Resummation of Jet Shape and Extracting Properties of Quark-Gluon Plasma
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1 Jet Shape Resummation of Jet Shape and Extacting Popeties of Quak-Gluon Plasma Los Alamos National Laboatoy May 13, 014 QCD Evolution 014, Santa Fe In collaboation with Ivan Vitev
2 Outline Jet Shape In this talk, Jet shapes in poton collisions useful in quak jet and gluon jet discimination Resummation of phase space logaithms log /R using SCET Factoization theoem Renomalization goup evolution Possible issues about non-global logaithms (put aside fo now)
3 Outline Jet Shape In this talk, Jet shapes in poton collisions useful in quak jet and gluon jet discimination Resummation of phase space logaithms log /R using SCET Factoization theoem Renomalization goup evolution Possible issues about non-global logaithms (put aside fo now) Wok in pogess, Jet shapes in heavy ion collisions Medium induced splitting functions using SCET G (known) Medium modifications at fist ode in opacity O(L/λ)
4 Jet Shape Jet shape, integal and diffeential (Ellis, Kunszt, Sope) 50 R dψ() d 0 10 quak gluon Ψ J (, R) = i < E T i i <R E T i Ψ = 1 N J Ψ J (, R) N J J ψ(, R) = d Ψ d Ψ() quak gluon
5 Jet Shape Jet shape, integal and diffeential (Ellis, Kunszt, Sope) 50 R dψ() d 0 10 quak gluon Ψ J (, R) = i < E T 1.0 i i <R E quak T 0.8 i gluon Ψ = 1 N J 0.6 Ψ J (, R) Ψ() 0.4 N J J ψ(, R) = d Ψ d Jet shape pobes the enegy distibution inside a jet Quak jets ae moe localized vs. gluon jets ae moe spead out
6 Jet Shape Jet shape, integal and diffeential (Ellis, Kunszt, Sope) 50 R dψ() d 0 10 quak gluon Ψ J (, R) = i < E T 1.0 i i <R E quak T 0.8 i gluon Ψ = 1 N J 0.6 Ψ J (, R) Ψ() 0.4 N J J ψ(, R) = d Ψ d Jet shape pobes the enegy distibution inside a jet Quak jets ae moe localized vs. gluon jets ae moe spead out Lage logaithms of the fom α n s log m /R (m n) need to be esummed
7 Motivation I Jet Shape Quak-gluon discimination Many SM and BSM signals have quak-heavy final states QCD backgounds ae mostly gluon-heavy Quak and gluon jets have diffeent jet substuctues
8 Motivation I Jet Shape Quak-gluon discimination Many SM and BSM signals have quak-heavy final states QCD backgounds ae mostly gluon-heavy Quak and gluon jets have diffeent jet substuctues Being able to distinguish quaks fom gluons is vey impotant
9 Motivation I Jet Shape Quak-gluon discimination Many SM and BSM signals have quak-heavy final states QCD backgounds ae mostly gluon-heavy Quak and gluon jets have diffeent jet substuctues Being able to distinguish quaks fom gluons is vey impotant _ q q q q g q ~ o χ g q ~ χ o q ~ q ~ χ 1o o χ 1 g g h W W h _ q q q _ q gluon fusion vecto boson fusion (Left) Gluino decay chain with a quak-heavy final state (Right) Diffeent higgs poduction mechanisms with quak o gluon jets in the final state
10 Motivation II Jet Shape Chaacteizing the popeties of the quak-gluon plasma Modification of jet shapes contains infomation about the medium Quak and gluon jets get diffeent medium modifications
11 Motivation II Jet Shape Chaacteizing the popeties of the quak-gluon plasma Modification of jet shapes contains infomation about the medium Quak and gluon jets get diffeent medium modifications Pecision jet shape calculation in medium is vey impotant
12 Motivation II Jet Shape Chaacteizing the popeties of the quak-gluon plasma Modification of jet shapes contains infomation about the medium Quak and gluon jets get diffeent medium modifications Pecision jet shape calculation in medium is vey impotant (Top) The CMS diffeential jet shape measuements in pp and PbPb collisions with diffeent centalities (Bottom) Ratio of medium and vacuum jet shapes ( )
13 Jet Shape Jet shape calculations in pqcd (Seymou, Vitev et al) pqcd calculation with a paamete R sep fits the CDF data. Resummation pefomed using the modified leading logaithmic appoximation Initial state adiation and powe coections examined R sep 3 1 E T = 45-55GeV R 0 sep = E T [GeV] 10 1 LO w/o IS LO LO + PC LO + PC + RS ψ(/r) E T = GeV R sep = 1.4 E T = 50-77GeV ψ(/r) E T = 45-55GeV R sep =.0 LO w/o IS LO LO + PC LO + PC + RS R sep = E T = 50-77GeV R sep = / R (R=0.7) / R (R=0.7)
14 Jet Shape Jet shape calculations in pqcd (Vitev, Boston Jet Physics Wokshop 014) The CMS jet shape modification data is still not explained vey well
15 Jet Shape Jet shape calculations in pqcd (Yuan et al) Ψ() < 11 GeV 97 GeV < P T The compaison between the pqcd esummed esult and the CDF data "looks" petty good The blue cuve is the NLO pqcd calculation
16 Jet Shape Jet shape calculations in pqcd (Yuan et al) Ψ() < 11 GeV 97 GeV < P T Howeve, The compaison between the pqcd esummed esult and the CDF data "looks" petty good The blue cuve is the NLO pqcd calculation
17 Jet Shape Jet shape calculations in pqcd (Yuan et al) Ψ() < 11 GeV 97 GeV < P T Howeve, Jets ae econstucted using cone algoithms at Tevaton Soft adiation is ignoed Issues about non-global logaithms ae ignoed The logaithmic pecision ode is unclea Does not look at diffeential jet shape The compaison between the pqcd esummed esult and the CDF data "looks" petty good The blue cuve is the NLO pqcd calculation
18 Jet Shape Jet shape calculations in pqcd (Yuan et al) Ψ() < 11 GeV 97 GeV < P T Howeve, Jets ae econstucted using cone algoithms at Tevaton Soft adiation is ignoed Issues about non-global logaithms ae ignoed The logaithmic pecision ode is unclea Does not look at diffeential jet shape The compaison between the pqcd esummed esult and the CDF data "looks" petty good The blue cuve is the NLO pqcd calculation Let s esum phase space logs using SCET
19 Jet Shape Soft Collinea Effective Theoy (SCET) Sepaate physical degees of feedom by a systematic expansion in powe counting Matching SCET with QCD. Integate out the had modes. Futhe integate out the off-shell modes collinea Wilson lines Soft secto soft Wilson lines Soft-collinea decoupling at leading powe Factoization theoem QCD n n SCET Soft coss talk Figue: Factoization in SCET
20 Powe counting Jet Shape Jet shape has dominant contibutions fom the collinea secto Ψ() = E< c + E s < E c <R + E s <R E< c E c <R +O(λ) o O(λ ) Just a eminde, p c : Q(1,λ,λ) and p s : Q(λ,λ,λ) o Q(λ,λ,λ ) Contibutions fom the (ulta)soft modes ae powe suppessed λ is of O(R) because of dynamical theshold enhancement (and Λ) Fo small jets (R 1) the powe coections ae small
21 Powe counting Jet Shape Jet shape has dominant contibutions fom the collinea secto Ψ() = E< c + E s < E c <R + E s <R E< c E c <R +O(λ) o O(λ ) Just a eminde, p c : Q(1,λ,λ) and p s : Q(λ,λ,λ) o Q(λ,λ,λ ) Contibutions fom the (ulta)soft modes ae powe suppessed λ is of O(R) because of dynamical theshold enhancement (and Λ) Fo small jets (R 1) the powe coections ae small We will essentially do calculations only in a collinea secto
22 Powe counting Jet Shape Jet shape has dominant contibutions fom the collinea secto Ψ() = E< c + E s < E c <R + E s <R E< c E c <R +O(λ) o O(λ ) Just a eminde, p c : Q(1,λ,λ) and p s : Q(λ,λ,λ) o Q(λ,λ,λ ) Contibutions fom the (ulta)soft modes ae powe suppessed λ is of O(R) because of dynamical theshold enhancement (and Λ) Fo small jets (R 1) the powe coections ae small We will essentially do calculations only in a collinea secto Tems of O() and O(R) ae small, but O(/R) is not necessaily small
23 Factoization theoem Jet Shape p T,y E R J 1 J Factoization theoem fo the diffeential coss section of an anti-k T R jet with p T, y, enegy E inside the cone, and an enegy cutoff Λ outside to ensue N-jet configuation dσ dp TdydE = H(p T, y,µ)j ω 1 (E,µ)J (µ)...s 1,,...(Λ,µ) Λ Fo the diffeential jet ate dσ = H(pT, y,µ)j1(µ)j(µ)...s1,,...(λ,µ) dp Tdy
24 Factoization theoem Jet Shape p T,y E R J 1 J Factoization theoem fo the diffeential coss section of an anti-k T R jet with p T, y, enegy E inside the cone, and an enegy cutoff Λ outside to ensue N-jet configuation dσ dp TdydE = H(p T, y,µ)j ω 1 (E,µ)J (µ)...s 1,,...(Λ,µ) Λ Fo the diffeential jet ate dσ = H(pT, y,µ)j1(µ)j(µ)...s1,,...(λ,µ) dp Tdy Hee J ω 1 (E,µ) = X c 0 χ ω(0) X c X c χ ω(0) 0 δ(e Ê < (X c, algoithm)) and ω = E J is twice the jet enegy J i(µ) ae the "unmeasued jet functions" (Ellis, Vemilion, Walsh, Honig, Lee) All the jet and soft functions have R dependence
25 Jet shape in SCET Jet Shape The aveaged enegy inside the cone fo this jet is E ω = 1 dσ de dσ E = H(pT, y,µ)je 1(µ)J (µ)...s 1,,...(Λ,µ) dp dp T dy TdydE H(p T, y,µ)j = JE 1(µ) 1(µ)J (µ)...s 1,,...(Λ,µ) J 1(µ) Hee J E (µ) = de E J ω (E,µ) is called the "jet enegy function."
26 Jet shape in SCET Jet Shape The aveaged enegy inside the cone fo this jet is E ω = 1 dσ de dσ E = H(pT, y,µ)je 1(µ)J (µ)...s 1,,...(Λ,µ) dp dp T dy TdydE H(p T, y,µ)j = JE 1(µ) 1(µ)J (µ)...s 1,,...(Λ,µ) J 1(µ) Hee J E (µ) = de E J ω (E,µ) is called the "jet enegy function." The integal jet shape, aveaged ove all jets, is Ψ = 1 dp dσ Tdy σ total dp Tdy Ψω, whee Ψω = JE (µ)/j(µ) JR E(µ)/J(µ) = JE (µ) JR E(µ) PS
27 Jet shape in SCET Jet Shape The aveaged enegy inside the cone fo this jet is E ω = 1 dσ de dσ E = H(pT, y,µ)je 1(µ)J (µ)...s 1,,...(Λ,µ) dp dp T dy TdydE H(p T, y,µ)j = JE 1(µ) 1(µ)J (µ)...s 1,,...(Λ,µ) J 1(µ) Hee J E (µ) = de E J ω (E,µ) is called the "jet enegy function." The integal jet shape, aveaged ove all jets, is Ψ = 1 dp dσ Tdy σ total dp Tdy Ψω, whee Ψω = JE (µ)/j(µ) JR E(µ)/J(µ) = JE (µ) JR E(µ) PS Using the collinea SCET Feynman ules, the jet enegy function J E (µ) is calculated at O(α s) fo quak jets and gluon jets
28 Jet shape in SCET Jet Shape The aveaged enegy inside the cone fo this jet is E ω = 1 dσ de dσ E = H(pT, y,µ)je 1(µ)J (µ)...s 1,,...(Λ,µ) dp dp T dy TdydE H(p T, y,µ)j = JE 1(µ) 1(µ)J (µ)...s 1,,...(Λ,µ) J 1(µ) Hee J E (µ) = de E J ω (E,µ) is called the "jet enegy function." The integal jet shape, aveaged ove all jets, is Ψ = 1 dp dσ Tdy σ total dp Tdy Ψω, whee Ψω = JE (µ)/j(µ) JR E(µ)/J(µ) = JE (µ) JR E(µ) PS Using the collinea SCET Feynman ules, the jet enegy function J E (µ) is calculated at O(α s) fo quak jets and gluon jets Non-global logs of the fom log Λ/Q in the soft secto cancel, but thee ae still potential non-global logs in J E (µ) non-global phase space logaithms non-global logaithms in the collinea secto the stong-enegy-odeing phase space may not be contibuting to the leading non-global logs hee
29 Jet Shape Renomalization goup evolution of jet enegy functions dj qe (, R,µ) d lnµ dj ge (, R,µ) d lnµ = = [ C FΓ cusp ln ω tan R ] γ µ J q [ C AΓ cusp ln ω tan R ] γ µ J g J qe J ge (, R,µ) (, R,µ)
30 Jet Shape Renomalization goup evolution of jet enegy functions dj qe (, R,µ) d lnµ dj ge (, R,µ) d lnµ = = [ C FΓ cusp ln ω tan R ] γ µ J q [ C AΓ cusp ln ω tan R ] γ µ J g J qe J ge (, R,µ) (, R,µ) The anomalous dimensions of the jet enegy functions ae γ J q = 3C F, γ J g = β 0 = 11 3 CA TFnf
31 Jet Shape Renomalization goup evolution of jet enegy functions dj qe (, R,µ) d lnµ dj ge (, R,µ) d lnµ = = [ C FΓ cusp ln ω tan R ] γ µ J q [ C AΓ cusp ln ω tan R ] γ µ J g J qe J ge (, R,µ) (, R,µ) The anomalous dimensions of the jet enegy functions ae γ J q = 3C F, γ J g = β 0 = 11 3 CA TFnf The same anomalous dimensions as the unmeasued jet functions The anomalous dimensions ae independent Ψ ω is enomalization goup invaiant Ψ ω = JE (µ) J E R (µ) = JE (µ j ) J E R (µj R) UJ(µj,µ jr ) Choosing natual scales µ j and µ jr to eliminate lage logaithms
32 Natual scales Jet Shape Jet enegy functions at O(α s) ω JqE (, R,µ) = αsc [ F 1 ω tan π ln µ 3 ln ω tan µ ln X ln ω tan µ + 3π 4 +6X 3 1 ( X X X ) 4 X4 + X log X tan R ], whee X = tan tan R R
33 Natual scales Jet Shape Jet enegy functions at O(α s) ω JqE (, R,µ) = αsc [ F 1 ω tan π ln µ 3 ln ω tan µ ln X ln ω tan µ + 3π 4 +6X 3 1 ( X X X ) 4 X4 + X log X tan R ], whee X = tan tan R R The scale µ j = ω tan EJ eliminates lage logaithms at O(αs) J E (µ) and JR(µ) E have the same anomalous dimensions but diffeent scales
34 Natual scales Jet Shape Jet enegy functions at O(α s) ω JqE (, R,µ) = αsc [ F 1 ω tan π ln µ 3 ln ω tan µ ln X ln ω tan µ + 3π 4 +6X 3 1 ( X X X ) 4 X4 + X log X tan R ], whee X = tan tan R R The scale µ j = ω tan EJ eliminates lage logaithms at O(αs) J E (µ) and JR(µ) E have the same anomalous dimensions but diffeent scales R µ µ jr E J R RG evolution between µ j and µ jr esums log /R µ j E J
35 Jet Shape Resummed jet enegy functions log /R s ae esummed using the familia RG kenels in SCET (i = q, g) Ψ i ω JiE (, R) = (, R,µ j ) JR ie(r,µ j R ) exp[ C i S(µ j,µ jr )+ A J i(µ j,µ jr )] αs(µ) α S(ν,µ) = α s(ν) dα Γcusp(α) β(α) α s(ν) dα β(α ), A X(ν,µ) = ( µ ) j Ci A Γ (µ jr,µ j ) ω tan R αs(µ) dα γ X(α) α s(ν) β(α)
36 Jet Shape Resummed jet enegy functions log /R s ae esummed using the familia RG kenels in SCET (i = q, g) Ψ i ω JiE (, R) = (, R,µ j ) JR ie(r,µ j R ) exp[ C i S(µ j,µ jr )+ A J i(µ j,µ jr )] αs(µ) α S(ν,µ) = α s(ν) dα Γcusp(α) β(α) α s(ν) dα β(α ), A X(ν,µ) = ( µ ) j Ci A Γ (µ jr,µ j ) ω tan R αs(µ) dα γ X(α) α s(ν) β(α) Ψ() quak LO quak NLL gluon LO gluon NLL dψ() d quak LO quak NLL gluon LO gluon NLL Integal and diffeential jet shapes of 100 GeV quak and gluon jets at LO and NLL
37 Jet Shape Compaison with the CMS data ( ) dψ() d Diffeential jet shape in poton collisions with cente of mass enegy of.76 TeV
38 Jet Shape Compaison with the CMS data ( ) dψ() d Diffeential jet shape in poton collisions with cente of mass enegy of.76 TeV The blue bands (LO and NLL) ae fo R=0.3 anti-k T jets with p T > 100 GeV and 0.3 < η < Resummation is impotant The geen band is fo R=0.3 cone jets - The diffeence fo jets econstucted using diffeent algoithms is of O(/R) Bands ae theoy uncetainties estimated by vaying µ j and µ jr Fo the egion R we need highe ode fixed ode calculations and powe coections
39 Jet Shape Compaison with the CMS data ( ) GeV pt 60 GeV.0 dψ() d GeV pt 600 GeV.0 dψ() d Diffeential jet shape in poton collisions with cente of mass enegy of 7 TeV
40 Jet Shape Compaison with the CMS data ( ) GeV pt 60 GeV.0 dψ() d dψ() d GeV pt 600 GeV The blue band (NLL) is fo R=0.7 anti-k T jets with η < 1 Fo low p T jets powe coections ae significant Fo high p T jets the SCET calculations epoduce the peak egion vey well Diffeential jet shape in poton collisions with cente of mass enegy of 7 TeV
41 Jet Shape Compaison with the CMS data ( ) GeV pt 60 GeV.0 dψ() d dψ() d GeV pt 600 GeV The blue band (NLL) is fo R=0.7 anti-k T jets with η < 1 Fo low p T jets powe coections ae significant Fo high p T jets the SCET calculations epoduce the peak egion vey well SCET woks in jet shape! Diffeential jet shape in poton collisions with cente of mass enegy of 7 TeV
42 Jet Shape Jet shape in heavy ion collisions z Heavy ion collisions ceate a stong inteacting medium called quak-gluon plasmas Jets passing though QGP ae obseved to be "quenched" Glaube gluon inteaction povides tansvese momentum kicks, p G : Q(λ,λ,λ) SCET G descibes the in-medium jet fomation mechanism Jet shape gets modified when the jet passes though QGP Ψ() = JE,vac J E,vac R + J E,med + J E,med R = JE,vac J E,vac R J E,vac R J E,vac R + J E,med R + J E,vac R J E,med + J E,med R Lage logaithms in Ψ vac () = J E,vac ae esummed Thee ae no lage logaithms in J E,med at fist ode in opacityo(l/λ) (Landau-Pomeanchuk-Migdal effect) /J E,vac R
43 Jet Shape In-medium jet enegy functions With the medium induced splitting functions at hand, we calculate the medium modifications of jet enegy functions In the small x limit, the medium induced splitting functions ae dn q qg = CFαs 1 L d z dxd k π x 0 λ d q 1 σ el dσ el d q We use the effective coss section 1 σ el k q [ k (q 1 cos k ) dσ el d q = ( (q k ) z )] xω m in static QGP π(q +m ) Thee is no soft-collinea divegence when integating ove x and k The RG evolution of jet enegy functions is the same as in vacuum
44 Peliminay esult Jet Shape 1.4 Ρ PbPb Ρ pp We plot the atio of the diffeential jet shapes in lead-lead and poton-poton collisions fo gluon jets with p T = 100 GeV and y = 0 Fo quak jets the cuve is quite diffeent The data is fo the centality bin between 30 50% We haven t aveaged jet shapes with the appopiate coss sections Powe coections seem to be impotant aound R Calculations evaluated fo static QGP with λ g = 1 fm, L = 4.5 fm, m = 0.75 GeV
45 Conclusions Jet Shape Jet shape is calculated in the SCET collinea secto The factoization theoem is witten down Jet enegy functions ae calculated at O(α s) fo quak and gluon jets Global logaithms ae esummed to NLL using RG evolution Nice ageement with the ecent CMS data
46 Conclusions Jet Shape Jet shape is calculated in the SCET collinea secto The factoization theoem is witten down Jet enegy functions ae calculated at O(α s) fo quak and gluon jets Global logaithms ae esummed to NLL using RG evolution Nice ageement with the ecent CMS data Wok in pogess Look into issues about non-global logaithms Calculate jet shapes in heavy ion collisions using SCET G Help studying the popeties of the quak-gluon plasma
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