The Fourth Generation Quark and the 750 GeV Diphoton Excess

0.12 MB·

by  Yu-Jie Zhang

TheFourthGenerationQuarkandthe750GeVDiphotonExcess
Yu-Jie Zhang 1,2, Bin-Bin Zhou 1, and Jia-Jia Sun 1
∗
1 KeyLaboratoryofMicro-nanoMeasurement-ManipulationandPhysics(Ministry
ofEducation)andSchoolofPhysics,BeihangUniversity,Beijing100191, China
2 CASCenterforExcellenceinParticlePhysics,Beijing100049, China
(Dated: February18,2016)
Recently,theCMSandATLAScollaborationshavereportedadiphotonpeakat750GeVintheRunIIof
LHCat13TeV.Weassumethattheheavyfourthgenerationquarkdoubletz, ywith380GeVmass,andthe
widthofz,t ismuchlessb quark. Thenweshowthatthecontributionsofthe(zz¯ yy¯)/p2boundstate
ηzy(1S)tothediphotonmeasurementsthroughσ(pp→ηzy(1s)→γγ)are5.6+52..68fb+atpS=13TeV.They
areconstantwiththe750GeVdiphotonexcessmeasuredbytheCMSantATLAS−collaborations.
6
PACSnumbers:12.60.-i,14.80.-j,14.40.Pq
1
Keywords:Phenomenologyofmodelsbeyondthestandardmodel,HadronicColliders,Heavyquarkonia
0
2

n INTRODUCTION higherorder[53–56],andtheleadingorder(LO)resultsare
a givenhere,
J
] 5 pthoeRrtReecudennaItIdloyi,pfLhthHoetCoCnaMte1xS3ceTasensVda:tA7T5L0AGSecVolwlaibthorwatidiotnhs45haGveeVrien- Γ(ηzy→gg) = 16αs(m3mz)η22z|yRs(0)|2,
h 6α(m )2(e2 e2)2 R (0)2
p (6 3)fb CMS[1] Γ(η γγ) z z+ y | s |
p- σ(pp→γγ)≈½ (10±±3)fb ATLAS[2]. (1) zy→ = mη2zy
e 50α(mz)2 Rs(0)2
h Alotofstudies havebeendonehere [3–46]. Westudy = 27m2| | ,
[ the possibility that it is a bound states of the fourth gen- ηzy
1 eration quarkand anti-quarkhere. The fourth generation Γ(ηzy→gg) 72αs(mz)2 4 102, (2)
v quarksandleptonswereproposedabout30yearsago[47]. Γ(ηzy γγ) = 25α(mz)2 ∼ ×
→
9 In another hand, the branching fraction Br(H τµ)
53 (d0i.c8a4t+−e00t..h3397e)%foumrethasguerneedrbatyioCnMnSecuotlrlianboohraetrieo.n[48]m→aybein=- wAnhdertehtehwei|dRtsh(0o)f|eisletchterorawdeiaaklwdeacvaeyfumnocdtieonosfpoufηrezyηzaytocaringibne.
5 givenas,
In this letter, we assume that, the heavy fourth gen-
0
2. 2er/a3t,eequark1z/3,,yanwditthhe38m0oGdiefiVedmCaKssManmdatcrihxaregleemeeznt=s Γ(ηzy→HH) = Γ(ηzy→Hγ)=0,
0 y = − Γ(η f f¯)
16 |tVhzeqw|∼idt|Vhyoqf′|z≪, y1qfuorarqk=isdm,usc,hbleasnsdbqq′u=aruk,, ict,wti.llTfohremn Γ(ηzzyy→→γγ) = 0,
v: thebound statesuchas zu¯ or zd¯, whichislong lifeparti- Γ(ηzy→W+W−) 2,
i cleanddonotdecayinthedetector. Thentheboundstate Γ(ηzy γγ) ∼
X (zz¯+yy¯)/p2quarkoniumstatesηzy(1S)willbefirstparti- Γ(ηz→y ZZ)
r clewithfourthgenerationquarkcomponentwhichmaybe → 3,
a Γ(η γγ) ∼
measured at LHC. The fourth generation quark had been zy→
sloewarecrhleimdibtylietshebeCtwMeSenco6l8la7baonrdat7io8n2GateVpfSor=a8llpTeoVs,siabnledvtahle- ΓΓ((ηηzzyy→Zγγγ)) ∼ =0.5. (3)
→
uesofthebranchingfractionsintothethreedifferentfinal
We ignore the O(m2/m2), O(m2/m2), O(m2 /m2), and
statesassuming strongproduction[49]. Sowerequirethe H z Z z W z
O(m2/m2)here. The HZ and tt¯widthsofη areenhance
widthofz, yquarkismuchlessbquarkanditwillnotdecay f z z
inthedetectors. Theboundstatesoffourthgeneratequark bymz4/m4Z andmz2mt2/m4Z respectively,
havebeenstudiedinRef.[50–52]Inthenextsection,thede-
Γ(η HZ) 81m4
cFainyaollfyη,azys(u1ms)misapryreissegnitveedn,.andtheproductionisfollowed. Γ(ηzz→→γγ) = 256Cw2S2wzm4Z ∼3×103,
Γ(η tt¯) 243m2m2
z→ z t 1 103. (4)
DECAY Γ(ηz→γγ) = 512Cw2S2wm4Z ∼ ×
The HZ decay model of η is dominant, which is consis-
z
First, we study the decay mode of η (1s) states. The tentwithRef.[50]. Butifweconsider theelectroweakde-
zy
diphoton and digluon decay widths have been studied to caymodeofηzy(zz¯p+2yy¯),wecangetΓ(ηzy →f f¯)=Γ(ηzy →
2
HZ) 0,whichiscanceledbetweenzz¯and yy¯. Theratios non-relativisticboundstates[53],thenα 0.162. Thevari-
s
of ΓΓ((ηη=zz→→VγVγ)) aregivenhere, aatsiothnealhmydertohgoedniastoumsedrahdeiarel,waanvdetfuhnectteisotn∼fsunctionisselect
Γ(η W W ) 81
Γz(η→z→+γγ)− ∼ 128S4w 1+m2y/mz2 2 ∼3, R1s(r)=2×q3/2×e−qr. (10)
Γ(η ZZ) 32S2 ¡ 24S2 9 2¢ Thenwegettheradialwavefunctionsofηzy(1S)is
z→ w− w+ 0.8,
Γ(ηz→γγ) ∼ ¡ 1024Cw4S4w ¢ ∼ q = 98GeV
Γ(ηz→Zγ) 8S2w−3 2 0.2. (5) |R1s(0)|2 6.9GeV3. (11)
Γ(ηz→γγ) ∼ ¡32Cw2S2w¢ ∼ mη2zy =
deTcahyeweliedctthr,oawnedakΓtdoetc(ηazyyw(1ids)t)hisΓm(ηuzcyh(1lse)ssthgegn).thestrong If we consider the LO Coulomb potential only, |Rm1sη2(z0y)|2 ∼
∼ → 0.1GeV,wihchisconsistentwiththeresultin[50].Ifwecon-
The radial wave functions at origin R (0) can be given
s
| | sider the LO Coulomb and higgs exchange potential only,
throughtheSchrodingerequationwithstaticpotential.The
ourresultisconsistentwiththeresultin[50,52]. Theother
gluonexchangepotential hadbeencalculatedtotwoloop
potentialtermsabsorbthewavefunctiontotheoriginand
result[57–59],threeloop[60,61].Weuseonelooppotential
for S 0states [62,63]here, wherethe O(α2s )potential is enhanceqinEq.(10).
= mz Inanotherhand,αs(mz) 0.092,α(mz) 1/120. Wecan
included[64–69] ∼ ∼
getthepropertiesofη (1S)states[53],
zy
4α α2 31 10 2α2
Vgluon(r) = − 3rs −3πsr 3 − 9 nf −m rs2 E1 = −10GeV,
µ ¶ z M 2m E 750GeV,
4πα2sδ(~r) 2αs ~2 1~r(~r~)~ , Γ(η (1s) ηzyg(1gs)) = 0.30z+GeV1,=
− 3m2 +3m2r ∇ +r2 ∇ ∇ zy → =
z z · ¸ Γ(η (1s) γγ) 0.86MeV,
zy
→ =
wherenl =5isthenumberoflight-quarkflavors.Thepho- Br(ηzy(1s) γγ) 2.8 10−3. (12)
tonexchangepotentialis → = ×
5 α
V (r) , (6) PRODUCTION
photon
= −18 r
The Higgs exchange potential had been calculated to one Theleadingorder(LO)partoncrosssectionofη (1s)can
zy
loop, where the large fermion mass is canceled out and begetthrough[73]:
hence producesno enhancement for the radiative correc-
tions [70,71]. Sothatthe Higgsexchange potential in the σˆLO(gg→ηzy(1s)) = σ0Mη2zy(1s)δ(sˆ−Mη2zy(1s)) (13)
momentumspaceisgivenas[51,72]:
and
VHiggs(r) = −gz2e4−πmrHr Ã1+2πm2z2v2+167πm2t2v2!, (7) σ0 = 8Mπ32 ΓLO(ηzy(1s)→gg) (14)
ηzy(1s)
whereg mz, gz2 0.2,v 246GeV,andm 125GeV. wheresˆistheinvariantenergysquaredofinitialstatesgg.
z= v 4π∼ = H=
TherelativisticcorrectionsofkineticenergyandHiggsex- Andthehadroniccrosssectionofηzy(1s)is
change potential and the contributions of ghost of W, Z
σ (pp η (1s))
are[51] LO → zy
1dx τ
(~2)2 1 σ0τ f(x)f( )
Vrel.(r)=− 4∇mz3 −2v2δ(~r) = ΓLOZ(ητzy(x1s) ggx)π2 1dx τ
m2He−mHr−m2Ze−mZr+2mW2 e−mWr. (8) = Mηzy(1s)→S 8 Zτ x f(x)f(x), (15)
+ 16πv2r
whereτ M2 /S,andS istheinvariantmasssquareof
Thefirsttermarethe relativistic correctionsofkinetic en- = ηzy(1s)
initialproton-proton.Thenitscontributiontothediphoton
ergy.Thetotalpotentialis
distributionis
V(r) V (r) V (r) V (r) V (r) (9)
= gluon + photon + Higgs + rel. σLO(pp ηzy(1s) γγ)
→ →
In the numerical calculation, the strong coupling con- ΓLO(ηzy(1s) γγ)π2 1dx τ
→ f(x)f( ), (16)
stant can be determined through αs(mzvz/2) ∼ vz in the = Mηzy(1s)S 8 Zτ x x
3
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