Quarks for Dummies TM * Modeling (e/ /-N Cross Sections from N Cross Sections from Low to High Energies: from DIS to Resonance, to Quasielastic Scattering Modified LO PDFs, w scaling, Quarks and Duality** FNAL Near Detector Workshop Arie Bodek, Univ. of Rochester (work done with Un-Ki Yang, Univ. of Chicago) http://www.pas.rochester.edu/~bodek/Neutrino-N Cross Sections from FNAL03.ppt Arie Bodek, Univ. of Rochester 1 (e/ /-N Cross Sections from N cross sections at low energy Neutrino interactions - Quasi-Elastic / Elastic (W=Mp) + n --> - + p (x =1, W=Mp) well measured and described by form factors (but need to account for Fermi Motion/binding effects in nucleus) e.g. Bodek and Ritchie (Phys. Rev. D23, 1070 (1981) Resonance (low Q2, W< 2) + p --> - + p + n Poorly measured , Adding DIS and resonances together without double counting is a problem. 1st resonance and others modeled by Rein and Seghal. Ann Phys 133, 79, (1981) Deep Inelastic + p --> - + X (high Q2, W> 2) well measured by high energy experiments and well described by quark-parton model (pQCD with
NLO PDFs), but doesnt work well at low Q2 region. X=1 1st resonance GRV94 LO (quasi)elastic F2 integral=0.43 Arie Bodek, Univ. of Rochester (e.g. SLAC data at Q2=0.22) Issues at few GeV : Resonance production and low Q2 DIS contribution meet. The challenge is to describe ALL THREE processes at ALL neutrino (or electron) energies HOW CAN THIS BE DONE? Subject of this TALK 2 MIT SLAC DATA 1972 e.g. E0 = 4.5 and 6.5 GeV e-P scattering A. Bodek PhD thesis 1972 [ PRD 20, 1471(1979) ] Proton Data Electron Energy = 4.5, 6.5 GeV Data The electron scattering data in the Resonance Region is the Frank Hertz Experiment of the Proton. The Deep Inelastic Region is the Rutherford Experiment of the proton SAID V. Weisskopf * (former faculty member at
Rochester and at MIT when he showed these data at an MIT Colloquium in 1971 (* died April 2002 at age 93) What do The Frank Hertz and Rutherford Experiment of the proton have in common? A: Quarks! And QCD Arie Bodek, Univ. of Rochester 3 Initial quark mass m I and final mass ,mF=m * bound in a proton of mass M -N Cross Sections from -N Cross Sections from Summary: INCLUDE quark initial Pt) Get scaling (not x=Q2/2M ) for a general parton Model Is the correct variable which is Invariant in any frame : q3 and P in opposite directions. PI ,P0 q3,q0 PI0 +PI 3 quark photon = 0 3 PP +PP q=q3,q0
2 2 2 2 2 (q+PI ) =PF q +2PI q+PI =mF PF= PF0,PF3,mF=m* PF= PI0,PI3,mI P= P0 + P3,M Special cases: (1) Bjorken x, xBJ=Q2/2M, -> x 2, m F 2 : Slow Rescaling For m F 2 = m I 2 =0 and High (2) Numerator as in charm production (3) Denominator: Target mass term =Nachtman Variable Q +m +A W = for m2I ,Pt=0 =Light Cone Variable =Georgi Politzer Target {M[1+ (1+Q2 / 2)]+B} Mass var. (all the same ) 2 2 F
Most General Case: w= (Derivation in Appendix) [Q2 +B] / [ M (1+(1+Q2/2) ) 1/2 +A] (with A=0, B=0)<<<<<<<< where 2Q2 = [Q2+ m F 2 - m I 2 ] + { ( Q2+m F 2 - m I 2 ) 2 + 4Q2 (m I 2 +P2t) }1/2 Bodek-Yang: Add B and A to account for effects of additional m2 from NLO and NNLO (up to infinite Arie order) QCD effects. For case w with P2t =0 Bodek, Univ. of Rochester 4 ORIGIN of A, B: QCD is an asymptotic series, not a converging series- at any order, there are power corrections Higher Order QCD Corr. Mi Pti,Mi F2ORDER -N q-qbar loops = Renormalon Power Corr. F2ORDER -N F2QCD-0 { 1 + C1 (x,Q) S + C2 (x,Q) S2 + . CN (x,Q) S N } F2 = F2ALL ORDERS = (Experiment)- F2ORDER N =(Theory) --> (The series is Truncated) F2 = Power Corrections = (1/ Q2) a2,N D2 (x,Q2) + (1/ Q4) a4,N D4 (x,Q2) 1. In pQCD the (1/ Q2) terms from the interacting quark are the missing higher order terms. Hence, a2,N and a4,N should become smaller with N. 2. The only other HT terms are from the final state interaction with the spectator quarks, which should only affect the low W region. 3. Our studies have shown that to a good approximation, if one includes the known target mass (TM) effects, the spectator quarks do not affect the average level of the low W cross section as predicted by pQCD if the power corrections from the interacting quark are included.
A, B in w model multi-gluon emission as m2 added to m f , m I Pt Arie Bodek, Univ. of Rochester 5 Old Picture of fixed W scattering - form factors (the Frank Hertz Picture) e +i k2 . r e r +i k1.r Mp OLD Picture fixed W: Elastic Scattering, Resonance Production. Electric and Magnetic Form Factors (GE and GM) versus Q2 measure size of object (the electric charge and magnetization distributions). Elastic scattering W = Mp = M, single final state nucleon: Form factor measures size of nucleon.Matrix element squared |
|2 between initial and final state lepton plane waves. Which becomes: | < e -N Cross Sections from i k2. r | V(r) | e +i k1 . r > | 2 q = k1 -N Cross Sections from k2 = momentum transfer GE (q) = {e i q . r (r) d3r } = Electric form factor is the Fourier transform of the charge distribution. Similarly for the magnetization distribution for GM Form factors are relates to structure function by: 2xF1(x ,Q2)elastic = x2 GM2 elastic (Q2) x-1) Mp e +i k2 . r
e +i k1 . r q Mp MR Resonance Production, W=MR, Measure transition form factor between a quark in the ground state and a quark in the first excited state. For the Delta 1.238 GeV first resonance, we have a Breit-N Cross Sections from Wigner instead of x-N Cross Sections from 1). 2xF1(x ,Q2) resonance ~ x2 GM2 Res. transition (Q2) BWW-1.238) Arie Bodek, Univ. of Rochester 6 Duality: Parton Model Pictures of Elastic and Resonance Production at Low W (High Q2) Elastic Scattering, Resonance Production: Scatter from one quark with the correct parton momentum , and the two spectator are just right such that a final state interaction Aw (w, Q2 ) makes up a proton, or a resonance. Elastic scattering W = Mp = M, q X= 1.0 =0.95 Mp X= 0.95 =0.90 Mp single nucleon in final state.
The scattering is from a quark with a very high value of , is such that one cannot produce a single pion in the final state and the final state interaction makes a proton. Aw (w, Q2 ) = x-1) and the level is the {integral over , from pion threshold to =1 } : local duality Mp (This is a check of local duality in the extreme, better to use measured Ge,Gm, Ga, Gv) Note: in Neutrinos (axial form factor within 20% of vector form factor ) Resonance Production, W=MR, e.g. delta 1.238 resonance. The scattering is from a quark with a high value of , is such R M that that the final state interaction makes a low mass resonance. Aw (w, Q2 ) includes Breit-N Cross Sections from Wigners. Local duality Also a check of local duality for electrons and neutrinos With the correct scaling variable, and if we account for low W and low Q2 higher twist effects, the prediction using QCD PDFs q (, Q2) should give an average of F2 in the elastic scattering and in the resonance region. (including both resonance and continuum contributions). If we modulate the PDFs with a final state interaction resonance A (w, Q2 ) we could also reproduce the various Breit-N Cross Sections from Wigners + continuum. Arie Bodek, Univ. of Rochester 7 Photo-production Limit Q2=0 Non-Perturbative - QCD evolution freezes Photo-production Limit: Transverse Virtual and Real Photo-production cross sections must be equal at Q2=0. Non-perturbative effect. There are no longitudinally polarized photons at Q2=0 L (, Q2) = 0 limit as Q2 -->0 Implies R (, Q2) = L/T ~ Q2 / [Q2 +const] --> 0 limit as Q2 -->0
l -proton, ) = virtual T (, Q2) limit as Q2 -->0 virtualT (, Q2 ) = 0.112 mb 2xF1 (, Q2) / (JQ2 ) limit as Q2 -->0 virtualT (, Q2 = 0.112 mb F2 (, Q2) D / (JQ2 ) limit as Q2 -->0 or F2 (, Q2) ~ Q2 / [Q2 +C] --> 0 limit as Q2 -->0 Since J= [1 - Q2/ 2M =1 and D = (1+ Q2/ 2 )/(1+R) =1 at Q2=0 Therefore l -proton, ) = 0.112 mb F2 (, Q2) / Q2 limit as Q2 -->0 If we want PDFs down to Q2=0 and pQCD evolution freezes at Q2 = Q2min Then F2 (, Q2) = and F2 QCD (, Q2) Q2 / [Q2 +C] l -proton, ) = 0.112 mb The scaling variable x does not work since F2QCD (, Q2 = Q2min) /C -proton, ) = T (, Q2)
At Q2 = 0 F2 (, Q2) = F2 (x , Q2) with x = Q2 /( 2Mreduces to one point x=0 However, a scaling variable w= [Q2 +B] / [ M (1+(1+Q2/2) ) 1/2 +A] works at Q2 = 0 F2 (, Q2) = F2 (c, Q2) = F2 [B/ (2M, 0] limit as Q2 -->0 Arie Bodek, Univ. of Rochester 8 Very high x F2 proton data (DIS + resonance) (not included in the original fits Q2=1. 5 to 25 GeV2) Q2= 25 GeV2 Ratio F2data/F2pQCD F2 resonance Data versus F2pQCD+TM+HT Q2= 1. 5 GeV2 pQCD ONLY Q2= 3 GeV2 Q2= 25 GeV2 Ratio F2data/ F2pQCD+TM pQCD+TM Q2= 9 GeV2 Q2= 15 GeV2 Q2= 25 GeV2 Ratio F2data/F2pQCD+TM+HT pQCD+TM+HT Q2= 25 GeV2 x x pQCD + TM + higher twist describes very high x DIS F2 and NLO resonance F2 data well. (duality works) Q2=1. 5 to 25 GeV2 Arie Bodek, Univ. of Rochester pQCD+TM+HT Aw (w, Q2 ) will
account for interactions with spectator quarks 9 F2, R comparison with NNLO QCD+TM black => NLO HT are missing NNLO terms (Q2>1) Size of the higher twist effect with NNLO analysis is really small (but not 0) a2= -0.009 (in NNLO) versus 0.1( in NLO) - > factor of 10 smaller, a4 nonzero Arie Bodek, Univ. of Rochester 10 Modified LO PDFs for all Q2 (including 0) New Scaling Variable Photoproduction threshold 1. Start with GRV98 LO (Q2min=0.8 GeV2 ) - describe F2 data at high Q2 2. Replace XBJ = Q2 / ( 2M with a new scaling, w Multiply all PDFs by a factors Kvalence and Ksea for photo prod. Limit +non-perturbative effects at all Q2. w= [Q2+MF2 +B ] / [ M (1+(1+Q2/2)1/2 ) + A] F2(x, Q2 ) = K * F2QCD( w, Q2) * A (w, Q2 ) A: initial binding/target mass effect plus NLO +NNLO terms ) B: final state mass effect (but also photo production limit) MF =0 for non-charm production processes MF =1.5 GeV for charm production processes 3. Do a fit to SLAC/NMC/BCDMS/HERA94 H, D data.- Allow the normalization of the experiments and the BCDMS major systematic error to float within errors. A. INCLUDE DATA WITH Q2<1 if it is not in
the resonance region. Do not include any resonance region data. F2(x, Q2 < 0.8) = K * F2( w, Q2=0.8) For sea Quarks K = Ksea = Q2 / [ Q2+Csea ] at all Q2 For valence quarks (from Adler sum rule) K = Kvalence = [1- GD 2 (Q2) ] [Q2+C2V] / [Q2+C1V] GD2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4 = elastic nucleon dipole form factor squared Freeze the evolution at Q2 = 0.8 GeV2 Above equivalent at low Q2 K = Ksea -- > Q2 / [ Q2+Cvalence ] as Q2-> 0 Resonance modulating factor A (w, Q2 ) = 1 for now [Ref:Bodek and Yang [hep-ex 0210024] Arie Bodek, Univ. of Rochester 11 2 = 1268 / 1200 DOF Dashed=GRV98LO QCD F2 =F2QCD (x,Q2) Solid=modified GRV98LO QCD F2 = K(Q2) * F2QCD( w, Q2) SLAC, NMC,BCDMS (H,D) HERA 94 Data ep Arie Bodek, Univ. of Rochester 12 Comparison of LO+HT to neutrino data
on Iron [CCFR] (not used in this w fit) Construction Apply nuclear corrections using e/ scattering data. (Next slide) Calculate F2 and xF3 from the modified PDFs with w Use R=Rworld fit to get 2xF1 from F2 Implement charm mass effect through w slow rescaling algorithm, for F2 2xF1, and XF3 w PDFs GRV98 modified ---- GRV98 (x,Q2) unmodified Left neutrino, Right antineutrino The modified GRV98 LO PDFs with a new scaling variable, w describe the CCFR diff. cross section data (E=30300 Arie Bodek, Univ. of GeV) Rochester well. E= 55 GeV is shown 13 Comparison with F2 resonance data [ SLAC/ Jlab] (These data were not included in this Q = 0.07 GeV 2 Q2= 0.8 5 GeV2 Q2= 3 GeV2 Q2= 1 5 GeV2 2
Q2= 0.22 GeV2 Q2= 1. 4 GeV2 Q2= 9 GeV2 Q2= 2 5 GeV2 w fit) w fit The modified LO GRV98 PDFs with a new scaling variable, w describe the SLAC/Jlab resonance data very well (on average). Even down to Q2 = 0.07 GeV2 Duality works: The DIS curve describes the average over resonance region (for the First resonance works for Q2> 0.8 GeV2) These data and photoproduction data and neutrino data can be used to get A(W,Q2). Arie Bodek, Univ. of Rochester 14 Comparison with photo production data mb (not included in this w fit) SLOPE of F2(Q2=0) -P)= 0.112 mb { F2(x, Q2 = 0.8 )valence /Cvalence + F2(x, Q2 = 0.8 )sea/ Csea }
= 0.112 mb { F2(x, Q2 = 0.8 )valence /0.221 + F2(x, Q2 = 0.8 )sea/ 0.381} The charm Sea=0 in GRV98. Dashed line, no Charm production. Solid line add Charm cross section above Q2=0.8 to DIS Fermilab HERA ) ) Arie Bodek, Univ. of Rochester Energy from Photon-Gluon Fusion calculation 15 Modified LO PDFs for all Q2 (including 0) Results for Scaling variable FIT results for K photo-N Cross Sections from production threshold w= [Q2+B ] /[ M (1+(1+Q2/2)1/2 ) +A] A=0.418 GeV2, A=initial binding/target mass effect plus NLO +NNLO terms ) B= final state mass from gluons plus initial Pt.
Very good fit with modified GRV98LO 2 = 1268 / 1200 DOF Next: Compare to Prediction for data not included in the fit Compare with SLAC/Jlab resonance data (not used in our fit) ->A (w, Q2 ) Compare with photo production data (not used in our fit)-> check on K production threshold Compare with medium energy neutrino data (not used in our fit)- except to the extent that GRV98LO originally included very high energy data on xF3 1. 2. 3. B=0.222 GeV2 (from fit) F2(x, Q2) = K * F2QCD( w, Q2) * A (w, Q2 ) F2(x, Q2 < 0.8) = K * F2( w, Q2=0.8) For sea Quarks we use K = Ksea = Q2 / [Q2+Csea] Csea = 0.381 GeV2 (from fit) For valence quarks (in order to satisfy the Adler Sum rule which is exact down to Q2=0) we use K = Kvalence = [1- GD 2 (Q2) ] [Q2+C2V] / [Q2+C1V] GD2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4 = elastic nucleon dipole form factor squared. we get from the fit C1V = 0.604 GeV2 , C2V = 0.485 GeV2 Which Near Q2 =0 is equivalent to: Kvalence ~ Q2 / [Q2+Cvalence] With Cvalence=(0.71/4)*C1V/C2V=
=0.221 GeV2 [Ref:Bodek and Yang hep-ex/0203009] Arie Bodek, Univ. of Rochester 16 Origin of low Q2 K factor for Valence Quarks Adler Sum rule EXACT all the way down to Q2=0 includes W2 quasi-N Cross Sections from elastic - = W2 (Anti-neutrino -Proton) + = W2 (Neutrino-Proton) q0= AXIAL Vector part of W2 Adler is a number sum rule at high Q2 =1 is -N Cross Sections from F2 = F2 (Anti-neutrino -Proton) = W2 Vector Part of W2 [see Bodek and Yang hep-ex/0203009] and references therein at fixed q 2= + F2 = F2 (Neutrino-Proton) = W2 Q2 we use: dq0) = d ( )d Arie Bodek, Univ. of Rochester 17 Valence Quarks Fixed q2=Q2
Adler Sum rule EXACT all the way down to Q2=0 includes W2 quasi-N Cross Sections from elastic Quasielastic -function 1 = (F-2 -F+2 )d/ Integral of Inelastic + Integral Separated out (F-2 -F+2 )d/ both resonances and DIS For Vector Part of Uv-N Cross Sections from Dv the Form below F2 will satisfy the Adler Number Sum rule If we assume the same form for Uv and Dv ---> [Ref:Bodek and Yang hep-ex/0203009] Arie Bodek, Univ. of Rochester 18 Valence Quarks Adler Sum rule EXACT all the way down to Q2=0 includes W2 quasi-N Cross Sections from elastic This form Satisfies Adler Number sum Rule at all fixed Q2 -N Cross Sections from F2 = F2 (Anti-neutrino -Proton) + F2 momentum = F2 (Neutrino-Proton While sum Rule has QCD and Non Pertu. corrections
Use : K = Kvalence = [1- GD 2 (Q2) ] [Q2+C2V] / [Q2+C1V] Where C2V and C1V in the fit to account for both electric and magnetic terms And also account for N(Q2 ) which should go to 1 at high Q2. This a form is consistent with the above expression (but is not exact since it assumes no dependence on or W (assumes same form for resonance and DIS) Here: GD2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4 = elastic nucleon dipole form factor [Ref:Bodek and Yang hep-ex/0203009] Arie Bodek, Univ. of Rochester 19 Summary Our modified GRV98LO PDFs with a modified scaling variable w and K factor for low Q2 describe all SLAC/BCDMS/NMC/HERA DIS data. The modified PDFs also yields the average value over the resonance region as expected from duality argument, ALL THE WAY TO Q2 = 0 Our Photo-production prediction agrees with data at all energies. Our prediction in good agreement with high energy neutrino data. Therefore, this model should also describe a low energy neutrino cross sections
reasonably well USE this model ONLY for W above Quasielastic and First resonance. , Quasielastic is isospin 1/2 and First resonance is both isospin 1/2 and 3/2. Best to get neutrino vector form factors from electron scattering (via Clebsch Gordon coefficients) and add axial form factors from neutrino measurments. We will compare to available low enegy neutrino data, Adler sum rule etc. This work is continuing focus on further improvement to w (although very good already) and Ai,j,k (W, Q2) (low W + spectator quark modulating function). What are the further improvement in w - more theoretically motivated terms are added into the formalism (mostly intellectual curiosity, since the model is already good enough). E.g. Add Pt2 from Drell Yan data. New proposed experiments at Fermilab/JHF to better measure low energy neutrino cross sections in off-axis beams. For Rochester NUMI proposal see http://www.pas.rochester.edu/~ksmcf/eoi.pdf Arie Bodek, Univ. of Rochester 20 Correct for Nuclear Effects measured in e/ expt. Comparison of Fe/D F2 data In resonance region (JLAB) Versus DIS SLAC/NMC data In TM (C. Keppel 2002). Arie Bodek, Univ. of Rochester 21 Arie Bodek, Univ. of Rochester 22 GRV98 Comparison with F2 resonance data [ SLAC/ Jlab] (These data were not included in this w fit) Q2= 0.07 GeV2
Q2= 0.22 GeV2 Q2= 0.8 5 GeV2 Q2= 1. 4 GeV2 Q2= 9 GeV2 Q2= 3 GeV2 Q2= 2 5 GeV2 Q2= 1 5 GeV2 The modified LO GRV98 PDFs with a new scaling variable, w describe the SLAC/Jlab resonance data very well (on average). Local duality breaks down at x=1 (elastic scattering) and Q2<0.8 in order to satisfy the AdlerArie Sum Number of Uv-Dv Valence quarks = 1. 23 Bodek,rule).I.e. Univ. of Rochester When does duality break down Momentum Sum Rule has QCD+non- Perturbative Corrections (breaks down at Q2=0) but ADLER sum rule is EXACT (number of Uv minus number of Dv is 1 down to Q2=0). Int F2P Elastic peak 1.0000000 0.7775128 0.4340529 0.0996406 0.0376200 0.0055372 0.0001683 0.0000271 0.0000040 DIS high Q2 Integral F2p Q2 0 0.07 0.25
0.85 1.4 3 9 15 25 Q2= 0.8 5 GeV2 0.17 In proton : QPM Integral of F2p = 0.17*(1/3)^2+0.34*(2/3)^2 = 0.17 neutron=0.11) Where we use the fact that 50% carried by gluon 34% u and 17% d quarks Q2= 0.07 GeV2 Q = 3 GeV 2 (In 2 Q2= 1 5 GeV2 Q2= 0.22 GeV2
Q2= 1. 4 GeV2 Q2= 9 GeV2 Q2= 2 5 GeV2 Adler sum rule (valid to Q2=0) is the integral Of the difference of F2/x for Antineutrinos Arie Bodek, Univ. of Rochester 24 and Neutrinos on protons (including elastic) Note that in electron scattering the quark charges remain But at Q2=0, the neutron elastic form factor is zero) Just like in p-p scattering there is a strong connection between F2(elastic) elastic and inelastic proton scattering (Optical Theorem). Quantum Mechanics (Closure) requires a strong connection between elastic and inelastic scattering. Momentum F2(elastic) sum rule breaks down, Neutron but the Adler sum rule (which includes the elastic part, is exact and is equal to the NUMBER of Uv-Dv Q2 = 1. (F2(x)/x) Arie Bodek, Univ. of Rochester 25 Also Related to Old Formulation of Gottfried Sum Rule Stein et al PRD
12, 1884 (1975)-1 -HISTORY Arie Bodek, r Now we know that we must subtract neutron and proton For the modern form of the Gottfried Sum Rule to get rid of the sea quarks -- Which give infinity in the above Expressions. With QCD we know also that Gottfried sum rule has QCD corrections (unlike the Adler sumofrule which is exact. Univ. Rocheste 26 A multi-institutions group is forming to investigate both weak and electromagnetic Form factors1. Quasielastic form factors - (see work of Budd, Bodek Arrington) 2. DIS/Photoproduction -- Bodek/Yang 3. New Group effort for Resonance and Nuclear Effects. Plan: 1. New Hall A data on F2 and R in resonance region for H and D coming out (see talk by Keppel). Hadronic Final State data at Jlab taken in Hall B. 2. A Rochester near detector group forming to participate in extending these JLAB measurements to include other targets: e.g. Carbon, Scintillator (K2K) , Acrylic (close to Water-SuperK) , Calcium (close to Liquid Argon- Icarus), Fe (used by MINOS And CCFR). Maybe targets to mimic existing Bubble Chamber Data on neutrinos. - open to suggetions. Arie Bodek, Univ. of Rocheste r 27 ine of Works Update parameters in old Quark Harmonic Oscillator n-Seghal model to describe Vector EM Resonance m factors for the old SLAC + new Jlab Data On H D. Update Inelastic continuum in Rein-Seghal to agree with
ek/Yang. Converting EM Vector to Weak Vector form factors the Various isospin rules of elastic, resonance and inealstic ng isospin coefficients) Axial form factor (and Fp) - need to compare to old and new utrino data. Cannot Predict from first principles for the onances or quasielastic. Quasielastic - Axial Form factor, Fp being studies - Bodek/Budd nelastic - Axial F2 understood from V-A QPM, Fp also derstood Resonances - Axial form factors need thought and comparison data (e.g. look at production of hyperons for which there ata. e work needed for Nuclear Effects Final States. Arie Bodek, Univ. ofand Rocheste 28 r Revenge of the Spectator Quarks Stein etal PRD 12, 1884 (1975)-2 Note: at low Q2 (for Gep) [1 -W2el]= 1 -1/(1+Q2/0.71)4 = 1-(1-4Q2/0.71) = = 1- (1-Q2 /0.178) = -> Q2 /0.178 as Q2 ->0 At low Q2 it looks the same as Q2 /(Q2 +C) -> Q2 /C P is close to 1 and gives deviations From Dipole form Arie Bodek, Univ. of Rocheste r (5%) factor 29
Revenge of the Spectator Quarks -3 - History of Inelastic Sum rules C. H. Llewellyn Smith hep-ph/981230 Arie Bodek, Univ. of Rocheste r 30 Revenge of the Spectator Quarks -4 - History of Inelastic Sum rules C. H. Llewellyn Smith hep-ph/981230 Arie Bodek, Univ. of Rocheste r 31 S. Adler, Phys. Rev. 143, 1144 (1966) Exact Sum rules from Current Algebra. Valid at all Q2 from zero to infinity. - 5 Arie Bodek, Univ. of Rocheste r 32 F. Gillman, Phys. Rev. 167, 1365 (1968)- 6 Adler like Sum rules for electron scattering. Arie Bodek, Univ. of Rocheste r 33 F. Gillman, Phys. Rev. 167, 1365 (1968)- 7 Adler like Sum rules for electron scattering. Therefore the factor And C is different [1 -W2el]= 1 -1/(1+Q2/0.71)4 for the sea quarks. = 1-(1-4Q2/0.71) =
W2nu-p(vector)= d+ubar = 1- (1-Q2 /0.178) = W2nubar-p(vector) =u+dbar -> Q2 /0.178 as Q2 ->0 1= W2nubar(p)-W2nu(p)= For VALENCE QUARKS FROM THE ADLER SUM RULE FOR the Vector part of the interaction = (u+dbar)-(d+ubar) As compared to the form Q2 /(Q2 +C) -> Q2 /C = (u-ubar)- (d-dbar) = 1 INCLUDING the x=1 Elastic contribution Therefore, the inelastic part is reduced by the elastic x=1 term. Arie Bodek, Univ. of Rocheste r 34 Summary continued Future studies involving both neutrino and electron scattering including new experiments are of interest. As x gets close to 1, local Duality is very dependent on the spectator quarks (e.g. different for Gep. Gen, Gmp, Gmn, Gaxial, Gvector neutrinos and antineutrinos
In DIS language it is a function of Q2 and is different for W1, W2 , W3 (or transverse (--left and right, and longitudinal cross sections for neutrinos and antineutrinos on neutrons and protons. This is why the present model is probably good in the 2nd resonance region and above, and needs to be further studied in the region of the first resonance and quasielastic scattering region. Nuclear Fermi motion studies are of interest, best done at Jlab with electrons. Nuclear dependence of hadronic final state of interest. Nuclei of interest, C12, P16, Fe56. (common materials for neutrino detectors). Arie Bodek, Univ. of Rochester 35 NEUTRINOS On neutrons both quasielastic On quarks And resonance+DIS production possible. -N Cross Sections from -N Cross Sections from
NEUTRINOS -d W+ d -N Cross Sections from 1/3 W+ On Neutrons u +2/3 N=udd possible Both quasi+Res -N Cross Sections from -N Cross Sections from NEUTRINOS -u P=uud or Res W+ W+ On Protons uuu Res only state On protons only resonance+ DIS P=uud
u +2/3 Not possible +5/3 production possible. Arie Bodek, Univ. of Rochester 36 NEUTRINOS On nucleons On neutrons both quasielastic And resonance+DIS production possible. First resonance has different mixtures of I=3/2 And I=1/2 terms. Neutrino and electron induced production are Better related using Clebsch Gordon Coeff.. (Rein Seghal model etc) -N Cross Sections from NEUTRINOS W+ On Neutrons 1st reson X=1 N=udd quasielastic Both quasi+Res 0 P=uud or Res NEUTRINOS
-N Cross Sections from W+ On Protons X=1 uuu Res only state On protons only resonance+ DIS zero production possible. P=uud 1st reson Arie Bodek, Univ. of Rochester 37 On Protons both quasielastic ANTI-NEUTRINOS bar And resonance+DIS production possible. + bar + W-N Cross Sections from W-N Cross Sections from u d +2/3
-N Cross Sections from 1/3 bar bar N=udd or Res P=uud + W-N Cross Sections from W-N Cross Sections from N=udd d Not possible -N Cross Sections from 1/3 -N Cross Sections from 4/3 ddd On Neutrons only resonance+ DIS Arie Bodek, Univ. of Rochester production possible. 38 Neutrino cross sections at low energy
Neutrino oscillation experiments (K2K, MINOS, CNGS, MiniBooNE, and future experiments with Superbeams at JHF,NUMI, CERN) are in the few GeV region Important to correctly model neutrino-nucleon and neutrino-nucleus reactions at 0.5 to 4 GeV (essential for precise next generation neutrino oscillation experiments with super neutrino beams ) as well as at the 15-30 GeV (for future factories) - NuInt, Nufac The very high energy region in neutrino-nucleon scatterings (50-300 GeV) is well understood at the few percent level in terms QCD and Parton Distributions Functions (PDFs) within the framework of the quark-parton model (data from a series of e// DIS experiments) However, neutrino differential cross sections and final states in the few GeV region are poorly understood. ( especially, resonance and low Q2 DIS contributions). In contrast, there is enormous amount of e-N data from SLAC and Jlab in this region. Intellectually - Understanding Low Energy neutrino and electron scattering Processes is also a very way to understand quarks and QCD. - common ground between the QCD community and the weak interaction community, and between medium and HEP physicists. Arie Bodek, Univ. of Rochester 39 Future Progress Next Update on this Work, NuInt02, Dec. 15,2002 At Irvine. Finalize modified PDFs and do duality tests with electron scattering data and Whatever neutrino data exists. Also --> Get A(w,Q2) for electron proton and deuteron scattering cases (collaborate with Jlab Physicists on this next stage). Meanwhile, Rochester and Jlab/Hampton physicists Have formed the nucleus of a collaboration to expand the present Rochester EOI to a formal NUMI Near Detector off-axis neutrino proposal (Compare Neutrino data to existing and future data from Jlab). --contact person, Kevin McFarland. Arie Bodek, Univ. of Rochester 40
Tests of Local Duality at high x, How local Electron Scattering Case INELASTIC High Q2 x-N Cross Sections from -N Cross Sections from >1. QCD at High Q2 Note d refers to d quark in the proton, which is the same as u in the neutron. d/ u=0.2; x=1. F2 (e-N Cross Sections from P) = (4/9)u+(1/9)d = (4/9+1/45) u = (21/45) u F2(e-N Cross Sections from N) = (4/9)d+(1/9)u = (4/45+5/45) u = (9/45) u F2(e-N Cross Sections from N) /F2 (e-N Cross Sections from P) = 9/21=0.43 Elastic/quasielastic +resonance at high Q2 dominated by magnetic form factors which have a dipole form factor times the magnetic moment F2 (e-N Cross Sections from P) = A G2mP(el) +BG2mN(res c=+1) F2 (e-N Cross Sections from N) = AG2mN(el) +BG2mN(res c=0) TAKE ELASTIC TERM ONLY F2(e-N Cross Sections from N) /F2 (e-N Cross Sections from P) (elastic) = 2N2P2 =0.47 Close if we just take the elastic/quasielastic x=1 term. Different at low Q2, where Gep,Gen dominate. Since Gep=0.
Arie Bodek, Univ. of Rochester 41 Tests of Local Duality at high x, How local Neutrino Charged current Scattering Case INELASTIC High Q2, x-N Cross Sections from -N Cross Sections from >1. QCD at High Q2: Note d refers to d quark in the proton, which is the same as u in the neutron. d/ u=0.2; x=1. F2 ( -N Cross Sections from P) = 2x*d F2( -N Cross Sections from N) = 2x*u F2 (bar -N Cross Sections from P) = 2x*u F2( bar-N Cross Sections from N) = 2x*d F2( -N Cross Sections from P) /F2 ( -N Cross Sections from N) =d/u= 0.2 F2( -N Cross Sections from P) /F2 ( bar-N Cross Sections from P) =d/u=0.2 F2( -N Cross Sections from P) / F2( bar-N Cross Sections from N) =1 F2( -N Cross Sections from N) /F2 ( bar-N Cross Sections from P) =1 Elastic/quasielastic +resonance at high Q2 dominated by magnetic
form factors which have a dipole form factor times the magnetic moment F2 ( -N Cross Sections from P) -N Cross Sections from > A= 0 (no quasiel) + B(Resonance c=+2) F2( -N Cross Sections from N) -N Cross Sections from > A Gm ( quasiel) + B(Resonance c=+1) F2 (bar -N Cross Sections from P) -N Cross Sections from > A Gm ( quasiel) + B(Resonance c=0) F2( bar-N Cross Sections from N) -N Cross Sections from > A= 0( no quasiel) + B(Resonance c=-N Cross Sections from 1) TAKE quasi ELASTIC TERM ONLY F2( -N Cross Sections from P) /F2 ( -N Cross Sections from N) =0 F2( -N Cross Sections from P) /F2 ( bar-N Cross Sections from P) =0 F2( -N Cross Sections from P) / F2( bar-N Cross Sections from N) =0/0 F2( -N Cross Sections from N) /F2 ( bar-N Cross Sections from P) =1 FAILS TEST MUST TRY TO COMBINE Quasielastic and first resonance) Arie Bodek, Univ. of Rochester 42 Pseudo Next to Leading Order Calculations Use LO : Look at PDFs(Xw) times (Q2/Q2+C) And PDFs ( w) times (Q2/Q2+C) q Xw= [Q +B] / [ 2M +A ] w= [Q2 +B] / [ M (1+(1+Q2/2) 1/2 ) +A ]
Pi= Pi0,Pi3,m I Pf, m F =m* P= P0 + P3,M Where 2Q = [Q + m F - m I ] + [ ( Q + m F - m I ) + 4Q (m I +P2t) ] 1/2 (for now set P2t =0, masses =0 excerpt for charm. 2 2 2 2 2 2 2 2 2 2 Add B and A account for effects of additional m2 from NLO and NNLO effects. There are many examples of taking Leading Order Calculations and correcting them for NLO and NNLO effects using external inputs from measurements or additional calculations: e.g. 2. Direct Photon Production - account for initial quark intrinsic Pt and Pt due to initial state gluon emission in NLO and NNLO processes by smearing the calculation with the MEASURED Pt extracted from the Pt spectrum of Drell Yan dileptons as a function of Q2 (mass). 3.
W and Z production in hadron colliders. Calculate from LO, multiply by K factor to get NLO, smear the final state W Pt from fits to Z Pt data (within gluon resummation model parameters) to account for initial state multi-gluon emission. 4. K factors to convert Drell-Yan LO calculations to NLO cross sections. Measure final state Pt. 3. K factors to convert NLO PDFs to NNLO PDFs 4. Prediction of 2xF1 from leading order fits to F2 data , and imputing an empirical parametrization of R (since R=0 in QCD leading order). 5. THIS IS THE APPROACH TAKEN HERE. i.e. a Leading Order Calculation with input of effective initial quark masses and Pt and final quark masses, all from gluon emission. Arie Bodek, Univ. of Rochester 43 Initial quark mass m I and final mass ,mF=m * bound in a proton of mass M -N Cross Sections from -N Cross Sections from Page 1 INCLUDE quark initial Pt) Get scaling (not x=Q2/2MDETAILS q=q3,q0 Is the correct variable which is Invariant in any frame : q3 and P in opposite directions. PI ,P0 q3,q0 PI0 +PI 3 quark photon = 0
PP +PP3 PP0 =M,PP3 =0 InLABFrame: PI0LAB +PI 3LAB 0 3 = PI LAB +PI LAB =M M 2 2 0 3 0 3 0 3 (PI +PI )(PI PI ) (PI ) (PI ) = = M(PI 0 PI 3) M(PI 0 PI 3) 0 3 2 2 M(PI PI ) =(mI +Pt ) 3 2
2 (2) : PI 0 +PI3 =M m ,Pt 0 2PI 0 =M +(m2I +Pt2) /(M ) I M 2 I 2 2 F (q+PI ) =P P= P0 + P3,M 2 2 2 q +2PI q+PI =mF 2(PI 0q0 +PI3q3 )=Q2 +mF2 mI2 Q2 =q2 =(q3 )2 (q0 )2 InLABFrame: Q =q =(q ) 2 2 3 2 2 [M +(mI2 +Pt2 )/(M )] +[M (mI2 +Pt2 )/(M )]q3 =Q2 +mF2 m2I :General
Set: m2I ,Pt =0 ( fornow) M +Mq3 =Q2 +m2F 2 (1) : PI PI =(mI +Pt )/(M ) 3 2 PF= PF0,PF3,mF=m* PF= PI0,PI3,mI 2 2 2 Q +mF Q +mF = = formI2,Pt=0 3 3 M( +q ) M(1+q /) PI0 PI3 =(mI2 +Pt2 )/(M ) 0 mI ,Pt 0 = Q2 +mF2 M[1+ (1+Q2 / 2 )]
formI2,Pt=0 Specialcases: DenomTM term,NumSlowrescaling 2PI =M (m +Pt )/(M ) M Arie Bodek, Univ. of Rochester 44 initial quark mass m I and final mass mF=m* bound in a proton of mass M -N Cross Sections from -N Cross Sections from Page 2 INCLUDE quark initial Pt) DETAILS For the case of non zero mI ,Pt (note P and q3 are opposite) PI ,P0 0 = 3 PI +PI PP0 +PP3 q3,q0 quark photon InLABFrame: PP0 =M,PP3 =0 (1) : 2PI0 =M +(mI2 +Pt2) /(M ) (1) : 2PI3 =M (m2I +Pt2 )/(M )
PF= PI0,PI3,mI 2 q=q3,q0 PF= PF0,PF3,mF=m* P= P0 + P3,M 2 2 2 2 (q+PI ) =PF q +2PI q+PI =mF Q2 =q2 =(q3 )2 2 2 2 2 2 3 [M +(mI +Pt )/(M )] +[M (mI +Pt )/(M )]q =Q2 +mF2 m2I -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from -N Cross Sections from 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from M and group terms in qnd 2 M 2 (q3) - M [Q2+ m F 2 - m I 2 ] + [m I 2+Pt 2 (q3) 2 ] = 0 a b c Keep all terms here and : multiply by
2 General Equation => solution of quadratic equation = [-N Cross Sections from b +(b 2 -N Cross Sections from 4ac) 1/2 ] / 2a use (2q3 2) = q 2 = -Q 2 and (q3) = [+Q 2/ 2 ] 1/2 = [+4M2 x2/ Q 2 ] w = 1/2 [Q2 +B] / [ M (1+(1+Q2/2) ) 1/2 +A] where 2Q2 = [Q2+ m F 2 - m I 2 ] + [ ( Q2+m F 2 - m I 2 ) 2 + 4Q2 (m I 2 +P2t) ] 1/2 Add B and A to account for effects of additional m2 from NLO and NNLO effects. or 2Q2 = [Q2+ m F2 - m I 2 ] + [ Q4 +2 Q2(m F2 + m I 2 +2P2t ) + (m F2 - m I 2 ) 2 ] 1/2 w = [Q2 +B] / [M [+4M2 x2/ Q 2 ] 1/2) +A] (equivalent form) 2 2 1/2 w = x [2Q2 + 2B] / [Q2 + (Q4 +4xArie MBodek, Q2)Univ. +2Ax ] (equivalent form) of Rochester 45 Model 2 / Data
Fit PDF used Scaling Variable Power Param Photo limit A(W,Q2) Reson. Ref. -- e-N DIS/Res Q2>0 F2p F2d * f(x) Xw= (Q2+B)/ (2M+A) A=1.64 B=0.38 X/Xw C=B =0.38 AP(W,Q) AD(W,Q)
Bodek et al e/ --N, DIS Q2>1 MRSR2 TM=Q2/TM+ a2= -0.104 a4= - 0.003 Q2>1 NA 1.0average Yang/ Bodek e/ --N, DIS Q2>1 MRSR2 a2= -0.009 a4= -0.013 Q2>1 NA 1.0average Yang/ Bodek
Xw= (Q2+B)/ (2M+A) A=1.74 B=0.62 Q2/ (Q2+C) C=0.19 1.0average Bodek/ Yang w= (Q2+B) / (TM+A) A=.418 B=.222 comple x 1.0average DOF QPM-0 Published 1979 NLO-2 Published 1999 NNLO-3 Published 2000
LO-1 published 2001 1470 /928 DOF 1406 /928 DOF 1555 e/--N, /958 DIS DOF * f(x) * f(x) GRV94 f(x)=1 Q2>0 LO-1- published 1268 e/ --N, /1200 DIS 2002 DOF HERA Q2>0 LO-1Future
work 2002-3 TBA e/ --N, --N, --N, DIS/Res Q2>0 GRV98 f(x)=1 GRV? or other * f(x) Renormalon model for 1/Q2 TM=Q2/TM+ Renormalon model for 1/Q2 w= (Q2+B..Pt2)/ (TM+A) A=TBA B=TBA Pt2 = TBA Arie Bodek, Univ. of Rochester PRD-79 PRL -99
EPJC -00 NuInt01 Bodek/ Yang NuFac02 comple x Au(W,Q) Ad(W,Q) ? Spect. Quark dependent Bodek/ Yang Nutin02 +PRD 46 e-P, e-D: Xw scaling MIT SLAC DATA 1972 Low Q2 QUARK PARTON MODEL 0TH order (Q >0.5) 2 e-P scattering Bodek PhD thesis 1972 [ PRD 20, 1471(1979) ] Proton Data Q2 from 1.2 to 9 GeV2 versus W2= (x/xw)* F2(Xw)*AP (W,Q2)-- QPM fit. e-D scattering from same publication. NOTE Deuterium Fermi Motion Q2 from 1.2 to 9 GeV2 versus W2= (x/xw)* F2(Xw)*AD(W,Q2) --QPM fit. Arie Bodek, Univ. of Rochester 47 e-P, e-D: Xw scaling MIT SLAC DATA 1972 High Q2 QUARK PARTON MODEL 0TH order (Q >0.5)
2 e-P scattering Bodek PhD thesis 1972 [ PRD 20, 1471(1979) ] Proton Data W2= (x/xw)* F2(Xw)*AP (W,Q2)-- QPM fit e-D scattering from same publication. NOTE Deuterium Fermi Motion W2= (x/xw)* F2(Xw)*AD(W,Q2) --QPM fit. Q2 from 9 to 21 GeV2 versus Q2 from 9 to 21 GeV2 versus Arie Bodek, Univ. of Rochester 48 F2, R comparison with NNLO QCD-works => NLO HT are missing NNLO terms (Q2>1) Size of the higher twist effect with NNLO analysis is really small (but not 0) a2= -0.009 (in NNLO) versus 0.1( in NLO) - > factor of 10 smaller, a4 nonzero Arie Bodek, Univ. of Rochester 49 Future Work - part 1 Implement A e/(W,Q2) resonances into the model for F2 with w scaling. For this need to fit all DIS and SLAC and JLAB resonance date and Photo-production H
and D data and CCFR neutrino data. Check for local duality between w scaling curve and elastic form factors Ge, Gm in electron scattering. - Check method where its applicability will break down. Check for local duality of w scaling curve and quasielastic form factors Gm. Ge, GA, GV in quasielastic electron and neutrino and antineutrino scattering.- Good check on the applicability of the method in predicting exclusive production of strange and charm hyperons Compare our model prediction with the Rein and Seghal model for the 1st resonance (in neutrino scattering). Implement differences between and e/final state resonance masses in terms of A ( i,j, k)(W,Q2) ( i is the interacting quark, and j,k are spectator quarks). Look at Jlab and SLAC heavy target data for possible Q2 dependence of nuclear dependence on Iron. Implementation for R (and 2xF1) is done exactly - use empirical fits to R (agrees with NNLO+GP tgt mass for Q2>1); Need to update Rw Q2<1 to include Jlab R data in resonance region. Compare to low-energy neutrino data (only low statistics data, thus new measurements of neutrino differential cross sections at low energy are important). Check other forms of scaling e.g. F2=(1+ Q2/ W2 (for low energies) Arie Bodek, Univ. of Rochester 50 Future Work - part 2 Investigate different scaling variable parameters for different flavor quark masses (u, d, s, uv, dv, usea, dsea in initial and final state) for F2. , Note: w = [Q2+B ] / [ M (1+ (1+Q2/2) 1/2 ) +A ] assumes m F = m i =0, P2t=0 More sophisticated General expression (see derivation in Appendix): w =[ Q 2+B ] / [M (1+ (1+Q2/2) 1/2 ) +A] with 2Q2 = [Q2+ m F2 - m I 2 ] + [ ( Q2+ m F2 - m I 2 ) 2 + 4Q2 (m I 2 +P2t) ] 1/2
or 2Q2 = [Q2+ m F2 - m I 2 ] + [ Q4 +2 Q2(m F2 + m I 2 +2P2t ) + (m F2 - m I 2 ) 2 ] 1/2 Here B and A account for effects of additional m2 from NLO and NNLO effects. However, one can include P2t, as well as m F , m i as the current quark masses (e.g. Charm, production in neutrino scattering, strange particle production etc.). In w, B and A account for effective masses+initial Pt. When including Pt in the fits, we can constrain Pt to agree with the measured mean Pt of Drell Yan data.. Include a floating factor f(x) to change the x dependence of the GRV94 PDFs such that they provide a good fit to all high energy DIS, HERA, Drell-N Cross Sections from Yan, W-N Cross Sections from asymmetry, CDF Jets etc, for a global PDF QCD LO fit to include Pt, quark masses A, B for w scaling and the Q2/(Q2+C) factor, and A e/(W,Q2) as a first step towards modern PDFs. (but need to conserve sum rules). Put in fragmentation functions versus W, Q2, quark type and nuclear target Arie Bodek, Univ. of Rochester 51 Examples of Current Low Energy Neutrino Data: Quasi-elastic cross section tot/E Arie Bodek, Univ. of Rochester 52 Examples of Low Energy Neutrino Data: Total (inelastic and quasielastic) cross section E GeV Arie Bodek, Univ. of Rochester 53 Examples of Current Low Energy Neutrino Data: Single charged and neutral pion production Old bubble chamber language Arie Bodek, Univ. of Rochester 54
Look at Q2= 8, 15, 25 GeV2 very high x data-backup slide* Ratio F2data/F2pQCD+TM+HT Q2= 9 GeV2 Pion production threshold Now Look at lower Q2 (8,15 vs 25) DIS and resonance data for the ratio of F2 data/( NLO pQCD +TM +HT} High x ratio of F2 data to NLO pQCD +TM +HT parameters extracted from lower x data. These high x data were not included in the fit. o The Very high x(=0.9) region: It is described by NLO pQCD (if target mass and higher twist effects are included) to better than 10% Q2= 15 GeV2 Aw (w, Q2 ) Q2= 25 GeV2 Arie Bodek, Univ. of Rochester 55 Importance of Precision Measurements of P(->e) Oscillation Probability with and Superbeams Conventional superbeams of both signs (e.g. NUMI) will be our only windows into this suppressed transition Analogous to |Vub| in quark sector (CP phase could be could be origin of matter-antimatter asymmetry in the universecould be (The next steps: sources or beams are too far away)
Studying P(-N Cross Sections from >e) in neutrinos and anti-N Cross Sections from neutrinos gives us magnitude and phase information on |Ue3| Matter effects http://www-numi.fnal.gov/fnal_minos/ new_initiatives/loi.html A.Para-NUMI off-axis http://www-jhf.kek.jp/NP02 K. Nishikawa JHF off-axis http://www.pas.rochester.edu/~ksmcf/eoi.pdf K. McFarland (Rochester) - off-axis near detector NUMI http://home.fnal.gov/~morfin/midis/midis_eoi.pdf). J. Morfin (FNAL- )Low E neutrino reactions in an onaxis near detector at MINOS/NUMI Arie Bodek, Univ. of Rochester Sign of m23 Ue3| 56 Event Spectra in NUMI Near Off-Axis, Near On-Axis and Far Detectors (The miracle of the off-axis beam is a nearly monoenergetic neutrino beam making future precision neutrino oscillations experiments possible for the first time Far 0.7o OA Far 0.7o OA Near 0.7o OA (LE) Near 0.7o OA (ME) 1
2 3 4 5 6 GeV Neutrino Energy Near On-Axis (LE) Near On-Axis (ME) 1 Arie Bodek, Univ. of Rochester 2 3 4 5 6 GeV Neutrino Energy 57 http://nuint.ps.uci.edu http://neutrino.kek.jp/nuint01/ (NuInt02) (NuInt01) Note: 2nd conf. NuInt02 to Be held at UC Irvine
Dec 12-15,2002 Needed even for the Low statistics at K2K Bring people of All languages And nuclear and Particle physicists Arie Bodek, Univ. of Rochester 58 What do we want to know about low energy reactions and why Reasons Intellectual Reasons: Understand how QCD works in both neutrino and electron scattering at low energies different spectator quark effects. (There are fascinating issues here as we will show) How is fragmentation into final state hadrons affected by nuclear effects in electron versus neutrino reactions. Of interest to : Nuclear Physics/Medium Energy, QCD/ Jlab communities IF YOU ARE INTERESTED
QCD Practical Reasons: Determining the neutrino sector mass and mixing matrix precisely requires knowledge of both Neutral Current (NC) and Charged Current(CC) differential Cross Sections and Final States These are needed for the NUCLEAR TARGET from which the Neutrino Detector is constructed (e.g Water, Carbon, Iron). Particle Physics/ HEP/ FNAL /KEK/ Neutrino communities IF YOU ARE INTERESTED IN NEUTRINO MASS and MIXING. Arie Bodek, Univ. of Rochester 59 Charged Current Processes is of Interest Charged -N Cross Sections from Current: both differential cross sections and final states Neutrino mass M2: -> Charged Current Cross Sections and Final States are needed: The level of neutrino charged current cross sections versus energy provide the baseline against which one measures M2 at the oscillation maximum.
Measurement of the neutrino energy in a detector depends on the composition of the final states (different response to charged and neutral pions, muons and final state protons (e.g. Cerenkov threshold, non compensating calorimeters etc). muon response W+ 0 EM shower EM response N Arie Bodek, Univ. of Rochester N nucleon response + response 60 Neutral Current Processes is of Interest Neutral -N Cross Sections from Current both differential cross sections and final states SIGNALe transition ~ 0.1% oscillations probability of e. e e-N Cross Sections from in beam N P
Z N -N Cross Sections from > EM shower W+ Backgrounds: Neutral Current Cross Sections and Final State Composition are needed: Electrons from Misidentified in NC events without a muon from higher energy neutrinos are a background Z N SIGNAL 0 N Arie Bodek, Univ. of Rochester +
N 0 EM shower FAKE electron background 61 Dynamic Higher Twist- Power Corrections- e.g. Renormalon Model Use: Renormalon QCD model of Webber&Dasgupta-N Cross Sections from Phys. Lett. B382, 272 (1996), Two parameters a2 and a4. This model includes the (1/ Q2) and (1/ Q4) terms from gluon radiation turning into virtual quark antiquark fermion loops (from the interacting quark only, the spectator quarks are not involved). F2 theory (x,Q2) = F2 PQCD+TM [1+ D2 (x,Q2) + D4 (x,Q2) ] D2 (x,Q2) = (1/ Q2) [ a2 / q (x,Q2) ] (dz/z) c2(z) q(x/z, Q2) q-qbar loops D4 (x,Q2) = (1/ Q4) [ a4 times function of x) ] In this model, the higher twist effects are different for 2xF1, xF3 ,F2. With complicated x dependences which are defined by only two parameters a2 and a4 . (the D2 (x,Q2) term is the same for 2xF1 and , xF3 ) Fit a2 and a4 to experimental data for F2 and R=FL/2xF1. F2 data (x,Q2) = [ F2 measured + F2 syst ] ( 1+ N ) : 2 weighted by errors where N is the fitted normalization (within errors) and F2 syst is the is the fitted correlated systematic error BCDMS (within errors). Arie Bodek, Univ. of Rochester 62 What are 1/Q2 Higher Twist Effects- page 1 Higher Twist Effects are terms in the structure functions that behave like a power series in (1/Q2 ) or [Q2/(Q4+A)], (1/Q4 ) etc.
Pt (a)Higher Twist: Interaction between Interacting and Spectator quarks via gluon exchange at Low Q2-at low W (b) Interacting quark TM binding, initial Pt and Missing Higher Order QCD terms DIS region. ->(1/Q2 ) or [Q2/(Q4+A)], (1/Q4 ). While pQCD predicts terms in s2 ( ~1/[ln(Q2/ 2 )] ) s4 etc In the few GeV region, the terms of the two power series cannot be distinguished, In NNLO p-QCD additional gluons experimentally or theoretically emission: terms like s2 ( ~1/[ln(Q2/ 2 )] ) s4 Spectator quarks are not Involved. (i.e. LO, NLO, NNLO etc.) Arie Bodek, Univ. of Rochester 63 Modified LO PDFs for all Q2 region? Philosophy 1. We find that NNLO QCD+tgt mass works very well for Q 2 > 1 GeV2. 2. That target mass and missing NNLO terms explain what we extract as higher twists in a NLO analysis. i.e. SPECTATOR QUARKS ONLY MODULATE THE CROSS SECTION AT LOW W. THEY DO NOT CONTRIBUTE TO DIS HT. 2. However, we want to go down all the way to Q 2=0. All NNLO and NLO terms blow up. However, higher twist formalism in terms of initial state target mass binding and Pt, and final state mass are valid below Q 2=1, and mimic the higher order QCD terms for Q2>1 (in terms of effective masses, Pt due to gluon emission). 3. While the original approach was to explain the empirical higher twists in terms of NNLO QCD at low Q2 (and extract NNLO PDFs), we can reverse the
approach and have higher twists Model non-perturbative QCD, down to Q2=0, by using LO PDFs and effective target mass and final state masses to account for initial target mass, final target mass, and missing NLO and NNLO terms. I.e. Do a fit with: 4. F2(x, Q2 ) = K(Q2 ) F2QCD( w, Q2) A (w, Q2 ) (set Aw (w, Q2 ) =1 for now - spectator quarks) K(Q2 ) is the photo-production limit Non-perturbative term. 5 w= [Q2+B ] / [ M (1+(1+Q2/2) 1/2 ) + A] 6. B=effective final state quark mass. A=enhanced TM term, [Ref:Bodek and Yang hep-ex/0203009] previously used Xw = [Q2+B] /[2M + A] Arie Bodek, Univ. of Rochester 64 At High x, NNLO QCD terms have a similar form to the kinematic -Georgi-Politzer TM effects -> look like enhanced QCD evolution at low Q Final At high x, Mi,Pt from multi gluon emission by A term TM state F2 fixed Q2 x < C mass Target Mass ): mass QCD initial state quark(G-N Cross Sections from ->P look liketgt enhanced evolution or enhance target mass effect.Add a term A
Initial state target mass TM< x TM = Q2/ [M (1+ (1+Q2/2 ) 1/2 ) +A ] proton target mass effect in Denominator plus enhancement) C= [Q2+M*2 ] / [ 2M] (final state M* mass) X=0 At high x, low Q2 TMx (tgt mass (and the PDF is higher at lower x, so the low Q2 cross section is enhanced . Combine both target mass and final state mass: C+TM = [Q2+M*2+B] / [ M (1+(1+Q2/2) 1/2 ) +A ] - includes both initial state target proton mass and final state M* mass effect) - Exact derivation in Appendix. Add B and A account for additional m2 from NLO and NNLO effects. X=1 F2 Target mass effects QCD evolution [Ref:Georgi and Politzer Phys. Rev. D14, 1829 (1976)]] x=0.6 Mproton Arie Bodek, Univ. of Rochester Ln Q2
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Chapter 24-1: Introduction to Polymers and Biopolymers General
Take a polymer and be able to identify the monomer units Be generally aware of the importance of polymers in our everyday lives Be generally aware of the "unintended consequences" of our society's addiction to synthetic polymers Be aware that...McGraw-Hill/Irwin Copyright 2013 by The McGraw-Hill Companies, Inc.
A Note on the PowerPoint Slides... These PowerPoint slides contain selected exhibits, figures, and tables from the chapters as well as objectives for the chapters. For some chapters, we include extra lecture slides and in-class exercises that we have compiled...