Jhep04(2020)002

JHEP04(2020)002 d Springer April 1, 2020 , : March 16, 2020 March 17, 2020 Yu-Bin Liu : : February 12, 2020 : a,b Revised Published Accepted Received [email protected] , Shu-Min Zhao, SSM) introduces three singlet right- a,b,c Published for SISSA by https://doi.org/10.1007/JHEP04(2020)002 µν and muon magnetic [email protected] , SSM Zγ Jin-Lei Yang, µν → [email protected] a,b , h problem and generate three tiny neutrino masses in the MSSM, µ [email protected] . 3 , Hai-Bin Zhang, SSM. Besides, we consider the two-loop electroweak corrections of muon 2002.04370 a,b,e The Authors. a,b µν Supersymmetric Standard Model ( c Supersymmetry Phenomenology

To solve the ν , [email protected] is 6.6, which still is plenty of space to prove the existence of new physics. In in the from Zγ Zγ µ → → School of Physics, NankaiTianjin University, 300071, China College of Physics, ChongqingChongqing, University, 400044, China E-mail: [email protected] Key Laboratory of High-precision ComputationApplication and of Quantum FieldBaoding, Theory 071002, of China Hebei Province, Institute of theoretical Physics, ChineseBeijing, Academy 100190, of China Sciences, Department of Physics, HebeiBaoding, University, 071002, China b c e d a Open Access Article funded by SCOAP contributions compared with one-loop electroweak corrections. Keywords: ArXiv ePrint: present observed 95% CL upperh limit on signal strength ofthis the work, 125 GeV we Higgs investigate bosonh the decay signal strengthanomalous of magnetic the 125 dipole GeV moment Higgs (MDM) boson in decay channel the model, which also make important Abstract: the handed neutrino superfields,sneutrinos. which The lead mixing affects to the lightest the Higgs boson mixing mass of and the the Higgs couplings. Higgs The doublets with the Chang-Xin Liu, and Tai-Fu Feng Higgs boson decay dipole moment in the JHEP04(2020)002 , ], 5 1 10 6 ] 6 (1.1) 11 [ . and its , which 0 in a new ]. But no Zγ Zγ 10 Zγ 10 – → . → 7 [ h h → ) can be detected Zγ h b, τ → = h f ( ¯ f , there is still plenty of space f ]. Testing the SM nature of the Zγ . → 16 – → h 14 h 14 GeV . 0 ) and 6 – 1 – 10 Z,W . = ], the measured mass of the Higgs boson now is [ ] will detect the Higgs boson decay V 5 = 125 ( – 13 3 h ∗ – is observed and the present observed 95% CL upper limit m 11 ]. So, for the decay VV 9 Zγ Zγ is crucial for broadening our understanding of the electroweak → → 7 Zγ h → γγ h , → h 9 → γγ h h 13 1 2 → 12 h SSM µν 5.1 Muon MDM 5.2 The decay ]. Combining the updated data [ or high energy largemay collider see [ the indicationrate of compared new to physics.symmetry spontaneously Moreover, broken the (EWSB) measurementHiggs pattern of boson [ state and inspecting possible deviations in its coupling to the SM particles which is consistent withLHC the also value has of reportedevidence the for the standard the searches model decay for (SM)on the its in rare signal the decay strength errorfor process is range. new 6.6 physics The [ physics (NP). model In to show this how large paper, new we physics contributions. will In investigate the future, the high decay luminosity Therefore, the accurate Higgs bosonspace mass gives for the most the stringent standard constraintsearching on for model parameter the and properties itsboson of various decays the extensions. Higgsby boson. The precise Now, next values. the step signal The is strengths signal focusing for strength on the for Higgs their combined final states is 1 A great success of the2 Large Hadron Collider (LHC) is the discovery of the Higgs boson [ 1 Introduction 6 Summary A Form factors 3 The rare decay 4 Two-loop corrections of muon5 MDM Numerical analysis Contents 1 Introduction 2 The JHEP04(2020)002 ] ), T Zγ 83 , (2.1) (1.2) → 82 Z,W are the ], h c i ] and SM 6 = e SSM have 64 V µν (the index ( ]. To be more ∗ , and ˆ i 62 c i ˆ e ˆ d , , SSM briefly, about i VV c , k ˆ ν c i ˆ ν c j µν c u j ˆ e → ˆ SSM [ ν b i c i = ˆ L , we give the decay width ˆ h ν µν , a d 3 , T i ˆ 10 ijk H ˆ L κ − γγ ij , 3 1 e 10 Y i supersymmetric standard model , and the right-handed neutrino → + ˆ d d × respectively show the numerical + ν b , u ˆ i h H c j 6 ˆ 7) ˆ ˆ H u d . a b i d 7 ˆ ˆ Q from H and , we introduce the a c d i = ˆ µ ν 8 ˆ u 2 i H . T i ˆ ] of the minimal supersymmetric standard λ H ij ˆ Q d ab includes the two-loop electroweak corrections 55 Y , 4 – 2 – = (26 and section + − − d c j 5 c j ˆ ˆ u ˆ H ν SM µ a i , i a a 0 ˆ d ˆ Q L ˆ b b u u − H problem [ . Section ˆ ˆ H H µ ij ij exp µ Zγ ν u = a , and the masses of the Higgs bosons in the Y Y T d = → ab µτ ˆ SSM to see how large new physics contributions. µ H h ]. ab + a , → µν 47 ∆ ]. In this paper, we will investigate the 125 GeV Higgs boson decay = – ] through introducing three singlet right-handed neutrino superfields 0 u h ]. In near future, the Muon g-2 experiment E989 at Fermilab [ ˆ 63 SSM. Simultaneously, the accurate theoretical prediction of the muon 14 H 60 – W 81 SSM contains Yukawa couplings for neutrinos, two additional types of , ), – – ] µν + u 61 in the 56 µν ] can solve the ˆ b, τ 65 48 H 54 ,[ SSM Zγ – = c i 3). The neutrino superfields lead the mixing of the neutral components of the = ν , 48 f → µν 2 ( T , u h ¯ ˆ f H deviation from the SM, constituting an augury for new physics. In our previous f = 1 The paper is organized as follows. In section In addition, the current difference between the experimental measurement [ As one of the candidates of new physics, the i SSM) [ σ ( → c i µν ˆ denotes the transposition) represent SU(2) doublet superfields, and ˆ where In addition to thepotential MSSM of the Yukawa couplingsterms for involving quarks the and Higgs chargedsuperfields doublet leptons, ˆ superfields the super- the superpotential and the soft SUSY-breakingand terms. the signal In strength section of of the muon anomalousanalysis MDM. and summary. Section Some formulae are collected in appendix. 2 The work, we have studiedprecise, the here muon we MDM will at considerframework one-loop of the level the two-loop in diagrams the ofanomalous the MDM muon can anomalous conduce MDM to in constrain strictly the the parameter space of the model. still stands as apredictions potential for the indication muon of anomalous MDM theSM have extensions existence been [ of discussed in new thewill physics. framework measure of Up various the muon toa anomalous now, 5 MDM several with unprecedented precision, which may reach theoretical prediction of the muon anomalous magnetic dipole moment (MDM) [ represents an interesting but not yet conclusive discrepancy of 3.5 standard deviation, which ν Higgs doublets with the sneutrinos,In which our is different previous from work,h the Higgs the sector Higgs of bosonbeen the MSSM. researched decay [ modes channel physics. Within various theoreticalhas frameworks, been the discussed 125 [ GeV Higgs boson decay ( model (MSSM) [ will represent a major undertaking of modern particle physics and a probable probe of new JHEP04(2020)002 c 1 i 3 ν , M 2 , (2.2) , and . 2 c ˆ . λ i = 1 . , , and c . 3 2 ˆ λ + H M c k i, j, k + H , ˜ ν 3 c j c j ˜ ˜ e ν M b i c i ˜ ˜ ν L a are generated, with d ijk ) H b u c = 1, and j κ ij ˆ ˜ H ν ) κ a ∗ e d 12 c i A a j Y ˆ ( ˜ H ν ˜ e L 1 3 µ c ∗ ij A ˜ 2 ν a i ab + ˜ L . m ]. b + ( u ij ˜ . c j + 2 L H denotes the spin of the concerned ˜ c d 96 . a a d u , b i m and SSM are given by S ˜ H H Q 95 + a i , the tree-level scalar potential receives c ∗ i a d ) of the singlet neutrino superfields ˆ + H a u µν ˆ ˜ c j ν L c i ˜ i b H d 1 u ]. ) H ν ) explicitly violate lepton number and R- soft ∗ ˜ ˆ λ ij c i λ u H ) 1 L ]. ˜ 96 i λ d 2 H d ˜ 2.1 λ ε – c ij A Y 1 ˜ m 2 d ( 50 ab d , – 3 – 91 M ab m A , + 49 a + d + ]. R-parity is violated if either the baryon number − 87 + ( 2 c j , H c ˜ c j j λ ˜ ∗ u 60 ˜ 2 a ν ˜ ∗ u d – c i a i 50 ˜ a i λ ], the authors analyzed the gravitino dark matter can- , H ˜ 2 u ˜ ˜ L 56 Q d [ b 94 c ij u b 49 u M 2 H ˜ – 2 u , once the electroweak symmetry is broken. The last term S H i H m ]. + m c i 91 ij ij +2 ˜ ν ) are dimensionless matrices, a vector, and a totally symmetric 3 ) SSM also was analyzed [ + 90 h + ν B ˜ λ u ) is not conserved, where i – c j κ Y 3 a j Y µν ˜ e λ L +3 ν ˜ λ ˜ u ∗ Q L 3 84 c i A ∗ , A = ˜ ( e a i ( 1) M ˜ c ij h ab 49 -term contributions [ µ Q ˜ , and − 2 e ab ij λ F 1 2 ]. In refs. [ m SSM, whose lifetime is long lived compared to the current age of the ˜ 2 Q , 2 are SU(2) indices with antisymmetric tensor = ( − + + + , 97 and m µν R E = c - and j = 1 u,d,e,ν ˜ ν D Y D soft a, b ij SSM can generate three tiny neutrino masses at the tree level through TeV scale ν −L Y The general soft SUSY-breaking terms of the The dark matter candidate must be stable on the cosmic timescale, so that it is still In supersymmetric (SUSY) extensions of the standard model, the R-parity of a particle In the superpotential, if the scalar potential is such that nonzero vacuum expecta- µν ) or lepton number ( = , respectively. In addition to the terms from 1 i B ˆ Here, the first two linesnext contain mass two squared lines terms consist ofdenote squarks, of sleptons, Majorana the and trilinear masses Higgses. scalar corresponding The λ couplings. to SU(3), In SU(2), thethe and last usual line, U(1) gauginos didate in the Universe. The gravitinobe turns searched through out gamma-ray tomatter observations candidate be with in Fermi-LAT. an the Recently, interesting the candidate axino dark for DM, which may longer stable. In thisthe context, dark the neutralino matter or (DM). thecan However, sneutrino still other are be SUSY no used particles longer as such candidates candidates as for [ the gravitino oraround the today axino [ seesaw mechanism [ is defined as ( component field. The lastparity. two terms R-parity in breaking eq. implies ( that the lightest supersymmetric particle (LSP) is no tion values (VEVs) ofare the induced, scalar the components effectiveε (˜ bilinear terms generates the effective Majorana massesthe for neutrinos at the electroweak scale. Therefore, addition, tensor. are generation indices. Thefollowing. summation convention is implied on repeating indices in the singlet up-type quark, down-type quark and charged lepton superfields, respectively. In JHEP04(2020)002 – 98 (2.6) (2.7) (2.8) (2.9) (2.3) (2.4) (2.5) (2.10) 8 CP-even × , , , c i i ν ν ) υ limit, we give an υ R , . 2 ) + c i A + , ν 1 = υ m RR = ) 2 H ) + ∆ c ]. The mixing gives a i i = ν m ν R (˜ i (˜ 1 i c i i 53 2 2 , + 3∆ . The radiative corrections ˜ ν + h √ (∆ + 2 + ∆ β √ ], 1 2 υ < 50 < β , ) ]. Comparing with the MSSM, ) 63 c (2 i i + 2 sin 2 49 ν ν 63 , (˜ (˜ λ λ i 2 Z sin 2 ν A + 2 Z = = m υ c i − c i m 2 W ν ˜ = ν ˜ ν c , SSM. In the large i 2 W . 1 2 W /υ i κ 2 c s ˜ d u u e ν ], and so on. In the following numerical 2 H i µν h υ υ υ λ − 2 W i 2 m d s λ e i h β 2 = ξ λ 110 λυ λ , i – 4 – λ β 3 , λ ≈ A u 2 sin 2 . 2 h 109 υ is the mass squared of the right-handed sneutrino, tan 1 + + m 2 1 c 2 H = c ) 2 2 R ν ν 1 i m β υ 0 2 X u m 1 2 κυ , , 2 R A ) H u d ( c h υ m β υ ν cos 2 2 Z + + − κυ ], SPheno [ are the radiative corrections [ u m d sin 2 , d + 4 108 iP iP RR ' = 1 2 2 υ λυ – κ 3 1 + h + √ √ A = ξ 2 H d u √ 106 i h h m 0 d = ( ' and ∆ H = = 1 1 h R 0 0 d u SSM gets an additional term 2 R 2 2 X SSM, the left- and right-handed sneutrino VEVs lead to the mixing of the H H A m µν µν , ∆ comes from the mixing of the neutral components of the Higgs doublets with R 1 1 2 X can be computed more precisely by some public tools, for example, FeynHiggs [ A 1 in the In the Once the electroweak symmetry is spontaneously broken, the neutral scalars develop 2 H 1 ], SOFTSUSY [ m 2 H m 4 105 section, we willHiggs use boson the mass about FeynHiggs-2.13.0 the to MSSM calculate part. the radiative corrections for the where ∆ Here the right-handed sneutrinos, and whose concrete expressions are given by where neutral scalar mass matrix,rich phenomenology which in can the beapproximate Higgs seen expression sector for in of the the refs. lightest [ Higgs boson mass [ neutral components of the Higgs doublets with the sneutrinos producing an 8 and in general the VEVs: One can define the neutral scalars as JHEP04(2020)002 , , , , 0 F F − α 1 W S A + α (3.2) (3.1) /c ) hS 2 W g s , f ) boson, the Q W SSM, where − W ]. In figure hW W SSM, where , λ f γ γ g Z Z θ 16 µν W , , µν 2 ) x are ( i 1 denotes the charged hff , cos χ g i 2 A 3 . The form factors f

L, R in the 2 ) I n hχ , S i in the ˜ 1 g = W f χ ˜ f denotes the charged scalars, Zγ = ( hW W n ) ) , λ ( ˜ g Zγ f 1 i ˜ α f and S χ → S v , λ x i i → ˜ ˜ W ˜ , ˆ ) + ( W f f f ¯ h χ χ , λ ]. i i 2 f h x coupling, which is built up by the / W χ α ( 1 1 53 n S 0 Zχ , λ S /c n g A x f ) A γγ ( gauge boson, C x i ˜ 0 2 f 2 Z W ( 2 W e 1 χ

2 → s A 3 m h h / m m W f − m 1 ˜ 2 α SSM can be mainly given as h f gauge boson, 2 Z ˜ i Q 2 S f A 2 h = 2 Z χ 4 h m µν i m W i g m m ˜ − χ f hff − α i n Zχ is the 3 f ˆ v g S – 5 – g ˜ − I f f n hχ i + α ˆ v 1 χ W ]. In the supersymmetric models of the SM, there Q is the i f c hS . The concrete expressions of g 15 m N = (2 hχ γ γ 3 h N Z Z , g ) and the supersymmetric partners [ W A f g i 1) f − I ¯ m χ v Q i ) can be seen in ref. [ 4 − ,D , ˆ W 2 1 L,R is the mixing angle of sfermions π + I Zχ 2 Z n S t, b, τ = m 2 W f X t,b,τ U X C 64 c θ F 2 X Zγ = = = ± = e 1 ˜ /m , m,n f f ]. And the expressions of F S 2 i h f − W αG ( × +(2 + + → 61 m i /c boson loops [ = ¯ χ ) h i ± i ± = 4 χ ) = χ 2 W F S in the framework of the F S W i 1 i s S n λ f Zγ n Zχ C , g Q Zγ 2 h → − → f shows the sfermions. Therefore, the decay width of the loop induced Higgs h /m and θ ( 2 i are showed in appendix coupling in the SM is similar to the ˜ h h h i f 2 ¯ χ 1 m i NP A Zγ sin Γ . The one-loop diagrams contributing to the decay Zχ n 3 f = 4 I C → i shows the sfermions. and can be found in ref. [ x h ˜ f = ( ˜ 2 f / ˜ f 2 1 ˜ f h ˆ where v A g with scalars, and boson decay heavy top quark and are more kinds ofthird-generation particles fermions can make ( contributionswe to plot the the LO one-loop decaydenotes diagrams width, the contributing fermions to and the the decay charginos, denotes the fermions and theand charginos, 3 The rare decay The Figure 1 JHEP04(2020)002 (4.1) (3.4) (3.5) (3.3) is the h SM h ) β β , charged scalars c µ χ , χ ( f ) ] ) h NP h SM SSM is mediated by 61 Zγ ∗ SSM. Γ Γ ), we can quantify the / / µν γ µν ) ) → VV 3.5 µ µ h gg gg ( , → )–( ) ) → → NP h , in the ( 3.3 h h Zγ Zγ ( ( αβ NP F → → Zγ ) + Γ Γ NP SM µ l h h Γ Γ ( ( − → α γγ , αβ Z,W S ) ) h σ NP SM h NP h SM X = → µ gg gg Γ Γ V l h µ BR BR ( a = → → ) 0 η β µ bosons, standard fermions ) + b µ NP χ χ ) ) ν h h ¯ ( f e ( ( – 6 – m f W gg gg 4 (ggF) NP (ggF) SM − ) + Γ → → → = NP SM h BR BR h h gg W σ σ ( ( ( µ µ at leading order (LO) in the . When the supersymmetric particles are more heavy, → ˜ = NP MDM f h NP NP SM h SM Γ h Γ Γ Γ Γ L Zγ ( ggF Zγ = ≈ µ NP → SSM can be given as the eﬀective Lagrangian b,τ,c,s X h = − f + Γ µν W is a physical quantity that can be observed directly, and it can be (ggF) (ggF) ' NP SM Zγ h NP and sfermions σ σ ) 0 η β µ Γ i a ν χ χ ( → χ h − . The main two-loop rainbow diagram (a) and Barr-Zee type diagrams (b,c) in which µ µ W The decay width of , charginos α 4 Two-loop corrections ofThe muon muon MDM MDM in the where we neglected thetotal little decay contribution width which ofsignal is the strength SM rare for Higgs or the boson. invisible, Higgs boson and Through decay the eqs. channel Γ ( and the total decay width of the 125 GeV Higgs boson in the NP is [ normalized to the SMthe values, Higgs where production ggF cross stands sections for gluon-gluon fusion. One can evaluate charged heavy particle loopsS built up by the contributions of supersymmetricboson particles decay will be small.written by The signal strength of Higgs Figure 2 a closed fermion loopcontributions to is the attached muon tointernal MDM particles. the are virtual obtained gauge by bosons attaching or a Higgs photon on ﬁelds, all the possible corresponding ways to the JHEP04(2020)002 ], β (4.5) (4.6) (4.7) (4.2) (4.3) (4.4) , γ ) α , 0 η γ χ ) [ SSM are . Includ- β 0 η ) ) i 2 µ χ 0 η 0 η ) β χ χ 2 µν W χ = 2) R

β β (a-c). Under 0 η C − W χ χ R 2 0 η αβ W χ W χ β L L g χ C σ ( β 0 η C C 1 2 χ 0 η 0 η W χ R β χ χ W χ R C = β β

C µ W χ R − a W χ W χ R R C + 2 C C

0 η ]. SSM can be written by − 0 η χ + − χ β 0 η 62 β . µν χ 0 η 0 η ]. , β χ χ z W χ L , β β , W χ L 53 ) ln C W χ L γh µ β loop C 0 η z z W χ W χ

R R χ a − χ C β β 0 η C C − − 6( χ + χ 0 η 0 η ], the main two-loop rainbow diagram 1 two µ y y β χ χ S − L a W χ L β β 80 ) ln C WS µ , C 2 + W χ is the mass of the muon, L 2 ( a

y W χ W χ χ L L 0 η 75 C µ < 2 ( χ + C C χ − ( ( loop β m 1 < ) x S − L < < − α – 7 – , the concrete expression can be approximately ) W χ C R 2 S SSM, the two-loop corrections are given as WW µ one µ ( ) ) can be found in ref. [ − α a W C a − − 2 S

α α < , µν , m 2 S 2 S m = o ) = ln = + can be found in ref. [ ) 2 W loop , m 2 h 2 F ∗ 2 , m , m −

) 0 η 2 W C m m loop 0 η 4 χ , m 0 η 2 W 2 W χ χ β − one µ χ 2 F µ SUSY x, y, z 0 9 β are the contributions corresponding to ﬁgure , m a ( χ a m , m , m m 2 F two µ W χ J R − α ( 2 γh µ 2 F 2 F W χ a L S g L m ' C J 1 + ln ( C m m 0 η , a F C

β ( ( 3 χ ( J 10 χ m β J J 8 3 5( < 4 2 W WS µ 2 3 4 3 m + n π F 2 W m − W χ L 4 , a µ − − = m 2 µ π m C 4 9 36 ( 128 2 µ 1 9 16 2 9 179 m F m π WW µ < . Here, we ignore some two-loop diagrams which have low contributions, F √ m − − − F a m 32 F G 2 G − 192 G + + + +11 × ) represents the operation to take the real part of a complex number, the = = = SSM, there are many free parameters. We can take some appropriate parameter denotes the muon which is on-shell, ··· ( γh µ µ µν WS µ l < a WW µ a a represents the electromagnetic field strength and muon MDM, The two-loop diagrams can give important contributions to the muon MDM in a αβ concrete expressions for couplings 5 Numerical analysis In the space, so that we can obtain a transparent numerical results. First, we make the minimal where Here, where the terms the assumption written as reasonable parameter space. According to(a) refs. [ and Barr-Zee typeshown diagrams in (b,c) figure contributing todue the to muon the MDM decoupling theorem. in the In the F ing two-loop electroweak corrections, the muon MDM in the where the one-loop corrections where JHEP04(2020)002 . , ] γ c 3 2 s ˜ u M 116 X ], we SSM (5.4) (5.1) (5.2) (5.3) – = 90 , m → , µν 2 1 114 ij , , ¯ B δ = 1 TeV, ij M ij i e δ δ c , ,M c c i i ˜ e Y ˜ c c ˜ 2 ν 2 d 300 GeV and e ν ν m − λ, A m m υ ======, ], we can take rea- , in that both get β, υ i , c i ˜ c ij c ij L ij ij κ γ ν GeV) in the ˜ ˜ 2 ν ij 2 d ) u 49 s A d 4 e m Y X i Y Y − e u d ] and BABAR [ , A A A (10 i → ( l d . = = υ 4 m ¯ 113 B , − ij ij ∼ O ) ) = i d 10 u = 2 TeV, i ν 112 Y Y e SSM in ref. [ υ × d = 500 GeV, u 3 , , λ 2 A A , µν λ ( ]. Through our previous work [ c 1 ( ˜ jk 19) d 6 A . δ , m , υ 0 , m , m ij ,Y ij ij 4, i δ ij ij . δ d d c i δ δ κδ c = i ˜ i ˜ 2 u 2 e υ κ greatly affect the lightest Higgs boson mass. e ν m ], BELLE [ 49 2 , . = 0 A Y a m m c 1 β = ˜ u – 8 – κ = = = = = 111 i m d ij c ij c ij ij 1, ˜ e 2 e ˜ ) ijk 2 u . ) = (3 ]. To agree with experimental observations on quark ) = ν γ κ Y s 63 3 and tan κ ν , = 0 2 X , c 3 A A ,Y 1 ˜ ( u ( λ i ˜ , Q , can be constrained by the minimization conditions of the u u → m ij ij υ m u c d i m ¯ , L L ˜ B . The current combined experimental data for the branching 2 ν ]. So in the following, we also consider the constraint from the t V V stand for the up-quark, down-quark and charged lepton masses, γ i i A = m s 68 i u d l i Br( Y Y X = u m 3. , , m Y 3 = = , m , u ij → , jk ij δ ) and left-handed sneutrino VEVs ij 2 δ ij ij A measured by CLEO [ i δ ¯ 7 δ and d λ, Y = 1 TeV for simplicity. Considering the direct search for supersym- u B ˜ ]. ij ], we take ˜ i 2 Q 2 L , λ − i Y Y ν γ 6 e d denotes the CKM matrix. s Y m m κδ A A 117 † (10 X = 1 d , m = = = = = L i = i V u ij ij ij ) → u enhancements from a Higgsino-sfermion-fermion interaction vertex with a down- ν ˜ ˜ ijk L 2 L d ∼ O 2 Q λ m Y κ V SSM [ λ β ¯ i A m B 5 TeV. For simplicity, we will choose the gauginos’ Majorana masses m ν . A = . i, j, k Y µν ( ] t = 6 A V In the supersymmetric model, there is a close similarity between the anomalous mag- Through analysis of the parameter space of the = 2 2 , 1 3 u give [ In the next numericalin analysis, the we use our previous work about the rare decay netic dipole momentlarge of tan muon andfermion the Yukawa coupling branching [ ratiobranching of ratio of ratio of metric particles [ M As key parameters, Therefore, the freeand parameters that affect our next analysis are tan plings via the TeV scale seesaw mechanism. sonable parameter values toA be where the and we can find the valueshave of discussed the in masses from detail PDG how [ the neutrino oscillation data constrain neutrino Yukawa cou- and where neutral scalar potential seen inmixing, ref. one [ can have flavor violation (MFV) assumptions for some parameters, which assume JHEP04(2020)002 c 3 is × ≤ ≤ ˜ u c 7 4 m . ν ). In (5.6) (5.5) − υ , where 10 1.2 SSM and 4 68 GeV × . . µν is large, the c 92 ν . c ν υ λυ . Here the steps varying with the SSM with 3 3 a 1 µν ≡ R and figure SSM could reach the given in eq. ( µ (b) pictures the ratio 3 σ = 3 µν 0 SSM with 124 2 . . SSM with 2 M µν µν in the MSSM can be about 12% when ) and the ratio a is small. R loop in the SUSY µ c − a is large. Here, when , we plot figure ν γ SUSY µ υ c s 1 , two µ ν a MSSM X a υ ) ( loop loop − → − − SSM. We define the physical quantity loop ¯ − one µ two µ B ), when µν 4 40 2 – 9 – a a SSM experimental error is considered. two µ 1.2 µν a ≡ σ ) , which coincides with the decoupling theorem. We ( c a ν R υ loop . Normalized to the one-loop corrections of the muon TeV 1 4 0.3 c − TeV 1 14 0.5 / ν β TeV 1 4 0.3 / 3 c / υ ˜ c u t two µ ν and the muon anomalous MDM in the a Parameters Min Max Step tan v m A ( 4 , where a 3 SSM. − ≡ 10 − 10 µν m R 10 × × can reach around 16% when 06 . 9 . Scanning parameters for the muon MDM with a . 4 R 49 ≤ , we plot the muon anomalous MDM , where the gray area denotes the muon MDM at 3 ≤ ) c 3 ν γ µ s υ Table 1 52 GeV, the branching ratio of a . X ∆ (a), the numerical results show that the muon anomalous magnetic dipole moment 125 is decoupling with increasing ≤ → 3 To see the difference of two-loop contributions of muon MDM between the To show the two-loop contributions of the muon MDM, figure In figure Through scanning the parameter space in table ≤ ¯ 10 varying with the parameter B − h a SUSY µ anomalous MDM in the the MSSM, we define the physical quantity R MDM, the ratio one-loop corrections of thetions. muon MDM The are numerical decouplingsmall. results quickly also Therefore, than the show the two-loop that two-loop corrections the correc- also ratio make important contributions to the muon figure a can see that the valueexperimental of center the value muon shown anomalous in MDM eq. ( m Br( 10 parameter parameter space isthe broad light enough stop to massfrom contain 1 is TeV. the easily possibility ruled of out more. bythe the red Considered experiment, dots that we are theafter scan being corresponding the constrained physical by quantity’s parameter the values lightest of Higgs the boson remaining mass parameters in the to show the ratiopresent of numerical two-loop analysis, corrections we to scanare the one-loop large, parameter corrections because space of shown the the in running muon table MDM. of the To program is not very fast. However, the scanning 5.1 Muon MDM Firstly, we analyze the muon MDM in the JHEP04(2020)002 ), is 1. . c 1 . In ν 2.8 SSM . We υ . 4 µν Zγ Zγ ggF → , where the µ in eq. ( 2 h β . 9 (a), we plot the . 5 sin 2 2 Z m 2 W (a), we can see that the c (b). 2 W 4 2 s e i (b), we can know that when β λ i 4 λ 2 . In figure β (a) and tan c ν υ , where the gray area denotes the muon MDM c respectively denote two-loop contributions of is around 3 TeV. When the parameter ν and tan v can be down to 0.90 and up to 1.05. Here, the c – 10 – c ν ν υ υ ggF Zγ . The numerical results show that 0 MSSM ) µ β varies with is around 20%. In figure m loop m R − R . two µ SSM gets an additional term (b) vary with a can be more large. Here, compared to the MSSM, the varies with a µν m R m Zγ through scanning the parameter space shown in table R R and ( SSM and those of the MSSM, which can be given in section Figure 4 6 → varying with tan µν SSM h (a) and ggF Zγ µν ) µ = 6, the signal strength loop SUSY µ and figure a − β can reach about 27%, when 5 . two µ , we show that m a . is small, the ratio R 4 σ 0 β . green dots are theafter corresponding being physical constrained quantity’s bysignal the values strength experimental of constraints the above. remaining InWhen parameters figure tan lightest Higgs boson in the neutrinos with the neutralinos. 5.2 The decay In this subsection, we presentplot the figure numerical results of the signal strength for ratio large, the maximum of thetan ratio has extra right-handed neutrinosSimultaneously, the which right-handed can neutrino give superfields new lead contributions to to the the mixing muon of MDM. right-handed Here, ( muon MDM of the figure Figure 3 at 3 JHEP04(2020)002 , γγ . c ν → υ h 300 GeV, & . We can see 1 β ˜ τ . . β m Zγ → h SSM are in agreement SSM can easily account µν µν SSM have been investigated. (b) versus tan (b) versus the parameter varying with tan µν ggF γγ µ . ggF γγ Zγ/γγ β µ R ) in the (a) and b, τ ggF Zγ µ 4 40 2 = – 11 – f ( ¯ f (a) and the ratio 700 GeV and the lightest stau mass f TeV 1 4 0.3 TeV 0.4 4 0.2 TeV 1 14 0.5 & / β TeV 1 4 0.3 / ggF Zγ / c 3 → / 1 2 ], the signals of the Higgs boson decay channels ˜ c u µ t ˜ t ν h Parameters Min Max Step tan v M m A 61 m almost is around 1, which is consistent with the experimental ggF γγ µ . The signal strength ), and . Scanning parameters for the Higgs boson decay . In ref. [ Z,W ggF γγ µ = (b), we also picture the signal strength Figure 5 Table 2 5 V . The signal strength ( ∗ VV In figure Figure 6 → signal strength h When the lightest stopthe mass signal strengths ofwith these those Higgs in boson the decay SM. channels in the comparing with the MSSM. Thus, thefor lightest the Higgs boson mass in around the 125 GeV, especially for smallthat tan the signal strength value in the error range. Here, the relatively large stop mass and stau mass reduce the JHEP04(2020)002 ) in ggF γγ are γγ µ c i which ggF Zγ in the ν → µ c ν SSM has 71, when h Zγ υ . ( 0 µν , which may → NP . In addition, . Γ h Zγ / ) ggF Zγ µ → (a). The numerical Zγ Zγ/γγ h 6 R → . h ( SSM is in accord with that 55 NP . in figure Γ µν c ν υ ≡ can give more large contributions directly affects the mass of chargino. c ). Thus, the signal strength in the c ν ν SSM, being different from the MSSM. υ SSM still has a large deviation from 1, Zγ/γγ γγ υ γγ R µν µν → → h can have a large deviation from 1, when the h ( in the ]. However, high luminosity or high energy large NP – 12 – ggF Zγ 9 µ Zγ (b). We can see that 0 versus the parameter (b), the numerical results show that the signal strength → 6 5 deviation from the SM, constituting an augury for new h ) than Γ ggF Zγ σ µ Zγ SSM. In near future, the Muon g-2 experiment E989 at Fermi- → SSM, the three singlet right-handed neutrino superfields ˆ in figure is small. The parameter problem of the MSSM and generate three tiny Majorana neutrino h c c µν µν ( decay still is 6.6 [ ν ν µ υ υ NP (a) and figure Zγ 5 SSM can be around 16%. Compared to the MSSM, the leads to the mixing of the neutral components of the Higgs doublets with → c µν ν h υ ] built in the future will detect the Higgs boson decay SSM still has a large deviation from 1, even though the signal strength 13 µν – ] will measure the muon anomalous magnetic dipole moment with unprecedented SSM is in keeping with that in the SM. 11 83 SSM has a large deviation from 1, through small value of the parameter µν , in the 82 Here, we also consider the two-loop corrections of the muon anomalous MDM in the In this paper, we analyze the signal strength of the Higgs boson decay To see more clearly, we also plot the ratio We plot the signal strength Through figure is small. Here, small value of the parameter µν SSM. Normalized to the one-loop corrections of the muon MDM, the two-loop cor- SSM. Even though the signal strength of SSM also can be a dark mater candidate. The right-handed sneutrino VEVs lead to the c Zγ ggF ν physics beyond the SM. extra right-handed neutrinos whichMDM. can Therefore, the give two-loop new correctionsanomalous also contributions MDM make in to important the contributions the tolab the muon [ muon anomalous precision, which may reach a 5 strength of the collider [ see the indication of new physics. µν rections in the µν in the SM, the signaldue strength to of the smalldoublets mass of with chargino the and the sneutrinos. mixing of The the present neutral observed components of 95% the CL Higgs upper limit on the signal masses at the tree levelµν through the seesaw mechanism.mixing The of gravitino the or neutral thethe components axino mixing would in of affect the the the lightesta Higgs Higgs rich doublets boson phenomenology mass with in and the the the sneutrinos. Higgs Higgs couplings, sector which Therefore, of gives the 6 Summary In the framework of the introduced to solve the υ to the decay widththe Γ affects the mass of chargino anddoublets leads with to the the sneutrinos. mixing of the neutral components of the Higgs The small chargino mass gives athe large parameter contribution to the signalthe strength sneutrinos. The mixingwhich affects is the different lightest from Higgs the boson MSSM. mass and the Higgsversus couplings, the parameter µ in the results present that thevalue signal of strength the parameter JHEP04(2020)002 (A.6) (A.7) (A.1) (A.2) (A.3) (A.4) (A.5) , i pp ]. ) 1 − , λ ( SPIRE ) g IN − Phys. Rev. Lett. ][ τ, λ ) , ( 1 (2012) 1 1 I − τ GeV with the CMS ( (2017) 047 g 2 τ h B 716 11 2 125 ) . 1; 1 λ λ 5 + 2 − τ ≥ τ JHEP ( , − , arXiv:1207.7235 1 1; [ + 2 W 2 W ≤ , τ < Phys. Lett. c i s TeV ) , ]. 1 iπ − 2 τ λ , τ > − ( = 13 2 f (2012) 30 SPIRE s 1 + , /τ /τ IN − √ i iπ 1 1 ) ) – 13 – ][ 1 1 − − − − − 1 1 B 716 λ τ ) + ( /τ /τ ( p p f 1 1 f τ, τ h τ, λ − − − − ( Combined measurement of the Higgs boson mass in 2 √ ]. 2 ) 1 + 1 ) , 1 1 ]. ), which permits any use, distribution and reproduction in I 2 1 ) λ TeV with the ATLAS and CMS experiments λ − p p − 2 log τ 8 τ τ Phys. Lett. ( τ, λ 2 W 2 W − SPIRE Observation of a new particle in the search for the Standard Model ( c , s f τ, τ SPIRE 1 2( 2 1 + 1 1 arcsin IN h I − √ IN and Observation of a new boson at a mass of Measurements of properties of the Higgs boson decaying into the ) − arXiv:1503.07589 ][ + τ − 2 λ [ ][ − 3 log , 1 ) 2 ) ) − CC-BY 4.0 − = 7 − λ collaboration, τλ 4 1 1 4 τ s τ − This article is distributed under the terms of the Creative Commons τ, λ τ, λ τλ √ arcsin − √ √ τ 2( ( ( 1 1 W 2(    −            I c I collaboration, collaboration, collaboration, ) = ) = ) = ) = ) = ) = ) = (2015) 191803 τ τ ( ( g τ, λ τ, λ τ, λ τ, λ τ, λ f arXiv:1706.09936 arXiv:1207.7214 ( ( ( ( ( ATLAS, CMS collisions at 114 CMS four-lepton final state in[ pp collisions at ATLAS Higgs boson with the[ ATLAS detector at the LHC CMS experiment at the LHC 2 0 1 2 1 / I I A A 1 [3] [4] [1] [2] A Attribution License ( any medium, provided the original author(s) and source areReferences credited. Open Access. A Form factors The work has(NNSFC) been with Grants supported No.talent by 11705045, support the No. program National of 11647120,Strength No. the Natural Promotion Hebei project. 11535002, Science Province, the Foundation and youth of Midwest top-notch Universities China Comprehensive Acknowledgments JHEP04(2020)002 B , 10 ]. and , Phys. (2018) pp ` , ] 4 ] (2016). pp JHEP Hγ collisions , SPIRE Phys. Lett. → D 98 , Phys. Lett. IN ∗ (2014) 8 − → , e ][ boson in + Z ZZ ]. e boson coupling ]. Z → Z B 732 coupling ]. channel in H SPIRE ]. Phys. Rev. SPIRE IN , ``γ IN and a photon in arXiv:1307.5515 HZγ arXiv:1806.05996 SPIRE [ [ [ Z IN SPIRE CERN-TH-2016-113 ][ , IN hep-ph/0503173 Phys. Lett. [ ][ ]. , (1986) 744] [ ]. (1988) 231 (2013) 587 (2018) 152 SPIRE ]. TeV with the ATLAS detector (2008) 1 The Higgs photon — IN 11 ][ Higgs particle production by ]. 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