Higgs Physics and Dark Matter
Marcela Carena Fermilab and Uchicago Invisibles17 Workshop, UZH, Zurich, June 12, 2017 New Physics Landscape after the Higgs Discovery
mH << MP ? A. Pomarol, WIN2015
Towards naturalness No{ new TeV-physics
“fermionizing” the Higgs relaxation Supersymmetry mechanism? “marrying” a fermion: arXiv:1504.07551 Higss Higgsino
Multiverse mH~MP
Compositeness mH~MP
mH~MP mH~MP mH~MP The “transvestite” Higgs: mH~125 GeV m ~M { mH~MP H P new TeV-physics H = mH~MP
How far are we willing to go? Trusting the SM up to the Planck scale Looking under the Higgs lamp-post: 200 Instability
Non
GeV 150 -stability - in perturbativity t Meta
M 100 Stability At the edge SM valid up to mass of Stability M Top Planck 50
0 SUSY 0 50 100 150 200 MSSM
Higgs mass Mh in GeV extensions
Composite Higgs MSSM mh 125
mh ~ 125 GeV Stop Soft Mass NMSSM + mh ~ 125 GeV: At low tanβ naturally compatible with NMSSM stops at the electroweak Stop mixing scale, thereby reducing Splitting in stop SUSY breaking the degree of fine tuning mass parameters can to get EWSB accommodate one light stop with minimal impact to gluon fusion
Looking under the Higgs lamp-post:
At the edge SM valid up to No Higgs above a of Stability MPlanck certain scale, at which MSSM SUSY the new strong extensions dynamics turns on Composite è dynamical origin of Higgs EWSB 125 New strong resonance masses constrained by EW data and direct searches Higgs è scalar resonance much lighter that other ones
Additional option: 2HDMs to explain flavor @EW scale Higgs bosons as the Frogatt-Nielsen Flavon
All these BSM alternatives can affect Higgs production & decay signal strengths Higgs Properties in good agreement with SM predictions
Still direct measurement of bottom & top couplings subject to large uncertainties Moderate deviations from SM predictions possible
In Run 2 data, suppression of bottom coupling still present
HL- LHC : precision on most relevant couplings will be better than/about 10%
Composite Higgs Models The Higgs as a pseudo Nambu-Goldstone Boson (pNGB)
Inspired by pions in QCD
QCD with 2 flavors: global symmetry
SU(2)L x SU(2)R/ SU(2)V. Higgs is light because is the pNGB -- a kind of pion – of a new strong sector π+- π0 are Goldstones associated to spontaneous breaking Mass protected by the global symmetries
δ
A tantalizing alternative to the strong dynamics realization of EWSB Georgi,Kaplan’84 Higgs as a PNGB Light Higgs since its mass arises from one loop
Mass generated at one loop: explicit breaking of global symmetry due to SM couplings
The Higgs potential depends on the chosen global symmetry AND on the fermion embedding in the representations of the symmetry group Higgs mass challenging to compute due to strong dynamics behavior
m2 m2M2 /f 2 H / t T
Composite-sector characterized by a coupling gcp ≫ gSM and scale f ~ TeV
New heavy resonances è mρ ~ gcp f and Mcp ~ mρ cosψ New Heavy Resonances being sought for at the LHC Minimal Composite Higgs models phenomenology -- All About Symmetries -- Choosing the global symmetry [SO(5)] broken to a smaller symmetry group [SO(4)] -- at an intermediate scale f larger the electroweak scale -- such that: the Higgs can be a pNBG, the SM gauge group remains unbroken until the EW scale and there is a custodial symmetry that protects the model from radiative corrections
Higgs couplings to W/Z determined Higgs couplings to SM fermions by the gauge groups involved depend on fermion embedding SO(5) è SO(4) With Notation MCHMQ-U-D SO(5) ×U(1) smallest group: GEW ⊃ SM SO(5) & cust. sym. & H = pNGB Representations
Other symmetry patterns, some with additional Higgs Bosons Generic features:
Suppression of all partial decay widths and all production modes
Enhancement/Suppression of BR’s dep.
on effects of the total width suppression 5 Minimal composite Higgs model
Minimal Composite Higgs Models (MCHM) [47–53] represent a possible explanation for the scalar nat- uralness problem, wherein the Higgs boson is a composite, pseudo-Nambu–Goldstone boson rather than an elementary particle. In such cases, the Higgs boson couplings to vector bosons and fermions are 5 Minimal compositemodified with Higgs respect model to their SM expectations as a function of the Higgs boson compositeness scale, f . Corrections due to new heavy resonances such as vector-like quarks [54] are taken to be sub-dominant. Minimal CompositeProduction Higgs Models or decays (MCHM) through [47– loops53] represent are resolved a possible in terms explanation of the contributing for the scalar particles nat- in the loops, as- uralness problem,suming wherein only the contributions Higgs boson is from a composite, SM particles. pseudo-Nambu–Goldstone It is assumed that bosonthere are rather no than new production or decay an elementary particle.modes besides In such those cases, in the the Higgs SM. boson couplings to vector bosons and fermions are modified with respect to their SM expectations as a function of the Higgs boson compositeness scale, f . Corrections dueThe to new MCHM4 heavy resonances model [47 such] is as a minimal vector-like SO(5) quarks/SO(4) [54] are model taken where to be the sub-dominant. SM fermions are embedded in Production or decaysspinorial through representations loops are resolved of SO(5). in terms Here of the contributing ratio of the particles predicted in coupling the loops, scale as- factors to their SM suming only contributionsexpectations, from, SM can particles. be written It in is the assumed particularly that there simple are no form: new production or decay modes besides those in the SM. = = = 1 ⇠ , The MCHM4 model [47] is a minimal SO(5)/SO(4) model whereV theF SM fermions are embedded in (10) spinorial representations of SO(5). Here the ratio of the predicted coupling scale factors to their SM 2 2 p expectations, , canwhere be written⇠ = v in/ f theis particularly a scaling parameter simple form: (with v being the SM vacuum expectation value) such that the SM is recovered in the limit ⇠ 0, namely f . The combined signal strength, µh, which is = V = F != 1 ⇠ , !1 equivalent to the coupling scale factor, = pµh, was measured using the combination(10) of the visible decay channels [10] and is listed in Model 2 of Table 1. The experimental measurements are interpreted 2 2 p where ⇠ = v / f inis the a scaling MCHM4 parameter scenario (with by rescalingv being the the SM rates vacuum in di expectation↵erent production value) such and thatdecay the modes as functions of SM is recovered in the limit ⇠ 0, namely f . The combined signal strength, µh, which is the coupling scale! factors = V!1= F, taking the same production and decay modes as in the SM. This equivalent to the coupling scale factor, = pµh, was measured using the combination of the visible decay channels [is10 done] and isin listed the same in Model way 2 as of described Table 1. The in Section experimental3. The measurements coupling scale are interpreted factors are in turn expressed as 5 Minimal composite Higgs model in the MCHM4 scenariofunctions by of rescaling⇠ using Eq. the rates (10). in di↵erent production and decay modes as functions of the coupling scaleFigure factors2(a) = showsV = theF, taking observed the same and expected production likelihood and decay scans modes of as the in Higgs the SM. compositeness This scaling para- is done in the sameMinimal way as Composite described Higgs in Section Models3 (MCHM). The coupling [47–53] representscale factors a possible are in explanation turn expressed for the asscalar nat- meter,uralness⇠, in problem, the MCHM4 wherein the model. Higgs boson This model is a composite, contains pseudo-Nambu–Goldstone a physical boundary boson restricting rather than to ⇠ 0, with the functions of ⇠ using Eq. (10). SMan Higgs elementary boson particle. corresponding In such cases, to ⇠ the= 0. Higgs Ignoring boson this couplings boundary, to vector the bosons scaling and parameter fermions are is measured to be modified with respect to their SM expectations as a function of the Higgs boson compositeness scale, f . Figure 2(a) shows⇠ = the1 observedµh = and0.18 expected0.14, likelihood while the expectation scans of the Higgs for the compositeness SM Higgs boson scaling is 0 para-0.14. The best-fit value meter, ⇠, in the MCHM4Corrections model. due Thisto new± model heavy contains resonances a physicalsuch as vector-like boundary quarks restricting [54] are to taken⇠ 0, to be with sub-dominant.± the observed for ⇠ is negative because µh >1 is measured. The statistical and systematic uncertainties are of SM Higgs boson correspondingProduction or decays to ⇠ = through0. Ignoring loops this are boundary, resolved in the terms scaling of the parameter contributing is particles measured in theto be loops, as- similarsuming size. only Accounting contributions from for the SM lower particles. boundary It is assumed produces that there an observed are no new (expected) production upperor decay limit at the 95% ⇠ = 1 µ = 0.18 0.14, while the expectation for the SM Higgs boson is 0 0.14. The best-fit value h CLmodes± of ⇠ besides< 0.12 those (0.23), in the corresponding SM. to a Higgs boson compositeness± scale of f > 710 GeV (510 GeV). observed for ⇠ is negative because µh >1 is measured. The statisticalΛ and systematic uncertaintiesΛ are of 14 ATLAS 14 ATLAS
The observed limit is strongerSimplest than Minimal expected-2ln Composite because µ > Higgs1 was measured-2ln [10]. h -1 -1 / s = 7 TeV, 4.5-4.7 fb s = 7 TeV, 4.5-4.7 fb similar size. AccountingThe MCHM4 for the model lower [ boundary47] is a minimal produces SO(5) anSO(4) observed12 model (expected) where the upper SM12 fermions limit at the are 95%embedded in s = 8 TeV, 20.3 fb-1 s = 8 TeV, 20.3 fb-1 CL of ⇠ < 0.12 (0.23),spinorial corresponding representations to a of Higgs SO(5). boson Here compositeness the ratio10 of theMCHM4 scale predicted of f coupling> 71010 GeV scale (510 factorsMCHM5 GeV). to their SM Similarly, the MCHM5 model [48, 49] is an SO(5)/SO(4) Obs. model where the SM Obs. fermions are embedded in 8 8 expectations,MCHM4, canè be writtenfermions in the in particularly spinorial simple4 representation form: Exp. of SO(5) Exp. The observed limit is stronger than expected because µh >1 was measured [10]. fundamental representations of SO(5). Here6 the measured rates are6 expressed in terms of ⇠ by rewriting = = 4 = ⇠ , 4 Similarly, the MCHM5the coupling model scale [48, 49 factors] is an SO(5) [V , /FSO(4)] as: modelV F where1 the SM fermions are embedded in (10) 2 2 fundamental representations of SO(5). Here the measured rates0 areV p= expressed1 ⇠ in terms0 of ⇠ by rewriting where ⇠ MCHM5= v2/ f 2 isè a scaling fermions parameter in fundamental (with v being 5 the representation SM vacuum expectation of SO(5) value) such that the the coupling scale factors [V , F] as: −0.8 −0.6 −0.4 −0.2 ⇠0 0.2 0.4 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 (11) ⇠ f 1 2 ξ µ ξ SM is recovered in the limit = 0, namely⇠ F =.p The combined, signal strength,2 2 h, which is V ! 1 !1(a) MCHM4p1 ⇠ ξ = v(b)/MCHM5 f equivalent to the coupling scale factor, = pµh, was measured using the combination of the visible 1 2⇠ Figure 2: Observed (solid) and expected (dashed) likelihood scans of the Higgs compositeness(11) scaling parameter, decay channels2 [210] and is listed = in Modelp ⇠ 2, in, of the Table MCHM4 and1. MCHM5 The models. experimental The expected curves measurements correspond to the SMare Higgs interpretedboson. The line at where ⇠ = v / f . TheF measurementsF of and [10] are given in Model 3 of Table 1. The likelihood κ 1.8 ⇠ 2 ln ⇤ =V0 corresponds toF the most likely value of ⇠ within the physical region ⇠ 0. The line at 2 ln ⇤ = 3.84 ATLAS p1 in the MCHM4 scenario by rescaling the ratescorresponds in to di the↵ one-sidederent upper production limit at approximately and the decay 95% CL (2 modesstd. dev.), given as⇠ functions0. of scans of ⇠ in MCHM51.6 ares = shown7 TeV, 4.5-4.7 fb-1 in Figure 2(b). As with the MCHM4 model, the MCHM5 model contains 2 2 the coupling scale factors s = =8 TeV, 20.3V fb=-1 F, taking the same production and decay modes as in the SM. This where ⇠ = v / f . The measurements of1.4 V and F [10] are given in Model 3 of Table 1. The likelihood a physicalis done in boundary the same way restricting as described to ⇠ in Section0, with3. the The SM coupling HiggsModel scale bosonLower factors limit corresponding on aref in turn expressed to ⇠ = as0. Ignoring this scans of ⇠ in MCHM5 are shown in Figure1.2 2(b). As with the MCHM4 model, the MCHM5Obs. Exp. model contains MCHM4 boundary,functions of the⇠ using composite Eq. (10). Higgsξ=0.1 bosonξ=0.0 scaling parameterMCHM4 is determined710 GeV 510 GeV to be ⇠ = 0.12 0.10, while a physical boundary restricting to ⇠ 0,1 withξ=0.2 the SM Higgs boson corresponding to ⇠ = 0. Ignoring this ξ=0.3 MCHM5 780 GeV 600 GeV ± 0.8 0.00 0.10 is expected for theξ=0.1 SM Higgs boson. As above, the best-fit value for ⇠ is negative because boundary, the compositeFigure 2 Higgs(a) shows boson the observed scaling parameterand expectedTable is likelihood 3: determinedObserved and expected scans to lower of be limits the⇠ at theHiggs= 95% CL0 compositeness. on12 the Higgs0 boson.10, compositeness while scaling scale para-f in the ± ξ=0.2 Best fit SM CERN-PH-EP-2015-191 µ > 0.6 ξ=0.3 MCHM4 and MCHM5 models. ± 0.00 0.10 is expectedhmeter,1 is for⇠ measured., in the the SM MCHM4 Higgs Accounting model. boson.MCHM5 This for As model the above,Obs. boundary contains 68% theCL Exp. best-fit 68% a producesCL physical value boundary an for observed⇠ is restricting negative (expected) to because⇠ 0, upper with the limit at the 95% 0.4 ± ⇠ = Obs. 95% CL Exp. 95% CL µh >1 is measured.CLSM Accounting of Higgs⇠ < 0.10 boson for (0.17), corresponding the boundary corresponding to produces0. Ignoring to a an Higgs observed this boson boundary, (expected) compositeness the scaling upper parameter limit scale at of isthe measuredf 95%> 780 to GeV be (600 GeV). 0.8 0.9 1Figure 1.13 shows 1.2 the two-dimensional 1.3 likelihood for a measurement of the vector boson ( ) and fermion ⇠ = 1 µh = 0.18 0.14, while the expectation for the SM Higgs boson is 0 0.14. The best-fitV value CL of ⇠ < 0.10 (0.17), corresponding to a Higgs boson compositeness(F) coupling scale factors scale in the [ ofV , Ff] plane,> 780 overlaid GeV with predictions (600 as GeV). parametric functions of ⇠ for ± κV ± observed for ⇠ is negative because µh >1 isthe measured. MCHM4 and MCHM5 The models statistical [55–57]. Table and3 systematicsummarises the lower uncertainties limits at the 95% CL are on the of Figure 3: Two-dimensional likelihood contours in the [ , ] couplingHiggs boson scale factor compositeness plane, where scale2 ln in⇤ = these2.3 and models. V F similar size.2 ln Accounting⇤ = 6.0 correspond approximately for the tolower the 68% CL boundary (1 std. dev.) and produces the 95% CL (2 std. an dev.), observed respectively. (expected) upper limit at the 95% The coupling scale factors predicted in the MCHM4 and MCHM5 models are shown as parametric functions of the CL of ⇠ < 0.12Higgs boson (0.23), compositeness corresponding parameter ⇠ = v2/ f 2. The to two-dimensional a Higgs likelihood boson contours compositeness are shown for reference scale of f > 710 GeV (510 GeV). and should not be used to estimate the exclusion for the single parameter6 Additional⇠. electroweak9 singlet The observed limit is stronger than expected9 because µh >1 was measured [10]. A simple extension to the SM Higgs sector involves the addition of one scalar EW singlet field [41, 58– 63] to the doublet Higgs field of the SM, with the doublet acquiring a non-zero vacuum expectation value. Similarly, theThe lighter MCHM5 Higgs boson modelh is taken [48 to be, 49 the observed] is an Higgs SO(5) boson./SO(4) It is assumed model to have the where same the SM fermions are embedded in production and decay modes as the SM Higgs boson does,This3 with spontaneous only SM particles symmetry contributing breaking to leads loop- to mixing between the singlet state and the surviving state of fundamentalinduced representations production or decay modes. of In SO(5). this model, Hereits productionthe the doublet and measured decay field, rates resulting are modified rates in two CP-even according are expressed Higgs bosons, where in termsh (H) denotes of ⇠ theby lighter rewriting (heavier) of to: the pair. The two Higgs bosons, h and H, are taken to be non-degenerate in mass. Their couplings to 2 the coupling scale factors [V , F] as:h = fermionsh,SM and vector bosons are similar to those of the SM Higgs boson, but each with a strength reduced ⇥ 2 by a common scale factor, denoted by for h and 0 for H. The coupling scale factor (0) is the sine h = h,SM (13) ⇥ (cosine)V of= the h–1H mixing⇠ angle, so: BRh,i = BRh,i,SM , 2 2 1 2⇠ + 0 = 1 . (11)(12) where h denotes the production cross section, h denotes the totalF decay= p width, BRh,i denotes, the branch- ing ratio to the di↵erent decay modes i, and SM denotes their respective valuesp1 ⇠ in the Standard Model. For the heavier Higgs boson H, new decay modes such as H hh are possible if they are kinematically 10 2 2 ! where ⇠ = allowed.v / f In. this The case, measurementsthe production and decay rates of of theV Handboson areF modified[10] withare respect given to those in of Model 3 of Table 1. The likelihood scans of ⇠ ina SM MCHM5 Higgs boson with are equal shown mass by inthe branching Figure ratio2(b). of all new As decay with modes, the BRH MCHM4,new, as: model, the MCHM5 model contains 2 = , H 0 ⇥ H SM a physical boundary restricting to ⇠ 0,2 with the SM Higgs boson corresponding to ⇠ = 0. Ignoring this 0 H = H,SM (14) 1 BRH,new ⇥ ⇠ = . . boundary, the composite Higgs boson scaling parameter is determined to be 0 12 0 10, while BR , = (1 BR , ) BR , , . ± 0.00 0.10 is expected for theH i SM Higgs H new boson.⇥ H SM i As above, the best-fit value for ⇠ is negative because ± 3 The decays of the heavy Higgs bosons to the light Higgs boson, for example H hh, are assumed to contribute negligibly to ! µh >1 is measured.the light Higgs boson Accounting production rate. The contaminationfor the from boundary heavy Higgs boson produces decays (such as H anWW observed) in light Higgs (expected) upper limit at the 95% ! boson signal regions (h WW) is also taken to be negligible. CL of ⇠ < 0.10 (0.17), corresponding! to a Higgs boson compositeness scale of f > 780 GeV (600 GeV).
11
9 More diverse Minimal Composite Higgs models confronting data h to di-photons h to ZZ
+ h ZZ % ATLAS 95 CL ( ) 1.4 + + + ⌦ ⇥ + + * * ⌦ · MCHM , MCHM , + - - 5 10 ⌦ Simple + * * - - MCHM , MCHM14⌅1⌅10 ·+ * ** * 14⌅14⌅10
* SM + + * ·· * ⇥ + +*+* · + * * * B * * + +*++++ +· 1.2 ⇤ / + ++ *- +- ++ + * * ** ⇤⇤ ⇥ *8*/29++*·+* *· *+ * - - JHEP 08 (2016) 045 ⇤ ⌦ ⇥ +**+ +*+*+ ** * * * ** ⇤ ⇤ ⇥ ⇥ + * ++++*+·+ *** B ⇥⇥ ⇥ ++ ++***+ + +**** *** * ⇤ ⇤ ⇥ ⇥⇥ + * ****++***+**+··++******** Run* 1 coupling results ⌦ ⇥ ⇥ ⇥⇥ × * * · *** ⌦ * **+*·*+·*··*·+·*·******* ⇤ ⇥ ⇤ ⇥ ⇥⇥ ⇥ ⇥ ++ +·***·*··*··**+***** * ⌦⇤⇤⇤⇥⇥ ⌦⇤ ⇤⌦ ⇥ ⇥ ⇥ +++++ +*·*··*+·*·**·**·******** MCHM ⌅ ⇤⌅ ⇤⇤ ⇤⇤⇤⇤ ⇤ ⇥⇤ ⇥ ⇥⇤⇥⇥⇥⇥⇥⇥⇥⇥ ⇥ + + *+*·*+*· *· · +** *** 14 14 10 ⇥⇤⇥⇤⇤⇤⇤⇤⌦⇥⇤⇥⌦⇥⇤⇥⇤⇥⇤⇤⌦⇤⇤ ⇥⇤⇥⇤⇥⇥⇥⇥⇥⇥⇥⇥ ⇥ · ·* * ⇥ ⇤⇤⇤ ⇤ ⇥⇥⇥ ⇥ ⇥ + ++ · · * ·* · *** VH ⇤ ⇤ ⇤ ⇥⇤⇥⇤⇤⇥⇥ ⇤⇤⇥⇥⇤⌦⌦⌦⇥⌦⇤⌦⇥⇥⇥ ⇥⇥⇥⇥ + ++·*· · · * · ** *** ** ⇤ ⇤⇤ ⇥ ⇥⇤⇥⇥⇥ ⇥⇤⇤⇥⇤⇥⇥⇥⇥⇥⇥⇤⇥⌦⇥⇥⇥⇤⌦⇥⌦⇥⌦⇥⇥⇥ ⇥⇤⇥⇥⇥⇥⇥⇥⇤⇥⇥⇥⇥⇥⇥⇥⇥ + +·· ·*** ⇥⇥⇤⇥⇥⌦⌦⇥⇤⇥⌦⇥⌦⇥⇥⇥⇥ · · · ·* ⇤ ⇤ ⇥ ⌦⇥ ⌦⌦⌦⇥⇤⇥⇥ ⇥⇥ ⇥⇥ + ·· · · ** * ⇤⇥⇤ ⇤⇥⇤⌦⇥⌦⌦⇥⌦⇥⌦⇥⇥^⌦^⌦⇥^^^⌦^⇥^⌦^⌦⇥^^⇥^^⇥⇥⇥⇥⇥⇥⇥⇥ MCHM ⌅ ⌅ · · · × ⇤⇤⇤ ⇤ ⇤ ⌦⌦⇤⌦⇤⌦⇥⌦⇥^⇤⌦^^⇥^⌦^⇥⌦^^^⌦^⇥^^^^⇥^^⇥⌦⇥^⇥⇥⇥⇥⇥ 10 5 10 ×× ×× × × × × × × × ×× × · × ⇤ ⇤ ⇤ ⌦⌦⇤⌦⌦⇥⌦⌦⇥⌦⇥⌦⇥^⇥^⇥^ ⇥⇥ ⇥⇥ - - ××××××××× ××××× ×× × × × 1.0 ⇥⇥⇥⇥⇥⇥⌦ ⇥⌦ ⇥⌦ ⇥ ⇥⌦ ⇥ ⌦⇥ ×××××××××××× ×× ⇥⇥⇥⇥ ⇥ ⇥ ⇥ ××× ⇥⇥ 0.1 × qqH ⇥ ⇥ • Signal strength: × × ⇥ ⌥ m=s /s obs SM MCHM5⌅5⌅10 0.3 • m=1 means that data observation is MCHM5⌅10⌅10 0.8 compatible - - with the SM = expectation. ⌃ ⇧ 0.5 • m=0 means that no signal 0.4 0.6 0.8 1.0 1.2 is observed. + × / ⌥ Bosonic production Bosonic ggH ⇤ ttH B BSM
M.C., Da Rold, Ponton’14 Fermionic production
After EWSB: ε = vSM/f and precision data demands f > 500 GeV
• More data on Higgs observables may distinguish between different realizations in the fermionic sector, providing information on the nature of the UV dynamics Two Higgs Doublet Composite Models
Data on Higgs signal strengths è almost Alignment: h125 almost SM
[SO(6)/SO(4) x SO(2)] x U(1) with fermions in 6plet rep. J. Mrazek et al.1105.5403 De Curtis et al. 1602.06437 Precision Higgs measurements
2 2 KV: main dependence on ξ = v / f cos ↵ cos↵ ˜ 1 ⇠ V ' RUN1 KF: dependence on thep Higgs mixing
c↵c↵˜ 1 2⇠ t ' c✓ c c ˜ + s✓ (s + s ˜) p1 ⇠ u u Small violation of custodial symmetry M.C., Davidovich, Machado, Panico, to appear. Small violation of CP, only after C P and C invariance broken by 1 2 inclusion of the bottom sector Θ ≠ 0, but CPC2HDM=C1P C2 preserved. Additional Higgs Sector SO(6)/SO(4) x SO(2)] x U(1) with fermions in 6plet rep. - masses almost degenerate - Fermiophilic (HDIM at alignment) - Second Higgs doublet gets vev’s that are misaligned: custodial invariance broken
H2 is mainly H, but is defined as the custodial triplet component
H3 is mainly A, but is defined as the custodial singlet component
Solid: tanθu = tanθd= tanθτ = 0.1 M.C., Davidovich, Machado, Panico, to appear Dashed: tanθu = 0.1; tanθd= tanθτ = 1
Searches for additional Higgs Bosons SO(6)/SO(4) x SO(2)] x U(1) with fermions in 6plet rep
CMS-WW-HIG-16-023 ZZ: CMS-HIG-16-034
H2 H2 H3 H3
CMS-hZ-HIG-14-01 Hi à h h à 4b or 2b 2 γ CMS run1
H3 H H3 2 Composite pNGB Higgs Models predict light Fermions Pair production, single production, or exotic Higgs production of vector-like fermions [masses in the TeV range and possibly with exotic charges: Q = 2/3,−1/3, 5/3,8/3,−4/3]
× · · + · SS di-leptons vector-like × Q × × 5/3 · × × - - · × × × × × ] × · × - - · · ×* · *·× × *× * ····· × * - - ··· * × × * ××·××·· × × *× * · × ·×
· · * × ··×··×× * × **· * [ - - ··×·×× ×* *· * * · · * ××···×·· ××× *×*× × * * ) * - -×·×+··*××·*× *+ ×* × * / ··×· * * * * ×·· ·+××*····+**× × × * ( ·· ·×*** * +* * * ××*··×*·×*·*×·**·*×××+× * * **** * - **·-*·* ×*× *+***×* *× × ×** * * ** *+**×+×·*×·+**+*+*** × * *× ** +·*×+**×·*+ ×++×·***+* ++ * * ** * ** * * * * * ·++*+·*+×*+**+*× * ** * * ** * * * ×+ ++*+×+** *** * * + * * ×++++ +*+ +*+ + * * * * *× +·++·++·+*+**++*++ + * + * * ×* * * ·++ ++++* + ×+ * * * +++ * * * * * * * * ·· * * * * [ ] CMS Searches:
× × · × 95% CL Exclusions + vector-like × T - - · × × Large variety × × × × ] × ×·× - - × · × × × - - × ×·· ×× × × · × × × of signatures, * ×× · [ - - × × × · ··× × × ××·· ··· ··× × ) × ×· * - ×- × ×× · ·×· ×· ×·× × ·×× ·×* * * ( ××××··· · * * × ×× · ×· × × ×* * - - · ×× ×·×· ·×·×× × ×× * many with ·×× ·× ··· * ··× × · ×· ·××··×· +* **** + * * * ×··×···×· · + ·* *+ * * * * ** × × ·×*×+ ***·+×*+**** * * * * * * * * ·+ *×·*·*·**++*+**** * * * * ***** * ·+·* +**·*** +*++·*+*·*+* *** +** * ** ** ***** * * ++++*++* ++*+**+* * +* ** *+** * ** *** *+ ** * * *** * energetic leptons ++×+·+++*+*++*+ *+ *+ + * * * * *** * ·++· +++·+·+ +* *+ * * ** * * * * * * **** * * * *
[ ]
M.C., Da Rold, Ponton’14 LHC exclusion for Mf < 800 GeV] Composite Twin Higgs may elude color top partners at the TeV scale An Elementary Higgs Boson e.g. Minimal SUSY: a 2HDM, type II
If the mixing in the CP-even sector is such that cos (β-α) = 0 The couplings of the lightest Higgs to fermions and gauge bosons are SM.
H and A couplings to down (up)-quarks are enhanced (suppressed) by tanβ This situation is called ALIGNMENT and occurs for
• large values of mAè Decoupling
• specific conditions independent of MAèAlignment without Decoupling
Valid for any 2HDM
Gunion and Haber ’03
If no CP violation in the Higgs sector:
Craig, Galloway,Thomas’13 ; M.C, Low, Shah, Wagner ‘13 More explicitly, since s = c in the alignment limit, we can re-write the above matrix ⇥ equation as two algebraic equations: 3
2 2 2 2 2 ˜ 2 2 (C1) : mh = v L11 + t⇥v L12 = v ⇥1c⇥ +3⇥6s⇥c⇥ + ⇥3s⇥ + ⇥7t⇥s⇥ , (41)
2 2 1 2 2 2 ˜ 2 1 ⇥2 (C2) : mh = v L22 + v L12 = v ⇥2s⇥ +3⇥7s⇥c⇥ + ⇥3c⇥ + ⇥6t⇥ c⇥ . (42) t⇥ ⇥
Recall that ⇥˜3 =(⇥3 + ⇥4 + ⇥5). In the above mh is the SM-like Higgs mass, measured to
be about 125 GeV, and Lij is known once a model is specified. Notice that (C1) depends
on all the quartic couplings in the scalar potential except ⇥2, while (C2) depends on all the
quartics but ⇥1. If there exists a t⇥ satisfying the above equations, then the alignment limit
would occur for arbitrary values of mA and does not require non-SM-like scalars to be heavy! Henceforth we will consider the coupled equations given in Eqs. (41) and (42) as required conditions for alignment. When the model parameters satisfy them, the lightest CP-even Higgs boson behaves exactly like a SM Higgs boson even if the non-SM-like scalars are light. A detailed analysis of the physical solutions will be presented in the next Section.
C. Departure from Alignment
B. Departure from AlignmentSo far we have analyzed solutions for the alignment conditions (C1) and (C2) in general 2HDMs. However, it is likely that the alignment limit, if realized in Nature at all, is
Phenomenologically it seemsonly likely approximate that and alignment the value of willt⇥ does only not be need realized to coincide approximately, with the value at the rather than exactly. Thereforeexact it is alignment important limit. Itto is consider therefore important small departures to study the approach from the to alignment align- and An Elementary Higgs Boson understand patterns of deviations in the Higgs couplings in the “near-alignment limit,” ment limit, which we do in thiswhich subsection. was introduced in Section III B.
e.g. Minimal SUSY: a 2HDM,Since the type alignment II limit is characterizedAlthough we derived by c the⇥ near-alignment=0,itiscustomarytoparametrizethe conditions (C1 )and(C2 )inEqs.(49)and (50) using the eigenvalue equations, it is convenient to consider the (near-)alignment limit departure fromC. alignment Departure by from considering Alignment a Taylor-expansions in c⇥ [7, 8], which defines the If the mixing in the CP-even sector is such that cos (βfrom-α) a = slightly 0 di erent perspective. Adopting the sign choice (I) in Eq. (16) and using the
deviation of the ghV V couplingsexpression from thefor the SM mixing values. angle, However, , in Eq. (21), this we can parametrization re-write the ghdd and hasghuu thecouplings So far we have analyzed solutions for the alignment conditions (C1) and (C2) in general The coupling of the lightest Higgs to fermions and gauge bosonsas is follows SM-like. drawback that2HDMs. deviations However, in the it is Higgs likely couplingthat the alignment to down-type limit, if fermions realized in are Nature really at controlled all, is s ghdd = gf = A gf , (68) H and A couplings to down (up)-quarksby aret⇥ cenhanced⇥ , whichonly approximate(suppressed) could be and(1) the whenby value tant⇥β ofis t⇥ large.does not Therefore, need to coincide we choose with to the parametrize value at the the c⇥ 2c2 + 2s2 O A ⇥ B ⇥ exact alignment limit. It is therefore important to study the approach to alignment and departure from the alignment limit by a parameter whichc is⇧ related to c⇥ by Deviations from gAlignmenthuu = gf = B gf . (69) This situation is called ALIGNMENT understandand occurs patterns of for deviations in the Higgs couplingss⇥ in the2c2 “near-alignment+ 2s2 limit,” A ⇥ B ⇥ which was introduced in Section1 III B. 2 ⇧2 c⇥ where = t⇥ ,s⇥ = 1 t⇥ . (43) • large values of m è Decoupling See N. Shah’s talk A Although we derived the near-alignment2 conditions (C1 )and(C2 )inEqs.(49)and 2 2 2 2 12 ⇤2 2 2 2 Sign( 12)( 22 mh)/c and = 12 The/s . couplings Further, m hofis down the mass= fermionsM of the= lightestaremA not(⇥ 3only+ ⇥4 the)v s⇥ ⇥7v s⇥t⇥ ⇥6v c⇥ , (70) M M3 (50)B using|M the| eigenvalue equations,A it isc convenient⇥ to consider the (near-)alignment limit • specific conditions independent of M èTheAlignment same conditions2 2 without can also be derivedDecoupling using results presented in Ref. [8]. CP-even HiggsA bosonThen and atii leadingmh > 0,i order=ones1, in2 thatby , Eq.the dominate (20). Higgs Therefore couplingsthe Higgs Eq. 2 (72) becomewidthm2 implies but also tend⇥ c m2 M from a slightly{ di }erent perspective.= AdoptingM11 theh = signm2 + choice⇥ v2 (I)s + in⇥ Eq.v2 ⇥ (16)+2⇥ andv2c usingh the. (71) to be the ones which Bdiffer at mosts from Athe SM5 ones⇥ 1 t 6 ⇥ s 0and 0(74)⇥ ⇥ ⇥ expressionA ⇥ for the mixingB ⇥ angle,1 2 2 , in Eq. (21), we can re-write1 ⇥ the ghdd and ghuu couplings ghV V Again1 itt is⇥ instructive gV ,g to considerHV V first takingt⇥ g theV , pseudo-scalar mass to be heavy:(44) mA . Departures from Alignmentat the alignment limit. ⇥ 2 ⇥ ⇥⇤ as follows ⇤In this limit we⌅ have m2 s and m2 s , leading to s /c 1andc /s 1. We A ⇥ A B ⇥ A 2 ⇥ ⇥ ⇥ ⇥ Now in the near-alignment limit, where theghdd alignment(1 is only ) g approximate,f ,g one canHdd derive t⇥(1 + t⇥ )gf , (45) quantized by an exp. in cos (β-α), BUT ⇥ recover the familiars alignment-via-decoupling⇥ limit. On the other hand, alignment without g2hdd = gf = A 1gf , (68) ghdd = A ghuu gf(1decoupling + t ) couldgf ,g occurc⇥ by settingHuu2c(75)2 directly+ 2st 2 (1 )gf . (46) Higgs –bottom coupling is controlled by η = cos t 2 2 2 ⇥ 11 ⇥ ⇥ β-α β 1 (1 / )c⇥ A ⇥ B B A B ⇧ c 2For small departures gfromhuu2 = alignment,gf = the parameterB ηg=f can. , be determined (69) (72) We see= 1 characterizess 1 A + the(1 departure/ ) fromgf , s the alignment2(76)2 limit2 A2 of notB only ghdd but also gHuu. Impact of Precision Higgs measurements on A/H searchesO A stronglyB ⇥ c + s ⌥ ⇧ Bas⌃ a function of the quartic couplings ⇥and the⇥ Higgs masses where, explicitly,⇥ A B 2 which, when comparingOn with the Eq. other (45), hand, implies the deviation in the ghuu and⇧gHdd are given by t⇥ , which is doubly correlated to the proximity to Alignment wherewithout decoupling 1 2 suppressed in2 the large t⇥2 regime. Moreover,= termsm2 + neglected⇥˜ v2s2 + ⇥ abovev2s2 t are+3⇥ ofv2 orders c + ⇥ v2andc2 =0 are, (73) ⇥ = s 1 A = s B A2 ,. h (77)3 ⇥ 7 ⇥ ⇥ 6 ⇥ ⇥ 1 ⇥ 12 B 2 A s⇥ 2 2 2 ⇧ B ⌃ = BM = m (⇥3 +⇤⇥4)v s⇥ ⇥7v s⇥t⇥ ⇥6v c⇥ , ⌅(70) never multiplied by positive powers ofA t⇥, which could invalidate the expansion in when Therefore, the ghdd coupling is enhanced (suppressed)A ifis nothingc⇥ < 0( but> the0). It alignment is easy to condition verify (C1) in Eq. (41). The alignment condition (C2) B2 A 2 2 m ⇥ c⇥ m that the above equationt⇥ is is large.identical to the near-alignmentwould11 condition beh obtained (C12⇥)inEq.(49).The if the2 representation2 in Eq.2 (22) is usedh instead, leading to = = M = mA + ⇥5v s⇥ + ⇥1v +2⇥6v c⇥ . (71) A B s⇥ t⇥ s⇥ condition (C2⇥)couldagainbeobtainedusingEq.(22). There are some interesting features regarding⇥ the pattern of17 deviations. First, whether Tuesday, NovemberAgain 19, it 2013 is instructive to consider first taking the pseudo-scalar mass to be heavy: m . It is useful to analyze Eq. (76) in di erent instances. For example, when ⇤6 = ⇤7 =0, A ⇥⇤ the coupling to fermions is suppressed2 or enhanced2 relative to the SM values, is determined one obtains In this limit we have mAs and mAs , leading to s /c⇥ 1andc /s⇥ 1. We ˜ 2 A 2⇥ 2 B ⇥ ⇥ ⇥ by the sign of ⇤:SMghdd⇤3sand⇤g1Huuc v are suppressed (enhanced) for positive (negative) , while recover the familiar alignment-via-decoupling limit. On the other hand, alignment without ghdd 1+s gf . (78) the trend⇤ in g⇤ and g is the⌅ ⌦ opposite. In addition, as 0, the approach to the SM decouplinghuu couldBHdd occur by setting directly ⌅ Hence, for ⇤˜ > ⇤ > ⇤ , a suppression↵ of g will take place for values of t larger than 3 SM values1 is the fastesthdd in ghV V and the slowest in ghdd. This is especially true in the large t⇥
the ones necessary to achieve the alignment limit. On the contrary, for ⇤1 > =⇤SM ,> ⇤˜3, (72) regime, which motivates focusing on precise measurementsA B of ghdd in type II 2HDMs. larger values of t will lead to an enhancement of ghdd. where, explicitly, 1 Our parametrization of c⇥ = t⇥ can also be obtained by modifying Eq. (39), which On the other hand, for ⇤7 =0andlargevaluesoft ,oneobtains ⌅ 1 defines the alignment limit, as follows:2 2 ˜ 2 2 2 2 2 2 2 ⇤SM ⇤˜3 =⇤7t v mh + ⇥3v s⇥ + ⇥7v s⇥t⇥ +3⇥6v s⇥c⇥ + ⇥1v c⇥ =0, (73) g 1+s B A s⇥ g , (79) hdd ⇤ ⇤ ⌅⇤ ⌦ f ⌅ B 2 is nothing but the alignments⇥ s⇥c condition⇥ (C1)s in Eq.1 (41). Thes⇥ alignment condition (C2) ˜ ↵ = t⇥ . (47) which shows that for ⇤SM > ⇤3 wouldand ⇤7 positive, be obtainedg⇧hdd is ifsuppressed the representation2 at⌃ values⇧ of t inlarger⌃ Eq. than (22)⇧ is used⌃ instead, leading to = s⇥c⇥ c⇥ c c⇥ A those necessary to obtain the alignment limit, and vice versa. ⌥ ⌥ ⌥ 17 One can in fact pushThe the eignevalue preceding analysis equation further for bym derivingh in Eq. the (40) condition is modified giving rise accordingly, to a particular deviation from alignment. More specifically, the algebraic equation dictating
the contour ghdd/gf = r, where r =1,canbeobtainedbyusingEq.(75):2 L11 L12 s 2 s 2 1 s⇥ ⌅ v = m m t . (48) 2 h A ⇥ 2 1 ⇧mLh L2 ⌃ ⇧2 2c ⌃ 2 1 ⇧ c ⌃ ⇧ c ⌃ m = A B + 12 v ⇤22 ⇤ v t 2⇤ v t , (80) ⇥ A R( ) 1 s s2 5 1 6 ⌥ ⌥ ⌥ ⌥ From the above, taking 1andexpandingtofirstorderin , we obtain the “near- 18 ⇤ alignment conditions”,
2 2 2 2 2 2 (C1⇥):m = v L + t v L + t (1 + t )v L m , (49) h 11 ⇥ 12 ⇥ ⇥ 12 A 2 2 1 2 1 2 2 2 (C2⇥):m = v L + t v L t (1 + t )v L ⇥m . (50) h 22 ⇥ 12 ⇥ ⇥ 12 A ⇥ We will return to study these two conditions in the next section, after first analyzing solutions for alignment without decoupling in general 2HDMs.
12 H1 Q H1 H1 U H1 H1 Q H1 H1 U H1 ! ! ! U U ! Q Q U U Q Q ! ! ! ! ! H1 ! H2 ! ! H1 H2 H1 Q H2 Q H1 U H2 U (a) (a) (b) (b) ! ! ! !
H1 H1 H1 H1 Q H1 H1 Q H1 U U H1 U ! Q ! Down CouplingsDown Fermion in the CouplingsMSSMU ! for for low small values values of µ Q of µ! ! Q H2 ! U H2 DownDown FermionH1 Fermion Couplings Couplings forH1 small values for small of µ values of µ DownOnly Loop22Down Couplings relevantDown Fermion Fermion(no in Couplings! Alignment) theQ MSSM Couplings forH2 small for values low for of ! valuesµsmallU values ofH2 µ of µ H1 H1 Only(stopOnlyOnly Loop22contribution) Loop22 Loop22 relevant relevant relevant (c)! For tan ⇥ 5(d) and! mA 200 GeV Only Loop22Down relevant Fermion (no Couplings Alignment) for small values of µ 2 In this(stop (stopregime, 2contribution) contribution)2 6 ,7 0 , and (c)! ForFor tan tan⇥ ⇥5 and5m andForA m200A tan GeV200⇥ GeV5(d) and! m 200 GeV v L11 = M(stopZ cosOnly contribution)+ Loop22 Loop11' relevant A 2 2 2 For tan ⇥ 5 and m 200 GeV 22 (stop22 2 2 contribution)2 H1 2 H1 2 2 A v L v2=L11M= MgcosZ cos+ 2gsin + Loop112M+ Loop12 0 SM For tan ⇥ 5 and mA 200 GeV v L12112=In˜M thisZZcos1 (stopregime,2 2+ contribution) Loop11 Z 6 ,7 Q , H and1 0.26 U mHA1 + M Z Impact2 2of1 vv Precision2L 113=2==2MM2 cosZ2cos =Higgssin 2 ++ Loop12 Loop110 .'measurements125 sin on A/Hcos ⇥2 searches2 strongly 12 2 Z 2 2 2 H1 ' mA + M22ZH1 2 2 vvLL22' 12v2=2=LM11ZMsin =Z 2cosM 4 + 2Z2sin Loop22cos2 v+ Loop12'+2 Loop112 sin ' cos ⇥ mmA +mMZ v L =v ML11sin= M+Z Loop22cos + Loop11 1 SM 2 A2 h 21 2 2 v 2L2212 2= Z 2MZ2gcos1 +U gsin2 ! M+Z Loop12Q H sin' Q !cosm⇥A✓ m ◆ U mH + M correlatedv L22 = M to2sin ˜the + Loop22proximity2 to Alignment without✓ 0 .26h2 ◆decoupling2 2 A 22 Z2 v2 L1212vZ =L 123=2M= ZMcos2 cos 2 sin =sin ++ Loop12 Loop122 0.125 2 ' sinmA mh cosm⇥ +mM + M v ML22' = 3M sin Z 4M+ Loop22v2 A'SuppressionA factor in the' LHC✓ channels ◆ at A 2AZ 2Z 2 Z 2 Z42 2 2! 2SUSYQ H1 t Suppression factort in! the ULHC channelssinH sin1 at' cos ⇥cos ⇥2 mA2 mh2 2 v L22+v =L22Mh=t MlogsinZ2 sin + + Loop22 Loop22+U ! 1 2 Q ! m✓ m ◆ ' v2 8⇡2 Z H m2 M 2 Suppression 12theMthe 22012--2013 Hfactor 2012--2013 in the run LHCrun channels' ' at A mAh mh Small µ as analyzed by✓ ATLAS/CMSt ◆ SUSY ✓ ( λ6,7SUSY ∝ µ◆ Αt≃ 0 => No Alignment✓ ✓ ◆ ) ◆ 2 ! 2 2 ! 2 (e) theSuppression 2012--2013(f)M. Carena,M. P.Carena,run Draper, factor P.T. Liu,Draper, C. W. T. ,arXiv:1107.4354in Liu, C.the W. ,arXiv:1107.4354 LHC channels at MZ 3 4 MSUSYQ H1At Suppression factorAt in the LHC channelsH1 at ! ! U Bottom coupling 2 in+ the MSSMh logH 2 + Suppression1 Hfactor2Draper,Liu,C.W.’10 in the LHC channels at 2 2 t 2 2 M. Carena,2 P. Draper, T. Liu, C. W. ,arXiv:1107.4354 thethe 2012--2013 2012--2013 run run ' v 8⇡ mt M 12M ⇤ SUSY theSUSY 2012--2013 run FIG. 1: One-loop⇤ diagrams contributing✓ to (e) the! ◆ the coefficient, Z6,oftheHiggsbasisoperator,✓ ◆ (f)! M. Carena,M. P.Carena, Draper, P.T. Draper,Liu, C. W. T. ,arXiv:1107.4354 Liu, C. W. ,arXiv:1107.4354 ⇤ (H†H1)(H†H2).UsingtheinteractionLagrangiangiveninEq.(51),onesee sthattheparametric M. Carena, P.Draper,Liu,C.W.’10 Draper, T. Liu, C. W. ,arXiv:1107.4354 1 1 A/Hà ττ
⇥ ⇤ 4 3 3 4 3 2 dependenceFIG. for the 1: sixOne-loop diagrams⇤ are:diagramsht sβc βX contributingt Yt for (a) and to (b); theht s theβcβX coet forfficient, (c) andZ (d);6,oftheHiggsbasisoperator, and
⇥ ⇤ 4 3 h s c X Y for⇤ (e) and (f). ⇥ t β β t t † † (H1H1 )(H1H2).UsingtheinteractionLagrangiangiveninEq.(51),oneseesthattheparametric ⇤
⇥ 4 3 3 4 3 2 dependence⇤ for the six diagrams2 4 4 are: h4t s2 cβXt Yt for (a) and (b); ht s cβXt for (c) and (d); and where we have used Eq. (46) to write v s ht =4mt /vβ. Using Eqs. (55) and (56) in theβ ⇥ β 4 3
⇥ evaluation h t ofsβ Eq.c βX (30)tYt yieldsfor⇤ (e) and (f). ⇤ 4 2 1 2 2 3mt Xt(Yt Xt) Xt tβ cβ α ⇤ 2 − 2 mh + mZ + 2 2 −22 4 41 24 2. (57) Carena, Low, Shah,− C.W.’13m m 4π v M 6M where we⇥ ≃ haveH usedh Eq. (46) to write vS sβht =4− mSt /v . Using Eqs. (55) and (56) in the FIG. 2: Ratio of the value of the down-type fermion couplings to Higgs− bosonsWednesday," to March their 13, 2013 SM values All vector boson# branching$% 3 2 At large tβ we have Xt(Yt Xt) µ(Attβ µ)andX (Yt Xt) µA (Attβ 3µ), in which in the case of low µ (L1j Carena,0), as obtained Low,evaluation from Shah, Eq. (96), C.W.’13 and of d Eq. 0. (30) yields ratios tsuppressed byt enhancement ⇥Enhancement ⇥ of bottom−⌅ quark≃ and− tau couplings− ≃ independent− of tan FIG. 2: Ratio of the value of the down-typeCarena,case, Eq. fermionLow, (57) Shah, couplings can be C.W.’13 rewritten to Higgs bosonsWednesday, in the to March followingtheir 13, 2013 SM values approximate form, For moderate or large ⇥ values of tanβ of the bottom decay4 width 2 We can reach theTuesday, same November conclusion 19, 2013 by using Eq. (21) for s in this regime,Wednesday, March 13, 20131 2 2 3mt Xt(Yt Xt) Xt inFIG. the case 2: Ratio of low ofµ the(L value0), of asthe obtained down-type from fermion Eq. (96), couplings and to Higgs0. bosons to their 4 SM values 2 2 1j ⇥ 1 d t⌅β cβ α 32m− 2 mh + mAZ + 2 2 −A2 1 2 . (57) EnhancementCarena,2 of2 bottom Low, 2 Shah,− quark2 C.W.’13 andt tau couplingst independent2 t of tan tβ cβ α (mA +−mZ )s⇥c⇥ m + m⇥ ≃+ mH mhAtµtβ 1 µAll4π1 vvectorMS boson. − 6 MbranchingS in the case of low µ (L1j 0),s = as obtained from Eq.2 (96), and2 d h 0. Z , 2 2 2 (96)Wednesday, March 13, 2013 2 2 FIG. 2: Ratio of the value− of the≃ m down-typem fermion couplings2 4π tov HiggsM− bosons" to their− 6M SM values− − 2M # $% ⇥Enhancement2 2 2 2 2 H of2 bottom2 h 2 ⌅2 2 quark andS tau couplingsS independentS of tan We can reach theTuesday, same November conclusion 19, (2013 bymA using+ mZ ) Eq.s⇥c⇥ (21)+ m− forAs⇥s+ "minZ thisc⇥ m regime,h & # $ # 3 $'% 2 At large t we have X (Y X ) µ(A t µ)andratiosX suppressed(Y X ) (58)µA by( enhancementA t 3µ), in which in the case of low⇤µ (L1j Carena,0), as obtained Low,β from Shah, Eq. (96),C.W.’13 andt td 0. t t β t t t t t β We can reach theTuesday, same> November conclusion 19, 2013 by using⇥Enhancement2 Eq. (21)2 for s in this of regime,⇥ bottom−⌅ quark≃ and− tau couplings− ≃ independent− of tan which, for mA 2mh and moderate t⇥ implies ⇥ (mA + mZ )s⇥c⇥ Wednesday, March 13, 2013 of the bottom decay width FIG. 2: Ratio ofs the= value of the down-typeCarena,case, Eq. fermionLow, (57) Shah, couplings can be C.W.’13, rewritten to Higgs bosons(96) in the to followingtheir SM values approximate form, For moderate2For22 ormoderate2 large values2 to large of 15tan tanβ β and small µ 2 2 2 2 (2ms +mm2 +2)sm⇥c⇥ 2 2 ⇥ 2 We can reach(m theTuesday,+ samem ) sNovember conclusionc + A m 19,AZs 2013 by+ usingZm c Eq.m (21) for s in this regime,Wednesday, March 13, 2013 FIG. 2: Ratio ofs the= valueA ofZ the ⇥ down-type⇥ A ⇥ fermion.Z ⇥ couplingsh , to Higgs(97) bosons(96) to their SM values in the case of low µ (L1j 0), as obtained c ⌅ m2 fromm2 Eq. (96), and2 d 0. 4 2 2 2 è2 2 2 no2⇥ dependenceA2 2 h 2 2 12 on tanβ or on the3m stop mixing A A ⇤ (m⇥AEnhancement+ mZ ) s⇥c⇥ + mA s⇥ + mZ c2⇥ ofm⇥2h bottom⌅ 2 quark2 andt tau couplingst independent2 t of tan which, for m > 2m and moderate t implies tβ cβ α (mA + −mZ )s⇥c⇥ m + m + Atµtβ 1 µ 1 . in theThis caseA clearly ofh low demonstratesµ (L1j that0),s⇥ in = asthis obtained case the deviation from of Eq. ( s2 (96),/c⇥)from1dependsonlyon and2 d h 0. Z , 2 2 2 (96) 2 2 ⇤ − m m 2 4π v M 6M 2M è> All vector⇥Enhancement boson 2 BR’s2 2≃ 2suppressed2 H of2⇥ bottom2 h 2 ⌅by2 enhancement2 quark andS tauof bottom couplings− decayS − independent width− S of tan which,We can formm reachandA is2m the independenthTuesday,and same moderate November of conclusiont . Int⇥ otherimplies 19, words,(2013 bym2 A using+ alignmentm2 Z ) Eq.s⇥c is⇥ (21) only+ m achieved− forAs⇥s+ in"min theZ thisc⇥ decouplingm regime,h & # $ # $'% A ⇥ s m + m (58) A Z . (97) Carena, Haber, Low, Shah, C.W. ’14 2 2 2 ⇤ 2 2 2 2 ⇥ We canlimit, reachmA themTuesday,Z ,m sameh. > November conclusion c⇥s ⌅ 19,mm 2013A by+ usingmmh Eq. (21) for s in this regime, which,⇤ for mA 2mh and moderateA (mtZ⇥ 2implies+ m2 )s c 2 2 A. Z ⇥ ⇥ (97) This also agreess with = our expressions c⇥ ⌅ regardingmA mh the approach to the alignment limit via, (96) This clearly demonstrates that in this case the deviation of2 ( s /c22⇥)from1dependsonlyon2 2 15 2 2 2 2 (m2s + m2A +)2smcZ 2 2 2 decoupling, Eq. (77). In this regime(m + 5,6m,7 are) verys c small+A implyingm Zs +⇥ m⇥ c m s = A Z ⇥ ⇥ A2 ⇥ 2 .Z ⇥ h , (97)(96) mThisA and clearly is independent demonstrates of t⇥ that. In in other this casewords, the alignment deviation c is⇥ of only⌅ ( ms achieved/c⇥)from1dependsonlyonm in the decoupling ⇤ 2 2 2 2 2 A2 2 h 2 2 2 2 2 2 2> 2 (2 mA + mZ ) s⇥c⇥ + m2As⇥ 2+ mZ c⇥ m⇥h limit,mwhich,A andm is for independentmm,m . 2m of tand⇥.m InA moderate othermh, words,andt alignmentimplies is only(mZ achieved+ mh) . in the decoupling(98) A ⇤ ThisZ Ah clearlyhB demonstrates⌅ that⇥ in thisB caseA ⌅ the deviation of ( s /c⇥)from1dependsonlyon 2 2 2 ⇤ limit,Thism alsoA agreesmZ ,m withh>. our expressions regarding the approach to the alignment limit⇥ via which,In⇤ for Fig.mmA 2 weAand display is2m independenth theand value moderate of ofs t/c⇥⇥.in Int⇥ the otherimpliesmA words,tan2 ⇥ plane, alignment2 for low isvalues only of achievedµ, for in the decoupling s mA + mZ This also agrees with2 our expressions2 2 regarding the approach to the. alignment limit via (97) decoupling,which Eq. the(77). radiative In this corrections regime 5 to,6,7 theare matrix very element small implyingL112 and L122 are small, Eq. (96). As limit, mA mZ ,mh. c⇥ ⌅ m 2 m 2 ⇤ s mA + mh decoupling,expected Eq. (77). from Inour this discussion regime above, 5,6,7 theare down-type very small fermion implyingA couplingsZ to the Higgs become This also2 agrees2 with our expressions regarding2 2 2 the. approach to the alignment limit via(97) m m , and c⇥ ⌅ m(m +mm ) . (98) This clearly demonstratesB ⌅ A h that in this caseB A the⌅ deviationAZ h of ( s /c⇥)from1dependsonlyon decoupling,2 Eq. (77).2 In this regime24 5,6,7 are very2 small2 implying mA mh, and (mZ + mh) . (98) mThisA and clearly is independent demonstratesB ⌅ of t that⇥. In in other thisBcase words, A the⌅ alignment deviation is of only ( s achieved/c )from1dependsonlyon in the decoupling In Fig. 2 we display the value of s /c⇥ in the mA tan⇥ plane, for low values of⇥µ, for 2 2 2 2 2 2 2 m m , and (m + m ) . (98) Inlimit,m Fig.and 2m we is display independentm ,m the value. of of ts ./c In⇥Ain other theh m words,A tan⇥ alignmentplane, for low is only valuesZ achieved of µ,h for in the decoupling whichA the radiativeA ⇤ correctionsZ h to theB ⌅⇥ matrix element L11 and L12Bare small,A ⌅ Eq. (96). As expectedwhichThis the from radiativealso2 our agrees discussion corrections2 with2 above, our to the the expressions matrix down-type element fermion regardingL11 couplingsand L the12 are approach to small, the Higgs Eq. to become (96). the As alignment limit via limit, mAIn Fig.mZ 2,m weh. display the value of s /c⇥ in the mA tan⇥ plane, for low values of µ, for expected from⇤ our discussion above, the down-type fermion couplings to the Higgs become decoupling,This alsowhich Eq. agrees the(77). radiative with In this our corrections regime expressions24 5 to,6,7 theare regarding matrix very element small the approach implyingL11 and L to12 are the small, alignment Eq. (96). limit As via expected from our discussion24 above, the down-type fermion couplings to the Higgs become decoupling, Eq. (77). In2 this regime2 5,6,7 are very small implying2 2 mA mh, and (mZ + mh) . (98) B ⌅ 24B A ⌅ m2 m2 , and (m2 + m2 ) . (98) In Fig. 2 we displayB the⌅ valueA ofh s /c in the mB Atan⌅ plane,Z forh low values of µ, for ⇥ A ⇥ whichIn Fig. the 2 radiative we display corrections the value to of thes matrix/c inelement the m L11tanandplane,L12 are for small, low values Eq. (96). of µ, As for ⇥ A ⇥ expected from our discussion above, the down-type fermion couplings to the Higgs become which the radiative corrections to the matrix element L11 and L12 are small, Eq. (96). As
expected from our discussion above, the down-type24 fermion couplings to the Higgs become
24 M. Carena, I. Low, N. Shah, C.W.’13 M. Carena, I. Low, N. Shah, C.W.’13 Impact of PrecisionCarena, Haber, Low,Higgs Shah, C.W.’14 measurementsHiggs Decay oninto A/H Gauge searches Bosons strongly Higgs Decay into Gauge Bosons correlated to the proximityMostly determinedto Alignment by the without change decouplingof width Mostly determined by the change of width Higgs decays into gauge bosonsSmall mostly μ determined by bottom decay width Small μ µ/MSUSY =2,At/MSUSY 3 µ/MSUSY =2,At/MSUSY 3 ' Small µ (no Alignment) ⇥ Sizeable' µ ~ 2 M ⇥ (Alignment) ⇥ M. Carena, I. Low, N. Shah, C.W.’13⇥ SUSY ⇥ ⇥ ⇥ ⇥ Carena, Haber, Low, Shah, C.W.’14 Higgs Decay into Gauge Bosons ⇥ ⇥ ⇥ ⇥ 1.4 1.4 ⇥ Mostly determined by⇥ the change of⇥ width ⇥
1.3 1.3 Small μ µ/MSUSY =2,At/MSUSY 3 ' 1.2 1.2
⇥ ⇥
⇥ ⇥ 1.1 1.1 1.0 1.0 ⇥ ⇥ 1.4 ⇥ ⇥ 1.3 CP-odd Higgs masses of order 200 GeV and tanβ = 10 OK in the alignment case CP-odd Higgs masses of order 200 GeV and1.2 tanβ = 10 OK in the alignment case
⇥ Tuesday, November 19, 2013 CP-odd Higgs masses of order 200 GeV and tanβ ~10 are allowed in the ⇥ ⇥ Tuesday, November 19, 2013 alignment case, but alignment is in tension⇥ with naturalness in the MSSM 1.1 M.C., I. Low, N. Shah, Wagner’13 1.0 e.g. Tauphobic Benchmark MC, Heinemeyer, Stal, Wagner, Weiglein’14 CP-odd Higgs masses of order 200 GeV and tanβ = 10 OK in the alignment case ⇥ Tuesday, November 19, 2013 ⇥ M. Carena, I. Low, N. Shah, C.W.’13 M. Carena, I. Low, N. Shah, C.W.’13 Impact of PrecisionCarena, Haber, Low,Higgs Shah, C.W.’14 measurementsHiggs Decay oninto A/H Gauge searches Bosons strongly Higgs Decay into Gauge Bosons correlated to the proximityMostly determinedto Alignment by the without change decouplingof width Mostly determined by the change of width Higgs decays into gauge bosonsSmall mostly μ determined by bottom decay width Small μ µ/MSUSY =2,At/MSUSY 3 µ/MSUSY =2,At/MSUSY 3 ' Small µ (no Alignment) ⇥ Sizeable' µ ~ 2 M ⇥ (Alignment) ⇥ M. Carena, I. Low, N. Shah, C.W.’13⇥ SUSY ⇥ ⇥ ⇥ ⇥ Carena, Haber, Low, Shah, C.W.’14 Higgs Decay into Gauge Bosons ⇥ ⇥ ⇥ ⇥ 1.4 1.4 ⇥ Mostly determined by⇥ the change of⇥ width ⇥
1.3 1.3 Small μ µ/MSUSY =2,At/MSUSY 3 ' 1.2 1.2
⇥ ⇥
⇥ ⇥ 1.1 1.1 1.0 1.0 ⇥ ⇥ 1.4 ⇥ ⇥ 1.3 CP-odd Higgs masses of order 200 GeV and tanβ = 10 OK in the alignment case CP-odd Higgs masses of order 200 GeV and1.2 tanβ = 10 OK in the alignment case
⇥ Tuesday, November 19, 2013 CP-odd Higgs masses of order 200 GeV and tanβ ~10 are allowed in the ⇥ ⇥ Tuesday, November 19, 2013 alignment case, but alignment is in tension⇥ with naturalness in the MSSM 1.1 M.C., I. Low, N. Shah, Wagner’13 1.0 e.g. Tauphobic Benchmark MC, Heinemeyer, Stal, Wagner, Weiglein’14 CP-odd Higgs masses of order 200 GeV and tanβ = 10 OK in the alignment case ⇥ Tuesday, November 19, 2013 ⇥ Heavy Supersymmetric Particles Heavy Heavy Higgs Bosons HiggsHeavy : Supersymmetric A Bosons: variety of decayParticlesA variety Branching of decayRatios Branching Ratios Carena, Haber, Low, Heavy Shah, Craig, HiggsC.W.’14 Galloway, Bosons Thomas’13; : A variety Suof etdecay al. ’14, Branching ‘15; M.C, Ratios Haber, Low, Shah, Wagner.’14 Carena, Haber, Low, Shah, C.W.’14 DependingDepending on the on values the of values μ and tan ofβ different µ and search tan βstrategies different must besearch applied. strategies must be applied Depending on the values of μ and tanβ different search strategies must be applied.
PRGPRG DOW DOW P DOW DOWΜ"Μ"# P # W Β " " PRG PRG PK# Μ"# P4 WDQ Β" PKPKK Μ" Μ"#4 PP#44 WDQW Β Β" Β" PK Μ"# P4 WPΒ K" Μ"# P4 W Β " PK Μ" P4 WDQ Β" PK P4 WDQ KK KK KK EE EE KK WW WW EE EE WW WW EE == ΤΤ ΤΤ == EE EE " "
" == ΤΤ " + + + ! ΤΤ + ! ! == ! EE
%5 KK " " %5 " %5 %5 KK WW :: " + + + ! WW + ! ! ΤΤ ! ΤΤ ::
%5 KK %5 %5 KK WW %5 :: WW == ΤΤ ΤΤ :: :: H Χ Χ L M H Χ L Χ M == P$ P+ !*H9" P ::!*H9" P$ + Χ Χ L M Χ L Χ M H (a) (b) (a) (b) At large tanβ, bottom and tau decay modes dominant. As tanβ decreases decays into SM-like Higgs and wek bosons Pbecome$ relevant P !*H9" PRG ! " P$ +DOW PK DOW Μ"# P4P W+Β " *H9 PRG PK Μ"# P4 WDQ Β" PK Μ"# P4 WDQ Β" A PK Μ"# P4 W Β " (a) (b) EE EE (a) WW (b)WW At large tanβ, bottom and tau decay modes dominant.EE EE As tanβ decreases decays into SM-like Higgs and wek bosons become relevant PRG DOW P DOW Μ"# P W " K= PRG P Μ"# P WDQ Β" ΤΤ K 4 Β P Μ"# P W " K ΤΤ 4 PK Μ"K=# P4 WDQ Β" K 4 Β Sizeable tanβ è very close to alignment, dominant bottom and tau decays; " " " " $ $ $ ! ! $ ! WW EEWW ! whileEE g ≃ g%5 ΤΤ≃ g ≃g ≃WW 0 ΤΤ WW %5
%5 Hhh HWW HZZ AhZ %5 EE EE Production& mainly' via large bottom couplings: bbH Χ L Χ M Χ& Χ' L M K= ΤΤ JJ JJ ΤΤ K= Smaller tanβ è some departure from alignment,K= Χ L Χ M Hà hh, WW, ZZ and tt (also (A è hZ, tt) " " Χ Χ "
L M Χ Χ " $ $ L M $ ! ! $
! WW ! WW
%5 ΤΤ ΤΤ P $ %5 %5 become! " relevant. Production mainly via top loops in gluon fusion P$ *H9 %5 P$ !*H9" P$ (c) & ' (d) (c) (d) Χ Χ & ' à If low µ, then charginoL andM neutralino channels openΧ L Χ upM ( impact on H/A ττ ) FIG. 5: Branching Ratio of the heavy CP-evenFIG. Higgs 7: andBranching CP-odd Higgs Ratio dec ofJJays the heavyas a function CP-even of Higgs and CP-odd Higgs decays as a functionJJ of alt mod the respective Higgs mass in the mh and mh scenarios for tan β =10K=and for diΧffalterentΧ valuesmod Χ Χ the respective Higgs mass in the mhL andM mh scenarios for tan β =4different values of the L M Χ L Χ M of the Higgsino mass parameter µ. Higgsino mass parameterµ. P$ P$ !*H9" P !*H9" P$ the width beyond the bottom-quark and tau-lepton ones, the hZ channel$ being the most are displayed in Fig. 8 with the values of At defined in the on-shell scheme. Observe that relevant one. As(c) we discussed before, this is in sharp contrastalt with(d)what happens in the for the mh scenario larger(c) values of mQ are necessary for smaller values of(d)µ.Onthe heavy CP-even Higgs boson, for which at mAcontrary,300 GeV in the the mh BR(Hmod scenario,ττ) is larger only of values a few of m are obtained for larger values of µ.The FIG. 5: Branching Ratio of the heavy CP-evenFIG. Higgs≃ 7: andBranching CP-odd Higgs Ratio→ dec ofays the heavyas a function CP-evenQ of Higgs and CP-odd Higgs decays as a function of alt mod the respective Higgs mass in the mh and mh thescenarios respective for Higgstan β mass=10and in the for mh diffalterentand values mhmod scenarios for tan β =4different values of the 20 22 of the Higgsino mass parameter µ. Higgsino mass parameter µ.
the width beyond the bottom-quark and tau-lepton ones, the hZ channel being the most are displayed in Fig. 8 with the values of At defined in the on-shell scheme. Observe that relevant one. As we discussed before, this is in sharp contrastalt with what happens in the for the mh scenario larger values of mQ are necessary for smaller values of µ.Onthe heavy CP-even Higgs boson, for which at mA 300 GeV the BR(Hmod ττ) is only of a few contrary,≃ in the mh scenario,→ larger values of mQ are obtained for larger values of µ.The
20 22 The challenging A/H è tt channel: lnterference effects Triangle loop function
SM Higgs: real and slowly varying Once above the threshold, imaginary piece increases and real piece decreases. Background real Real Interference from the real part of the propagator and real part of loop function (shifts the mass peak) Im. Interference from the imaginary part of propagator with imaginary part of loop function (rare case, changes signal rate) Impact of interference effect in A/H à tt at the LHC
Projections for A/H ètt in Type II 2HDM M.C., Liu ‘16
ATLAS-2016-073
First interference studies at ATLAS Carena, Haber, Low, Shah, C.W.’15 N. Shah’s talk Naturalness and Alignment in the NMSSM see also Kang, Li, Li,Liu, Shu’13, Agashe,Cui,Franceschini’13 Carena, Haber, Low, Shah, C.W.’15 Carena, Haber, Low, Shah, C.W.’15 • It is well known that in the NMSSM there are new contributions to the lightest CP- N. Shah’s talk even Higgs mass, N. Shah’s talk 3 Naturalness and Alignment in the NMSSM NaturalnessW and= SHAlignmentuHd + S in the NMSSM 3 see also Kang, Li, Li,Liu, Shu’13, Agashe,Cui,Franceschini’13 Naturalnesssee also Kang, and Li, Li,Liu, the Shu’13, Alignment Agashe,Cui,Franceschini’13 in the NMSSM It is well known that in the NMSSM there are new contributions to the lightest CP- It is well known that in the2 NMSSM there are •new contributions to the lightest CP- • 2 M.C,2 Haber,v Low,2 Shah, Wagner.’152 2 evenAlso Kang,Higgs Li, mass, Liu, Shu’13; Agashe, Cui, Franceschini ’13 even Higgs mass,mh sin 2 + MZ cos 2 + t˜ 3 ' 2 3 W = SHuHd + S W =Superpotential SHuHd + S λ S HuHd è µeff = λ 3 It is perhaps less known that it leads to sizable3 corrections to the mixing between • 2 the MSSM like CP-even• Well knownstates. 2 Inadditional the Higgs contributions basis, to mh 2 2 v 2 2 2 2 2 v 2 2 2 mh sin 2 + MZ cos 2 + t˜ mh sin 2 + MZ cos 2 + t˜ ' 2 •2 Less well' 1known:2 2 2 2 2 2 MS(1, 2) mh MZ cos• 2 It is perhapsv Stopsin less Contribution+ known t˜ that it leadsat alignment to sizable corrections to the mixing between • It is perhaps less sizeable known' tan contributionsthat it leads to sizableto the corrections mixing the MSSM between to likethe CP-evenmixing MSSM between states. CP-even In the eigenstatesHiggs basis, the MSSM like CP-even states. In the Higgs basis, Carena, Haber, Low, Shah, C.W.’15 The last term is the one appearing in the Interesting,MSSM, that after are some small simple for algebra,2 moderate one can1 mixingshow that2 2 2 2 2 • 1 M (1, 2) Last term mfrom MSSM;M cos 2 small forv sin + ˜ and small values Mof 2(1tan, 2) m2 M 2 cos 2 2v2 sin2 +S ' tan h Z t S h Z t˜ moderate/small2 2 µA and small tanβ ' tan ˜ = cos 2 (m M ) t The last termt is the one appearingh in Zthe MSSM, that are small for moderate mixing So, alignmentThe last termleads is to the a onedetermination appearing in ofthe lambda, MSSM,• that are small for moderate mixing • • and small values of tan and small values of tan l = Alignment leads to λ in the restricted range 0.62 to 0.75, • The values of lambda end up in a very narrow •range,So, between alignment 0.65 leads and to a0.7 determination for of lambda, So, alignment in agreementleads to a determination with perturbativity of lambda, up to the GUT scale allvalues• of tanbeta, that are the values that lead to naturalness with perturbativity The values of lambda end up in a very narrow range, between 0.65 and 0.7 for up to the GUT scale • L = The values of lambda end up in a very narrow range, between ±0.65 and 0.7 for • 2 2 allvalues of tanbeta, that are the values that lead to naturalness with perturbativity = l
m M cos 2 H allvalues of tanbeta, that are2 the valuesh thatZ lead to naturalness with perturbativity = up to the GUT scale 2 up to the GUT scale alt v2 sin m2 M 2 cos 2 2 2 2 = h Z m M cos 2 2 = 2 = h Z v2 sin 2 2 l Alignment in the doubletv Higgssin sector of the NMSSM = ± allows for light stops with moderate mixing b b
(a) (b) For moderate mixing, It is clear that low values of tan < 3 leadFIG. to 2: Leftlower panel corrections : The blue shaded to the band Higgs displays mass the valuesparameter of as aat function the alignment of tan , necessary values for alignment for m = 125 3 GeV. Also shown in the figure as a green band are values of that h ± lead to a tree-level Higgs mass of 125 3 GeV. Right panel : Values of M necessary to obtain a ± S 125 GeV mass for values of fixed by the alignment condition and stop mixing parameter Xt =0
and Xt = MS. The dominant two-loop corrections are included.
Since µ 2 is the diagonal Higgs squared-mass parameter at tree-level in the absence of | | supersymmetry breaking, it is necessary to demand that µ M . Furthermore, the SM- | | ⌧ S like Higgs mass in the limit of small mixing is approximately given by 2 [cf. Eq. (48)]. M11 The one-loop radiative stop corrections to 2 exhibited in Eq. (50) that are not absorbed M12 in the definition of 2 are suppressed by µ/M (in addition to the usual loop suppression M11 S factor), as shown in Eq. (53), and thus can be neglected (assuming tan is not too large) in obtaining the condition of alignment. Hence, satisfying Eq. (53) fixes , denoted by alt,
as a function of mh, mZ and tan ,
2 2 alt 2 mh mZ c2 ( ) = 2 2 . (55) v s The above condition may only be fulfilled in a very narrow band of values of =0.6–0.7 over the tan range of interest. This is clearly shown in Fig. 2, where the blue band exhibits
16 alt alt MA GeV , k = l 2, mh=125 GeV l=0.65 3.0 0.35 700 H L ê 800 0.30 2.5 0.25 300
b 400 2.0 0.20
500 max tan 600 k 0.15
1.5 0.10
200 0.05 1.0 0.00 100 150 200 250 300 1.5 2.0 2.5 3.0 m GeV tan b
(a) (b) » » H L AligningFIG. 3: Left the panel :singlets Values of MA leading to a cancellation of the mixing of the singlet with the SM-like Higgs boson in the Higgs basis, shown in the µ –tan plane. The values of were fixed | | so that the alignment condition among the doublet components is fulfilled. Values of = 1 close AligningCarena, Haber,the Low,Singlet Shah, C.W.’15 2 to the edge of the perturbativity consistency region were selected. Right Panel: Maximum values of • The previous formulae assumed consistent implicitly with perturbativity that the as a singlets function of aretan eitherfor =0 decoupled,.65. or not significantlyIf singlet mixedalso at with LHC the MSSMreach, CP-even precision states Higgs data demands high degree of alignment. the following condition: M 2 s2 s • The mixingThe mass mixing matrix mass element matrix between element the singlets betweenA and2 + the the2 SM-like=1 singlet. Higgs and is the SM-like(57) Higgs is approximately given by 4µ2 2 We shall take 0.65, as required by the alignment condition given in Eq. (55), and '2 2 2 1 mA sin 2 sin 2 M (1, 3) 2 vµ2 , where1 the latter is a consequence of the perturbativeNeeds consistency to vanish of the theory in upalignment S ' 4µ2 2 to the Planck✓ scale, as shown in the right panel◆ of Fig. 3. It follows that in order to satisfy If one assumes alignment, the expression inside the bracket must cancel • Eq. (57) the mass parameter MA must be approximately correlated with the parameter µ, For tanβ < 3 and λ ~ 0.65, plus κ in the perturbative regime, it follows that in order 2 µ If one assumes tan < 3 and lambda of order 0.65, andM in addition| | . one asks for (58) • to get small mixing in the Higgs sector,A m⇠ As and µ are correlated kappa in the perturbative regime, one inmediately conclude that2 in order to get In the parameter regime where 100 < µ < 300 GeV (so that no tree-level fine tuning is small mixing in the Higgs sector, the CP-odd Higgs is⇠ correlated| | ⇠ in mass with the 2 µ < < parameter mu, namely necessary to achieve electroweak symmetry breaking) and 1 tan 3, we see that MA is mA | | ⇠ ⇠ somewhat larger than µ . This is shown in the left panel of Fig. 3, in which the values of | | ⇡ sin2 Since both of them small is a measure of naturalness, we see again that alignment • MA leading to the cancellation of the mixing with the singlet CP-even Higgs state is shown and naturalnessSince come both together mA and in a beautifulµ should way bein the small, NMSSM we see again that alignment and naturalness come together in a beautiful18 way in the NMSSM • Moreover, this ensures also that all parameters are small and the CP-even and CP-odd singletsMoreover, (and singlino) this become ensures self alsoconsistently that all light parameters are small and the CP- even and CP-odd singlets and singlino become self consistently light m = 2µ of interest for Dark Matter S˜ NMSSM properties close to Alignment
Singlet Spectra and decays
- Heavier CP-even Higgs can decay to lighter ones: mhS < 2 MH - Anti-correlation between singlet –like CP-even and CP-odd masses
- CP-even light scalar, hS, mainly decays to bb and WW ;
- CP odd light scalar, aS, mainly decays to bb
MSSM-like A and H decays: -- A/H decays significantly into top pairs; BRs ~ 20% to 80% (dep. on tanβ ) decays may be depleted by decays into charginos/neutralinos (10% to 50%)
-- Other relevant decays: H è hhS and A à ZhS (20% to 50%, dep on mass)
H è hh and A è hZ decays strongly suppressed due to alignment Others: H àhs hs; HàAs Z; AàAs hs; AàAs h of order 10% or below
Ongoing searches at the LHC are probing exotic Higgs decays
• Complementarity between gg àAà Z hS àll bb and ggà hS à WW searches
CMSCMS 1505.03831 1505.03831 CMS PAS HIG-15-001 HVV/SM HVV/SM ~10% ~10%
• Promising Hà h hS channels with hs à bb or WW (4b’s or bbWW) • Searches for H à ZA or Aà ZH should consider should consider to
replace Z by h125 (with A/H à aS/hS)
• Channels with missing energy: A à h as; H à Z as with as à neutralinos possible for tanβ ~ 4 to 6 (lighter singlet spectrum) 6 6 6 case, the amplitude becomes proportional to case, the amplitude becomes proportional to case, the amplitude becomes proportional to md 1 1 md 1 1 ad cos (m + µ sin 2 ) 2 µ sin cos 2 2 . ad (14)cos (m + µ sin 2 ) 2 µ sin cos 2 2 . (14) m ⇠ cos1 1 mh mH ⇠ cos mh mH a d cos (m + µ sin 2 ) µ sin cos 2 . (14) d ⇠ cos m2 m2 We can do a similar exerciseh for a neutralinoH scattering o↵ anWe up-type can do quark, a similar which exercise gives for a neutralino scattering o↵ an up-type quark, which gives We can do a similar exercise for a neutralino scattering o↵ an up-type quark, which gives m 1 1 mu 1 1 a u sin (m + µ sin 2 ) + µ cos cos 2 . (15) au sin (m + µ sin 2 ) + µ cos cos 2 . u (15) 2 2 m 1 1 2 2 ⇠ sin mh mH u ⇠ sin mh mH 6 6 au sin (m + µ sin 2 ) +µ cos cos 2 . (15) ⇠ sin m2 m2 h H Include the contributions from all quarks, including the gluon induced ones, the SI scattering Include the contributions from all quarks,case, includingcase, the the amplitude amplitude the gluon becomes becomes induced proportional proportional ones, the to to SI scattering Include the contributions from all quarks, including the gluon induced ones, the SI scattering cross section can be expressed as cross section can be expressed as 6 mmdd 11 1 1 ad cos (m + µ sin 2 ) µ sin cos 2 . (14) cross section can be expressed as ad cos (m + µ sin 2 ) 22 µ sin cos 2 2 2 . (14) ⇠⇠coscos mmh mHm a 2 a case, the amplitude becomes proportional toh ( pH) q (p) q (p) aq 2 (p) aq ap = fTq + fTG mp, (16) We can do a similar exercise for a neutralino scattering o↵ an up-type quark,mq which27 gives mq (p) aq 2 (ap)p = aq fTq We can+ dof aTG similar exercisem forpm, ad neutralino scattering o1(16)↵ an q up-type=u,d,s quark,1 which givesq=c,b,t ! ap = f + f mp, m 27 (16)m ad cos (m + µ sin 2 ) µ Xsin cos 2 . X(14) Tq TG q q ! cos m2 m2 mq 27 qm=u,d,sq q=c,b,t mu ⇠ 1 h 1 H q=u,d,s q=c,b,t ! mDark Matter(p) Direct1 Detection(p) 1 (p) (p) X Xau u sin (m + µ sin 2 ) 2 + µ cos cos 2 2 . (15) X X au wheresin (mf + =0µ sin.017 2 ) 0+.008,µ cosf cos=0 2 .028 . 0.014, f (15)=0.040 0.020 and f 0.91 are We can do⇠ asin similar exerciseTu for a neutralinomh2 scatteringTd o↵ anm up-typeH 2 quark,4 whichTs gives TG (p) (p) (p) ⇠ sin (p) m± m ± ± ⇡ (p) (p) (p) (p) h H where fTu =0.017 0.008, fTd =0.028 0.014, fTs =0.040 0.020 andof parameters,fTG the amplitude0.91 from light are Higgs exchange and heavy Higgs exchange exactly where fTu =0.017 0.008, fTd =0.028 0.014, fTs =0.040 0.020Include and fTG the contributions0.91 are fromtheStarting allquarkm quarks, to form probe including factors the the Higgs [36, gluon1 37] portal induced defined ones, as the1 SI scattering ± ± ± u cancel against each⇡ other, which we call generalized blind spots, since they provide a more ± ± ± Include the contributions⇡ fromau all quarks,sin ( includingm + µ sin the 2 ) gluon2 + inducedµ cos cos ones, 2 the2 . SI scattering(15) ⇠ sin general version of the ones previouslym discussed in the literature, that are presentm for very the quark form factors [36,the 37] quark defined form as factors [36, 37] defined as cross section can be expressed as h H cross section can be expressed as large values of the non-standard Higgs masses. (p) (p) (p) Include the contributions from all quarks, including SI scatteringmSimilarpfTq ,f cross calculationTG section=1 isfor proportionalf Tqneutrons. to (17) with Fu fu +2 27 fTG 0(.p15) and(pF) d = fTd2 +(pf)Ts + 27 fTG 0.(14.p) The(p) first term(p) denotes2 (p) | the| contributionCP-even⌘ Higgs mass eigenstates can of be expressed theX in lightest terms of the gauge eigenstates Higgs as and its cancellation leads to the traditional ⌘ ⇥ with⇡Fu fu +2 fTG 0.15 and⇡Fd = fTd + fTs + fTG 0.14. The first term1 X 27 . Using equations (14) and27 (15), then the SI scatteringh cross= (cos ↵ sectionHu sin ↵ Hd) is proportional(1) 2 to ⌘ ⇥ ⇡ ⇡ 1 p2 1 denotes the contribution of the lightest Higgs and its cancellation leadsSI to the. traditional Using(p) equations(p) blind (14) and spot (15), scenarios then the SI [29]. scattering The1 (p) cross second( sectionp) term2 is proportional is the contribution to of the heavy Higgs and as p (Fd + Fu )(m + µ sin 2 ) + µ tan cos 2 H (= F(sind↵ Hd++cosF↵ Huu). /tan ) (2) , (18) denotes the contribution of the lightest Higgs and its cancellation leads2 to the traditionalp2 2 2 ⇠ mh mH 2 (p) 1 Therefore, the down-quark contribution to the( SIp) amplitude> is proportional to 1 blind spot scenarios [29]. The second term is the contribution of the heavySI (F HiggsSI+ F and(p))((m asp) +mentionedµ(p)sin 2 ) before+ µ tan1 for cos values 2 ( F of µ+ F(p)(mp)/ tan(andp)2 ) large2 1 , tan(18) may become of the same order as p d u (F + F )(m + µ sin 2 ) + µ tanm d cossin ↵ 2dg h( cosF↵ g uH + F /tan ) , (18) (p) p (p) d (pu) 2 (p) 2 (p) a (p) +(p) ⇠d . u (3) 2 2 ⇠ 2 m d ⇠ cos m2 2 | |m2 m blind spot scenarios [29]. The second termwith iswithF the contributionf ⇠+2 f of the0.15 and heavyh F m Higgs=h f + andf + ash f H 0.14. The firstH m termH > u Destructiveu 27interferenceTG betweend Tdh andTs H✓ contributions27 TG ◆ for mentioned before for values of µ m and large tan may become of the same⌘ order⇥ as the⇡ SM-like HiggsGiven the interactions one. ⇡ (p) (p) (p) (p) (p) 2 (p) (p) ((pp)) ((p) (p) (p) 2 (p) | |⇠ > denotes the contribution2 of the lightest Higgs and itsp cancellation˜ ˜ p 2˜ a ˜ a leads to the traditional with Fu negativefu +2 valuesf 0of.15 µ and (cos2FL β=2g 0Ynegative)Hfu BHuHu+⇤ f2gW Hu+t H u⇤ +(uf d)(4)0.14. The first term mentioned before for values of µ m andwith F largeu f tanu +2 mayf become027.15TG of and theF same= f d order+ f Td as+ Tsf 27 $TG0.14. The first term ⇠ ⌘ ⇥⌘ 27 TG ⇡⇥ ⇡ d Td Ts 27 TG ⇡ ⇡ the SM-like Higgs one. | | In the above,and the decomposition we have of a neutralino used mass eigenstate the proton scattering amplitudes to define the spin indepen- denotesblind spot thedenotes contribution scenariosStill the [29]. contribution room of The the second lightestfor of thea term SUSY Higgs lightest is the and HiggsWIMP contribution its and cancellation itsmiracle cancellation of the leads heavy leads to Higgs the to the traditional and traditional as the SM-like Higgs one. ˜ = N B˜ + N W˜ + N H˜ + N H˜ , (5) > i1 i2 i3 d i4 u In the above, we have used the proton scattering amplitudes to defineOnementioned the can spin doblind beforea similar indepen- spot for calculation scenarios valuesdent of [29]. forµ scattering neutrons, Them secondand and large cross term the tan expression section. is themay contribution become Theis very result ofsimilar. of the the same remainsIndeed, heavy order Higgs valid as and afteras including the neutron contri- blind spot scenarios [29]. The second| |⇠ term is the contribution of the heavy Higgs and as > (n) In the above, we have used the proton scatteringthe SM-likementioned Higgs amplitudes one. before for to values define of theµ m spin and indepen- large tan may become of the same order as dent scattering cross section. The result remains valid after including the neutron contri- butions,> since⇠ for a neutralino scattering o↵ aneutrontheformfactorsarefTu =0.011, mentioned before for values of µ m |and| large tan may become of the same order as dent scattering cross section. The result remainsIn the above,(then valid) SM-like we after have Higgs including used( one.n) the| |⇠ proton the scattering neutron(n) amplitudes contri- to define(n) the spin indepen- (n) (n) butions, since for a neutralino scattering o↵ aneutrontheformfactorsarethe SM-likefTu Higgs=0.011, one. fTd =0.0273, fTs =0.0447 and fTG =0.917 [38] and therefore Fu 0.15 and Fd 0.14, dent scatteringIn thecross above, section. we have The used result the remains proton scattering valid after amplitudes including to the define neutron the spin contri- indepen- ⇡ ⇡ (n) (n) butions,(n since) for a neutralino scattering(n) o↵ aneutrontheformfactorsare(n) (p) f (n()p)=0.011, fTd =0.0273, fTs =0.0447 and fTG =0.917 [38] and therefore Fu 0.In15 the and above,Fdentd scatteringwe0 have.14, used crosssame the section. as protonFu Theand scattering resultTuFd remains. amplitudes valid after to defineincluding the the(n spin) neutron indepen- contri- ⇡ butions, since for⇡ a neutralino scattering o↵ aneutrontheformfactorsarefTu =0.011, (p) (p) (n) (n) (n) dent scattering cross section.(n The) result remains(n valid) after including the neutron(n) contri- same as Fu and F . f =0.0273, f =0.0447 and f =0.917(n [38]) andbutions, therefore(n) since forF auTherefore, neutralino(n)0.15 scattering and the tree-levelF o↵ aneutrontheformfactorsare0. scattering14, (n) cross section(n) fTu due=0.011, to the light and heavy CP-even Higgs d Td Ts TG fTd =0.0273, fTs =0.0447 and fTG =0.917 [38] andd therefore Fu 0.15 and Fd 0.14, (n) (n) ⇡ (n) ⇡ ⇡ (n) (n)⇡ (n) (p) (p) butions, sincef(pTd) for=0 a.0273, neutralino(p) fTs =0 scattering.0447 and fTG o↵ =0.917aneutrontheformfactorsare [38] and therefore Fu 0.15f andTu =0.011,Fd 0.14, Therefore, the tree-levelsame scattering as Fu crossand sectionF . due to the light and heavysame as CP-evenFu and HiggsFd . exchange cancel against each other when⇡ ⇡ d (n) Destructive(n) (p )Interference(p) for(n negative) values of μ and constructive( interferencen) (n) f =0.0273,sameforf positive as=0Fu .values0447and Fof andd μ . (cos(2f =0.917β) negative). [38] and therefore Fu 0.15 and F 0.14, exchange cancel against each other when Td Therefore, theTs tree-level scatteringTG cross section due to the light and⇡ heavy CP-evend Higgs⇡ Therefore, the tree-level scattering cross section(p) dueTherefore, to(p the) the light tree-level and scatteringheavy CP-even cross(p section) Higgs due(p) to the light and heavy1 CP-even( Higgsp) 1 sameexchange as Fu canceland F againstd . each other when (Fd + Fu )(m + µ sin 2 ) 2 Fd µ tan cos 2 2 , (19) exchange cancel against each other when mh ' mH (p) exchange(p) cancel against1 each(p) other when 1Therefore, the tree-level scattering cross section due to the light and heavy CP-even Higgs (F + F )(m + µ sin 2 ) F µ tan cos 2 , (19) 1 1 d u 2 d 2 (p) (p) (p1) 1 mh ' mH (Fd + Fu )((p)m +(pµ) sin 2 ) 2 Fd µ tan(p ) cos 2 2 , (19) exchange cancel against each(Fd other+ Fu when)(m + µmsinh ' 2 ) 2 Fd µ tan mcosH 2 2 , (19) (p) (p) 1 (p) 1 mh ' mH (Fd + Fu )(m + µ sin 2 ) 2 Fd µ tan cos 2 2 , (19) mh ' (p) (p) mH 1 (p) 1 (Fd + Fu )(m + µ sin 2 ) 2 Fd µ tan cos 2 2 , (19) mh ' mH 6 6 case, the amplitude becomes proportional to case, the amplitude becomes proportional tomd 1 1 ad cos (m + µ sin 2 ) 2 µ sin cos 2 2 . (14) ⇠ cos mh mH m 1 1 a d cos (m + µ sin 2 ) µ sin cos 2 . (14) d ⇠ Wecos can do a similar exercisem for2 a neutralino scatteringm2 o↵ an up-type quark, which gives h H We can do a similar exercise for a neutralinomu scattering o↵ an up-type1 quark, which gives 1 au sin (m + µ sin 2 ) 2 + µ cos cos 2 2 . (15) ⇠ sin mh mH m 1 1 a u sin (m + µ sin 2 ) + µ cos cos 2 . (15) u ⇠ Includesin the contributions fromm2 all quarks, includingm2 the gluon induced ones, the SI scattering h H cross section can be expressed as Include the contributions from all quarks, including the gluon induced ones, the SI scattering cross section can be expressed as (p) aq 2 (p) aq ap = fTq + fTG mp, (16) mq 27 mq q=u,d,s q=c,b,t ! (p) aq 2 (p) X aq X ap = fTq + fTG mp, (16) (p) mq 27 (p) mq (p) (p) where f q==0u,d,s.017 0.008, f q==0c,b,t.028! 0.014, f =0.040 0.020 and f 0.91 are TuX ± Td X ± Ts ± TG ⇡ (p) the quark(p) form factors [36, 37](p defined) as (p) where f =0.017 0.008, f =0.028 0.014, f =0.040 0.020 and f 0.91 are Tu ± Td ± Ts ± TG ⇡ the quark form factors [36, 37] defined as of this phenomenon. We find out that indeed, as can be seen from Eqs. (18)–(20),H -11 negative theH parameter space of the CMSSM. Our expressions10 provide an analytical understanding SI SI before [30, 31, 33], and the suppression in DDMD was identified numericallyp from a scan of Blind p -11 s values of µ haves two10 e↵ects on the scattering amplitudes : On one hand, they suppress Spot of this phenomenon. We find out that indeed, as can10 be-12 seen from Eqs. (18)–(20), negative the parameter space of the CMSSM. Our expressions provide an analyticalFuture understanding theRegion coupling of the- lightest12 neutralino to the lightest CP-even Higgs boson.Sensitivity On the other 10 10-13 values of µ have two e↵ectsBlue on the: µ = scattering2M amplitudes(Xenon1T, : On one hand, they suppress of this phenomenon.hand, they lead We to a find negative out that interference indeed, between as can bethe seen light 1 from and heavy Eqs. (18)–(20),Higgs exchange negative LZ) - the10- coupling13 of the lightest neutralinoRed : µ =2 toM1 the lightest10 CP-even14 Higgs boson. On the other values ofamplitudes.µ have two For su e ↵ectsciently on low the values scattering of mA (large amplitudes values of tan : On) the one heavy hand, Higgs they exchange suppress 100 200 500 1000 2000 5000 1 ¥ 104 2 ¥ 104 100 200 500 1000 2000 5000 1 ¥ 104 2 ¥ 104 contribution mayhand, become they dominant. lead to On a negative the other interference hand, for large between values of them lightthe SM and heavy Higgs exchange the couplingHuang, of the Wagner, lightest ‘15 neutralino to theMA lightestGeV CP-even Higgs boson.A On the other MA GeV contribution becomesamplitudes.Application dominant For andof suthe the naiveciently main blind contribution low spot valuesformula offromgivesm AMA exchange(large = 478 valuesGeV of a heavy of tan Higgs ) the heavy Higgs exchange hand, they lead to a negative interference betweenH L the light and heavy Higgs exchange H L comes from the interference with the SM-like one and is only suppressed by 1/m2 . FIG.contribution 2: SI scattering may become cross dominant. section as On a function the other of hand,mAA for for tan large = values 50 (up of m left),A the tan SM = 30 (up amplitudes. For su ciently low values of mA (large values of tan ) the heavy Higgs exchange contribution becomes dominant and the main contribution from exchange of a heavy Higgs contribution may becomeright) and dominant. tan = On 10 the (down other left), hand,µ for2 largeM1 and values tan of m= 30the,µ SM 4M1 (down right). The red III. NUMERICAL STUDY⇠ A ⇠ comes from the interference with the SM-like one and is only suppressed by 1/m2 . contribution becomesdots dominant are for the andµ> the0 main case, contribution and blue dots from are exchange for µ<0 of case. a heavy The Higgs green shaded areaA are excluded by To perform a numerical study of the SI scattering cross section when all sfermions2 are comes from the interferencethe CMS withH, A the SM-like⌧⌧ searches. one and The is orange only suppressed line is the by LUX 1/m limit,A. and the blue line is the projected ! heavy, the relevant parameters are the Bino mass MIII.1, the NUMERICAL Wino mass M2, the STUDY Higgsino mass Xenon 1T limit µ, the CP odd Higgs mass mA and tan . In the following, we will concentrate on the case III. NUMERICAL STUDY in which LSP is mostlyTo perform bino-like a for numerical simplicity, study but the of analysis the SI can scattering be. easily cross generalized section when all sfermions are to the case in whichheavy, LSP the is relevant wino-like. parameters In the traditional are the blind Bino spot mass scenario,M , the at Winomoderate mass M , the Higgsino mass To perform a numerical study of the SI scattering cross section when1 all sfermions are 2 or large valuesis of enhanced tan the blind by spot tan condition, , but sincem + µµ singrows 2 =0,canonlybesatisfiedif together with tan , the down-Higgsino component µ, the CP odd Higgs mass mA and tan . In the following, we will concentrate on the case heavy, theµ is relevant very large, parameters which makes are the the obtention Bino mass of theM right1, the thermal Wino relicmass densityM2, the very Higgsino di cult. mass 13 1 | | isin suppressed which LSP roughly is mostly by bino-like tan .Atlarge for simplicity,mA, but the the cross analysis section can approaches be easily generalized 10 pb , which µ, the CPThe odd generalized Higgs massblind spots,m and instead, tan may. In be the obtained following, for smaller we will values concentrate of µ , which on may the case A | | isto below the case the in atmospheric which LSP is and wino-like. di↵use In supernova the traditional neutrino blind spot backgrounds. scenario, at There moderate are various in whichbe LSP consistent is mostly with the bino-like ones necessary for simplicity, to obtain a but thermal the analysis DM density. can be easily generalized In order tocontributions analyzeor large the values parameters to of tan this consistent asymptoticthe blind with spot the value, generalized condition, including blindm + spots,µ squarks,sin we 2 first=0,canonlybesatisfiedif incomplete cancellation of the to the case in which LSP is wino-like. In the traditional blind spot scenario, at moderate look at the parameterµ is very space large, away which from the makes traditional the obtention blind spot, ofµ the right2M1 thermal. We use relic density very di cult. or large values of tancouplings| | the blind and spot loop condition, e↵ects. m + µ sin 2 =0,canonlybesatisfiedif⇠ ISAJET [39] to calculate the spectrum and the SI scattering cross section for di↵erent TheWe generalized also analyze blind the spots, relic instead, density. may Considering be obtained a for thermally smaller values produced of µ , neutralino which may DM, the µ is veryvalues large, of tan which and makesm , which the obtention agrees with of MicrOMEGA the right thermal 2.4.5 [38] relic almost density perfectly. very di We cult. | | | | be consistentA with the ones necessary to obtain a thermal DM density. The generalized blindannihilation spots, instead, cross may section be obtained is too for small smaller for values Bino-like of µ DM,, which which may leads to DM density over In order to analyze the parameters consistent with the| | generalized blind spots, we first be consistent with theabundance, ones necessary while to the obtain annihilation a thermal is DM too density. e cient for pure wino or Higgsino-like DM, which look at the parameter space away from the traditional blind spot, µ 2M1. We use In order to analyzeresults the parametersin under abundance consistent withunless the the generalized LSP is heavier blind spots, than we 1 TeV first [41,⇠ 42] or 2.7 TeV [42, 43], ISAJET [39] to calculate the spectrum and the SI scattering cross section for di↵erent look at the parameter space away from the traditional blind spot, µ 2M1. We use values of tan and mA, which agrees with MicrOMEGA⇠ 2.4.5 [38] almost perfectly. We ISAJET [39] to calculate the spectrum and the SI scattering cross section for di↵erent values of tan and mA, which agrees with MicrOMEGA 2.4.5 [38] almost perfectly. We Restrictions on MA from Dark Matter Roglans, Spiegel, Sun, Huang, C.W.’17 See also Badziak, Olechowski, Szczerbiak’17 Assuming the neutralinos provide the Putting Constraints Together : whole relic Αssuming density that (non-thermal)the Neutralinos provides theAssuming whole Observed ThermalAssuming Relic Density ThermalRelic Relic :Density Density 11 Upper Bound on MA for negative values of μ (destructive interference) 9 Upper bound on MA fοr µ< 0 Blue : Allowed Red : Excluded Green : To be Probed by LZ Grey : Underabundance Figure. 5: Constraints on the µ M1 plane under relic density constraints and the present and projected DDMD con- | | straints. The well-tempered region (µ M1)naturallyattainsthecorrectrelicdensity,whiletheregionbelowmayattain ' the correct value if MA is tuned to mediate resonant annihilation. The required value of MA is constrained by the LUX Figure. 3:Strong Upper bounds Restrictions on M due on tothe 2016 Well LUX Tempered bounds and Region projected (region DDMD between bounds 100 dashed times stronger white thanlines) LUX, Strong Restrictions onA the Well Temperedand 100 times strengthenedResonant LUX bound on SI cross section. Annihilation The blue region is allowed by theto 100 timestune strengthened LUX respectively (µ<0), assuming the observed relic density in thebound; whole the parameter blue and the green space. regions The are allowed value under of M currentA is LUX chosen bound. to Note be that at the boundaries of the LUX con- Region (regionAt the edge between of the region dashed restricted white by precision lines)straint (red)electroweak and of thethe LUX/100 measurements.correct constraint (green) aboverelic the blue density region correspond to (M the boundaries~2 in Fig.M 3 where) the the maximum value allowed by these bounds, and is indicated by the color scale. (Note that the color scheme di↵ers from A 1 More easily realized if alignment condition isupper fulfilled. bound on MA is quickly lifted to infinity. The constraints below the blue region are due to the overcompensation in the previous plot such that the regions where the SI cross sectionthe scatteringis allowed cross as sectionM from thePlus heavyis always Higgs blind contribution. shown inspot blue.) Theeffect for RoglansAdditional, Spiegel,Sun,Huang contributions to the, HiggsWagner sector, ’17 like in the NMSSMA !1 makes this scenario region betweenmore the realistic, white dashed due lines to constraints represents the on well-tempered stop sector. region. Under the strengthened bound a much larger Also Badziak, Olechowski,Szczerbiak ‘17 direct detection bounds portion of the µ M1 plane is constrained. The dashed line below corresponds to where theB. left LZ hand Reach side and of BlindEq. 6 isSpots zero, | | corresponding to the vanishing of the neutralino coupling to the SM Higgs. Below this line the blind spot cannot be obtained The lack of observation of a signal at the LZ experiment would constrain us to a narrow since the left hand side of Eq. 6 becomes negative. region of allowed parameter space for thermal dark matter, namely the A-funnel region displayed in Fig. 5, plus the well-tempered region for values of MA consistent with the It is interesting to investigate the region toupper be bound probed obtained by in future Fig. 3. The DDMD reach of LZ experiments. goes far beyond the natural values of the In case of no detection, future experiments willspin independent push the cross experimental section for values of limits the gaugino below and Higgsino the masses of order of the weak scale, and therefore pushes the parameters towards the blind spot values. Alternatively, decoupled scattering cross section in greater regions of the µ M plane. In particular, the one could consider the event1 of an LZ detection of Dark Matter in the currently allowed projected bounds of the LZ experiment are approximatelyrange. In order 100 to fix times ideas and stronger show the complementaritythan those from of di↵erent search methods in the LUX experiment [17]. Fig. 3 reveals that, assuming a dark matter density consistent with the observed one, these stronger bounds would constrain MA in the entire region left of the well-tempered region, and in part of the region to the right as well. As before, if a thermal origin of the dark matter relic density is assumed, the well-tempered region may be achieved, but the upper bound on MA would become smaller than about 300 GeV. A more complete description of the exclusion state of the A-funnel region takes into account the upper bound on MA presented above as well as the lower bound due to the overcompensation of the heavy CP-even Higgs contribution. As mentioned before, the region allowed by LUX and relic density considerations roughly correspond to the blue and dark green region in Fig. 3, where the required value for resonant annihilation M 2M is below A ' 1 the upper bound set by LUX. (For µ>0, the correct relic density can be achieved near the Blind Spots in Direct DM detection in the NMSSM Possible to have a three way cancellation between the hs, h and H contributions Cheung, Papucci, Sanford, Shah, Zurek ’14 Singlino-Higgsino opens a region of destructive interference for µ positive assumed 90% composition Baum, M.C, Shah, Wagner µ < 0 µ > 0 to appear Blind Spots in Direct DM detection in the NMSSM Baum, M.C, Shah, Wagner, Normalized to to appear Xenon1T arXiv:1705.06655 and including PICO-60 arXiv:1702.07666 Assuming thermal relic density 4 ] not apply acoustic or fiducial cuts, resulting in the larger 2 10-37 exposure shown in Table I. Instead, given 99.5 ± 0.1% ef- ficiency to reconstruct at least one bubble in the bulk for a multiple-bubble event, every passing event is scanned 10-38 for multiplicity. This scan reveals 3 multiple-bubble events in the WIMP search dataset. Based on a detailed Monte Carlo simulation, the background from neutrons is 10-39 predicted to be 0.25 ± 0.09 (0.96 ± 0.34) single(multiple)- bubble events. PICO-60 was exposed to a 1 mCi 133Ba source both before and after the WIMP search data, 10-40 which, compared against a Geant4 [20] Monte Carlo sim- PICO-60 C F ulation, gives a measured nucleation efficiency for elec- 3 8 ± × −10 tron recoil events above 3.3 keV of (1.80 0.38) 10 . 10-41 Combining this with a Monte Carlo simulation of the ex- SD WIMP-proton cross section [cm 101 102 103 ternal gamma flux from [15, 21], we predict 0.026 ± 0.007 WIMP mass [GeV/c2] events due to electron recoils in the WIMP search expo- sure. The background from coherent scattering of 8B FIG. 3. The 90% C.L. limit on the SD WIMP-proton cross solar neutrinos is calculated to be 0.055 ± 0.007 events. section from PICO-60 C3F8 plotted in thick blue, along The unmasking of the acoustic data, performed after with limits from PICO-60 CF3I(thickred)[10],PICO-2L completion of the WIMP search run, reveals that none of (thick purple) [9], PICASSO (green band) [14], SIMPLE (or- ange) [34], PandaX-II (cyan) [35], IceCube (dashed and dot- the 106 single bulk bubbles are consistent with the nu- ted pink) [36], and SuperK (dashed and dotted black) [37, 38]. clear recoil hypothesis defined by AP and the NN score, The indirect limits from IceCube and SuperK assume anni- as shown in Fig. 2. hilation to τ leptons (dashed) and b quarks (dotted). The We use the same procedure and calibration data de- purple region represents parameter space of the constrained scribed in Ref. [8] to evaluate nucleation efficiency curves minimal supersymmetric model of [39]. Additional limits, not for fluorine and carbon recoils. We adopt the standard shown for clarity, are set by LUX [40] and XENON100 [41] (comparable to PandaX-II) and by ANTARES [42, 43] (com- halo parametrization [22], with the following parame- Need to relax/enlarge−2 −3 scan parableto to IceCube).most efficiently populate the blind spots ters: ρD=0.3 GeV c cm , vesc =544km/s,vEarth =232km/s,andvo =220km/s.Weusetheeffec- tive field theory treatment and nuclear form factors de- ] scribed in Refs. [23–26] to determine sensitivity to both 2 10-38 spin-dependent and spin-independent dark matter inter- actions. For the SI case, we use the M response of Table 1 in Ref. [23], and for SD interactions, we use the sum of ′ ′′ the Σ and Σ terms from the same table. To implement 10-40 these interactions and form factors, we use the publicly available dmdd code package [26, 27]. The calculated limits at the 90% C.L. for the spin-dependent WIMP- proton and spin-independent WIMP-nucleon elastic scat- 10-42 tering cross-sections, with no background subtraction, as PICO-60 C F a function of WIMP mass, are shown in Fig. 3 and 4. 3 8 These limits are currently the world-leading constraints in the WIMP-proton spin-dependent sector and indicate 10-44 an improved sensitivity to the dark matter signal of a SI WIMP-nucleon cross section [cm 100 101 102 factor of 17, compared to previously reported PICO re- WIMP mass [GeV/c2] sults. Constraints on the effective spin-dependent WIMP- FIG. 4. The 90% C.L. limit on the SI WIMP-nucleon cross- neutron and WIMP-proton couplings an and ap are cal- section from PICO-60 C3F8 plotted in thick blue, along culated according to the method proposed in Ref. [28]. with limits from PICO-60 CF3I(thickred)[10],PICO-2L (thick purple) [9], LUX (yellow) [44], PandaX-II (cyan) [45], The expectation values for the proton and neutron spins 19 CRESST-II (magenta) [46], and CDMS-lite (black) [47]. for the F nucleus are taken from Ref. [23]. The allowed While we choose to highlight this result, LUX sets the −2 region in the an − ap plane is shown for a 50 GeV c strongest limits on WIMP masses greater than 6 GeV/c2.Ad- WIMP in Fig. 5. We find that PICO-60 C3F8 improves ditional limits, not shown for clarity, are set by PICASSO [14], the constraints on an and ap, in complementarity with XENON100 [41], DarkSide-50 [48], SuperCDMS [49], CDMS- other dark matter search experiments that are more sen- II [50], and Edelweiss-III [51]. sitive to the WIMP-neutron coupling. Outlook The 125 GeV Higgs can be accommodated in many BSM scenarios with light partners Precision measurements of the Higgs signals call for a significant degree of alignment that in turn has important implications for the searches for additional Higgs bosons and Dark Matter In the MSSM: Alignment calls for sizeable mu or heavy MA Dark Matter at the Well tempered, Bino-Higgsino region, may avoid constraints provided extra Higgs bosons are light. This calls for alignment Departure from Alignment yield A/H decays into gauge bosons, h and top pairs (Ewikinos) In the NMSSM: Necessary degree of alignment without decoupling is tied to a light Higgsino, Singlino and singlet –like Higgs sector, and allows for light stops with moderate mixing. Good for achieving the 125 Higgs mass and compatible with perturbavity up to M GUT New search channels for A/H decaying to Higgs like singlets and gauge bosons Blind spots for Direct DM searches may profit from Light Singlino-Higgsino region (TBC) Composite Higgs Models (PNGB) Model Building constrained by Higgs precision data Can have Heavy Higgs bosons with non universal couplings to WW/ZZ + CP violation emerging in the bottom quark and tau lepton sectors