have found that one can compensate small leptoquarkYukawas by scaling up λ , which is itself bounded from above only by perturbativityrequirements [4].The correlation between the h → τ µ and τ → µγ branching ratios in presenceof the (3 , , − /
3) leptoquark state for | λ | < m ∆ >
600 GeV is depicted inleft-hand side panel in Fig. 1 with a pink stripe, demonstrating that τ → µγ basicallyexcludes this LQ state as an explanation of h → τ µ signal. ∆ = ( , , / ) case The Yukawa couplings of the ∆ leptoquark to SM fermions are L ∆ = y Lij E i ∆ a ∗ Q j,a − y Rij U i ∆ a (cid:15) ab L j,b + h.c. , (13)The h → τ µ decay rate in this case isΓ( h → τ µ ) = 9 m h m t π v | g ( λ, m ∆ ) | (cid:0) | y Lµt y Rtτ | + | y Lτt y Rtµ | (cid:1) . (14)Allowed values for the Higgs portal coupling λ can be inferred from a global fit to theHiggs data as has been done for the portal coupling of the (3 , , − /
3) state.5he decay width of τ → µγ are proportional to the couplings responsible for h → τ µ : B ( τ → µγ ) = αm τ π Γ τ m t m h ( x t ) (cid:0) | y Rtτ y Lµt | + | y Rtµ y Lτt | (cid:1) . (15)In this leptoquark scenario the bound on B ( τ → µγ ) excludes sizable B ( h → τ µ )due to the strict correlation between the two observables. See the orange stripe inleft-hand side panel in Fig. 1, where the portal coupling is restricted to | λ | < h → τ µ vs. h → τ e A positive indication for h → τ µ decay can be combined with stringent experimentallimits on µ − e LFV processes to constrain τ − e processes. In particular, in models withtree-level h → τ µ (EFT, THDM III) the product of the B ( h → τ e ) and B ( h → τ µ )is bounded from above by the rates of µ → eγ and µ − e conversion on nuclei. This isdue to the fact that tree level Higgs decays to τ µ ( τ e ) depend on y µτ,τµ ( y eτ,τe ) whilethe same sets of couplings contribute at the loop level to µ → eγ and µ − e conversionvia diagrams with a virtual τ . In the effective theory framework, the contributionsto the µ → eγ process stemming from a virtual τ are m τ enhanced with respect todiagrams with intermediate µ or e states [8] leading to c τL (cid:39) m τ m µ − x τ − x τ − x τ m h (1 − x τ ) y ∗ µτ y ∗ τe , x τ = m τ m h , (16)where we have neglected the effects of the light lepton masses. The coefficient c τR isobtained from Eq. (16) by replacing y ij → y ∗ ji . The µ → eγ branching fraction is thussensitive to a distinct combination of the LFV Yukawas: B ( µ → eγ ) (cid:39) B µ → eγ (cid:0) | y µτ y τe | + | y τµ y eτ | (cid:1) , B µ → eγ = 185 . (17)On the other hand, µ − e conversion on nuclei is most sensitive to vector cur-rent effective operators ( eγ ν P L,R µ ) ( qγ ν q ). The branching fraction B ( µ → e ) Au ≡ Γ( µ → e ) Au / Γ capture Au can be put in the form B ( µ → e ) Au = B µe (cid:0) | y eτ y µτ | + | y τe y τµ | (cid:1) , B µe = 4 . × − , (18)where the relevant numerics have been taken from Ref. [14] (also c.f. [4]). The com-plementary information on the LFV couplings extracted from µ → eγ and µ − e conversion allows for correlation between the Higgs LFV h → τ µ and h → τ e decays: B ( h → τ µ ) B ( h → τ e ) = 8 × − (cid:20) B ( µ → eγ )10 − (cid:21) + 3 × − (cid:20) B ( µ → e ) Au − (cid:21) . (19)6he best experimental limit on B ( µ → e ) Au < × − (at 90% C.L.) was achievedby the SINDRUM II Collaboration [15] while the best upper bound on B ( µ → eγ ) < . × − (at 90% C.L.) was recently determined by the MEG Collaboration [16].Note that with the current experimental data the sum on the right-hand side ofEq. (19) is completely saturated by the µ − e conversion contribution. Combiningthe two bounds with the central value for the h → τ µ branching fraction in Eq. (1)leads to an upper bound B ( h → τ e ) < .
26 . This is above the current indirectconstraint coming from searches for τ → eγ [9] which reads B ( h → τ e ) < .
19 . Futureimprovements of bounds on µ → eγ and especially µ − e , and assuming B ( h → τ µ )stays at the percent level, will indirectly probe B ( h → τ e ) at the 10 − level [4]. Similaranalysis can be carried over to the THDM III framework, where the resulting boundon h → τ e renders this decay invisible at the LHC (green region in right-hand sidepanel in Fig. 1). Motivated by the experimental indication of h → τ µ events by the CMS Collaborationwe have examined the implications of LFV Higgs decays at the percent level onseveral extensions of the SM. We have shown how a tentative B ( h → τ µ ) signal canbe combined with other Higgs measurements to yield a robust lower bound on theeffective LFV Higgs Yukawa couplings to taus and muons. In explicit NP models,the τ → µγ constraint is generically more severe. In fact, an eventual observation of h → τ µ at the LHC together with indirect constraints would point in the directionof an extended SM scalar sector, minimal example being THDM of type III. Wehave also examined models where h → τ µ is generated at loop level to demonstratedifficulties with these models. Finally, we have combined the signal of h → τ µ withexperimental limits on µ → eγ decays and µ − e conversions in nuclei to yield robustbounds on B ( h → τ e ). In particular, considering only the Higgs EFT effects, the twoLFV Higgs decay rates could still be comparable. On the other hand, the THDM IIIcannot accommodate both branching ratios at the percent level. It turns out thatcurrently planned improvements in experimental searches for µ − e LFV processeswill be able to probe the product B ( h → τ µ ) B ( h → τ e ) at the 10 − level in genericEFT and to order 10 − or better within the THDM III. References [1] Georges Aad et al.
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