Interpreting 750 GeV Diphoton Excess with R-parity Violating Supersymmetry
IInterpreting
GeV Diphoton Excess with R-parity Violating Supersymmetry
Ran Ding, Li Huang, Tianjun Li,
2, 3 and Bin Zhu Center for High-Energy Physics, Peking University, Beijing, 100871, P. R. China State Key Laboratory of Theoretical Physics and Kavli Institute for Theoretical Physics, China(KITPC), Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China Institute of Physics Chinese Academy of sciences, Beijing 100190, P. R. China
We propose an supersymmetric explanation of the diphoton excess in the Minimal Supersymmet-ric Standard Model with the leptonic R-parity violation. Where the sneutrino serves as the 750GeV resonance and produced through quark anti-quark annihilation. With introducing appropri-ate trilinear soft parameters, we show that the diphoton branching ratio is significantly enhancedcompared with the conventional MSSM. The parameter space favored by diphoton excess stronglyindicates the mass of smuon and stau fall into the range − (375-480) GeV, which depend-ing on the electroweakino masses. In addition, the R -parity-violating trilinear couplings involvedwith second generation quarks are both favored by compatibility of diphoton excess and low-energyconstraints.
1. Introduction –Recently, both ATLAS and CMS re-ported an excess on diphoton channel around the invari-ant mass M (cid:39) GeV in the run II data of LHC at √ s = 13 TeV. For ATLAS observation, the local signifi-cance of the excess reaches . σ with a best-fit width ofabout 45 GeV ( Γ /M (cid:39) . ) [1]. While for CMS observa-tion, the local significance is . σ and the best-fit prefersa narrow width [2]. The corresponding signal cross sec-tions can be estimated as: σ pp → γγ (cid:39) (cid:26) (10 ± fb for ATLAS [1] , (6 ± fb for CMS [2] . (1)Although it may be eventually identified as a fluctu-ation, the possibility of a new resonance is likely to bestrong hints for new physics beyond the standard model(BSM). Which has inspired many model building effortsin various phenomenological frameworks [3–37].One of the most intriguing problems is then whetheror not this excess can be interpreted in the framework ofSupersymmetry (SUSY). In this direction, current worksfocus on the heavy Higgs candidates in the Minimal Su-persymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM) [7].Unfortunately, it is found that the diphoton branchingratio reaches only O (10 − ) even in the case of tan β ∼ which is the lower limit required by the RenormalizationGroup Equation (RGE) of Yukawa couplings. As a re-sult, one has to introduce extra vector-like fermions toalleviate the discrepancy of diphoton rate between themodel prediction and experimental requirement. In thispaper, we suggest a novel approach to explain such ex-cess without the need of any ad-hoc addition of extraparticles. We consider the framework of Leptonic R -parity-violating (LRPV) MSSM, where the 750 GeV reso-nances is identified with the sneutrino and produced viaquark anti-quark annihilation. The diphoton excess isthen originated from its loop-induced decay. With intro-ducing appropriate LRPV soft breaking trilinear terms,the diphoton branching ratio receives significant enhance-ment compared with conventional MSSM due to the con- tribution of sleptons in the loop.The organization of paper is as follows: In section 2,we introduce our model and illustrate the mechanism ofdiphoton enchantment. In section 3, we then explore theparameter space in our model with taking into accountrelevant LHC limits and low-energy constraints. The lastsection is devoted to conclusion.
2. LRPV MSSM – We start with the superpotentialof LRPV model [38]: W = Y ijd Q i H d D cj + Y iju Q i H u U cj + Y ije L i H d E cj + µH u H d + 12 λ ijk L i L j E ck + λ ijk L i Q j D ck . (2)In above equation, the SU (2) L and SU (3) C indices havebeen suppressed. i, j, k = 1 , , are the the fam-ily indices and a summation is implied. Q i ( L i ) are the SU (2) L doublet quark (lepton) superfields. D cj and U cj ( E cj ) are the SU (2) L singlet down- and up-quark (elec-tron) superfields, respectively. λ and λ are trilinearcouplings. The lepton number is automatically violatedby λ ijk L i L j E ck and λ ijk L i Q j D ck operators and the firstterm is anti-symmetric in i, j indices. In our model, sneu-trino serves as GeV resonance. We therefore only listthe relevant soft interactions for sneutrino sector: − L soft = T ijkλ ˜ ν iL ˜ e jL ˜ e ∗ kR + T ijkλ ˜ ν iL ˜ d βjL ˜ d ∗ γkR δ βγ + ˜ ν ∗ iL ( m l ) ij ˜ ν jL , (3)where the fields with tilde denote the scalar fermion su-perpartners. As is shown in Eq. 2 and 3, the productionand decay properties of sneutrino are determined by λ ijk , λ ijk , T ijkλ and T ijkλ . Here we only consider the first gener-ation sneutrino ˜ ν e as a illustration. It is straightforwardto include the other generations by multiplying a factorto the signal strength if one takes the degenerate massspectrum. In order to compute the loop-induced decay ˜ ν e → γγ , we divide the sneutrino into its CP-even andCP-odd part, ˜ ν e = 1 √ ν + e + i ˜ ν − e ) . (4) a r X i v : . [ h e p - ph ] M a y We first investigate the contributions from fermionicloop. This calculation is analogous to the CP-even/oddneutral Higgs decay into diphoton and into di-gluon inthe MSSM. One obtains following partial widths [39],
Γ(˜ ν ± e → γγ ) = α m ν ± e π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) j =1 N c m d j e d j λ jj A ± / ( τ d j )+ (cid:88) j =2 m l j λ jj A ± / ( τ l j ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (5) Γ(˜ ν ± e → gg ) = α s m ν ± e π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) j =1 m d j λ jj A ± / ( τ d j ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (6)where the sum in Eq. 5 (Eq. 6) runs over all down-fermions (down–quarks). Furthermore, N c = 3 is thenumber of colors and α ( α s ) is the QED (QCD) finestructure constant. e d j = − / is the electric chargeof down-type quarks, τ = 4 m /m ν with m the mass ofparticles running in loop. The loop function A ± / is givenby [40], A +1 / = − τ (1 + (1 − τ ) f ( τ )) ,A − / = − τ f ( τ ) ,f ( τ ) = arcsin [1 / √ τ ] , if τ ≥ −
14 [ln 1 + √ − τ − √ − τ − iπ ] , if τ < . (7)The structure of A ± / implies that A ± / /m → when m → . This feature indicates that loop contributionfrom quarks and leptons are highly suppressed exceptfor the third generation, i.e., bottom quark and tau lep-ton. While including the contribution of third gener-ation fermions also introduce a new decay modes like Γ(˜ ν → b ¯ b ) and Γ(˜ ν → τ + τ − ) , which considerably sup-press the branching ratio of diphoton mode. Moreover,the production of sneutrino through b ¯ b channel is ex-pected to be much smaller than that of first two genera-tion quarks. Due to the above reasons, we do not considerthe case of third generation and assuming j, k = 1 , for λ jk and λ jk .We then take into account contribution from sfermions.As we will show later, which plays a crucial role in dipho-ton enhancement. The decay modes in Eq. 5 and 6 can besafely neglected in this case. Notice that we can simplytreated CP-even ˜ ν + as the resonance since the sfermionloops can not give any contribution to CP-odd ˜ ν − . Thecorresponding partial widths are given by, δ Γ(˜ ν + e → γγ ) = α m ν ± e π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) j =1 N c m d j e d j sin 2 θ T jjλ A +0 ( τ ˜ d j )+ (cid:88) j =2 m l j T jjλ sin 2 θ A +0 ( τ ˜ l j ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (8) δ Γ(˜ ν + e → gg ) = α s m ν ± e π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) j =1 m d j T jjλ sin 2 θ A +0 ( τ ˜ d j ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (9)where A +0 = τ (1 − τ f ( τ )) . (10)In this case, the mass eigenstates of sleptons (only sec-ond and third generations are involved since T jjλ is anti-symmetric in , j indices.) and squarks (can be boththree generations) do not coincide with the gauge eigen-states due to introduce non-zero mixing trilinear terms.Here θ /θ being the mixing angle between left-handedand right-handed slepton/squarks, respectively. In orderto enhance diphoton partial width as much as possible,we assume maximal mixing scenario in this paper, i.e.,setting θ = θ = π/ . As a consequence, the masseigenstates tend to have a large splitting thus the con-tributions from heavier ones can be ignored in the loopcalculation.One immediately find that both δ Γ(˜ ν + → γγ ) and δ Γ(˜ ν + → gg ) are proportional to T λ /m ˜ f . To enhancethe diphoton partial width effectively, one thus preferslarge soft trilinear term T λ and relatively light sfermion.Unfortunately, the di-gluon partial width is also receivedenhancement in this way and the ratio of two modes isroughly estimated as α s /α . As a result, the total effectof sfermion loops actually reduces the diphoton branch-ing ratio. The simplest way to solve this dilemma ischoose T ijkλ = 0 , which forbidding the contribution ofsquarks and only leaving sleptons in the loop. One thushas Γ γγ ≡ δ Γ(˜ ν + e → γγ )= α m ν ± e π (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:88) j =2 m l j T jjλ sin 2 θ A +0 ( τ ˜ l j ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) , (11)and δ Γ(˜ ν + e → gg ) = 0 .We finally obtain a valid recipe in LRPV MSSM whichsuccessfully enhances diphoton partial width while avoid-ing unwanted di-gluon mode.In the rest of this section, we deal with other importantdecay modes of sneutrino: • Decaying into first two generation di-quarks via
LQD c operator with the partial width, Γ d ¯ d ≡ Γ(˜ ν + e → d j ¯ d k ) = 316 π | λ jk | m ˜ ν + e . (12)It is the inverse process of sneutrino productionthus unavoidable and dominates the branching ra-tios in general. This decay mode leads to dijet finalstates and impose stringent constraint on λ jk . • Decaying into di-lepton via
LLE c operator, whichis severely limited by LHC di-lepton resonancesearches [47]. This decay mode can not be forbid-den kinematically due to the lightness of leptons.We thus assuming λ ijk is negligible to remove thisdangerous mode. • Decaying into squark and slepton pairs due to thesoft trilinear terms T λ ˜ ν L ˜ d L ˜ d ∗ R and T λ ˜ ν L ˜ e L ˜ e ∗ R , re-spectively. Among them, the di-squark mode is au-tomatically vanished since we have taken T λ = 0 .While for di-slepton mode, we must keep large T λ since it is also responsible for enhancing the dipho-ton partial width. We therefore forbid di-sleptonmode kinematically by setting m ˜ µ, ˜ τ > GeV. • Decaying into electroweakinos (neutrlinos andcharginos) through gauge interaction. They havefollowing partial widths [41]: Γ χl ≡ Γ(˜ ν + e → ˜ χ a ν e , ˜ χ + a e − )= Cg π m ˜ ν + e (cid:32) − m χ + a m ν + e (cid:33) . (13)Where the coefficient C = | N a | ( C = | V a | ) forthe neutralinos (charginos) case. with N a and V a the elements of mixing matrix. • Finally, decaying into neutral gauge bosons Zγ and ZZ via the same loop diagram as the diphotonmode. However, their contributions to the totaldecay width are much smaller than other modesdiscussed above. We therefore neglect these twomodes in the following discussion and numericalcalculations.In summary, one leaves three modes in the decay patternof sneutrino: ˜ ν e → γγ via slepton loops, ˜ ν e → d j ¯ d k and ˜ ν e → ˜ χ ν e , ˜ χ + e − . The total decay width is then Γ tot =Γ γγ + Γ d ¯ d + Γ χl , with the branching ratio of diphotonand di-quark modes are respectively BR γγ = Γ γγ / Γ tot and BR d ¯ d = Γ d ¯ d / Γ tot .
3. Diphoton excess and LHC constraints –In thissection, we investigate the diphoton signal rate in ourmodel. For this purpose, we use
SARAH [42] to gener-ate
UFO model file [43], and
MadGraph5_aMC@NLO [44] tocalculate the production cross section of sneutrino with
CTEQ6L1 [45] parton distribution function (PDF). Basedon the discussion in section 2, we have following input pa-rameters: [ m ˜ l , m ˜ χ ± , m ˜ χ , T jjλ , λ jk ]. Where the inde-pendent components of T jjλ and λ jk are T jjλ = T , λ and λ jk = λ , , , , respectively.Before showing our results, we make some commentson the choice of parameters in the numerical analysis. Wework in the framework of simplified SUSY models, withonly involving sleptons and electroweakinos in the massspectrum. In this scenario, one can take either light orheavy electroweakinos, which has significant impact on the total decay width of sneutrino. The current LHClimits on RPV SUSY models are reviewed in Ref. [46].Those related to our model are constraints on LLE c and LQD c interactions. For LLE c operator, by assuming ˜ χ as a lightest supersymmetric particle (LSP) and us-ing simplified models, one obtains following approximateupper bounds on superpartner masses: • gluino masses m ˜ g > GeV, • light stop masses m ˜ t > GeV, • charged slepton masses m ˜ l > GeV, • sneutrino masses m ˜ ν > GeV, • wino-like chargino masses m ˜ χ ± > GeV.It is obviously that above limits can be easily escapedthrough chosing heavy gluino and squarks and arrangingthe mixing matrix of charginos. Moreover, noticed thatwe assumed the relevant couplings λ is negligible in ourmodel. Therefore, these bounds are still relaxed signifi-cantly even we do not apply the heavy spectrum. Sim-ilarly, constraints based on LQD c operators also do notthreat our model since the relevant searches are mainlyinvestigated with stop-pair production and setting stopmasses up to 1 TeV. Based on above discussion, we choose m ˜ χ ± , ˜ χ = 350 (800) GeV for the case of light (heavy) elec-troweakinos, and taking gluino and squarks are heavierthan 1 TeV. In order to extract the key features from theparameter space, we further make following assumption: • The soft trilinear couplings T λ are fixed as T λ = T λ = 10 TeV. • Due to the PDF dependence, the luminosity ra-tios between 8 TeV and 13 TeV are distinct forfirst and second generation quarks. It is then in-teresting to examine their contributions separately.For this aim, We treated λ and λ as inde-pendent operators. Furthermore, the non-diagonalcouplings λ and and λ are combined as a sin-gle operator (labeled by λ , ) with λ = λ to account for mixed contributions of first two gen-eration quarks. In the numerical calculation, weassume that each operators contributes one at atime. Finally , we use λ tot2 to denote the universalcouplings with λ = λ = λ = λ .In table I, we list cross sections of sneutrino produc-tion at LHC TeV ( TeV) respectively correspond tocouplings λ , λ , λ , and λ tot2 . Where the typicalvalue is taken as | λ | = 1 . Their cross sections fall intothe region O (10 − pb and possessing following order, σ pp → ˜ ν e ( λ ) > σ pp → ˜ ν e ( λ , ) > σ pp → ˜ ν e ( λ ) . (14)Which is resulted from PDF dependence of first and sec-ond generation quarks. In the narrow width approxima-tion, the diphoton signal rate can be calculated as σ pp → γγ (cid:39) σ pp → ˜ ν e | λ jk | · BR γγ . (15)Currently, the most stringent LHC constraint for ourmodel coming from dijet and diphoton resonance searchesperformed at LHC 8 TeV. Corresponding upper boundsat confidence level yield σ pp → jj < . pb [48] and σ pp → γγ < . fb [49, 50], respectively. Since they havedifferent impact on the model parameter space, we dis-cuss them one by one. We start with dijet constraint.The cross section of dijet final states resulted from ˜ ν e decay is given by, σ pp → jj (cid:39) σ pp → ˜ ν e | λ jk | · BR d ¯ d , (16)In addition, selectron decay ˜ e ± L → u j ¯ d k / ¯ u j d k also con-tributes to dijet final states. Whose cross section can bewell approximated by, σ ( pp → ˜ e − L → ¯ u j d k ) (cid:39) σ pp → ˜ e − L | λ jk | · BR ¯ ud ,σ ( pp → ˜ e + L → u j ¯ d k ) (cid:39) σ pp → ˜ e + L | λ jk | · BR u ¯ d . (17)Where BR ¯ ud ( u ¯ d ) = Γ ¯ ud ( u ¯ d ) / (Γ ¯ ud ( u ¯ d ) + Γ χl ) . Γ ¯ ud ( u ¯ d ) and Γ χl are obtained by replacing m ˜ ν e in Eq. 12 and13 to m ˜ e ∓ L , respectively. In Eq. 17, we have ignored theloop-induced decay modes W Z and
W γ since they arehigh suppressed compared with tree-level ones. Noticethat the mass splitting for the left-handed slpeton aredetermined by model independent relation m e L − m ν e = − cos(2 β ) m W [51], we thus have m ˜ e ± L = 754 GeV for m ˜ ν e = 750 GeV and tan β = 10 . Which indicates contri-bution coming from ˜ e ± L must be taken into account sincetheir masses are close to ˜ ν e . Similar to table I, crosssections of ˜ e ± L production at LHC 8 TeV are listed intable II.We first investigate the case of light electroweakinos.We require that signal cross sections respectively satisfythe CMS and ATLAS observations which are listed inEq. 1, with imposing the dijet upper bound σ pp → jj < . pb. In figure 1 and 2, we respectively display the allowedregions for each independent operator in [ m ˜ µ, ˜ τ , λ ijk ] plane for CMS and ATLAS observations. In addition, thelargest total decay width can be reached in each param-eter regions are also shown. There are some importantresults can be learned from these figures: • All the independent couplings can fit the CMS ob-servation. The upper bounds of allowed regionsfor different couplings λ have inverse hierarchywith that of production rate in Eq. 14 since asmaller production cross section makes a largerupper bound of coupling. Furthermore, λ and λ , give roughly comparable parameter spacewhile λ and λ tot2 coupling hold relatively smallregions. Which is due to the fact that λ hasthe smallest production cross section, making it canonly fit the signal rate in a narrow mass regions. Onthe other hand, λ tot2 gives the largest senutrino pro-duction with the smallest diphoton branching ratio. As a result, it takes moderate diphoton signal rate.While the dijet constraint is most stringent for λ tot2 ,thus significantly reduces its parameter space. • For ATLAS observation, only λ and λ , cou-plings are survived with tiny parameter space while λ and λ tot2 couplings are totally excluded. Thiscan be explained as follows: ATLAS observationprefer large signal cross section, while senutrinoproduction resulted from λ coupling is too smallto reach such signal rate. On the other hand, for λ tot2 coupling, the reason is similar with the case ofCMS. But for ATLAS case, required diphoton sig-nal rate and dijet limit can never be balanced thustotally exclude λ tot2 in whole parameter space. • The largest total decay width corresponding toCMS (ATLAS) observation is about ( ) GeV,which is provided by λ ( λ , ) coupling. Es-pecially, best-fit width Γ tot = 45 GeV suggested byATLAS observation can never be satisfied in ourparameter space.
Production cross section (pb) λ λ λ , λ tot2 σ pp → ˜ ν e . . . . σ pp → ˜ ν e
30 2 . . . TABLE I. Production cross sections of ˜ ν e at LHC 13 TeV and8 TeV respectively correspond to couplings λ , λ , λ , and λ tot2 . Where the typical value is taken to be | λ | = 1 .Production cross section (pb) λ λ λ , λ tot2 σ pp → ˜ e − L . . . . σ pp → ˜ e + L . . . . TABLE II. Similar with table I, but for ˜ e ± L at LHC 8 TeV. We further address constraint from diphoton channel.Since current upper limit for this channel is σ pp → γγ < . fb, compatibility of diphoton excess between LHC TeVand TeV has to be examed. In figure 3, we presentallowed parameter space in the same plane with imposingboth dijet and diphoton constraints. where the diphotonsignal rate at LHC 8 TeV is computed as σ pp → γγ (cid:39) σ pp → ˜ ν e | λ jk | · BR γγ . (18)In this case, we find that the parameter space for AT-LAS observation is entirely ruled out. Even for CMS re-sult, allowed parameter regions for different couplings arealso changed dramatically. To be specific, the parame-ter space is disappeared for λ tot2 coupling; getting smallerfor λ and λ , couplings; while keeping almost un-changed for λ coupling. To understand such behav-iors, one noticed that the growth of production cross sec-tions at LHC TeV and TeV are different for thefirst and second generation quarks. From table I, we findthat the increasing of cross sections for ˜ ν e production aregiven by, σ pp → ˜ ν e σ pp → ˜ ν e ( λ ) (cid:39) . , σ pp → ˜ ν e σ pp → ˜ ν e ( λ , ) (cid:39) . ,σ pp → ˜ ν e σ pp → ˜ ν e ( λ ) (cid:39) . , σ pp → ˜ ν e σ pp → ˜ ν e ( λ tot2 ) (cid:39) . . (19)Due to different PDF dependence, the growth ratio forsecond generation quarks are higher than that of firstgeneration, leading to the couplings involved with sec-ond generation quarks ( λ and λ , ) have more sig-nificant increasing on signal rate. Meanwhile, the growthof observed diphoton signal rate from LHC 8 TeV to 13TeV are estimated as σ pp → γγ σ pp → γγ (cid:39) (cid:40) (10 ± fb . fb ∼ . − . for ATLAS , (6 ± fb . fb ∼ − for CMS . (20)Based on Eq. 19 and 20, it is clearly that none of cou-plings in our model can fit the ATLAS observation andsimultaneously guarantee the compatibility of diphotonexcess between LHC TeV and TeV. On the otherhand, the situation is much better for CMS observation.In this case, couplings λ and λ , are more advan-tageous since they are benefit from large growth ratio ofsecond generation quarks, thus preserving the compati-bility of diphoton excess as much as possible. While for λ coupling which only involved with first generationquarks, whose increasing of cross section is slightly largerthan the lower bound of growth of CMS diphoton signalrate, thus disfavored by compatibility of diphoton excess.Finally, coupling λ tot2 is totally excluded due to stringentdijet bound although possessing second smallest of in-creasing.Next, we briefly discuss the case of heavy electroweaki-nos. The remarkable difference is that the decay moderelated to electroweakinos is kinematically forbidden inthis case, leading to Γ χl = 0 . Which clearly enhances thebranching ratio of diphoton mode, while with the price ofreducing total decay width. Similar with the case of lightelectroweakinos, the parameter space for ATLAS obser-vation is also disappeared after imposing both dijet anddiphoton constraints at LHC 8 TeV. We thus only presentresults on CMS observation in Fig. 4. The changing ofparameter space are summarized as follows: • the allowed mass regions for smuon/stau are ex-tended up to about 480 GeV, • the largest total decay width in each parameter re-gions are correspondingly reduced. For instance, Γ tot respectively drop to GeV and GeV for λ and λ .Before ending up this section, we mention that theparameter space of λ in Figs. 3 and 4 should be alsoconsistent with the exisiting low-energy constraints. The indirect bounds coming from various low energy experi-ments are collected in Ref. [38], those most related to ourmodel are listed blow : λ ≤ × − (cid:18) m ˜ f
100 GeV (cid:19) (cid:16) m ˜ g/ ˜ χ
100 GeV (cid:17) [ ββ ν ] ,λ k ≤ . (cid:16) m ˜ d kR
100 GeV (cid:17) [ V ud ] ,λ k ≤ . (cid:16) m ˜ d kR
100 GeV (cid:17) [ A F B ] ,λ j ≤ . (cid:16) m ˜ u jL
100 GeV (cid:17) [ Q W (Cs)] . (21)In above equation, m ˜ f and m ˜ g/ ˜ χ respectively denotesfermion, gluino/neutralino masses. The notations inthe brackets stand for the corresponding low-energy con-straints which are illustrated as follows: • ββ ν : neutrinoless double beta decay of nuclei,constraining by the lower limit on the half-life of Ge isotope [52] [53]; • V ud : charged current universality in the quark sec-tor, constraining by the experimental value of theCKM matrix element V ud [54]; • A F B : forward-backward asymmetries of fermionpair production process via Z boson resonant e + e − → Z → f ¯ f , constraining through the exper-imental values of A fF B measured by CERN LEP-I [54]; • Q W (Cs) : deviation of the weak charge Q W to itsSM value, constraining by the parity violating tran-sitions in Cs [55] [56].One can see that most of low-energy constraints relyon squark and gluino masses which are decoupled inour spectrum, thus are harmless for the parameterspace of λ . The only threatening constraint com-ing from the ββ ν , which involved with charged slep-ton and neutralino masses thus imposing very stringentbound on λ . In the case of light electroweakinoswith ( m ˜ e L , m ˜ χ ) = (754 , GeV, the first equa-tion of Eq. 21 implies λ ≤ . . As a consequence,the allowed regions for λ in Figs. 3 are totally ex-cluded. On the other hand, for light electroweakinos with ( m ˜ e L , m ˜ χ ) = (754 , GeV, the corresponding limit is λ ≤ . . Which still allowing some parameter spacefor λ and λ tot2 . Conclusion –In summary, we have proposed an super-symmetric explanation of the diphoton excess within the We do not include limit coming from the neutrino masses andmixings since which relys on assumptions of the generation struc-ture of λ [38], which are not specified in our model. In addition,we adopt more recent result in Ref. [53] for limit from neutrino-less double beta decay.
375 380 385 390 395 400 405 4100.10.20.30.40.50.60.70.8 m ΜŽ , ΤŽ H GeV L Λ ij k Λ , G tot d
11 GeV Λ , G tot d
30 GeV Λ , G tot d
14 GeV Λ , G tot d
13 GeV
CMS Σ
13 TeV H pp ® ΝŽ e ® ΓΓ L Î ± Σ H pp ® ΝŽ e , e Ž L ± ® jj L d FIG. 1. The allowed region for the diphoton excess requiredby CMS observation on the [ m ˜ µ, ˜ τ , λ ijk ] plane with only con-sidering constraint from dijet constraint at 8 TeV LHC. Herethe mass of electroweakinos are fixed as m ˜ χ ± , ˜ χ = 350 GeV.The regions with purple, green, blue and orange color corre-spond to contributions of λ , λ , λ , and λ tot2 , respec-tively. For comparison, the largest total decay width for eachparameter region is also shown.
376 378 380 382 384 386 388 3900.140.160.180.200.220.240.260.280.30 m ΜŽ , ΤŽ H GeV L Λ ij k Λ , G tot d Λ , G tot d
14 GeV
ATLAS Σ
13 TeV H pp ® ΝŽ e ® ΓΓ L Î ± Σ H pp ® ΝŽ e , e Ž L ± ® jj L d FIG. 2. Similar with figure 1, but for the ATLAS observation.Notice that in this case the parameter space for λ and λ tot2 are totally excluded thus do not presented here. framework of LRPV MSSM. Where the 750 GeV reso-nance is identified as sneutrino and produced by q ¯ q ini-tial state. With introducing relatively large trilinear softparameter T jjλ , the branching ratio of diphoton mode
375 380 385 390 395 400 405 4100.10.20.30.40.50.60.70.8 m ΜŽ , ΤŽ H GeV L Λ ij k Λ , G tot d
11 GeV Λ , G tot d
30 GeV Λ , G tot d
14 GeV
CMS Σ
13 TeV H pp ® ΝŽ e ® ΓΓ L Î ± Σ H pp ® ΝŽ e ® ΓΓ L < Σ H pp ® ΝŽ e , e Ž L ± ® jj L d FIG. 3. The allowed region for the diphoton excess requiredby CMS observation on the [ m ˜ µ, ˜ τ , λ ijk ] plane with consider-ing both dijet and diphoton constraints at 8 TeV LHC.
380 400 420 440 460 480 - - - - - m ΜŽ , ΤŽ H GeV L L og Λ ij k Λ , G tot d Λ , G tot d
17 GeV Λ , G tot d Λ , G tot d CMS Σ
13 TeV H pp ® ΝŽ e ® ΓΓ L Î ± Σ H pp ® ΝŽ e ® ΓΓ L < Σ H pp ® ΝŽ e , e Ž L ± ® jj L d FIG. 4. The allowed region for the diphoton excess re-quired by CMS observation on the [ m ˜ µ, ˜ τ , log λ ijk ] plane withconsidering constraints from both dijet and diphoton reso-nance searches. Here the mass of electroweakinos are fixed as m ˜ χ ± , ˜ χ = 800 GeV. received significantly enhancement compared with con-ventional MSSM. The important features and predictionsof our model are summarized as follows: • In our model, the sneutrino resonance is producedvia q ¯ q annihilation. Which is distinct from modelsproduced by gg initial state. The two productionchannel can be distinguished in principle by usingangular distributions with sufficiently large statis-tics. • With considering dijet and diphoton constraints atLHC 8 TeV, our model can successfully fit the CMSdata in sizeable parameter regions. While for largesignal cross section and a width of GeV sug-gested by ATLAS data, the parameter space is en-tirely ruled out. Fitting the excess strongly favorsthe mass of stau and smuon within the range of − ( − ) GeV for the case of light(heavy) electroweakinos. Which is a strong predic-tion for mass spectrum of slepton sector. • The predicted total decay width can reaches ( )GeV for light (heavy) electroweakinos. • The low-energy constraint from neutrinoless dou-ble beta decay imposes severe bound on coupling λ . Combined with the compatibility of dipho-ton excess between LHC TeV and TeV, thecouplings involved with second generation quarkshave more advantages.
Note added – After a few days we submitted ourpaper to arXiv, Ref. [57] appeared, which explains thediphoton excess using the similar scenario. The differenceis that the authors consider degenerate electron or mounsneutrino as the resonance and producing only throughfirst generation quarks. In addition, they do not discussthe compatibility of diphoton excess between LHC TeVand TeV.
Acknowledgements – This research was supported inpart by the Natural Science Foundation of China undergrant numbers 11135003, 11275246, and 11475238 (TL). [1] The ATLAS collaboration, ATLAS-CONF-2015-081.[2] CMS note, CMS PAS EXO-15-004, “Search for newphysics in high mass diphoton events in proton-protoncollisions at 13 TeV".[3] R. Franceschini et al. , arXiv:1512.04933 [hep-ph].[4] A. Pilaftsis, arXiv:1512.04931 [hep-ph].[5] D. Buttazzo, A. Greljo and D. Marzocca,arXiv:1512.04929 [hep-ph].[6] S. Knapen, T. Melia, M. Papucci and K. Zurek,arXiv:1512.04928 [hep-ph].[7] A. Angelescu, A. Djouadi and G. Moreau,arXiv:1512.04921 [hep-ph].[8] Y. Nakai, R. Sato and K. Tobioka, arXiv:1512.04924[hep-ph].[9] M. Backovic, A. Mariotti and D. Redigolo,arXiv:1512.04917 [hep-ph].[10] Y. Mambrini, G. Arcadi and A. Djouadi,arXiv:1512.04913 [hep-ph].[11] K. Harigaya and Y. Nomura, arXiv:1512.04850 [hep-ph].[12] E. Molinaro, F. Sannino and N. Vignaroli,arXiv:1512.05334 [hep-ph].[13] C. Petersson and R. Torre, arXiv:1512.05333 [hep-ph].[14] R. S. Gupta, S. Jäger, Y. Kats, G. Perez and E. Stamou,arXiv:1512.05332 [hep-ph].[15] B. Bellazzini, R. Franceschini, F. Sala and J. Serra,arXiv:1512.05330 [hep-ph].[16] M. Low, A. Tesi and L. T. Wang, arXiv:1512.05328 [hep-ph].[17] J. Ellis, S. A. R. Ellis, J. Quevillon, V. Sanz and T. You,arXiv:1512.05327 [hep-ph].[18] S. D. McDermott, P. Meade and H. Ramani,arXiv:1512.05326 [hep-ph].[19] T. Higaki, K. S. Jeong, N. Kitajima and F. Takahashi,arXiv:1512.05295 [hep-ph].[20] Y. Bai, J. Berger and R. Lu, arXiv:1512.05779 [hep-ph].[21] D. Aloni, K. Blum, A. Dery, A. Efrati and Y. Nir,arXiv:1512.05778 [hep-ph].[22] A. Falkowski, O. Slone and T. Volansky,arXiv:1512.05777 [hep-ph].[23] C. Csaki, J. Hubisz and J. Terning, arXiv:1512.05776 [hep-ph].[24] P. Agrawal, J. Fan, B. Heidenreich, M. Reece andM. Strassler, arXiv:1512.05775 [hep-ph].[25] A. Ahmed, B. M. Dillon, B. Grzadkowski, J. F. Gunionand Y. Jiang, arXiv:1512.05771 [hep-ph].[26] J. Chakrabortty, A. Choudhury, P. Ghosh, S. Mondaland T. Srivastava, arXiv:1512.05767 [hep-ph].[27] L. Bian, N. Chen, D. Liu and J. Shu, arXiv:1512.05759[hep-ph].[28] D. Curtin and C. B. Verhaaren, arXiv:1512.05753 [hep-ph].[29] S. Fichet, G. von Gersdorff and C. Royon,arXiv:1512.05751 [hep-ph].[30] W. Chao, R. Huo and J. H. Yu, arXiv:1512.05738 [hep-ph].[31] S. V. Demidov and D. S. Gorbunov, arXiv:1512.05723[hep-ph].[32] J. M. No, V. Sanz and J. Setford, arXiv:1512.05700 [hep-ph].[33] D. Becirevic, E. Bertuzzo, O. Sumensari and R. Z. Fun-chal, arXiv:1512.05623 [hep-ph].[34] P. Cox, A. D. Medina, T. S. Ray and A. Spray,arXiv:1512.05618 [hep-ph].[35] A. Kobakhidze, F. Wang, L. Wu, J. M. Yang andM. Zhang, arXiv:1512.05585 [hep-ph].[36] S. Matsuzaki and K. Yamawaki, arXiv:1512.05564 [hep-ph].[37] B. Dutta, Y. Gao, T. Ghosh, I. Gogoladze and T. Li,arXiv:1512.05439 [hep-ph].[38] R. Barbier et al. , Phys. Rept. , 1 (2005)doi:10.1016/j.physrep.2005.08.006 [hep-ph/0406039].[39] S. Bar-Shalom, G. Eilam, J. Wudka andA. Soni, Phys. Rev. D , 035010 (1999)doi:10.1103/PhysRevD.59.035010 [hep-ph/9809253].[40] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson,Front. Phys. , 1 (2000).[41] V. D. Barger, G. F. Giudice and T. Han, Phys. Rev. D , 2987 (1989). doi:10.1103/PhysRevD.40.2987[42] F. Staub, Comput. Phys. Commun. , 1792(2013) doi:10.1016/j.cpc.2013.02.019 [arXiv:1207.0906 [hep-ph]]. F. Staub, Comput. Phys. Commun. , 1773(2014) doi:10.1016/j.cpc.2014.02.018 [arXiv:1309.7223[hep-ph]].[43][43] C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mat-telaer and T. Reiter, Comput. Phys. Commun. , 1201(2012) [arXiv:1108.2040 [hep-ph]].[44] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer andT. Stelzer, JHEP , 128 (2011) [arXiv:1106.0522[hep-ph]]; J. Alwall, R. Frederix, S. Frixione, V. Hirschi,F. Maltoni, O. Mattelaer, H.-S. Shao and T. Stelzer etal. , JHEP , 079 (2014) [arXiv:1405.0301 [hep-ph]].[45] P. M. Nadolsky, H. L. Lai, Q. H. Cao, J. Hus-ton, J. Pumplin, D. Stump, W. K. Tung andC.-P. Yuan, Phys. Rev. D , 013004 (2008)doi:10.1103/PhysRevD.78.013004 [arXiv:0802.0007 [hep-ph]].[46] A. Redelbach, Advances in High Energy Physics, vol.2015, Article ID 982167, 2015 [arXiv:1512.05956 [hep-ex]].[47] G. Aad et al. [ATLAS Collaboration], Phys. Rev. D ,no. 5, 052005 (2014) doi:10.1103/PhysRevD.90.052005[arXiv:1405.4123 [hep-ex]].[48] CMS Collaboration [CMS Collaboration], CMS-PAS- EXO-14-005.[49] G. Aad et al. [ATLAS Collaboration], Phys. Rev. D ,no. 3, 032004 (2015) doi:10.1103/PhysRevD.92.032004[arXiv:1504.05511 [hep-ex]].[50] CMS Collaboration [CMS Collaboration], CMS-PAS-HIG-14-006.[51] S. P. Martin, Adv. Ser. Direct. High Energy Phys. , 1(2010) [Adv. Ser. Direct. High Energy Phys. , 1 (1998)][hep-ph/9709356].[52] H. V. Klapdor-Kleingrothaus et al. , Eur. Phys. J. A ,147 (2001) doi:10.1007/s100500170022 [hep-ph/0103062].[53] B. C. Allanach, C. H. Kom and H. Pas, JHEP , 026 (2009) doi:10.1088/1126-6708/2009/10/026[arXiv:0903.0347 [hep-ph]].[54] K. Hagiwara et al. [Particle Data Group Col-laboration], Phys. Rev. D , 010001 (2002).doi:10.1103/PhysRevD.66.010001[55] J. L. Rosner, Phys. Rev. D , 073026 (2002)doi:10.1103/PhysRevD.65.073026 [hep-ph/0109239].[56] J. S. M. Ginges and V. V. Flambaum, Phys.Rept.397