Stefan Schlenstedt DESY Zeuthen

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


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


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


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...


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


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


F2 values at lowest ever x-Q2:

w.r.t. previous measurements: - extension of kinematic range- higher precision



Regge models provide a good description of the transition region



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


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)


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


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


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


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?


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


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


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 =


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


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


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


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


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:


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


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


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


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


( ) ( ) ( )[ ]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)


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


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)


• 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


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


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)


NC and CC e–p Cross Sections

Unification of charged and neutral currents!

1998+99 data!


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

Stefan Schlenstedt DESY Zeuthen

Documents

medium q2

q2 dependence

q2 mz02where

neglectedat low q2

gev2 x

transition region of

q2 bin typical error

exchanged x