Transcript ppt - Zeus
Diffractive PDFs Paul Laycock University of Liverpool BLOIS 2007 Overview ● Diffractive DIS at Hera – ● Comparison of Experimental Techniques – ● ● Rapidity gap, MX and leading proton techniques Factorisation, NLO QCD Fits and Diffractive PDFs – MY, t and xIP dependences factorise from Q2 and β dependences – QCD and the unconstrained high z gluon Diffractive dijets – ● Kinematics and Observables Factorisation holds in diffractive DIS Combined fit and Diffractive PDFs – Diffractive PDFs with more constraints on the gluon Paul Laycock Diffractive PDFs BLOIS 2007 Page 2 Diffractive DIS Kinematics and Observables Large Gap in Rapidity ` Cross section: Paul Laycock Diffractive PDFs BLOIS 2007 Page 3 Experimentally selecting Forward Proton Spectrometer ep eXp Large Rapidity Gap in H1 Large z 64, z 80m Rapidity Gap e p Measure Leading Proton (FPS) No proton dissociation X Require Large Rapidity Gap (LRG) spanning at least 3.3 < η < ~7.5 Measure the t dependence Kinematics measured from X system, integrate |t| < 1.0 GeV2, MY < 1.6 GeV Low detector acceptance High detector acceptance → precision Paul Laycock Diffractive PDFs BLOIS 2007 Page 4 Latest Zeus results – MX and LRG Zeus and H1 both comparing LRG and MX methods Shown here – Zeus LRG (blue) and Zeus MX (red) Reasonable agreement but ongoing work to understand the differences Paul Laycock Diffractive PDFs BLOIS 2007 A wealth of precision data to Page 5 add to future diffractive PDFs Two Levels of Factorisation QCD hard scattering collinear factorisation (Collins) at fixed xIP and t Applied after integration over measured MY and t ranges `Proton vertex’ factorisation of β and Q2 from xIP, t, and MY dependences Paul Laycock Diffractive PDFs BLOIS 2007 Page 6 H1 Inclusive Data Overview LRG: MY < 1.6 GeV Q2 GeV2 FPS: Y=p 2.7 Q2 24 GeV2 Paul Laycock Diffractive PDFs BLOIS 2007 Page 7 Detailed Comparison LRG v FPS • LRG measurement also done with FPS bins • Form ratio of measurements as a function of xIP, β and Q2 ( M Y 1.6 GeV) 1.23 0.03 (stat.) (Y p) 0.16 (syst.) MY dependence factorises from xIP, β and Q2 within 10% (non-normalisation) errors Paul Laycock Diffractive PDFs BLOIS 2007 Page 8 Effective Pomeron Intercept Independent of β and Q2 From fits to LRG and MX data, with current experimental precision: • Data compatible with no dependence of aIP(0) on Q2 (Zeus and H1) or β (H1) • The xIP dependence also factorises from Q2 and b • xIP, t and MY dependences factorise from the Q2 and β dependences within errors → Data support Proton Vertex Factorisation Paul Laycock Diffractive PDFs BLOIS 2007 Page 9 r D(3) (b , Q2 , xIP ) at xIP 0.01 Study β and Q2 dependences at fixed xIP Analogous to making an inclusive F2 measurement at each value of xIP Paul Laycock Diffractive PDFs BLOIS 2007 Page 10 Q2 Dependence in More Detail Fit data at fixed x, xIP to rD A B ln Q2 such that d D r B d ln Q 2 Divide results by f IP / p ( xIP ) to compare different xIP values Different xIP measurements agree Derivatives large and positive… suggests large gluon Paul Laycock Diffractive PDFs BLOIS 2007 Page 11 H1 2006 DPDF Fit - Overview DPDF aIP(0) IP component: • Fit aIP(0) (xIP dependence). • Simultaneously, fit 5 parameters of DPDFs (β and Q2 dependences) using NLO QCD. Paul Laycock IR component: • Fit nIR one parameter for normalisation. • All flux parameters taken from previous H1 data. PDFs taken from Owens-p. Diffractive PDFs BLOIS 2007 Page 12 H1 2006 DPDF Fit - Details • Fit is stable with variations of, e.g. bmax – the maximum value of β allowed in the fit. • Fit stable for Q2min > 8.5 GeV2. Q2 8.5 GeV2 (and M X 2 GeV, b 0.8) • Fit all data with: Q2 8.5 GeV2 (and M X 2 GeV, b 0.8) DPDF • Parameterise quark singlet zS(z,Q02) and gluon zg(z,Q02) densities, where z is parton momentum fraction (= b for QPM). aIP(0) IP component: • Fit aIP(0) (xIP dependence). • Simultaneously, fit 5 parameters of DPDFs (β and Q2 dependences) using NLO QCD. Paul Laycock • Parameterisation used is zS( z, Q02 ) Aq z Bq (1 z )Cq and zg ( z, Q02 ) A (1 z)Cg (gluon insensitive to Bg) g • Results reproducible with Chebyshev polynomials. Diffractive PDFs BLOIS 2007 Page 13 DPDFs from inclusive data • Fit A Q02 = 1.75 GeV2 c2 ~158 / 183 d.o.f. • Fit B Drop Cg - gluon is parameterised as a constant at the starting scale! c2 ~164 / 184 d.o.f. Q02 = 2.5 GeV2 • Quarks very stable • Gluon similar at low z • No sensitivity to gluon at high z Paul Laycock Diffractive PDFs BLOIS 2007 Page 14 A Closer Look at the High z Region We have only singlet quarks, so DGLAP evolution equation for F2D …. dF D a 2 s Pqg g + Pqq S 2 d ln Q 2 + At high b, relative error on derivative grows, q qg contribution to evolution becomes important … sensitivity to gluon is lost Paul Laycock Diffractive PDFs BLOIS 2007 Page 15 Compare to diffractive dijets in DIS We can compare the predictions of Fit A and Fit B with the experimental measurement of diffractive dijets in DIS This process is particularly sensitive to the gluon Paul Laycock Diffractive PDFs BLOIS 2007 Page 16 Compare to diffractive dijets in DIS At low zIP (< 0.3) Fit A and Fit B are similar The data are in good agreement with the predictions, consistent with factorisation (more on factorisation in A. Bonato’s talk) At high zIP the diffractive dijet data clearly prefer Fit B Paul Laycock Diffractive PDFs BLOIS 2007 Page 17 Combined fit of dijet and inclusive data • The diffractive dijet data can be used as an additional constraint in a NLO QCD fit procedure • Details similar to the inclusive case but can now consrtain 3 parameters for the gluon • Very good simultaneous fit of both inclusive and dijet data achieved Diffractive PDFs Paul Laycock BLOIS 2007 Page 18 Combined fit DPDFs from H1 The singlet and gluon are constrained with similar precision across the kinematic range To be published very soon! Paul Laycock Diffractive PDFs BLOIS 2007 Page 19 Summary ● ● ● ● A wealth of inclusive data from H1 and Zeus using LPS, MX and LRG methods (I didn’t have time to show it all!) Proton vertex factorisation holds: MY, t and xIP dependences factorise from β and Q2 DPDFs from NLO QCD fits to b, Q2 dependences (H1 2006 DPDF Fits A+B) – Quark singlet very well constrained (~5%) – Gluon constrained to ~15%, but poorly known at high z Combined fit to inclusive and dijet data finally constrains both the quark and the gluon to similar precision H1 2007 Jets DPDF to appear soon – use it! Paul Laycock Diffractive PDFs BLOIS 2007 Page 20 BACK-UP SLIDES FOLLOW Paul Laycock Diffractive PDFs BLOIS 2007 Page 21 Effective Pomeron Intercept Independent of β and Q2 From fit to LRG data: a ( 0 1.118 0.008 ( exp. IP +0.029 - 0.010 ( theory • No dependence of aIP(0) on Q2 or β • The xIP dependence also factorises from Q2 and b • xIP, t and MY dependences factorise from the Q2 and β dependences within errors → Data support Proton Vertex Factorisation Paul Laycock Diffractive PDFs BLOIS 2007 Page 22 t Slope Dependence on β or Q2? B measured double differentially in (b or Q2) at fixed xIP • t dependence does not change with b or Q2 at fixed xIP Paul Laycock Diffractive PDFs BLOIS 2007 Page 23 t dependence from FPS measurements B(xIP) from fit to • Fitting low xIP data to B BIP 2a 'IP ln(1/ xIP ) yields: -2 2,0 -2 a 'IP 0.060.19 GeV B 5.5 GeV 0.06 IP 0.7 • B(xIP) data constrain IP, IR flux factors in proton vertex factorisation model Paul Laycock Diffractive PDFs BLOIS 2007 Page 24 Comparison of H1 LRG, H1 FPS, ZEUS LPS Data • ZEUS (LPS) and H1 (FPS) Leading Proton Data agree very well (they agree to 8% cf. 10% normalisation uncertainities) • ZEUS LPS and H1 FPS scaled by global factor of 1.23 to compare with LRG MY < 1.6 GeV • Very good agreement between Leading Proton and LRG methods after accounting for proton diss’n • Both experimental techniques measure the same cross section Paul Laycock Diffractive PDFs BLOIS 2007 Page 25 Paul Laycock Diffractive PDFs BLOIS 2007 Page 26 Q2 derivative and gluon/quark ratios If then Diffractive 0.7 Inclusive 0.3 At low x, gluon:quark ratio ~ 70%/30%, common to diffractive and incl Paul Laycock Diffractive PDFs BLOIS 2007 Page 27