Phenomenology at low Q 2

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1 Phenomenology at low Q 2 Lecture II Barbara Badelek Warsaw University and Uppsala University JLAB June 2006 B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

2 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

3 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

4 Important practical example: radiative corrections Extraction of the Born events from measurements demands removing the QED background radiative corrections procedure. The following processes contribute up to α 3 to the Born cross section: B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

5 Practical example: radiative corrections...cont d σobs = v σ1γ + σtail = v σ1γ + σinel + σel + σqel (1) v virtual corrections + many soft photon emission. Same for the polarised cross sections. Range of kinematical variables from which the radiative tails contribute to the cross section measured at the point A(Q 2, ν); parallel lines: W = const (Badelek, Bardin, Kurek, Scholz, Z. Phys. C66 (1995) 591). Even if we measure at DIS, information on F1, F2 (or R, F2 ) needed down to Q 2 =0! B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

6 Practical example: radiative corrections...cont d σ Define the radiative correction: η(x, y ) = σ 1γ. Example of its magnitude, calculated for µp at meas 280 GeV in two approaches: FERRAD35 (open symbols) and TERAD86 (closed symbols): Important! η(x, y ) may be both > and < than 1. Strongest departure from 1 at low x and highy (i.e. low x and low Q 2 ) due to (quasi)elastic tails. Hadron method removing the elastic tail! Hadron method used by SMC for x<0.02. Monte Carlo: few percent DIS lost, otherwise no biases (at high x too many DIS lost). COMPASS: hadrons in the trigger B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

7 Practical example: radiative corrections...cont d p Example of systematic errors on F2 due to QED RC for µp at 90 GeV (NMC, Nucl. Phys. B483 (1997) 3). B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

8 What do the data show around Q 2 = 1 GeV 2? Figure from ICHEP2004, abstract B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

9 What do the data show around Q 2 = 1 GeV 2?...cont d % #. " # # " ZEUS 1995 df 2 /dlnq Gluons softer x? Figure from hep-ex/ x! "#$ &%'% )( &"* #$ +-,.0/1#$#$ ':;+ <, = )( #$%>#@? % $ACBEDGFH7 IKJ? ; = * L * $ % E,? %M #@? #N #$ &" O * $ % +'#@? % #$ * O#@? P#$%# #$ #$ &" + #$ *A #N "Q * N % + + +! R +1 #@ &"* #$ + B. Badelek (Warsaw & Uppsala) + "* V =,W +' K8 " I Ẍ IZŸ IJ? L[E\ Low Q +']9^:_Q`" 2, lecture &"* II #$ &% ba? %Mc ed % # & f +g,. HUGS, June / 39

10 What do the data show around Q 2 = 1 GeV 2?...cont d H σ r 2 Q 2 =1.5 GeV 2 Q 2 = 2 GeV 2 Q 2 = 2.5 GeV 2 Q 2 = 3.5 GeV Q 2 = 5 GeV 2 Q 2 = 6.5 GeV 2 Q 2 = 8.5 GeV 2 Q 2 = 12 GeV Q 2 = 15 GeV 2 Q 2 = 20 GeV 2 Q 2 = 25 GeV 2 Q 2 = 35 GeV Q 2 = 45 GeV 2 Q 2 = 60 GeV 2 Q 2 =90 GeV 2 Q 2 =120 GeV Q 2 =150 GeV 2 H1 prel H1 QCDfit NMC BCDMS x!#"%$'&)(!+*,.-!/* 01(!24351()367-98:88135*, -!<; 1-5=-!*, -! + *,-?>A@CBEDF7-!G* &IH!HKJLMH NO(!+*P+L,*P9QI IR?#5 -(KS TEU8F-?8:=-!VWX! =-! K* 8YDF7-!Z*[Y\W]!1(+L *,!^RK*_7]:##?#K* 8aÈbcd;e*,5!+RIf78PB0! (hg_ijc blk/; 8Fm624!18PB4S 8F-+ (36245n9E8:=-!Vo8 * pèqsrztac iu\y*e3:!#5^1(v-!2!* wf"0$'&6xsvo=ff'*[y(!-+*e*c1(z36245nn6{8f w#fo+*_* '-!V 78#*Y} 3:-!#78M=-! (98~*,-?*[1]:135*P+*, -!hdf-!~>? ƒ!x 98p(!{8F362 8:81(0 l*[*m7]*ms Figure from hep-ex/ B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

11 What do the data show around Q 2 = 1 GeV 2?...cont d F 2 (x = Q2 /sy, Q 2 ) 10 3 ZEUS BPT 1997 ZEUS SVX 1995 ZEUS 1994 ZEUS 1997 ZEUS QCD fit ZEUS Regge fit H1 SVX 1995 H y=0.8 ( 4096) 10 2 y=0.7 ( 2048) y=0.6 ( 1024) y=0.5 ( 512) 10 y=0.4 ( 256) y=0.33 ( 128) y=0.26 ( 64) 1 y=0.2 ( 32) y=0.12 ( 16) y=0.05 ( 8) 10-1 y=0.025 ( 4) y=0.015 ( 2) y=0.007 ( 1) Q 2 (GeV 2 ) Figure from: ZEUS, Eur. Phys. J. C7 (1999)609 B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

12 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

13 F p 2 in the low Q2, low x region Goal Excellent compendium of nucleon structure functions: Cooper-Sarkar, Devenish, De Roeck, Int. J. Mod. Phys. A13 (1998) 3385 Measurements of F 2 and R are described by different parametrizations, depending on underlying physics ideas. They are either physics motivated fits or models of dynamic origin and have to have a proper asymptotic behaviour: at Q 2 0 fulfilling the conditions F 2 = O(Q 2 ), F 1 M + F 2 pq M q 2 = O(Q2 ). given in Lecture I, eq.(3) and at Q 2 joining the QCD improved parton model expressions, valid in the DIS region. Parametrizations are usually valid in limited kinematic intervals. Below follows the review of most important physics ideas at low Q 2 and the resulting parametrizations. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

14 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

15 F p 2 in the low Q2, low x region DL (see e.g. Donnachie, Landshoff, Z. Phys. C61 (1994) 139) Based of the Regge model which describes well the energy dependence of the photoproduction cross section = low Q 2 data as well? F 2 = (F 2 ) P + (F 2 ) R each of the above terms (soft pomeron, reggeon) is ( Q 2 Q 2 + MR,P 2 ) αr,p x (1 αr,p) (1 x) β R,P By construction the W dependence of σ γ p is weak (as for hadron-hadron). Result: low W data well reproduced but not the high W (i.e. HERA) data; for Q 2 > 0.4 GeV 2 the DL model has too weak energy dependence. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

16 F p 2 in the low Q2, low x region DL...cont d σ tot γ*p(µb) (scaled) 10 5 ZEUS BPC 95 ZEUS 94 E665 DL GRV(94) H1 94 H1 SVTX 95 ZEUS, H1 γp low W γp Q 2 (ZEUS) ALLM 0.00 (x 256) 0.11 (x 128) (x 64) 0.20 (x 32) 10 3 Q 2 (E665) 0.23 (x 16) 0.31 (x 8) 0.25 (x 16) 0.30 (x 8) 0.40 (x 4) (x 4) 0.59 (x 1) 0.50 (x 2) 0.65 (x 1) 1.50 (x 1/2) (x 1/2) 3.00 (x 1/4) 2.80 (x 1/4) 6.50 (x 1/8) Figure from Abramowicz, Levy, hep-ph/ (x 1/8) W 2 (GeV 2 )! "#$ "&%' (()(* %' "+(-,. "%' "/0,21435,. )6798:3); 0<= (%> ; B. Badelek ( 6"; B%>0 ;C "?D <%E >(,. F; B(* B>GH -I(* ('J! K%' (L0 M / >N- O%A "(0, (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

17 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

18 F p 2 in the low Q2, low x region GRV (Glück, Reya, Vogt, Eur. Phys.J. C5 (1998) 461) One of the global fits of parton distributions. Contrary to other approaches (MRS, CTEQ), results do not strongly depend on the (nonperturbative) input parametrization at Q 2 0. Original idea: at low scale Q 2 = µ 2 the nucleon contains only valence quarks. Other partons (gluons, sea) are generated dynamically through DGLAP as Q 2 e.g. in processes: q qg, g q q. However data required both valence gluons and valence sea, of valence-like (small at low x) input distributions = a structure of constituent quarks? Valence distributions taken at Q 2 0 =4 GeV2 and evolved backwards to µ 2. Valence-like sea and gluons at µ 2 parametrized in a simple way. Scale µ 2 set so that gluons there are as hard as valence (e.g. u v ) distribution; observe that the evolution softens gluons. Finally normal evolution to high Q 2 and fit of the distribution parameters. Currently µ 2 = 0.3 GeV 2 ; calculations are perturbatively stable for observables like F 2. However they are applicable only to the leading twists (LT) of QCD while at low Q 2 a contribution of HT may be nonnegligible. Thus the calculations describe the reality only for Q 2 > 0.6 GeV 2. Indeed they agree with data for Q 2 > 0.8 GeV 2. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

19 F p 2 in the low Q2, low x region GRV...cont d F F Q 2 = 0.11 GeV 2 Q 2 = 0.15 GeV 2 Q 2 = 0.20 GeV F 2 F Q 2 = 0.25 GeV 2 Q 2 = 0.30 GeV 2 Q 2 = 0.40 GeV 2 ZEUS BPC 95 ZEUS 94 H1 94 H1 SVTX 95 E665 DL CKMT BK Q 2 = 0.50 GeV 2 Q 2 = 0.65 GeV 2 ABY GRV(94) Q 2 = 1.50 GeV 2 Q 2 = 3.00 GeV 2 Q 2 = 6.50 GeV x x x B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

20 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

21 Parametrizations of F 2 in the low Q 2, low x region JKBB (Kwieciński, Badełek, Z. Phys. C43 (1989) 43; Phys. Lett. B295 (1992) 263) The starting point is the Generalised Vector Meson Dominance (GVMD) representation of the structure function F 2 (x, Q 2 ): F 2 [x = Q 2 /(s + Q 2 M 2 ), Q 2 ] = Q2 Mv 4 σ v (s) 4π v γv 2 (Q 2 + Mv 2 ) + 2 Q2 The function Φ(Q 2, s) is expressed as follows: Q 2 0 dq 2 Φ(Q 2, s) (Q 2 + Q 2 ) 2 F (v) 2 (x, Q 2 ) + F (p) 2 (x, Q2 ) (2) Φ(Q 2, s) = 1 Q 2 dq 2 π Im AS F Q 2 2 (x, Q 2 ) (3) Asymptotic structure function F2 AS(x, Q2 ) assumed to be given. By construction, F 2 (x, Q 2 ) F2 AS(x, Q2 ) for large Q 2. The first term in (2) corresponds to the low mass vector meson dominance. Contribution of vector mesons heavier then Q 0 is included in the integral in (2). This integral can be looked upon as the extrapolation of the (QCD improved) parton model for arbitrary Q 2 (including Q 2 =0). The representation (2) is written for fixed s and is expected to be valid at s Q 2, i.e. at low x but for arbitrary Q 2 and above the resonances. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

22 F p 2 in the low Q2, low x region...cont d JKBB...cont d Choosing the parameter Q 2 0 > (M2 v ) max where (M v ) max is the mass of the heaviest vector meson included in the sum one explicitly avoids double counting when adding two separate contributions to F 2. Q 0 should be smaller than the mass of the lightest vector meson not included in the sum. Representation (2) for the partonic part F (p) 2 (x, Q2 ) may be simplified as follows: F (p) 2 (x, Q 2 Q2 ) = (Q 2 + Q0 2) F 2 AS ( x, Q2 + Q0 2 ) (4) where Q 2 + Q0 2 x = s + Q 2 M 2 + Q0 2 Q2 + Q 2 0 2Mν + Q 2 0 (5) Simplified parametrization (4) connecting F (p) 2 (x, Q2 ) to F2 AS by an appropriate change of the arguments posseses all the main properties of the second term in (2). Apart from Q0 2, constrained by physical requirements, the representation (2) does not contain any other free parameters except those which are implicitly present in F2 AS. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

23 F p 2 in the low Q2, low x region...cont d JKBB...cont d 9 9 9! "$#&%'(#*)+,-%#%"./#021# '3"+1#546%"87:9<;5=?>A@ 9B 4C"D#0)+ E6%GF@ H46%"DIKJMLON P '3/E E?,:%4C"$#5RQST#%H$#*)+.F 45#0)!,-U/4V%/3EWJX,YI/E 4 )+Z[3/E5#5\'5%]LON P %,: "134^K13EV3RQSY_a`<`b P %c,( " #046"2HdEV3RQSefhg P %c,( UcE023m:H45U "n4c"do\<p kmpq46%r/:,-z<461#546%"ds'*% 7(9 H1 Collaboration, a1%n,?ztf 45#0) #*)+Z#us#0)+st%Z3E&%'?vn%""+<13)d46f"+Z8w:"+Z<)+%x DESY P Z )+ZnEy4C"+QS:#0)+z!%Z3E! #"$&%('*),+-./'102'135476,874:95'#4!64!)<;>=<?.*41-@),;BAC9564!6D3EFAC./6G4!6D3IH1./6,+J+C+K'*H,4L?M6D3ON7PMQ:P %'gsc,(3e E6 #ae5k P Z%#3#ZtEy4C"+3{<tE E QS #0)+\t%Z3Es%/'T 2Z3EV }~"+Z if 46134C"d }<4 P Z )+Z *Z%d#3#Z RTSLU ),+)#8V-35H,4L?M6D3W6,8>X )4Y=*)D.Z?[6-<+\=*),;:-@'V+\6<8^]`_bä? 3dce'Tf_ZgDhjik95'lH1./6,+V+Y+*'*H,4L?M6D3G+m)D./'n0d-<;L4L?oA^;?M'*prq?L4:924:95'8:)TH,4Z6D.!+Y?s35pT?MH*)4Z'*p E 4C"+QSf#0)+8t%dZ3E%'\oE/ 213}Ss mj$ "+Zƒpq%Hq# P '3/E ETE 4C"+Q "+Z #0)+Ot%dZ3Em%'s.Z3Em#\/E k P Z%#3#Z? 3r4t95'vu@wx-./'OaM3C-0dyG'1.Z+#? 3zy.{)THZ >',4L+!gDhmik95'\'1.V./6.!+v./'!AC.{'V+*'13^4}4:95'#+,4Z)4L?+,4L?MH*),;7)D35pI+!~>+<4!'102)4L?MH\'1.J./6D.!+ E 4C"+3{<E6*H$QkmoE6%rI2/E("+%3t/Ey4 #ˆ4V%" "+1 #/4^"+#5463nf"+%# 4C"+13E02ZZ$k )Tpp'*p2?s3(^-@)Tp./)4/-./',h# k-<;;y+!~^0 y>6,;+o)./'ep)4!)o8l./6d0 4:9G?+O)D35)<;ƒ~+V?+* 6*AY'13d+!~^0dyG6,;+I)D./'lAC./',=<?M6>-<+V;o~ B. Badelek (Warsaw & Uppsala) Š Low Q 2, An-y<;?+195'*pdp)4!)j8./60 `ŴaLHV?./HV;M'V+!g, ^Š\ T BŒ a:4:.!?m)d3@w;m'v+!gj)d35p`žj% ä lecture II HUGS, June +*^-@)D./'V+ZgDh#cm;[6y@),;C356D.J02),;? )4L?M6D / 39

24 F p 2 in the low Q2, low x region...cont d JKBB...cont d F F 2 F 2 F Q 2 = 0.11 GeV 2 Q 2 = 0.15 GeV 2 Q 2 = 0.20 GeV 2 Q 2 = 0.25 GeV 2 Q 2 = 0.30 GeV 2 Q 2 = 0.40 GeV 2 ZEUS BPC 95 ZEUS 94 H1 94 H1 SVTX 95 E665 DL CKMT BK ABY Q = 0.50 GeV Q = 0.65 GeV GRV(94) df 2 /dlogq F 2 (model JK + BB) continuous - df 2 /dlogq 2 broken - df VMD 2 /DLOGQ2 dotted - df part 2 /dlogq2 points - ZEUS data (Vancouver 1998) Q 2 = 6.50 GeV 2 Q 2 = 1.50 GeV 2 Q 2 = 3.00 GeV x x x x B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

25 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

26 F p 2 in the low Q2, low x region Martin-Ryskin-Stasto (Martin, Ryskin, Stasto, Eur. Phys. J. C7 (1999) 643) Exploits further the idea of BBJK. Perturbative and non-perturbative QCD contributions separated by the distance configurations of the q q pair in the γ q q: small distance configurations (kt 2 > k 0 2 ) given by pqcd (unified equations, DGLAP + BFKL, unintegrated gluon distribution); large distance configurations (kt 2 < k 0 2 ) given by VMD (for low q q fluctuation masses, M 2 < Q0 2), and additive quark model (for high q q masses, M2 > Q0 2). Excellent description of the data throughout the whole Q 2 region, including Q 2 =0. Fitted (at x <0.05) are 3 parameters of the gluon distribution; scales k0 2 and Q2 0 chosen as: k0 2 =0.2 GeV2 (crucial) and Q0 2 =1.5 gv2. Choice of k0 2 yields physically sensible g and F L. Interference between states of different q q masses is crucial for description of the data. Importance of the perturbative contribution in the non-perturbative domain. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

27 F p 2 in the low Q2, low x region Martin-Ryskin-Stasto...cont d γ * M 2 p M 2 z,k T Im A qq+p p Fig.1 σ γ*p (µb) W=245 GeV (x128) W=210 GeV (x64) W=170 GeV (x32) W=140 GeV (x16) W=115 GeV (x8) W=95 GeV (x4) W=75 GeV (x2) W=60 GeV (x1) Fig.5 Fit A (k 0 2 =0.2 GeV 2 ) Fit B (k 2 0 =0.5 GeV 2 ) ZEUS-BPC H1-95 H1-94 H1 ZEUS Mainusch-thesis Q 2 (GeV 2 ) B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

28 F p 2 in the low Q2, low x region Martin-Ryskin-Stasto...cont d F L (x,q 2 ) Fit A: (k 0 2 = 0.2 GeV 2 ) Fit B: (k 0 2 = 0.5 GeV 2 ) BKS MRST W=210 GeV Q Fig.8 2 (GeV 2 ) B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

29 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

30 F p 2 in the low Q2, low x region ALLM97 (Abramowicz, Levy, hep-ph/ ) Parametrization of the σ tot (γ p) at W 2 > 3 GeV 2 (above resonances). Valid everywhere in x and Q 2 (including photoproduction). Based on Regge type approach; extention to large Q 2 compatible with QCD. Observe that it is a fit of 23 parameters to all the data Fit contains contributions of the pomeron (P) and reggeon (R): of the form F 2 (x, Q 2 Q 2 ) = Q 2 + m0 2 [ ] F2 P (x, Q2 ) + F2 R (x, Q2 ) F2 P (x, Q2 ) = c P (t)x α(t) P (1 x) b P (t), F2 R (x, Q2 ) = c R (t)x α(t) R (1 x) b R (t) where and t = ln 1 = 1 + W 2 M 2 x P Q 2 + mp 2, ( lnq 2 + Q0 2 Λ 2 / ln Q2 0 Λ 2 ) 1 = 1 + W 2 M 2 x R Q 2 + mr 2 (6) (7) (8) (9) Here M is the proton mass; m0 2, m2 P, m2 R, Q2 0 allow a smooth transition to photoproduction. For Q 2 mp 2, Q2 mr 2, x P x, x R x; c R, a R, b R, b P Q 2 ; c P, a P Q 2. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

31 F p 2 in the low Q2, low x region ALLM97...cont d "!$#&%(' )+*"#,#.-/#1032$ (σ":l2]d<=1h+27*"#\^q /`badco;98e!f8egh#i2$#w!7 eff 8e!$#l2$*"=mDF#Q=eH2$*"#l^n /òaqpr=?@"#1d3y γ p σtot γ p at HERA energies) B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

32 F p 2 in the low Q2, low x region ALLM97...cont d σ tot γ*p(µb) (scaled) 10 5 ZEUS BPC 95 ZEUS 94 E665 H1 94 ZEUS, H1 γp DL GRV(94) H1 SVTX 95 low W γp Q 2 (ZEUS) ALLM 0.00 (x 256) 0.11 (x 128) (x 64) Q 2 (E665) 0.20 (x 32) 0.25 (x 16) (x 16) 0.30 (x 8) 0.31 (x 8) 0.40 (x 4) (x 4) 0.50 (x 2) 0.65 (x 1) (x 1) 1.50 (x 1/2) (x 1/2) 3.00 (x 1/4) (x 1/4) 6.50 (x 1/8) (x 1/8) W 2 (GeV 2 ) ! "#$ "&%' (()(* %' "+(-,. "%' "/0,21435,. )6798:3); 0<= (%> ; ( 6"; B%>0 ;C "?D <%E >(,. F; B(* B>GH -I(* ('J! K%' (L0 M / >N- O%A "(0, ; QP2 > >"R0 SH > > 6T0 "R(AJ! #"$ &%%'%( "$ )* %,+- )."/ )0+2143$56+- '7 98 : :);,3,< %/=> "$ A ' 2 :BDC. "$EA F).%+G IH2JKJLNMPO'C.A EAQR : : FSA )NTU+- FK F) VG).7W?%X I+Y LNZ\[DZ2]\) F) VE= UAV ]:_ B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

33 %& F p 2 in the low Q2, low x region ALLM97 the transition region σ tot (γ p) = 4π2 α Q 2 + 4M 2 x 2 Q 2 (1 x) Q 2 F 2 (W 2, Q 2 ); σ tot (γp) = lim 4π 2 α F 2 Q 2 0 Q 2 (limit at fixed ν) C"!d#$ %&. ()%C%'^*,+e- f0 *:()% ^*.C+g0 5 #$ %&' ()%!C7-8d-d ^*9; Q(=-N%& 9 %& *,+.- /0 *(1% * ! Transition at Q 9; %j - H% G % IKJ,LM9 -N%E-;kX% H% & <-N* lcrsot <$-N & % H %EFNm%? A@B C *9D9;%EF- C% HG 2 : 1 3 GeV IKJ,LM9 -N%E-O-*9P%& C% Q-N* CR;STQ$-N C%& C 2? *>-*9P%& 0 qra -N & F(1S F0 &Ss-J$ = [?:%$%% Ht$uvw9-N%j-@ V JXWCYAG[Z\-N E-NS =%& = ^]-N%& *X@ B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

34 F p 2 in the low Q2, low x region ALLM97 the transition region! #"$ %&' & ( ()*%+%, -+.0/ 12 -)3% -'( /( (+/+ -9: ;)</%& (9= - % #>? & A@B #2 C9:%D$/ E% GFEHJI+KL9 /%D//-9M%& N O P-'RQ:S,T;J/( N%& + (R %DJUKWVXVCY0ZA[A@ B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

35 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

36 F p 2 in the low Q2, low x region ZEUS Regge fit (ZEUS, Eur. Phys. J. C7 (1999) 609) Combines the Q 2 dependence of the VMD with the energy dependence from the Regge model: ( ) ( ) Q F 2 (x, Q 2 2 M 2 ) = 4π 2 0 α M 2 + Q 2 [A ] R (W 2 ) αr 1 + A P (W 2 ) α P 1 where A R, A P, M 0 are constants; α R, α P are reggeon and pomeron intercepts. Fixed: M 2 0 = 0.53 GeV2, α R = Remaining 3 parameters fitted to Q 2 =0 data at W 2 >3 GeV 2. Result: α P = ± B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

37 F p 2 in the low Q2, low x region ZEUS Regge fit...cont s F 2 (x,q2 ) ZEUS BPT 1997 ZEUS SVX 1995 ZEUS BPC 1995 ZEUS 1997 ZEUS Regge fit H1 SVX 1995 E665 Q 2 =0.045 GeV 2 Q 2 =0.065 GeV 2 Q 2 =0.085 GeV 2 F 2 (x = Q2 /sy, Q 2 ) 10 3 ZEUS BPT 1997 ZEUS SVX 1995 ZEUS 1994 ZEUS 1997 ZEUS QCD fit ZEUS Regge fit H1 SVX 1995 H F 2 (x,q2 ) Q 2 =0.11 GeV 2 Q 2 =0.15 GeV 2 Q 2 =0.2 GeV y=0.8 ( 4096) y=0.7 ( 2048) 0.2 y=0.6 ( 1024) F 2 (x,q2 ) Q 2 =0.25 GeV 2 Q 2 =0.3 GeV 2 Q 2 =0.4 GeV 2 10 y=0.5 ( 512) y=0.4 ( 256) y=0.33 ( 128) y=0.26 ( 64) F 2 (x,q2 ) Q 2 =0.5 GeV x Q 2 =0.65 GeV x x y=0.2 ( 32) y=0.12 ( 16) y=0.05 ( 8) y=0.025 ( 4) y=0.015 ( 2) y=0.007 ( 1) Q 2 (GeV 2 ) B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

38 Outline 1 Important practical example: radiative corrections 2 What do the data show around Q 2 = 1 GeV 2? 3 Parametrizations of F p 2 in the low Q2, low x region Goal DL GRV JKBB Martin-Ryskin-Stasto ALLM97 ZEUS Regge fit 4 Summary B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

39 Summary Apart of physics interest, knowledge of structure functions also outside the DIS region is necessary, e.g. due to radiative corrections. Several approaches determining F 2 at low Q 2 exist: physics motivated fits and fully dynamical models. Observe that the resulting F 2 parametrizations are valid in limited Q 2 (and/or x) intervals. B. Badelek (Warsaw & Uppsala) Low Q 2, lecture II HUGS, June / 39

Phenomenology at low Q 2

Phenomenology at low Q 2 Lecture IV Barbara Badelek Warsaw University and Uppsala University HUGS @ JLAB June 26 B. Badelek (Warsaw & Uppsala) Low Q 2, lecture IV HUGS, June 26 / 37 Outline High energy