Scalar Explanation of Diphoton Excess at LHC
aa r X i v : . [ h e p - ph ] A p r Scalar Explanation of Diphoton Excess at LHC
Huayong Han, Shaoming Wang and Sibo Zheng
Department of Physics, Chongqing University, Chongqing 401331, P.R. China
Abstract
Inspired by the diphoton signal excess observed in the latest data of 13 TeV LHC,we consider either a 750 GeV real scalar or pseudo-scalar responsible for this anomaly.We propose a concrete vector-like quark model, in which the vector-like fermion pairsdirectly couple to this scalar via Yukawa interaction. For this setting the scalar is mainlyproduced via gluon fusion, then decays at the one-loop level to SM diboson channels gg, γγ, ZZ, W W . We show that for the vector-like fermion pairs with exotic electriccharges, such model can account for the diphoton excess and is consistent with the dataof 8 TeV LHC simultaneously in the context of perturbative analysis.1
Introduction
The first data at the 13 TeV Large Hadron Collider (LHC) was released on December 152015 [1, 2]. It shows an excess in diphoton final state at the invariant mass M ≃
750 GeV,with local significance of order 3.9 σ and 2.6 σ for ATLAS and CMS, respectively. In con-trast, no excesses in the Standard Model (SM) diboson channels such as γγ, ZZ, W W, ZW ,dilepton and dijet were seen in the old data of 8 TeV LHC [3, 4, 5, 6, 7, 8, 9, 10, 11].If the diphoton excess is indeed a hint of some new physics beyond SM, for an on-shell decay to diphoton it should be due to either spin-0 or spin-2 scalar φ . To explainthe observed excess, the cross section σ ( pp → φ → γγ ) is required to satisfy the signalstrength of order, σ ( pp → φ → γγ ) | √ s =13 TeV ≃ (8 ±
3) fb . (1.1)Such SM singlet scalar which is responsible for the excess has stimulated extensive inter-ests, see Ref.[12]- Ref.[54].In this paper, we propose a concrete vector-like quark model, in which the vector-likefermion pairs directly couple to φ via tree-level Yukawa interaction. Under our setup, φ is mainly produced via gluon fusion, then decays at the one-loop level to SM dibosonchannels gg, , ZZ, W W , with the colored vector-like fermion pair running in the Feynmanloop. For the vector-like fermion pairs with exotic electric charges, such model can accountfor the diphoton excess, and is consistent with the data of 8 TeV LHC simultaneously inthe context of perturbative analysis.This paper is organized as follows. In Sec.2 we address the matter content in thevector-like quark model, define the parameter space, and summarize the experimentallimits on φ and vector-like quark at the 8 TeV LHC. In Sec.3 we explore the parameterspace for φ either being a real scalar or pseudo-scalar. Finally, we conclude in Sec. 4. In order to reproduce the on-shell decay φ → γγ , which is a loop process for the SMsinglet φ , we directly couple φ to a fermion doublet Ψ, the latter of which is a subsectorof vector-like quark model as defined in Table 1. In this table, another fermion doublet˜Ψ is added in order to evade the gauge anomaly problem.1atters SU (3) c SU (2) L U (1) Y φ
0Ψ = ( ψ , ψ ) T q ψ ˜Ψ = ( ˜ ψ , ˜ ψ ) T ¯ ¯ - q ψ Table 1: Matters and their SM quantum numbers in the vector-like quark model. Anotherfermion doublet ˜Ψ is added to make sure that the model is free of gauge anomaly.For simplicity, we assume that the mass M ˜Ψ for ˜Ψ is obviously larger than the mass M Ψ for Ψ. Below the mass scale M ˜Ψ the effective Lagrangian in the new physics is describedby , L BSM = 12 ( ∂φ ) − m φ φ + i ¯Ψ γ ν D ν Ψ − M Ψ ¯ΨΨ + L Yukawa , (2.1)where L Yukawa = yφ ¯ΨΨ , (scalar) ,iyφ ¯Ψ γ Ψ , (pseudo-scalar) . (2.2)In Eq.(2.1) scalar mass m φ ≃
750 GeV, y is the Yukawa coupling constant. We assignthe electric charge for Ψ as Q ψ , = q ψ ± in unit of e . For either case in Eq.(2.2) φ ismainly produced by gluon fusion, and decays to diphoton via Ψ in the Feynman loop.Now we address the parameter ranges for { y, M Ψ , Q ψ } in the parameter space. First,if one allows φ decaying into ψ , ¯ ψ , , the total decay width for φ would be dominated bythis channel, which leads to a very small branching ratio Br( φ → γγ ) typically of order ≤ − as a result of the fact, Γ( φ → γγ )Γ( φ → gg ) ∼ . (2.3)To account for the observed signal strength in Eq.(1.1), we must forbid this decay channel,and impose M Ψ > m φ /
2. Second, Γ( φ → γγ ) / Γ( φ → gg ) is roughly proportional to Q ψ .In order to obtain Br( φ → γγ ) as large as possible, one may choose large Q ψ . Finally,a perturbative theory requires the Yukawa coupling constant y ≤ √ π . Based on theconsiderations above, we mainly focus on the following parameter ranges,375 GeV < M Ψ < , Q ψ = { / , / , / , − / } , < y < √ π. (2.4) The effective Lagrangian as analyzed in the previous version of this manuscript is a simplification ofthis concrete one. .2 Constraints Experimental constraints on φ mainly arise from limits at the 8 TeV LHC [3, 4, 5, 6, 7, 8,9, 10, 11], which are shown in Table 2. The γγ , Zγ , ZZ , W W and di-jet limits are shownin the red, green, purple, black and blue curve, respectively, above which the regions areexcluded. cross sections upper bounds (fb) colors σ ( pp → γγ ) 1 . σ ( pp → Zγ ) 4 green σ ( pp → ZZ ) 12 purple σ ( pp → W W ) 40 black σ ( pp → di-jet) 2500 blueTable 2: Experimental limits on φ at 8 TeV LHC.Experimental limits on vector-like quark ψ are sensitive to its electric charge assign-ments. If the electric charge Q ψ takes special values { / , / , / , − / } , in which caseit allows mixing between ψ , and SM quarks, decay channels such as ψ , → { tW, bW } occur. Otherwise, if ψ , takes some exotic electric value, which forbids the mixing effect,these limits can be obviously relaxed. In this situation for ψ , pair produced at the LHC,they first hadronize into heavy “mesons”, and then decay to SM final states. In Table 3we show the experimental limits at the 8 TeV LHC for different electric charges Q ψ andassumptions on its decay channel.charge lower mass bound (GeV) assumption Refs Q ψ = 8 / ψ → tW + ) = 100% [55, 56] Q ψ = 5 / ψ → tW + ) = 100% [57] Q ψ = 2 / ψ → { bZ, bH } ) = 100% [58, 59, 60] Q ψ = − / ψ → { bZ, bH } ) = 100% [61]Table 3: Lower mass bounds on M Ψ at 8 TeV LHC for benchmark electric charge Q ψ = { / , / , / , − / } . Note that in our case ψ and ψ have degenerate masses, and Q ψ = Q ψ −
1. The lower mass bound can be relaxed by adjusting the branching ratio.3
00 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = − / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 2 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 5 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 8 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV Figure 1: Yellow bands are the observed signal strength at 13 TeV LHC. Curves refer toexperimental limits shown in Table 2. Each panel corresponds to a benchmark electriccharge Q ψ = { / , / , / , − / } , respectively. M Ψ is fixed to be 10 TeV. In this section we consider the SM singlet real scalar as the explanation of diphotonexcess. In Fig.1 the yellow bands correspond to the observed diphoton excess in theparameter space for fixed M Ψ = 10 TeV and four benchmark electric charges Q ψ = { / , / , / , − / } . In this figure, curves refer to experimental limits shown in Table2, above which regions are excluded. Q ψ = {− / , / , / } : For these three benchmark electric charges those regionsin the yellow band below the the red solid curve can explain the observed diphotonexcess and are consistent with the experimental limits on φ in Table 2 simultaneously.Furthermore, regions on the right hand of vertical dotted line survive after we take intoaccount the constraints on vector-like quark in Table 3. Given the same M Ψ the Yukawa4
00 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = − / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 2 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 5 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV
400 600 800 1000 1200 1400 1600 1800 2000012345678910 m ψ ( GeV ) y Q ψ = 8 / γγ @13TeV γγ @8TeV γZ @8TeV ZZ @8TeV WW @8TeV jj @8TeV Figure 2: Similar to Fig.1 yellow bands correspond to the observed signal strength at 13TeV LHC, and curves refer to limits in Table 2.coupling constant y as required to explain the diphoton excess tends to decrease as | Q ψ | increases. Q ψ = 2 /
3: In contrast to the three benchmark electric charges above, the modelwhich actually corresponds to the 4th SM fermion generation is excluded by the Zγ limitat 8 TeV LHC. The reason arises from the fact that the production cross section for σ ( pp → φ ) · Br( φ → γγ ) is not a strictly monotonic function of Q ψ . Now we proceed to discuss the alternative explanation of diphoton excess via a SM singletpseudo-scalar. Similar to Fig.1, the yellow bands in Fig.2 correspond to the diphotonexcess. Q ψ = {− / , / , / } : Similar to the SM real scalar singlet, there are viable pa-rameter spaces for these three benchmark electric charges. Fig.1 and Fig.2 show that allof these parameter spaces are in the perturbative region, which is an interesting feature5hannel Q ψ = − / Q ψ = 5 / Q ψ = 8 / γγ σ ( pp → φ ) · Br( φ → WW/ZZ) in unit of fb in theparameter spaces of Fig.1 and Fig. 2 at the 13 TeV LHC.for this model. Our analysis indicates that the parameter spaces are not sensitive to theexperimental limits in Table 3 in comparison with those in Table 2. In Table 4 we showthe ranges for production cross sections σ ( pp → φ ) · Br( φ → WW/ZZ) in the parameterspaces of Fig.1 and Fig. 2 at the 13 TeV LHC. Q ψ = 2 /
3: Similar to the real scalar explanation in Fig.1, vector-like quark with Q ψ = 2 / In this paper, we consider the possibilities that either a SM singlet scalar or singlet pseudo-scalar is responsible for the diphoton excess at 750 GeV in the 13 TeV LHC. To analyzethe allowed parameter space, we take the experimental limits at 8 TeV LHC. For the fourbenchmark electric charges Q ψ = {− / , / , / , / } we find that there are viable pa-rameter spaces except for Q ψ = 2 /
3. Moreover, all of these viable parameter spaces arein the perturbative region, which differ from some attempts in Ref.[12]- Ref.[54] to addressthe diphoton excess. Given the fact that branching ratios for decays φ → { γγ, ZZ, W W } are all of the same order, signal excesses in pp → φ → W W and pp → φ → ZZ will beexposed for larger integrated luminosity. Acknowledgments
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