Introduction to Quantum ChromoDynamics and the parton model

Transcription

1 Introduction to Quantum ChromoDynamics and the parton model Pavel Nadolsky Southern Methodist University Dallas, TX, USA TMD Collaboration Summer School June 22, 2017

2 Objectives of the lectures Review core principles of hadronic theory in high-energy scattering Present a survival kit for this school: basic ideas, simple processes, and easy calculations in order to help you understand more detailed material in other lectures Focus on the simplest case of collinear factorization for unpolarized cross sections 2

3 QCD is a vast subject to cover Lectures given at CTEQ summer schools since 1991 ( introduce to many aspects of QCD. I am indebted to lectures by George Sterman and Wu-Ki Tung. I will show their classical slides on the subject P. Nadolsky, TMD school 3

4 References and assignment CTEQ summer school lectures each lecturer covers the subject of QCD from a complementary viewpoint! To prepare for our afternoon discussions, please read I will cover this material only selectively. Please read and ask questions. Many textbooks and reviews on quantum field theory and QCD G. Sterman, An Introduction to Quantum Field Theory; also his TASI lectures, hep-ph/ J. C. Collins, Foundations of perturbative QCD Handbook on Perturbative QCD J. Campbell, J. Huston, W. J. Stirling, hep-ph/

5 Outline 1. The parton model for high-energy scattering 2. Asymptotic freedom and confinement Infrared safety Factorization 3. Applications to three instructive processes i. e + e hadroproduction ii. (semi-)inclusive deep inelastic scattering, or (SI) DIS iii. vector boson production /Drell-Yan process 4. Unpolarized collinear parton distribution functions (PDFs) future of the TMD analysis 5

6 Now I have questions for you From time to time, I will ask questions to check if you are following me. Just answer what you can. Please raise your hand if you are an undergraduate student a graduate student a postdoc you have studied quantum field theory you took other specialized courses in particle physics 6

7 What s in the title? A 1-minute poll for everyone Can you define in 1-2 sentences: 1. What is quantum chromodynamics (QCD)? 2. What is the parton model? Are they the same? Choose: 3: If you can define both 4: If you can define neither 7

8 Parton model vs. QCD: definitions The parton model is an order-of-magnitude model describing scattering on a highly boosted composite quantum particle (parent, or target) in terms of scatterings on the particle s constituents (partons). The parton model invokes only most fundamental QFT properties, such as Lorentz invariance and weakness of short-distance parton interactions. To accurately predict scattering rates, a more fundamental theory is needed. QCD, the fundamental SU 3 c gauge theory of the Standard Model Lagrangian, is such quantitative fundamental theory. Nucleon quarks 8

9 The inner world of a hadron Atom Nucleus Nucleon Quarks & gluons The structure of the hadron drastically changes as the resolution of the microscope (scattering process) increases 9

10 The inner world of a hadron Atom Nucleus Nucleon Quarks & gluons A short-distance probe (virtual photon, heavy boson, gluon) resolves increasingly small structures inside the nucleon. 10

11 A variety of nonperturbative functions can be introduced to describe the rich Internal structure of nucleons. Which core principles enable us to determine these functions? I will review them by starting with simple examples, such as unpolarized collinear parton distributions 11

12 Our electroweak microscopes : three instructive processes to probe the hadronic structure Involve scattering of an electroweak boson on quasi-free quarks (always perturbative) emerging from, and fragmenting into, nonperturbative hadronic states 12

13 1.e + e hadrons at LEP Hadrons View in the e + e frame Hadrons Simplest Feynman diagram q μ

14 1.e + e hadrons at LEP q μ Notations: q μ is the 4-momentum of the Z boson Q and q T are Lorentz invariants Q 2 q μ q μ is the invariant mass of Z In the e + e c.m. (lab) frame, the Z boson is at rest, initial-state EM radiation is neglected q μ lab = Q 1 t, 0 x, 0 y, 0 z 14

15 1.e + e hadrons at LEP q μ q T 2 q t μ qtμ, where q t μ is the part of q μ that is orthogonal (in the covariant sense) to the quark s and antiquark s momenta: q t μ = q μ C p q μ D p q μ q t p q = q t p q = 0 If quark masses are negligible compared to the other energy scales (0 m q 2 Q 2, s ): C = p q q p q p q ; D = p q q p q p q 15

16 1.e + e hadrons at LEP q μ When only a qq pair is produced, the quark and anti-quark momenta are exactly back-to-back in the lab frame and equal in the magnitude: p q = p q p q θ When additional radiation is emitted, p q and p q are misaligned by an angle θ. This angle in the e + e c.m. frame can be expressed as θ = q T /Q. That is, q T /Q is an indicator of the additional radiation 16 p q Recoil (extra particles)

17 2.AB VX at the Large Hadron Collider and Tevatron aka Drell-Yan process V = γ, W, Z View in the AB c.m. frame Simplest Feynman diagram φ η q T Q 0 P. Nadolsky, TMD school 17

18 2.AB VX at the Large Hadron Collider and Tevatron q μ The same Lorentz-invariant definitions apply: Q 2 = q μ q μ q T 2 q t μ qtμ, q t μ = q μ C p q μ D p q μ 18

19 2.AB VX at the Large Hadron Collider and Tevatron q μ In the lab frame (AB c.m. frame), the boson moves with 4-momentum q μ = (q 0, q T, q 3 ) q T is naturally interpreted as the transverse momentum of the vector boson in the lab frame But, an angular variable φ η q T /Q can be also constructed in DY process. It indicates additional radiation and is an analog of the non-collinearity angle θ in e + e hadroproduction 19

20 3.(SI)DIS ea ebx at Jefferson Lab, HERA, EIC, View in the γ p c.m. frame Simplest diagram: q μ θ = q T /Q 20

21 3.(SI)DIS ea ebx at Jefferson Lab, HERA, EIC, View in the γ p c.m. frame To get the Breit (brick-wall) frame: a) Boost in the γ direction to make Its momentum purely spacelike b) Flip the z axis q μ Breit = Q 0 t, 0 x, 0 y, 1 z 21

22 3.(SI)DIS ea ebx at Jefferson Lab, HERA, EIC, View in the γ p c.m. frame Now a silly question to you: Why did I draw hadrons as disks, not circles? 22

23 3.(SI)DIS ea ebx at Jefferson Lab, HERA, EIC, View in the γ p c.m. frame Answer: All rapidly moving particles are highly Lorentz-contracted. (Ultra-thin pancakes) Their longitudinal size practically does not matter. But, the interaction depends on the transverse positions of the particles (impact parameter b) 23

24 Space-time diagrams: rest frame of an event E x 0 = ct World lines of light signals (at angles π/4 and 3π/4) E x 3 = z 24

25 Space-time diagrams: rest frame of an event E Cartesian coordinates x 0 0 x 3 x 0 Absolute future World lines of light signals (at angles π/4 and 3π/4) E x 3 x 0 x 3 0 Absolute past x μ = x 0, x 1, x 2, x 3 {ct, x, y, z} x μ = x 0, x 1, x 2, x 3 {ct, x, y, z}

26 Space-time diagrams: Light-cone coordinates Light-cone coordinates provide an intuitive alternative to the Cartesian coordinates. They are especially convenient for various collider calculations. 26

27 Space-time diagrams: Light-cone coordinates x x 0 x + x 3 x μ LC = x +, x, x T { x0 + x 3, x0 x x LC,μ = x +, x, x T, x 1, x 2 }

28 World-line of a point moving with V = Vx = const x x 0 x 0 x + φ 0 x 1 The world line must be within π 4 < φ 0 < π 4 to the x0 axis 28

29 Reference frame moving with V = Vx = const x x 0 x 0 x + δ x 3 x 3 As V c, both x 0 and x 3 axes align with the x + or x axis; δ 0 29

30 Can you visualize radiation from a highly boosted object? For example, radiation of electromagnetic waves from a relativistic electron As a gauge theory, QCD is like quantum electrodynamics in many aspects Quarks are QCD-charged spin-1/2 fermions (analogs of electrons) Gluons are spin-1 bosons that carry the strong force (analogs of photons) 30

31 Here is an EM wave from a radiating point source at rest: The wave from the point source is spherical: z E r, t = E 0 cos (kr ωt) r E 0 cos (k(r x 0 )) r ωt = 2πx 0 /λ;. kr = 2πr/λ Assume no attenuation (no energy loss from the wave) Question (sketch on the paper for 1 minute): How will the wave change if the source quickly moves to the right (in the direction of the arrow?) 31

32 An EM wave of a proton moving with v = +Vz (to the right) The wave is distorted by Doppler effect z The forward wave has dependence E r, x 0, θ = 0 = E 0 cos (kx ) r (contracted wavefronts) E r, x 0, θ = π = E 0 cos (kx + ) r (extended wave fronts) 32

33 An EM wave of a proton moving with v = +Vz (to the right) Waves radiated in the past in the proton s rest frame have compressed into a small interval Δx ; the future has extended into a large Δx + z By Heisenberg principle, the boosted object in the +z direction has large Δp + and small Δp (small Δp + and large Δp for an object boosted in the z direction) This is the first indication that the the x + and x dependence of relativistic interactions can be separated (factorized) 33

34 End of module 1 34