Craig Roberts Physics Division

Calories for Quarks

Craig Roberts

Physics Division

Craig Roberts: Calories for Quarks: The Origin of Mass

2

Origin of Mass The 2013 Nobel Prize in Physics was awarded to Higgs

and Englert following discovery of the Higgs boson at the Large Hadron Collider.

The Higgs boson is often said to give mass to everything. However, that is wrong. It only gives mass to some very simple particles, accounting for only one or two percent of the mass of more complex things like atoms, molecules and everyday objects, from your mobile phone to your pet llama. The vast majority of mass comes from the energy needed to hold quarks together inside nuclei.

23.Sep.2014: ECT* (89p)

I will explain this remarkable emergent phenomenon, contained in Nambu's share of the 2008 Nobel Prize, and discuss its connection with the peculiar feature of confinement in QCD; viz., the fact that quarks are forever imprisoned, never reaching the freedom of a particle detector. I will also describe why confinement guarantees that condensates, quantities that were once commonly viewed as constant mass-scales that fill all spacetime, are instead wholly contained within hadrons; and show how contemporary and future terrestrial experiments can help complete the book on the Standard Model


3

Collaborators: 2012-Present1. Rocio BERMUDEZ (U Michoácan);2. Shi CHAO (Nanjing U)3. Ming-hui DING (PKU);4. Fei GAO (PKU)5. S. HERNÁNDEZ (U Michoácan);6. Cédric MEZRAG (CEA, Saclay)7. Trang NGUYEN (KSU);8. Khépani RAYA (U Michoácan);9. Hannes ROBERTS (ANL, FZJ, UBerkeley);10. Chien-Yeah SENG (UM-Amherst)11. Kun-lun WANG (PKU);12. Shu-sheng XU (Nanjing U)13. Chen CHEN (USTC);14. J. Javier COBOS-MARTINEZ (U.Sonora);15. Mario PITSCHMANN (Vienna);16. Si-xue QIN (U. Frankfurt am Main, PKU);17. Jorge SEGOVIA (ANL);18. David WILSON (ODU);

23.Sep.2014: ECT* (89p)

22. Adnan BASHIR (U Michoácan);23. Stan BRODSKY (SLAC);24. Gastão KREIN (São Paulo)25. Roy HOLT (ANL);26. Yu-xin LIU (PKU);27. Hervé Moutarde (CEA, Saclay)28. Michael RAMSEY-MUSOLF (UM-Amherst)29. Alfredo RAYA (U Michoácan);30. Jose Rodriguez Qintero (U. Huelva)31. Sebastian SCHMIDT (IAS-FZJ & JARA);32. Robert SHROCK (Stony Brook);33. Peter TANDY (KSU);34. Tony THOMAS (U.Adelaide)35. Shaolong WAN (USTC)36. Hong-Shi ZONG (Nanjing U)

Students, Postdocs, Asst. Profs.

19. Lei Chang (U. Adelaide)20. Ian Cloet (ANL)21. Bruno El-Bennich (São Paulo);


4

Collaborators: 2012-Present1. Rocio BERMUDEZ (U Michoácan);2. Shi CHAO (Nanjing U)3. Ming-hui DING (PKU);4. Fei GAO (PKU)5. S. HERNÁNDEZ (U Michoácan);6. Cédric MEZRAG (CEA, Saclay)7. Trang NGUYEN (KSU);8. Khépani RAYA (U Michoácan);9. Hannes ROBERTS (ANL, FZJ, UBerkeley);10. Chien-Yeah SENG (UM-Amherst)11. Kun-lun WANG (PKU);12. Shu-sheng XU (Nanjing U)13. Chen CHEN (USTC);14. J. Javier COBOS-MARTINEZ (U.Sonora);15. Mario PITSCHMANN (Vienna);16. Si-xue QIN (U. Frankfurt am Main, PKU);17. Jorge SEGOVIA (ANL);18. David WILSON (ODU);

23.Sep.2014: ECT* (89p)

22. Adnan BASHIR (U Michoácan);23. Stan BRODSKY (SLAC);24. Gastão KREIN (São Paulo)25. Roy HOLT (ANL);26. Yu-xin LIU (PKU);27. Hervé Moutarde (CEA, Saclay)28. Michael RAMSEY-MUSOLF (UW-Mad)29. Alfredo RAYA (U Michoácan);30. Jose Rodriguez Qintero (U. Huelva)31. Sebastian SCHMIDT (IAS-FZJ & JARA);32. Robert SHROCK (Stony Brook);33. Peter TANDY (KSU);34. Tony THOMAS (U.Adelaide)35. Shaolong WAN (USTC)36. Hong-Shi ZONG (Nanjing U)

Students, Postdocs, Asst. Profs.

19. Lei Chang (U. Adelaide)20. Ian Cloet (ANL)21. Bruno El-Bennich (São Paulo);


523.Sep.2014: ECT* (89p)

Standard Model

6

Standard Model- Formulation

23.Sep.2014: ECT* (89p)


The Standard Model of Particle Physics is a local gauge field theory, which can be completely expressed in a very compact form

Lagrangian possesses UY(1)xSUL(2)xSUc(3) gauge symmetry– 19 parameters, which must be determined through comparison

with experiment• Physics is an empirical science

– UY(1)xSUL(2) represents the electroweak theory• 17 of the parameters are here, most of them tied to the Higgs boson, the

model’s only fundamental scalar, something like which has now been seen• This sector is essentially perturbative, so the parameters are readily

determined– SUc(3) represents the strong interaction component

• Just 2 of the parameters are intrinsic to SUc(3) – QCD• However, this is the really interesting sector because it is Nature’s only

example of a truly and essentially nonperturbative fundamental theory • Impact of the 2 parameters is not fully known. One might even be zero.

7

Standard Model- Complete?

There are certainly phenomena Beyond the Standard Model– Neutrinos have mass, which is

not true within the Standard Model

– Empirical evidence: νe ↔ νμ, ντ

… neutrino flavour is not a constant of motion• The first experiment to detect

the effects of neutrino oscillations was Ray Davis' Homestake Experiment in the late 1960s, which observed a deficit in the flux of solar neutrinos νe

• Verified and quantified in experiments at the Sudbury Neutrino Observatory

23.Sep.2014: ECT* (89p)


A number of experimental hints and, almost literally, innumerably many theoretical speculations about other phenomena

8

Death of Super-String Theory?

23.Sep.2014: ECT* (89p)


9

Top Open Questions in

Physics23.Sep.2014: ECT* (89p)


10

Excerpt from the top-10

Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?

Quantum chromodynamics is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside.

23.Sep.2014: ECT* (89p)


11

23.Sep.2014: ECT* (89p)


Quantum Chromodynami

cs

Quantum Chromodynamics

QCD: The piece of the Standard Model that describes strong interactions.

The physics of neutrons, protons, pions, etc. – i.e., Hadron Physics – is a nonperturbative problem in QCD

Notwithstanding the 2013 Nobel Prize in Physics, the origin of 98% of the visible mass in the Universe is – somehow – found within QCD

23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass

12

13

Facilities23.Sep.2014: ECT* (89p)


14

FacilitiesQCD Machines

China– Beijing Electron-Positron Collider

Germany– COSY (Jülich Cooler Synchrotron)– ELSA (Bonn Electron Stretcher and Accelerator)– MAMI (Mainz Microtron)– Facility for Antiproton and Ion Research,

under construction near Darmstadt.New generation experiments in 2018 (perhaps)

Japan– J-PARC (Japan Proton Accelerator Research Complex),

under construction in Tokai-Mura, 150km NE of Tokyo.New generation experiments to begin soon

− KEK: Tsukuba, Belle Collaboration Switzerland (CERN)

– Large Hadron Collider: ALICE Detector and COMPASS Detector“Understanding deconfinement and chiral-symmetry restoration”

23.Sep.2014: ECT* (89p)


http://www.ihep.ac.cn/english/E-Bepc/index.htm

http://www2.fz-juelich.de/ikp/cosy/en/



http://www-elsa.physik.uni-bonn.de/Hadronenphysik/index_en.html

http://www.kph.uni-mainz.de/eng/index.php



http://www.fair-center.eu/Location.208.0.html

http://j-parc.jp/index-e.html

http://belle.kek.jp/

http://aliweb.cern.ch/

http://wwwcompass.cern.ch/

15

FacilitiesQCD Machines

USA– Thomas Jefferson National Accelerator Facility,

Newport News, VirginiaNature of cold hadronic matterUpgrade underway

Construction cost ≈ $370-million New generation experiments in 2015

– Relativistic Heavy Ion Collider, Brookhaven National Laboratory, Long Island, New YorkStrong phase transition, 10μs after Big Bang

23.Sep.2014: ECT* (89p)


A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detector

http://jlab.org/index.html

http://www.bnl.gov/rhic/

http://www.bnl.gov/rhic/STAR.asp

16

Jefferson Lab23.Sep.2014: ECT* (89p)



17

Thomas Jefferson National Accelerator Facility (JLab)

Driving distance: Washington DC to JLab ≈ 270km

23.Sep.2014: ECT* (89p)


18


1984 … DoE provided initial funding for research, development and design

1987 … Construction began on Continuous Electron Beam Accelerator Facility (CEBAF) - February 13

1994 … Accelerator reached design energy of 4 GeV Construction cost in $FY14 ≈ $1-Billion Goal … Write the book about the strongest force

in nature – the force that holds nuclei together – and determine how that force can be explained in terms of the quarks and gluons of quantum chromodynamics (QCD).

23.Sep.2014: ECT* (89p)


19

Thomas Jefferson National Accelerator Facility (JLab) One of the primary reasons for building CEBAF/JLab

Prediction: at energy-scales greater than some a priori unknown minimum value, Λ, cross-sections and form factors will behave as

power = ( number valence-quarks – 1 + Δλ ) Δλ=0,1, depending on whether helicity is conserved

or flipped … prediction of 1/k2 vector-boson exchange

logarithm = distinctive feature & concrete prediction of QCD Claims were made that Λ = 1GeV! So, JLab was initially built to reach 4GeV.

23.Sep.2014: ECT* (89p)

Parton model scaling

QCD scaling violations

e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973)


20

Thomas Jefferson National Accelerator Facility (JLab) 1994 – 2004

o An enormous number of fascinating experimental results

o Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different,

o Suggesting that quark-quark correlations play a crucial role in nucleon structure

But no sign of parton model scaling and certainly not of scaling violations

23.Sep.2014: ECT* (89p)

Particle physics paradigm

Particle physics paradigm


21


2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV

2014 … 12GeV commissioning beams now being delivered to the experimental halls

Final cost of upgrade isapproximately $370-Million

Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]

23.Sep.2014: ECT* (89p)

http://arxiv.org/abs/arXiv:1208.1244

http://arxiv.org/abs/arXiv:1208.1244


22

What is QCD?

23.Sep.2014: ECT* (89p)

23

Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field TheoryThis is not true of QED – cannot be defined nonperturbatively

No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeV

Increasingly probable that any extension of the Standard Model will be based on the paradigm established by QCD – Extended Technicolour: electroweak symmetry breaks via a

fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)

– Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity

23.Sep.2014: ECT* (89p)


(not an effective theory)QCD is a Theory

wikipedia.org/wiki/Technicolor_(physics)

http://inspirehep.net/record/895220?ln=en


http://en.wikipedia.org/wiki/Technicolor_(physics)

24

What is QCD?

Lagrangian of QCD– G = gluon fields– Ψ = quark fields

The key to complexity in QCD … gluon field strength tensor

Generates gluon self-interactions, whose consequences are extraordinary

23.Sep.2014: ECT* (89p)


25

QED is the archetypal gauge field theory Perturbatively simple

but nonperturbatively undefined

Chracteristic feature: Light-by-light scattering; i.e., photon-photon interaction – leading-order contribution takesplace at order α4. Extremely small probability because α4 ≈10-9 !

cf.Quantum Electrodynamics

23.Sep.2014: ECT* (89p)


Relativistic Quantum Gauge Field Theory: Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless

Similar interaction in QED Special feature of QCD – gluon self-interactions

What is QCD?


26

3-gluon vertex

4-gluon vertex

23.Sep.2014: ECT* (89p)

27

Running couplings

Quantum gauge-field theories are all typified by the feature that Nothing is Constant

Distribution of charge and mass, the number of particles, etc., indeed, all the things that quantum mechanics holds fixed, depend upon the wavelength of the tool used to measure them– particle number is generally not conserved in quantum field theory

Couplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them

23.Sep.2014: ECT* (89p)


QED cf. QCD?


28

2004 Nobel Prize in Physics : Gross, Politzer and Wilczek

e

QED

mQ

Qln

32

1)(

Q

NQ

f

QCD

ln)233(

6)(

fermionscreening

gluonantiscreening

23.Sep.2014: ECT* (89p)

Add 3-gluon self-interaction5 x10-5=0.7%

500%


29

Strong-interaction: QCD

Asymptotically free– Perturbation theory is valid

and accurate tool at large-Q2

– Hence chiral limit is defined Essentially nonperturbative

for Q2 < 2 GeV2

23.Sep.2014: ECT* (89p)

Nature’s only (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produce

30

Confinement?

Millennium prize of $1,000,000 for proving that SUc(3) gauge theory is mathematically well-defined, which will necessarily prove or disprove the confinement conjecture

23.Sep.2014: ECT* (89p)



31

What is Confinement?

23.Sep.2014: ECT* (89p)

32

Wilson Loop & the Area Law

23.Sep.2014: ECT* (89p)


τ

z

C is a closed curve in space, P is the path order operator

Now, place static (infinitely heavy) fermionic sources of any charge at positions

z0=0 & z=½L

Then, evaluate <WC(z, τ)> as a functional integral over gauge-field configurations

In the strong-coupling limit, the result can be obtained algebraically; viz.,

<WC(z, τ)> = exp(-V(z) τ )

where V(z) is the potential between the static sources, which behaves as V(z) = σ z

Linear potentialσ = String tension

33

Light quarks & Confinement

A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”

23.Sep.2014: ECT* (89p)


Folklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.

34


Problem: PionsThey’re extremely light16 tonnes of force makes a lot of them.

23.Sep.2014: ECT* (89p)


35


Problem: 16 tonnes of force makes a lot of pions.

23.Sep.2014: ECT* (89p)


36

Light quarks & Confinement In the presence of

light quarks, pair creation seems to occur non-localized and instantaneously

No flux tube in a theory with light-quarks.

Flux-tube is not the correct paradigm for confinement in hadron physics

23.Sep.2014: ECT* (89p)


G. Bali et al., PoS LAT2005 (2006) 308

http://inspirebeta.net/record/694488?ln=en


Confinement QFT Paradigm: – Confinement is expressed through a dramatic

change in the analytic structure of propagators for coloured states

– It can almost be read from a plot of the dressed-propagator for a coloured state


37

Normal particleConfined particle

σ ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm

Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale)

State described by rapidly damped wave & hence state cannot exist in observable spectrum


38

Plane wave propagation Feynman propagator for

a fermion describes a Plane Wave

A fermion begins to propagate

It can proceed a long way before undergoing any qualitative changes

23.Sep.2014: ECT* (89p)

meson

meson

meson

meson

Baryon


39

Quark Fragmentation A quark begins to

propagate But after each “step” of

length σ, on average, an interaction occurs, so that the quark loses its identity, sharing it with other partons

Finally, a cloud of partons is produced, which coalesces into colour-singlet final states

23.Sep.2014: ECT* (89p)

meson

meson

meson

meson

Baryon

σConfinement is a dynamical phenomenon!


40

QCD

Remarkably simple Lagrangian density

23.Sep.2014: ECT* (89p)


41

Massless QCD

Remarkably simple Lagrangian density Classically, the massless theory does not possess a mass-scale

The theory is “conformally invariant”Everything is massless: gluons and quarks. There are no bound states (no length-scale to define a size)

This is not our Universe

23.Sep.2014: ECT* (89p)

0


42

Massless QCD

Remarkably simple Lagrangian density Define the quantum field theory via a Functional Integral,

which generalises the Feynman path integral for quantum mechanics.

How does that help?

23.Sep.2014: ECT* (89p)

0

Spontaneous(Dynamical)Chiral Symmetry Breaking

The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu

"for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"


4323.Sep.2014: ECT* (89p)

Nambu – Jona-LasinioModel


44

Treats a massless (chirally-invariant) four-fermion Lagrangian & solves the gap equation in Hartree-Fock approximation (analogous to rainbow truncation)

23.Sep.2014: ECT* (89p)

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I

Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345–358 Dynamical Model Of Elementary Particles

Based On An Analogy With Superconductivity. IIY. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254

45

Chiral Symmetry

Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbative chiral symmetry

A related concept is Helicity, which is the projection of a particle’s spin, J, onto it’s direction of motion:

For a massless particle, helicity is a Lorentz-invariant spin-observable λ = ± ; i.e., it’s parallel or antiparallel to the direction of motion– Obvious:

• massless particles travel at speed of light• hence no observer can overtake the particle and thereby view its

momentum as having changed sign23.Sep.2014: ECT* (89p)


pJ


46

Gap Equation23.Sep.2014: ECT* (89p)

47

Nambu—Jona-Lasinio Model Gap equation

NJL gap equation

23.Sep.2014: ECT* (89p)


Free fermion piece

Interactions

48

Some algebra NJL gap equation is an equation for fermion mass⇒

Chiral limit, m=0– Clearly, one solution is M=0. – That is the solution in perturbation theory … Start with no mass, end-

up with no mass.

Suppose, on the other hand, that M ≠ 0 so that it can be cancelled– This nontrivial solution can exist if-and-only-if one can satisfy 3π2 mG

2 = C(M2,1)

NJL model& a mass gap?

23.Sep.2014: ECT* (89p)


Critical coupling for dynamical mass generation?

49

NJL model& a mass gap?

Can one satisfy 3π2 mG2 = C(M2,1) ?

– C(M2, 1) = 1 − M2 ln [ 1 + 1/M2 ]• Monotonically decreasing function of M• Maximum value at M = 0; viz., C(M2=0, 1) = 1

Consequently, there is a solution iff 3π2 mG2 < 1

– Typical scale for hadron physics: Λ = 1 GeV• There is a M≠0 solution iff mG

2 < (Λ/(3 π2)) = (0.2 GeV)2

Interaction strength is proportional to 1/mG2

– Hence, if interaction is strong enough, then one can start with no mass but end up with a massive, perhaps very massive fermion

23.Sep.2014: ECT* (89p)


Critical coupling for dynamical mass generation!

Dynamical Chiral Symmetry Breaking

mG=0.17GeV

mG=0.21GeV


50

Impact Appears fairly simple, perhaps, but

these two papers have had an enormous impact

Together, cited more than 5950 times Google Scholar returns ≈ 9820 items for

the term “Nambu – Jona-Lasinio” Defined the paradigm for dynamical

chiral symmetry breaking

23.Sep.2014: ECT* (89p)

51

DCSB: Mass from Nothing


52


DCSB is a fact in QCD– Dynamical, not spontaneous

• Add nothing to QCD , No Higgs field, nothing! Effect achieved purely throughquark+gluon dynamics.

– It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for ≈98% of the proton’s mass.• Higgs mechanism is (almost) irrelevant to light-quarks.

23.Sep.2014: ECT* (89p)



53

Calories for quarks One of the most

important figures in the Standard Model of Particle Physics

98% of the mass in this room owes to the phenomenon that produces this behaviour

23.Sep.2014: ECT* (89p)

54

Just one of the terms that are summed in a solution of the simplest, sensible gap equation

Where does the mass come from?

Deceptively simply picture Corresponds to the sum of a countable infinity of diagrams.

NB. QED has 12,672 α5 diagrams Impossible to compute this in perturbation theory.

The standard algebraic manipulation tools are just inadequate

23.Sep.2014: ECT* (89p)


αS23

55


Vacuum Condensates?23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass

Universal Conventions

Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)“The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”

23.Sep.2014: ECT* (89p)


56

http://en.wikipedia.org/wiki/QCD_vacuum

57

“Orthodox Vacuum”

Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!

23.Sep.2014: ECT* (89p)


u

u

ud

u ud

du


58

However, just like gluons and quarks, and for the same reasons:Condensates are confined within hadrons. There are no vacuum condensates.

Historically, DCSB has come to be associated with the presumed existence of spacetime-independent condensates that permeate the Universe.

23.Sep.2014: ECT* (89p)

59

Confinement contains

condensates23.Sep.2014: ECT* (89p)


60

GMOR Relation



61

GMOR Relation

Valuable to highlight the precise form of the Gell-Mann–Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195

o mπ is the pion’s mass o Hχsb is that part of the hadronic Hamiltonian density which

explicitly breaks chiral symmetry. The operator expectation value in this equation is evaluated

between pion states. Un-approximated form of the GMOR relation doesn’t make

any reference to a vacuum condensate23.Sep.2014: ECT* (89p)

Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)






http://prc.aps.org/abstract/PRC/v85/i1/e012201



62

GMOR is synonymous with “Vacuum Quark

Condensate”23.Sep.2014: ECT* (89p)


63

GMOR Relation

Demonstrated algebraically that the so-called Gell-Mann – Oakes – Renner relation is the following statement

Namely, the mass of the pion is completely determined by the pion’s scalar form factor at zero momentum transfer Q2 = 0. viz., by the pion’s scalar charge

23.Sep.2014: ECT* (89p)


Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)







64

Hadron Charges

Matrix elements associated with hadron form factors Scalar charge of a hadron is an intrinsic property of

that hadron … no more a property of the vacuum than the hadron’s electric charge, axial charge, tensor charge, etc. …

23.Sep.2014: ECT* (89p)


65

“Orthodox Vacuum”

Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!

23.Sep.2014: ECT* (89p)


u

u

ud

u ud

du

66

New Paradigm Vacuum = perturbative hadronic fluctuations

but no nonperturbative condensates Hadrons = complex, interacting systems

within which perturbative behaviour is restricted to just 2% of the interior

23.Sep.2014: ECT* (89p)


u

u

ud

u ud

du

“EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”

23.Sep.2014: ECT* (89p)


67

“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010

Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046

Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model

experiment*103

8 4620

4

HG QCDNscondensateQCD

Paradigm shift:In-Hadron Condensates

“The biggest embarrassment in

theoretical physics.”

http://www.newscientist.com/article/mg19325911.700-dark-energy-seeking-the-heart-of-darkness.html


68

23.Sep.2014: ECT* (89p)

Grand Challenge

69

Overarching Science Challenges for the coming

decade: 2014-2023 Discover the meaning of confinement Determine its connection with DCSB

(dynamical chiral symmetry breaking) Elucidate their signals in observables

… so experiment and theory together can map the nonperturbative behaviour of the strong interaction

It is unlikely that two phenomena, so critical in the Standard Model, tied to the dynamical generation of a single mass-scale and masses of all the normal particles, can have different origins and fates.

23.Sep.2014: ECT* (89p)


70

Enigma of Mass23.Sep.2014: ECT* (89p)


Pion’s Goldberger-Treiman relation


71

Pion’s Bethe-Salpeter amplitudeSolution of the Bethe-Salpeter equation

Dressed-quark propagator

Axial-vector Ward-Takahashi identity entails

Pseudovector componentsnecessarily nonzero.

Cannot be ignored!

Owing to DCSB& Exact inChiral QCD

23.Sep.2014: ECT* (89p)

Miracle: two body problem solved, almost completely, once solution of one body problem is known

Maris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273

B(k2)



72

Enigma of mass

The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz.,

Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.

This emphasises that Goldstone's theorem has a pointwise expression in QCD

Hence, pion properties are an almost direct measure of the dressed-quark mass function.

Thus, enigmatically, the properties of the massless pion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.

23.Sep.2014: ECT* (89p)


fπ Eπ(p2) = B(p2)

73

Parton structure of

hadrons23.Sep.2014: ECT* (89p)


Valence quarks

74

Parton Structure of Hadrons

Valence-quark structure of hadrons– Definitive of a hadron.

After all, it’s how we distinguish a proton from a neutron– Expresses charge; flavour; baryon number; and other Poincaré-

invariant macroscopic quantum numbers– Via evolution, determines background at LHC

Foreseeable future will bring precision experimental study of (far) valence region, and theoretical computation of distribution functions and distribution amplitudes– Computation is critical– Without it, no amount of data will reveal anything about the theory

underlying the phenomena of strong interaction physics

23.Sep.2014: ECT* (89p)


75

Pion’s Wave Function23.Sep.2014: ECT* (89p)


76

Pion’s valence-quark Distribution Amplitude

Following a workshop in Brazil (2012), methods were developed that enable direct computation of the pion’s light-front wave function

φπ(x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré-covariant wave-function onto the light-front

Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.

xα (1-x)α, with α≈0.323.Sep.2014: ECT* (89p)


Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].




http://prl.aps.org/abstract/PRL/v110/i13/e132001







77

Pion’s valence-quark Distribution Amplitude

Continuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB

23.Sep.2014: ECT* (89p)


Asymptotic

RL

DB

Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].












78

Elastic Scattering23.Sep.2014: ECT* (89p)

e(p) + H(q) → e(p’) + H(q’)

79

Elastic Form FactorsStructure of Hadrons

Elastic form factors– Provide vital information about the structure and composition of the

most basic elements of nuclear physics. – They are a measurable and physical manifestation of the nature of

the hadrons' constituents and the dynamics that binds them together. Accurate form factor data are driving paradigmatic shifts in our

pictures of hadrons and their structure; e.g., – role of orbital angular momentum and nonpointlike diquark

correlations– scale at which p-QCD effects become evident– strangeness content– meson-cloud effects– etc.

23.Sep.2014: ECT* (89p)



80

Hard Exclusive Processes& PDAs

In the theory of strong interactions, the cross-sections for many hard exclusive hadronic reactions can be expressed in terms of the PDAs of the hadrons involved

Example: pseudoscalar-meson elastic electromagnetic form factor

o αS(Q2) is the strong running coupling, o φπ(u) is the meson’s twist-two valence-quark PDAo fP is the meson's leptonic decay constant

23.Sep.2014: ECT* (89p)

It was promised that JLab would verify this fundamental prediction


81

Pion electromagnetic form factor

In 2001 – seven years after beginning operations, Jefferson Lab provided the first high precision pion electroproduction data for Fπ between Q2 values of 0.6 and 1.6 (GeV/c)2.

23.Sep.2014: ECT* (89p)

2006 & 2007 – new result, at Q2=2.45 (GeV/c)2

Authors of the publications stated: “still far from the transition to the Q2 region where the pion looks like a simple quark-antiquark pair” disappointment and surprise

Result imagined by many to be QCD prediction

JLab Data

Evaluated with φπ = 6x(1-x)

40 years of lQCD only provides access to this small domain, which is already well-mapped by experiments


82


Year 2000 prediction for Fπ(Q2) – P.Maris & P.C. Tandy,

Phys.Rev. C62 (2000) 055204

Problem … used brute-force computational method … unable to compute for Q2>4GeV2

23.Sep.2014: ECT* (89p)


JLab Data

Shape of prediction suggested to many that one might never see parton model scaling and QCD scaling violations

Factor of three discrepancy



83


Plans were made and an experiment approved that use the higher-energy electron beam at the 12 GeV Upgrade at Jefferson Lab.

The Upgrade will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2, which will probe the pion at double the resolution.

23.Sep.2014: ECT* (89p)

Projected JLab reach

Will there be any hint of a trend toward the asymptotic pQCD prediction?




84

New AlgorithmNew Insights

23.Sep.2014: ECT* (89p)


85



Pion electromagnetic form factor Solution – Part 1

– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD

23.Sep.2014: ECT* (89p)

Real QCD prediction – obtained with realistic, computed PDA


86

Pion electromagnetic form factor Solution – Part 1

– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD

Solution – Part 2– Algorithm used to

compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2

23.Sep.2014: ECT* (89p)

Real QCD prediction – obtained with realistic, computed PDA

Predictions: JLab will see maximum Experiments to 8GeV2 will see

parton model scaling and QCD scaling violations for the first time in a hadron form factor

Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)

maximum

Agreement within 15%








87

Implications

Verify the theory of factorisation in hard exclusive processes, with dominance of hard contributions to the pion form factor for Q2>8GeV2.

Notwithstanding that, normalisation of Fπ(Q2) is fixed by a pion wave-function whose dilation with respect to φπ

asy(x)=6x(1-x) is a definitive signature of DCSB– Empirical measurement of the strength of DCSB in the

Standard Model – the origin of visible mass Close the book on a story that began thirty-five years ago Paves the way for a dramatic reassessment of pictures of

proton & neutron structure, which is already well underway

23.Sep.2014: ECT* (89p)

88

Epilogue23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass


89

Calories for quarks

QCD, an apparently simple element of the Standard Model Classically, in the massless theory, the stress-energy tensor,

Tμν, is associated with a conserved Noether current

Quantisation destroys that conservation lawThe Noether current becomes anomalous

At the most fundamental level, this is the origin of (almost) all visible nonleptonic mass in the Universe

Running masses for the gluons and quarks are the inevitable consequence … and their effects are measurable

23.Sep.2014: ECT* (89p)

Tμν

90

Table of ContentsI. AbstractII. Standard ModelIII. Death of Super- String Theory?IV. Quantum ChromodynamicsV. FacilitiesVI. QCD is a Theory VII. What is Confinement?VIII. ConfinementIX. Dynamical Chiral Symmetry BreakingX. Gap EquationXI. Calories for quarksXII. Overarching Science Challenges

23.Sep.2014: ECT* (89p)


XIII. Enigma of MassXIV. Pion Elastic FFXV. Epilogue

Craig Roberts Physics Division

Documents

Transcript of Craig Roberts Physics Division