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The partonic structure of protons and nuclei: from current facilities to the EIC Alberto Accardi Hampton U. and Jefferson Lab Frontiers in Nuclear and Hadronic Physics Galileo Galilei Institute, Florence, Italy 20-24 February 2017 Plan

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The partonic structure of protons and nuclei: from current facilities to the EIC Alberto Accardi

Hampton U. and Jefferson Lab

“Frontiers in Nuclear and Hadronic Physics” Galileo Galilei Institute, Florence, Italy 20-24 February 2017

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GGI, Feb 2017 – Lecture 1 accardi@jlab.org 2

Plan of the lectures

 PART 1: QCD factorizatjon and global PDF fjttjng

  • Lecture 1 – Hadrons, partons and Deep Inelastjc Scatuering
  • Lecture 2 – Parton model
  • Lecture 3 – The QCD factorizatjon theorem
  • Lecture 4 – Global PDF fjts

 PART 2: Parton distributjons from nucleons to nuclei

  • Lecture 5 / 6

 PART 3: The next QCD frontjer – The Electron-Ion collider

  • Lextures 7 / 8
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Plan of Part 1

 Lecture 1 – Motjvatjon – Quarks, gluons, hadrons – Deep Inelastjc Scatuering (DIS)  Lecture 2 – Parton model – DIS revisited – Collinear factorizatjon and Parton Distributjon Functjons (PDFs) – Limitatjons  Lecture 3 – The QCD factorizatjon theorem – QCD factorizatjon, universality of PDFs – DIS, Drell-Yan (DY) lepton pairs, W and Z productjon, hadronic jets  Lecture 4 – Global PDF fjts – How to make a fjt, and use its results – Fits as community service (e.g., measure PDFs, apply to LHC) – Fits as a tool to study hadron and nuclear structure

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GGI, Feb 2017 – Lecture 1 accardi@jlab.org 4

Resources

 Textbooks – Povh et al., “Partjcles and Nuclei,” Springer, 1999 – Halzen, Martjn, “Quarks and leptons,” John Wiley and sons, 1984 – Lenz et al. (Eds.), “Lectures on QCD. Applicatjons,” Springer, 1997

  • esp. lectures by Levy, Rith, Jafge

– Devenish, Cooper-Sarkar, “Deep Inelastjc Scatuering,” Oxford U.P., 2004 – Feynman, “Photon-hadron interactjons,” Addison Wesley, 1972 – Collins, “Foundatjons of perturbatjve QCD”, Oxford U.P, 2011  PDFs and Global QCD fjttjng – Jimenez-Delgado, Melnitchouk, Owens, “Momentum and helicity distributjons in the nucleon”, arXiv:1306.6515 – Forte, Watu, “Progress in partonic structure of proton”, arXiv:1301.6754 – J.Owens, “PDF and global fjttjng”, 2007 / 2013 CTEQ summer school  Lectures (from the CTEQ pedagogical page) – W.K. Tung, “pQCD and parton structure of the nucleon” – B. Poetuer, “Calculatjonal Techniques in pQCD: The Drell-Yan Process”

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Lecture 1 – Motivation

 An illustrated introductjon – Hadrons are made of quarks and gluons – How to probe the partonic structure of hadrons  Deep Inelastjc Scatuering (DIS) – A bit (!) of kinematjcs – Cross sectjon – Structure functjon  A taste of the parton model

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An illustrated introduction

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Motivation: quarks, gluon, hadrons...

 The strong force is described in terms of colored quarks and gluons:  But only color neutral hadrons can be detected – color confjnement – How can one understand, say, proton and neutrons in terms of quark and gluons? – And, for that matuer, what's the evidence for quarks and gluons?

a quark a gluon “color”

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Hadrons are made of quarks

 6 fmavors (and 3 colors): up, down, strange

– light

charm, botuom, top

– heavy

spin ½; charge (elm, weak) isospin (u = ½, d = – ½) strangeness (s = 1)  Confjned in “colorless” hadrons – mesons – 2 quarks – baryons – 3 quarks – Tetraquarks (?) – Pentaquarks (???) – Hybrids (quarks+gluons) … – Glueballs ...

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nucleons

Hadrons are made of quarks

 6 fmavors (and 3 colors): up, down, strange

– light

charm, botuom, top

– heavy

spin ½; charge (elm, weak) isospin (u = ½, d = – ½) strangeness (s = 1)  Confjned in “colorless” hadrons – mesons – 2 quarks – baryons – 3 quarks – Tetraquarks (?) – Pentaquarks (???) – Hybrids (quarks+gluons) … – Glueballs ...

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Fractjonal momentum:

Nucleons are made of 3 quarks…

Parton Distributjon Functjons (PDF)

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Nucleons are made of 3 quarks…

Fractjonal momentum:

Parton Distributjon Functjons (PDF)

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… and gluons, and sea quarks …

Parton Distributjon Functjons (PDF)

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… and gluons, and sea quarks …

Parton Distributjon Functjons (PDF)

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… spinning and orbiting around...

Much studied at: JLab, HERMES, COMPASS, RHIC Fundamental topic at: JLab 6, Electron-Ion-Collider (EIC)

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...and interacting inside nuclei EMC efgect discovered more than 30 years ago: – A ≠  p,n – quarks / hadrons modifjed inside a nucleus – stjll a theoretjcal mystery

? ?

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Evidence for quarks and gluons

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Evidence for quarks and gluons – a whirlwind tour

 Baryon spectroscopy – light sector (u, d, s), ground state – J=3/2+: |q1↑ ,q2↑ ,q3↑ ⟩ – J=1/2+: |q1↑ ,q2↑ ,q3↓ ⟩

Fig: [from Povh et al.] totally symmetric w.fn.

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Evidence for quarks and gluons – a whirlwind tour

 Baryon spectroscopy – light sector (u, d, s), ground state – J=3/2+: |q1↑ ,q2↑ ,q3↑ ⟩ spin symmetric, color antjsymmetric – J=1/2+: |q1↑ ,q2↑ ,q3↓ ⟩ spin antjsymmetrics, color symmetric

Fig: [from Povh et al.]

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Evidence for quarks and gluons – a whirlwind tour

 e+ + e – annihilatjon into hadrons – quark-mediated process

[htup://www.quantumdiaries.org/author/richard-ruiz/]

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Evidence for quarks and gluons – a whirlwind tour

naïve quark model 3-loop calculatjon [from Partjcle Data Book, pdg.lbl.gov]

 e+ + e – annihilatjon into hadrons – quark-mediated process

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Evidence for quarks and gluons – a whirlwind tour

 Jets in high-energy e+ + e – collisions – Hadron produced in 2, 3, … N, high-energy collimated “jets” – Evidence of common origin from a parton

Fig.: 2- and 3-jet events

  • bserved by the JADE

detector at PETRA [from Povh et al.]

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Probing the quark and gluon structure of a hadron

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Probing the nucleon parton structure

 Need large momentum transfer Q2 = qm qm to “resolve” partons  Example 1: Deep Inelastjc Scatuering (DIS) – Photon wave-length in rest frame, neglect proton mass M/Q ≪ 1: – E.g., for x=0.1, Q 2 =4 GeV2 (and puttjng back c and hbar), l = 10-17 m = 10-2 fm to be compared with Rp ≈ 1 fm

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Probing the nucleon parton structure

 Need large momentum transfer Q2 = qm qm to “resolve” partons  Example 1: Deep Inelastjc Scatuering (DIS)

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Probing the nucleon parton structure

 Need large momentum transfer Q2 = qm qm to “resolve” partons  Example 2: Lepton-pair productjon (“Drell-Yan” process)

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Probing the nucleon parton structure

 Need large momentum transfer Q2 = qm qm to “resolve” partons  Example 3: jet productjon in p+p collisions

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Deep Inelastic Scattering

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Kinematics

 Inclusive lepton-hadron scatuering: – Notatjon: – Masses:

Virtual photon momentum Hadronic fjnal state momentum

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Kinematics

 Inclusive lepton-hadron scatuering: – Notatjon: – Masses:

Virtual photon momentum Hadronic fjnal state momentum

Neglect compared to q2 (MeV vs. GeV)

 The photon is virtual: q2 <

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Kinematics

 Inclusive lepton-hadron scatuering: – Notatjon: – Masses:

Virtual photon momentum Hadronic fjnal state momentum

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Kinematics

 Measuring q2 (see [Levy]):

– Scatuered lepton – Hadronic fjnal state – Mixed methods

 Inclusive lepton-hadron scatuering: – Notatjon: – Masses:

Virtual photon momentum Hadronic fjnal state momentum

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Kinematics

 Lorentz invariants

inelastjcity * Bjorken x beam energy loss * virtuality (fjnal state) invariant mass center-of-mass energy * interpretatjon valid in hadron rest frame, see later

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Kinematics

 Lorentz invariants

inelastjcity * Bjorken x beam energy loss * virtuality (fjnal state) invariant mass center-of-mass energy

– Ex.1 (easy) – Do these 6 invariants exhaust all possibilitjes? – Ex.2 (easy) – Are all 6 independent of each other? Prove that:

* interpretatjon valid in hadron rest frame, see later

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Kinematics

 Kinematjc limits on invariants – Q2 > – 0 <

xB < 1

  • By baryon number conservatjon the fjnal state must contain

at least 1 proton, if the target is a proton: Then,

  • All fjnal state hadrons are on-shell:

Then, so that

pi pj

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Kinematics

 Kinematjc limits on invariants, cont'd – n ≥

  • Ex.3 (easy) Hint: use defjnitjon and

– 0 ≤

y ≤ 1

Consider the “target rest frame” such that Then,

  • Ex.4 (hard): fjnd a Lorentz invariant proof
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Kinematics

 Kinematjc plane – theoretjcal – Pick xB , Q2, y as independent variables

Theoretjcal prejudice: can use pQCD only if Q2 large “enough”

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Kinematics

 Kinematjc plane – in practjce

HERA

e+p collider

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Kinematics

 Kinematjc plane – in practjce

HERA

e+p collider fjxed target experiments Fixed-angle spectrometers

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Cross section

 DIS in the target rest frame (for collider, Breit frames see [Levy]) – invariants  Cross sectjon – Ex.5 (med) : prove this (hint: work out dQ2/dq ) – Ex.6 (hard) : directly show that r.h.s. Is Lorentz invariant

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Cross section

 DIS in the target rest frame (for collider, Breit frames see [Levy]) – invariants  Cross sectjon – Ex.5 (med) : prove this (hint: work out dQ2/dq ) – Ex.6 (hard) : directly show that r.h.s. Is Lorentz invariant – and also

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Cross section

Deep inelastjc (large W, more partjcles) Inelastjc (resonance region) (W for only a few partjcles) Elastjc: W=M (no energy to produce any other partjcle)

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Cross section

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Structure functions

 Leptonic and hadronic tensors – 1 photon exchange – Electron is elementary: Lmn can be calculated perturbatjvely  Lorentz decompositjon + gauge invariance = structure functjons

¹0 only for W ±, Z 0 boson exchanges

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Structure functions

 Lorentz decompositjon + gauge invariance = structure functjons  Note: – F1 , F2 , F3 are Lorentz invariants (the tensor structure is explcitly factorized out) – Most general structure compatjble with Lorentz and gauge invariance, no missing functjons – Ex.7 (med) : convince yourself of these 2 statements (gauge invariance implies qmW mn = 0)

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Structure functions and cross section

 The cross sectjon (for a g exchange) reads  Using

  • ne obtains
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Structure functions

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Structure functions

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Structure functions

Same as if target was a free spin ½ partjcle: The photon is scatuering on quasi-free quarks

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Structure functions

 Note: evolutjon with Q 2 and rise at low-x (here come the gluons!)

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A taste of the parton model

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A taste of the parton model

 The photon scatuers on quasi-free quarks – Empirical evidence: F2 = 2xBF1 – Photon wave-length in rest frame, neglect proton mass M/Q ≪ 1: – E.g., for x=0.1, Q 2 =4 GeV2 (and puttjng back c and hbar), l = 10-17 m = 10-2 fm to be compared with Rp ≈ 1 fm

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A taste of the parton model

 DIS ≈ photon-quark elastjc scatuering  Interpretatjon of xB – Parton carries fractjon x of proton's momentum: km = x pm – 4-momentum conservatjon: k' = k+q – Partons have zero mass: k 2 = k' 2 = 0  The virtual photon probes quarks with x = xB

p k' quark i p proton proton k

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A taste of the parton model

 Beware: There is an inconsistency in the derivatjon: – From k = xp follows that quarks are massive, Mq = xM !!  A heuristjc way out is to work in the “infjnite momentum frame”, where so that one can neglect the proton's mass: – This frame is also important to betuer justjfy the parton model – But quarks should be massless in any frame

  • The problem lies in the defjnitjon of x
  • We'll see a betuer solutjon in tomorrow's lecture

– Similarly, the vector 3-momentum is not a Lorentz-invariant scale

  • In fact, M can be neglected compared to Q, not ,

as we shall see

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Lecture 1 – recap

 Hadrons are made of quarks and gluons – Partonic structure probed in DIS, DY, jets, .... (we'll see more)  Deep Inelastjc Scatuering (DIS) – The master method to measure quarks and gluons – Invariant kinematjcs, target rest frame – Cross sectjon, parametrized in terms of structure functjons  A taste of the parton model – Phenomenological evidence for quasi-free quarks, gluons – Some trouble in heuristjc, textbook arguments  Next lecture: Parton model, parton distributjons (PDF) – (QCD improved) parton model – More kinematjcs – Factorizatjon, universality: Drell-Yan, W and Z, jets