nPDF constraints from the large hadron electron collider

This is an elec onic ep in o he o iginal a icle. This ep in may di e om he o iginal in pagina ion and ypog aphic de ail. Au ho (s): Ti le: Yea : Ve sion: Please ci e he o iginal e sion: All ma e ial supplied ia JYX is p o ec ed by copy igh and o he in ellec ual p ope y igh s, and duplica ion o sale o all o pa o any o he eposi o y collec ions is no pe mi ed, excep ha ma e ial may be duplica ed by you o you esea ch use o educa ional pu poses in elec onic o p in o m. You mus ob ain pe mission o any o he use. Elec onic o p in copies may no be o e ed, whe he o sale o o he wise o anyone who is no an au ho ised use . nPDF cons ain s om he la ge had on elec on collide Helenius, Ilkka; Paukkunen, Hannu; A mes o, Nes o Helenius, I., Paukkunen, H., & A mes o, N. (2016). nPDF cons ain s om he la ge had on elec on collide . In DIS 2016 : P oceedings o he 24 h In e na ional Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s (A icle 276). SISSA. PoS : P oceedings o Science, DIS2016. h ps://doi.o g/10.22323/1.265.0276 2016 PoS(DIS2016)276 nPDF cons ain s om he La ge Had on Elec on Collide Ilkka Helenius∗a, Hannu Paukkunenbcd and Nes o A mes od aDepa men o As onomy and Theo e ical Physics, Lund Uni e si y, Söl ega an 14A, SE-223 62 Lund, Sweden bUni e si y o Jy askyla, Depa men o Physics, P.O. Box 35, FI-40014 Uni e si y o Jy askyla, Finland cHelsinki Ins i u e o Physics, P.O. Box 64, FI-00014 Uni e si y o Helsinki, Finland dIGFAE, Uni e sidade de San iago de Compos ela, E-15782 Galicia, Spain E-mail: [email p o ec ed],[email p o ec ed], [email p o ec ed] An upda ed analysis ega ding he expec ed nuclea PDF cons ain s om he u u e La ge Had on Elec on Collide (LHeC) expe imen is p esen ed. The new s udy is based on a mo e lexible small-xpa ame iza ion which p o ides less biased unce ain y es ima es in he egion whe e he e a e cu en ly no da a cons ain s. The e ec o he LHeC is quan i ied by di ec ly including a sample o pseudoda a acco ding o he expec ed p ecision o his planned expe imen . As a esul , a signi ican educ ion o he small-xunce ain ies in sea qua ks and gluons is obse ed. XXIV In e na ional Wo kshop on Deep-Inelas ic Sca e ing and Rela ed Subjec s 11-15 Ap il, 2016 DESY Hambu g, Ge many ∗Speake . c Copy igh owned by he au ho (s) unde he e ms o he C ea i e Commons A ibu ion-NonComme cial-NoDe i a i es 4.0 In e na ional License (CC BY-NC-ND 4.0). h p://pos.sissa.i / PoS(DIS2016)276 nPDF cons ain s om he LHeC Ilkka Helenius 1. In oduc ion The La ge Had on Elec on Collide (LHeC) p ojec consis s on he cons uc ion o a new elec on accele a o p o iding an elec on beam ha would collide wi h he had on beam om he La ge Had on Collide (LHC). The design also allows a synch onous ope a ion o e-p collisions a he LHeC and p-p collisions a he LHC, as well as eplacing he p o on beam wi h hea y ions. A de ailed desc ip ion abou he design can be ound in he concep ual design epo [1]. Accu a ely de e mined pa on dis ibu ion unc ions (PDFs) a e essen ial o all pe u ba i e QCD (pQCD) based heo y p edic ions. This holds also o nuclea collisions, whe e he nuclea modi ica ions o he PDFs a e needed o ob ain a p ecise pQCD baseline o hea y-ion physics a he LHC, and also o u u e high-ene gy collide s, such as he Fu u e Ci cula Collide (FCC) [2]. In his alk we ocus on he cu en s a us o he nuclea PDFs (nPDFs), and quan i y he po en ial o e-Pb collisions a he LHeC o imp o e he accu acy o he u u e nPDF analyses. O he in e es ing e-Aphysics a e desc ibed e.g. in Re s. [1,3]. 2. New baseline nPDF i The nPDFs can be de e mined ia a simila global analysis as he ee p o on PDFs. The scale e olu ion is gi en by he DGLAP equa ions, bu a non-pe u ba i e inpu unc ion (x,Q2 0)a he ini ial scale Q2 0o he i is equi ed o he xdependence. The ansa z o (x,Q2 0)should include enough eedom o cap u e all he ele an ea u es o da a used in he analysis bu , on he o he hand, keep he numbe o pa ame e s easonable o ensu e he con e gence o he i and no o be sensi i e o he luc ua ions o he indi idual da a poin s. The da a used in he cu en i s comes om deep inelas ic sca e ing (DIS), D ell-Yan dilep- on p oduc ion and inclusi e pion p oduc ion in d-Au collisions a RHIC. Since mos o he da a a e om ixed- a ge expe imen s, he limi ed collision ene gy es ic s he kinema ic each o he da a, as discussed e.g. in Re . [3]. The e o e, he cu en i s NCTEQ15 [4], KA15 [5], DSSZ [6], EPS09 [7] and HKN07 [8] include da a ha a e es ic ed o x&5·10−3and Q2.100 GeV2. The ecen dije , cha ged had on and W±/Zda a om p-Pb collisions a he LHC p o ide some addi ional cons ain s o he nPDF analyses [9], bu in p ac ice do no inc ease he small-x each. Wi h he LHeC, he kinema ic each o e-ADIS c oss sec ion could be ex ended by mo e han h ee o de s o magni ude in bo h xand Q2p o iding a kinema ic each compa able o he cu en p o on PDF i s. The nPDF unce ain ies a e usually quan i ied ia he Hessian me hod [10], which allows a simple way o s udy how he unce ain ies p opaga e in o physical obse ables. Wi hin his me hod he pa ame e s (in a diagonalized basis) a e allowed o a y wi hin some ∆χ2 alue (he e, ∆χ2= 17). The unce ain y es ima es a e always ied o he unc ional o m o (x,Q2 0), especially in he egion whe e he e a e no guidance om he da a. In he EPS09 analysis [7] he a ios Ro pa on densi ies in a bound p o on inside a nucleus o e ha in a ee p o on we e pa ame ized wi h a piecewise unc ion, REPS09(x) =      a0+(a1+a2x)(e−x−e−xa),x≤xa b0+b1x+b2x2+b3x3,xa≤x≤xe c0+(c1−c2x)(1−x)−β,xe≤x≤1 .(2.1) 1 PoS(DIS2016)276 nPDF cons ain s om he LHeC Ilkka Helenius This unc ional o m does no allow much eedom o he small-xbeha iou , as shown in he le - hand panel o Figu e 1— he unc ion a small xis mono onic. Theo e ically, his kind o beha iou appea s easonable bu since global i s should a he indica e he unce ain y o igina ing om he used da a, a mo e lexible o m should be used o s udy he ealis ic po en ial o he LHeC. The small-x o m used in his s udy is R(x≤xa) = a0+a1(x−xa)2+√x(xa−x)a2logx xa+a3log2x xa+a4log3x xa,(2.2) which p o ides much mo e eedom o he small-xbeha iou educing he bias due o he ansa z signi ican ly. This is illus a ed in he igh -hand panel o Figu e 1, showing he R(x<xa,Q2 0)wi h a ew di e en possible pa ame e alues. Figu e 1: The i unc ion beha iou om he EPS09-s yle ansa z (le ) and om he new ansa z wi h mo e eedom a small alues o xused in his s udy ( igh ). To ha e a mo e ealis ic es ima e o he cu en unce ain ies, a new baseline i was pe - o med. The se up o he baseline i was e y simila as in he EPS09 analysis, bu now including he mo e lexible o m om Eq. (2.2) a low x. The new baseline i e lec s he lack o con ol a small alues o x om he da a by p o iding as ly la ge unce ain ies han he o iginal EPS09 analysis, as shown in Figu e 2, e en hough he da a cons ain s a e he same. 3. Fi o pseudoda a The impac o he LHeC pseudoda a on he nPDF unce ain ies was s udied by pe o ming a new nPDF analysis using pseudoda a gene a ed acco ding o LHeC expec a ions, bu o he wise keeping he de ails as in he baseline i . The pseudoda a we e gene a ed o neu al cu en (NC) DIS assuming pe -nucleon luminosi ies Lep =10 b and LePb =1 b. The kinema ical window s udied was 10−5<x<1 and 2 <Q2<105GeV2and he da a we e based on he EPS09 nPDFs, including also ealis ic luc ua ions wi h he ci ed luminosi ies [11]. A compa ison be ween he baseline i and he gene a ed pseudoda a is shown in Figu e 3displaying a ios o educed c oss sec ions be ween e-Pb and e-p collisions. Figu e 3shows also he co esponding compa ison a e including he pseudoda a in o he i . A d as ic educ ion o he nPDF unce ain ies is obse ed once he pseudoda a a e included o he analysis. 2 PoS(DIS2016)276 nPDF cons ain s om he LHeC Ilkka Helenius 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 EPS09 EPS09 EPS09 x R alence (Pb) x Rsea (Pb) x Rgluon (Pb) Ri(x,Q2=1.69 GeV2) Pb 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 EPS09 EPS09 EPS09 x R alence (Pb) x Rsea (Pb) x Rgluon (Pb) Ri(x,Q2=10 GeV2) Pb Figu e 2: The nPDF modi ica ions o alence (le ) and sea (middle) qua ks, and gluons ( igh ) a Q2=1.69 GeV2(uppe panels) and Q2=10 GeV2(lowe panels). The dashed lines show he unce ain y acco ding o he EPS09 analysis and he colou band he esul o he new baseline i wi h he mo e lexible low-xpa ame iza ion. To s udy he imp o emen s in mo e de ail, Figu e 4compa es he nPDF unce ain ies o alence qua ks, sea qua ks and gluons om he baseline i and om he new i including also he pseudoda a. The la ge-x alence qua ks a e al eady well cons ained by he cu en da a bu he imp o emen is signi ican o he small-xsea qua ks and gluons. Imp o emen like his would subs an ially solidi y he pQCD baseline o he hea y-ion physics a he LHC, and also a he FCC, al eady om pT∼3 GeV/c on. 4. Summa y The impac o he NC DIS da a om he LHeC o he nPDFs has been s udied. To ob ain a mo e ealis ic es ima es han he p esen nPDF unce ain ies, a new baseline i was pe o med applying a mo e lexible o m o he small-xbeha iou ha is included in he cu en i s. Due o he new pa ame iza ion, he baseline analysis possesses signi ican ly la ge small-xunce ain ies han he cu en public analyses. A se o pseudoda a was gene a ed acco ding o he expec ed LHeC speci ica ions, and a new i including he pseudoda a was pe o med and he unce ain ies we e compa ed o he baseline i wi hou he pseudoda a. The esul s show a subs an ial educ ion o small-xunce ain ies o sea qua ks and gluons, imp o ing he accu acy o pQCD baseline o hea y-ion collisions in he kinema ic egion ele an o he LHC and he FCC. Acknowledgmen s This esea ch was suppo ed by he Eu opean Resea ch Council g an Ho LHC ERC-2011- 3 PoS(DIS2016)276 nPDF cons ain s om he LHeC Ilkka Helenius 0.6 0.8 1.0 1.2 Q2=2GeV2Q2=5GeV2Q2=10GeV2Q2=20GeV2Q2=50GeV2 0.4 0.6 0.8 1.0 1.2 0.4 0.6 0.8 1.0 1.2 10-6 10-4 10-2 1 Q2=100GeV2 10-4 10-2 1 Q2=200GeV2 10-4 10-2 1 Q2=500GeV2 10-4 10-2 1 Q2=1000GeV2 10-4 10-2 1 Q2=2000GeV2 LHeC pseudoda a Baseline i xxxxx Ra io o he educed c oss-sec ions 0.6 0.8 1.0 1.2 Q2=2GeV2Q2=5GeV2Q2=10GeV2Q2=20GeV2Q2=50GeV2 0.4 0.6 0.8 1.0 1.2 0.4 0.6 0.8 1.0 1.2 10-6 10-4 10-2 1 Q2=100GeV2 10-4 10-2 1 Q2=200GeV2 10-4 10-2 1 Q2=500GeV2 10-4 10-2 1 Q2=1000GeV2 10-4 10-2 1 Q2=2000GeV2 LHeC pseudoda a LHeC i xxxxx Ra io o he educed c oss-sec ions Figu e 3: Ra ios o he educed NC DIS c oss sec ion be ween e-Pb and e-p collisions. The gene a ed pseudoda a a e shown wi h ed ma ke s and compa ed o he baseline i (uppe panels) and o a new i using he LHeC pseudoda a (lowe panels). The i unce ain ies a e shown wi h yellowish colou bands. S G-279579 and by Xun a de Galicia (Conselle ia de Educacion) — H. P. and N. A. a e pa o he S a egic Uni AGRUP2015/11. N. A. is suppo ed by he People P og amme (Ma ie Cu ie Ac ions) o he Eu opean Union Se en h F amewo k P og amme FP7/2007-2013/ unde REA g an ag ee- men #318921 and Minis e io de Ciencia e Inno aciónn o Spain unde p ojec FPA2014-58293- C2-1-P. I .H. has been suppo ed by he MCne ITN FP7 Ma ie Cu ie Ini ial T aining Ne wo k, con ac PITN-GA-2012-315877 and has ecei ed unding om he Eu opean Resea ch Council (ERC) unde he Eu opean Union Ho izon 2020 esea ch and inno a ion p og amme (g an ag ee- men No 668679). Re e ences [1] LHEC STUDY GROUP collabo a ion, J. L. Abellei a Fe nandez e al., A La ge Had on Elec on Collide a CERN: Repo on he Physics and Design Concep s o Machine and De ec o ,J. Phys. G39 (2012) 075001, [a Xi :1206.2913]. [2] A. Dainese e al., Hea y ions a he Fu u e Ci cula Collide ,a Xi :1605.01389. 4 PoS(DIS2016)276 nPDF cons ain s om he LHeC Ilkka Helenius 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 x R alence (Pb) x Rsea (Pb) x Rgluon (Pb) Ri(x,Q2=1.69 GeV2) Pb Baseline LHeC 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 0.2 0.6 1.0 1.4 10-5 10-4 10-3 10-2 10-1 10-5 10-4 10-3 10-2 10-1 x R alence (Pb) x Rsea (Pb) x Rgluon (Pb) Ri(x,Q2=10 GeV2) Pb Baseline LHeC Figu e 4: The nuclea modi ica ion o he PDFs o alence qua ks (le ), sea qua ks (middle) and gluons ( igh ) o wo scales Q2=1.69 GeV2(uppe panels) and Q2=10 GeV2(lowe panels). The baseline i is shown as yellowish colou bands and he i including also LHeC pseudoda a as da k ed bands. [3] I. Helenius, H. Paukkunen and N. 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