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Structure Functions at HERA. Stefan Schlenstedt DESY Zeuthen. Introduction The “transition region” of low Q 2 and x F 2 at medium Q 2 : F 2 slopes, QCD fits F L F 2 charm Large Q 2 NC/CC cross sections Summary and perspectives. Workshop on - PowerPoint PPT Presentation
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1
Stefan SchlenstedtDESY Zeuthen
Workshop onExclusive and Semiexclusive Processes,
JLab, 20/5/99
• Introduction• The “transition region” of low Q2 and x
• F2 at medium Q2: F2 slopes, QCD fits
• FL
• F2charm
• Large Q2 NC/CC cross sections• Summary and perspectives
Structure Functions at HERA
JLab, May 20, 1999 SemiExclusive Workshop 2
S = (k+P)2, = energy in the ep c.m.s.
Q2 = -(k-k')2 = -q2 = virtuality of the exchanged
X = Q2/(2P • Q) = fraction of proton momentumcarried by the struck quark
y = (P• q)/(P• k) = fraction of beam lepton energytransferred to the photon
W2 = ys = energy in the *p c.m.s.
Q2 = xys
e(k) e'(k')
*(q)
p(P)
xPW2
Q2
Introduction
p (820 GeV)e+ (27.5 GeV)
e- (27.5 GeV) p (920 GeV)1998-99
1994-97
(equivalent to 47-50 TeV fixed target energy)
s
JLab, May 20, 1999 SemiExclusive Workshop 3
HERA Kinematic Range
HERA has unique “depth of field” on the proton structure: • Q2 from ~ 0.04 GeV2 to ~ 105 GeV2
• x down to 10-6
extension by two orders of magnitude both in x and Q2
JLab, May 20, 1999 SemiExclusive Workshop 4
F2 Measurement at HERA
F2:Higher and higher precision measurement over a wide
kinematic range
Hig
h Q
2
Low Q2
Explore new kinematic regions:where does the Standard Model
break down?
Study the transition fromPhotoproduction (Q2 0)to DIS (Q2 > few GeV2):
where does pQCD begin to dominate?
We have to precisely measure F2 to • get handle on QCD evolution and • constrain PDF’s
JLab, May 20, 1999 SemiExclusive Workshop 5
HERA Luminosity
Lumi good for physics 1994-99
Luminosity available for physics (ZEUS):
1994-97 48 pb-1 e+p s = 300 GeV
1998-99 16 pb-1 e–p s = 320 GeV+ running July 99-April 00
EW physics at HERA just starting...
JLab, May 20, 1999 SemiExclusive Workshop 6
The ep Neutral Current Cross Section
d2σNCe±p
dxdQ2=
2πα2
xQ4 ⋅
Y+⋅F2 x,Q2( )−y2FL x,Q2
( )mY−⋅ xF3 x,Q2( )[ ]
F2 =x⋅ Ai2 ⋅(qi(x)
i=quarks∑ +q i(x))
quark densities
xF3 =x⋅ Bi2 ⋅(qi (x)
i=quarks∑ −q i(x)),
02 12 ≅−= xFFFL for not too large y
2)1(1 yY −±=±
relevant for Q2 MZ02
where:
(QED radiative corrections have been neglected)
At low Q2, Ai are the quark electric charges
JLab, May 20, 1999 SemiExclusive Workshop 7
High precision p structure at low x-Q2
• In 1997 ZEUS installed a silicon tracker (BPT)in front of a calorimeter (BPC) to improve the detection of positrons at small scattered angles
• The BPC/T allows F2 (or ) to be measuredwith high precision in the range:
0.045 < Q2 < 0.65 GeV2 6 ·10-7 < x < 1·10-3
• 3.9 pb-1 collected in 6 weeks during 1997geometrical acceptance 4-14% depending on the (x,Q2) bin
• Typical error: 2.6% (stat) 3.3% (syst)
totγ * pσ
JLab, May 20, 1999 SemiExclusive Workshop 8
F2 values at lowest ever x-Q2:
w.r.t. previous measurements: - extension of kinematic range- higher precision
High precision p structure at low x-Q2
JLab, May 20, 1999 SemiExclusive Workshop 9
Regge models provide a good description of the transition region
High precision p structure at low x-Q2
JLab, May 20, 1999 SemiExclusive Workshop 10
Extrapolation to Photoproduction
By assuming Q2 dependence of of GVDM:
can extrapolate data to compare with real photoproduction cross-section tot
p (Q2 = 0):
)(),( 222
0
2022* WQm
mQW p
totp
tot
totp = 42/Q2 F2
totγ * pσ
JLab, May 20, 1999 SemiExclusive Workshop 11
Extrapolation to Photoproduction
W2 dependence of totp à la Regge:
totp(W2) = ARW 2(R-1) + APW 2(P-1)
Results (R = 0.5, free parameters: AR, AP, P )• Fit 1: P = 1.087 0.004(stat) 0.008(syst)• Fit 2: P = 1.105 0.001(stat) 0.007(syst)
JLab, May 20, 1999 SemiExclusive Workshop 12
F2 at Medium Q2: Precision Data
Recent data made measurement of F2 possible with improved precision due to higher event statistics andthe new backward silicon tracker in H1:• typical errors 1% (stat) and 3-4% (syst)
approaching fixed target experiments!• Syst. error dominant up to Q2 1000 GeV2
• Strong rise of F2 at HERA regime (q(x) F2/x quark density is zooming up)
• Good agreement between H1 and ZEUS
Q2 = 15 GeV2
JLab, May 20, 1999 SemiExclusive Workshop 13
Overview of F2 Measurements
• NLO DGLAP gives good description of the HERA, NMC and BCDMS data
• Scaling violations well interpreted by QCD
Bjorkenscaling
Scaling violationby gluons
JLab, May 20, 1999 SemiExclusive Workshop 14
Slopes of F2
x-slope small at small Q2, then increases
Fit F2 = const · x-eff at small x
:ninformatio oflot acontain
fixedat ln
and , fixedat ln
ln slopes The
2222
1x
Qd
dFQ
d
Fd
x
JLab, May 20, 1999 SemiExclusive Workshop 15
This is in relation with the W2 dependence of cross sections,since 1/x ~ W2 at small x, eff = pom(0) - 1Soft pomeron: eff 0.08LO BKFL: eff 0.5NLO BFKL: eff ???
Fit to F2 x-eff vs. Q2 at small x
• Smooth rise of the slope parameter eff -larger than Regge models even at low Q2
• F2 is rising sea is rising. What about gluons?
JLab, May 20, 1999 SemiExclusive Workshop 16
dF2(x,Q2)/dlnQ2
At small x, quark pair creation from gluons dominates scaling violations dF2(x,Q2)/dlnQ2 const · xg(x,Q2)
Different behaviour atsimilar Q2 but smaller x -
turning over of gluon distribution
at small x?
Logarithmic slopedF2/dlnQ2
derived from datafitting:F2 = a + b ·ln Q2
in bins of fixed x
JLab, May 20, 1999 SemiExclusive Workshop 17
QCD Fit to F2
ZEUS DGLAP NLO fit: • Gluon (xg), Sea quark (xS) and u - d difference (xud)
parameterised as: A·x·(1-x) · polynomial in x• Input u,d valence distributions from MRS(R2)• Apply momentum sum rule
ZEUS 1995
• Inner error bands: exp. Errors on s, mc andstrange quark content Ks
• Outer error bands: variation of Q0
2 and xg(x) parameterised with Chebycheff polinomials.
Strong rise of gluon density at large Q2
but consistent with zero at Q2 = 1 GeV2
JLab, May 20, 1999 SemiExclusive Workshop 18
QCD Fit to F2 : Gluon and Singlet
ZEUS 1995
• At Q2 = 1 GeV2, Sea is still rising but Gluon at small x is compatible with zero• Uncertainty for gluon at lowest x,Q2 is large
Although error band goes negative (possible in NLO backward evolution):
• FL and F2charm stay positive
• the fit can be extended down to Q2 = 0.4 GeV2 without deteriorating its quality NLO DGLAP does not break down before the formalism becomes suspect
)( :ondistributisinglet Quark ,,
isdui
i qxxqx +=Σ =
JLab, May 20, 1999 SemiExclusive Workshop 19
ZEUS bpt (red square)
F2(x,Q2) vs. = log(x0/x)·log(1+Q2/Q02)
Phenomenological investigation by D. Haidt:in the HERA domain with x < 0.001 (Sea region)F2 has a simple form in the empirical variable
= log(x0/x) ·log(1+Q2/Q02)
where x0 = 0.04 and Q02 = 0.5 GeV2
• F2(x,Q2) F2()• Linearity: F2() = const ·• Representation valid in perturbative and non-perturbative regions of Q2
• consistent with MRST for Q2 > 1.25 GeV2
JLab, May 20, 1999 SemiExclusive Workshop 20
DIS cross section:
(for Q2 << MZ2 and neglecting radiative corrections)
Reduced cross section:
H1 uses the “Subtraction method”:access to FL from high y cross sections using assumption on F2 by extrapolation of DGLAP fit from low y
d2σNCep
dxdQ2=
2πα2
xQ4 ⋅ 1+(1−y)2( )F2 x,Q2
( ) −y2FL x,Q2( )[ ]
Extraction of FL
σr =F2 −y2
1+ 1−y( )2 ⋅ FL
→ F2 −FL at large y
JLab, May 20, 1999 SemiExclusive Workshop 21
Extraction of FL
F2QCD is the H1 QCD NLO preliminary fit for y < 0.35
• extrapolate the fit results to high y• FL = [1+(1-y)2] / y2 ·(F2
QCD - r)
xs
Qy
2
=ℜ
JLab, May 20, 1999 SemiExclusive Workshop 22
Extraction of FL
Extracted FL consistent with pQCD (yellow band) -at highest y systematically higher
Cross check and extension towards low Q2 done byanother method (indicated by star in the figure).
FL = FLQCD
JLab, May 20, 1999 SemiExclusive Workshop 23
Charm cross section in DISis expected to be dominatedby Boson-Gluon-Fusion
F2charm
from D*, D0 in DIS
F2 ⇒ xg(x) ⇒ σ CC ≡xg(x) ⊗ BGF ⇒ F2charm
F2charm⇐ σCC ⇐ measure D*,D0
( )Direct measurement of F2
charm
Very effective test of QCD:F2
charm calculable from pQCD knowing xg(x)
• Measurement of visible D*, D0 cross section,• extrapolation outside kinematic region in pT, • extract F2
charm:
JLab, May 20, 1999 SemiExclusive Workshop 24
pQCD DGLAP fit
• Steep rise of F2charm as we go to lower x
• Indication that BGF is the dominant mechanism for charm production at HERA
F2charm
from D*, D0 in DIS
JLab, May 20, 1999 SemiExclusive Workshop 25
F2charm/F2 vs. x in Q2 bins
• F2charm rises more rapidly than F2
dominated by gluon contribution, while F2 has also quarks
• F2charm is 25% of F2 at low x and high Q2
JLab, May 20, 1999 SemiExclusive Workshop 26
High Q2 Neutral Currents
d2σNCe±
p
dxdQ2 =2πα2
xQ4 ⋅ Y+˜ F 2 x,Q2
( )−y2FL x,Q2( )mY−xF3 x,Q2
( )[ ]
where:
Y± =1±(1−y)2
˜ F 2 x,Q2( ) =F2
em+Q2
Q2 +MZ2 F2
γZ +Q2
Q2 +MZ2
⎛
⎝ ⎞ ⎠ ⎟
2
F2Z
F3 =Q2
Q2 +MZ2 F3
γZ +Q2
Q2 +MZ2
⎛
⎝ ⎞ ⎠ ⎟
2
F3Z
Handle on xF3 is given by the sign due tothe different charge of the lepton beam.Need luminosity with e– beams to access xF3
e e'*,Z0
p
q
p remnant
JLab, May 20, 1999 SemiExclusive Workshop 27
High Q2 Neutral Currents : de+p/dQ2
• de+p/dQ2 falls over 7 orders of magnitude
• NLO QCD fit to low Q2 data (Q2 < 120 GeV2) works well for high Q2 triumph of QCD!
• Larger luminosity needed to constrain PDFs
• Slight excess at Q2 > 15000 GeV2 remains
JLab, May 20, 1999 SemiExclusive Workshop 28
( ) ( ) ( )[ ]23
22224
2
2
2
,,,2
QxFxYQxFyQxFYxQdxdQ
dL
pe
NC−+ −?=
±
mπασ
High Q2 Neutral Currents: e+ vs. e-
For Q2 > 3000 GeV2 all e–p measurements areabove e+p, in agreement with SM Z interference
( 5pb-1 taken in 98/99)
JLab, May 20, 1999 SemiExclusive Workshop 29
High Q2 Charged Currents
d2σCCe±
p
dxdQ2=
GF2
2πx⋅
MW2
Q2 +MW2
⎡
⎣
⎤
⎦ ⎥
2
⋅Φ±(x,Q2)
where, in naive QPM:
Φ+(x,Q2) =(u +c )+(1−y)2 ⋅(d+s+b)
Φ−(x,Q2) =(u+c)+(1−y)2 ⋅(d +s +b )
• probe valence u,d quarks at large x and Q2
• dCC/dQ2 shape is sensitive to propagator mass
e W
p
q’
p remnant
q
JLab, May 20, 1999 SemiExclusive Workshop 30
High Q2 Charged Currents: de+p/dx
• Reasonable agreement between SM and data• At high x data systematically above SM (CTEQ4)
Need for Bodek & Yang like treatment of d/u ratio(d/u = 0.2 for x 1)
JLab, May 20, 1999 SemiExclusive Workshop 31
• Unconstrained fit to dCC/dQ2: measurement of the mass of spacelike W
complementary to e+e- and pp timelike measurements.
Preliminary results:
no evidence for anomalous space-like EW sector.
• Use Standard Model relation:
Exploiting
correlation between shape and normalization in a model
dependent fit.
A sensitive electroweak consistency check!
(PDG: MW = 80.41 ± 0.10 GeV)
GF =πα
2MZ
2
MW2 (MZ
2 −MW2 )
11−Δr(MW)
Extract MW at MH = 100 GeV, MT = 175 GeV:
Note: the above is not a measurement, but indicates the sensitivity of the CC cross section to
MW assuming the Standard Model.
GeV )(0.05-
0+ )(
0.03-
0.03+pdf)(
0.31-
0.30+syst)(
160
130)stat(
250
24050.80 HTW MM
.-
.+
.-
.+M =
PreliminaryPreliminary
GeV pdf)( syst)()stat(9.80 2.1
3.1
3.4
0.5
6.4
9.4
−+
−+
−+=WM
MW from dCC/dQ2
GeV syst)(3.4)stat(3.32.81 ±±=WM
JLab, May 20, 1999 SemiExclusive Workshop 32
GF depends very strongly on MW
sensitivity to MW within the Standard Model
MW [GeV]
GF [
GeV
-2]
1 contourof 2 distrib.
ZEUS modeldependent fit
MW from dCC/dQ2
JLab, May 20, 1999 SemiExclusive Workshop 33
High Q2 Charged Currents: e+ vs. e-
e-p data an order of magnitude above e+p, since
e-p (u+c) while e+p (1-y)2 ·(d+s)
probing different quark flavours
(1998-99 data)
(1994-97 data)
JLab, May 20, 1999 SemiExclusive Workshop 34
NC and CC e–p Cross Sections
Unification of charged and neutral currents!
1998+99 data!
JLab, May 20, 1999 SemiExclusive Workshop 35
Small Q2: • F2 data at lowest ever x-Q2 can be described
by Regge parameterisations
Medium Q2:• precision approaching fixed target data• NLO DGLAP pQCD fit ok down to Q2 1 GeV2
F2 rise at small x,Q2 seems driven by Sea quarks• F2
charm grows up to 25% of F2
Large Q2: • NC - triumph of QCD: NLO fit extrapolation ok - need more lumi to constrain PDFs• CC - need for Bodek &Yang d/u ratio for x 1
- spacelike-W mass consistent with timelikeUnification of Neutral & Charged currents measured
Perspectives:FL: direct measurement needs dedicated runsxF3: needs more e- dataHigh Q2: HERA high luminosity programme:
deliver 1 fb-1 2001 2005
Summary and Perspectives