DeepDeep InelasticInelastic ScatteringScattering (DIS)(DIS)
Dr. Un-ki Yang Particle Physics Group The University of Manchester [email protected] Un-ki Yang, Frontier of Particle Physics II - DIS 1 Un-ki Yang, Frontier of Particle Physics II - DIS 2 DeepDeep InelasticInelastic ScatteringScattering (DIS)(DIS)
Lepton-nucleon scattering • Discovery of quarks • Quark-parton model • Structure Functions
Quantum Chromodynamics (QCD)
Applications to proton-proton(or antiproton) scattering (Tevatron and LHC)
Lecture note:www.hep.man.ac.uk/~ukyang/dis/dis_lec1_09.pdf
Un-ki Yang, Frontier of Particle Physics II - DIS 3 Elastic and Inelastic scattering
Electron-proton scattering can be described Electron-Proton Scattering as an exchange of a virtual photon.
At low Q2 (momentum carried by photon is low), its wavelength is long compared with the size of the proton. It will be the proton as a point. At medium Q2, its wavelength is comparable to the size of proton. Photon begins to resolve the finite size of P the proton. At high Q2, its wavelength is much shorter than the size of proton. Photon resolve the internal structure of the proton.
Un-ki Yang, Frontier of Particle Physics II - DIS 4 Elastic electron - proton scattering
Electron-Proton Scattering Assumption • Exchange of a single virtual photon
• Relativistic electron (E>>me) • Spin-less electron θ • Proton is a point charge For spin-less electron (Rutherford scatt.)
d! # 2 = α(=e2 / 4π ) 2 4 $ P d" 4E sin 2 ≈ 1 / 137 For spin ½ electron (Mott scatt.) 2 2 Q = !(k ! k ') d! # 2 cos2 $ = 2 2 2 2 4 $ " d" 4E sin 2 = 4E sin 2
Un-ki Yang, Frontier of Particle Physics II - DIS 5
Elastic electron-proton scattering with a particular charge distribution
For an elastic scattering with a particular charge distribution, ρ(r), the scattering amplitude is modified by a form factor.
! ! F(q) = ! d 3reiq•r "(r)
Form factor: Fourier transformation of the spatial charge distribution. - For zero momentum transfer, the form factor is one for unit charge. " d 3r!(r) =1
Un-ki Yang, Frontier of Particle Physics II - DIS 6
Inelastic electron-proton scattering
Inelastic scattering: energy and angle e(k',E') of the scattered electron are 2 indep. e (k,E) θ variables γ (q) Form Factor: F(Q2 ,ν): Structure N (P,M) W Functions: W1, W2 for two polarization states of the virtual photon (long & transverse) 2 2 ! Q = 4EE' sin 2 W is the mass of the hadronic 2 2 W = (P + q) system = P2 + 2P "q + q2 2 2 2 2 d! # cos $ = M + 2M# ! Q = 2 W (%,q2 ) +W (%,q2 )tan 2 $ ' 2 4 $ [ 2 1 2 ] d"dE 4E sin 2 ν=E-E’ y= /E ν 7 (inelasticity) Un-ki Yang, Frontier of Particle Physics II - DIS
Summary for Form Factor
Point charge target: F(Q2)=constant photon always see all of it’s charge
F
Q2 Elastic electron-proton scattering: photon see less charge as Q2 is increased : F(Q2)
F
Q2 Inelastic electron-proton scattering: F(Q2 ,ν) − structure function
Un-ki Yang, Frontier of Particle Physics II - DIS 8 SLAC-MIT e-P inelastic scattering
SLAC-MIT group (Bloom et al.) in 1969 performed an experiment with high-energy electron beams (7-18 GeV).
Scattering of electrons from a hydrogen target at 60 and 100.
Only electrons are detected in the final state - inclusive approach
Un-ki Yang, Frontier of Particle Physics II - DIS 9 Unexpected results from SLAC e-P scattering
νW2
2 The ratio of σ /σMott : no Q dependence, and very weak W dependence. 2 Structure Function, νW2 has no Q dependence. What does it mean? Scattering against something like pointlike - a point is a point regardless of it’s λ
Un-ki Yang, Frontier of Particle Physics II - DIS 10 Quark-Parton Model
The nucleon is made of point-like free quarks with spin ½.
Scattering off the nucleon is incoherent sum of elastic scattering off quarks: Inelastic electron-proton scattering => elastic electron-quark scattering.
The probability, f(x) for a quark to carry momentum fraction x, does not depend on the process or nucleon energy but is intrinsic property for high energy nucleon.
This quark-parton model was first proposed by Richard Feynman.
This model explains of no Q2 dependence in Structure Functions (“Bjorken scaling”)
Un-ki Yang, Frontier of Particle Physics II - DIS 11 Elastic electron-quark scattering
Let’s consider the angular dependence for the total spin=0 and 1 cases
Before Scattering After Scattering Total spin=0 e q e q
+z direction d! Both spin and helicity (-) are conserved: no angular dependence "1 dy Before Scattering After Scattering Total spin=1 e q e q +z direction
d! 2 1! cos" Spin is not conserved.: angular dependence " (1# y) , y = dy 2 2 d! 2 2 2 y For a single quark " eq [1+ (1# y) ] / 2 = eq [ + (1# y)] dy 2
Un-ki Yang, Frontier of Particle Physics II - DIS 12 Elastic electron-quark scattering
Differential cross section for electron-quark scattering
2 2 2 d ! 4" ME 2 y = eq [ + (1# y)] dxdy Q4 2 Assume that the momentum fraction of the proton carried by quark is x, and the probability for a quark to carry momentum fraction x is f(x) d 2! 4" 2 ME % y2 ( = e2 xf (x) + 1$ y 4 (#i q i )' ( )* dxdy Q & 2 ) Compared with the inelastic electron-proton scattering.
d! 4# 2 E 2 cos2 $ = 2 W (%,q2 ) + W (%,q2 )tan2 $ d"dE Q4 [ 2 1 2 ]
d 2! 4" 2 ME $ y2 ' MW ->F = 2xF (x,Q2 ) + 1# y F (x,Q2 ) 1 1 4 & 1 ( ) 2 ) νW ->F dxdy Q % 2 ( 2 2
Un-ki Yang, Frontier of Particle Physics II - DIS 13 Parton Model and Scaling
2xF (x,Q2 ) = F (x,Q2 ) = e2 xf (x) 1 2 !i qi i Structure Functions, 2xF1(x,Q2) and F2(x,Q2) only depends on x, but no Q2 dependence (“Bjorken scaling”) according to quark-parton model, which agrees with results from the SLAC-MIT experiment. • Proton consists of many point-like quarks • Quark has a spin ½ • Callan – Gross relation holds : no contribution from longitudinally polarized virtual photon.
2xF1 = F 2 ∗ - 2xF1 ~ γ T ∗ ∗ - F2 ~ ( γ T + γ L) Thus, a point-like quarks can be only probed by the transversely polarized photon.
Un-ki Yang, Frontier of Particle Physics II - DIS 14 Callan – Gross relation
Phys.Rev.D20:1471,1979. R value is closed to zero
No contribution from a longitudinally polarized virtual photon
Thus, quark spin cannot be 0, but 1/2
What R value would you expect if quark spin is 0? homework F ! 2xF R = 2 1 2xF1
Un-ki Yang, Frontier of Particle Physics II - DIS 15 Quark distributions inside nucleon
valence
sea
quark-antiquark pair from vacuum
Un-ki Yang, Frontier of Particle Physics II - DIS 16 Quark distributions
Un-ki Yang, Frontier of Particle Physics II - DIS 17 Nucleon structure functions
F (x) = e2 xf (x) 2 !i qi i
Proton and neutron structure functions, considering no strange quark
• up(x): probability to find a u quark in a proton with momentum fraction x • un(x): probability to find a u quark in a neutron with momentum fraction x
How did we know that u and d quarks have fractional electric charges, 2/3 and -1/3 respectively? Proposed by the Gell-Mann quark model, and confirmed by the SLAC-MIT experiment Un-ki Yang, Frontier of Particle Physics II - DIS 18 Quark Model (1964)
Gell-Mann et al proposed a quark model to explain many hadrons observed with accelerators in the 1950’s and 1960’s • Hadrons are either baryons (3 quark bound states) or mesons (quark-antiquark pairs) • There are 3 types of quark (up, down and strange; u, d, s) and 3 types of antiquark with opposite electric charge • Quarks (anti-quarks) are spin 1/2 fermions (anti-fermions) • Quarks carry fractional electric charge (u:+2/3 e; d & s: -1/3 e) for example, proton (uud), neutron(ddu) • All hadrons are well specified according to this quark model, and even predicted missing members (like Ω- baryon) • But Gell-Mann was afraid of claiming a quark as a real physical object (no one has every seen a quark!) • Is this quark same as what Feynman’s quark-parton model mentioned? - yes, quark is found to have spin-1/2 and fractional charges given by this model.
Un-ki Yang, Frontier of Particle Physics II - DIS 19 Nucleon structure functions
• For isospin symmetry under strong interaction (p=uud, n=udd)
• From now, we drop the suffix, use quark distributions inside proton
• Take separate contributions of the valence and sea
Un-ki Yang, Frontier of Particle Physics II - DIS 20 Quark charge?
Bodek PhD. MIT 1972 As x0, sea quarks are dominated.
en F2 10S eP ! ! 1 F2 10S As x1, valence quarks are dominated (mainly u quark)
en F2 4dv + uv 1 eP ! ! F2 dv + 4uv 4
en F2 4dv + uv + 10sea eP = F2 dv + 4uv + 10sea
Un-ki Yang, Frontier of Particle Physics II - DIS 21 Sum Rules from Quark-Paron Model
GLS sum rule: there are 3 valence quarks 1 (u (x) + d (x))dx = 3 ! v v 0 Gotttfried sum rule
1 (u (x) ! d (x))dx = 1 " v v 0 Other relations
1 " (u(x) ! u(x))dx = 2 0 1 1 dx xf (x) = 1 (d(x) ! d (x))dx = 1 ! "i i " 0 0 1 " (s(x) ! s (x))dx = 0 0
Un-ki Yang, Frontier of Particle Physics II - DIS 22 Gluon?
Sum of the momenta of all quarks should be the total proton momentum 1 dx xf (x) = 1 ! "i i 0 But all valence and sea quarks by u an d quarks carry only 50%. P n Basically, integrals of F2 and F2 didn’t add up to 1. Missing mom entum is carried by neutral parton “gluon”.
p F n F2 2
0.2 0.4 0.6 x 0.2 0.4 0.6 x
Un-ki Yang, Frontier of Particle Physics II - DIS 23 Scaling violation? (1973)
Scaling violation appears except x~0.2-0.3 region (earlier SLAC-MIT exp.)
F2(x) → F2(x,Q²) : point-like quark seen by a photon has a structure. This scaling violation from a gluon emission, way before PETRA discovers gluon (figure?)
SLAC-MIT group used “scaling invariance” (earlier measurements) as a discovery of quarks, but later they wanted to claim “scaling violation”. Of course, “Observation of scaling violation…” paper was rejected from PRL, finally it was accepted to Phys. Lett B52, 1974 with a modified title “Tests of scaling of the proton.. “
Un-ki Yang, Frontier of Particle Physics II - DIS 24 Summary
Feynmann’s parton model was very successful in describing nucleon structure. Parton was identified as quark which was proposed by Gell-Mann. The valence quarks are the simple quark model constituents, and the sea quarks are concentrated at small x.
o The integral of F2(x) over all x gives the total momentum fraction carried by the valence and sea quarks is only 0.5. o Q² scale violations in the structure functions: F2(x) → F2(x,Q²) : quark radiates gluons. Evidence for neutral parton (“gluon”) inside nucleon, which couples to quarks. All lead to Quantum Chromodynamics (QCD)
Un-ki Yang, Frontier of Particle Physics II - DIS 25 References
• Quarks and Leptons by F. Halzen: Ch 8, 9, and 10 • J. Friedman, H. Kendall, and R. Taylor, 1990 Nobel lectures • QCD CTEQ handbook: http://www.phys.psu.edu/~cteq
Un-ki Yang, Frontier of Particle Physics II - DIS 26