Confronting the QCD photon structure with recent data

Transcription

1 Confronting the QCD photon structure with recent data JiříChýla Center for Particle Physics, Institute of Physics, Prague Concept of photon structure Basic facts and formulae Semantics: plea for a common language PDF of the photon QCD effects in data on interactions of quasireal photons Virtual photon structure: why QCD effects in data on interactions of virtual photons? Resolved longitudinal photon: why not? Details in JHEP4(2)7; PRD 62 (2), 425; PL B488 (2), 289; EPJ C6 (2), 47, EPJ C8 (2), 723

2 Concept of photon structure All the present knowledge of the structure of the photon comes from experiments at the ep and e + e colliders, where the incoming leptons act as sources of transverse and longitudinal virtual photons f γ T (y, P 2 ) = α ( +( y) 2 ) 2π y f γ L (y, P 2 ) = α 2π (Quasi)real photon: 2( y) y P 2. ) P 2 2m2 ey P 4, P 2 Λ QCD Small masses of light quarks implies nonperturbative QCD effects which necessitate the introduction of the concept of PDF of the photon. Expected to have (almost) the same properties as truly real photon. Virtual photon: smooth transition from the essentially nonperturbative to the perturbative region for P 2 Λ QCD, in practice P 2 2GeV 2. 2

3 Basic facts and formulae PDF of the photon satisfy the system of inhomogeneous evolution equations dσ(x, M) dlnm 2 = δ Σ k q + P qq Σ+P qg G, dg(x, M) dlnm 2 = k G + P Gq Σ+P GG G, dq NS (x, M) dlnm 2 = δ NS k q + P NS q NS, ( where δ NS 6n f e 4 e 2 2), δ Σ =6n f e 2 and k q (x, M) = α 2π k G (x, M) = α 2π [ [ k () q (x) + α s(m) 2π k() q (x)+ ( αs (M) 2π ( α s (M) 2π k() G (x)+ αs (M) 2π ) 2 k q (2) (x)+ ) 2 k (2) G (x)+ ] ],, P ij (x, M) = α s (M) 2π P () ij ( ) 2 (x)+ αs (M) P () ij 2π (x)+. P () ij,k() q,k () G are unique but all higher order splitting functions arbitrary. 3

4 The structure function F γ 2 (x, Q2 ) is given as x F γ 2 (x, Q2 )=q NS (M) C q (Q/M)+ α 2π δ NSC γ + e 2 Σ(M) C q (Q/M)+ α 2π e2 δ Σ C γ + e 2 G(M) C G (Q/M), where C q,c G,C γ can be expanded in powers of α s (µ) C q (x, Q/M) = δ( x) + α s(µ) 2π α s (µ) C G (x, Q/M) = 2π C γ (x, Q/M) = C () γ i= (x, Q/M) + α s(µ) 2π C() q (x, Q/M)+, C() G (x, Q/M)+, C() γ (x, Q/M)+, C γ () (x, Q/M) = (x 2 +( x) 2 )ln Q2 ( x) M 2 + κ(x) x where κ(x) 8x( x). Cγ as well as k q () =(x 2 +( x) 2 ) come from pure QED, which provides the lowest order contribution to F γ 2 in the form n x F f ( ) γ,qed 2 (x, Q 2 )= e 2 i q QED i (x, Q)+q QED i (x, Q) + α 2π 6n f e 4 C γ () (x, ) 4

5 QED distributions functions of the real photon dσ(e γ e qq) dxdq 2 = 2πα2 xq 4 F γ 2,q (x, Q2 ) ( +( y) 2) can be separated it into two parts F γ,dir 2,q (x, Q 2 ) α 2π 6e4 qx F γ,res 2,q (x, Q 2 ) α 2π 6e4 qx where, denoting κ(x) =8x( x), F γ 2,q (x, Q2 )= α 2π 2e4 l x [ k q () ln Q2 M 2 x [ k () q (x)ln M 2 ( x) m 2 q [ k () q (x)ln Q2 ( x) m 2 qx ] +6x( x), ] +2x( x), the latter coming from region of almost collinear γ qq splitting and defining the QED parts of quark and gluon distribution functions of the photon q QED (x, M) α 2π 3e2 qk () q (x)ln M 2 ( x) m 2 q +2x( x), G(x, M). ] + κ(x) 5

6 The presence of the inhomogeneous terms implies that their general solutions can be written as a sum D(x, M) =D PL (x, M, M )+D HAD (x, M, M ). of a particular solution of the full inhomogeneous equations and a general solution, called hadron-like (HAD), of the corresponding homogeneous ones. A subset of the former resulting from the resummation of contributions of diagrams describing multiple parton emissions off the primary QED vertex γ qq and vanishing at M = M, are called point-like (PL). 6

7 q PL NS(n, M,M)= 4π α s (M) [ ( ) 2P () ] αs qq (M) (n)/β a NS (n) α s (M ) a NS (n) α k () NS (n) 2πβ 2P qq () (n)/β where the presence of α s in the denominator is often interpreted as evidence that q PL NS(n, M,M) α α s but this is untenable because switching QCD off by sending Λ RS for fixed M,M reduces the above expression to the purely QED contribution q PL NS(x, M, M ) q QED NS (x, M, M )= α 2π k() NS (x)lnm2 M 2. 7

8 Basic features of hadronlike and pointlike parts of photonic PDFs The separation inherently ambiguous. Only their sum relevant for calculation of cross sections of hard processes Separation important for multiple interactions (PYTHIA). Both parts describe QCD effects, but exhibit different factorization scale dependence: hadron-like part entirely due to QCD effects, whereas point-like part dominated by QED splitting γ qq. as well as virtuality dependence pointlike: slow logarithmic decrease hadronlike: fast powerlike decrease Both generate gluons rise at low x 8

9 9

10 Factorization scale dependence

11 Virtuality dependence For P 2 2 GeV 2 only the pointlike parts of PDF relevant!

12 Semantics: plea for a common language Agreement on semantics is a prerequisite for any meaningful discussion of the photon structure. I prefer the terminology advocated by GRV: Direct & resolved photon Pointlike & hadronlike contributions QED & QPM contributions Unfortunately, different names are used for the same content Bare photon instead of direct photon contribution Anomalous part instead of pointlike part of photonic PDF VMD part instead of hadronic part of photonic PDF andevenworse,one notion is used in different meanings Pointlike and hadronlike instead of direct and resolved contribution LO and NLO interpreted differently than for R e + e 2

13 Example of resulting confusion: OPAL papers on dijets, F γ 2 and F γ 2c : dijets [EPJC (999), 547]: see just resolved contribution but says photons appear resolved through its fluctuations into hadronic components F γ 2 F γ 2c [EPJC 8 (2), 5]: see dominant hadron-like contribution but claims photon must contain a significant hadron-like component at low x. [EPJC 6 (2), 579]: see excess over hadron-like contribution but claims the measurement suggests a nonzero hadron-like component of F γ 2,cc 3

14 4

15 PDF of the photon Transverse photon Glück, Reya, Vogt (992): P 2 =, HAD+PL Glück, Reya, Stratmann (995): P 2 M 2 /5, HAD+PL Schuler, Sjöstrand (995): P 2 M 2, HAD, PL separately Glück, Reya, Schienbein (999): improved GRS (995) other less often used: AFG, WHIT, GS new: Cornet, Jankowski, Krawczyk, Lorca (23): P 2 =, heavy quarks Longitudinal photon Friberg, Sjöstrand (2): rescaled D γ T p Chýla (2): LO QCD evolution dynamically generated from QED contribution, P 2 M 2. 5

16 QCD effects in interactions of quasireal photons Scaling violations in F γ 2 (x, Q 2 ) Magnitude of F γ 2 (x, Q 2 )atlowx Jets in γp collisions Jets in γγ collisions Heavy quarks in γp collisions Heavy quarks in γγ collisions 6

17 Fits to PDF of the photon.5.5 xu fl (x; Q 2 )=ff # of data points model N no TPC χ 2 χ 2 / DOF χ 2 χ 2 / DOF Q 2 = GeV 2 CJKL FFNS cjkl GRV LO xd fl (x; Q 2 )=ff Q 2 = GeV 2 SaSD GRS LO SaSD GRS LO FFNS CJKL CJKL xs fl (x; Q 2 )=ff Q 2 = GeV 2.8 xg fl (x; Q 2 )=ff.6 Q 2 = GeV Still poor fit and large differences between extracted PDF at moderate x.4.3 xc fl (x; Q 2 )=ff Q 2 = GeV 2.3 xb fl (x; Q 2 )=ff Q 2 = GeV x x

18 Fits to PDF of the proton Data set N MRST MRST MRST MRST.7.2 J H ep ZEUS ep BCDMS µp BCDMS µd NMC µp NMC µd SLAC ep SLAC ed E665 µp E665 µd CCFR F νn CCFR F νn NMC n/p E65 DY Tevatron Jets Total

19 Scaling violations in F γ 2 F 2 γ / α + N 2 OPAL L3 DELPHI (prl) ALEPH (prl) JADE PLUTO TASSO AMY TOPAZ TPC GRV (LO) Fit Fit ± σ N < x > Q 2 [GeV 2 ] inconclusive! 9

20 F γ 2 (x, Q2 ) at low x F γ 2(x)/α OPAL, <Q 2 >=.9 GeV 2 L3, <Q 2 >=.9 GeV 2 PLUTO, <Q 2 >=2.4 GeV 2 TPC-2γ, <Q 2 >=2.8 GeV 2 GRV LO Q 2 =.9 GeV 2 GRV LO Q 2 =2.8 GeV 2 SASD Q 2 =2.8 GeV 2 QPM Q 2 =2.8 GeV 2 (a) F γ 2(x)/α.8.6 OPAL, <Q 2 >=.7 GeV 2 OPAL, <Q 2 >=8.9 GeV 2 PLUTO, <Q 2 >=9.2 GeV 2 DELPHI, <Q 2 >=2. GeV 2 L3, <Q 2 >=.8 GeV 2 GRV LO Q 2 =8.9 GeV 2 GRV LO Q 2 =2. GeV 2 SASD Q 2 =2. GeV 2 WHIT Q 2 =2. GeV 2 QPM Q 2 =2. GeV 2 (a) F γ 2(x)/α.6.4 OPAL, <Q 2 >=3.7 GeV 2 L3, <Q 2 >=5. GeV 2 PLUTO, <Q 2 >=4.3 GeV 2 TPC-2γ, <Q 2 >=5. GeV 2 GRV LO Q 2 =3.7 GeV 2 GRV LO Q 2 =5. GeV 2 SASD Q 2 =5. GeV 2 WHIT Q 2 =5. GeV 2 QPM Q 2 =5. GeV 2 (b) F γ 2(x)/α.75 OPAL, <Q 2 >=7.8 GeV 2 OPAL, <Q 2 >=7.5 GeV 2 TOPAZ, <Q 2 >=6. GeV 2 L3, <Q 2 >=23. GeV 2 ALEPH, <Q 2 >=2.7 GeV 2 GRV LO Q 2 =6. GeV 2 GRV LO Q 2 =23. GeV 2 SASD Q 2 =23. GeV 2 WHIT Q 2 =23. GeV 2 QPM Q 2 =23. GeV 2 (b) x x 2

21 F γ 2 (x, Q2 ) at low x & new GRS parameterization F 2 γ (x,q 2 ) /α GRS (NLO) GRS (LO) GRV γ (NLO) GRV γ (LO) SaS D OPAL (.9) OPAL (.86) L3 set (.9) L3 set2 (.9) Q 2 =.9 GeV 2 OPAL (3.7) OPAL (3.76) F 2 γ (x,q 2 ) /α OPAL (.7) OPAL (7.5,7.8) GRS (NLO) GRS (LO) GRV γ (NLO) GRV γ (LO) SaS D Q 2 =.7 GeV Q 2 =3.7 GeV 2 x Q 2 =7.8 GeV 2 x small x measurements imply that photon must contain a dominant hadron-like component at low x 2

22 Jets in γp collisions d 4 σ ep dydx γ,dx p,dcos Θ = f γ/e 32πs ep y f γ,eff (x γ )f p,eff (x p ) x γ x p dσ d cos Θ dσ / dlog(x γ,jets ) [nb] H data PHOJET (GRV) PYTHIA (GRV) f γ,eff (x γ )=[q(x γ )+q(x γ )+(9/4)g(x γ )] f p,eff (x p )=[q(x p )+q(x p )+(9/4)g(x p )].2. gluons quarks direct γ - x γ,jets α - x γ (q(x γ ) + q (x γ ) + 9/4 g(x γ )) H Data GRV 92 quark/antiquark contribution α - x γ g(x γ ) H jet data, 996 H single particles, 994 GRV 92 GRS 99 SaSD LAC 2 - x γ - x γ 22

23 dσ/de T jet (pb/gev) Dortmund, July 22, Jets in direct photoproduction ZEUS ZEUS x γ obs >.75 NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty < η jet,2 < 2.4 (x 2) Cross section/theory ZEUS 2 < η jet,2 < < η jet < 2.4 < η jet2 <.5 < η jet < < η jet2 < - < η jet < < η jet2 < (x 2) < η jet < 2.4 < η jet2 < (x ).5 < η jet,2 < -3-5 < η jet < - < η jet2 < (x.5) - < η jet,2 < (x.) < η jet,2 < (x.) E T jet (GeV).2 < η jet < - < η jet2 <.8.25 obs - < η jet,2 < ZEUS x γ >.75 NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty E T jet (GeV) Data in very good agreement with predictions of perturbative QCD 23

24 dσ/de T jet (pb/gev) Dortmund, July 22, Jets in resolved photoproduction ZEUS obs ZEUS x γ <.75 NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty < η jet < < η jet2 < (x 2) < η jet,2 < 2.4 (x 5) < η jet < 2.4 < η jet2 < (x ) Cross section/theory 2 < η jet,2 < ZEUS < η jet < 2.4 < η jet2 < 3 < η jet < < η jet2 < < η jet,2 < -2 < η jet,2 < (x.) 4 2 < η jet < - < η jet2 < < η jet,2 < (x.) < η jet < - < η jet2 (x.5) < E T jet (GeV) < η jet,2 < obs ZEUS x γ <.75 NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty E T jet (GeV) The data fall less steeply with increasing transverse energy than do the NLO QCD predictions, and show sensitivity to the parton densities of the photon. Neither the AFG-HO nor the GRV-HO parameterizations convoluted with the NLO matrix elements fully describe all features of the data. 24

25 Jets in γγ collisions dσ/d η jet [pb] OPAL x + γ or x - γ <.75 NLO / ( +δ ) hadr PYTHIA SaS D PYTHIA MIA contribution η jet Good agreement of OPAL data with NLO calculations using GRV HO PDF in the region dominated by the single resolved photon contribution, where soft underlying collision (realized by multiparton interaction in PYTHIA) does not occur. [pb] jet dσ/d η cntr jet η cntr [pb] jet dσ/d η fwd jet η fwd 25

26 dσ/d η jet [pb] OPAL x ± γ <.75 NLO / ( +δ hadr ) PYTHIA SaS D PYTHIA MIA contribution but significant disagreement with NLO calculations in the region dominated by the double resolved photon contribution, where multiparton interaction is important. [pb] η jet 5 [pb] Implications for ep collisions at low E T : avoid processes influenced by soft underlying collisions! jet dσ/d η cntr 5 jet dσ/d η fwd jet η cntr jet η fwd 26

27 bb production in ep collisions σ vis (ep b X) ZEUS Data / Theory H µ p rel T H µ impact param. (prel.) ZEUS e - p rel T σ b (p T > p T min ) (nb) 2.5 ZEUS Q 2 < GeV 2,.2 < y <.8 η b < 2 2 z } Q 2 < GeV 2 NLO QCD 2 Q 2 (GeV 2 ).5 NLO QCD m b = 4.5 GeV, µ = m T /2 m b = 4.75 GeV, µ = m T m b = 5. GeV, µ = 2m T p T min (GeV) Clear excess over PQCD at Q 2 = but data not quite consistent at high Q 2 27

28 bb production in γγ collisions Comparison with L3 and OPAL DELPHI New DELPHI data suggest striking agreement between the three LEP experiments and dramatic disagreement of their data with PQCD despite the fact that this process is expected to be the cleanest test of PQCD my view: current calculations are not truly NLO QCD because they do not include order α 2 α 2 s direct photon contribution. 28

29 QCD analysis of σ(γγ QQ) In the conventional approach the NLO QCD approximation is defined by taking into account the first two terms in expansions of direct, as well as single and double resolved photon contributions σ dir = σ () dir + σ() dir α s(µ) + σ (2) dir (M,µ)α2 s(µ) + σ (3) dir (M,µ)α3 s(µ) +, σ sr = σ sr () (M)α s (µ) + σ sr (2) (M,µ)αs(µ) 2 + σ sr (3) (M,µ)αs(µ) 3 +, σ dr = σ (2) dr (M)α2 s(µ) + σ (3) dr (M,µ)α3 s(µ) + to the total cross section where σ () dir σ(γγ QQ) =σ dir + σ sr + σ dr. comes from pure QED and equals [( ) σ () dir = σ + 4m2 Q s 8m4 Q s 2 ln +β β β ( )] + 4m2 Q s, 29

30 Direct photon contribution to σ(γγ QQ) At the order α 2 α 2 s diagrams with light quarks appear and we can distinguish (to all orders) three classes of contributions, differing by the charge factor CF : Class A: CF = e 4 Q. Comes from diagrams in which both primary photons couple to heavy quarks or antiquarks. Class B: CF = e 2 Q e2 q. Comes from diagrams in which one of the primary photons couples to a heavy and the other to a light quark-antiquark pair. Class C: CF = e 4 q. Comes from diagrams in which both photons couple to light qq pairs. 3

31 For classes B and C the corresponding diagrams involve (and massless light quarks) initial state mass singularities that must be subtracted and put into the corresponding PDF of the photons. Because of different charge factors C F classes A, B and C do not mix under renormalization of α s and factorization of mass singularities. The order α 2 α 2 s direct photon contributions of all three classes are needed for theoretical consistency: A: for the calculation of class A direct photon contribution (which does not mix with any other) to be performed in a well-defined RS B: For factorization scale invariance of the sum of direct and resolved photon contributions. C: dtto. Classes B,C can be defined also for the PL parts of single and class C for PL parts of double resolved photon contributions. Classes A,B,C can be treated separately as they do not mix. 3

32 Virtual photon structure: why Operational definition of the virtual photon: P 2 GeV 2 Λ 2 QCD. Inthis region the concept of resolved virtual photon can be discarded but there are good reasons for using it provided the photon lifetime is much longer than the interaction time, i.e. if P 2 M 2. cross section contains singular terms: [ ] M 2 f(x) dτ + g(x)m2 q τ min τ τ 2 + h(x)p 2 τ 2 where τ min = xp 2 + m2 q ( x) After integration we get in units of 3e 2 qα/2π ( ) [ ] M q QED (x, m 2 q,p 2,M 2 2 ( )=f(x)ln τ min + f(x)+ g(x)m2 q + h(x)p 2 τ min τ min ) M 2 f T (x) =x 2 +( x) 2, g T (x) = x, h T (x) =, f L (x) =, g L (x) =, h L (x) =4x 2 ( x). 32

33 This expression vanishes for τ min M 2 and simplifies for τ min M 2 ( q QED (x, m 2 q,p 2,M 2 M 2 )=f(x)ln ) f(x)+ g(x)m2 q + h(x)p 2 xp 2 + m 2 q/( x) xp 2 + m 2 q/( x). x( x)p 2 m 2 q : real photon, onlyγ T, ( M q QED (x, m 2 q,,m 2 )=(x 2 +( x) 2 2 ) ( x) )ln +2x( x) m 2 q x( x)p 2 m 2 q : bothγ T and γ L q QED T (x,,p 2,M 2 )= ( x 2 +( x) 2) ln q QED L (x,,p 2,M 2 )=4x( x) ( ) M 2 xp 2 +2x( x) The above terms come from the collinear region and are thus of partonic nature. There are regular terms, which also yield constant terms. QCD: adds further parton emissions off the primary qq pair. QCD-improved PDF of γ : a way how to include part of higher order perturbative corrections that have clear partonic interpretation. 33

34 Has the QCD renormalization-group-improved parton content of virtual photons been observed? M. Glück, E. Reya, and I.Schienbein (PRD D63 (2), 748) It is demonstrated that present e+e- and DIS ep data on the structure of the virtual photon can be understood entirely in terms of the standard naive quark-parton model box approach. Thus the QCD renormalization group (RG) improved parton distributions of virtual photons, in particular their gluonic component, have not yet been observed. The appropriate kinematical regions for their future observation are pointed out as well as suitable measurements which may demonstrate their relevance. Still true? Not quite! What to look for: deviation of data from the NLO direct photon QCD calculations as these include the QED part of resolved γ T and γ L. H and ZEUS data on dijet production in low Q 2 region provide evidence for effects beyond purely QED structure of the photon. 34

35 Order αα 2 s and αα 2 s JETVIP calculations dσ ep /dηdlnp 2 [nb] η η NLO QCD calculations well approximated by the sum of LO direct and LO resolved contributions evaluated with QED distributions of virtual photons. 35

36 Resolved longitudinal photons: why not? OPAL Data on F γ,qed 2 (x, P 2,Q 2 ) for Q 2 P 2 suggests it, par- its contribution has clear tonic interpretation and the H data seem to need it as well. But it is not mandatory. F γ 2 / α F γ 2 / α F γ 2 / α data.8 F2 γ.6 (a).4 F2(P γ 2 =) (b) < Q 2 > = 2.2 GeV 2.2 < Q 2 > = 4.2 GeV x x F γ 2 / α (c) (d).75.5 < Q 2 > = 8.4 GeV 2.25 < Q 2 > = 2.4 GeV x x (e) F γ 2 / α F γ 2 / α.5 < Q 2 > = 2. GeV 2.5 < Q 2 > = 3 GeV x x (f) 36

37 QED contribution: 37

38 QCD evolution of γ L similar to that of hadrons: M 2 =3,,,, GeV 2 in decreasing order, dashed line corresponds to QED 38