PHYS 6610: Graduate Nuclear and Particle Physics I

H. W. Grießhammer INS Institute for Nuclear Studies The George Washington University Institute for Nuclear Studies Spring 2021

II. Phenomena 4. Deep Inelastic Scattering and Partons

Or: Fundamental Constituents at Last

References: [HM 9; PRSZR 7.2, 8.1/4-5; HG 6.8-10]

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.0 (a) Inelastic Scattering → Deep Inelastic Scattering DIS

0 0 Breit/Brick-Wall Frame: no energy transfer E −E = 0; momentum transfer maximal~pBreit = −~pBreit. 1 3 Probe wave length λBreit ∼ p =⇒ Dissipate energy and momentum into small volume λBreit. Q2

2 2 −2 −2 Now Q & (3.5GeV) ∼ (0.07fm) rN : λ Energy cannot dissipate into whole N in ∆t ∼ c [Tho] =⇒ Shoot hole into N, breakup dominates.

Deep Inelastic Scattering DIS N(e±,e0)X: inclusive, i.e. all outgoing summed.

 p · q 0 Now characterised by Lorentz-Invariant: ν = = E − E > 0 energy transfer in lab M lab lab  2 independent variables 2 02 2 2 2 2  Invariant mass-squared W = p = M + 2p · q + q = M + q (1 − x) out of (θ,q2 = −Q2,   −q2 = Q2 ⇑ E0 ,ν,W,x) Bjørken-x = ∈ [0;1]: inelasticity (elastic scattering: x = 1) lab 2p · q = 2Mν

2 Dimension-less structure functions F1,2(x,Q ) parametrise most general elmag. hadron ME.

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.1 (b) Experimental Evidence

E,Q2 %: Resonances broaden & disappear into continuum for W ≥ 2.5 GeV total depends only weakly on Q2 at ﬁxed W M =⇒ elastic on point constituents. Mott (elastic point)

[HG 6.18] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.2 2 Structure Functions F1,2 are Q -Independent at Fixed Bjørken-x

2 2 2 2 d σ 2α 02 2 θ F2(Q ,x) 2F1(Q ,x) 2 θ (I.7.6) 0 = 2 E cos + tan dΩ dE lab Q 2 ν M 2 Q2 F dimensionless, Q2,ν → ∞ but x = ﬁxed: F cannot dep. on Q2, only on dimensionless x. 1,2 2Mν 1,2

SLAC data proton 2 GeV2 < Q2 < 30 GeV2 world data proton, x = 0.225

[HG 6.20] Data: no new scale (e.g. mass, constituent radius)! back-scattering events =⇒ F 6= 0: fermions. 1 [Tho 8.11] 1 =⇒ Interpretation: Virtual photon absorbed by charged, massless spin- 2 point-constituents: PARTONS. Idea: Bjørken 1967; name: Feynman 1969; soon identiﬁed with Gell-Mann’s “quarks” of isospin.

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.3 (c) Sequence of Events in the Parton Model [HM 9, PRSZ]

Scaling: independence of Q2 at ﬁxed x. Not a sign ofQCD, but only that no new scale in nucleon: point-constituents. Scale-Breaking as sign of “small” interactions between constituents → QCD’s DGLAP-WW (Part III)

1 =⇒ DIS is elastic scattering onP ARTONS: charged, m ≈ 0 spin- 2 point-constituents.

Problem: Partons not in detector −→Conﬁnement hypothesis (later). =⇒ Assume that collision proceeds in two well-separated stages:

(1) Parton Scattering: Timescale in Breit frame: struck parton partons ∆x 1 fm γ t ≈ ≈ λ ≈ 0.05 for Q2 (4GeV)2. rearrange parton c Q c into =⇒ Photon interacts with one parton near-instantaneously, hadrons takes snapshot of parton conﬁguration, frozen in time. partons in nucleon spectator partons (2) Hadronisation: ﬁnal-state interactions rearrange partons into hadron fragments, covert collision energy into new particles (inelastic!). 1 fm Much larger timescale thadronisation ≈ ≈ 0.2 tparton. typ. hadron mass∼ 1GeV c

=⇒ Describe Scattering and Hadronisation independently of each other, no interference.

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.4 (d) Relating Elastic Parton Scattering & Nucleon DIS

What is the Bjørken-x? – The Inﬁnite Momentum Frame

⊥ µ Problem: Transverse momenta~pq of partons sum to zero, but cannot simply infer them from p ! parton momentum parton momentum 2 Solution: Use W,Q → ∞ to boost qµ along N-momentum axis~p N momentum N momentum Lorentz boost into Inﬁnite Momentum Frame IMF. against q µ

k boost k ⊥ Transverse parton momenta unchanged, but longitudinal now pq −→ γ pq M,|~pq |. ⊥ =⇒ Transverse motion time-dilated: Hadronisation indeed much slower: rearranging by~pq → 0.

IMF is also a Breit/Brick-wall frame: =⇒ Parton carries momentum fraction 0 ≤ ξ ≤ 1 of total nucleon momentum.

! Assume Elastic Scattering on Parton: (ξ p)2 = (ξ p + q)2 =⇒ 2ξ p · q + q2 = 0; (ξ p)2 cancels.

−q2 Q2 Bjørken-x = fraction of hadron momentum which is carried by =⇒ ξ = = = x: b 2p · q 2M ν parton struck by photon in Inﬁnite Momentum Frame IMF.

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.5 No, Not That IMF – And Not That IMF Either

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.6 2 1 2 2 Q 2 d σ(Q ,x = p·q ) Z d σ(ξp) Sum cross sections, =⇒ 2 = dξ q(ξ) 0 ∑ 0 elastic dΩ dE all partons q dΩ dE no QM interference. inel 0 on parton 2 2 2 Q p→ξp Q Q p→ξp with δ[1 − ] −→ δ[1 − ] = ξδ [ξ − ] and M2 ≡ p2 −→ (ξp)2 = ξ 2M2 2p · q 2ξp · q 2p · q | {z } = δ(ξ − x): parton momentum must match exp. kinematics 1 2 2 2 Z 2 d σ(Q ,x) 2α 2 θ 02 2 ξ ξ Q 2 θ 0 = 2 cos E dξ ∑ Zq q(ξ) + 2 2 tan δ(ξ − x) dΩ dE inel Q 2 all partons q ν ξ 2M ν 2 0 | {z } = x/M slaughter δ distribution 2 2 2 d σ(Q ,x) 2α 2 θ 02 2 x 1 2 θ 0 = 2 cos E × ∑ Zq q(x) + tan dΩ dE inel Q 2 all partons q ν M 2

Compare Elastic and Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons.

=⇒ Relate Inelastic to Elastic Cross Section eµ → eµ on Point-Fermion in lab frame:

2 ! 0 2 dσ Zα 2 θ E Q 2 θ 0 E elastic (I.7.4): = cos 1 + tan with E = dΩ 2 θ 2 E 2M2 2 E el 2E sin 2 1 + M (1 − cosθ)

θ use −Q2 ≡ q2 = (k − k0)2 = −2k · k0 = −2EE0(1 − cosθ) = −4EE0 sin2 m → 0! 2 e 2 0 2 0 2 d σ 2Zα E 2 θ E Q 2 θ 0 E =⇒ = cos 1 + tan δ[E − ] E0 Q2 E M2 E dΩ d el 2 2 2 1 + M (1 − cosθ)

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.7 2 1 2 2 Q 2 d σ(Q ,x = p·q ) Z d σ(ξp) Sum cross sections, =⇒ 2 = dξ q(ξ) 0 ∑ 0 elastic dΩ dE all partons q dΩ dE no QM interference. inel 0 on parton 2 2 2 Q p→ξp Q Q p→ξp with δ[1 − ] −→ δ[1 − ] = ξδ [ξ − ] and M2 ≡ p2 −→ (ξp)2 = ξ 2M2 2p · q 2ξp · q 2p · q | {z } = δ(ξ − x): parton momentum must match exp. kinematics 1 2 2 2 Z 2 d σ(Q ,x) 2α 2 θ 02 2 ξ ξ Q 2 θ 0 = 2 cos E dξ ∑ Zq q(ξ) + 2 2 tan δ(ξ − x) dΩ dE inel Q 2 all partons q ν ξ 2M ν 2 0 | {z } = x/M slaughter δ distribution 2 2 2 d σ(Q ,x) 2α 2 θ 02 2 x 1 2 θ 0 = 2 cos E × ∑ Zq q(x) + tan dΩ dE inel Q 2 all partons q ν M 2

Compare Elastic and Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons.

=⇒ Relate Inelastic to Elastic Cross Section eµ → eµ on Point-Fermion in lab frame:

2 0 2 0 2 d σ 2Zα E 2 θ E Q 2 θ 0 E elastic (I.7.4): = cos 1 + tan δ[E − ] E0 Q2 E M2 E dΩ d el 2 2 2 1 + M (1 − cosθ) E0 E E0 E EE0 use δ[E0 − ] = 1 + (1 − cosθ) δ[E0 − E + (1 − cosθ)] E 1 + E (1 − cosθ) E M M M | {z } | {z } | {z } 2 = 1 by δ -distribution = −ν = Q /(2M)

Q2 1 Q2 1 Q2 1 = δ[ν − ] = δ[1 − ] = δ[1 − ] = δ[1 − x] 2M ν 2Mν ν 2p · q ν as expected for elastic scattering X 2 2 2 2 d σ 2α 2 θ 02 2 1 Q 2 θ Q =⇒ 0 = 2 cos E Z + 2 tan δ[1 − ] dΩ dE el Q 2 ν 2M ν 2 2p · q 2 2 2 2 d σ 2α 2 θ 02 F2(Q ,x) 2 F1(Q ,x) 2 θ inelastic (I.7.6): = cos E + tan d dE0 Q2 2 M 2 = x Ω inel ν z }| { Q2 =⇒ F of elastic on 1 point-fermion with momentum p only dep. on x: F (Q2,x) = Z2 δ[1− ] 2 2 2p · q

Compare Elastic and Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons,

each with charge Zq and weighted by its Parton Distribution Function PDF q(ξ): probability that scattered parton carries momentum fraction [ξ;ξ + dξ] (in IMF).

2 2 2 2 d σ 2α 2 θ 02 2 1 Q 2 θ Q elastic (I.7.4): 0 = 2 cos E Z + 2 tan δ[1 − ] dΩ dE el Q 2 ν 2M ν 2 2p · q

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.7 1 2 2 2 Z 2 d σ(Q ,x) 2α 2 θ 02 2 ξ ξ Q 2 θ 0 = 2 cos E dξ ∑ Zq q(ξ) + 2 2 tan δ(ξ − x) dΩ dE inel Q 2 all partons q ν ξ 2M ν 2 0 | {z } = x/M slaughter δ distribution 2 2 2 d σ(Q ,x) 2α 2 θ 02 2 x 1 2 θ 0 = 2 cos E × ∑ Zq q(x) + tan dΩ dE inel Q 2 all partons q ν M 2

Compare Elastic and Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons,

each with charge Zq and weighted by its Parton Distribution Function PDF q(ξ): probability that scattered parton carries momentum fraction [ξ;ξ + dξ] (in IMF).

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.7 Compare Elastic and Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons,

each with charge Zq and weighted by its Parton Distribution Function PDF q(ξ): probability that scattered parton carries momentum fraction [ξ;ξ + dξ] (in IMF).

2 2 2 2 d σ 2α 2 θ 02 2 1 Q 2 θ Q elastic (I.7.4): 0 = 2 cos E Z + 2 tan δ[1 − ] dΩ dE el Q 2 ν 2M ν 2 2p · q 2 1 2 2 Q 2 d σ(Q ,x = p·q ) Z d σ(ξp) Sum cross sections, =⇒ 2 = dξ q(ξ) 0 ∑ 0 elastic dΩ dE all partons q dΩ dE no QM interference. inel 0 on parton 2 2 2 Q p→ξp Q Q p→ξp with δ[1 − ] −→ δ[1 − ] = ξδ [ξ − ] and M2 ≡ p2 −→ (ξp)2 = ξ 2M2 2p · q 2ξp · q 2p · q | {z } = δ(ξ − x): parton momentum must match exp. kinematics 1 2 2 2 Z 2 d σ(Q ,x) 2α 2 θ 02 2 ξ ξ Q 2 θ 0 = 2 cos E dξ ∑ Zq q(ξ) + 2 2 tan δ(ξ − x) dΩ dE inel Q 2 all partons q ν ξ 2M ν 2 0 | {z } = x/M slaughter δ distribution 2 2 2 d σ(Q ,x) 2α 2 θ 02 2 x 1 2 θ 0 = 2 cos E × ∑ Zq q(x) + tan dΩ dE inel Q 2 all partons q ν M 2

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.7 Structure Functions F2 and F1 and Callan-Gross Relation

Idea: DIS = incoherent superposition of elastic scattering in IMF on individual partons,

each with charge Zq and weighted by its Parton Distribution Function PDF q(ξ): probability that scattered parton carries momentum fraction [ξ;ξ + dξ] (in IMF).

2 2 2 d σ(Q ,x) 2α 2 θ 02 2 x 1 2 θ =⇒ 0 = 2 cos E ∑ Zq q(x) + tan dΩ dE inel Q 2 all partons q ν M 2

2 2 2 2 d σ 2α 2 θ 02 F2(Q ,x) 2 F1(Q ,x) 2 θ compare to 0 = 2 cos E + tan dΩ dE inel Q 2 ν M 2

2 2 2 1 2 =⇒ F2(Q ,x) = ∑ Zq x q(x) and F1(Q ,x) = ∑ 2 Zq q(x) all partons q all partons q

with F2(x) = 2x F1(x) Callan-Gross Relation All Q2-independent and just result of incoherent scattering on point-fermions.

Each parton q has its own charge Zq and Parton Distribution Function q(x): Zu,u(x); Zd,d(x);. . . Aside: Resist temptation to interpret (ξp)2 = ξ 2M2 as parton mass: depends on x, i.e. on kinematics!

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.8 Callan-Gross: Evidence for Point-Fermions in Nucleon

Expect for DIS (Q2,W2 → ∞, x ﬁxed ﬁnite):

Callan-Gross Relation 2x F1(x) = F2(x) 2 with F2(x) = x∑Zq q(x) q just from scattering on point-fermions.

Experimentally veriﬁed; corrections fromQCD.

[Tho 8.4]

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.9 (e) Constituents of the Nucleon in the Parton Model

Quarks probability distrib. u(x),d(x),s(x),... of quark ﬂavour with momentum fraction x (in IMF).

Antiquarks with PDFs u¯(x),... only via vacuum ﬂuctuations: virtual qq¯ pairs.

Neutral Partons gluon PDF g(x) carries momentum, spin, angular momentum,. . .

=⇒ Valence Quarks qv(x) := q(x) − q¯(x) cannot disappear. =⇒ Follow initial quarks to detector.

Valence quarks carry some (not all) nucleon properties: baryon number, charge. (still: these are not the constituent quarks!) 1 1 1 Z Z ( Z ( N N N 2 in proton (uud) N 1 in p (uud) norm: dx u (x) − u¯ (x) = dx uv (x) = ; dx dv (x) = 1 in neutron (ddu) 2 in n (ddu) 0 0 0 =⇒ Sea Quarks q¯s(x) = q¯(x), qs(x) = q(x) − qv(x): All that is not valence. 1 1 Z Z sea created in qq¯ pairs =⇒ qs(x) 6= q¯s(x), but norm: dx [qs(x) − q¯s(x)] = 0 = dx sea(x) 0 0 1 N 2 N 4 N N 1 N ¯N N N =⇒ F2 (x) = ∑Zq q (x) = u (x) + u¯ (x) + d (x) + d (x) + s (x) + s¯ (x) + ··· + 0g(x) x q 9 9 4 1 4 1 = uN(x) + dN(x)+ uN(x) + u¯N(x) + dN(x) + d¯N(x) + sN(x) + s¯N(x) + ... 9 v 9 v 9 s s 9 s s s s | {z } | {z } valence contribution sea contribution sea(x)

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.10 One cannot get the number of valence quarks from any peak position. Books like [HM ﬁg. 9.7, Per 5.8, Tho ﬁg. 8.9] are WRONG!!

What PDFs to Expect – QUALITATIVELY!

quark-distribution momentum-distribution xq(x) q(x) (not usually quoted) x q(x) (usually quoted)

3 partons each carries 1/3 of nucleon only constituents: q(x)= δ (1/3−x) momentum 3 non-interacting valence quarks valence valence

1/3 1 x 1/3 1 x

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.11 One cannot get the number of valence quarks from any peak position. Books like [HM ﬁg. 9.7, Per 5.8, Tho ﬁg. 8.9] are WRONG!!

What PDFs to Expect – QUALITATIVELY!

quark-distribution momentum-distribution xq(x) q(x) (not usually quoted) x q(x) (usually quoted)

etc. width set by Fermi Add instantaneous momentum of partons in nucleon interactions: valence valence distribute momentum & energy

1/3 1 x 1/3 1 x Fermi motion broadens peak

Maximum of momentum distribution xmax shifted to right: d dq(x ) [x q(x )] = q(x ) + x max = q(x ) > 0 dx max max max max dx max | {z } But all momentum 1 = 0 Z still carried by Momentum integral still ∑ dx xq(x) = 1. q valence quarks. 0

What PDFs to Expect – QUALITATIVELY!

quark-distribution momentum-distribution xq(x) q(x) (not usually quoted) x q(x) (usually quoted) ~1/5 in exp shift to left amount depends on interaction etc. can be smaller or larger than before Add any interactions: valence valence distribute momentum & energy to partons without charge (gluons) 1/3 1 x 1/3 1 x All maxima shifted to left – how much depends on interactions. 1 Z Momentum carried R Still q(x)=1(2) but momentum int. now smaller: ∑ dx xq(x)< 1. by valence quarks q 0 decreases.

What PDFs to Expect – QUALITATIVELY!

Strike valence: quark-distribution momentum-distribution xq(x) (not usually quoted) (usually quoted) q(x) x q(x) ~1/5 in exp depends on depends on interaction interaction etc. total total Strike sea: valence valence

etc. sea ~ 1/x from bremsstrahlung sea Add qq¯ sea: x x Take momentum away 1/3 1 1/3 1 Maxima again shifted to left – how much depends on interactions. again from valence and 1 couple to photon. Expect bremsstrahlung-like spectrum ∼ for sea, adds to valence. x =⇒ most likely for =⇒ For x → 0: q(x) diverges, but mom. distribution xq(x) nonzero. small x =ˆ small ξp Small-x region particularly interesting to probe Momentum integral =⇒ interactions with and between neutral constituents (glue). even smaller.

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.11 What PDFs to Expect – QUALITATIVELY!

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.11 (f) What DIS Tells Us About Nucleon Structure: xq(x)

[Tho 8.17] [Mar 5.18] 1 max. at 0.2, not 3 !

– Valence quarks dominate as x & 0.5 – Sea dominates for x → 0: bremsstrahlung 1 – Peaks of F2 and q(x) not at 3 but 0.17 & 0.2. =⇒ Interactions in nucleon, neutral constituents.

1 Z Sum Rules: e.g. momentum: dx x[g(x) + ∑q(x)] = 1 [PDG 2012 18.4: logarithmic scale!] q 0 observable valence sea gluons other total nucleon momentum 31% 17% 52% —— 100% nucleon spin [30...50]% ∼ 0%? lots% orbital ang mom. 100% (fake) “spin crisis”

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.12 How To Dis-Entangle Parton Distributions

(1) By target: p vs. n (deuteron), 3H etc. =⇒ PDFs inside proton vs. neutron etc.

(2) By helicity: polarised beam & ejectile:~eN →~eX via virt. γ selects parton helicity/spin

e e

[PRSZR] (3) By neutrinos: νN → e−X, ν¯ N → e+X, νN → νX, ν¯ N → νX: already 100% polarised helicity weak int. =⇒ different linear combinations of q(x) and q¯(x), selects quark ﬂavour & helicity Trick: use “invisible” neutrino beam, detect muons (no neutrals!)

[PRSZR]

(4) By “Drell-Yan process”: use strong interactions in NN → X =⇒ can now see glue g(x) directly, and q(x),q¯(x). Gluon PDFs: integrals from sum rules, Z Z e.g. momentum dx xg(x) = 1 − ∑ dx xq(x). q PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.13 Isospin: Proton uud vs. Neutron ddu =⇒ up(x) =? dn(x), dp(x) =? un(x)

n n =⇒ u(x) := up(x) = dn(x) F2 sea Low x: sea dominates, isospin-symmetric =⇒ p ≈ p → 1 Xexp. p n F2 sea d(x) := d (x) = u (x) n F 4dv + uv 1 Fn(x) 4d + u + sean High x: valence dominates; data: =⇒ 2 ≈ → in exp. 2 v v Fp 4u + d 4 p = p 2 v v F (x) dv + 4uv + sea 2 explained if uv carries more momentum than dv ↔p=(uud) (not Coulomb!)

[HM]

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.14 1 1 Another Sum Rule: [Fp(x) − Fn(x)] = [u − d ] + [seap − sean] x 2 2 3 v v Sea on average not quite isospin-symmetric (except at very low x). 1 1 Z dx p 1 Z Gottfried Sum Rule [F (x) − Fn(x)] = + dx [seap − sean] x 2 2 3 0 0

Next Muon Collab. (CERN) at Q2 = (2GeV)2:

GΣR = [0.228 ± 0.007] 1 Z =⇒ dx [d¯ − u¯] ≈ 0.16 0 (assumes s ≈ s¯ ≈ 0)

=⇒ Light sea on average not ﬂavour-symmetric: u¯ < d¯!

→ Meson Cloud Model. . .

[HM]

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.15 EMC collaboration 1983 (g) PDFs in Nuclei: The EMC Effect [PRSZR 8.5]

Regions where sea dominates: Regions where valence dominates: A A x . 0.06: F2 signiﬁcantly smaller than free 0.3 . x . 0.8: F2 slightly smaller than free; A minimum at x ≈ 0.65 0.06 . x . 0.3: F2 slightly larger than free =⇒ avg. momentum of bound partons smaller; Effects increase with A. invest momentum in binding (gluons)? A x & 0.8: F2 % 1: individual N x > 1 possible: suck momentum from other N.

No Established Explanation Yet:

“shadowing” Multi-quark cluster? “anti-shadowing” qq-int. across nucleon boundaries? 1 “EMC Effect”% x → 0: resolution bad =⇒ & xp “Overcrowding”: nucleons Effects increase with A. in nucleus share sea?

“Nuclear Shadowing”: low-x photons

[PRSZ, 6th ed.] react with surface by virtual mesons?

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.16 (h) Generalising Parton Distributions

2 PDFs: ~pparton = x~p, transverse parton momentum negligible =⇒ q(x,Q ) → Extension: add impact bq ↔~pq⊥, q-& N-spin orientations, mom. transfer,. . . =⇒ Most general parametrisation: over 20 functions, each with more than 5 parameters:

Wigner Distributions, including Transverse Momentum Distributions TMDs and Generalised Parton Distributions GPDs: fun for years to come. . .

Challenging; co-motivation for Jlab ugrade: many parameters, many functions, small effects.

[Ji seminar 2014] PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.17 Example Transverse Momentum Distributions TMDs

Add impact parameter bq ↔~pq⊥ transverse quark momentum. Interpretation: snapshot of quark distribution q(x,b,Q2) in nucleon perpendicular to~p. [Burkhardt 04]

“Nucleon Tomography”

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.18 Next: 5. Quarks in e+e− Annihilation

Familiarise yourself with: [PRSZR 9.1/3; PRSZR 15/16 (cursorily); HG 10.9, 15.1-7; HM 11.1-3; Tho 9.6]

PHYS 6610: Graduate Nuclear and Particle Physics I, Spring 2021 H. W. Grießhammer, INS, George Washington University II.4.19 Alt: Compare Elastic/Inelastic Cross Sections more careful: [HM ex. 9.3ff; CL]