Multiple hard scattering and parton correlations in the proton

Transcription

1 Multiple hard scattering and parton correlations in the proton M. Diehl Deutsches Elektronen-Synchroton DESY QCD Evolution Workshop, Santa Fe, 12 May 2014 DESY

2 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 Multiple hard scattering and parton correlations in the proton 2

3 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 (namely X) M. Diehl Multiple hard scattering and parton correlations in the proton 3

4 Multiparton interactions (MPI) secondary (and tertiary etc.) interactions generically take place in hadron-hadron collisions predominantly low-p T scattering underlying event (UE) at high collision energy (esp. at LHC) can be hard multiple hard scattering many studies: theory: phenomenology, theoretical 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 M. Diehl Multiple hard scattering and parton correlations in the proton 4

5 Relevance for LHC example: pp H + Z b b + Z Del Fabbro, Treleani 1999 multiple interactions contribute to signal and background + µ µ _ H b b Z + b _ µ µ H Z b _ b + µ µ Z b _ b + µ µ Z b same for pp H + W b b + W study for Tevatron: Bandurin et al, 2010 M. Diehl Multiple hard scattering and parton correlations in the proton 5

6 Double vs. single hard scattering + µ µ + µ µ Z H Z H b _ b double hard scattering: net p T of produced system (Z or b b pair) hard scale Q (e.g. M Z) single hard scattering: p T distribution up to values Q no generic suppression for transv. mom. Q : b _ b dσ single d 2 p Z d 2 p b b dσ double d 2 p Z d 2 p b b Λ2 Q 2 but since single scattering populates larger phase space : σ single 1 Q 2 σ double Λ2 Q 4 however: double hard scattering enhanced at small x M. Diehl Multiple hard scattering and parton correlations in the proton 6

7 Space-time structure p k r k r k r k r p k r k r q 1 q 2 k r k r momentum conservation r + r = 0 transverse parton momenta not the same in amplitude A and in A cross section R d 2 r F (x i, k i, r)f ( x i, k i, r) Fourier trf. to impact parameter: F (x i, k i, r) F (x i, k i, y) cross section R d 2 y F (x i, k i, y)f ( x i, k i, y) interpretation: y = transv. dist. between two scattering partons = equal in both colliding protons M. Diehl Multiple hard scattering and parton correlations in the proton 7

8 Cross section formula q1 q2 dσ double = 1 dx 1 d x 1 dx 2 d x 2 C ˆσ 1 ˆσ 2 d 2 y F (x 1, x 2, y) F ( x 1, x 2, y) C = combinatorial factor ˆσ 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 ˆσ i differential in further variables (e.g. for jet pairs) can extend ˆσ i to higher orders in α s get usual convolution integrals over x i in ˆσ i and F Paver, Treleani 1982, 1984; Mekhfi 1985,..., MD, Ostermeier, Schäfer 2012 M. Diehl Multiple hard scattering and parton correlations in the proton 8

9 Cross section formula for measured transv. momenta q1 q2 dσ double dx 1 d x 1 d 2 q 1 dx 2 d x 2 d 2 q 2 = 1 ˆσ1 ˆσ2 C» 2Y Z Z d 2 k i d 2 ki δ(q i k i k i) i=1 d 2 y F (x i, k i, y) F ( x i, k i, y) F (x i, k i, y) = k T dependent two-parton distribution has structure of a Wigner function: k 1, k 2 = transv. parton momenta averaged over A and A y = transv. distance between partons averaged over A and A M. Diehl Multiple hard scattering and parton correlations in the proton 9

10 Cross section formula for measured transv. momenta q1 q2 dσ double dx 1 d x 1 d 2 q 1 dx 2 d x 2 d 2 q 2 = 1 ˆσ1 ˆσ2 C» 2Y Z Z d 2 k i d 2 ki δ(q i k i k i) i=1 d 2 y F (x i, k i, y) F ( x i, k i, y) F (x i, k i, y) = k T operator definition as for TMDs dependent two-parton distribution F (x i, k i, y) = FT p q` 1 z i (x i,k i ) 2 z 1 2 Γ2 q` 2 z 2 q`y 1 2 z 1 Γ1 q`y z 1 p essential for studying factorization, scale dependence, etc. similar def for collinear distributions F (x i, y) bilinear op s q Γ i q at different transv. positions not a twist-four operator but product of two twist-two operators M. Diehl Multiple hard scattering and parton correlations in the proton 10

11 Pocket formula if two-parton density factorizes as where f(x i) = usual PDF F (x 1, x 2, y) = f(x 1) f(x 2) G(y) if assume same G(y) for all parton types then cross sect. formula turns into with 1/σ eff = R d 2 y G(y) 2 dσ double dx 1 d x 1 dx 2 d x 2 = 1 C dσ 1 dσ 2 1 dx 1 d x 1 x 2 x 2 σ eff scatters are completely independent underlies bulk of phenomenological estimates pocket formula fails if any of the above assumptions is invalid and if further terms must be added to original expression of cross sect. M. Diehl Multiple hard scattering and parton correlations in the proton 11

12 Experimental investigations (only a sketch) CDF 4 jets (1993) CDF γ + 3 jets (1997) CDF reanalysis, Bahr et al (2013) D0 γ + 3 jets (2009) ATLAS W + 2 jets (2013) CMS W + 2 jets (2013) ATLAS 4 jets (thesis 2013) σ eff [mb] double charm production (c cc c) at LHCb (2011, 2012): J/Ψ + J/Ψ, J/Ψ + C, C + C with C = D 0, D +, D + s, Λ + c M. Diehl Multiple hard scattering and parton correlations in the proton 12

13 Parton correlations if neglect correlations between two partons F (x 1, x 2, y) = R d 2 y f(x 1, y + y) f(x 2, y ) where f(x i, y) = impact parameter dependent single-parton density and if neglect correlations between x and y of single parton f(x i, y) = f(x i)f (y) with same F (y) for all partons then G(y) = R d 2 y F (y ) F (y + y) 2 x 1 x y d 2 b x 2 y y + y x 2 M. Diehl Multiple hard scattering and parton correlations in the proton 13

14 Parton correlations if neglect correlations between two partons F (x 1, x 2, y) = R d 2 y f(x 1, y + y) f(x 2, y ) where f(x i, y) = impact parameter dependent single-parton density and if neglect correlations between x and y of single parton f(x i, y) = f(x i)f (y) with same F (y) for all partons then G(y) = R d 2 y F (y ) F (y + y) for Gaussian F (y) with average y 2 σ eff = 4π y 2 = 41 mb y 2 /(0.57 fm) 2 determinations of y 2 from GPDs and form factors: (0.57 fm 0.67 fm) 2 is σ eff 10 to 20 mb from experimental extractions if F (y) is Fourier trf. of dipole then 41 mb 36 mb complete independence between two partons is disfavored or something is seriously wrong with σ eff cf. Calucci, Treleani 1999; Frankfurt, Strikman, Weiss ; Blok et al 2013 M. Diehl Multiple hard scattering and parton correlations in the proton 14

15 Correlations involving x F (x 1, x 2, y) = f(x 1 ) f(x 2 ) G(y) cannot hold for all x 1, x 2 most obvious: energy conservation x 1 + x 2 1 uu(x1, x2, k = 0)/u(x2) often used to suppress region of large x 1 + x 2: F (x 1, x 2, y) = (1 x 1 x 2) n f(x 1) f(x 2) G(y) significant x 1 x 2 correlations found in constituent quark model Rinaldi, Scopetta, Vento: arxiv: x2 = 0.2 x2 = 0.4 x2 = 0.6 plot shows R d 2 y F uu(x 1, x 2, y)/f u(x 2) is x 2 independent if factorization holds x1 unknown: size of correlations when one or both of x 1, x 2 small M. Diehl Multiple hard scattering and parton correlations in the proton 15

16 Correlations involving x and y single-parton distribution f(x, y) is Fourier trf. of generalized parton distributions(gpds) at zero skewness information from exclusive processes and theory HERA results on γp J/Ψ p give y 2 const + 4α log(1/x) with α 0.15 GeV 2 = (0.08 fm) 2 for gluons at x 10 3 lattice simulations strong decrease of y 2 with x above 0.1 seen by comparing moments R dx x n 1 f(x, y) for n = 0, 1, 2 expect similar correlations between x i and y in two-parton dist s even if two partons are not independent in double parton scattering y unobservable: dσ R d 2 y F (x i, y) F ( x i, y) in f(x, y) impact parameter is Fourier conjugate to measurable momentum transfer M. Diehl Multiple hard scattering and parton correlations in the proton 16

17 Correlations involving x and y single-parton distribution f(x, y) is Fourier trf. of generalized parton distributions(gpds) at zero skewness information from exclusive processes and theory HERA results on γp J/Ψ p give y 2 const + 4α log(1/x) with α 0.15 GeV 2 = (0.08 fm) 2 for gluons at x 10 3 lattice simulations strong decrease of y 2 with x above 0.1 seen by comparing moments R dx x n 1 f(x, y) for n = 0, 1, 2 expect similar correlations between x i and y in two-parton dist s even if two partons are not independent Consequence for multiple interactions: if interaction 1 produces high-mass system have large x 1, x 1 smaller y more central collision secondary interactions enhanced Frankfurt, Strikman, Weiss 2003, study in Pythia: Corke, Sjöstrand 2011 M. Diehl Multiple hard scattering and parton correlations in the proton 17 x 1 _ x 1 b

18 Spin correlations q1 q2 polarizations of two partons can be correlated even in unpolarized target already pointed out by Mekhfi (1985) quarks: longitudinal and transverse pol. gluons: longitudinal and linear pol. in general not suppressed in hard scattering for q q l + l have dˆσ q q/dω = dˆσ q q/dω for many channels parton pol. also changes angular distribution consequences for double scattering rate and differential distributions Manohar, Waalewijn 2012; Kasemets, MD 2012 M. Diehl Multiple hard scattering and parton correlations in the proton 18

19 Spin correlations how important are spin correlations? large effects expected in valence quark region study in bag model: Chang, Manohar, Waalewijn: arxiv:1211:3132 F x1,0.4,k uu u u u u u u u u t F x1,0.4,k ud u d u d u d u d t plots show F (x 1, x 2 = 0.4, k ) for different pol. combinations k = Fourier conjugate to y unknown: size of correlations when one or both of x 1, x 2 small change with scale talk by Tomas Kasemets on Thursday 1 M. Diehl Multiple hard scattering and parton correlations in the proton 19

20 Color structure quark lines in amplitude and its conjugate can couple to color singlet or octet: q1 q2 1 F ( q 2 1q 2) ( q 1 1q 1) 8 F ( q 2 t a q 2) ( q 1 t a q 1) 8 F describes color correlation between quarks 1 and 2 is essentially unknown (no probability interpretation as a guide) for two-gluon dist s more color structures: 1, 8 S, 8 A, 10, 10, 27 for k T integrated distributions: color correlations suppressed by Sudakov logarithms Mekhfi but not necessarily negligible for moderately hard scales Manohar, Waalewijn arxiv:1202:3794 used SCET methods U = Sudakov factor, Q = hard scale U Μ UΝ U Μ only M. Diehl Multiple hard scattering and parton correlations in the proton 20

21 Scale and energy dependence sdσ 2 i=1 dxi d xi d2 q i sdσ 2 i=1 dxi d xi l l q1 q2 1 Λ 2 Q 2 1 l1 l2 l 1 l1 l2 l 1 1 Λ 2 Λ 2 Q 2 Q 2 l1 l2 1 Λ 2 Q 2 Λ 2 Q 2 l1 l2 interference between single and double scattering: leading power when differential in q i power suppressed when R d 2 q i, twist-three parton distributions at small x 1 x 2 x expect single scattering x λ with xf(x) x λ double scattering x 2λ interference? how do three-particle correlators behave for small x? M. Diehl Multiple hard scattering and parton correlations in the proton 21

22 Behavior at small interparton distance for y 1/Λ in perturbative region F (x 1, x 2, y) dominated by graphs with splitting of single parton find strong correlations in x 1, x 2, spin and color between two partons e.g. 100% correlation for longitudinal pol. of q and q can compute short-distance behavior: F (x 1, x 2, y) 1 splitting fct usual PDF y2 M. Diehl Multiple hard scattering and parton correlations in the proton 22

23 Scale evolution for collinear distributions without color correlation if define two-parton distributions as operator matrix elements in analogy with usual PDFs F (x 1, x 2, y; µ) p O 1(0; µ) O 2(y; µ) p f(x; µ) p O(0; µ) p where O(y; µ) = twist-two operator renormalized at scale µ F (x i, y) for y 0 : separate DGLAP evolution for partons 1 and 2 d d log µ F (xi, y) = P x 1 F + P x2 F two independent parton cascades R d 2 y F (x i, y) : extra term from 2 4 parton transition since F (x i, y) 1/y 2 Kirschner 1979; Shelest, Snigirev, Zinovev 1982 Gaunt, Stirling 2009; Ceccopieri 2011 which evolution eq. is relevant for double hard scattering? M. Diehl Multiple hard scattering and parton correlations in the proton 23

24 Deeper problems with the splitting graphs Fā1,a2 Fa1,ā2 contribution from splitting graphs in cross section R gives divergent integrals d 2 y F (x 1, x 2, y) F ( x 1, x 2, y) R dy 2 /y 4 double counting problem between double scattering with splitting and single scattering at loop level MD, Ostermeier, Schäfer 2011; Gaunt, Stirling 2011; Gaunt 2012 Blok, Dokshitzer, Frankfurt, Strikman 2011; Ryskin, Snigirev 2011, 2012 same problem for jets: Cacciari, Salam, Sapeta 2009 possible solution: subtract splitting contribution from two-parton dist s when y is small will also modify their scale evolution; remains to be worked out M. Diehl Multiple hard scattering and parton correlations in the proton 24

25 Deeper problems with the splitting graphs Fā1,a2 Fa1,ā2 contribution from splitting graphs in cross section R gives divergent integrals d 2 y F (x 1, x 2, y) F ( x 1, x 2, y) R dy 2 /y 4 also have graphs with single PDF for one and double PDF for other proton What is double parton scattering? Blok et al, ; Gaunt 2012 M. Diehl Multiple hard scattering and parton correlations in the proton 25

26 Sudakov factors for k T dependent distributions, i.e. measured q i : Sudakov logarithms for all color channels close relation with physics of parton showers for double Drell-Yan process can adapt Collins-Soper-Sterman formalism for single Drell-Yan include and resum Sudakov logs in k T dependent parton dist s MD, D Ostermeier, A Schäfer 2011 for jet production inherit problems of usual TMD factorization at leading double log accuracy: singlet and octet dist s 1 F and 8 F have same Sudakov factor as in single scattering beyond double log: Sudakov factors mix singlet and octet dist s M. Diehl Multiple hard scattering and parton correlations in the proton 26

27 Factorization? open problem (for TMD and collinear formulations): exchange of gluons in Glauber region Not discussed in this talk: multiparton interactions in pa collisions small-x approach connection with diffraction, AGK rules Bartels, Salvadore, Vacca 2008 ridge effect in pp and pa Dumitru et al 2011;... M. Diehl Multiple hard scattering and parton correlations in the proton 27

28 Conclusions multiple hard scattering is not generically suppressed in sufficiently differential cross sections current phenomenology relies on strong simplifications have several elements for a formulation of factorization but important open questions still unsolved crosstalk with single hard scattering at small distances closely related with evolution equations (1 2 parton splitting) Glauber gluon exchange double hard scattering depends on detailed hadron structure including correlation and interference effects corresponding nucleon matrix elements largely unknown theoretical activity only started transverse distance between partons essential subject remains of high interest for understanding high-multiplicity final states at LHC study of hadron structure in its own right M. Diehl Multiple hard scattering and parton correlations in the proton 28