JHEP01(2019)224 Springer January 3, 2019 January 26, 2019 January 30, 2019 : : : November 21, 2018 3. : . β Revised while the observed Higgs Accepted Published Received β Published for SISSA by https://doi.org/10.1007/JHEP01(2019)224 [email protected] . It is found that the presence of singlino at an , S M GeV. We analyse the constraints on the effective framework, 8 10 . 3 . 1811.06297 The Authors. c Supersymmetry Phenomenology

We investigate a scenario in which supersymmetry is broken at a scale , GeV leaving only a pair of Higgs doublets, their superpartners (Higgsinos) and [email protected] 14 10 ≥ S E-mail: Indian Institute of ScienceSector Education 81, and SAS Research Mohali, Nagar, Knowledge Manauli City, 140306, India Open Access Article funded by SCOAP ArXiv ePrint: intermediate scale significantly improves thestable stability or of metastable electroweak vacuum vacuummass and for together allows almost with a the all limit the on values the of charged tan HiggsKeywords: mass favours tan fermions which successfully evade thethe constraints singlino from mass the direct is arising detection from experiments the stability if of electroweakand vacuum, the observed mass limits and on couplings thesupersymmetric of masses the standard of Higgs, the model other at scalars, by matching it with the next-to-minimal a gauge singlet fermionat (singlino) low besides energy. the The standardof Higgsino-singlino model the mixing fermions electrically induces and neutral a gaugeerate components small bosons of splitting in Higgsinos between GUT the which scale otherwisethermal masses supersymmetry. remain dark almost matter The degen- if lightestting the combination induced Higgsino of by mass the them singlino scale provides turns is a the close viable neutral to components 1 of TeV. Higgsinos into The pseudo-Dirac small mass split- Abstract: M V. Suryanarayana Mummidi and Ketan M. Patel Pseudo-Dirac Higgsino dark mattersupersymmetry in GUT scale JHEP01(2019)224 4 18 30 8 ] in which only some of the superpartners are – 1 – 21 2 , 1 S 7 M 26 12 6 18 22 20 11 22 10 7 1 3 17 ], which are potential candidates for the unification of all the fundamental forces, 3 B.1 Gauge couplings B.2 Yukawa couplings B.3 Quartic scalar couplings A.1 Inelastic scattering A.2 Elastic scattering 3.3 Scalar spectrum 2.1 Matching with2.2 NMSSM at Higgsino dark matter 3.1 Dark matter 3.2 Vacuum stability and perturbativity in scenarios like split-supersymmetryrequired [ to be closetheories to [ the weak scale.remains the The same essential as roletypically long played expected as by that it the SUSY SUSY is in breaking broken superstring scale at in such any theories scale is below close to the the string string scale. scale. In fact, it is 1 Introduction If supersymmetry (SUSY)breaking does is not not stabilize restrictedtractive the to features electroweak stay of low in scale energy the then supersymmetry,and such vicinity particle the as of candidate(s) precision scale the gauge of coupling of weak weakly unification scale. interacting its dark Most matter of (DM), the could other also at- be achieved C Results for different values of top pole mass B Renormalization group equations 6 Summary A Constraints from the direct detection dark matter searches 4 Numerical analysis 5 Results and discussions 3 Phenomenological constraints Contents 1 Introduction 2 Framework JHEP01(2019)224 . We 1 ]. While ]. In this GeV. The 18 8 22 10 . GeV [ ]. The presence of 8 followed by the re- 18 4 10 . The effective theory is ˜ . S -parity in the underlying R . Some relevant technical details 6 ]), the breaking of SUSY and unified 13 – 4 – 2 – and summary in section ]. The mixing of Higgsinons with bino, wino and/or the 5 21 ]. An effective theory involving the THDM and a pair of Hig- 19 GeV because of the constraints arising from the stability of electroweak which is assumed close to the GUT scale. The assumed hierarchy among S 10 ]. The scale can be raised up to the GUT scale if SM is replaced by the M 17 – ] and it is shown compatible with the vacuum stability constraints [ 14 . The details of numerical analysis are described in section 3 20 , The paper is organized as follows. In the next section, we outline the effective frame- The pure Dirac Higgsino DM is already ruled out because of its large elastic scattering In the post Higgs discovery era, scenarios of high scale SUSY are constrained by the 18 are provided in three appendices. work and discuss itsdetails of matching various with phenomenological constraints NMSSMsection applicable at on the the underlying SUSYsults framework and in breaking discussion scale. in section We provide find that the Higgsino-singlino-Higgs Yukawa interaction canbetween induce the required neutral mass splitting components ofsame Higgsinos interaction if the also singlinoshown improves mass that scale the viable is Higgsino stability DMspectrum of consistent with with electroweak stable the or vacuum current experimental metastableframework significantly. observations of electroweak can vacuum GUT be and It scale obtained scalar within supersymmetry. is the GUT scale supersymmetry. We considerof Higgsinos an augmented effective by theory a consists singletmatched with fermion, of the namely THDM next-to-minimal the supersymmetric and singlino standard abreaking model scale pair (NMSSM) at the SUSY the different scales and corresponding mass scales of particles are depicted in figure radiative corrections from supersymmetric particles canof induce splitting neutral between the components masses of Higgsinosconstraints making can them be Majorana evaded. fermionsonly and if However, hence the the the above masspaper, required we scale amount discuss of of a the possibility mass in other splitting which supersymmetric is pseudo-Dirac Higgsino particles obtained DM is can be reconciled with vide a potentially viablesupersymmetric candidate theory. of However, DM the givenfrom second the an possibility DM unbroken is direct disfavoured detection by experiments. the null results cross section with nucleons [ stability can further bebelow improved the if GUT there scale existsgsinos [ strongly at the coupled weak rightin scale handed [ as neutrinos remnants ofthe GUT weak scale scale supersymmetry Higgsinos has improve also the been convergence studied of gauge couplings, they can also pro- that the standard model (SM)terpart cannot — be the matched minimal with supersymmetricscale its standard is simplest model above supersymmetric 10 (MSSM) coun- —vacuum if [ the SUSY breaking two-Higgs-doublet model (THDM) asadditional a Higgs low doublet energy helps effective in theory achieving [ a stable electroweak vacuum in this case. The higher spacetime dimensions (seegauge for symmetry example, are [ oftenbreaking administered of by SUSY a at common the mechanism GUT which scale. gives risemeasured to Higgs the mass and stability of the electroweak vacuum. For example, it is known Similarly, in a class of models based on supersymmetric grand unified theories (GUT) in JHEP01(2019)224 . 2 , ∗ 1 =1. (2.5) (2.2) (2.3) (2.4) (2.1) H 2 21  ) iσ 1 − H = = † 2 , 2 , 12 H c  1  . )( c H . j R 2 u H † 1  c 2 H ) + h ( H 2. The scalar potential 2 4 ij / u H λ Y † 2 indices and 2, respectively. = 1 H , + / L ) + . . )( c 1 1 Y i 2 2 . ˜ S − c H ! H . H − † 2 † ij 1 0 ˜ d − u d H ˜ ˜ ., H Y i ˜ H H L H . + h c (  . ± )( c . 7  1 2 and +

i L l,S ˜ d λ / ˜ S H 2 as SU(2) ˜ Q ˜ q, = + h † H , 1 L + h · d ˜ ˜ t S = 1 W, + H j R ,H,A,H 2 ) + ˜ u + ( d H e ˜ = 1 2 B, ˜ ˜ j R 3 Y H H ˜ H H  , † d ˜ g, H 1 λ  u 2 † , L 1 with hypercharge ˜ – 3 –  can be written as H H µ H α, β 2 + b b b bbb 2 H h , + ! ij t 2 12 1 e S H S 2 A )( 0 ˜ u ) + − µ M u Y 1 M ij H m M 2 d . ˜ ˜ h H , ˜ H H with Y + THDM H µ † 1 kin † 2 1 THDM L

− β + H L ) L H H ( 1 2 d ) represents free Lagrangian of a pair of fermions, namely = ( 6 ij = doublets with ˜ e = H H H 2 u λ 2 † ( Y 2 ˜ 2.1 ij λ L ˜ H 3 denote three generations of SM fermions and d L H α  , H ) + Y L 2 i L u 2 2 +  , 2 ˜ L ) H i L 2 m 2 ( ) Q 1 + = 1 H + αβ † 1 H  = 1 † 1 H i, j = Y ( H H have the same gauge quantum numbers as those of Higgsinos in the † 1 ( 5  2 1 d λ H −L 2 ˜ λ u,d  2 1 H ˜ · H , which are SU(2) m + + ] and their explicit forms are: d u ˜ . Schematic representation of hierarchy among the various mass scales in the framework. ˜ = H H 23  V The second term in eq. ( and u ˜ where The fields MSSM [ H and respectively. Here The first term denotes thecontains Lagrangian a pair of of the weak most doublet scalars and general Yukawa two-Higgs-doublet interactions model terms which in 2 Framework We consider an effective theoryrenormalizable below Lagrangian: the SUSY breaking scale described by the following Figure 1 JHEP01(2019)224 . 2 u , 2 S 1 ˜ H well M H (2.8) (2.9) (2.6) (2.7) S -parity  µ is chiral R S  ˆ b S . .. c . c and ) given . µ 2.6 + h +h symmetry under ]) and 3  ] d 2 S 23 ˜ , κ as real and positive. Z H 24 · 3 S 1 ˆ S κA b H 3 1 3 κ which lead to  is known to generate po- S + + ˜ and S : S 2 2 ] and therefore the coupling 4 ˜ M λ S ˆ y S S A 25 . S S & + 2 possesses a , 2 b ] for examples. µ i  λ S . L u , c + + . m ˜ 26 S H , S ˆ † 2 µ S = 0 (2.10) , S 24 c + h H c µ as its submultiplets. The corresponding . It is given as: κ  ˜ S + 2 , ) and ˜ A ˜ S S 1 S 2 S  ) + 3 d S µ d = H 2 y ( ˆ µ H H κ + h · · – 4 –  u = u − d ∼ O S ˆ . ˜ H S H H possesses a global U(1) symmetry under which S c · (  b M kin problem, see [ are assumed to be proportional to the corresponding 2 ˜ ˆ S H S = L µ H λ L λ c  and scalars soft = ˜ V + S ˜ ˜ ) or by the Majorana mass term in eq. ( λA S S 2  , L y are odd while all the other fields are even. Origin of this d 2.7 + + ˜ ˜ H S ), is the well-known NMSSM. We therefore match the effec- 2 MSSM  | and a complex scalar ) includes gauge invariant renormalizable Yukawa interactions , u u S W ˜ | ˜ 2.1 S ˜ H 2.1 H † and 2 S 1 = H m . We also assume  u,d W S + ˜ ˜ S H in eq. ( 1 M y is the standard MSSM superpotential (see for example [ L contains a Majorana mass term of the singlino = MSSM ˜ soft S ˜ S V L − MSSM ˜ H have equal and opposite charges. However, this symmetry is broken either by the = W d ˜ −L soft H In our setup, we assume The free Higgsino Lagrangian V needs to be suppressed. Typically, this is achieved by introducing a symmetry which S for brevity and consider the remainingA parameters phenomenologically consistent pseudo-Diracbelow Higgsino the DM scale requires both Yukawa couplings in thetentially superpotential. dangerous The quadratic divergences termc in linear supergravity in [ forbids such term.often In utilized the to most solve the popular so-called versions of the NMSSM, the same symmetry is soft SUSY breaking sector can be parametrized in terms of the following potential. The trilinear scalar couplings in parameters. The most general superpotential of NMSSM is given as [ where superfield with singlino 2.1 Matching with NMSSMA minimal at supersymmetric setup whichdescribed can by provide UV completiontive of theory an effective with theory, NMSSM at the SUSY breaking scale and obtain constraints on various remain uncharged under thisfermions symmetry. in As this a framework. result,which It the the can Higgsinos also fields become besymmetry pseudo-Dirac noticed in that the effectivein theory the can underlying be UV attributed supersymmetric to theory. the presence of unbroken and Yukawa interactions in eq. ( The last terminvolving in the eq. fermions ( Similarly, JHEP01(2019)224 , , ) 0. S λ , and and and 2.1 M S ) are term → u (2.12) (2.13) (2.11) µ µ D µ W , b 2.2 H µ symmetry µ, b = in eq. ( 2 2 Z L H in eq. ( still depend on and the from the theory 2 S m S , soft M V at  and arises from the i 2 S 1 S λ µ 12 µ m symmetry of λ m + , 2 A 2 λ , Z 2  The effective theory below A 2 S are found to be suppressed by a 1 S 2 S , S , b ˜ = 0 7 . Our assumption of real ). m b ˜ , m 6  4 , 12  , the resulting effective potential is ) using the identities y λ − 2 S 2.2 2 − S S 2 S  m S 1 b ˜ m = b 1 ˜ 2.2 2 S m ,  3 /M  µ S and − 2 S − µ and 2 S 5 b µ + 1 2 S λ 1 = 0 µ 2 λ . The parameters µ ), this implies 2 λ ˜  have vanishing values in the limit A 2 S are odd. The symmetry keeps the parameters m λ  ij S ]. The effective theory, therefore, does not give + respectively, while ) e A 2 ˜ 2 m i R – 5 – ˜ S 12 Y 2 λ u 2 S e µ 27 2 S 2.13 S µ λ , y − 2 m A b ˜ H = ˜ m
m λ + = ), ( 2 2 S 2 Y − ij and − u λ 2 ) that the precise values of g ˜ , respectively. Further suppression could be obtained ˜ 1 m y Y and − 1 and A i R S + (  2.12
7 d  d , 2 = = 2 2 2 2.11 , 6 2 Y S H g 1 λ ˜ g ij λ S µλ d y µ µ/M , the couplings ˜ , S 2 . After integrating out the singlet scalar + Y λ − 1 4 S d ˜ 2 2 A m 2 2 ˜ W H g 2 M g ' − ' and , 1 2 λ is physical mass of 7 2 1 & S 1 4 λ λ 2 S H ) leads to S under control and prevents them from taking large values through µ ). Further, the matching between the Yukawa interactions in = = ' ' − ' − /M m S 2.7 6 1 3 4 5 S + : 2.9 λ λ λ λ λ µ 2 S M S ), ( m M . This implies the following tree level matching conditions at the SUSY implies real values for couplings in eq. ( ∗ . One finds that d 2.3 q S S H ). With ˜ b 2 in eq. ( ≈ M iσ S 2.10 and − m . |  µ S MSSM λ It can be noticed from eq. ( b soft = Small imaginary values for these couplings can get induced through RGE because of the presence of CP , A M V terms of superpotential 1 | 1 λ CP conserving type II versionrise of to THDM low [ energy flavourtype-II or THDM. CP violating effects additional to those already anticipatedviolation in in the SM. However, this is not a new source of CP violation and therefore we neglect such effects. which vanish at renormalization group evolution (RGE)is effects. softly broken In by the theA effective terms theory, proportional the to obtained from the NMSSM with the aforementioned conditions, resembles the well-known the details of SUSYin breaking eq. sector ( despite offactor the of simplification at achieved least throughif ansatz Together with conditions in eqs.under ( which the fields at where ˜ generated by the soft massesin of those in eq. ( F and keeping only thematched with leading the order THDM termsH potential in given inbreaking eq. scale ( We then compute the complete scalar potential of the theory from JHEP01(2019)224 . 1 λ H (2.21) (2.17) (2.18) (2.20) (2.14) (2.16) (2.19) (2.15) are well S , M  . c . . +h   d S 2 ˜ H v · µ µ 2 .  H ) , S O , µ , .  ( +    u 2 2 2 2 2  = 246 GeV. Identifying linear ., ˜ 2 0 2 v v y H 4 π c v = 0. Further integrating out the S ˜ χ † v . 1 ) 2 2 1 µ c c 2 1 4 S 2 , S ' S S H v d v 3 ≡ µ µ 1 , m ! µ µ  + + + h ( 2 y c N 0 1 4 4 2 1 2 0 0 d u 2 2 + 1 1 ˜ S θ χ y v d − v v ˜ ˜ µ N H H µ m 1 1 + c c − N + 

are real and positive for real values of 2 1 ) = . 2 ) with v † M 2 S − + N  with 2 , : d v 1 µ S U T 2 2 p 1 ( S c 2.7 ˜ µ , v v 2 2 S S H 2 S µ – 6 – N · 1 1 v = d v µ µ µ ), 2 2 1 2 ! 2 2 2 ), ( c , d = Diag ! d v d v and + H ) N N = − 0 1 0 2  S θ 2.6 µ θ 2.15 N T ˜ ˜ − − χ χ µ S
− U 2 ( µ µ 2 µ

c ), ( 2 sin i cos ), ( mass N 2 N , the mass term for neutral components can be written as    y i √ i ' ' such that T / 2.4 + M i 0 1 0 2 =  N 2 2 ˜ ˜ χ χ , − L 2.12 0 T N u θ N ) = , v 0 1  N θ ˜ . m m 0 S u U χ H µ ˜ , M sin H ( u,d 0 d † cos i 1 as ˜ ˜ − ˜ c H H 0 H u i ≡ 

i ˜  H S H = , = 1 h 0 d µ c 2 ˜ N are vacuum expectation values (VEVs) of the neutral components of N H  U 2 v + ˜ H : L 0 2 and ˜ χ such that = 1 . v 2 ˜ eff H < m H In the basis, L is given by 0 1 ˜ χ S As it can beThe seen unitary matrix from representing eqs. neutralino ( mixing is m and one obtains the following expressions for the tree level neutralino masses with a convention where and combinations of with The electroweak symmetry breakingcharged then components contributes of into the masses for the neutral and µ with the following matching conditions at One of the main aimsdark of this matter. study is toemphasized, We show the the therefore existence Higgsinos of discuss and viable theirdescribed the pseudo-Dirac interactions Higgsino by Higgsino in the the terms mass effective insinglino theory spectrum eqs. below from ( in the detail. low energy As spectrum, the already effective Higgsino Lagrangian at scale below 2.2 Higgsino dark matter JHEP01(2019)224 ), Z = ≈ + rad  2.20 (2.22) (2.23) (2.24) χ in this m 1 TeV in µ ) remains ≈  µ 2.24 S ]. Nevertheless, µ 21 , rad  ]. The resulting mass can be paired to form ., m 28 c 0 2 . χ + ∆ . + h boson, the elastic scattering 1 TeV, one obtains ∆ 2 2 2 2 + and ˜ Z v v ˜ ≈ χ 0 1 2 2 + c c χ µ S S ˜ χ µ µ + +  2 4 2 2 1 ˜ 1 χ v v m 1 1 c c = . + = = 0 then ˜ ] including the non-perturbative Sommerfeld c . 0 1 2 0 ˜ χ v 30 S ) can proceed through the exchange of the 1 m – µ – 7 – m + h is almost pure Higgsino like for N 2 28 d v − − 0 1 d can be combined to form a Dirac fermion ˜ + χ 0 2 ˜ H = ˜ χ ˜ χ + 0 1 u u,d m ˜ , we expect that the same result holds in THDM. χ ˜ ˜ H has vector coupling with H → m ≡ µ χ A.2 0 − N = m  + ˜ χ ∆ . As ˜ χ m mass C χ ]. The contribution from the first two terms in eq. ( ≡ 28 − L  m . ∆ is mass of chargino at the tree level. As it can be seen from eq. ( (such as ˜ λ with mass term µ is radiatively induced mass splitting. For T N if the mass of DM particle is close to 1 TeV. This implies also  = † 2 ) rad   − ) as discussed in appendix d ˜ χ m S ˜ H m ( v/µ , ( Experiments based on the direct detection of DM are known to put stringent con- The charged components of This result is obtained for the SM. Since the coupling of DM with new scalars of THDM is suppressed + u O 2 ˜ H boson. The scattering cross section,Higgsinos, which turns is out unambiguously determined too for large aof and given any therefore mass statistically this of significant case signal is in disfavoured the by the direct non-observation detection experiments [ by the present framework. straints on pure Diraca Higgsino Dirac DM. fermion, namely Ifwith ∆ ˜ nucleon The nature of theframework. lightest Assuming neutralino that ˜ itverse, its makes relic all abundance is of estimated thecorrections in [ to DM DM produced annihilation cross thermally sections.is in It obtained the is Early found that Uni- the observed relic abundance 3 Phenomenological constraints We now discuss thescribed set in of the constraints previous which section. are imposed3.1 on the effective Dark framework matter de- where ∆ 341 MeV at one looppositive [ for real chargino and neutralino. In addition,electroweak bosons it make is the known chargino that heaviersplitting loop than between the corrections the neutralino induced chargino [ by and the the SM lightest neutralino can be written as where the contributions induced by dim-5 operators generates splitting between the masses of  Further, it is convenient to define the splitting between the masses of neutralinos as JHEP01(2019)224 0 ≤ → m (3.1) N ) and + 200 keV. 0 1 2.20 χ > 0 m ] on anti-protons ]. Higgsino mass 37 31 , . Using eq. ( are Majorana fermions 22 S ]. The constraints from 0 2 µ GeV for ∆ χ 8 . We find that the present 34 , 10 is very small. Such processes . and ˜ 33 0 . A.1 . 0 0 1 m χ m GeV 8 boson. ] exclude Higgsino DM with mass while those of the latter are negligible , if ∆ 10 2 , Z µ 35 , is still subject to the constraints from 0 1 . χ N ) determine the values of quartic couplings  at loop level, which subsequently leads to 2 1 v + S 2 0 0 2 boson. Considering this, a lower limit on ∆ µ 2.11 c – 8 – Zγ ˜ χ m Z 0. In this case, ˜ , + 2 2 → > 2 ∆ γγ v 500 GeV. Nevertheless, the almost pure Higgsino DM 0 1 , N c ≥ m 0 1 + ≈ ZZ ˜ χ 0 1 S m χ µ ] observations do not put any such limit. The strongest indirect ] using the then available data from XENON 10 and XENON 200 keV, at 90% confidence level. In the present framework, this GeV, can induce the required ∆ 36 8 22 ≥ 10 0 . m (1) numbers, we find . S O µ at tree level and 1 TeV considered in our framework remains unconstrained from the current boson, respectively. We find that the scattering cross sections of the first as A.2 ]. This however also requires the stop masses − ≈ i Z c 32 W , can also occur in the underlying framework through the exchange of THDM + N W The Higgsino DM can give rise to indirect signatures through their pair annihilation The spin-independent and spin-dependent elastic scattering processes, like ˜ The inelastic scattering, ˜ + 0 1 ˜ indirect detection experiments. 3.2 Vacuum stability andThe perturbativity matching conditions obtainedin in eq. terms ( of the gauge couplings and several of NMSSM parameters. With the assumed the observations of330 gamma-ray GeV by while HESS Fermi-LAT [ [ search constraints on Higgsino DM arisewhich from put the a latest conservative AMS-02 limit results [ with mass results are in agreementin with appendix the current experimental limits. This isinto described in detail the production of gammaHiggsino rays DM and from anti-protons. the indirect The searches latest are constraints reviewed on in almost [ pure χ scalars or type of interactions arebecause suppressed of due pseudo-Dirac to nature ofscalar Higgsino spectrum and DM. couplings, After we determining estimate these the cross constraints sections on and the show that the obtained splitting can also benonzero induced [ radiatively through stop-top loopIn our if framework, the all stop thesinglino, mixing super-partners with angle can is have GUT scale masses while the presence of A similar bound on gauginoof mass scale Higgsino was with obtained earlier bino in or the case wino in was which responsible the mixing for mass splitting [ 100 experiments. Wefrom update XENON this 1T. analysisobservations The for from details the the are latest direct describedmass available detection in splitting, data, experiments appendix ∆ including lead those bound to translates a into lower an boundassuming upper on limit neutralino on the singlino mass scale and hence they do not have vector coupling with the direct detection experimentsarise for through Majorana the ˜ t-channel exchangehas of been derived in [ this constraint can be evaded if ∆ JHEP01(2019)224 t ). M (3.3) (3.2) 2.11 ) may 2.2 ]. Hence, it is absent (for 19 are suppressed , down to the 4 7 , 18 λ 6 [ S ). Note that with λ , 2 M . λ  1 B 2.11 λ ] and ). The requirement of Q 5 GeV √ 18 3.2 λ with appropriately chosen  S 10 |  82 . 3 as can be seen from eq. ( M 2 λ 4 | symmetry of the effective theory ) with [ λ ) are found to be satisfied as a 2 , , , . dominantly decides the stability of Z 1 + log 3.2 0 0 0 0 3.2 . 4 λ > > > > 41 1 2 2 2 − , the couplings λ λ λ λ , for the absolute stability of electroweak 1 1 S t & λ λ M M
p p 2 ∼ λ – 9 – + + 1 in the scalar potential remain negligible at all the ) which determine the stability or metastability of S and λ 2 3 3 are positive while 7 , ˜ ), respectively. They are even more suppressed if λ λ λ m 6 √ 2 S 3.3 1 , , S 5 1 λ ] including the quantum effects. This was generalized + + M  λ λ 4 √ 3 39 S λ can be made positive at λ µ/M ( 4 + 2 + λ O 2 ) or eq. ( 4 λ µ < µ λ . Further, the approximate 3.2 + 2 S 2 ] in which the running of 1 λ ) and M λ 1 S 19 λ , ), the contribution from singlino-Higgsino loop modifies the running ≈ , the couplings S . Secondly, even if the tree level enhancement in √ /M 18 S S λ 4 b S M A M µ . The remaining quartic couplings must satisfy the following conditions, ( ≈ S ∼ O λ M S and A ] ˜ m and/or λ is the renormalization scale. 38 S  Q M S and drives its value toward the positive side while running from ] for THDM scalar potential after mapping the underlying potential into single filed The first three of the conditions listed in eq. ( In a more conservative approach, it is assumed that the scalar potential in eq. ( 4  18 λ λ Unlike in the casevalues of of MSSM, example, if of as it can be seen from appropriate RG equations given in appendix µ < µ is the last condition in eq.scalar ( potential, respectively. The sameat has the been the GUT case scale forvacuum. [ THDM matched However, with two MSSM importantmatching differences with arise NMSSM in modifies boundary the condition present for framework. Firstly, the where consequence of the high scale boundary conditions given in eq. ( potential using the firstmetastable vacuum three replaces of the last the condition conditions in given eq. ( in eq. ( through quantum tunnelling. However, the lifetimegreater of than electroweak the vacuum current is age requiredSuch of to the a be Universe minimum in of ordersingle to potential scalar make is it field, termed phenomenologically is viable. as estimatedin metastable in [ vacuum [ and its lifetime, in case of have multiple minima and the electroweak vacuum can decay into a more stable minimum at the intermediate scalesvacuum between [ by factors of A forbids them from taking large valuesof through the running terms effects. involving the Therefore, couplings scales the contributions below hierarchies in the scales, i.e. JHEP01(2019)224 , 2 ]. ]. ), A H 19 42 H M (3.4) , , thus 3 GeV h H and  1 M bosons are H is identified Z h and A ] which is briefly . For a consistent and M 19 h  ) and charged Higgs H W M ). At the minimum, the . The state in THDM of type II. 2 A β with at 95% confidence level [ . Their expressions are given i α H h , γ λ . This replacement allows us to break the electroweak symmetry + 1 . The physical CP even neutral i 2 and that of the observed Higgs, we s λ /v + cos and . ] is considered. In order to account H h 2 , using the method described in [ 1 v → 3) GeV v h 40 b , , and  ≡ M and β α H v β 1 055 . sin H represents the physical mass of pseudo-scalar 0 580 GeV , tan − A = (125 ≥ A – 10 – translates into lower limits on . This, through the results of the latest global | ≤ M = h  is assumed to be heavier than ) M  ) can be replaced by appropriate functions of h α H M H ZZ H M − 2.2 M β and → ). The quoted lower bound on the mass of charged Higgs ]. Here, 2 h ) and a CP odd and neutral ( 3.4 cos( 38  | in eq. ( α H H and ) and therefore they are constrained from the observed signal 12 α − m + sin and known parameters − W 1 and the masses of heavy CP even Higgs ( + β β ], implies that the deviation from the so-called alignment limit, i.e. ( and 2 α W α H 2 41 m , tan → . , A 1 α h = cos M m 2, cannot be greater than 0.055 in the case of THDM of type II which gives rise H MS renormalization scheme while tan π/ and quartic couplings [ , the experimentally measured value from [ h v ) are also determined in terms of = ] with all the necessary details. ,  Since the masses of different scalars are correlated in the framework under considera- We consider the following set of constraints on the masses of Higgs bosons and the The VEVs of the neutral components of M α β 19 H − M boson arises form theNote observed that branching this ratio bound of is applicable for almost alltion, we values find of that tan themaking lower limit all these on scalars heavier than 580 GeV. Such heavy scalars already satisfy the direct from the measured meanproportional value. to Further, sin thestrengths couplings of of fit performed in [ β to the second constraint in eq. ( For for theoretical uncertainties in estimating the Higgs mass, we allow a deviation of in [ mixing angle with the observed SM likematching Higgs between the and theoretically predictedcovert mass the of running massThe into pole mixing mass, angle namely ( tan Higgs in express the masses of CPparameters even neutral and chargedHiggs Higgs bosons bosons can in be terms obtainedsuch of as that the linear unknown combinations of neutral components in outlined in the following. giving rise to fivetwo CP physical even Higgs and bosons:parameters charged two ( CP even and electrically neutral ( The matching of thequartic effective couplings theory which in withscalars. turn the In provides NMSSM order useful to determines correlations checkof the among the these viability values the scalars of of and masses such impose of all correlations,eters various of we THDM the experimental the evaluate constraints the potential. on mass We the spectrum closely remaining follow free the procedure param- and notations of [ 3.3 Scalar spectrum JHEP01(2019)224 ] ] ]. 44 41 are 20 t M , see [ using the − 0.104 GeV 1.759 GeV 0.499 MeV S µ + M µ e τ µ → ]. However, such m m m s MS scheme. See for should be corrected B 580 GeV, the masses 46 i , Parameter Value λ ≥ 20 , we use the latest PDG A t M 1 GeV in M . ]. With this choice of SUSY 11 2.72 GeV 2.58 MeV ]. 52.75 MeV = 173 ]. For t 43 , 19 M ], we first evolve the gauge and Yukawa 19 b s d 19 m m m Parameter Value . The values of Yukawa couplings at , the one loop threshold corrections in Yukawa 1 – 11 – S M ). The tree level matching of and vanishing trilinear parameters. Although such a  ]. The obtained values of gauge couplings and fermion 2.11 S µ ]. 0.61 GeV 1.21 MeV 163.35 GeV 19 M 45 remain approximately degenerate in this framework. It is from the experimental values of gauge couplings and fermion as it can be seen from the relevant expressions given in [ ∼ and hence they are negligible in the present framework. . We obtain the values of gauge and Yukawa couplings at the t  S 2 t c u B M ) H using one loop RGE equations as the quartic couplings do not con- S m m m are listed in table 9 GeV [ ]. . S µ/M t 0 19 Parameter Value and M M µ/M  to A 1 . t , M H 1.1631 0.46315 0.65403 = 173 t M . The SM parameters at renormalization scale 1 2 3 g g g Following a similar procedure as described in [ Parameter Value spectrum and from thecouplings fact are that found to beor suppressed by by the the smallness degeneracy in of The the threshold masses corrections of in the quarticlinear superpartners couplings couplings are or also ( suppressed by either vanishing tri- by one loop thresholdcorrections depend corrections on which the aredetails exact of explicitly details SUSY given of breaking. in the Forto simplicity, SUSY [ we be spectrum assume degenerate all and the with hencechoice squarks, mass require of sleptons explicit and SUSY gauginos spectrumbreaking is based very on specific, flux it compactification, is see naturally for realized example in [ the models of SUSY average couplings from tribute in their running atmatching this level. conditions given We then in obtain eq. the ( quartic couplings at top quark pole mass scale masses measured at thedescribed in different our scales. previousmasses work The at [ procedure the scale ofextracted this from with the fermion relevant details masses as is described in [ The viability of the proposedin framework the with previous respect section, is toimplementing investigated the by 1-loop various solving corrected constraints, two-loop discussed matching RGE conditions. equationsfor numerically the The and underlying one and frameworkand two are loop are generated beta listed using in functions publicly appendix available package SARAH [ imposed by the electroweak precision observables [ 4 Numerical analysis search bounds and limits arisingfor from example the and flavour observables references suchof therein. as the We scalars also observefound that that such for a heavy and degenerate spectrum of scalars always satisfies the constraints Table 1 details, appendix C of [ JHEP01(2019)224 . ) ). ), 0 2. 3) . . 1 m . In 3.3 (5.1) (4.1) 2.14 S 2.15 . M 03 (0 β . 0 , ).  ≥ 2 2 GeV and two g λ 6 14 2.17 ) and eq. ( − 10 1 and tan 3.2 using the obtained 2 Y × & g β 3 λ GeV as well. Once the in eq. ( − = 2 using full two loop RGE 16 µ 3 S S λ 10 µ M × , we perform this analysis for and tan as described in the above, all + 2 4 200 keV, implies , λ A S  , for e  = 2 > M M λ 2 Y 2 for two example values of , † S 0 g e 3 3 Y at the scale m M  using the conditions given in eq. (  and 0 − . The results of the numerical analysis iteratively until the couplings converge d . From the obtained results, we find an d 2 β 1 t m β β and v λ M ∆ 2 and and  + 2 Tr i + 2 i , c c GeV, for a viable pseudo-Dirac Higgsino DM   72 d – 12 –  e . 8 and tan 2 2 2 Y Y ). In this case, the perturbativity constraint alone † g † 10 d e A 3 ≈ Y Y 3.1 . The stability and metastability of the potential is M   ≤ − 2 t S λ 2 µ and back to S M λ µ . We also evolve the effective operators given in eq. ( S t arising from the vacuum stability, perturbativity and neu- M + 2 + 6 Tr + 2 Tr λ M    to u u d using appropriate two loop RGE equations. All these couplings ] in the context of neutrinos. The neutralino mass spectrum is t Y Y Y t and † † † u u d M 48 M β Y Y Y , ). We have derived the above equations following a procedure similar are found, we select some benchmark points and evaluate the low as function of input parameters . We repeat all these cases for    Q 47 to λ S α , simultaneously checking their viability to produce large enough ∆ S S M (ln ) GeV for all the values of tan 6 Tr 6 Tr 6 Tr µ , we obtain the coefficients µ 7    = S = 1 TeV, as required by the observed DM abundance, and evaluate the 2 2 2 µ λ using the one loop beta functions: (10 2 1 π π π dX/d d µ A c c 5 µ 16 16 16 = has direct implication to the boundary value of to = = = λ X = 10 S 2 1 β d A c c µ β S β β We set After obtaining the values of quartic couplings at µ = 0 and λ which is a direct consequenceimplies of a eq. ( robustwithin upper this bound, framework. tralino mass difference areall displayed these in cases, figures the perturbativityThe of latter the leads effective to theorythat non-perturbative disfavours the values bound for from thefor direct top detection quark experiment, Yukawa ∆ coupling.approximate relation: We find are discussed in the next section. 5 Results and discussions The constraints on tan sample values of Since A consistent values of energy spectrum and constraints on where to the one giventhen in obtained [ by substituting the values of vacuum stability constraints on the values of tan to their input valueschecked supplied at at the intermediaterespectively. scales After using the convergence the isHiggs conditions achieved, mixing we given angle calculate in thevalues eq. masses of of ( quartic scalars couplings at andfrom the the gauge, Yukawa and quarticequations. couplings are At evolved down to After integrating out theare singlino evolved at from this scale,are the again gauge, evolved from Yukawa and quartic couplings JHEP01(2019)224 , , 1 λ . 8] . 0 A 1 3.2 , 1 ≥ . and [1 λ S ∈ if µ β β . For example, 3 ]. This conclusion is directly modifies the and λ 2 19 , as it can be seen from the 18 = 0, λ λ A GeV. The region shaded in grey is GeV. As discussed in section 14 plane for different values of 14 10 λ 10 - × β × = 2 = 2 S S – 13 – M M ) and S 1 GeV and M . = λ = 173 A = 200 keV (solid), 2 MeV (dashed) and 20 MeV (dot-dashed). t 0 m M = 0 ( λ A = 1 TeV, . The regions corresponding to absolute stability (unshaded), metastability (green) and µ 3) for enhances the stability of potential in two ways. For . 0 λ The presence of Higgsino-singlino-Higgs Yukawa interaction also has interesting impli- ≥ λ changed in the present frameworkstability, metastability for and large instability enough contoursthe values displayed of in electroweak figures vacuum remains( stable or metastablelarge for all values of tan cations on the stabilityTHDM of matched the with electroweak MSSM vacuum.is at allowed the It by GUT is the scale, known absolute only stability that of a in the narrow the electroweak range case vacuum in [ of tan pure Figure 2 instability (orange) of theand electroweak vacuum for in tan disfavoured by the non-perturbativity oflines at correspond least to one or ∆ more couplings. The vertical black contour JHEP01(2019)224 is S ), on M 3.4 . However, the S M ≈ and obtain the scalar GeV. λ 2 16 A 10 × = 0. We find that change in . The results are displayed in λ in order to achieve metastabil- β = 2 A λ S M 2, and hence rescues the electroweak = 0 is disfavoured by the low energy / 2 2 λ and tan A > g A 2 but for λ M 2 5 for . – 14 – 0 is still able to improve the stability of the vacuum. ≥ 4 λ λ GeV, has negligible effects on the results of vacuum stability. 8 . Same as in figure -10 5 200 keV, from each of the panels in figure , making it positive for , it can also be observed that the instability regions grow when ≥ 4 λ 3 0 Figure 3 in the running of as function of parameters m λ t . As it can be seen, and M 5 2 and 4 We now discuss the consequences of the low energy constraints, listed in eq. ( , within the range 10 S , allowed by ∆ the parameters of theλ underlying framework. For this,spectrum we select at two benchmarkfigures values of contribution of This indirect effect requiresity or relatively absolute larger stability valuesµ in of comparison to theFrom figures case with increased because of the relatively longer running. boundary value of vacuum from instability. This direct effect becomes feeble if JHEP01(2019)224 3 ≤ and GeV, β β 14 2000 2000 GeV GeV 10 400 GeV. 14 14 × < A = 2 =2×10 =2×10 M S S 1500 1500 S ,M ,M M S S 1 or =M =M λ λ [GeV] [GeV] A A GeV, 055, respectively. . β < 1000 1000 M M 5 0 GeV,A GeV,A . 5 5 | = 10 ) α =10 =10 S S S µ − 500 500 , there is no such restrictions on the β S , as it can be seen from the lower left | )

M cos( λ=0.5,μ λ=0.1,μ

1 1 6 5 4 3 2 6 5 4 3 2

| α β β tan tan = − = 1 TeV, λ β requires either tan µ A results into relatively heavier SM like Higgs h λ – 15 – cos( M | 2000 2000 1 GeV, GeV GeV . 580 GeV and 14 14 , the observed Higgs mass typically requires tan & . The grey region is disfavoured by perturbativity while the 5  λ = 173 H A =2×10 =2×10 t 1500 1500 S S M and M and 4 =0,M =0,M = 125 GeV (solid black), 122 GeV (dotted black) and 128 GeV (dashed λ λ λ . For the cases with h [GeV] [GeV] 5 A A M 1000 1000 M M GeV,A GeV,A plane for and 5 5 A 4 =10 =10 ]. The observed range in M S S - β 19 500 500 [ and it is always possible to obtain 125 GeV Higgs for some values of tan 4 λ . Contours of λ λ=0.5,μ λ=0.1,μ

2 1 5 4 3 2 1 6 5 4 3 6

as well as by the upper bound on β β tan tan which are allowed by stable/metastable vacuum and other low energy constraints. As  H A panels in figures values of M it can be seenin from all figures the viable cases. constraints. In thisthrough case, large valueThe first of is ruled outM by perturbativity while the later is disfavoured by the lower bound on Figure 4 black) on tan and for different valuesunshaded, of green and orange regions correspondelectroweak vacuum, to respectively. absolute The stability, metastability region andis on instability the disfavoured of left by side the of constraint the dashed and dotted red contours JHEP01(2019)224 2 GeV . 2000 2000 GeV GeV 14 14 = 172 t =2×10 =2×10 M S S 1500 1500 ]. In the absence ,M ,M S S 55 for – =M =M from the mean value, 5 λ λ [GeV] [GeV] 49 σ ]. Therefore, the present A A , GeV. 1000 1000 M M 7 and 56 34 , GeV,A GeV,A , 4 7 7 . 22 22 = 10 and +1 =10 =10 S C S S µ 500 500 1 GeV, in our analysis so far. The σ . 1 −

λ=0.5,μ λ=0.3,μ

1 1 6 5 4 3 2 6 5 4 3 2

300 MeV [ β β tan tan = 173 but for t & 4 ]. The decay of chargino into neutralino and M  . In order to quantify these effects, we repeat 52 t , m – 16 – M 50 2000 2000 GeV GeV 14 14 5 GeV [ < =2×10 =2×10 1500 1500 S S . Same as in figure 0 m =0,M =0,M λ λ [GeV] [GeV] A A 1000 1000 M M Figure 5 GeV,A GeV,A 7 7 =10 =10 S S 500 500 λ=0.5,μ λ=0.3,μ

2 1 5 4 3 2 1 6 5 4 3 6

β β tan tan The discovery prospects of light Higgsinos at colliders, with the other SUSY particles We have used the top quark pole mass, , are sensitive to the precise value of h of coloured superpartners, the Higgsinostherefore their are production produced rate through is relatively onlyto smaller. weak be Further, interactions highly the and collider insensitive searches if are ∆ charged known pion is also difficultframework seems to to detect remain if unconstrained ∆ from the current collider searches of Higgsinos. our analysis corresponding toand the results 174 GeV displayed in whichrespectively. figures are The top obtained results quark are pole shown in masses appendix at much heavier, have been widely studied, see for example [ results, in particular, the constraintM arising from the stability of vacuum and prediction for JHEP01(2019)224 ]. C 556 60 . ]. A (5.2) ]. All 57 19 and SU(3) ). Therefore 528 and 0 L . 5.2 0 , R ≈ 005 . 0  716 . = 0 -parity. The Higgsino-singlino-Higgs S R W θ to evade the direct detection constraints. α/α 2 0 − ]. The future electron-proton colliders may m sin or below. This may change the derived results 1) eV. Such an almost pure Dirac-like Higgsino W 49 − . – 17 – S θ 8 2 (0 M / 3 ) GeV which is one or two orders of magnitude lower sin ] for more details). One obtains ≈ O 14 5 8 59 0 = (10 m 3 2 O b b − − -parity is unbroken, the lightest of the neutral components of 2 1 1 TeV. However, in the absence of any other new physics below ] b b R ∼ 59 , 673, bringing it closer to the value as required in eq. ( 3 are effective beta function coefficients of U(1), SU(2) . , R ≡ 58 2 , = 0 R = 1 i for i b The problem can be circumvented minimally by introducing a gauge singlet Majorana Although the underlying framework is shown to accommodate TeV scale pseudo-Dirac DM is already disfavoured by the direct detection experiments. fermion, namely the singlino,Yukawa interaction which gives rise is to odd thetry under Higgsino-singlino breaking, mixing which through induces electroweak symme- large enough ∆ rise to an effectivea theory pair which of contains Higgsinos.Higgsinos the can SM If be with dark anachieved if matter additional its candidate. Higgs mass doubletthe is The and GUT observed scale, thermal the relic neutralmass components abundance splitting of between can Higgsinos them, be are ∆ almost degenerate with very tiny to obtain a precise limit on the parameters of6 the underlying framework. Summary There exists a class of models in which supersymmetry is broken at the GUT scale giving lifetime require new effects atdepending the on scale the exactnism nature is of invoked these for newmay non-vanishing effects. also neutrino Further, modify masses if then thethese the the vacuum cases type-I presence stability require seesaw of constraints dedicated mecha- singlet if analysis neutrinos similar they to are the strongly one coupled presented [ in this paper in order gsinos lead to it improves the convergence offication the gauge turns couplings out significantly. to However, bethan the what of scale is the of naively uni- expected fromIn the this latest case, experimental achieving limit the on precise the unification proton lifetime and/or [ satisfying constraints from the proton where gauge couplings, respectively (see [ for the SM and THDM, respectively. The THDM together with a pair of weak scale Hig- Higgsino DM consistent with GUTOne scale of SUSY the breaking, pertinent itto is issues precision not with unification complete the of inone-loop, GUT the all requires SM aspects. scale [ gauge SUSY couplings. breaking is The that convergence of it the does couplings, not at lead sufficient centre-of-mass energywith through a tagging of pairalso the of provide photon neutralinos a produced or potentialdedicated platform charginos in analysis for [ association in the these searches directions,obtained of for in almost-degenerate the the Higgsinos ranges underlying of [ framework, would masses be and useful. couplings of Higgsinos It is more feasible to probe almost-degenerate Higgsinos at future lepton colliders with JHEP01(2019)224 is esc for v T S (A.1) is the N M and σ ) in our , i.e. the v ( esc f min v v ] using Maxwellian 65 in addition to (1) Higgsino-singlino-Higgs , ] v O 3 obs is the local DM density in our d 65 v 3 ) v v ( . This interaction can be recorded f . T m ) is estimated in [ obs max v v min v 3] and with A.1 3 GeV/cm Z , . 2 . σ χ [1 = 0 of mass ρ – 18 – ∈ χ 2 T T ρ X µ β , streaming with velocity distribution m χ χ T (1) Yukawa coupling between Higgsino, singlino and m m N 2 3 in almost all the cases discussed in this paper. It is O , of the nucleus in the direct detection experiments, such R ) is the reduced mass of the nucleus-DM system, = ] for estimation of & E T R 65 β 1 TeV, tan m dR of mass dE ≈ + χ µ χ GeV. The allowed by perturbativity constraints. However, the observed Higgs m ( 8 / β T 10 ] GeV, m 7 . χ 10 S m is the minimum velocity of DM that can trigger a nuclear recoil of energy , µ 5 takes into account for the relative motion between the earth and the rest frame is the maximum velocity of DM in the galaxy which is equal to = min ]. The differential rate of such events is given by [ [10 v T obs ∈ µ 64 v max – v S We find that viable pseudo-Dirac Higgsino DM puts an upper bound on the singlino µ 61 . R scattering cross section of DMparticle particle physics with framework. nucleus which The is integraldistribution determined in for by eq. velocities. the ( underlying The obtainedwhere result depends on of DM. We use the result of [ where number of target nuclei ingalaxy. the detector, E minimum velocity required for DM particle in order to escape from the galaxy. galaxy can interact withby target observing nucleus the recoil energy, as [ A Constraints from theA.1 direct detection dark Inelastic matter scattering searches A dark matter particle Acknowledgments This work is supportedresearch grant by under Early INSPIRE Career Faculty AwardDepartment Research (DST/INSPIRE/04/2015/000508) of from Award Science the (ECR/2017/000353) and Technology, and Government of by India. a shown that the viable pseudo-Diracconstraints, Higgsino can DM, be consistent obtained with within otherfor the phenomenological underlying framework of GUTYukawa scale coupling. superymmetry mass scale, Higgs makes the electroweakall vacuum the metastable values or of tan stablemass together at with all constraints the onplings scale the strongly charged up disfavour Higgs to tan mass and Higgs to gauge boson cou- vacuum. In orderwhich to minimally quantify accommodates these the effects,between singlino effective we with theory match parameters MSSM. and the We thoseysis effective of derive with NMSSM matching theory and one conditions with perform loop two NMSSM with loop threshold RGE respect corrections anal- to in the order various to phenomenological check constraints. the viability of effective theory We show that the same Yukawa interaction also improves the stability of the electroweak JHEP01(2019)224 2 , is 1 0 0 can χ , are (A.4) (A.5) (A.2) (A.3) 0 1 0 m χ m ) is the is Fermi ], Xenon R F 62 ) for given E . If ∆ ( G ) and kinetic X and ∆ F A.5 . is given by 0 1 , the minimum + ˜ χ 2.18 R 0 2 X ), ( , m ˜ χ E q , 2 + d, s, b µ ) A.3 → χ R ). In this case ˜ qγ = E 0 1 ( X q ), ( ˜ → is then given by χ F 2.22 µ , + R γ 2 X 0 1 A.1 0 2   E χ ˜ p 0 ). Using eq. ( χ . ], and Xenon 1T with 278.8 live + 3) for ) N m / χ 63  ) 1 W 2.14 1 for pseudo-Dirac Higgsinos in our R θ W − 2 θ + ∆ E bosons as the couplings between ˜ T ≈ 2 µ T 2 ( R θ Z sin / m E q T using eqs. ( 1 ) is replaced by inelastic cross section, µ T Q  4 sin − 2 as given by eq. ( R m R ), see eq. ( − A.1 0 − S E  boson: ]. The values of parameters, 1 TeV, the number of events estimated using q and (1 m 3 T R – 19 – 1 T Z 64 ( − v/µ m E ∼ ( 2 2 n F T χ O 1 in eq. ( √ G N √ u, c, t m  m θ 2 σ = = 2 T √ ). In the framework under consideration, the dominant q µ π X sin 2 min = 2 F 8 ), one obtain the following effective interaction between the i v G + − 0 2 min = ˜ v 2.14 3) for . The results are then compared with the data collected by the = χ / R arises from the exchange of E → 2 (2 with mass difference ∆ / X Inelastic Inelastic 0 2 σ + Inelastic L is weak mixing angle. We have sin 2 χ σ 0 1 ) is number of neutrons (protons) in a given nucleus and W ) is 1 χ p that can give rise to nuclear recoil with energy θ q (˜ N and ˜ σ Q ( ]. ( 0 1 min ≡ n 66 v q χ 3 N T is a pure Higgsino DM with and quarks after integrating out the We estimate the total number of events In the case of pseudo-Dirac Higgsinos discussed in the paper, we have Majorana neu- In the case of elastic scattering with a nucleus, i.e. 2 χ , 0 1 Inelastic ˜ range of recoil energy experiments: Xenon 10 with 58.6100 with live 224.6 days live of days of data datadays and and of a a data target target with mass mass target of of mass 34 kg 5.4 of [ 1300 Kg Kg [ [ where nuclear form factor whichnucleus parametrizes [ the distributions of protons and neutrons in the constant and framework. The effective spin-independentand inelastic proton cross section or between neutronusing the the are neutralinos above estimated results. byneutralinos summing and This nucleus gives over the the following valance result quark for contributions the cross section between the χ where and the scatteringσ cross section contribution to and THDM scalars are suppressedterm by of Higgsinos in eq. ( small enough, the nuclear recoilvalue can of also be observed in direct detection experiments. The the above formulae turnsexperiments such out as to Xenon 10DM be and is much Xenon disfavoured. 100. larger Therefore, than the the case total of puretralinos observed Dirac events ˜ Higgsino in the scatter inelastically off the nucleus giving rise to a process: ˜ velocity of DM particle required to produce nuclear recoil with energy If JHEP01(2019)224 (A.6) 1 TeV in order , ≈ 0 1 0 1 ˜ χ ˜ χ , 0 1 ˜ ) χ m . β ) ) β H + H α + 2000 g α + cos( h sin( d 200 keV for h d g + ≥ ( 1000 + β 0 S β µ v m sin 2 sin α + 500 [GeV] α µ 0 1 cos = 650 km/sec while the lower black lines are for ∼ χ Z sin . 2 0 1 m . The regions below solid, dashed and dotted lines c – 20 – 0 1 ˜ 2 χ esc ˜ χ c 5 v + γ m + µ β γ β 200 0 1 , cos ˜ χ 2 2 cos θ α g α + for given sin 2 Y 0 cos 2 1 100 cos g ) gives rise to spin-dependent (SD) contribution while the re- c

m

1

Z 150 100 300 250 200

4 0 ] [ Δ − c q keV m g A.6 = = = boson and THDM scalars, one obtains the following relevant effective h Z H ⊃ − . We find a conservative limit ∆ g Z g g . 6 ˜ eff H L . Constraint on ∆ ) and are given by 2.14 = 500 km/sec. . esc The first term inmaining eq. terms induce ( spin-independentintegrating (SI) out contributions the to the elastic scattering. Upon where In this section we discusslying the framework. elastic scattering The of pseudo-Dirac relavanteq. Higgsino terms ( DM can in be the under- read from the effective Lagrangian given in displayed in figure to evade the constraints from direct detection experiments on pseudo-Dirac HiggsinoA.2 DM. Elastic scattering tively. The upperv red lines correspond to excluded with 90% confidence levelthan if the theoretically observed estimated number number of of events events in are accordance greater with poisson statistics. The results are Figure 6 are disfavoured at 90% confidence level by the Xenon 1T, Xenon 100 and Xenon 10 data, respec- JHEP01(2019)224 . = ) p ( (B.1) TG (A.7) (A.8) (A.9) d, s, b f for the = ]. Hence, SI p q σ = 125 GeV, 68 , h for  009 and M . 2) ]. The couplings β , 2, (2 C 44 = 0 β cos  π/   ) ) 2) p q φ S , ( T s b α/ = µ f (1 C α β q , − ]. Typically, the neutrino ¯ 5 qq , c,b,t ) − 0 1 ]. We estimate γ X = S is the renormalization scale. Q 61 ˜ q 029, χ µ = cos β µ . 0 1 67 ) Q p ¯ ˜ qγ χ q H which is much smaller than the 5, − ( TG . b 0 1 f = 0 + Θ( 2 ˜  Q χ ) 5 2 = 1) p 27 q H = 1 , ( 2 cm γ T d H b q h (2 f µ C β b + H M γ β 57 + Θ( , ) g 0 1 ) − p 2 p ˜ ( 1) χ and it vanishes otherwise. The one and T q µ , f + 019, f and 10 q 2 p 3 . (1 0 C q φ hence it is negligible in our framework. − q h µ 2 T h b β b ≈ , dominates over the DM signal [ θ 4 2 π ) F h Q 2 = 0 M g µ SI p √ G ) – 21 – = u, c, t u,d,s σ p  θ cm − X ( T u = Q > Q SI q p S f q = + Θ( Q 48 σ µ   q m 0) 4 − cos 2 , 2 φ (2 C φ 10 q q for β g + Θ( M X X p  S ∼ β 0) , µ ), we compute SI cross section of DM with a single proton m = = 2 8 ) = 1 for (1 C  0 sin 2 β GeV. We find A.7 Q π  5 h,H 1 α/ ) of current generation experiments [ Elastic SD Elastic SI X 2 = − 16 2 φ π L L 1  sin Q = 10 = cm 16 − + p S f 44 µ = = − are obtained from the lattice computation [ q H 10 b dC ) dQ p ( − T q & Q f = represents gauge, Yukawa or quartic couplings and is mass of proton. The factors q h b u,d,s C p = 1 TeV and m Using the first in eq. ( P H − where The step function Θ( two-loop beta functions for the different couplings are as the following. framework which are obtained using publiclyevolve available according package SARAH to [ the following equation: B Renormalization group equations We list 2-loop renormalization group equations for various couplings appearing in our M sensitivity ( background, with cross section it remains challenging tofrom constraint their the elastic pseudo-Higgsino scattering DM signatures. discussed in this framework and 1 values of parameters favoured by our results, i.e. tan where where The SD cross section is proportional to cos 2 which is given by operators: JHEP01(2019)224 ,  † u Y u Y  .  15 Tr † u − Y u  Y † , d 2 3   Y λ u d + Y Y † 2 2 d  λ Y d 3 2 + 20 Tr Y  + 2 2 +  4 15 Tr 3 g † u g d 5 Y  − Y † e  u d Y 108 Y 3 8 Y †  u e −  † + Y e Y 2 3  3 g Y  † e 2 2 u  g Y Y 1 2 u  Y + +9 + 20 Tr 75 Tr   2 3 † , u 2 2 – 22 – g  − 5 Tr g Y Tr 2 1 u u 2 3 g   Y − g Y 2 2 † u 45 u † , 2 1 g u 19 15 Y Y , g  † Y − u  2 4 +  u 2 3 Y 2 4 y 4 2 Y +45 g g y  + 440  2 1 + + 12 g 2 1 4 + 21 Tr +3Tr 2 3 2 g 3 2 , 2 2 y 3 g − 4 , g y 85 Tr  27 2 2 + 260 +17 2  2 + 4 9 g 2 3 2 − 2 2 g 1 + − 2 1 2 2 g g − g g 2 y 2 + 208  , 2 1  y 6 d + 120 g  † 2 9 2 49 u 11 + 20 160 2 Y 2 + 45 g 2 | Y + †  2 1 3 d g 20 17 − 2 + − u 1 2 y 1 y 1 8 4 Y 1 g | Y 2 1 − y   g † 80 180 9  d g 2 + 3 +  3 3 3 1    2 4 g Y , , 2 , 3 g g 2 | 3 d 3 3 λ 3 2 3 3 3 3 8 2 1 1 1 , , 10 2 g Y g g 600 3 3 g g g g 2 1 y 1267 + 1 −  |  25 Tr 10 1 2 15 50 g g 7 3 4   3 , , , , , , 2  1 1 1 5 λ 2 3 10 2 5 50 50 21 Tr − g − − − − u u u − , 3 Y Y Y 4 9 λ = 0 = 0 = = = 0 = 0 = 0 ======0 = = = = 0 + − 2) 0) 0) 1) 2) 1) 0) 1) 2) 0) 1) 2) 0) 0) 1) 2) 0) 0) 1) 2) , , , , , , , , , , , , , , , , 1 1 , , , , 3 3 3 2 3 3 3 2 2 2 2 2 1 1 1 1 (22) (21) u u u u g g (2 (2 (1 (1 (1 (2 (2 (2 (2 (1 (1 (1 (2 (1 (1 (1 g g g g g g g g g g g g g g g g (2 (1 (1 (1 Y Y Y Y β β β β β β β β β β β β β β β β β β β β β β B.2 Yukawa couplings B.1 Gauge couplings JHEP01(2019)224  ∗ 3 y   4 ∗ 4 y y 1  , 2 y 1   y λ † d + d 3 Y  Y +9 † † y u d d 480 2 ∗ 3 Y Y Y y y † d − u d 1 5 , 2 2 Y , Y d y Y   g 2 3 4  d Y 8  + d  † λ   Y d ∗ † 4 d Y − e † Tr ∗ 2  y e Y † + Y u Y y   3 9 4 † u 2 1 Y e d 4 2 1 Y 2 y Tr e +675 Y λ y Y g Y u 2 λ − , Y   d y 3 2 1 4  Y 2 4 1 † + 2  4 27 d † 8 Y  g u 2 y  + − † | Tr Y 3 480 e Y − − 2 2 3 4 4 ∗ 3 4 4 d   u Y 2 g  g y y − 41 2 Y | 2 e | 240 † + Y 1 2 2 2 60Tr 1 2 4 2 e g + ,  | 6 Y 2 1 g g y Y 3 2 1 − †  − − | 2 4 + y + e 108 − e y g d 1 1 u λ 2 |  1 3 4 Y 53 2 2 Y y  Y † λ Y 4 − g e e g  †  +  † y 2 9 4 − 3 u d  Y † 5 Y 40 4 e 540Tr 2 g 2 +675 3 2 Y − e Y   Tr λ − Y 2 2 g 160 8 u d −  2 − Y  15 e 3 g −   † 1 Y y Y 2 Tr 2 1 1 u  − Y λ † 4 2 2 † † y e g g | + d u 2 Y 2 4 9  g 2 1 4 + Y Tr +9 g Y Y u  +3 + g e y 2 3 † + 2 d 3 +495 − u | Y 2 d 3 4 ∗ 1 Y | , λ 2 g 1 4 Y Y   9 4 y Y – 23 – 1 d 2 1 g +Tr  +3 λ − d 1 d  +187 + y − g + Y 2  |  2 † y − 2 Y 2 1 Y | e † d +225  u † 2 † d g 6 4 3 d † u λ  | Y Y 8 y e  Y 31 15 Y y 15 +Tr Y e 1 † Y − † | † 3 2 d Y d d d d 540Tr 33 16 y Tr u 1 Y 2  2 +480 12 e + | Y + Y Y Y † Y † y g  Y 3 + e 4 d ) Y − 2 d d 9 4 d + −  † 2  1 4 2 2 λ 4 g 2 d Y 1 Y  Y † 2 Y 3 Y 18 g d  g e y † d g − Y † +5 g d  ∗ d 2 Y 4 Y 2 Y − +  ∗ 21 4 + Y | y 4 d Y 480  1 21 2 3 2  y d 2 4 1 d 16 1 8 Y y 4 − g Tr y +3Tr y Y − Y 2 | −  2 y Tr 2 2 ( 180Tr 2 2 + + 9 4 +223 6 2 2  g 2 , 2 4 g + g 9 4 3Tr 4 9 4 180Tr 4 2 g 3 −  g +9  2 Tr u 1 | , u −  λ − g 9 4 2 2 2 1 3 3 2 g 3 3 Y  − i − 1 4 − 8 Y e ,  g g g g  † 15 y 2 4 1 2 2 1 u u † +15 | † i  − Y 2 u d g g + g | 27 20 +2 2 4 Y Y 2 d 2 1 9 4 + Y | 32 Y 27 20 3 1 2 † + 3 g u g + Y u 2 1280 2 u d y −  | † λ  − 2  Y 1 2 2 | y Y u 1280 1280  1 4 + − Y Y 4 4 1 129 | † e 4 g 5 8 2 d u  , 3 8 † , † 4 Y   4 1 | d 1 y g 1 u d  + Y ) 2 ) | 3 Y − Y 2 g u g u y d Y e − † Y 4 2 + Y 1 4 2 2 4 1 ) y + e 2 y u 3 † Y Y Y Y +9 d | g 2 4 u u y 2 g y 3  ∗ 4 g 9 4 Y † † Y 12 † † 4 2 d 3 u y 113 600 Y d Y λ Y e 9 4 3 8 y e u 8 + +  600 g Y Y u ∗ Y  − 1 + Y 6 200 Y Y 2 38 + 1 2 + 1 1449 h − − e d u + 200 −  y 2 Y † 2  6 y 2 d y 2 4 d − 32 3  Y Tr Y Y  y h   ( ∗ ( 1 y  Y λ Y y  Tr  e e d d d d u u y ( , , 9 4 1 3 d 2 3 4 1 1 4 1 Y Y Y − Y Y Y Y Y 8 9 4 80 5 1 8 3 4 240 27 80 80 1 4 540Tr λ y  Y ======0 = = = = 0 = = + − + − + − + − + − − + − + + 1) 2) 0) 0) 1) 2) 1) 2) 0) 2) 0) 1) , , , , , , , , , , , , e e e d e d d d d d u u (1 (1 (2 (1 (2 (2 (1 (1 (2 (2 (1 (2 Y Y Y Y Y Y Y Y Y Y Y Y β β β β β β β β β β β β JHEP01(2019)224 4 λ  2 | † u 3  Y y † | e u 4 +160  Y Y λ 3 4 3 e 3  y y λ 4 Y 2 λ 1 |   y 4 y † ∗ 3 d 4 2  y y | | Y † , Tr λ 400 d 4 3 3 u  +160 y y Y − +43 y | 2 Y 1 2 1 1 d +180Tr 2 2 3 3 2 † 160 g y g u Y 3 y y y λ 9 2 2 Y − 2 2 1  1 λ g +1200 d 3 y 80 − y g 103 4 Y 2 y 1 Tr 8 | 400  2 − 27 3 ∗ 2 4 g 29 2 ∗  3 4 † 160 − | 20 | d ∗ y y − 3  y y 4   4  + | 3 2 Y † 2 1 y ∗ 3 y + 2 d | 2 y +3 ∗ | d 3 4 | λ | λ y 10 2 3 y Y 2 2 y 3 y Y 2 4 | y y d y 4 1 y | − 80 y  3 2 4 | 3 Y y y 4 2 1 +3 600 y λ +700 | 1 − λ | y  +900Tr y ∗ 3 4 2 y 1 3 6 − | +  9 2 y y +3 2 1 y y +2700 4 2 Tr 2 | 2 +10 † −  ∗ g d 2 2 300 4 y g y  −   3 2 | y y 18 Y y +60Tr 4 † | 4 † ∗ 4 y d 2 − 2 2 2 d e 1 40 27 4 2 y λ 2 y − 4 y | g Y y Y Y y 1 | 3 2 y 1 4 | d † + e | 5 2 4 y d λ y 2 y 3 Y 2 Y y | 2 Y 2 y | ∗ 2 +1900 y + 420  + +6  +1200 d | 2 g 2 y 2 2 2 2 4 4 2 +135 | g Y − 3 2 g +25 | y y Tr y Tr 4 3 450 y 2  1 4 +50 3  2 3 1 2 3 2 2 y y 3 † g | y 2 y | y g +15 λ y d 16 2 − | | 4 165 2 2 , 5 2 1 y 2 Y 4 − y e | y y + 4 | 2  | 1 d y 25 4 λ 2 + 1 2 Y | | 5 2 g Y y 2 † 18 y y 4 8000 e | | − | +540 – 24 –  2 2 y +  1 4 140 27 Y 2 | 4 1 − λ 2 y y e ∗ 3 2   | g +2700Tr +50 | Tr +900 10  3 2 y y Y ∗ ∗ 450 3 2 1 2 2 2 3 † 12 ) 4 +2400  3 d y y y y g y − | 2  + − † 4 y 2 2 1 2 e 258 Y 4 | − 2 2 − 2 3 2 y 2 1 g d y 45 4 | y 40 Y y g y 4  y +5 − 4 1 e | y Y + 1 4 ∗ 2 1 | −  3  y y + Y 2 1  y g y 2 | 2 80 2 4 4 1 y 240 +4 2 309 y |  275 2 | 2 g y ∗ λ 1 2 ( λ 4 4 3 2 Tr g | 29 − 19 y + − y 2 9 4 2 y Tr 1 ∗ | 4 1 2  +25 g 2 9  2 y − − | y | 4 240 400 − † g  ∗ 4125 3 3 2 +80 2 u 4 2 y − ∗ , 4 y y y ∗ y 4 − Y y 1 − 4 | +375 − ∗ 1 +20 y 4 2 2 1 | y  4 y u 2 2 2 2250 y 2 750 y 1 g + y 4 ∗ 4 |  y |  y , Y y 1 2 y 1   2 † y 4 1 † 4 y 2 − i e | − e  † y 4 g y 3 y y y e 4 2 2 λ | Y | 4 Y   y 2 2 2 600 y +36 2 y g Y +9 , e 6 2 † e 1 2 † 1 1 λ g 2 g d 3 e 27 20 e ∗ g 3 7 4 g 1 2 Y  − +70 y Y 4 y y 9 4 − Y Y Y † y † 2 2 2  8 2 u e − d e 2 | 1 − + −  | g y − 2 Y 4 Y Y Y +4 y 2 4 − ∗ 1 3 3 e y 2 | y u +75 3 4 +180Tr   g 2 1545 y y +390 | Tr 29 4 4 1 y | | Y Y y 2  4 3 4  4 255 20Tr 2 y g 1 | 4 2  − 2 e  | y  ∗ Tr Tr y y 2 y 4 g 1 y y  y 2 4 2 1 − 2 2 2 1 1 1 Y 1 | y 132 200 y 2 y 4 2 3 y y 2 | y y λ g g 1 4 1 y Tr 9 g y h 129 200 20 4 1 4 3 2 g y  y 2 1 1 e , , , , , , , , λ λ y g 4 1 200 − − Y 39 20 6 2 750 530 140 400 250 50 40 = 0 = 0 = = 0 = 0 = + = 0 = 0 = + = 0 = 0 = = = + − − +3 +900Tr − +21 +160 − − + − − − − +6 0) 1) 2) 0) 1) 2) 0) 1) 2) 1) 2) 2) 0) 1) , , , , , , , , , , , , , , e e 2 2 2 2 2 2 4 4 4 4 4 4 (2 (2 (2 (1 (1 (1 (2 (2 (2 (1 (1 (2 (1 (2 y y y y y y y y y y y y Y Y β β β β β β β β β β β β β β JHEP01(2019)224 ∗ 3 y  , 3 2 |  y 1 † 2 u y y ∗ 4 | Y  2 3  y † u ∗ 4 | e † y  d 3 Y y Y 4 5 2 3 y Y +43  e ∗ 3 | y y d 4 y Y 1  1 + 2 Y y Tr y †   y y e ∗ 2  1 2 2 1  3 2 2 2 y Y 1 y y g y Tr ∗ g 2 e g 2 3  2 Tr 2 y 9 Y 3 29 g | +43 y 2 8 2 2 2 | 27 4 80 y   2 3 309 y − g 4 2 2 y ∗ ∗ , 1 4 4 y 1 | | y + y  y y y 2 Tr |  4 1 + y +20 † ∗ 4 +60 3 4 y 1 † 1 u y y 1 e 255 | y 4 y y  y y Y y 7 2 Y 1 3 † 2 3 y 29 u 2 4 − u 140 +25 e y +10 y 1 y y 2  21 2 Y 1 λ − Y 4 2 2 2 2 Y y ∗ 2 − 180 2 g u y † y g y   y e 1 + y − 1 +3 2 1 † Y 2 − 53 2 y e 1 Y y 4  4 ∗ g  1 y  39 1  29 e  y Y 2 2 † y 1 d † 4 +21 e λ Y d g 18 2 1 y 27 40 + +10 − Tr 20 Y λ Y   Y y  2 2 ∗ ∗ 3 d 4 3  † | d  +60Tr 1 d 70 + y 5 2 y y 2 Y 480  λ 4 275 2 Tr y Y | 2 2 2 Y  ∗ 3 4 |  y  1 Tr 2 ∗ 1 + g d ∗ −  | 1 + 3 y 3 − λ y 1 20 y y 2 1 1 2 y Y 3 y 1 y | |  Tr y 8 | 3 1 9 4  y y Tr y y 2 45  4 † 1 2 2 y 1 2 ∗ u 1 1 2 2 1 2 2 3 1 y 40 y y 80 g , − 3 g y | g y y Y + +80 λ 2 3  1  u 2 2 − 9 2 8 +50  g − − 3 1 † +6 15 y + † 20 u g 80 Y † d 2 2 4  u  4 1 540 | − Y † g  Y † + y e Y y 4 + u − ∗ 4 u +4 u – 25 – +825 − 1 2 1 u y Y  2 2 +180Tr +20 255 Y y 45 | Y 2 | 1 y ∗ Y 4 e † ∗ λ 2 Y | 3 2 u e † 1  3 † y 5 | y u − y 3 u Y − 3 2 †  λ y Y y Y 2 1 3 4 d 2  1 Y y | 2  Y  e 9 | g y  y | 1 Y g 1 u 3 + d | Tr 1 Y 1 4 y d y y − 4 1 Y +180Tr 2 Y 160 Tr y y y Tr  4 2 Y y 4 y | 2 ∗ y 4    309 | ∗ 5 2 3 | 70 y 1 λ 4 2 , 2  1 y 2 3 +21 4 y  Tr y  6 g 20 g 4  y Tr y Tr + 4 y 2 1  ∗ 2 | † y | | Tr 1  2 1 1200 y 2 e y − 4 † 4 8 1 y 2 1 | 1 u 25 3 y 19 y 17 y 1 2 +36 1 2 Y y 2 y y y y − | Y y g 4 e | 9 4 1 + 3 y 2 4 2 − 3 − 40 ∗ + 9 4 4 u 6 27 | y Y 1 ∗ 4 g y ∗ 4 1 y 8 1 20 1 1 Y − − | 15 +160 80  y − − y y 3 − y − y 1 4  8  2  3 2 2 | y  45 +    y 4 † +  + λ Tr y 2 2 4 g + d † † † ∗ 3 2 29 † u u d λ 1 2 2 y  d y 1 y 1  + Y y | λ  Y Y † y y † Y 1 g y Y d d e  1 2 6  4 u u d y 2 2 u † Y y Y 3 y Y + d λ g Y Y Y † 27 20 − Y d e y +80 +160 d 7 4 1 4  Y 4 1060 †    9 4 2 2 +180Tr Y Y +6 2 u † 1  | Y d − d y 3 − 3 − † − g − 3   d Y Y e − 1 Tr Tr Tr Y λ y 2 ∗ 4 y ∗ 4 d 3 Y y 1 | 2 2 2  | d | Y 2 y | | | y Tr Tr Y 4 +4 4 1  e 1 y 1 Y y 3 3 3 4 3 103 ∗ ∗ 4 4 2 4 y g 1 y  y Tr Y 5 160 | y  y y y | y y y y 2 g 2 1 | Tr | | −  1 2 3 1  3 3  1 g 1 1 2 2 y Tr y y y y 2 y y  Tr 2 9 y 2 y y y y 2 1 129 200 20 1 3 y 3 2 2 2 1 y 3 g y , , , , , , , , y y λ λ y y 1 4 4 16 2 4 −  − 27 27 5 8 165 9 4 21 27 2 480 y 2 6 6 = 0 = 0 = = + = 0 = 0 = 0 = 0 = = = 0 = 0 − − − − + − + − + − +3 +3 − +70 +60Tr − − 0) 1) 2) 0) 1) 2) 2) 2) 0) 1) 0) 1) , , , , , , , , , , , , 3 3 3 3 3 3 1 1 1 1 1 1 (2 (2 (2 (1 (1 (1 (2 (1 (2 (2 (1 (1 y y y y y y y y y y y y β β β β β β β β β β β β JHEP01(2019)224  . † u Y   u  † † † u Y u e Y  Y Y u e 2 u | Y Tr Y Y  4 † 2 1 u †    y d g | † Y 1 d 4 ,  Y 1  u Tr λ † Y d λ y  e † 4 4 4 e 2 Y d 3 † 2 3 Y 850 4 3 e Y 2 y g λ Y 2 4 †  Y | 3 λ λ y e d y  4 1 Y e 3 − ∗ 4 2 4 1 λ 1 1  † +60Tr 2 e y 8 Y Y  λ d +68 y Y 11 λ y λ y  y 2 λ 2 † | d Y  2 +8 d 1 Y 3 1 2  2 2 Tr 2 g | 4 † 2 Y d 2 3 − e y Y λ 400 g  53 1 g 3 20 g 240 Tr +2  1 d † Y λ Y Tr y λ  d 2 1 3 2 − | 4 e − 20 λ 2 Y −  2 2 +160 2 255 Y 1 4 λ Tr † 2 λ 2 3 2 Y g g 3 10 d  − +20 u +8 y − +2700Tr 2 3 1 λ g − 2 1 λ Tr †  λ Y 2 4 2 4 u 4 Y +825 24 3 g 2 +390 1 2 − 2  λ g 2 1 4 | 2 | 1 45 d † λ † Y λ 3 g λ 4 4 g u 4  8 5 g g d − Y 3 5 y † u y y y Y 33 +20 4Tr u + Y † | | +4 2  9 1 d λ + Y d ∗ 10 4 2 +4 2 u Y 2 † 20  2 3 y 2 y 2 − 400 | e Y +160 117 +   Y y g 4 † u 2 Y +21 1 +24 4 g λ 3 d d | † 2 1 Y +  3 2 1 †   u g − Y 2 3 y λ u 4  + e Y † g Y y 3 4 Tr † , g , | d 6 2 3 Y e †  y λ 1 d Y 2 3 Y d  λ | +4 Tr   3 5 Y u 2 λ  1 Y d y y Y λ  Y 1 † 1 +24 2 1 d ∗ e 2 g e 160 Y 2 4 +8 103 1 Y d  12 20 4 − λ λ λ Y y Y Y y  g 4 16  Tr Y 2 5 − 9 † | λ − 400 e 24 d | − −  +  1 Tr 1 4 3 4  540Tr 4 40 Y  2 4 Tr 2 Y − ∗ 1 4  − λ y y λ † y + 1 ∗ 420 2 4 +60Tr | 1 d Tr λ 2 e +12 y 2 1 2 2 2 λ |  − 2 1 200 + y 3 1 4 y 1 3 λ 4 y Y 2073 1  † 2 4 y g 1 1 Y 2 λ g − d 1 g λ λ † y 3 λ e g g  λ e 2 λ − y Y 4 2 2 12 2 + | 9 2 5 2 2 λ Y +3 5 2 15 Y − 24 d ∗ g 3 +900Tr – 26 – 9 4 6 2 32 † g + 600 ∗ e 50 4 e 2 − − y Y y − g  | +180Tr 9 80 + + 3 y | 480 +  Y † Y −   †  4 − d 3 ∗ 4  − 12Tr u † † e 4     2 4 † e e 2 − 1 − y 4 † 2 − u y Y 8 2 λ | † † +15 4 3 Y | d Y λ 1 | d e 4 λ − Y Y λ g 3 2 d 4 259 1 1 Y 2 1 3 y y u 4 2 Y 3 1 e e y  λ Y Y y g y  Y u 2 1 λ λ g d − y Y 1 | e 2 λ d 1 Y Y † + | 160 y y 4  e Y 1 2 y Y g  Y Y 4 2 4   2 | 2  g 24 2 Y 2  15 12  4 5 9 g   λ 2 +4 e Tr g 9 5 +20 | Tr +6 2 y 1 Tr − 4 1 4 − | Y +1900 + Tr 4 +309 ∗ 2 4 3 +43 | 3 Tr − g 1 2 Tr Tr +20Tr 2 4 λ + 4 2 4 2 y | ∗  g y 4 2 1 4 − y 4 4 2 1 4 λ 2 | 3 3 1 4 g λ 2 8 λ  y 2 λ y 2 y g λ g 67 +4 λ | | | 2 2 y 1 † 2 3 2 4 λ 2 y +60Tr 1 Tr − d | 2 3 − +135 4 9 1 3 4 9 2  g g y g 1 y 5 2 λ 2 72 1 − y  g 4 Y y 4  2 | 1 78 8000 g | λ +10  † − + 2 d y 2 λ − † e 4 λ g − d 29 4 24 2 4 4 1 2 2 g 2 2 +6 Y − 15 − | y | Y  140 Y λ   4 y 1 g † g + 2 4 4 2 1 1 † e − 1 +4 d  † 275 3 d d 2 1 2 g 1 +540 d 3 + +3 − y λ y λ † Y λ Y  2  | 10 g λ | Y u Y g 4 1 2 4 15 1 Y λ † 2 − 2 †  6 +140  † u † e d 8 4 u d Y g d d g † g λ 2  − 2  40 9 e Y Y | Y | Y u + − 10 363 Y 4 1 Y Y 2 † 2 − − † e 3 Y d 5 3 | u u d 2  d Y g 12 +27 2 2   | e y Y y 3 + − Y | | 258 Y Y Y | Y +700  | 3 4 4  Y y 3 4 9 +54 d 4 6  1 1 d Tr + 1 5 4   | y 10 2 y y Tr  − y y | 2 1 | g g |  2 Y 2 Y 4 y 2 1 1 Tr | |  3 4 1 −  g Tr λ y  2 + 2 3 1 y 2 λ Tr Tr  3 λ Tr y y 3 2 2 2 1 1 1 λ Tr 2  2 3 2 3 1 3 3 4 | g | y 2 2 λ λ 3 3 40 27 y 2 4 g g g 1 2 4 100 153 480 1 λ 2 8 λ g λ g λ λ  g g , λ y ∗  λ 2 5 5 5 − − 1 3 2 27 3 2 24 54 3 y 24 24 64 16 400 2250 240 y = = 0 = +4 = = + + + +9 − − +12Tr +80 − − − − + + +12 − +1200 +80 − +180Tr − +60 + 2) 1) 2) 0) 0) , , , , , 1 1 1 1 1 (2 (1 (1 (2 (1 λ λ λ λ λ β β β β β B.3 Quartic scalar couplings JHEP01(2019)224 3 ∗ 4   y † † 4 3 d u ,  , 2 y y Y | Y †   2 d 2 2 1 2 4 3 d u 2 † † 2 y y | d Y y e  , y | λ Y Y 1 | 4 1 d 2 1 Y Y † 4 3  y 2 4 d  y y e Y   λ u y 1 | λ 1 2 4 | λ Y † 4 9 Y y  2 2 Y e 1 +10 λ 2 4 d  Tr 4 11 λ ∗ 4 4 † y λ g  , 2 2 Y 2 u ∗ 4 3 1 λ − Y y  4 1 2 λ Tr ∗ e 4 − g  y Y +10 4 λ ∗ ∗ 4 4 λ 3 2 5  g 4 y  Tr 2 † Y 12 4 2 3 u ∗ ∗ 2 − y 3 + y y d  | † 2 ∗ 4 3 λ − y u  g 15 4 † 2 y y 3 ∗ ∗ 20 Y 3 2 Y Tr 1 d y + 2 1 λ y 2 † y Y 1 y y y | 4  u 4 u 2 λ Y y | 4 1 +2 − + 1 Tr y u 4 4 200 4 3 λ y Y 4 Y 1533 g u 2 2 4 λ 4 2 4 1 y 2 28 y y y y Y 2 † d +40 12 | λ 2 2 4 u Y y y 1 3 λ 2 λ † λ 2  y +8 4 u + 4 3 27 † Y 2 1 15 2 λ  y y λ 2 Y y 4 2 u 1 − 2 3 | Y λ † λ  7 d λ g λ 2 2 y u Y y 3 −  3 λ u − + +2 8 2 1 Y 1 d Y † y − 2 − − +8 2 +6 2 λ 2 4 g  Y d  |   Y λ u − 4 +2 ∗ g ∗ ∗ 3 4 † 4 4 8 † †  1 λ Y  3 2 u e e 3 2 2  Y +18 2 1 y 4 y y y λ ∗ +22 2 y 24Tr d | Y − Y Y g 2 1 2 4 3 1 ∗ 2 y 3  2 y 3 + − Tr Y e u e 2 1 y y y + − Tr +4 ∗ y 4 λ 6 5 λ y 1 | 4 2  | 2 Y 1 Y 3 Y 2 | 2 2 4 2 λ y 1 1 Tr 4  y λ 4 ∗ y 4 4 11 +2 y 2 λ  g λ +  4 g  † λ 4 y 2 +12Tr | d Tr | 1 2 y y λ 2 2 3  λ g 2 | 3 4  4 Y +2 ∗ 4 2 5 27 y 3 5 3 24 Tr Tr 2 Tr 2 λ λ 24 2 12 y † − 3 2 d 3 +2 y ∗ y λ 4 λ u λ | y 4 2 4 2 2 2 g 2 y 2 3 2 − 3 2 − 1 1 3 y Y λ 2 2 4 | g Y g λ + λ + − ∗ 2 y † g y 4 y +8 λ 3 2    1 2 3 d 1 u 4 4 14 45 1 2 y − +2 2 † † 3 y 4 4 4 g g 12 λ Y e Y d λ λ y 2  | y +8 4 2 2 y λ | | 8 2 3 u 2 1 2 + 2 1 ∗ − Y Y 2  y ∗ − 4 5 − 2 3 4 33 e g y +40 2 2 λ y Y λ u +12 y 2 +  +3 − y y – 27 –  | λ 2 ∗ † 1 2 1 2 y † Y 7 2 Tr 2 | 4 | Y  u 1 u † | 4 − +16  g  y † y ∗ 28 u 4 4 4 † † 2 y 3 e Y λ u 3 d − † y Y † − ∗ 2 4 4  y e 3 5 2 d 2 y Y | λ λ 2 d +2 2 Y y − u Y 4 Y y y †  2 2 | 4 y 2 Y 2 u Y d e g 4 +2 Y d +10 d 4 3 2 ∗ Y λ 1 4 − y e 2 g d λ 2 Y 1 Y Y 4 λ 3 y  Y 1 Y λ +6 y 2 y 1  | 2 2 Y  g Y d ∗ − 1 1  2  3 +12 4 4 λ y   4 λ  g 15  2 y Y y  λ 2 2 4 λ 3 1 1 † y λ Tr ∗ 10 1 2 e 4 3 +2 | Tr Tr  2 g g y 4 4 +3 Tr Tr + y 15 1 y Tr  4 2 Y λ Tr 4 +2 2 12Tr 2 λ 4 3 6 2 λ 2 +2 2 3 1 ∗ 4 2 y 4 e 2 2 5 9 +2 λ 2 Tr λ | g λ g 2 12 50 1 λ ∗ y + 2 4 y y − ∗ λ g 3 4 Y 3 2 4 3 40 2 9 2 g 2 +8 y 2 2 2 2 1 2 λ ∗ 1 3 y y λ   | λ + − g | ∗ y 2 4 2 g 2 y 2 λ +2 † − 4 4 + − − 4 d +68 4 17  2 y g 3 y 4 +64 2 4 +27 3 y 24 4 12 Tr 2 +10 2 λ 5 Y ∗   3 45 | 1 λ 9 y 1 | | y 4 27 4 2 λ  4 − 4 † 2 ∗ 4 + y 4 2 − u y 2 1 1 − 4 − d 4 | 1 λ 3 g † λ ∗ − g 4 2 + d y g λ y y Y 4  y  − 2 Y 1  λ  λ | + 4 | y y 3 2 † 1 Y † † y  3 4 † 2 4 g † u u 1 u e 4 1 | u 3 ∗ 3 y d λ +2  g † 8 u +2 d λ Y 4 Y λ Y y 2 Y λ y 2 Y 1 λ 1 Y ∗ 191 4 +2 + 3 4 Y 10 3 † d 1 e  Y 2 y u +10 λ y g u u d y † 2 2 1 † u λ d 1 40 y Y | Y λ 1 2 Y d 2 − 9 2 − Y Y Y 9 5 + y +2 † +8 1 y ∗ 3 3 Y Y ∗ 3 λ  d 4 d 2 Y 4  2 2   − 2 y 28 y ∗ y d 4 | y −  | d − g Y | λ Y λ 4 2 4 − 4 y 3 Y 3 4 4 Tr 1 2 2 2 d | 2 2 2 Tr Y − Tr Tr  +12 λ 9 2 | 3 y 2 y y 4 4 g Tr  2 g g g 2 | | Y − 4 2 4 4 +22  3 3 | 1 y 2 4 2 2 2 y 1 1 1 2 2 λ g 2 ∗ 4 3 y − λ Tr λ λ y  2 |  λ y | 2 2 g g g 2 1 y Tr g λ 2 4 2 3 2 1 y Tr y 2 2 2 λ 1 1 2 |  10 4 2 2 2 g g 1 1 1 9 141 3 5 5 4 1 y y y λ λ g λ λ λ 1  2 λ g g g , , 4 ∗ 3 λ y λ 1 3 20 4 5 − 9 2 4 5 3 5 5 4 15 63 153 y λ y 12 33 12Tr 20 24 24 4 = + = 0 = = 0 = +2 = + + +22 + + − +12 − − + − − + − + − + +36 +6 + − − +8 2) 1) 0) 1) 2) 0) , , , , , , 4 4 4 4 4 4 (2 (2 (2 (1 (1 (1 λ λ λ λ λ λ β β β β β β JHEP01(2019)224 ,  3 λ + , ∗ 4  4 4 † y d 4 y 4 y  Y 3 λ 1 y 2 ∗ † 4 4 1 d y u 2 y 2 y 4 λ 3 y λ Y 2 3 Y 2 λ 3 4 y 1 4 2 2 λ − 11 d † 2 1 λ y  2 u 1 g 1 g λ   Y 2 g   2 4 y Y 2  † 3 3 λ 1 † d 2 y  λ λ † d d | y 27 20  2  4 λ 2 e 5 y 1 Y 12 11 2 2 † †  Y Y g 8 λ d Y + e d 2 4 λ 36 Tr +75 † y y d +   1 e u 40 | 4 Y Y 2 + Y 2 λ − 1  Y − λ y Y Y d e  2 + g 4 1 1  † 4 λ +4 1 2 3 d ∗ u 2 2 1 Y Y  g 4 +36 λ y  4 +2 2 λ 2 y y λ Y +22 g y Y 2 1 4   3 † 6 5 Tr g +2 ∗ ∗ 3 4 12Tr e 1  3 2 u Tr 3  λ λ λ 2 3 y y 1 2 Y y y λ 4 20 Y − 10 27 1 4 +5 Tr Tr 1 4 − λ 2 λ 45 e  4 2 1 λ † | λ 2 4 3 4 2 2 2 Tr 3 λ u λ  3 1 Y y 3 − λ 36 + 1 − 4 g 2 g  λ λ 2 λ 4 1 † Y + + y † y u 4 e † λ g 2 4 2 3 1 +4 6  g  | d d 1 1 − 22 − Y λ † 4 † g Y 3 4 + λ  9 4  +4 u 2 3 Y d Y λ λ − 1 1 5 u e y 2 2 1 4 3 ∗ λ 4 36 4 2 2 Y u λ Y  −  +40  4 y λ  Y  4 Y g − 2 y 15 y y 2 g 2 d † u 4 Y 2 − 2 † 2  ∗ u 3  1  3  + λ d 2  1  g † Y − Y † λ 4 † g y u y Y + e y † 3 d 4 g − Y u 2 +3 2   λ  2 3 Y u Tr Tr y Y d ∗ λ  Y 4 3 2 + g 2 Y 3 3 +6 d +6 3 e 2 3  † λ | 4 Y d 2 y Y 2 e u Tr 3 Tr λ λ 2 3 y 4 Y +24Tr λ g Y λ ∗ 4 − +18  4 Y   4 Y 3 1 2 15 Y 1 λ y λ  y 1 4  4 9 2  e  + | g +4 1 λ y 8 λ 2  1 4 † y Tr 71 λ λ ∗ Tr 3 + +10 Y d  2 2 +6 3 λ g y 3 Tr 4 − 4 1 9 Tr 1 4 Tr y 4 1 2 y g Y  20 16 3 Tr  2 y 1 6 5 − 2 3 g λ 3 ∗ 3 λ 2  1 y λ λ u † 2 y 2 2 g 3 2 e 2 † λ y 1 +12 4 y 1 − y +6 λ + d Tr 2 g Y y + 4 5 λ g − 4 2 λ 4 2 Y 2 4 4 2 27 20 3 λ λ  3 4 4 † 2 2 y 1 Y 3 u 2 e 2 +40 3 g y 2 4 λ 1 λ λ g g λ u − − 5 − λ g 3 Y 12 + Y y λ 3 g 12 2 12  2  3 4 ∗ 2 2 Y 2 2 4 1 – 28 – d  y 1 6 † 2  8 g  +12 ∗ 45 λ 2 3 4 12 u † − 63 10 y † g − λ † y u g Y +22 + 1 e 9  y d −  2 Y †  2 4 − Y  + + Tr d λ Y 2 4 Y − y u †  − 15 ∗ 4 † 33 20 d 2 4 3 e u λ 1 8 d y d  Y +11 2 † +6 Y  3 y +2 e 4 2 y Y λ 259 † λ 16 Y Y d − 3 Y Y 3 † d 2 2 + +20  λ u + 2 3 g Y 2 −  u  † d 3  y Y y y d 3 Y 2 2 1 − e 2 g 3 + 2 Y λ 2 2 2  Y Y λ  1 ∗ d 4 2 g +2 4 2 Y λ Tr 1 y 4 y Y 2 u 15 2 y Tr y 2 Tr y  y  4 3 d | Y 1 1 g λ 9 5 g  16  3  Y 3 λ 1 g y  3 2 † λ Y 1  1 + 3 5 11 11 λ d 2 λ  2 Tr y 2 Tr − 2 2 − 2 g  λ y 4  | Tr 1 g   2 3 Y  2 3 y 2 4 g 4 4 2 2 2 Tr , 2 +12 2 λ 4 d ∗ λ Tr 1 8 λ λ g g λ 3 11 λ 13 + 2 g Tr 2 ∗ +12Tr 4 y 4 + 1 y 200 4 Y 2 +2 +15 1893 2 3 45 λ 9 4 1 g ∗  3 y 2 g 4 12  12 − 12  2 12 λ 2 + 1 2 g +36 1 + 3 y λ  † | y  3 u − + + +2 g + 2 g 3 2 † y − − 4  −  2 4 d − Tr λ 2 2 14 Y 2 2 2 g 2  5 4 λ  y 3 33 10 9 5 2 2  27 | 4   171 100 λ Y  3 | 8 4 y 1 u g λ ∗ † 3 2 y † y 4 † u † − e 3 λ u u λ 4 2 4 g d 1 2  y + 2 Y − − 4 λ + − y − 2 2 4 2 Y Y λ Y | g g † Y λ y Y 2 4 1 2  λ u  200  + u e † λ λ  1 1 4 u d 40 u g † † λ † λ +6 Y † 9 2 1 40 9 d 4 ∗ e 4 4  y Y Y u y e 201 10 45 Y Y 4 1 Y 4 2 +2 u 2 − 4 − y λ Y Y 5   Y + d Y g   − 36 2 − y λ ∗ 2 d e 4 Y λ  + − + | e u 3 Y 4 ∗ ∗ 3 3 y 14 4 2 Y Y  3 9 6 4 2 Tr Tr 1 1 Y Y λ + + Tr Tr 10 λ  y y +12 3 y y 3 3 g g   λ 2 +2 3 3 3   − 2 | − y 4 3   Tr 2 λ λ 2 4 + 3 2 4 λ λ λ  1 2 y Tr λ y 2 4  3 2 2 1 2 Tr Tr g 2 2 1 3 3 4 1 Tr Tr λ y y 2 2 2 λ 1 3 3 2 λ y y 3 40 27 4 4 2 g λ g 2 1 1 153 100 2 4 2 4 2 2 4 2 2 λ g g λ λ λ y y λ 1 3 2 y g g g , λ g λ y λ y λ λ 2 4 2 4 − 17 27 9 4 9 4 15 3 2 36 6 64 36 2 15 12 y 80 4 = +2 = = + = 0 − − − + − + − − − − − +18 +6 − − +2 +11 +6 + − − +4 +24 +6 0) 0) 1) 2) , , , , 3 3 3 3 (2 (1 (1 (1 λ λ λ λ β β β β JHEP01(2019)224  3 4 ∗ 4 | λ ∗ 4 y 2 3 | y 3 y 4 | 2  y 4 +5 | 2 y 2 3 2 y 2 | 2 | | 3  y 1 λ 3 g 3 4 y  † , | y d y 2 3 3 y † λ | | d 4 2  Y 2 1  λ 3 +8 +5 y 4 Y ∗  2 d  2 g 1 1 3 λ 2 2 † λ u y 3 Y g u 16 3 4 2 2 y 4 g λ 2 8 Y λ +14 Y  4 2 λ λ λ y † − 4 15 u + 4 u 4 − λ | 2 3 2 3 +  | 2 3 2 1 +2 Tr 3 Y  Y g 12 2 λ 3 1 4 − λ  | λ 4 y d ∗ y 4  g  y y 4 2 4 4 1 2 | 3 +8 8 − | λ y Y 2 1 24 y 11  g 1 λ  λ 3 ∗ 2 | 4 3 λ y y  † 15  Tr 200 9 | y † e 4 2 2 y u 2 λ − 3 λ 3 2 − 3   20 4 g Y g − 4 Y − +100 y 9 2 +2 λ 2 y 2 Tr λ 2 e y | 4 2 3 4 1 | 4 4 u 24 λ 4 9 2 2 − 1 λ λ 4 | | 1 3 Y 2 g y 3 − +20 15 Y 2 g λ 2 3 2 λ 2 4 y − − λ − y 9  † 2 4 + λ 3 g 9 | y y u λ | | 2 2 2 2 + | |  2 2 1  2 1 λ | 2 | 2 4 2 17 38 +4 Y g † 1 2 − Tr λ g λ 4 d 4 g y y | 4 u 1  y 2 4 | | y y  + Y  1 4 y 2 100 | 3 Y | 2 4 1 15 +4 λ † | 20 d 2 y 1 u 2  2 2 y 20 λ 1400 2000 |  2 3 λ 3 4 y 117 Y † − y Y g − 2 + 1 u y 2 +24 − λ | − − 2  1 − u 4  g 2 , 2 3 Tr 2 Y 1 + 19 | | , g − 1 2 Y λ  3 4 u 100 λ  + 2 3 +14 4  2 y Tr +4  † 3 † 2 λ    1 2 | +40 y e Y 3 λ u y 2 2 3 2 3 2 2 2 | 10 + 2 4 2 4 λ | ∗ | 3 − g 4 4 ∗ 3 4 1 y Y  Y 3 λ λ λ 2 4 λ 1 2 4 y y λ λ Tr  e y g | | u − + 5 λ y g y 4 2 2 4 + 4 24 Y | 2 4 Tr + 24 2 2 + + Y 4 1 2 y  y ∗ y 3 λ | 1 +9 4 y 2 ∗ 3 †  λ 3 3 g 3 † g 1 | u 1 y + 4 u y 2 − g 1 +12 y y 3 y | λ λ 3 4 y 200 3 4 y 72 3 3 Y  3 4 Y 3 +24 2073 2 9 2 Tr 2 | λ 3 1 2 λ 4 u λ λ y u λ 4 4 4 y 1 4 λ y − + − λ λ 16 y 4 9 2 2 | 2 Y 2 + − +4 Y 2 g 2 λ λ 2 1 1   1 † g – 29 – − † 6 | 2 12 3 3 3 g , u  u y † − y − 2 − y +8 3 2 u g y +6 +6 9 † λ λ Y 2 9  2 ∗ | 2 1 Y u − 4 y ∗  4 2 Y 2 3 2 3 2 † 1 | 8 4 100 g u | y y u u 40 2 4 Y 2 − y y u 1 g 8 +4 2 4 y λ λ 1 2 | 2 2 4 +15 Y Y 3 Y 2 u | λ − y 259 3 2 Y − g g y − 3 λ |  2 3 3 y u 19 5  λ Y y y  2 2 24  3 4 2 1 2 λ 2 | | 2  λ | λ 1 +2 +2 Y 3 † 2  +  4 e 10 1 y 3 3 2 † g 4 4 4 Tr y 4 2 − u + − + g Tr 3 Y y − y 2 32 λ 3 9 5 λ λ g 1 Tr | 4 | 2 + Y +4 2 2 e − λ 9 5 g | 1 2 2  19 1 2 2 4 2 y 1 ∗ 3 1 4 u λ λ − 2 Y 4 3 | − g 2 4 | g λ λ y  λ y 4 y +60Tr 2 2 3 , 2 4 +9 Y +  y 3 64 4 4 2 2 1 1 2 2 λ ∗ 4 2 2 − 1 g | g 2 3 2 −   λ 8  y y g g y 1 | 28 67 g y 2 ∗   2 | 4 | − † † 2 4 λ Tr − d d 2 2 4 | 9 4 λ g 4 y 3 15 5 + λ 2 3  − 2 y Y Y 4 y − 2 63 4 1 3 | 9 | λ † 78 2 ∗ 4 λ +8 +8 − 3 +80 u y + 2 u u g 2 y 3 1 + 100 | y 12 12Tr y − 8 4 4 y 4 2 2 2 + 2 g 2 Y Y Y y  − 4 28 2 | λ 1 3 | 1 1 3 g g 4 | y 1 † † g † u − − 2 2 10  − 2 − u u y λ u y 4 y y 3 2 2 g 1 − † 2 4 Y y 3 2 λ 12 2 2  u Y Y  2 3 Y  λ y | g λ † + 2  | 2 g λ ∗ † y λ +3 +3 1 u † u u 2 u Y λ 4 u d − 2 2 2 g +8 1 2 y 3 3 1 2 40 9  Y | u Y Y 4 λ Y Y 2 363 10 Y g g ∗ 16 3 − ∗ † † 3 +4 | λ λ 2 u 4 Y  u u d u + − y − 2 4 2 2 y 2 2 y ∗ 4 Y +14 − + |  − | Y Y Y Y ∗ 2 1  2 − y g g y 3 +54 +3 +6 | 4 6 4 4 Tr |  1 1 1 d d ∗ y y    4 2 | 3 2 y 2 2 2 4 2 4 3 | g g g Tr Y Y +2 3 2 y 4 | 15 15 y y 3 4 1 ∗ λ Tr λ λ λ λ 1 4 2 | y Tr Tr λ   2   y | 2 2 2 4 2 2 g 2 1 1 1 1 2 y − − y 9 2 4 2 1 y | 1 λ  3 40 27 3 g g g g g g 1 153 100 100 1 2 3 y  4 λ λ λ   1 y λ y , , 3 3 λ g λ 2 50 2 5 5 9 5 4 − − 171 45 16 54 10 12 15 9 2 1 2 12 λ 12 λ 4 y = +4 = = + = 0 = 0 = + − +12Tr + − − + + +12 +4 − +9 +25 +25 + − + − + − − +36Tr 0) 0) 1) 2) 1) 2) , , , , , , 2 2 2 2 3 3 (2 (1 (1 (1 (2 (2 λ λ λ λ λ λ β β β β β β JHEP01(2019)224 , 8 2000 2000 GeV GeV 14 14 3 =2×10 =2×10 and ∗ 3 S S 1500 1500 ∗ 4 y ,M ,M y 7 S S 3 3 4 y 1 GeV, are =M =M y λ λ . [GeV] [GeV] 2 A A 1000 1000 M M λ GeV,A GeV,A +20 5 7 2 2 | 150 ∗ 3 =10 =10 3 S S 3 y = 173  500 500 4 y ∗ | | λ 2 2 | t 3 2 2 y  2 y

λ=0.5,μ λ=0.5,μ

λ

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y β β tan M tan | 4 1  24 y y 3 1 50 − y +4 2000 2000 2 GeV. 2 3 . − GeV GeV |  ∗ +20 2 3 ∗ 14 14 4 +4 1 4 y y y | 3 | y 3 2 2 2 2 y 2 | =2×10 =2×10 y 1500 1500 S S y 2 3 λ λ | . = 172 y y 2 2 1 9 | t =0,M =0,M g y 4 λ λ  17 − +20 [GeV] [GeV] 8 y ∗ 4 A A 2 M ∗ 4 4  2 15  1000 1000 | M M y 3 y ∗ 1 GeV,A GeV,A , obtained for 3 λ 3 3 y 5 7 + y y 6 y y | 2 5 2 =10 =10 2 | 2 + S S − | y +4 3 y 500 500 4  ∗  y 3 | y 2  2 y 16 | 2 but for y λ=0.5,μ λ=0.5,μ 2 ∗

2 λ and



6 5 4 3 2 1 6 5 4 3 2 1

2 λ β β tan λ tan y 2 5 2 1 | λ + , +8 5 4 g 3 4  −  | 4 y − 3 2 4 | 4 3 2 2000 2000 2 2 | GeV GeV – 30 – λ y y = 174 GeV and are displayed as figures g + + | 3 14 14 1 2 2 2 + y t  y | | 3  λ ∗ 4 3 2 =2×10 =2×10 2 1 − λ S S y y M y 1500 1500 − | g 3 3  ,M ,M 2 4 2 y S S y 2 | g 2 2 4 =M =M +5 λ λ y [GeV] [GeV] − y 3 2 +68 y 4 A A 1 | 3 2  1000 1000 M M g 2 4 | −  4 GeV,A GeV,A +8 λ + 2 2 7 5 | y 1 4 1 | λ +3 3 y =10 =10 y 2 S S y − 2 . Same as figures  + 500 500 | y  2 4 2 λ 2 2 2 2 4 | 2 GeV and | g 3 . g 4 λ 4

λ=0.3,μ λ=0.1,μ

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1 y

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+ y β β tan − tan | +20 | g + 2 4 ∗ 3 3 ∗ 3 4 3 5 λ y λ y y λ 2 2 3 3 2 4 − 3 2000 2000 g y = 172 y λ y GeV GeV 2 Figure 7 λ 1 5 | 1 8 14 14 t y 3 y − +7 − y +2 | 2 2 M 4 14 2 16 =2×10 =2×10 2 3 4 | 1 1500 1500 S S λ y   4 g λ 1 2 2 y | 2 y 16 | =0,M =0,M ∗ 2 9 λ λ 2 50 2 3  [GeV] [GeV]  y y , A A 4 |  λ 2 1000 1000 M M − λ y 4 8 GeV,A GeV,A 7 5 = = 0 +25 +2 − − + + =10 =10 S S 2) 1) , , 500 500 2 2 (2 (2 λ λ λ=0.3,μ λ=0.1,μ

β β

2 1 6 5 4 3 2 1 6 5 4 3

β β tan tan In this appendix, weon show the our effects results. of uncertaintyregenerated The in for results the shown measurement of inrespectively. top figures pole mass C Results for different values of top pole mass JHEP01(2019)224 ] 2000 2000 GeV GeV 14 14 ]. =2×10 =2×10 Nucl. Phys. S S Erratum 1500 1500 , , ,M ,M [ S S , =M =M λ λ ]. [GeV] [GeV] SPIRE SO(10), A A 1000 1000 M M IN GeV,A GeV,A D 5 7 ][ 5 =10 =10 S S SPIRE (2004) 65 500 500 hep-ph/0212348 IN [

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β β tan tan (2005) 073 B 699 ]. 06 2000 2000 GeV GeV 14 14 (2003) 056 =2×10 =2×10 1500 1500 SPIRE S S hep-ph/0302073 = 174 GeV. orbifold grand unified theories JHEP [ t IN 01 =0,M =0,M , λ λ D [GeV] [GeV] M - A A 5 1000 1000 M M Nucl. Phys. hep-ph/0403065 GeV,A GeV,A , 5 7 ]. [ ]. ]. grand unified theories via five-dimensional JHEP =10 =10 S S ]. 500 500 but for λ=0.5,μ λ=0.5,μ

SPIRE

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SPIRE β β tan tan SPIRE , (2003) 116004 IN SPIRE IN IN 4 SO(10) Superstring theory. Vol. 1: Introduction SO(10), ][ IN ][ (2004) 262 ][ 2000 2000 Constructing GeV GeV – 31 – ][ D Quarks and leptons between branes and bulk Bulk and brane anomalies in six-dimensions 14 14 Order and Anarchy hand in hand in Supersymmetric unification without low energy 5 D 67 =2×10 =2×10 S S 1500 1500 ,M ,M B 593 S S Split supersymmetry =M =M λ λ [GeV] [GeV] A A 1000 1000 M M ), which permits any use, distribution and reproduction in GeV,A GeV,A 7 5 ]. Phys. Rev. . Same as figures =10 =10 S S , hep-ph/0209144 hep-ph/0406088 500 500 hep-ph/0304142 [ Unification in Flavor hierarchy in [ Phys. Lett. arXiv:1407.2913

λ=0.3,μ λ=0.1,μ

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, SPIRE β β tan tan [ IN CC-BY 4.0 ][ 2000 2000 Figure 8 GeV GeV 14 14 This article is distributed under the terms of the Creative Commons (2003) 231 (2003) 209 (2005) 487] [ =2×10 =2×10 1500 1500 S S (2014) 095 ]. =0,M =0,M λ λ [GeV] [GeV] 09 A A B 648 1000 1000 M M B 563 B 706 GeV,A GeV,A 7 5 SPIRE =10 =10 S S IN hep-th/0405159 500 500 JHEP Lett. from heterotic strings [ wave function localization [ Cambridge Monographs on Mathematical Physics (1988) [ Phys. ibid. supersymmetry and signatures for fine-tuning at the LHC T. Kobayashi, S. Raby and R.-J. Zhang, F. Feruglio, K.M. Patel and D. Vicino, H.D. Kim and S. Raby, R. Kitano and T.-j. Li, T. Asaka, W. Buchm¨ullerand L. Covi, M.B. Green, J.H. Schwarz and E. Witten, T. Asaka, W. Buchm¨ullerand L. Covi, G.F. Giudice and A. Romanino, N. Arkani-Hamed and S. Dimopoulos, λ=0.3,μ λ=0.1,μ

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