QCD at the ILC: Effective Field Theory Methods

Transcription

1 QCD at ILC: Effective Field Theory Methods Sonny Mantry University of Wisconsin at Madison NPAC Theory Group Emerging Opportunities for International Linear Collider, March 18th, 2011

2 A selection of topics Top Quark Mass Event Shapes Strong coupling Constraining new physics N-jettiness Jet Shapes

3 Top Mass Extraction What is top mass? Top is colored parton. Top mass is a parameter of Lagrangian. Top mass is renormalization scheme dependent. top? top? Which top mass? Which mass scheme are experimentalists measuring? Not known! Mass scheme depends on method used to measure mass. Kinematic reconstruction no longer sufficient.

4 Threshold Scan (Fadin, Khoze; Peskin, Strassler;Hoang, Manohar, Stewart, Teubner) Top pair-production at threshold Shape of cross-section sensitive to top mass. Top width provides IR cutoff. Non-perturbative effects are small. QR 2 v t (b) Physics well understood LL, NLL, NNLL _ s (GeV) NRQCD is appropriate EFT. Well-defined relation to short distance mass; eg.1s mass NNLL results known. Precision: δm t 100 MeV

5 Top Mass From Jet Distributions e + e t tx Boosted top quark pair-production: (Fleming, Hoang, SM, Stewart) Q m t Γ t > Λ QCD Can we extract top mass far away from threshold? Which mass scheme? How do perturbative and non-perturbative effects modify relation between Lagrangian mass and experimental observable?

6 e + e t tx Observable (Fleming, Hoang, SM, Stewart) Top jet hemisphere mass distribution sensitive to top mass: dm 2 t d 2 σ dm 2 t M 2 t = ( ) 2 ( M 2 t = i X t p µ i soft particles i X t n-collinear n-collinear p µ i ) 2 thrust axis Peak region: hemisphere-a hemisphere-b M 2 t, t m2 (LC Simulation: Chekanov, Morguno) m Γ m

7 Top Mass From Jet Distributions e + e t tx Boosted top quark pair-production: Q m t Γ t > Λ QCD CM Energy Top Mass Top Width Nonperturbative scale Four scales in problem!

8 Kinematics of Top Jets e + e t tx High energy boosted tops: Q m -Collinear EffectiveTheory (SCET) High energy boosted tops: M 2 t, t m m Γ Heavy Quark Effective Theory (HQET)

9 A Symphony of Effective Field Theories Q Integrate out Hard Modes QCD Q m Γ Factorize Jets, Integrate out energetic collinear gluons Evolution and decay of top close to mass shell t top HQET n SCET Cross-Talk n m t t antitop HQET! t Q m t Γ t > Λ QCD

10 SCET Factorization Integrate out Hard Modes QCD Q Jets, Integrate etic collinear d s shell t top HQET n SCET Cross-Talk n m t t antitop HQET! t We are here d 2 σ dm 2 t dm 2 t = σ 0 H Q (Q, µ) M(m, µ) dl + dl J n (s t Ql +, m, µ)j n (s t Ql, m, µ)s hemi (l +, l, µ, m) Top Jet Function Anti-Top Jet Function Cross-talk function function universality; same as massless jets (Korchemsky, Sterman; Bauer,Lee, Manohar, Wise; Schwartz )

11 Final factorization Integrate out Hard Modes QCD Q Jets, Integrate etic collinear d s shell t top HQET n SCET Cross-Talk n m t t antitop HQET! t We are here dσ dm 2 t dm 2 t Hard modes integrated out Hard collinear modes integrated out Evolution and decay of top quarks close to mass shell Q ) = σ 0 H Q (Q, µ m )H m (m J,,µ m,µ m J ( ) ) dl + dl B + ŝ t Ql+, Γ t,µ B (ŝ t Ql, Γ t,µ S(l +, l,µ) m J m J ( ) ( 2 ) ( ) ( ) cross-talk

12 Top Mass From Jet Distributions a) b) p p QCD a) b) c) d) e) SCET dσ dm 2 t dm 2 t Q ) = σ 0 H Q (Q, µ m )H m (m J,,µ m,µ m J ( ) ) dl + dl B + ŝ t Ql+, Γ t,µ B (ŝ t Ql, Γ t,µ S(l +, l,µ) m J m J ( ) ( 2 ) ( ) ( ) Hard function at one loop: H Q (Q, µ Q )= 1 + α sc F 4π [ ( Q 2 ln 2 2 ) ( Q ln µ 2 Q µ 2 Q ) π2 3 ]

13 Top Mass From Jet Distributions a) b) c) d) e) f)!m 2 SCET top jet function a) b) c) d) e)!m boosted HQET jet function dσ dm 2 t dm 2 t Q ) = σ 0 H Q (Q, µ m )H m (m J,,µ( m,µ ) m J ( ) ) dl + dl B + ŝ t Ql+, Γ t,µ B (ŝ t Ql, Γ t,µ S(l +, l,µ) m J m J ( ) ( 2 ) ( ) ( ) SCET to HQET matching coefficient: H m (m, µ m ) = 1 + α sc F 2π ( ) ln 2 µ 2 m m + ln µ2 m 2 m π2 2 6

14 Resummation Equivalence of Top-Down vs. Bottom Up Top Down Running Bottom Up Running Scales Q Local Running Local Running H Q (Q, µ) H m (m, Q ) m, µ m, µ J n (s t Ql +, m, Γ, µ) J n (s t Ql, m, Γ, µ) S hemi (l +, l, µ) B + ( ŝ t Ql+ m, Γ, µ ) B ( ŝ t Ql m, Γ, µ ) S hemi (l +, l, µ) m Convolution Running Convolution Running Γ Running between different scales mostly affects only normalization!

15 Top Mass Scheme

16 Top Mass From Jet Distributions dσ dm 2 t dm 2 t Q ) = σ 0 H Q (Q, µ m )H m (m J,,µ m,µ m J ( ) ) dl + dl B + ŝ t Ql+, Γ t,µ B (ŝ t Ql, Γ t,µ S(l +, l,µ) m J m J ( ) ( 2 ) ( ) ( ) HQET Lagrangian determines dynamics of top-jet functions B: L ± = h v± ( iv± D ± δm + i 2 Γ t) hv± δm = m pole m EFT power counting defines top resonance mass schemes: δm ŝ t ŝ t Γ Note power counting of EFT breaks down for MSbar mass: δ m α s m Γ

17 Top Mass From Jet Distributions 13 A. Potential Jet-Mass Definitions and Anomalous Dimensions Some top resonance mass schemes: plore three resonance mass-schemes for m. With notation for δm in Eq. (8) y are defined d dŝ B(ŝ, δmpeak, Γ t,µ) R δm J = ŝ=0 =0, dŝ ŝb(ŝ, δm mom,µ) = 0, i 2 B(y, µ) Peak Mass Moment Mass m B tree non-zero width and satisfies δm Γ t power counting 0.00 criteria [12]. In b) and c) schemes ass Peak definition. is perturbatively more stable in top resonance mass scheme compared to pole mass scheme d dy B(y, µ) = e γ R E y= ie γ E /R (GeV-1) B.W. 1-loop (57) 1-loop m pole m J r R, and we must take R Γ t in order to satisfy power counting criteria. Different choices schemes, and are analogous to difference between a) MS and MS mass-schemes. Alls three (GeV) re free from leading renormalon ambiguities [65]. In following we will argue that only asonable scheme for higher order computations. Thus we will only use name jet-mass for -4 d d ln(iy) ln B(y, µ) iye γ E =1/R 0.05 as peak-mass, moment-mass, (Position and Mass: position-mass respectively. The peak-mass definition uses Jain, Scimemi,Stewart) q. (57) are all perturbative mass-schemes which stabilize peak position of jet function eme a) peak position is fixed to all orders in perturbation ory by definition. In scheme first moment, which provides a more local observable that is still sensitive to peak location. δm ŝ t ŝ t Γ still has non-locality induced by cutoff R on momentum space moment. A finite R ltraviolet divergences that occur for R. This type of moment divergence is a general.

18 dσ dm 2 t dm 2 t Top Mass From Jet Distributions Q ) = σ 0 H Q (Q, µ m )H m (m J,,µ m,µ m J ( ) ) dl + dl B + ŝ t Ql+, Γ t,µ B (ŝ t Ql, Γ t,µ S(l +, l,µ) m J m J ( ) ( 2 ) ( ) ( ) Electroweak Symmetry Breaking; Workshop Ma m J = M peak Γ(α s + ) QΛ QCD m δ m α s m Γ m 178 J dσ M t 178 H J 174 M t (GeV) 1 J N B A B B S dτ N (GeV) m J Clear relation between top mass and peak position

19 Massless Event Shapes

20 tail region: 2ΛQCD / f strong coupling α, see e.g. Ref. [1] for a s B#,"*)8CDEE; Event Shapes far-tail region: 1/3! τ One of most frequently studied event shape (Farhi; Korchemsky, Sterman; Tafat,...) t p"i!8,1),:)'0'1/4)81)!!!!"!#$%&, [2], (1) is "pthrust In peak region hard, jet, i " i A well known event shape; Thrust: soft particles Q, QΛ and QCD, and ΛQCD,n-collinear n-collinear! p"i l-state hadrons with mo-i t strongly peaked maximum. Theor!"#$%&%'()#*+",$+%'(&)'-)&+"'(.)$'/01%(. =>@%,).>,,%./*>&()! T = max,needs to sum large (1)(double) thrust t hat maximizes rightone log axis In th pi -<%)/>)&>&=%,/<,2#/*3% " i " fines thrust axis. We and account for fact that µ # S hemisphere-a Q, hemisphere-b (>A/),#-*#/*>& #"% variable τ = 1 T. For affected at leading order by a nonp "sum! Ω /Q 3 LL essless i is hadrons with mostron 1 /011 over all final-state N Figure 1: Six jet event initiated by a top quark pair, t t bw b W bqq b at tree level tion. We call this distribution *+,-. quarks 2,30143 N 3 LL separating two hemispheres is perpendicular to thrust axis and inters #"! Large logs in two-jet region:.d The unit vector t that maximizes rightone n function. axis 0 atnnll interaction point. The total tail invariant mass inside hemisphe distribution for τ > The region iseach popula Our analysis equally well to lepton+jets and dilepton channe NNLL applies e sensitive (RHS) of Eq. (1) defines thrust axis. We and a!") to value of broader dijets and 3-jet events. H n NLL (+,&-.( ln τmucharising more convenient variable τ = 1 T. For m nt measures how it are still well separated and sti from initial state. Assuming a c.m. energy Q " m one,affect m being αs!"( */"7() mass, one can employ hierarchy of scales es close to zero event butatnow ( ΛQCD, so uction of a pair of masslessrithms, quarks treeµslevel tion. τ 77%-)/>) Q " m " Γ > Λ!"' ack-to-back jets, carrying described by perturbation δ(τ ), so measured distribution for τ > 0 ory funct to establish a factorization orem for doubly differential top-antitop #$) correction parameters Ωi. Finally, c.m.) energy into each of sensitive in peak region top resonance: gluon!"% radiation anddistribution is to around value of broad populated by multijet events. He y plane orthogonal to d σ thrust value of an event measures how much st, M m it m Γ % 4#,-*5)6# mare.!"! dm dmscales becomes meaningle three dpoint event has!"##!1/2,!"##$!"#%!!"#%$!"#&! i τ! t t 2 2 t 2 t QCD t 2 t,t t 2 2

21 tail region: 2ΛQCD / f strong coupling Event αs, seeshapes e.g. Ref. [1] for a B#,"*)8CDEE; far-tail region: 1/3! τ One of most frequently studied event shape (Farhi; Korchemsky, Sterman; Tafat,...) t p"i!8,1),:)'0'1/4)81)!!!!"!#$%&, [2], (1) is "pthrust In peak region hard, jet, i " i A well known event shape; Thrust: soft particles Q, QΛ and QCD, and ΛQCD,n-collinear n-collinear! p"i l-state hadrons with mo-i t strongly peaked maximum. Theor!"#$%&%'()#*+",$+%'(&)'-)&+"'(.)$'/01%(. =>@%,).>,,%./*>&()! T = max,needs to sum large (1)(double) thrust t hat maximizes rightone log axis In th pi -<%)/>)&>&=%,/<,2#/*3% " i " fines thrust axis. We and account for fact that µ # S hemisphere-a Q, hemisphere-b (>A/),#-*#/*>& #"% variable τ = 1 T. For affected at leading order by a nonp "sum! Ω /Q 3 LL essless i is hadrons with mostron 1 /011 over all final-state N Figure 1: Six jet event initiated by a top quark pair, t t bw b W bqq b at tree level tion. We call this distribution *+,-. quarks 2,30143 N 3 LL separating two hemispheres is perpendicular to thrust axis and inters #"! Large logs in two-jet region:.d The unit vector t that maximizes rightone n function. axis 0 atnnll interaction point. The total tail invariant mass inside hemisphe distribution for τ > The region iseach popula Our analysis equally well to lepton+jets and dilepton channe NNLL applies e sensitive (RHS) of Eq. (1) defines thrust axis. We and a!") to value of broader dijets and 3-jet events. H n NLL (+,&-.( ln τmucharising more convenient variable τ = 1 T. For m nt measures how it are still well separated and sti from initial state. Assuming a c.m. energy Q " m one,affect m being αs!"( */"7() mass, one can employ hierarchy of scales es close to zero event butatnow ( ΛQCD, so uction of a pair of masslessrithms, quarks treeµslevel tion. τ 77%-)/>) Q " m " Γ > Λ!"' ack-to-back jets, carrying described by perturbation δ(τ ), so measured distribution for τ > 0 ory funct to establish a factorization orem for doubly differential top-antitop #$) correction parameters Ωi. Finally, c.m.) energy into each of sensitive in peak region top resonance: gluon!"% radiation anddistribution is to around value of broad Resummation populated by multijet events. He y plane orthogonal to d σ thrust value of an event measures how much st, M m it m Γ % 4#,-*5)6# mare.!"! dm dmscales becomes meaningle three dpoint event has!"##!1/2,!"##$!"#%!!"#%$!"#&! i τ! t t 2 2 t 2 t QCD t 2 t,t t 2 2

22 Event Shapes have been studied for a long time (Farhi; Korchemsky, Sterman; Tafat; Catani, Trentadue, Turnock,Webber,...) More recently revisited with SCET approach. (Bauer, Lee,Manohar,Wise; Fleming, Hoang,SM,Stewart;Schwartz;...) Factorization orem in two jet region in SCET: 1 dσ 2 σ 0 dτ = H(Q2,µ) dp 2 L dp2 R dkj(p2 L,µ) J(p2 R,µ) S T(k, µ)δ(τ p2 L + p2 R Q 2 k Q ) Hard scale physics µ H Q, µ Jet scale physics physics µ J Q τ µ S Qτ

23 Factorization orem in two jet region: 1 dσ 2 σ 0 dτ = H(Q2,µ) dp 2 L dp2 R dkj(p2 L,µ) J(p2 R,µ) S T(k, µ)δ(τ p2 L + p2 R Q 2 k Q ) Hard scale physics µ H Q, µ Jet scale physics physics µ J Q τ µ S Qτ Factorization probes physics at multiple scales: Strong coupling running is probed over large energy range run across interesting thresholds. Hard, jet, soft functions perturbative calculations can be sensitive to new virtual physics.

24 Strong Coupling Extraction in SCET (Becher, Schwartz; Abbate, Fickinger, Hoang, Mateu, Stewart) dσ/dτ δ(τ), #"% "! *+,-. #"! +... back-to-back quarks!")!"( /011 2,30143 N3 LL N3 LL NNLL NNLL NLL Ω 1 /Q Beyond tree-level involves gluon radiation; sensitive to strong coupling!"' Regions of thrust:!"%!"!!"##!!"##$!"#%!!"#%$!"#&!!""#$%&'()*+),-%.&'/0#,-&' peak region: 1#$%2&'3$%4#.$' τ 2Λ QCD /Q, tail region: 2Λ QCD /Q τ 1/3 far-tail region: 1/3 τ 1/2. } Resummation; SCET Fixed order

25 1 dσ 2 σ 0 dτ = H(Q2,µ) dp 2 L dp2 R dkj(p2 L,µ) J(p2 R,µ) S T(k, µ)δ(τ p2 L + p2 R Q 2 k Q ) 1 σ dσ dτ Q=m Z Fixed Order O(α 3 s) O(α 2 s) O(α s ) 1 σ dσ dτ Q=m Z Sum Logs, with S mod + gap N3 LL N3 LL NNLL NNLL NLL (c) τ (d) τ FIG. 9: Theory scan for errors in pure QCD with massless quarks. The panels are a) fixed-order, b) resummation with no nonperturbative function, c) resummation with a nonperturbative function using MS scheme for Ω 1 without renormalon subtraction, d) resummation with a nonperturbative function using R-gap scheme for Ω 1 with renormalon subtraction. Fixed Order results (Gehrmann-De Ridder, Gehrmann, Glover,Heinrich;Weinzierl) caption of Tab. II. Furrmore, we always consider five active flavors in running and do not implement bottom threshold corrections, since our lowest scale in profile functions ( soft scale µ S ) is never smaller than Resummation (Abbate, Fickinger, Hoang, Mateu, Stewart) (medium/purple) and O(α 3 s) (dark/red) fixed-order thrust distributions without summation of large logarithms. The common renormalization scale is chosen to be hard scale µ H. In fixed-order results

26 Υ!!$456/1 "*+!!!!,-,./$0123,0!!""#$%&'()*+),-%.&'/0#,-&' 1#$%2&'3$%4#.$' #! #! $!&'()!!!! The re O(α 3 s) + racy, ha α s (M Z ) = ± (0.0002) exp ± (0.0005) hadr ± (0.0009) pert N 3 LL accuracy - Included thrust data from Q=35 to 207 GeV. - Consistent treatment of power corrections. - Bottom quark mass effects included. - QED corrections at NNLL included.

27 Constraining Light Colored particles (Kaplan, Schwartz) n f Mass GeV - examined effect of new light colored particles on running of various objects in factorization orem. - looked at differential thrust distribution in different regions. - gluino mass bound: greater than about 53 GeV.

28 Angularities Generalized event shapes: τ a = 1 Q i E i (sin θ i ) a (1 cos θ i ) 1 a = 1 Q & )2'$+) & '/&8*"("# p T i e η i (1 a) 79-"&''/B*'-C*)+-0/'-%&'#*-!; B(8*'-C*)+-0/'-+>&%%-! &-4-5 &-4-6!"#"$%

29 Angularities!"#$%&'()*+,(-)'(.$)(/"-+&)+!"#"$%&"'()0!""#$%&'()+1-2+*+,&(-.&/0 12/3#45$6789: *+;#4B#C-/32D##1"*4:=#4%E#$%&A-A %!!"#"$%& %#!"#"' $) $( %! $' $% $# $! ) $! ( ' # %!!!"!#!"$!"$#!"%!"%#!"&!"&#!!!"!#!"$!"$#!"%!"%#!"& &# &! %# %! $# $! #!"#"($%)!"#"($ (! $( $! )( )! #( #! '( '! (!!!"!#!"$!"$#!"%!"%#!!!"!#!"!$!"!%!"!&!"'!"'#!"'$!"'%!"'&!"#

30 N-Jettiness (Stewart, Tackmann, Waalewijin)

31 Final State Restrictions X l + l + l + Jet b Jet a P a P b P a P b P a P b l X (a) Inclusive Drell-Yan production. l (b) Drell-Yan near threshold. l (c) Isolated Drell-Yan. (Stewart, Tackmann, Waalewijin) (Collins, Soper, Sterman; Bodwin) (Sterman; Catani,Trentadue,...) Jet 1 Jet b Jet 1 Jet a P a P b P a P b Final state restrictions: Jet 2 -different forms of factorization orems -different logs need to be summed; additional resummation -new non-perturbative functions can arise: (d) Dijet production near threshold. Jet 2 (e) Isolated dijet production. Beam Functions, TMDPDFs, soft functions,...

32 Event shape for N-Jets X l + l + l + Jet b Jet a P a P b P a P b P a P b l X l l (a) Inclusive Drell-Yan production. (b) Drell-Yan near threshold. (c) Isolated Drell-Yan. Jet 1 Jet 1 (Stewart, Tackmann, Waalewijin) P a P b P a Jet b Jet a P b Jet 2 (d) Dijet production near threshold. Jet 2 (e) Isolated dijet production. Can we describe se processes with event shapes?

33 N-Jettiness X l + l + l + Jet b Jet a P a P b P a P b P a P b l X l l (a) Inclusive Drell-Yan production. (b) Drell-Yan near threshold. (c) Isolated Drell-Yan. Jet 1 Jet 1 (Stewart, Tackmann, Waalewijin) P a P b P a Jet b Jet a P b Jet 2 (d) Dijet production near threshold. Jet 2 (e) Isolated dijet production. Can we describe se processes with event shapes? N-Jettiness Allows factorization of exclusive N-jet events. Resummation beyond LL. Additional jets are vetoed in appropriate limit of event shape. Reduced dependence on jet algorithms.

34 Function: S b l + 1 Jet 1 Jet function: J Beam function: B p Jet b Jet a p Jet 2 2 Jet 3 3 (c) pp leptons plus jets. l a Hard Function: H N-Jettiness event shape: τ N = 2 { } Q 2 min q a p k,q b p k,q 1 p k,..., q N p k Factorization: k dσ H J 1 J N B A B B S dτ N Limit of N infinitely narrow jets: τ N 0. restricts hard radiation between jets and beams

35 Function: S b l + 1 Jet 1 Jet function: J Beam function: B p Jet b Jet a p Beam function: Jet 2 2 Jet 3 3 (c) pp leptons plus jets. l a Initial parton is part of Beam Jet Hard Function: H Beam Function can be matched onto PDF (Stewart, Tackmann, Waalewijin) B n = I n,i f i, B n = I n,j f Generalized pt dependent Beam functions (ibfs) appear in pt distributions of Drell-Yan Process. (SM, Petriello)

36 ILC 1 Jet 1 e + e Jet 2 2 Precision studies at ILC of multijet final states using N-Jettiness. Analysis would be similar but without beam functions.

37 Jet Shapes and Jet Algorithms (Almeida, S.J.Lee, Perez,Sterman,Sung,Virzi;Ellis, Hornig,Lee, Vermilion,Walsh) Generalize global event shapes to jet shapes :!!"#$%&'("%$)*$" + ", $'**)&)-'#).*$#.$/$!"#%! % D!B $"('"%'*+*()',-./*')"')-*'01*)',-./ % τ a (jet) = 1 2E jet i jet p T i e η i (1 a)! 0"'%12"$.*"$3"#4%$%&'("5$-"'6"$.#&"2%$1*7"'%12"8!@!/ F E!"#$%&'%(& )*+!% Detailed study could allow one to distinguish jets with different origins. Could complement jet substructure techniques. (See talks by Tweedie, Wang)

38 QCD at ILC ILC provides clean environment: - good oretical control over QCD effects interfering with new physics. - allows precision studies of QCD itself. Factorization orems - separate perturbative and non-perurbative physics. - simultaneously probes physics at multiple scales. - sensitive to new physics through running and perturbative corrections to hard functions - Universal non-perturbative functions. - Power corrections get smaller at higher energies; more precision. Precision top quark mass measurements: - at threshold - far away from threshold Strong coupling measurements - precise measurements of strong coupling. -evolution over large energy range; probe of new thresholds. Precision studies of multiple jet events. - new event shape observable: N-jettiness - study of jet shapes and including jet algorithms in factorization orems.