Particle Physics WS 2012/13 ( )

Transcription

1 Particle Physics WS 01/13 ( ) Stephanie Hansmann-Menzemer Physikalisches Institut, INF 6, 3.101

2 Content of Today Structure of the proton: Inelastic proton scattering can be described by elastic scattering at point-like partons The quark parton model and it s experimental evidences Momentum distribution of valence and sea quarks inside the proton Comparison of ep, en, en, eν scattering results give handle to u,d valence and sea quark distributions

3 Inelastic Scattering p 1 e e p 3 inelastic scattering exitation of proton p p invariant mass W, p 4 W > M (baryon number conservation) deep inelastic scattering (DIS) proton gets split up in many pieces Need to variables to describe inelastic scattering process. (p 1 +p ) p 1 p Q = sxy energy loss of incoming particle Bjorken x fraction energy loss of incoming particle 4 momentum transfer square Lab frame: proton at rest p = (M,0,0,0) LI form ν = E 1 -E 3 ν = qp /M x = ;q = 1 elastic scattering x = Mν < 1 inelastic scattering Q qp y = (E 1 -E 3 )/E 1 y = qp /p 1 p q = (p 1 -p 3 ) q = (p 1 -p 3 ) 3

4 p 1 e e Inelastic Scattering p 3 p p invariant mass W, p 4 elastic scattering inelastic scattering Produce excited states e.g. Δ + (13) deep inelastic scattering (DIS); proton splits up in many final state particles 4

5 (In)elastic scattering x-section formular Rosenbluth formular [in lab frame: p = (M,0,0,0)]: dσ = α dω 4E 1 sin 4 ϴ/ E 3 E 1 Rosenbluth formular in LI form: G E q + τg M q 1 + τ cos ϴ + τ GM (q )sin ϴ/ f (Q ) f 1 (Q ) dσ 4π α = [ f dq Q 4 Q 1 y M y + 1 Q y f 1 (Q )] Inelastic cross section [in lab frame: p = (M,0,0,0)]: dσ = α [ F x,q de 3 dω 4 E 1 sin 4 ϴ/ ν Inelastic cross section in LI form: dσ 4π α = [ F x,q dxdq Q 4 x cos ϴ/ + M F 1 x, Q sin Θ/] 1 y M y Q + y F 1 (x, Q )] for Q >> M Form factors have been replaced by structure functions, which depend on two paramters, which cannot anymore interpreted as Fourier transforms of electric charge and magnetic moment distribution. elastic cross section inelastic cross section 5

6 The Quark Parton Model Before quarks and gluons were generally accepted, Feynman proposed that the proton was made up out of point-like constituents (partons). Two pictures of DIS: scattering from proton scattering from point-like parton (quark or gluon) within the proton p 1 e e p 3 p 1 e e p 3 p p W, p 4 p p W, p 4 In the parton model the basic interaction is ELASTIC scattering from a quasi-free spin ½ particle (quasi-free no IA among themselves) 6

7 The Quark Parton Model in Infinite Momentum Frame scattering from point-like parton (quark or gluon) within the proton e p e 3 p p 1 p after IA: q W, p 4 Infinite momenton frame : neglect proton mass, electron mass and any transverse momentum to the direction of the proton. before IA: p Q = ξ p ξ: frac. of proton momentum carried by parton p Q = ξ p + q p Q = ξ p + q + ξp q = m Q = 0 ξ = = m Q = 0 q p q = x Bjorken x can be identified as the fraction of the proton momentum carried by the quark, participating in the scatter process (in the frame where the proton has very high energy) 7

8 Elastic Scattering at point-like spin ½ target at rest Dirac cross-section: (point-like S=1/ particle, recoil, helicity term and spin-spin IA taken into account) In proton rest frame: dσ dω quark,x = α e i 4E 1 sin 4 ϴ/ E 3 E 1 (cos ϴ/ + Q M Q sin ϴ/) e i : quark charge in units of e p Q = x p p Q = x p = x M = M Q LI: dσ dq quark,x = 4πα e i 1 y + y Q 4 This is expression for the differential cross-section for elastic scattering from a parton with s=1/ carrying a fraction x of the proton momentum. Next: Need to account for quark momentum distribution within the proton: q p (x), parton momentum density (p in index is for parton of proton) 8

9 Expected Parton Distribution Function q p (x) q p (x) q p (x) / /3 single Dirac proton three static quarks three interacting quarks q p (x) sea valence three interacting quarks and additional sea quarks and energy carried by the gluons (50%) 0 1 1/3 valence quarks sea quarks + higher order q p (x) all quarks in proton q p v(x) valence quarks q p u(x) u quarks. 9

10 Bjorken Scaling Hypothesis dσ dq quark = dσ dq quark,x q i (x) dx = 4πα 1 y + y Q 4 e i q p i x dx sum over all quark species d ς dxdq proton = 4πα y 1 y + Q4 i e i q p i(x) Compare with electron proton cross-section in terms of structure functions: d ς dxdq proton = 4πα Q 4 1 y F (x, Q ) x + y F 1 (x, Q ) F (x,q ) = x F 1 (x,q ) = x i e i q p i(x) Bjorken scaling hypothesis: If the proton consists of point-like partons, structure functions for fixed x do not depend on Q. Structure functions are related to underlying momentum distribution! Callen-Cross relation: If the spin of the partons s=1/ than F (x) = x F 1 (x). 10

11 SLAC/MIT Experiment 11

12 SLAC/MIT Experiment (197) if scattering is caused by point-like constituents (partons) structure functions for fixed x must be independent of Q scale invariance scaline experimental observation: F 1 (x,q ) F 1 (x) Proton consists out of point-like partons! F (x,q ) F (x) 1

13 Gallan-Cross-Relation Quarks have Spin=1/! 13

14 The Nobel Prize in Physics 1990 for their pioneering investigation concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics 14

15 Quark Composition of the Proton/Neutron u u d q q valence quarks sea quarks u x u x dx = d x d x dx = 1 q s x q s x dx = 0 Quark composition of proton (heavy quarks in sea are strongly suppressed) u v (x) + d v (x) + u s x + u s x + d s x + d s x + (s s x + s s (x) ) u(x) = u v (x) + u s (x) d(x) = d v (x) + d s (x) Structure function of proton p = uud>: F ep (x) x = e i q i p i = 4 9 u p x + u p x d p x + d p x (sp x + s p (x)) Structure function of neutron n= udd>: F en (x) x = e i q i n i = 4 9 u n x + u n x d n x + d n x (sn x + s n (x)) 15

16 Quark Composition of Proton Isospin symmetry (of strong IA): symmetry under exchange of u d quarks Symmetry of proton and neutron: uud > udd > u x u p x = d n (x) u x u p x = d n (x) d x d p x = u n (x) d x d p x = u n (x) s x s p x = s n (x) s x s p x = s n (x) isospin symmetry F en (x) x = e i q i n i = 4 9 u n x + u n x d n x + d n x s n x + s n x = 4 9 d x + d x u x + u x s x + s x 1 0 F ep x dx = x 4 9 u x + u x d x + d x s x + s (x) dx 4 9 f u f d 1 0 F en x dx 4 9 f d f u 16

17 Quark Compostion of Proton F ep x dx F en x dx 4 9 f u f d 4 9 f d f u Experimental values: 4 9 f u f d f d f u 0.1 area: f u = 0.36 f d = % of proton momentum carried by u quarks 18% of proton momentum carried by d quarks Only about half of the momentum is carried by quarks! The rest is carried by gluons! 17

18 Electron-Nucleon Scattering F ep (x) x[ 4 9 u x + u x u x + u x ] F en x x[ 4 9 d x + d (x) u x + u x ] Scattering at an iso-scalar target N: #p = #n (e.g. C, Ca) F N x = 1 F ep x + F en x = 5 18 x u x + u x + d x + d x total momentum carried by quarks (neglecting heavier quarks) 1 Naively one would expect x u x + u x + d x + d x = 1 0 (if all momentum is carried by quarks) one finds however in experiments: F N x = F N x = 1 0 Only about half of the momentum is carried by quarks! The rest is carried by gluons! 18

19 Valence and Sea Quarks u v x dx = u x u x dx = d v x dx = d x d x dx = 1 q s x q s x dx = 0 No apriori expectation for the total number of sea quarks in the proton! Sea quarks arise from gluon quark/anti-quark pair production and with m u m d it is reasonable to expect: u s (x) = d s (x) = u s x = d s x = S(x) F ep (x) = x [ 4 9 u x + u x d x + d x ] = x [ 4 9 u v x d v x S x ] F en (x)= x [ 4 9 d v x u v x S x ] F en (x) F ep (x) = 4d v x + u v x + 10 S(x) 4u v x + d v x + 10S(x) 19

20 F en (x) F ep (x) = 4d v x + u v x + 10S(x) 4u v x + d v x + 10S(x) Valence and Sea Quarks Sea quarks come from g qq processes. Due to 1/q dependence of propagator way more likely to produce low energy gluons. Expect sea quarks to dominate at low energies. F en (x) F ep (x) 1 for x 0 Confirmed by experiment! At high x expect the sea contributions to be small F en (x) 4d x :u (x) v v F ep (x) 4u v x :d v (x) for x 1 Note: u v =d v would give ratio /3 for x 1 however experimentally observed: F en (x) 1 F ep (x) 4 for x 1 d v (x)/u v (x) 0 for x 1 d and u valence quark distributions have not the same shape! 0

21 Parton Distribution Functions of Proton Ultimatively functions obtained from fit to all data! d valence quarks have in average lower momentum than u valence quarks d quarks have in average higher momenta than u aboundance of heavier sea quarks are highly suppressed Sea quarks have lower momenta than valence Quarks. Gluons dominate at low Momenta. How to access sea quark distributions? How to access gluon distributions? 1

22 Neutrino-Nucleon scattering ν μ - ν μ + W u d ν μ - W d u ν μ + test u + d in anti-neutrino-nukleon scattering test d + u in neutrino-nukleon scattering u W d d W u different mixtures of valence and sea quarks are tested compared to ep or en scattering access to sea quarks!

23 Neutrino-Nucleon scattering x ν p 1 In CMS: p 1 = (E,0,0,E) p = (E,0,0,-E) p 3 = (E,E sinθ, 0, E cosθ) p 4 = (E, -E sinθ, 0, -E cosθ) z p 3 θ μ ; p d all masses << E, high relativistic approximation helicity = chirality Note for charged weak IA (W exchange) only left handed particles (right handed antiparticles) contribute! p 4 u helicity eigenstates: neutrion: u h=-1 (p 1 ) = E(0,1,0,-1) muon: u h=-1 (p 3 ) = E(-sinϴ/,cosϴ/,sinϴ/,-cosϴ/) d-quark: u h=-1 (p 1 ) = E(-1,0,1,0) u-quark: u h=-1 (p 1 ) = E(-cosϴ/,-sinϴ/,cosϴ/,sinϴ/) coupling and propagator for CC IA M fi = g w q :m W u h = 1 p 3 γ ξ u h = 1(p 1 ) g ξρ u h = 1 p 4 γ ρ u h = 1(p ) ν/μ current quark current 3

24 Neutrino-Nucleon scattering u h=-1 (p 3 ) γ ξ u h=-1 (p1) = E(cosϴ/,sinϴ/, -i sinθ/, cosθ/) u h=-1 (p 4 ) γ ρ u h=-1 (p) = E(cosϴ/,-sinϴ/, -i sinθ/, -cosθ/) M fi = 4g W E m W no angular dependence! ν p 1 μ ; p d S=0 before and after collision no preferred polar angle! p 4 u < M fi > = ½ 4g E W m W Neutrinos have always left handed helicity, however half of the quarks are right handed half are left handed Cross-section in CMS: dσ = 1 dω < M 64π s fi > = G F 4π s ς νq = G F 4π dω = G F π G F = g W 8m W 4

25 Anti-Neutrino-Nucleon scattering In CMS: p 1 = (E,0,0,E) p = (E,0,0,-E) p 3 = (E,E sinθ, 0, E cosθ) p 4 = (E, -E sinθ, 0, -E cosθ) all masses << E, high relativistic approximation helicity = chirality ν p 1 p 4 d S=1 in initial and final state! μ : p u helicity eigenstates: anti-neutrion: v h=+1 (p 1 ) = E(0,-1,0,1) anti-muon: v h=+1 (p 3 ) = E(sinϴ/,-cosϴ/,-sinϴ/,cosϴ/) d-quark: u h=-1 (p 1 ) = E(-1,0,1,0) u-quark: u h=-1 (p 1 ) = E(-cosϴ/,-sinϴ/,cosϴ/,sinϴ/) dσν q dω = G F 1 + cosθ s 16π 1 + cosθ dω = 16π 3 σ ν q = G F 3π 5

26 Summary of (Anti-)Neutrino-Nucleon Scattering Differential cross sections still given in CMS system, transform in LI notation... 6

27 CDHS Experiment at CERN ( ) CERN-Dortmund-Heidelberg-Saclay-Experiment 7

28 Neutrino-Nukleon scattering 8

29 Differential Cross-Section for ν-nucleon Scattering dς dy 9

30 Neutrino-Nucleon Scattering dσ νp dy = dσνq dy + dσνq dy = G sx F π d x + 1 y u x dx Compare to notation with structure functions d σ νp dxdy = G F s π [ (1-y) F νp (x) + y xf 1 νp (x) + y(1-y/)x F 3 νp (x) ] F 3 is special for weak IA, parity violating term. constant term: xd(x) + u x = F νp (x) term linear in y: -4xu(x) = F νp (x) + F νp 3 (x) term quadratic in y: xu(x) = xf νp 1 (x) - x F νp 3 (x) Similar for νn scattering: 30

31 Neutrino-Fe Scattering 31

32 Summary Inelastic Scattering of e-p established the Quark-Parton Model: The proton is made of point-like particle: valence quarks + low momentum sea quarks. (Bjorken-Scaling-Hypothesis (structur functions depend on one parameter only) was verified in data) Quarks are spin=1/ particles Structure functions can be associated to Quark momentum distributions Quarks carry 50% of the proton momentum, (the rest is carried by gluons) Exploiting en, ep, en and eν give a handle to measure the momentum distributions of valence and sea quarks in the proton 3

33 HERA accelerator complex at DESY/Hamburg stopped data taking in 006, experiments: ZEUS, H1 + HeraB (fix target B physics experiment) 33

34 H1 and ZEUS Experiment 34

35 Example of H1 Event 35

36 Example of ZEUS Event 36

37 (p 1 +p ) p 1 p Q = sxy Accessing the Low x Region energy loss of incoming particle Bjorken x Lab frame proton at rest LI form ν = E 1 -E 3 ν = qp /M x = ;q Mν x = Q qp fraction energy loss of incoming particle y = (E 1 -E 3 )/E 1 y = qp /p 1 p y max = 1 HERA: s 10 5 GeV Q = sxy y max = 1 for fixed target exp: s < 10 3 GeV HERA: x s p e p p 4E e E p 37

38 Scaling Violation F ep (x) low x values medium x values high x values Q Scaling violation can be explained by QCD evaluation! (see next lecture) 38