Theory of double parton scattering: basics and open questions M. Diehl Deutsches Elektronen-Synchroton DESY DESY Forum on Double Parton Scattering 19 and 20 May 2015 DESY
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Hadron-hadron collisions ◮ standard description based on factorization formulae cross sect = parton distributions × parton-level cross sect example: Z production pp → Z + X → ℓ + ℓ − + X Z ◮ factorization formulae are for inclusive cross sections pp → Y + X where Y = produced in parton-level scattering, specified in detail X = summed over, no details M. Diehl Theory of double parton scattering: basics and open questions 2
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Hadron-hadron collisions ◮ standard description based on factorization formulae cross sect = parton distributions × parton-level cross sect example: Z production pp → Z + X → ℓ + ℓ − + X ◮ factorization formulae are for inclusive cross sections pp → Y + X where Y = produced in parton-level scattering, specified in detail X = summed over, no details ◮ also have interactions between “spectator” partons their effects cancel in inclusive cross sections thanks to unitarity but they affect the final state X M. Diehl Theory of double parton scattering: basics and open questions 3
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Multiparton interactions ◮ secondary, tertiary etc. interactions generically take place in hadron-hadron collisions ◮ predominantly low- p T scattering � underlying event ◮ at high collision energy can be hard � multiple hard scattering ◮ many studies: theory: phenomenology, theory foundations (1980s, recent activity) experiment: ISR, SPS, HERA (photoproduction), Tevatron, LHC Monte Carlo generators: Pythia, Herwig ++ , Sherpa, . . . and ongoing activity: see e.g. the MPI@LHC workshop series http://indico.cern.ch/event/305160 ◮ this forum: concentrate on double hard scattering (DPS) M. Diehl Theory of double parton scattering: basics and open questions 4
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Single vs. double hard scattering ◮ example: prod’n of two gauge bosons, transverse momenta q T 1 and q T 2 q 1 q 1 q 2 q 2 single scattering: double scattering: | q T 1 | and | q T 1 | ∼ hard scale Q 2 both | q T 1 | and | q T 1 | ≪ Q 2 | q T 1 + q T 2 | ≪ Q 2 ◮ for transv. mom. ∼ Λ ≪ Q : dσ single dσ double 1 ∼ ∼ d 2 q T 1 d 2 q T 2 d 2 q T 1 d 2 q T 2 Q 4 Λ 2 but single scattering populates larger phase space : Q 2 ≫ σ double ∼ Λ 2 σ single ∼ 1 Q 4 M. Diehl Theory of double parton scattering: basics and open questions 5
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Single vs. double hard scattering ◮ example: prod’n of two gauge bosons, transverse momenta q T 1 and q T 2 q 1 q 1 q 2 q 2 single scattering: double scattering: | q T 1 | and | q T 1 | ∼ hard scale Q 2 both | q T 1 | and | q T 1 | ≪ Q 2 | q T 1 + q T 2 | ≪ Q 2 ◮ for small parton mom. fractions x double scattering enhanced by parton luminosity ◮ process dependent: enhancement or suppression by parton type (quarks vs. gluons), coupling constants, etc. M. Diehl Theory of double parton scattering: basics and open questions 6
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary A numerical estimate gauge boson pair production single scattering: qq → qq + W + W + suppressed by α 2 s J Gaunt et al, arXiv:1003.3953 based on pocket formula to be discussed shortly M. Diehl Theory of double parton scattering: basics and open questions 7
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Cross section formula x 1 ¯ x 2 ¯ q 1 q 2 x 1 x 2 dσ double x 2 = 1 Z d 2 y F ( x 1 , x 2 , y ) F (¯ C ˆ σ 1 ˆ σ 2 x 1 , ¯ x 2 , y ) dx 1 d ¯ x 1 dx 2 d ¯ C = combinatorial factor ˆ σ i = parton-level cross sections F ( x 1 , x 2 , y ) = double parton distribution (DPD) y = transv. distance between partons ◮ follows from Feynman graphs and hard-scattering approximation no semi-classical approximation required ◮ can make ˆ σ i differential in further variables (e.g. for jet pairs) ◮ can extend ˆ σ i to higher orders in α s get usual convolution integrals over x i in ˆ σ i and F M. Diehl Theory of double parton scattering: basics and open questions 8
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Pocket formula ◮ make simplest possible assumptions ◮ if two-parton density factorizes as F ( x 1 , x 2 , y ) = f ( x 1 ) f ( x 2 ) G ( y ) where f ( x i ) = usual PDF ◮ if assume same G ( y ) for all parton types then cross sect. formula turns into dσ double x 2 = 1 dσ 1 dσ 2 1 dx 1 d ¯ x 1 dx 2 d ¯ C dx 1 d ¯ x 1 dx 2 d ¯ x 2 σ eff d 2 y G ( y ) 2 with 1 /σ eff = R � scatters are completely independent ◮ underlies bulk of phenomenological estimates ◮ fails if any of the above assumptions is invalid or if original cross sect. formula misses important contributions (will encounter examples later) cf. Calucci, Treleani 1999; Frankfurt, Strikman, Weiss 2003-04; Blok et al 2013 M. Diehl Theory of double parton scattering: basics and open questions 9
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Pocket formula ◮ make simplest possible assumptions ◮ if two-parton density factorizes as F ( x 1 , x 2 , y ) = f ( x 1 ) f ( x 2 ) G ( y ) ◮ if neglect correlations between two partons R d 2 b F ( b ) F ( b + y ) G ( y ) = where F ( b ) = impact parameter distrib. of single parton 2 2 2 x 1 x 1 y b + y b d 2 b � ≈ x 2 × x 2 ◮ for Gaussian F ( b ) with average � b 2 � σ eff = 4 π � b 2 � = 41 mb ×� b 2 � / (0 . 57 fm) 2 phenomen. determinations of � b 2 � give (0 . 57 fm − 0 . 67 fm) 2 is ≫ σ eff ∼ 5 to 20 mb from experimental extractions ( � next talks) same conclusions for alternatives to Gaussian F ( b ) M. Diehl Theory of double parton scattering: basics and open questions 10
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Parton correlations at certain level of accuracy expect correlations between ◮ x 1 and x 2 of partons • most obvious: energy conservation ⇒ x 1 + x 2 ≤ 1 • significant x 1 – x 2 correlations found in constituent quark model Rinaldi, Scopetta, Vento 2013 • x i and y even for single partons see correlations between x and b distribution • HERA results on γp → J/ Ψ p give � b 2 � ∝ const + 4 α ′ log(1 /x ) with 4 α ′ ≈ (0 . 16 fm) 2 for gluons with x ∼ 10 − 3 lattice simulations → strong decrease of � b 2 � with x above ∼ 0 . 1 • plausible to expect similar correlations in double parton distributions even if two partons not uncorrelated impact on observables: R Corke, T Sj¨ ostrand 2011; B Blok, P Gunnellini 2015 M. Diehl Theory of double parton scattering: basics and open questions 11
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Spin correlations q 1 q 2 ◮ polarizations of two partons can be correlated even in unpolarized proton • quarks: longitudinal and transverse pol. • gluons: longitudinal and linear pol. ◮ can be included in factorization formula � extra terms with polarized DPDs and partonic cross sections ◮ if spin correlations are large → large effects for rate and final state distributions of double hard scattering A. Manohar, W. Waalewijn 2011; T. Kasemets, MD 2012 M. Echevarria, T. Kasemets, P. Mulders, C. Pisano 2015 ◮ large spin correlations found in MIT bag model Chang, Manohar, Waalewijn 2012 ◮ for x 1 , x 2 small: size of correlations unknown known: evolution to higher scales tends to wash out polarization unpol. densities evolve faster than polarized ones MD, T. Kasemets 2014 M. Diehl Theory of double parton scattering: basics and open questions 12
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Spin correlations ◮ can (almost) compute x 1 , x 2 moments of DPDs in lattice QCD ◮ pilot study for the pion G Bali, L Castagnini, S Collins, MD, M Engelhardt, J Gaunt, B Gl¨ aßle, A Sternbeck, A Sch¨ afer, Ch Zimmermann • V V : spin averaged − A VV A TT 1e-03 − A VT • TT : transverse spin corr. ∝ s u · s ¯ d find very small A T T ∼ − 0 . 1 × A V V 1e-04 • AA : longitudinal spin corr. even smaller (not shown) preliminary • V T : correlation ∝ y · s ¯ 1e-05 d maximal at small | y | , then decreases 0 5 10 15 20 |y|/a lattice spacing a ≈ 0 . 07 fm pion mass 280 MeV M. Diehl Theory of double parton scattering: basics and open questions 13
Introduction Theory level 1 Theory level 1.5 Theory level 2 Theory level 3 Summary Color correlations q 1 q 2 ◮ color of two quarks and gluons can be correlated ◮ suppressed by Sudakov logarithms Mekhfi 1988 1. . . . but not necessarily negligible � U Μ U Ν 0.8 � for moderately hard scales U Μ only 0.6 Manohar, Waalewijn arXiv:1202:3794 0.4 0.2 U = Sudakov factor for quarks 0. 10 100 1000 Q = hard scale Q from incomplete cancellation between graphs with real/virtual soft gluons M. Diehl Theory of double parton scattering: basics and open questions 14
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