Combined Inclusive Diffractive Cross Sections Measured with Forward - PowerPoint PPT Presentation

Diffraction 2012, M.
 Ruspa DIFFRACTION 2012, International Workshop on Diffraction in High Energy Physics Canary Islands (Spain), 10-15 September 2012 Combined Inclusive Diffractive Cross Sections Measured with Forward Proton Spectrometers at HERA 
 Marta Ruspa Univ. Piemonte Orientale & INFN-Torino, Italy

Kinematics of diffractive DIS Diffraction 2012, M.
 Ruspa Q 2 = virtuality of photon = = (4-momentum exchanged at e vertex) 2 W = invariant mass of γ * -p system M X = invariant mass of γ * -IP system x IP = fraction of proton’s momentum x IP 
 ´ 
 GAP
 carried by IP ß = Bjorken’s variable for the IP = fraction of IP momentum carried by struck quark = x/x IP t = (4-momentum exchanged at p vertex) 2 ´ 
 typically: |t|<1 GeV 2  Single diffraction: N=proton  Double diffraction: proton-dissociative system N 


  
 represents a relevant background 2

Diffractive cross section & structure functions Diffraction 2012, M.
 Ruspa D d σ γ * p 3 σ ep → e ' Xp ' D ⋅ d 2 W π Q  
 Diffractive cross section = 2 ) 2 dM X dW dM X α (1 + (1 − y ) dQ d σ bt ~ e dt  
 Diffractive structure function F 2 D(4) and reduced cross sections σ r D(4) and σ r D(3)  R D = σ L γ *p  Xp / σ T γ *p  Xp ;
 σ r D = F 2 D when R D = 0 3

Diffractive DIS at HERA Diffraction 2012, M.
 Ruspa Diffractive DIS Standard DIS x IP 
 ´ 
 GAP
 LRG ´ 
 4

Signatures and selection methods Diffraction 2012, M.
 Ruspa Proton Spectrometer (PS) method p
 Large Rapidity Gap (LRG) method hadronic system p'
 e'
 7

Signatures and selection methods Diffraction 2012, M.
 Ruspa Proton Spectrometer (PS) method p
 Large Rapidity Gap (LRG) method hadronic system near perfect acceptance at low x IP p'
 p-diss contribution no t measurement e'
 7

Signatures and selection methods Diffraction 2012, M.
 Ruspa Proton Spectrometer (PS) method p
 direct measurement of t, x IP high x IP accessible no p-diss contribution Large Rapidity Gap (LRG) method low statistics hadronic system near perfect acceptance at low x IP p'
 p-diss contribution no t measurement e'
 7

Available publications Diffraction 2012, M.
 Ruspa H1 LRG H1
Collab.,
Eur.
Phys.
J.
C48
(2006)
715
 H1
Collab.,
Eur.
Phys.
J.
C72
(2012)
2074
 ZEUS LRG ZEUS
Collab.,
Nucl.
Phys.
B816
(2009)
1

 Consistent results from the two methods H1 FPS H1
Collab.,
Eur.
Phys.
J.
C71
(2011)
1578
 Comparison H1-ZEUS H1
Collab.,
Eur.
Phys.
J.
C48
(2006)
749

 ZEUS LPS ZEUS
Collab.,
Nucl.
Phys.
B816
(2009)
1

 ZEUS
Collab.,
Eur.
Phys.
J.
C38
(2004)
43
 Combining the measurements can provide more precise and kinematically extended data than the individual sets 8

Available publications Diffraction 2012, M.
 Ruspa H1 LRG H1
Collab.,
Eur.
Phys.
J.
C48
(2006)
715
 H1
Collab.,
Eur.
Phys.
J.
C72
(2012)
2074
 Consistent results ZEUS LRG ZEUS
Collab.,
Nucl.
Phys.
B816
(2009)
1

 from the two methods Comparison H1-ZEUS H1 FPS H1
Collab.,
Eur.
Phys.
J.
C71
(2011)
1578
 H1
Collab.,
Eur.
Phys.
J.
C48
(2006)
749

 arXiv:1207.4864
 ZEUS LPS ZEUS
Collab.,
Nucl.
Phys.
B816
(2009)
1

 ZEUS
Collab.,
Eur.
Phys.
J.
C38
(2004)
43
 Combining the measurements can provide more precise and kinematically extended data than the individual sets Proton spectrometer results now combined (first combination in diffraction at HERA!) 9

Data sets for combination Diffraction 2012, M.
 Ruspa H1 FPS HERA II  [ Eur.Phys.J.
C71
(2011)
1578 ] Main H1 and ZEUS detectors used to Luminosity = 156.6 pb -1 reconstruct Q 2 , W and x, whereas Visible range |t| = 0.1 – 0.7 GeV 2 M x , ß , x IP and t derived from FPS/LPS Norm unc ~ ± 6% or from combined info H1+FPS/ZEUS+LPS  H1 FPS HERA I [ Eur.Phys.J.
C48
(2006)
749 ] Luminosity = 28.4 pb -1 Visible range |t| = 0.08 – 0.5 GeV 2 Norm unc ~ ± 10%  ZEUS LPS 2 [ Nucl.Phys.
B816
(2009)
1 ] Luminosity = 32.6 pb -1 Visible range |t| = 0.09 – 0.55 GeV 2 Norm unc ~ +11 -7%  ZEUS LPS 1 [ Eur.Phys.J.
C38
(2004)
43 ] Luminosity = 3.6 pb -1 Visible range |t| = 0.075 – 0.35 GeV 2 Norm unc ~ +12% - 10% 11

Data sets for combination Diffraction 2012, M.
 Ruspa H1 FPS HERA II  [ Eur.Phys.J.
C71
(2011)
1578 ] Main H1 and ZEUS detectors used to Luminosity = 156.6 pb -1 reconstruct Q 2 , W and x, whereas Visible range |t| = 0.1 – 0.7 GeV 2 M x , ß , x IP and t derived from FPS/LPS Norm unc ~ ± 6% or from combined info H1+FPS/ZEUS+LPS  H1 FPS HERA I [ Eur.Phys.J.
C48
(2006)
749 ] Luminosity = 28.4 pb -1 σ r D(3) combined Visible range |t| = 0.08 – 0.5 GeV 2 Norm unc ~ ± 10% Combination performed in the ZEUS  ZEUS LPS 2 visible t range |t| = 0.09 - 0.55 GeV 2 [ Nucl.Phys.
B816
(2009)
1 ] Luminosity = 32.6 pb -1 Prior to combining, ZEUS cross section Visible range |t| = 0.09 – 0.55 GeV 2 Norm unc ~ +11 -7% points swam to H1 (Q 2 , β , x IP ) grid using ZEUS DPDF SJ [ Nucl.Phys.
B831
(2010)
1]

  ZEUS LPS 1 [ Eur.Phys.J.
C38
(2004)
43 ] Luminosity = 3.6 pb -1 Visible range |t| = 0.075 – 0.35 GeV 2 Norm unc ~ +12% - 10% 11

σ r D(3) for combination Diffraction 2012, M.
 Ruspa H1 and ZEUS H1 FPS HERA II H1 FPS HERA I 0.09 !" t "! 0.55 GeV 2 ZEUS LPS 2 ZEUS LPS 1 x IP " rD(3) x IP " rD(3) ! =0.0018 ! = 0.0056 ! = 0.018 ! = 0.056 ! = 0.18 ! = 0.56 x IP = 0.025 0.0009 0 0.0025 0.025 0 0.0085 0.025 0 0.016 0.025 0 0.025 0.025 0 0.035 0.025 0 0.05 0.025 0 0.075 0.025 0 0.09 0.025 0 10 10 2 10 10 2 10 10 2 10 10 2 10 10 2 10 10 2 Q 2 (GeV 2 ) 12

Combination method Diffraction 2012, M.
 Ruspa 
χ 2 minimization which includes full error correlations  [ A.
Glazov,
AIP
Conf.
Proc.
792
(2005)
237 ] Used for previous combined HERA results [JHEP
1001
(2010)
109]
  Key assumption is that H1 and ZEUS are measuring the same cross sections at the  same kinematic points  Model independent check of the data consistency and reduction of the systematic uncertainty i m i ] i − i b j − µ 2 [ m ∑ γ j For a single data set: 2 ( m , b ) = j 2 b j χ exp + ∑ ∑ i m 2 µ i − i ( m i b j i ) 2 ) + ( δ i , uncor m δ i , stat γ j ∑ i j j measured cross section values i µ relative correlated systematic unc. i γ j combined cross section values i m relative statistical unc. i δ stat shifts of correlated systematic b j uncertainty sources in σ units relative uncorrelated systematic unc. i δ uncor Full χ 2 tot built from the sum of the χ 2 exp of each data set, assuming the individual data sets to be statistically uncorrelated minimized wrt m i and b j Χ 2 tot 13

Uncertainties Diffraction 2012, M.
 Ruspa Input cross sections published with their statistical and systematic uncertainties;  the latter classified into point-to-point uncorrelated and correlated Global normalisations included in the fit  H1 and ZEUS systematic uncertainties treated as independent  A few procedural uncertainties considered:  i. additive vs multiplicative nature of the error sources ii. correlated systematic error sources ZEUS-H1 iii. swimming factors applied to ZEUS points iv treatment of the uncertainty on the H1 hadronic energy scale 13

Results Diffraction 2012, M.
 Ruspa 352 data points combined to 191 cross section measurements Good consistency: χ 2 /n dof = 133/161 15

Results Diffraction 2012, M.
 Ruspa 352 data points combined to 191 cross section measurements Good consistency: χ 2 /n dof = 133/161 16

Results Diffraction 2012, M.
 Ruspa 352 data points combined to 191 cross section measurements Good consistency: χ 2 /n dof = 133/161 Influence of several correlated systematic uncertainties reduced significantly for the combined result Cross calibration brings average improvement of experimental uncertainty of 27% wrt most precise single data set (FPS HERA II) Correlated part of experimental uncertainty reduced from about 69% in FPS HERA II to 49% 17

Results Diffraction 2012, M.
 Ruspa 352 data points combined to 191 cross section measurements Good consistency: χ 2 /n dof = 133/161 Statistical uncertainty: 11% Statistical + correlated + uncorrelated: 13.8% Procedural uncertainty: 2.9% Total uncertainty on cross section 14.3% on average and 6% for most precise points Normalization uncertainty: 4% Q 2 = 2.5 - 200 GeV 2 Kinematic coverage extended wrt single input measurements β = 0.0018 - 0.816 x IP = 0.00035 - 0.09 |t| = 0.09 - 0.55 At low x IP , where the proton spectrometer data are free from proton dissociation background, these combined data provide the most precise determination of the absolute normalisation of the diffractive cross section 18

Combined σ r D(3) Diffraction 2012, M.
 Ruspa HERA H1 and ZEUS 0.09 !" t "! 0.55 GeV 2 x IP " rD(3) x IP " rD(3) ! =0.0018 ! = 0.0056 ! = 0.018 ! = 0.056 ! = 0.18 ! = 0.56 Q 2 =2.5 GeV 2 0.025 0 5.1 GeV 2 0.025 0 8.8 GeV 2 0.025 0 15.3 GeV 2 0.025 0 26.5 GeV 2 0.025 0 46 GeV 2 0.025 0 80 GeV 2 0.025 0 200 GeV 2 0.025 0 10 -3 10 -2 10 -3 10 -2 10 -3 10 -2 10 -3 10 -2 10 -3 10 -2 10 -3 10 -2 x IP 15