Structure functions and Structure functions and electroweak studies - PowerPoint PPT Presentation

Structure functions and Structure functions and electroweak studies at electroweak studies at HERA HERA Alexey Petrukhin (On behalf of H1 and ZEUS collaborations) LISHEP 2006, Workshop on Collider Physics

Content Content � Introduction to HERA � Deep Inelastic Scattering � Structure functions � Electroweak studies � Polarised physics � Summary and outlook

H1 and ZEUS at HERA H1 and ZEUS at HERA � HERA collider at DESY, Hamburg � ep accelerator ring, 27.5 x 920 GeV, GeV s ep = 319 � circumference: 6.3km � 4 experimental halls, 2 collider experiments: WM’06 Arena H1 ZEUS

H1 and ZEUS experiments H1 and ZEUS experiments � Nearly 4 π detector coverage � Delivering data since 1992 � HERA 2: higher luminosity since 2004

HERA luminosity and status HERA luminosity and status • Luminosity upgrade: mid 2000 – end 2001 • Longitudinal polarisation of e -beam for HERA 2 • Improvement in machine performance HERA delivered 300 Integrated Luminosity (pb -1 ) 250 200 150 100 50 0 0 200 400 600 800 1000 1200 1400 days of running

Inclusive Deep Inelastic Scattering at HERA Inclusive Deep Inelastic Scattering at HERA Neutral current Charged current e(k‘) e(k) e neutrino 2 2 γ /Z°(Q ) W(Q ) X X p(P) p(P) - four momentum transfer squared in the reaction 2 2 Q = ( k k ' ) 2 Q - fraction of the proton momentum carried by the parton x = - 2 P ( k k ' ) = - fraction of the lepton’s energy loss, 2 y Q sx = -center-of-mass energy squared 4 s E e E p

Cross sections and structure functions Cross sections and structure functions NC Cross Section: ~ σ 2 ( x , Q ) NC Reduced cross section: NC π ± σ α 2 2 2 ( ) 2 Y p y d e ~ ~ ~ [ ] = − NC m - Y F F x F + 2 L 3 2 4 dxd Q x Q Y Y + + 2 = ± Y 1 ( 1 y ) ± Dominant contribution Sizeable only at high y (y>~0.6) Contribution only important at high Q 2 CC Cross Section: (from γ Z interference) ± σ 2 2 4 ( p ) 1 1 d e G M [ ± ± ± ] = − 2 CC F W m W W xW y Y Y + − π 2 L 3 2 2 + 2 x 2 dxd 2 Q 2 ( ) Q M W σ ~ 2 Q ( x , ) CC Reduced cross section: CC

Structure functions Structure functions The proton structure function in QPM: � ∑ = + 2 - sum of the (anti)quarks density F e x [ q ( x ) q ( x )] 2 i i i distributions weighted with their i electric charge squared Structure function ~gluon density g(x) in NLO QCD and 0 in QPM F � L ∑ − - determines the valence quark ~ 2 [ ( ) ( )] xF e a x q x q x � 3 i i i i 2 distributions xq v ( x , Q ) i + = + + + ( ) W x d s u c � 2 flavour separation at high x − = + + + W x ( u c d s ) 2 � Combinations of structure functions allow to unfold PDF and check QCD as well as electroweak theory

Kinematic plane coverage Kinematic plane coverage Q 2 / GeV 2 � HERA extends HERA Experiments: kinematic plane H1 1994-2000 10 4 H1 ISR 2000 (Prel.) coverage to lower x ZEUS 1994-2000 2 Fixed Target Experiments: and higher Q by 2 1 10 3 = y NMC orders of magnitude BCDMS E665 10 2 SLAC � H1 and ZEUS overlap 10 with fixed target results in wide range of x 1 2 and Q 4 -1 0 0 . 10 0 = y -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 1 x

-x physics x physics Low Q - 2 2 Low Q

HERA F 2 2 Q 2 =2.7 GeV 2 3.5 GeV 2 4.5 GeV 2 6.5 GeV 2 Structure function F 2 Structure function F 2 1 0 2 8.5 GeV 2 10 GeV 2 12 GeV 2 15 GeV 2 • Precision measuremens at 2 low Q : F 2 ~2-3% 1 • F 2 rises towards low x 0 2 18 GeV 2 22 GeV 2 27 GeV 2 35 GeV 2 for all measured 2 Q bins em F 2 1 • H1 and ZEUS results are 0 2 45 GeV 2 60 GeV 2 70 GeV 2 90 GeV 2 in a good agreement with fixed target data in 1 the overlapping regions 0 2 -3 -3 120 GeV 2 150 GeV 2 10 1 10 1 ZEUS NLO QCD fit H1 PDF 2000 fit 1 H1 96/97 BCDMS ZEUS 96/97 E665 0 NMC -3 -3 10 1 10 1 x

Rise of F 2 towards low x Rise of F 2 towards low x • F 2 used to fit x-dependences 2 Q in bins for x<0.01 and W>12 GeV: 2 − = ⋅ 2 λ (Q ) F c(Q ) x 2 c(Q 2 ) 2 2 ~const. and • λ ~ ln(Q / Λ ) Q > 2 2 3.5 GeV for BPT Q = • 2 2 1 GeV Around λ deviates from log-dependence From soft hadronic interactions • λ → 0.08 it is expected that Q 2 → 0 for

2 2 F L at low Q – ‘shape’ method F L at low Q – ‘shape’ method = ⋅ − λ • Assume F 2 c x • Difference in the shape between σ and H1 Collaboration extrapolated F 2 vs x 2 is driven by y /Y mostly + 2 One F L bin per Q 2 Fit in Q bins: 2 y σ = − = ⋅ − λ , F F F c x fit 2 L 2 Y + Model dependent determination

F L extraction F L extraction H1 Collaboration 2 • Q Extracted F L is greater than 0 for all bins in

F L extraction F L extraction H1 Collaboration 2 • Q H1 NLO QCD fit is consistent with the data for wide range • Alekhin fit is in agreement with the data 2 • Q MRST and ZEUS NLO fits tend to be low at low

Future Future Direct measurement of F L can be performed only by measuring � 2 cross section for the same Q -x but with different proton beam energies (different y): σ = 2 − F f ( y ) F r L F 2 -F L

Expected precision of F L Expected precision of F L ZEUS and H1 expressed interest to perform low energy run − = 1 30pb , E 920GeV p − = 1 10pb , E 460GeV p MRST CTEQ

NC and CC unpolarised cross NC and CC unpolarised cross 2 2 sections, high Q sections, high Q

F 2 measurements F 2 measurements F 2 ⋅ 2 i H1 e + p x = 0.000050, i = 21 x = 0.000080, i = 20 10 6 ZEUS e + p x = 0.00013, i = 19 • F 2 across the whole kinematic plane x = 0.00020, i = 18 x = 0.00032, i = 17 BCDMS x = 0.00050, i = 16 10 5 2 NMC • Extend low Q measurements consistent x = 0.00080, i = 15 x = 0.0013, i = 14 with them x = 0.0020, i = 13 10 4 x = 0.0032, i = 12 x = 0.0050, i = 11 • Negative scaling violation for x>0.18: 10 3 x = 0.0080, i = 10 running of α s x = 0.013, i = 9 x = 0.020, i = 8 10 2 x = 0.032, i = 7 • Positive scaling violation for x<0.1: x = 0.050, i = 6 x = 0.080, i = 5 effect of high gluon density 10 x = 0.13, i = 4 x = 0.18, i = 3 • Scaling violations are well described over 1 x = 0.25, i = 2 2 4 orders of magnitude in x and Q by QCD x = 0.40, i = 1 -1 fit 10 H1 Collaboration -2 x = 0.65, i = 0 H1 PDF 2000 10 extrapolation -3 10 2 3 4 5 1 10 10 10 10 10 Q 2 / GeV 2

NC cross section and x F 3 NC cross section and x F 3 Q 2 = 1500 GeV 2 Q 2 = 5000 GeV 2 Q 2 = 12000 GeV 2 2 • At high Q the NC cross NC H1 PDF 2000: e + p 1 - e + p H1 94-00 σ + ∼ √ s = 319 GeV sections in e p and e p e − p e − p H1 98-99 0.75 scattering are different 0.5 0.25 • The results of measured 0 cross sections and structure 3 xF ∼ H1 function xF 3 are comparable 0.2 H1 PDF 2000 with corresponding SM H1 Collaboration expectations ( γ Z interference) 0.1 0 -1 -1 -1 10 1 10 1 10 1 x ~ 1 ~ ~ − + σ − σ ~ [ ] x F 3 NC NC 2 Y −

CC and NC cross section measurements CC and NC cross section measurements γ dominant • Unification of EM and weak Q > interactions in DIS for 2 2 M W • NC cross section exceeds CC 2 cross section at low Q γ Z interf. • Agreement between H1, ZEUS and QCD fit over seven orders diff. u,d of magnitude in cross section distribut. 2 M W 2 M Z

CC cross section CC cross section + - • CC e p e p allow to disantangle contributions of u and d quarks: HERA Charged Current H1 e - p H1 e + p 94-00 SM e - p (CTEQ6D) ~ σ + + + − + ZEUS e - p 98-99 ZEUS e + p 99-00 SM e + p (CTEQ6D) 2 ~ u c ( 1 y ) ( d s ) CC σ ∼ Q 2 = 280 GeV 2 Q 2 = 530 GeV 2 Q 2 = 950 GeV 2 σ ~ − σ + + − + 2 2 ~ u c ( 1 y ) ( d s ) CC 1 e + • most sensitive to 2 p d ( x , Q ) Q 2 = 1700 GeV 2 Q 2 = 3000 GeV 2 Q 2 = 5300 GeV 2 1 e − • most sensitive to 2 p u ( x , Q ) 0.5 e + • valence quarks suppressed 1 p Q 2 = 9500 GeV 2 Q 2 = 17000 GeV 2 Q 2 = 30000 GeV 2 − 0.75 by factor 2 ( 1 y ) 0.5 0.25 -2 -1 -2 -1 -2 -1 10 10 10 10 10 10 x

Parton density functions Parton density functions (PDFs) (PDFs) 1 xf(x,Q 2 ) • Cross section measurements H1 H1 PDF 2000 0.9 Q 2 =10 GeV 2 in ep interactions at HERA ZEUS-S PDF ZEUS-S PDF 0.8 allow PDF fits xu V 0.7 • H1 and ZEUS PDFs are in 0.6 reasonable agreement though xg( × 0.05) 0.5 there are differences in the shape of xg xg( x 0.05) 0.4 xd V xS( × 0.05) 0.3 xS( x 0.05) 0.2 0.1 0 -4 -3 -2 -1 10 10 10 10 x • Sea and gluon distributions are divided by a factor of 20

Electroweak physics Electroweak physics 2 • First HERA results on • Derived from NC DIS (high Q and EW parameters high x) • Combined fit to determine PDFs and • Result consistent with SM, comparative Z couplings to u and d quarks with determination at Tevatron v u v d H1 H1 v u -a u -v d -a d -PDF H1 v u -a u -v d -a d -PDF 1 1 v u -a u -PDF H1 v d -a d -PDF 68 % CL 68 % CL 0 0 Standard Model Standard Model -1 -1 CDF CDF -1 0 1 -1 0 1 a u a d

Polarised physics at HERA II Polarised physics at HERA II