gluon–gluon fusion or quark–antiquark annihilation?

12 Pages·2016·0.78 MB·English

Diphoton excess at 750 GeV: gluon–gluon fusion or
quark–antiquark annihilation?
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Citation Gao, Jun, Hao Zhang, and Hua Xing Zhu. “Diphoton Excess at
750 GeV: Gluon–gluon Fusion or Quark–antiquark Annihilation?”
The European Physical Journal C 76.6 (2016): n. pag.
As Published http://dx.doi.org/10.1140/epjc/s10052-016-4200-z
Publisher Springer Berlin Heidelberg
Version Final published version
Accessed Thu Jan 03 17:56:14 EST 2019
Citable Link http://hdl.handle.net/1721.1/103629
Terms of Use Creative Commons Attribution
Detailed Terms http://creativecommons.org/licenses/by/4.0/
Eur.Phys.J.C (2016) 76:348
DOI10.1140/epjc/s10052-016-4200-z
RegularArticle-TheoreticalPhysics
Diphoton excess at 750 GeV: gluon–gluon fusion
or quark–antiquark annihilation?
JunGao1,a,HaoZhang2,b,HuaXingZhu3,c
1HighEnergyPhysicsDivision,ArgonneNationalLaboratory,Argonne,IL60439,USA
2DepartmentofPhysics,UniversityofCalifornia,SantaBarbara,SantaBarbara,CA93106,USA
3CenterforTheoreticalPhysics,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA
Received:19May2016/Accepted:10June2016
©TheAuthor(s)2016.ThisarticleispublishedwithopenaccessatSpringerlink.com
Abstract Recently, ATLAS and CMS collaborations 19,26–30,32–34,38,41–45,48–57,59,63,65–69,71,72,75–
reported an excess in the measurement of diphoton events, 80,83–87,89,90,93–109,115–128,130–133,136,139–141].
which can be explained by a new resonance with a mass Whilethemodelsproposedvarysignificantly,therearesome
around 750 GeV. In this work, we explored the possibility commonfeaturessharedbymostofthem.Duetothequan-
ofidentifyingifthehypotheticalnewresonanceisproduced tum number of photon pair, most of the proposals suggest
throughgluon–gluonfusionorquark–antiquarkannihilation, thattheexcessiseitherduetogluon–gluonfusionorquark–
or tagging the beam. Three different observables for beam antiquark annihilation. Different production mechanisms
tagging,namelytherapidityandtransverse-momentumdis- can lead to very different UV models. Knowing the actual
tribution of the diphoton, and one tagged bottom-jet cross production mechanism responsible for the potential excess
section, are proposed. Combining the information gained is of great importance for understanding the underlying
fromtheseobservables,acleardistinctionoftheproduction theory.Unfortunately,verylittlecanbesaidfromthecurrent
mechanismforthediphotonresonanceispromising. data,exceptsomeconsiderationsbasedontheconsistencyof
experimentaldatafromtheLHCRun1andRun2.
In this work, we shall study the following problem: if
1 Introduction thediphotonexcesspersistsinfuturedata,andtheexistence
of a new resonance is established, is it possible to distin-
Very recently, both ATLAS and CMS collaborations pre- guishdifferentproductionmechanismswithenoughamount
sentednewresultsfromLHCRun2.Althoughmostofthe of data? One can compare this question with the more fre-
measurements can still be fit in the Standard Model (SM) quentlyaskedquestion,namely,howtotellwhetheranener-
framework nicely, some intriguing excesses are reported. getic hadronic jet in the final state is due to a quark or a
Of particular interest is the diphoton excess around 750 gluon produced from hard scattering. This is also known
GeVseenbybothcollaborations.TheATLAScollaboration as the quark and gluon jet tagging problem; see e.g. Refs.
reported an excess above the standard model (SM) dipho- [31,91,92,114].1 Onecanviewthequestionofdifferentiat-
tonbackgroundwithalocal(global)significanceof3.9(2.3) ingtheggfusionandqq¯ annihilationmechanismasafinal-
σ [3]. The CMS collaboration, with a little less integrated state-to-initial-statecrossingofthequarkandgluonjettag-
luminosity,alsoreportedanexcessat760GeVwithalocal ging problem. For this reason we will call it the quark and
(global)significanceof2.6(alittlelessthan1.2)σ [2]. gluonbeamtaggingprobleminthiswork,orbeamtagging
Though further data is required to establish the exis- forshort.Whileourcurrentworkinthebeamtaggingprob-
tence of a new resonance or other beyond the SM (BSM) lem was motivated by the diphoton excess, we believe that
mechanism responsible for the diphoton excess, significant our results will be useful even if the excess disappear after
theoretical efforts have been made to explain the possible moredataisaccumulated,becauseabumpmighteventually
diphotonexcessinvariousBSMscenarios[4–9,11–13,15– showupatadifferentplaceand/orinadifferentchannel.
ae-mail:[email protected]
1 Asomewhatrelateddiscussionhasalsobeenmadeintheliterature
be-mail:[email protected] ofthecolorcontentofBSMresonanceproduction[14,138],andthe
ce-mail:[email protected] taggingofinitial-stateradiation[112].
123
348 Page 2 of 11 Eur.Phys.J.C (2016) 76:348
Animportantfeatureofthebeamtaggingproblemisthat Therecouldalsobeeffectiveoperatorswithapseudoscalar.
mostoftheQCDradiationsfromtheinitial-statepartonsare But their long distance behavior is in-distinguishable from
intheforwarddirection,andthereforearehardtomakeuse the scalar case. Also the scalar has to couple to photon in
of.Thisiscontrastedwithfinal-statejettagging,inwhichthe order to be able to decay todiphoton. But that is irrelevant
informationofQCDradiationsinthejetplaycrucialrolein tomostofourdiscussion.
identifyingthepartonicoriginofthejet.Thisfeaturemakes Thanks to QCD factorization, the hadronic production
the beam tagging problem difficult. Based on the consider- crosssectionforScanbewrittenas
ation of general properties of initial-state QCD radiations, (cid:5) (cid:6) (cid:7)
we explore different observables which are useful for the σ0(i) =τ τ1 dxx fi/N1(τ/x)fi¯/N2(x)+(i ↔i¯) σˆ0(i),
beam tagging problem. First of all, we consider the rapid-
(2)
itydistributionofthediphotonsystem.Itiswellknownfrom
Drell–Yanproductionthatfortheqq¯initialstate,contribution where τ = M2/E2 . The operator in Eq. (1) leads to the
S CM
fromvalencequarkandseaquarkcanhavedifferentshapein
followingpartoniccrosssectiontothescalarproduction:
rapiditydistribution.Usingthisinformation,wefindthatit
(cid:3) (cid:4)
ispossibletodistinguishthevalence-quark scatteringfrom π α 2
sea-quarkorgluonscattering.Second,weconsiderthetrans- σˆ(g) = s ,
0 16(N2−1) 3π(cid:5)
versemomentum(QT)distributionofthediphotonsystem. (cid:3)c (cid:4) g
π v 2
It is well known that the QT distribution of a color neutral σˆ(q) = . (3)
systemexhibitsaSudakovpeakatlowQ duetoinitial-state 0 2N (cid:5) M
T c q S
QCDradiation.Interestingly,thestrengthofinitial-stateradi-
ationdiffersforquarkorgluoninducedhardscatteringand 2.1 Rapiditydistribution
leadstosubstantialdifferenceinthepositionoftheSudakov
peak. Using this information, it is possible to distinguish ItiswellknownthatforWandZbosonproductionintheSM,
light-quark scattering from bottom-quark or gluon scatter- contributionsfromdifferentpartonicchannelshavedifferent
ing.Lastly,tofurtherdifferentiatebottom-quarkinducedor shapes in rapidity distribution of the boson. Valence-quark
gluoninducedscattering,weconsidertaggingab-quarkjet contributionshaveadoubleshoulderstructurewhilethesea-
inthefinalstate. quarkcontributionspeakinthecentralregionduetodiffer-
Thepaperisorganizedasfollows:InSect.2.1westudy ent slopes of the parton distribution functions (PDFs) with
the rapidity distribution of the diphoton system, and pro- respecttoBjorkenx.Theresultsaresimilarforaresonance
pose using centrality ratio,defined as ratio of cross section of750GeVproducedat13TeVLHC.Onewaytoquantify
incentralrapidityregionandthetotalcrosssection,todis- theshapeofrapiditydistributionistousethecentralityratio,
criminateproductionmechanismduetovalence-quarkscat- whichisdefinedasratioofcrosssectionsincentralrapidity
tering from sea-quark or gluon scattering. In Sect. 2.2 we region |y| < y and the total cross sections. In Fig. 1 we
cut
studythetransverse-momentumdistributionofthediphoton showthecentralityratioasafunctionof y fora750GeV
cut
system, and propose the ratio of cumulative cross section resonance produced through different parton combinations
in two different transverse-momentum bins to discriminate at leading order (LO). The hatched bands show the corre-
light-quark scattering from bottom-quark or gluon scatter- sponding 68 % confidence level (C.L.) PDF uncertainties
ing.InSect.2.3,westudyb-taggedcrosssectiontofurther as calculated according to the PDF4LHC recommendation
discriminatebottom-quarkscatteringfromgluonscattering. [39],whicharesmallespeciallyforthevalence-quarkcon-
WeconcludeinSect.3. tributions.Theratiosapproachonewheny approachesthe
cut
endpoint of the rapidity distribution ∼2.8. As expected the
valence-quarkcontributionshavesmallervaluesfortheratio
than the ones from gluon or bottom quarks. The ratios are
2 Threemethodsforthebeamtaggingproblem
very close for gluon and bottom-quark or other sea-quark
contributions, since the sea-quark PDFs are mostly driven
Weconsiderthefollowingeffectiveoperatorswithanaddi-
by the gluon through DGLAP evolution. Taken y to be
cut
tionalsingletscalar S:
1,thecentralityratiosare0.74,0.77,0.63and0.50,forgg,
bb¯,dd¯,anduu¯channels,respectively.Assumingmostofthe
L =−1 αs SGa Ga,μν experimental systematics will cancel in the ratio and with
eff 43π(cid:5) μν highstatistics,itwillbepossibletodiscriminateunderlying
g (cid:3) (cid:4)
(cid:2) v theory with production initiated by valence quarks and by
+ (cid:5) Sq¯fqf +h.c. . (1) gluon or sea quarks. Higher-order perturbative corrections
f=u,s,d,c,b f maychangeabovenumberswhichdependonthefulltheory.
123
Eur.Phys.J.C (2016) 76:348 Page 3 of 11 348
(cid:10) (cid:3) (cid:4) (cid:11)
1.0 ln(M2/Q2) 22 4 1
gg × 4CA QS2 T − 3 CA−3Nf Q2
_ T T
0.8 bb 2P (ξ )
_ + ga 1 δ δ(1−ξ )
σtot 0.6 dudu_ 2PQ2T(ξ )bg 2 (cid:12)
ycut + gQb2T 2 δagδ(1−ξ1) +O(αs2) (4)
0.4
y
σ forgg-fusionproduction.Similarly,forqq¯induceddiphoton
0.2 LHC13TeV,M 750GeV production,wehave
(cid:8)
0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 dσ(q)(cid:8)(cid:8)(cid:8) = (cid:6)αs (cid:7)τσˆ(q)(cid:2)(cid:5) 1dx (cid:5) 1dx δ(x x −τ)
ycut dQ2T (cid:8)Q2>0 4π 0 a,b 0 1 0 2 1 2
T (cid:5) (cid:5)
Fityigr.e1gioCne|nyt|ra<lityyrcauttioan,ddetfihneetdoataslractrioososfscercotsiosnse,catsioanfiunnccetniotrnalorfapyicdu-t ×(cid:9)x11 dξξ11 fa/N1(x1/ξ1) x21 dξξ22 fb/N2(x2/ξ2)
× δaqδbq¯δ(1−ξ1)δ(1−ξ2)
(cid:10) (cid:11)
2.2 Diphotonatsmalltransversemomentum
ln(M2/Q2) 1
× 4C S T −6C
F Q2 FQ2
WenextconsiderthetransversemomentumQ ofthedipho- T T
T
tfoonrdsiypshtoemto.nIhnasthbeeeSnMc,otnrsaindsevreerdsaet-mNeoxmt-etnot-uNmexrte-stou-mLmeaadtiinogn +2PqQa2(ξ1)δq¯gδ(1−ξ2)
T (cid:12)
Logarithm(NNLL)level[58].Fullydifferentialdistribution 2P (ξ )
isalsoknownatfixednext-to-next-to-leadingorder(NNLO) + gQb2 2 δagδ(1−ξ1) +(q ↔q¯)+O(αs2),
[46]. Here we consider the case where the diphoton origi- T
(5)
natesfromthedecayofanewresonanceat750GeV.AtLO
inQCD, Q isexactlyzeroduetomomentumconservation
T where P (z)aretheLOQCDsplittingfunctions:
inthetransverseplane.However,asiswellknownfromthe ij
studyofDrell–Yanleptonpairtransverse-momentumdistri- (cid:13) (cid:14)
bution, QT is not peaked at zero but rather at finite trans- P (z)=C 1+z2 ,
versemomentum.Theshiftfrom QT =0tonon-zerovalue qq F 1−z +
(cid:15) (cid:16)
is mostly due to initial-state QCD radiation. For example, 1
P (z)= (1−z)2+z2 ,
ifthediphotonisproducedfrom gg fusion,theinitial-state qg 2
(cid:13) (cid:14)
gluoninoneprotoncansplitintotwogluonsbeforecolliding (1−z+z2)2 1
wisipthusthheedgtlouonnonf-rzoemrothQeoathsearrpersoutlotno.fTthheesdpilpihttointognpsroycsteesms. Pgg(z)=2C(cid:3)A z (cid:4) 1−z +
T
11 1
Forlarge QT,thestrongcouplingissmallandperturbative + CA− Nf δ(1−z),
6 3
expansionworkswell.However,when Q ismuchsmaller
T
than M ,largelogarithmsoftheratiobetween M and Q 1+(1−z)2
S S T P (z)=C . (6)
gq F
couldarise,whichspoilstheconvergenceoftheperturbative z
series.Asanexample,atNLO,thepartoniccrosssectionfor
the QT distributionofthediphotonsystematleadingpower ItisclearfromEq.(4)thatwhen QTisverysmall,theloga-
in Q2/M2 canbewrittenas rithmln(0,1)(M2/Q2)/Q2canbecomeverylargeandpertur-
T S S T T
bativeexpansioninα isnolongervalid.Theoriginofthese
s
(cid:8) large logarithms is due to long distance QCD effects: soft
dσ(g)(cid:8)(cid:8)(cid:8) = (cid:6)αs (cid:7)2τσˆ(g)(cid:2)(cid:5) 1dx (cid:5) 1dx δ(x x −τ) and/orcollinearradiationfrominitial-statepartons.Thanks
dQ2T (cid:8)Q2>0 4π 0 a,b 0 1 0 2 1 2 toQCDfactorization,thedynamicsofsoftand/orcollinear
T (cid:5) (cid:5) radiation can be well separated from the dynamics of UV
1 dξ 1 dξ
× ξ1 fa/N1(x1/ξ1) ξ2 fb/N2(x2/ξ2) physics. This is particular useful for us, because we would
(cid:9) x1 1 x2 2 liketoperformabeamtaggingstudyinawaythatdoesnot
relytoomuchontheunderlyingBSMmodels,e.g.,tree-level
· δ δ δ(1−ξ )δ(1−ξ )
ag bg 1 2 inducedorloop-inducedSproduction.FromEq.(4),onecan
123
348 Page 4 of 11 Eur.Phys.J.C (2016) 76:348
alsoseethattheleadinglogarithmictermdiffersbetweengg- A(i) =4C(i),
ifsusmioaninclryosdsuseectotiothneanddifqfeq¯reanncneihinilatthioenacssrooscsiasteecdticoonl,owrhfiacch- A(12i) =4C(i)(cid:3)(cid:3)697 − π32(cid:4)CA− 109Nf (cid:4),
tor, C = 3 versus C = 4/3. It is then expected that the
differeAnce can lead toFdifferent shape in the QT spectrum. B1(g) =−232CA+ 43Nf,
Since the perturbative expansion of the Q spectrum does
notconvergeatlow QT,resummationofthTelarge QT loga- B1(q) =−6CF, (9)
rithmsisrequiredbeforeonecanassessthesignificanceofthe
changeinshapeforthe QT spectrumwhenswitchbetween whereC(g) =CA,C(q) =CF.ThefunctionCi(ji)(x;μ)isthe
gg fusion and qq¯ annihilation. Fortunately, resumming the hard collinear factor. For NLL resummation, we only need
largelogarithmsduetosmalltransversemomentumhasbeen theirLOexpression:
studiedsincetheearlydaysofQCD[47,60–62,81,129].The
formalism developed in this pioneer work can be used in Ci(ji)(x;μ)=δijδ(1−x). (10)
our 750 GeV diphoton study with little change, thanks to
the universality of QCD at long distance. According to the Y(Q2,τ) denotes those terms which are not enhanced by
T
celebrated Collins–Soper–Sterman (CSS) formula [62],the ln(M2/Q2).Theycanbecomputedusinganaiveexpansion
S T
Q distributionofthediphotonsystemcanbewrittenasan inα .Sometimestheycouldhavelargeimpactatlarge Q .
T s T
inverseFouriertransformation: But in the region we are interested in, they can be safely
neglected.NotethatinEq.(7),whenbisverylarge,theinte-
(cid:5) (cid:5) (cid:5)
ddσQ(i2) = τσˆ0(i) ∞ d2b bJ0(bQT)(cid:2) 1dx1 1dx2 gαrsa(lμ¯f)odriμv¯erignetsh.eTehxepeoxniestnetnwceouolfdthheitLaanLdaanudpauolpeoaltes,mwahlelrμ¯e
T 0 (cid:5) a,b(cid:3) 0 0 (cid:4) indicatestheonsetofnon-perturbativephysicsinthatregion,
×δ(x x −τ) 1 dξ1C(i) ξ ;μ= b0 andanappropriateprescriptiontodealwiththeLandaupole
1 2 ξ ia 1 b is needed; see, e.g., Refs. [36,62,113,134]. We emphasize
(cid:3) x1 1(cid:4)(cid:5) (cid:3) (cid:4)
×fa/N1 xξ1;μ= bb0 1 dξξ2 Ci¯(bi¯) ξ2;μ=bb0 tthoaotmthuecChSoSnftohremUuVla idsyqnuaimteicgseonfertahleanudnddeorleysinngotpdroepceesnsd.
(cid:3) 1 (cid:4) x2 (cid:9)2 (cid:5) Remarkably, at NLL level, all the process dependent infor-
×f(cid:10)b/N2 xξ22;μ= bb0 exp − b02M/bS22(cid:11)(cid:12)dμ¯μ¯22 mσˆ0(ait)i,oanndhaivnethbeeelanbeenlc(oi)defodrivnatrhioeutsredeimpaerntosinoincacnrodscsoslelicntieoanr
factor.Thus,weexpectthatthestatementwemakefromthe
M2
× ln μ¯2S A(i)[αs(μ¯)]+B(i)[αs(μ¯)] QT spectrumisrathermodelindependent.
To quantify the discussion above, we calculate the Q
(cid:17) (cid:18) T
+ i ↔i¯ +Y(Q2,M2,E2 ), (7) spectrum of the 750 GeV diphoton system numerically for
T S CM
13TeVLHC.ThankstothepreviousQCDstudies,several
public computer codes are available which implement the
where J (x) is the zeroth order Bessel function of the first
0
kind, b0 = 2e−γE, γE = 0.577216... is Euler’s constant. rYeasnumanmdaHtioigngosfptrroadnusvcetirosne-,mbootmheinnttuhmeQloCgaDrifthrammsefworoDrkrealnld–
Thesummationofaandbareoverdifferentpartonspecies,
in the Soft-Collinear Effective theory framework [20–23].
u,u¯,d,...,g.A[α (μ¯)]andB[α (μ¯)]areuniversalanoma-
s s
Resummation of Q for 750 GeV diphoton resonance can
lousdimensionswhoseperturbativeexpansionscanbewrit- T
be easily accomplished by modifying those existing codes.
tenas
Specifically,wemodifyHqT,whichisbasedontheworkof
Refs.[35–37,74],andCuTe,whichisbasedontheworkof
(cid:3) (cid:4)
(cid:2)∞ α (μ) n Refs. [24,25], to calculate the transverse-momentum spec-
A(i)[α (μ)]= s A(i),
s 4π n trumofthehypothetical750GeVresonance.InHqT,aLan-
n=1(cid:3) (cid:4) daupoleisavoidedbydeformingtheb-spaceintegraloffthe
B(i)[α (μ)]=(cid:2)∞ αs(μ) n B(i). (8) realaxisslightly,whileinCuTe,theLandaupoleisavoided
s 4π n byimposingacutofffortheμ¯ integralatverysmallvalue.
n=1
Inbothcalculations,weusethefive-flavorscheme,namely
thebottomquarkistreatedasamasslesspartoninthePDFs.
In this work, we restrict ourselves to resummation of Q WecalculatetheQ spectrumbyturningonthecoupling
T T
logarithmsatNext-to-LeadingLogarithmic(NLL)accuracy of the diphoton resonance with each individual parton fla-
(i) (i) (i)
only,forwhichonlyA ,A ,andB areneeded.Theyare vor at one time. The differential distribution is plotted in
1 2 1
givenby[70,110,111] Fig. 2 for results from the two codes mentioned above at
123
Eur.Phys.J.C (2016) 76:348 Page 5 of 11 348
0.05 Table1 Ratio Rfora750GeVresonanceproducedat13TeVLHC,
_ _
uu bb initiatedbydifferentpartonflavorsaspredictedbytworesummation
0.04 dd_ cc_ codes,HqTandCuTe
unit gg ss_ R,NLL bb¯ cc¯ ss¯ uu¯ dd¯ gg
y
arbitrar 0.03 HCquTTe 01..9352 00..6882 00..5780 00..5656 00..5635 11..3522
0.02
T
Q
d
σ
d 0.01
LHC13TeV,M 750GeV PDFsliesaroundmuchlowervaluesthanthebottom-quark
HqT2.0,NLLresummed one.ItthusindicatesthattheSudakovpeakforbottom-quark
0.00
0 10 20 30 40 50 60 contribution has to show up at larger value of QT in order
Q GeV toaccommodatethefactthatitsthresholdishigher.Forthe
T
gluoncontribution,theshapeofthe Q spectrumisfurther
T
0.05 broadened, and has the largest value for the peak position.
_ _
uu bb This is mainly due to the difference in color factor. In the
_ _
0.04 dd cc gluoncase,theSudakovexponenthasastrongersuppression
unit gg ss_ effectsbecauseCA ∼ 2.25CF.Wehavecheckedthatifwe
ary 0.03 naivelychangethecolorfactorfromCA toCF forthegluon
bitr contribution,itspeakpositionmovetoamuchlowervalue.
ar FromFig.2,wecanseethattheresultsfromthetwocodes
0.02
T
Q usedforthecalculationaresimilar,althoughtheyhaveadif-
d
σ ferentframeworkforresummationandadifferenttreatment
d 0.01
LHC13TeV,M 750GeV of the Landau pole. The major difference comes from the
CuTe,NLLresummed bottom-quarkcontribution,wherethepeakpositiondifferby
0.00
0 10 20 30 40 50 60 about5GeV.Thisismainlyduetodifferentwaysinthetwo
QT GeV codestoavoidLandaupole.Becauseofthelargemassofthe
resonance, non-perturbative effects are less pronounced as
Fig. 2 QTdistributionatsmalltransversemomentumatNLLaccuracy
comparingwiththeW,Z bosonproductionintheSM,aswe
fortheresonanceproductioninitiatedbydifferentpartonflavors.The
twoplotsshowresultsobtainedfromtwopubliccodes,HqTandCuTe checkedbyvaryingthenon-perturbativeparameteravailable
inHqTandCuTe.Also,forthesamereason,thesubleading
termsin Q aresmallintheregionweplot.
T
Ideally,adetailedcomparisonofthenormalized Q dis-
T
NLL resummed accuracy. Comparing the distributions for tributionpredictedbyQCDfactorizationandtheLHCdata
production initiated by different parton combinations, the forthehypotheticalresonancewouldprovidemostinforma-
shapesaremostlydrivenbytwofactors:(a)thecolorfactor tionasregardsthebeamtaggingproblemfromQ spectrum.
T
inSudakovexponent,C forgluonversusC forquarks;(b) Inreality,thisisverydifficultduetothelimitedstatisticsand
A F
theevolutionofPDFs.Forlight-quarkcontributions,which experimental uncertainties in measuring the photon trans-
includesup,down,strange,andcharmquark,thepeakposi- verse momentum. To simplify the analysis, we introduce a
tion stay at low values, less than 10 GeV in general. For ratio R, which is defined as the cross section in Q bin of
T
bottom-quarkcase,thedistributionsarebroaderandshiftto [(cid:11) ,2(cid:11) ] to the one in Q bin of [0,(cid:11) ]. The optimal
T T T T
higher Q . The reason for the rightward shift of the bot- choice for (cid:11) differs for different center of mass energy
T T
tom contribution comparing to the light-quark contribution anddifferentresonancemass.Inourcurrentcase,wechoose
is as follows. For the formal treatment of the quark contri- (cid:11) = 20GeV.TheresultsfortheratioarelistedinTable1
T
bution in the CSS formula, Eq. (7), there are no essential basedoncurvesshowninFig.2forthetwocodesandvar-
differencebetweenlightquarkandbottomquark.Theonly ious parton flavors. We can see a clear distinction for pro-
differencecomesfromtheirPDFs,whichareevaluatedatthe duction initiated by light quarks, which favor a value of R
scaleb /b,theFourierconjugateof Q .WhiletheDGLAP lowerthan1,andproductioninitiatedbygluon,whichfavors
0 T
evolutionforlightquarkandbottomquarkarethesameinthe a value of R larger than 1. As noted above, prediction for
five-flavorscheme,theboundaryconditionsforthesePDFs bottom-quark initiated production are quite different, indi-
differ. For bottom quark, the threshold of the correspond- cating a larger theoretical uncertainty in the resummation
ingPDFliesaroundm ∼ 4.2 GeV,belowwhichthePDF treatmentofheavy-quarkinduceddiphotonproduction.This
b
vanishes.Ontheotherhand,thethresholdofthelight-quark uncertainty prevents us from distinguishing it from gluon
123
348 Page 6 of 11 Eur.Phys.J.C (2016) 76:348
¯ ¯ ¯
b S b b b b b S b S
b S b g
¯ ¯
¯b g g S g S b g b S g b g ¯b
Fig. 4 TheFeynmandiagramsoftheresonancewithonejetproduction
q S q q q¯ q¯ process.Inthisscenario,thenewresonanceisproducedviathebb¯initial
stateattheLHC
q¯ g g S g S
inducesalotofb-jetsfromthegb(b¯)initial-stateprocesses.
g g g g g g Theb-jetfractionintheISRjetsthenshouldbesignificant
andcanbetaggedattheLHCRun2.
For a simple estimation, we generate parton level signal
g S g S g S
eventswithMadGraph5[10]andCT14lloPDF(five-flavor
Fig. 3 TheFeynmandiagramsoftheresonancewithonejetproduction scheme)[82].ThesignaleventsareshoweredusingPythia6.4
processinggscenario [137] with Tune Z2 parameter [88]. The detector effect is
simulated using DELPHES 3 [40,73]. The b-tagging effi-
ciencyistunedtobeconsistentwiththedistributionshown
initiatedcase.Theuncertaintymightbereducedifthecalcu- in Ref. [1]. For the signal strength, we scale the inclusive
lationisextendedtoNNLLlevelconsistently,orusingfour- signalevents(withMLMmatchingscheme)tofitthecurrent
flavorschemeforthePDFs,whicharebeyondthescopeof data[2,3](inthiswork,weonlyfitthedatafromtheATLAS
thiswork.Wehavealsocheckedthetheoreticaluncertainties collaboration).Werequirethephotontosatisfy
fromothersources,e.g.,PDFsandpowercorrectionswhich
areatafewpercentlevelandcanbeneglectedsafely. |η|<1.37, or 1.52<|η|<2.37. (11)
The transverse energy of the leading (subleading) photon
2.3 Diphotonwithadditionalb-jet
should be larger than 40 (30) GeV. The leading and sub-
leading photon candidates are then required to satisfy the
In the previous two sections, we have shown that by mea-
conditions
suringtherapidityandtransverse-momentumdistributionof
thediphotonsystem,itispossibletodistinguishthevalence- Eγ1 Eγ2
quark induced diphoton production from sea-quark/gluon T >0.4, T >0.3. (12)
mγγ mγγ
induceddiphotonproduction,andlight-quarkinduceddipho-
tonproductionfromgluoninduceddiphotonproduction.In
Theinclusivediphotonspectrumisestimatedwith
thissection,wefocusontheremainingtwoproductionsce-
narios.Inthefirstscenario(gg),thenewscalarresonanceis (cid:13) (cid:6) mγγ (cid:7)1/45(cid:14)3.38(cid:6) mγγ (cid:7)−3.49
producedviathegluonfusionprocess.Inthesecondscenario 0.026 1− fb/GeV.
¯ 13TeV 13TeV
(bb),thescalarresonanceisproducedviabbinitialstate.We
(13)
willshowthata99.7%C.L.distinguishcanbereachedwith
lessthan10fb−1integratedluminosityat13TeVLHC.This
We solve the best-fit signal strength μ by maximizing [64,
meansifthe750GeVexcessisindeedanewresonance,we
135]
donotneedtowaitforlongtoknowitsproductionmecha-
(cid:19)
nism. (cid:13) (cid:14)
Inthegg scenario,thedominantproductionmodeofthe −2ln L({b}|{n}) , (14)
newresonanceisgluonfusionprocess.Withtheinitial-state L(μ{s}+{b}|{n})
radiation (ISR) effect, there are additional jets in the final
state. The Feynman diagrams for jet production at LO in wherethelikelihoodfunctionisdefinedby
QCD are shown in Fig. 3. Since in the small-x region the
(cid:20) xni exp(−x )
gluon PDF is much larger than other partons, it is easy to L({x}|{n})≡ i i . (15)
seethatmostoftheISRjetsaregluonandlight(especially (cid:13)(ni +1)
i
u andd)quarks.Theb-jetfractionintheISRjetsishighly
suppressedbythesmallnessofbottom-quarkPDF.Thuswe Both the gg and the bb scenario give 3σ discovery signifi-
expectthatthenumberofhardb-jetintheISRjetsissmall. cance.
In the bb scenario, we show the Feynman diagrams for Afternormalizingtheinclusivecrosssectiontothebest-fit
jetproductionatLOinQCDinFig.4.ThelargegluonPDF value,weselecteventswithatleastonehardjetinthefinal
123
Eur.Phys.J.C (2016) 76:348 Page 7 of 11 348
10 Table2 Thefractionofthebackgroundeventswithatleastoneaddi-
V] 13 TeV LHC tionalhardjet.Thefractionoftheeventswiththeleadingjetistagged
Ge asab-jetintheseevents.Inthelastline,weshowtheN+beventnumber
0 withtheassumptionthatallbackgroundeventsarefromthecorrespond-
2 gg scenario, inclusive
b/ 1 ingprocess
[fpT gg scenario, b-tag Background γγ γj jj
d bb scenario, inclusive
σ/
d bb scenario, b-tag N+j/Nincl 47.1% 66.3% 64.5%
10−1 N+b/N+j 1.85% 2.63% 5.03%
N+b/Nincl 0.871% 1.74% 3.24%
N+b(fb) 0.133 0.267 0.497
10−2
(cid:21)
100 200 300 400 500 (cid:22) (cid:10) (cid:17) (cid:18)(cid:11)
Leading-jet pT [GeV] CLg ≡(cid:22)(cid:23)−2log LL(cid:17)ssb++nnb||ssg++nnb(cid:18) , (17)
g b g b
Fig. 5 Transverse-momentumdistributionoftheleading-(b-)jet
andthebbscenariofromtheggscenariowith
(cid:21)
(cid:22) (cid:10) (cid:17) (cid:18)(cid:11)
satlagtoer.iJthemtsiwnitthheRfin=al0s.t4a.teWaeredreemcoannsdtrtuhceteledaudsininggjeatnttoi-khTavjeet CL ≡(cid:22)(cid:23)−2log L sg+nb|sb+nb , (18)
b L(s +n |s +n )
b b b b
|η|<2.5, and p >40GeV. (16)
T
respectively,wheres ,s ,andn aretheeventnumberswith
b g b
To suppress the SM background, we further require the theleadingadditionaljettaggedasab-jetinthescenariobb,
diphoton invariant mass to satisfy |mγγ − 750GeV| < scenarioggandtheSMbackground.InFig.6,weshowthe
150GeV.Transversemomentumdistributionsoftheleading discriminating abilities versus the integrated luminosity of
jetareshowninFig.5fordifferentproductionmechanisms theLHCinthe13TeVrun.Itisshownclearlyinthisfigure
withandwithoutrequiringtheleadingjetisb-tagged. that,evenwiththemostconservativeassumption(allback-
At13TeVLHC,inggscenariotheinclusiveone-jetevents groundeventsarefromthe jj process),onecandistinguish
containafractionof0.08fbb-jeteventsoutofatotalcross theggscenariofromthebbscenariowith8.8fb−1integrated
sectionof3.12fb.Alternatively,thefractionis1.21fboutof luminosity,anddistinguishthebbscenariofromtheggsce-
2.72fbinbbscenario. nariowith6.2fb−1integratedluminosityat13TeVLHC.If
Togiveanestimationofthepossibilityofdistinguishing the SM background are (a MC simulation will support this
the two production scenarios, we also need to simulate the assumption) γγ process dominant, one can distinguish the
SMbackgrounds.Therearelotsoftheoreticaluncertainties. gg scenario from the bb scenario with 6.0 fb−1 integrated
Onlyadatadrivenestimationofthebackgroundsisreliable luminosity,anddistinguishthebbscenariofromtheggsce-
at present. In this work, we make a simple estimation by nariowith3.3fb−1integratedluminosityat13TeVLHC.
rescaling the current background withluminosity. Thus we
onlyneedtocalculatethefractionofthebackgroundevents
with additional hard b-jet. The most important SM back- 3 Summaryandconclusion
groundsaretheirreducibleγγ processandthereducibleγj
and jj processeswithoneormorejetsfakedtobephotonin Recently,anintriguingexcessinthediphotoneventshasbeen
thedetector.Withthemasswindowcut,wecountthefraction reported both by the ATLAS and CMS collaboration. The
of events with at least one additional hard jet (N+j/Nincl), localsignificanceis3.9σ fromATLASand2.6σ fromCMS.
andthefractionoftheseeventswhoseleadingjetistaggedas Aftertakingintoaccountthelook-elsewhereeffect,thesig-
ab-jet(N+b/N+j).Sincethecutonthefirstandthesecond nificancereducesto2.3σ fromATLASand1.2σ fromCMS.
photontransverseenergyareasymmetric,therearealotof Althoughthecurrentexperimentalstatusisfarfromconclu-
eventswhichpassthecutswithadditionaljetsfromtheISR. sive, alarge number of BSM scenarios have been explored
TheresultsareshowninTable2.Withthedatadrivenback- to explain the diphoton excess. A significant number of
groundformulaEq.(13),thetotalbackgroundcrosssection theseBSMmodelscontainascalarresonanceproducedfrom
in600GeV<mγγ <900GeVis15.32fb. hadron-hadron collision and subsequently decay to dipho-
Sincethebackgroundcrosssectionissmall,weestimate ton system, whose mass is around 750 GeV. In this work,
theabilityofdistinguishingtheggscenariofromthebbsce- weinvestigatedwhetherthehadronicproductionmechanism
nariowith[64,135] forthehypotheticalnewscalarresonancecanbeidentified.
123
348 Page 8 of 11 Eur.Phys.J.C (2016) 76:348
5 tioninfive-flavorschemeversusfour-flavorscheme.Third,
L
C
inordertodistinguishthegluoninducedproductionfromb
quark induced production, we calculated the diphoton plus
4
jetproductionwithabtaggingontheleadingjetinfive-flavor
scheme.Wefindthatanadditionalbjetismorefavoredinb
3 13 TeV LHC quarkinducedproductionthaningluoninducedproduction.
Combiningtheknowledgegainedfromallthereobservables,
2 CL (γγ) wefindthattheperspectiveforidentifyingtheexactproduc-
b
CL (jj) tion mechanism for the hypothetical diphoton resonance is
b
CL (γγ) promising,thoughdetailedworkisneededinordertofurther
g
1 CL (jj)
g understandthetheoryandexperimentaluncertaintiesofour
current luminosity
methods,whichweleaveforfuturework.Lastly,weempha-
0 sizethatalthoughthecurrentworkismainlymotivatedbythe
0 5 10 15 20
diphotonexcessrecentlyreportedbytheATLASandCMS
Integrated Luminosity[fb-1]
collaboration,theproblemweproposedandthemethodswe
suggestedareusefulandinterestinginitselfeventheexcess
Fig. 6 Theabilityofdistinguishingthegg(bb)scenariofromthebb
(gg)scenario.Thesolidlinesarewiththeassumptionthatallofthe disappearsaftermoredataiscollected.
backgroundeventsarefromtheirreducibleγγbackground.Thedashed
linesarewiththeassumptionthatallofthebackgroundeventsarefrom Acknowledgments We thank Yotam Soreq and Wei Xue for help-
thereducible jjbackgroundwithtwojetsarefakedasphoton ful conversations. The work of H.Z. is supported by the U.S. DOE
underContractNo.DE-SC0011702.TheworkofH.X.Z.issupported
bytheU.S.DepartmentofEnergyundergrantContractNumberDE-
Thatis,isitmainlyproducedfrom gg fusionorqq¯ annihi- SC0011090.WorkatANLissupportedinpartbytheU.S.Department
lation. We dubbed this question the quark and gluon beam ofEnergyunderContractNo.DE-AC02-06CH11357.H.Z.ispleasedto
recognizethehospitalityoftheserviceofferedbytheAmtrakCalifornia
taggingproblem.Weexpectthatasuccessfulsolutiontothis
Zephyrtrain.
problem will play a key role in unraveling the mystery of
the750GeVdiphotonexcess.Wehaveperformedamodel OpenAccess ThisarticleisdistributedunderthetermsoftheCreative
independentstudiedofthisproblembyconsideringasetof CommonsAttribution4.0InternationalLicense(http://creativecomm
ons.org/licenses/by/4.0/),whichpermitsunrestricteduse,distribution,
effective operators between the hypothetical resonance and
andreproductioninanymedium,providedyougiveappropriatecredit
gluonorquark.Wediscussseveraldifferentialdistributions
totheoriginalauthor(s)andthesource,providealinktotheCreative
relevant for the determination of initial constituent for the Commonslicense,andindicateifchangesweremade.
750GeVexcess.Weconcentrateonthosedistributionswhich FundedbySCOAP3.
are more sensitive to QCD dynamics at long distance, and
thus less model dependent. To that end, we explored three
differentbutcomplementaryobservablesforbeamtagging.
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