Production of four-jets in single- and double-parton scattering within high-energy factorization

0.25 MB·

by  Krzysztof Kutak

Production of four-jets in single- and double-parton
scattering within high-energy factorization
7
1
0
2

b Krzysztof Kutak
e
F InstituteofNuclearPhysics,PolishAcademyofSciences,
Radzikowskiego152,31-342Kraków,Poland
4
2 E-mail: [email protected]

]
h
We report on a first study of 4-jet production in a complete high-energy factorization (HEF)
p
- framework[1,2]. Weincludeanddiscusscontributionsfrombothsingle-partonscattering(SPS)
p
e and double-parton scattering (DPS) and compare to the measured data. The DPS HEF result is
h
considerablysmallerthantheoneobtainedwithcollinearfactorization. Themechanismleading
[

tothisdifferenceisofkinematicalnature.Incontrasttothecollinearapproach,theHEFapproach
2
v nicelydescribesthedistributionofthe∆Svariable,whichinvolvesallfourjetsandtheirangular
0
correlations.
1
4
0
0
.
1
0
7
1
:
v
i
X
r
a
38thInternationalConferenceonHighEnergyPhysics
3-10August2016
Chicago,USA
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
Four-jet
1. Introduction
Sofar,complete(n≥4)-jetproductionviasingle-partonscattering(SPS)wasdiscussedonly
withincollinearfactorization. Resultsuptonext-to-leading(NLO)precisioncanbefoundin[3,4].
Here we report on recent study of production of four jets including SPS processes and Double-
parton scattering (DPS) within high-energy (k -)factorization (HEF) [5, 6, 7, 8] 1. Double-parton
T
scattering (DPS) was claimed to have been observed for the first time at the Tevatron [10]. In
the LHC era, with much higher collision energies available, the field has received a new impulse
andseveralexperimentalandtheoreticalstudiesaddresstheproblemofpinningdownDPSeffects.
Even just from purely theoretical point of view, the problem is quite subtle [11]. As for the non
perturbativeside, itisinprinciplenecessary, whenconsideringadouble-partonscattering, totake
intoaccountthecorrelationsbetweenthetwopartonscomingfromthesameprotonsandinvolved
in the scattering processes. Such an information should be encoded in a set of double parton
distribution functions (DPDFs), generalising usual parton distribution functions (PDFs). Some
successfulattemptstogeneralizetheusualevolutionandtohaverelevanceforphenomenologyare
becomingtoappearonlyrecently[13,14,15,16].
In the meanwhile, phenomenological and experimental studies of double-parton scattering
rely on factorized Ansatz for the DPDFs, which amount to neglecting momentum correlations
between partons and introducing an effective cross section, σ . The latter quantity is usually
eff
extracted from experimental data. In the present approach we will use the factorized Ansatz and
concentrateonthedifferencebetweenleading-ordercollinearandhigh-energy-factorizationresults.
The latter includes effectively higher-order corrections. For most of high-energy reactions the
single-parton scattering dominates over the double-parton scattering. The extraordinary example
is double production of cc¯ pairs [12]. For four-jet production, disentangling the ordinary SPS
contributions from the DPS corrections can be quite challenging for several reasons: first of all,
itisnecessarytodefinesufficientlysensitive,process-dependentobervables,w.r.t. whichtheDPS
differentialcrosssectionmanifestlydominatesatleastinsomecornersofphasespace.
2. Single-partonscatteringproductionoffourjets
TheHEFfactorizationformulaforthecalculationoftheinclusivepartonic4-jetcrosssection
attheBornlevelreads
(cid:90) dx dx
σB = ∑ 1 2d2k d2k F(x ,k ,µ )F (x ,k ,µ )
4−jets x x T1 T2 i 1 T1 F j 2 T2 F
i,j 1 2
(cid:32) (cid:33)
1 4 d3k 4
× ∏ l Θ (2π)4δ x P +x P +(cid:126)k +(cid:126)k −∑k |M(i∗,j∗→4part)|2.
2sˆ (2π)32E 4−jet 1 1 2 2 T1 T2 i
l=i l l=1
(2.1)
HereF(x ,k ,µ )isaTMD(TransversalMomentumDependent)[19]distributionfunction
i k Tk F
for a given type of parton carrying x momentum fractions of the proton and evaluated at the
1,2
1foroverviewoftheframeworksee[9]
1
Four-jet
factorizationscale µ . Theindexl runsoverthefourpartonsinthefinalstate,thepartoniccenter
F
of mass energy squared is sˆ=2x x P ·P; the function Θ takes into account the kinematic
1 2 i j 4−jet
cuts applied and M →4part is the gauge invariant matrix element for 2→4 particle scattering
with two initial off-shell legs calculated numerically with a numerical package [18]. It includes
symmetrization effects due to identity of particles in the final state and new degrees of freedom
introduced via(cid:126)k , which are the parton’s transverse momenta, i.e. the momenta perpendicular
Tk
to the collision axis. The formula is valid when the x’s are not too large and not too small when
complicationsfromnonlinearitiesmayeventuallyarise[17].
3. Double-partonscatteringproductionoffourjets
Single-partonscatteringcontributionsareexpectedtobedominantforhighmomentumtrans-
fer,asitishighlyunlikelythattwopartonsfromoneprotonandtwofromtheotheroneareenergetic
enough for two hard scatterings to take place, as the behaviour of the PDFs for large x suggests.
However,asthecutsonthetransversemomentaofthefinalstatearesoftened,awindowopensto
possiblyobservesignificantdoublepartonscatteringeffects,asoftenstatedintheliteratureonthe
subject. First of all, let us recall the formula usually employed for the computation of DPS cross
sections,adjustingittothe4-partonfinalstate,
dσB m dσB(i j →k l ) dσB(i j →k l )
4−jet,DPS = ∑ 1 1 1 1 2 2 2 2 , (3.1)
dξ dξ σ dξ dξ
1 2 eff i1,j1,k1,l1;i2,j2,k2,l2 1 2
where the σ(ab→cd) cross sections are obtained by restricting formula (2.1) to a single channel
andthesymmetryfactormis1unlessthetwohardscatteringsareidentical,inwhichcaseitis1/2,
so as to avoid double counting them. Above ξ and ξ stand for generic kinematical variables for
1 2
the first and second scattering, respectively. The effective cross section σ can be interpreted as
eff
ameasureofthetransversecorrelationofthetwopartonsinsidethehadrons,whereasthepossible
longitudinal correlations are usually neglected. In this paper we use σ provided by the CDF,
eff
D0collaborationsandrecentlyconfirmedbytheLHCbcollaborationσ =15mb,whenallSPS
eff
mechanismsofdoublecharmproductionareincluded.
3.1 ComparisontoCMSdata
AsdiscussedinRef.[21],sofartheonlyexperimentalanalysisoffour-jetproductionrelevant
fortheDPSstudieswasrealizedbytheCMScollaboration[20]. Thecutsusedinthisanalysisare
p >50GeVforthefirstandsecondjets, p >20GeVforthethirdandfourthjets,|η|<4.7and
T T
thejetconeradiusparameter∆R>0.5.
It goes without saying that the LO result with soft cuts applied needs refinements from NLO
contributions. For this reason, in the following we will always perform comparisons only to data
(re)normalisedtothetotal(SPS+DPS)crosssections. WhatisinterestingintheHEFresult, com-
paredtocollinearfactorization,isthedramaticdampingoftheDPScontribution. InFigs.1and2
wecomparethepredictionsinHEFtotheCMSdata. HereboththeSPSandDPScontributionsare
normalizedtothetotalcrosssection,i.e. thesumoftheSPSandDPScontributions. Inallcasesthe
renormalizedtransversemomentumdistributionsagreewiththeCMSdata. However,theabsolute
crosssectionsobtainedinthiscasewithintheHEFapproacharetoolarge.
2
Four-jet
1 p p fi 4 jets X s = 7 TeV 1 p p fi 4 jets X s = 7 TeV
1] 10-1 SPS HEF 1] 10-1 SPS HEF
-V 10-2 SPS collinear -V 10-2 SPS collinear
e e
[GT1100--43 DDPPSS HcoEllFinear [GT1100--43 DDPPSS HcoEllFinear
dp 10-5 dp 10-5
/ /
sd 10-6 |y| < 4.7 sd 10-6 |y| < 4.7
10-7 CMS data 10-7 CMS data
s1/ 10-8 13srtd,, 24ntdh jjeett:: ppT >> 5200 GGeeVV s1/ 10-8 13srtd,, 24ntdh jjeett:: ppT >> 5200 GGeeVV
T T
50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500
SPS HEFData 012...25551 Leading jet pT [GeV] SPS HEFData 012...25551 Leading jet pT [GeV]
50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500
Leading jet p [GeV] 2nd leading jet p [GeV]
T T
Figure1: ComparisonoftheLOcollinearandHEFpredictionstotheCMSdataforthe1stand2ndleading
jets. InadditionweshowtheratiooftheSPSHEFresulttotheCMSdata.
1 p p fi 4 jets X s = 7 TeV 1 p p fi 4 jets X s = 7 TeV
10-1 10-1
-1]V 10-2 SPS HEF -1]V 10-2 SPS HEF
Ge 10-3 SDPPSS cHoEllFinear Ge 10-3 SDPPSS cHoEllFinear
[T1100--54 DPS collinear [T1100--54 DPS collinear
/dp 1100--76 /dp 1100--76 13srtd, ,2 4ntdh jjeett:: ppTT >> 5200 GGeeVV
sd sd
10-8 10-8
s1/ 10-9 |y| < 4.7 1st, 2nd jet: p > 50 GeV s1/ 10-9 |y| < 4.7
10-10 CMS data 3rd, 4th jet: pT > 20 GeV 10-10 CMS data
T
SPS HEFData 246 50 100 150 3rd2 0l0eadin2g50 jet pT3 0 0 [GeV35]0 400 450 500 SPS HEFData 231 50 100 150 3rd2 0l0eadin2g50 jet pT3 0 0 [GeV35]0 400 450 500
50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500
3rd leading jet p [GeV] 4th leading jet p [GeV]
T T
Figure2: ComparisonoftheLOcollinearandHEFpredictionstotheCMSdataforthe3rdand4thleading
jets. InadditionweshowtheratiooftheSPSHEFresulttotheCMSdata.
Not only transverse momentum dependence is interesting. The CMS collaboration extracted
also a more complicated observables [20]. One of them, which involves all four jets in the final
state,isthe∆Svariable,definedinRef.[20]astheanglebetweenpairsoftheharderandthesofter
jets,where(cid:126)p (j,j )standsforthesumofthetransversemomentaofthetwojetsinarguments.
T i k
In Fig. 3 we present our HEF prediction for the normalized to unity distribution in the ∆S
variable. Our HEF result approximately agrees with the experimental ∆S distribution. In contrast
theLOcollinearapproachleadsto∆S =0, i.e. aDirac-deltapeakat∆S =0forthedistributionin
∆S. For the DPS case this is rather trivial. The two hard and two soft jets come in this case from
the same scatterings and are back-to-back (LO), so each term in the argument of arccos is zero
(jets are balanced in transverse momenta). For the SPS case the transverse momenta of the two
jetpairs(withhardjetsandsoftjets)areidenticalandhaveoppositedirection(thetotaltransverse
momentumofallfourjetsmustbezerofromthemomentumconservation). Thenitiseasytosee
thattheargumentofarccosisjust-1. Thismeans∆S =0. Theaboverelationsarenotfullfilledin
the HEF approach. The SPS contribution clearly dominates and approximately gives the shape of
3
Four-jet
the∆Sdistribution. ItisanywayinterestingthatwedescribethedataviapQCDeffectswithinour
HEFapproachwhichareinRef.[20]describedbyparton-showersandsoftMPIs.
10 p p fi 4 jets X s = 7 TeV
-1]d 13srtd,, 24ntdh jjeett:: ppT >> 5200 GGeeVV CMS data
S [ra 1 |y| < 4S.7PS T+ DPS
SPS HEF
D/ DPS HEF
s d 10-1
s1/
Data 1.50 0.5 1 D S1. 5 [rad] 2 2.5 3
Theory/ 0.510 0.5 1 1.5 2 2.5 3
D S [rad]
Figure3: ComparisonoftheHEFpredictionstotheCMSdatafor∆S spectrum. Inadditionweshowthe
ratioofthe(SPS+DPS)HEFresulttotheCMSdata.
Acknowledgments
TheworkofK.K.havebeensupportedbyNarodoweCentrumNaukiwithSonataBisgrant
DEC-2013/10/E/ST2/00656. ThepaperisbasedoncommonpublicationwithRafalMaciula,
MirkoSerino,AndreasvanHameren,AntoniSzczurek.
References
[1] K.Kutak,R.Maciula,M.Serino,A.SzczurekandA.vanHameren,JHEP1604(2016)175.
[2] K.Kutak,R.Maciula,M.Serino,A.SzczurekandA.vanHameren,Phys.Rev.D94(2016)no.1,
014019.
[3] Z.Bern,etal.,Phys.Rev.Lett.,109(2012),042001.
[4] SimonBadger,BenediktBiedermann,PeterUwer,andValeryYundinPhys.Lett.,B718(2013),965.
[5] S.Catani,M.CiafaloniandF.Hautmann,Phys.Lett.B242(1990)97.
[6] J.C.CollinsandR.K.Ellis,Nucl.Phys.B360(1991)3.doi:10.1016/0550-3213(91)90288-9
[7] M.Deak,F.Hautmann,H.JungandK.Kutak,JHEP0909(2009)121
doi:10.1088/1126-6708/2009/09/121[arXiv:0908.0538[hep-ph]].
[8] M.Deak,F.Hautmann,H.JungandK.Kutak,arXiv:0908.1870[hep-ph].
[9] S.Sapeta,Prog.Part.Nucl.Phys.89(2016)1doi:10.1016/j.ppnp.2016.02.002[arXiv:1511.09336
[hep-ph]].
[10] F.Abeetal.(CDFcollaboration)Phys.Rev.,D47(1993),4857.
[11] P.Kotko,A.M.StastoandM.Strikman,arXiv:1608.00523[hep-ph].
[12] RafalMaciulaandAntoniSzczurek(2013),1301.4469.
4
Four-jet
[13] MatteoRinaldi,SergioScopetta,MarcoTraini,andVicenteVento,JHEP,12(2014),028.
[14] WojciechBroniowski,EnriqueRuizArriola,andKrzysztofGolec-Biernat,arXiv:1602.00254
[15] KrzysztofGolec-Biernat,EmiliaLewandowska,MirkoSerino,ZacharySnyder,andAnnaM.
Stasto,Phys.Lett.,B750(2015),559.
[16] K.Golec-BiernatandA.M.Stasto,arXiv:1611.02033[hep-ph].
[17] P.Kotko,etal.JHEP,09(2015),106.
[18] A.vanHameren,arXiv:1611.00680[hep-ph].
[19] R.Angeles-Martinezetal.,ActaPhys.Polon.B46(2015)no.12,2501
doi:10.5506/APhysPolB.46.2501[arXiv:1507.05267[hep-ph]].
[20] SergueiChatrchyanetal.(CMS)Phys.Rev.,D89(2014)(9),092010.
[21] RafalMaciulaandAntoniSzczurekPhys.Lett.,B749(2015),57.
5