Power corrections to jet distributions at hadron colliders

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1 Power corrections to jet distributions at hadron colliders Lorenzo Magnea Università di Torino INFN, Sezione di Torino Work in collaboration with: M. Cacciari, M. Dasgupta, G. Salam. DIS 7 Munich 8//7

2 Outline Introduction Nonperturbative effects at TeV colliders Jet energy scale studies Discriminating power corrections esummation Factorization and resummation esummed jet p T distribution Power corrections Dipole resummation Jet size dependence MonteCarlo results Comparing algorithms Comparing parton channels Perspective

3 Nonperturbative effects at TeV colliders Why bother? Do power corrections matter for TeV jets? Λ/Q 3 true asymptotics? Precision measurements require precise jet energy scale % uncertainty M top GeV/c Steeply falling distributions magnify power corrections power corrections necessary to fit Tevatron data Hadronization and underlying event: different physics disentangle computable effects QCD dynamics in full colors. beauty from gauge invariance

4 Determining the jet energy scale CDF, hep-ex/57 Precision for the jet energy scale E T is important E T /E T = σ jet /σ jet 5GeV = Determining the jet energy scale is experimentally difficult ( ) p parton T = p jet T C η C MI C ABS C UE + C OOC Experimental issues: C η, C MI, C ABS Calorimeter and detector efficiencies Multiple interactions Theoretical input: C UE, C OOC Underlying event, hadronization, out-of-cone radiation Models, Monte-Carlo, analytic results?

5 Fitting jet distributions at Tevatron M.L. Mangano, hep-ph/9956 The ratio of single-inclusive jet E T distributions at different S should scale up to logarithms. Fit of CDF data with NLO QCD assuming E T -independent shift Λ in jet energy. Cross section ratio should scale up to PDF ad α s effects. Data can be fitted with shift in distribution. Small Λ has impact at high E T. σ(e T ) E n T δσ σ nδe T Several sources of energy flow in and out of jets.

6 Discriminating power corrections Sources of power corrections at hadron colliders Soft radiation from hard antenna hadronization. Calculable in perturbative QCD. Partially localized in phase space. Tools: resummations, dispersive techniques. Background soft radiation underlying event. Not calculable in perturbative QCD. Fills phase space (minijets?). Tools: models, Monte-Carlo. Experimental issues impact on theory. Detector coverage and phase space cuts. Jet algorithms, non-global logarithms.

7 Factorization and resummation Consider inclusive production of a jet with momentum p µ J in hadron-hadron collisions, near partonic threshold. Partonic threshold: s s + t + u [ log n ] (s )/s in the distribution. α n s + Sudakov logs arise from collinear and soft gluons, which factorize, with nontrivial color mixing

8 NLL jet E T distribution G. Sterman, N. Kidonakis, J. Owens... Factorization leads to resummation. For q q collisions d 3 σ E J d 3 = p J s exp [E F + E IN + E OUT ] Tr [HS]. Incoming partons build up a Drell-Yan structure X Z E IN = dz zn i ( h i= z νq α s ( z) Q i Z dξ h i + ( z) ξ Aq α s ξq i ) i. Note: N = N( u/s), N = N( t/s), Q = u/ s, Q = t/ s Outgoing partons near threshold cluster in two jets E OUT = X i=j, + Z ( dz zn h B i α s ( z)p i T + C i hα s ( z) p i T z Z z dξ ( z) ξ A i hα s ξp i ) T.

9 Color exchange near threshold Soft gluons change the color structure of the hard scattering. Choose a basis in color configuration space c () {r i } = δr r 3 δr r, c () {r i } = T A T A = δ r 3 r r r r r δ r3 r Nc δr r 3 δr r At tree level, for q q collisions» M {ri } = M c () {r i } + M c () {r i } M = M I M J tr c (I) c (J) Tr [HS] {r i } {r i } enormalization group resums soft logarithms H α s(p T ) P exp Tr [HS] H AB α s(µ «) S AB pt Nµ, αs(µ ) = Z p TN p T dµ µ Γ S α s(µ! p T ) S, α s N!! P exp Z p TN p T dµ µ Γ S α s(µ! ) Note: [ Γ q q S ] () = C F log ( t/s) + iπ...

10 Issues of globalness and jet algorithms esummations in hadron-hadron collisions require a precise definition of the observable. Precisely defining threshold For dijet distributions: M = (p + p ) differs from M = p p at LL level. For single inclusive distributions: fixed and integrated rapidity differ (N i N). Precisely defining the observable Jet algorithm: I safety a must. Jet momentum: four-momentum recombination p = P i E i sin θ i vs. p = P i E i sin θ eff. Beware of nonglobal logarithms Pick global observable: satisfied by x T distribution. Minimize impact of nonglobal logs: k algorithm for energy flows; joint distributions.

11 Soft gluons in dipoles Y. Dokshitzer, G. Marchesini Define eikonal soft gluon current. j µ,b X Np ω p µ i (k) = i= (k p i ) T b i ; Eikonal cross section is built by dipoles. X Np T b i =. i= j (k) = X ω (p i p j ) T i T j i>j (k p i )(k p j ) X T i T j w ij (k), i>j By color conservation, up to three hard emitters have no color mixing (unique representation content). T T = T + T = C F ; T T = T + T T 3, j (k) = T W () 3 (k) + T W () 3 (k) + T 3 W (3) (k), W () 3 = w + w 3 w 3. Note: W (i) jk isolates collinear singularity along i.

12 Soft gluons in dipoles Beyond three emitters different color representations contribute. The eikonal cross section acquires noncommuting dipole combinations j (k) = T W () 3 (k)+t W () 3 (k)+t 3 W (3) (k)+t W () (k)+t t A t(k)+t u Au(k). with noncasimir color factors T t = (T 3 + T ) = (T + T ), T u = (T + T ) = (T + T 3 ). The resulting distributions are collinear safe A t = w + w 3 w 3 w, A u = w + w 3 w w 3, Angular integrals yield momentum dependence of radiators dω π A t (k) = ln t s ; dω π A u(k) = ln u s. Dipole approach practical for power corrections.

13 Power corrections by dipoles Consider the single inclusive distribution for a jet observable O(y, p T, ), with an effective jet radius = ( y) + ( φ). Measure effect of single soft gluon emission on the distribution dipole by dipole at power accuracy. Define -dependent power correction O ± ij () Z ± dη dφ Z µf π µc dκ (ij) α T s κ (ij) k k T T T κ (ij) T Compute in-cone and out-of-cone contributions O ij () = O + ij () + O ij () = O+ ij () + O all ij p i p j p i k p j k δo± (k T, η, φ). () O in ij (). Express leading power dependence in terms of (universal?) moment of coupling A A (µ f ) = µf dk k α s (k ) k

14 adius dependence: p T distribution Let O = ξ T p T / S. In this case In-In dipole Z ξ T, () = S + In-Jet dipoles dη dφ π αs(k t) dk t k t k t cos φ = S A(µ f ) 6 +! s Z dφ ξ T,j () = dη S η +φ < π αs(κ t) dκ 3η t cos φ e κ t κ t (cosh η cos φ) 3 = A(µ f ) S « Jet-ecoil dipole In-ecoil dipoles ξ T,jr () = A(µ S f ) ξ T,r () = A(µ S f )

15 adius dependence: mass distribution For comparison, let O = ν J MJ /S. Now only gluons recombined with the jet contribute, and one finds nonsingular dependence. In-In dipole In-Jet dipoles ν J, () = A(µ S f ) O, ν J,j () = A(µ S f ) O 9, Jet-ecoil dipole In-ecoil dipoles ν J,jr () = A(µ S f ) O 9, ν J,r () = A(µ S f ) O.

16 Power corrections by MonteCarlo The analytical estimate of power corrections provided by resummation is valid near threshold. It can be compared with numerical estimates from QCD-inspired MonteCarlo models of hadronization. un MC at parton level (p), hadron level without UE (h) and finally with UE (u) Select events with hardest jet in chosen p T range, identify two hardest jets, define for each hadron level ( ) p (h/u) T = p (h/u) T, + p (h/u) T, p (p) T, p(p) T,. p (u h) T = p (u) T p(h) T. Compare results for different jet algorithms, hadronization models, parton channels.

17 MC power corrections: comparing jet algorithms Tevatron: 55 < p t < 7 GeV (bin ) 3 - Herwig qq->qq - kt cam Pythia qq->qq - siscone midpoint Herwig gg->gg UE - - hadronisation Pythia gg->gg

18 MC power corrections: quark channel Tevatron: qq channel, 55 < p t < 7 GeV (bin ) 3 - kt - Pythia Herwig siscone cam - - UE hadronisation midpoint

19 MC power corrections: gluon channel Tevatron: gg channel, 55 < p t < 7 GeV (bin ) 3 - kt - Pythia Herwig siscone cam - - UE hadronisation midpoint

20 MC power corrections: quark channel, scaled Tevatron: qq channel, 55 < p t < 7 GeV (bin ), SCALED!p t / f() [GeV] -!p t / f() [GeV] - UE: f() = " J () hadronisation: f() = / - kt Pythia Herwig - cam !p t / f() [GeV] -!p t / f() [GeV] - - siscone midpoint

21 MC power corrections: gluon channel, scaled Tevatron: gg channel, 55 < p t < 7 GeV (bin ), SCALED!p t / f() [GeV] - - kt!p t / f() [GeV] - Pythia Herwig - cam UE: f() = " J () hadronisation: f() = / !p t / f() [GeV] -!p t / f() [GeV] - - siscone midpoint

22 Disentangling hadronization Single inclusive jet distributions have Λ/p T power corrections from hadronization. Hadronization corrections are distinguishable from underlying event effects because of singular dependence. In a dispersive model the size of leading power corrections can be related to parameters determined in e + e annihilation. Power corrections near partonic threshold are qualitatively compatible with Monte Carlo results. Work in progress. Study rapidity dependence. Investigate role of jet algorithms. Combine with models of underlying event.

23 Perspective esummation and power correction studies at hadron colliders are interesting: the full power of nonabelian gauge invariance is displayed. esummation and power correction studies at hadron colliders are relevant: precision phenomenology requires reliable modeling of hadronization and underlying event. efined QCD tools are available: nonabelian exponentiation, dispersive methods, MonteCarlo simulations. Disentangling hadronization and underlying event is useful: different physics requires different tools. Disentangling hadronization and underlying event is possible: jet-size dependence is a (first) handle. Phenomenology of power corrections at hadron colliders is a realistic prospect.