Quantum ChromoDynamics and Hadron Physics. Anthony W. Thomas : CSSM Adelaide

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1 Quantum ChromoDynamics and Hadron Physics Anthony W. Thomas : CSSM Adelaide

2 Outline PART A : Hadron Structure Lattice QCD ) New insight into the QCD vacuum with and without quarks Precise calculations of hadrons masses especially N and New result for G s M : Strangeness Magnetic Moment of Proton

3 Outline PART B : Nuclear Structure Can QCD shed light on how Nuclear Physics works? YES Determine Scalar Polarizability of nucleon from lattice QCD ) Natural Saturation Mechanism. New results for Nucleon Form Factors in-medium

4 Outline PART C: Cosmology & Beyond the Standard Model Do the fundamental constants vary with time? Hint that α may have changed at 10-5 level over age of the Universe New generation of laboratory tests.. Results of PART A lead to precise interpretation of these measurements.

5 QCD and the Origin of Mass Where does the rest of the proton mass originate?

6 Powerful New Qualitative Insights from Lattice Simulations Non-trivial topological structure of vacuum linked to dynamical chiral symmetry breaking There are regions of positive and negative topological charge BUT they clearly are NOT spherical NOR are they weakly interacting!

7 Topology of QCD Vacuum Leinweber see CSSM web pages

8 Add Valence Quarks - Heavy V(r) G. Bali Constant force of order 10 tons! Flux tube forms between linear potential qq r (fm) BUT dominated by short-distance fluctuations No idea of what happens for light quarks!

9 Quark-Anti Anti-Quark Flux Tube: String Lasscock, Leinweber, Thomas& Williams

10 Physical Hadron Properties from Lattice QCD : State of the Art? Currently limited to m q > MeV Time to decrease m π by factor of 2 : 2 7» 100 NEED perhaps 500 Teraflops to get to 5 MeV! Furthermore EFT implies ALL hadronic properties are non-analytic functions of m q (N.B. m π» m q 1/2 : GMOR relation ) HENCE: NO simple power series expansion about m q = 0 : NO simple chiral extrapolation

11 Formal Chiral Expansion Formal expansion of Hadron mass: M N = c 0 + c 2 m π2 + c LNA m π3 + c 4 m π4 + c NLNA m π 4 ln m π + c 6 m π6 +.. Mass in chiral limit No term linear in m π (in FULL QCD there is in QQCD) First (hence leading ) non-analytic term ~ m q 3/2 ( LNA) Source: N! N π! N Another branch cut from N! π! N - higher order in m π - hence next-to-leading non-analytic (NLNA) c NLNA MODEL INEPENDENT c LNA MODEL INDEPENDENT Convergence?

12 Relevance for Lattice data Knowing χ PT, fit with: α + β m π2 + γ m π3 (dashed curve) Best fit with γ as in χ P T Problem: γ = c.f. model independent value -5.6!! ( From: Leinweber et al., Phys. Rev., D61 (2000) )

13 The Solution There is another SCALE in the problem - not natural in (e.g.) dim-regulated χpt Λ ~ 1 / Size of Source of Goldstone Bosons ~ MeV IF Pion Compton wavelength is smaller than source.. ( m π GeV ; m q MeV) ALL hadron properties are smooth, slowly varying (with m q ) and Constituent Quark like! (Pion loops suppressed like (Λ / m π ) n ) WHERE EXPANSION FAILS: NEW, EFFECTIVE DEGREE OF FREEDOM TAKES OVER

14 Extrapolation of Masses At large m π preserve observed linear (constituent-quark-like) behaviour: M H ~ m π 2 As m π ~ 0 : ensure LNA & NLNA behaviour: ( BUT must die as (Λ / m π ) 2 for m π > Λ) N N (a) N N (b) N Hence use: M H = a 0 + a 2 m π2 + σ LNA (m π,λ)+ σ NLNA (m π,λ) N (c) (d) Evaluate self-energies with form factor, finite range regulator, FRR, with Λ» 1/Size of Hadron

15 Behaviour of Hadron Masses with m π From: Leinweber et al., Phys. Rev., D61 (2000) Point of inflection at opening of N π channel» 3M» 2M Lattice data from CP-PACS & UKQCD BUT how model dependent is the extrapolation to the physical point?

16 Regularization Schemes Fit parameters { shown in black DR: Naïve dimensional regularization M N = c 0 + c 2 m π2 + c LNA m π3 + c 4 m π4 + c NLNA m π 4 ln m π + c 6 m π6 +.. BP: Improved dim-reg... for -π loop use correct branch point at m π = m π4 ln m π! ( 2 m π2 ) 3/2 ln ( + m π -[ 2 m π2 ] 1/2 ) - /2 (2 2-3m π2 ) ln m π - for m π < ; ln! arctan for m π > FRR: Finite Range Regulator use MONopole, DIPole, GAUssian and Sharp Cutoff in π-n and π- self-energy integrals: M N = a 0 + a 2 m π2 + a 4 m π4 + σ LNA ( m π, Λ) + σ NLNA (m π, Λ)? Is this more convergent with good choice of FRR?

17 Analysis of the Best Available Data Data : CP-PACS Phys Rev D65 ( 2002) Accuracy better than 1%! Sufficient to determine 4 parameters..

18 Analysis of the Best Available Data

19 Analysis of the Best Available Data

20 Analysis of the Best Available Data

21 Analysis of the Best Available Data

22 Analysis of the Best Available Data

23 Scheme Dependent Fit Parameters Regulator a 0 a 2 a 4 a 6 Λ D-R Sharp Monopole Dipole Gaussian ( Young, Leinweber & Thomas : hep-lat/ )

24 Finite Renormalization ) Physical Low Energy Constants True low energy constants, c 0, 2, 4, 6 should not depend on either regularization or renormalization procedure To check we need formal expansion of σ LNA and σ NLNA* : σ LNA (m π,λ) = b 0 + b 2 m π2 + c LNA m π3 + b 4 m π4 + + σ NLNA (m π,λ) = d 0 + d 2 m π2 + d 4 m π4 + c NLNA m π4 ln m π4 + Hence: c i a i + b i + d i and even though each of a i, b i and d i is scheme dependent, c i should be scheme independent! * Complete algebraic expressions for d i, b i given in hep-lat/ : for all regulators

25 Output: Chiral Coefficients, Nucleon Mass and Sigma Commutator ( Young, Leinweber & Thomas : hep-lat/ ) Regulator DR Sharp Monopole c c c m N (MeV) σ N (MeV) Systematic Error < 1%!! Dipole Gaussian CAUTION: Stat. error large (» 0.07 GeV) + NO finite V corrections applied

26 Role of Heavy Flavors in Normal Hadrons? Matter we see in the Universe is made of u and d quarks Great interest in role of strangeness in dense matter BUT what about normal hadrons?? Is there a large hidden strangeness component in the proton? Modern electron machines now tackling this with high precision measurements of parity violation (» 1 in 10 7 )

27 CS Lattice View of Magnetic Moments with Charge Symmetry p = 2/3 u p -1/3 d p + O N n = -1/3 u p +2/3 d p + O N 2p +n = u p +3 O N (and p + 2n = d p + 3 O N ) Σ + = 2/3 u Σ 1/3 s Σ + O Σ Σ - = -1/3 u Σ -1/3 s Σ + O Σ Σ + - Σ - = u Σ HENCE: O N = 1/3 [ 2p + n - ( u p / u Σ ) (Σ + - Σ - ) ] Just these ratios from Lattice QCD OR O N = 1/3 [ n + 2p ( u n / u Ξ ) (Ξ 0 - Ξ - ) ]

28 Constraint from Charge Symmetry O N Leinweber and Thomas, Phys. Rev. D62 (2000)

29 Equate ) Must Have Environment Dependence

30 u p valence valence : QQCD Data Corrected for Full QCD Chiral Coeff s Green curve includes direct coupling to loop New lattice data from Zanotti et al. ; Chiral analysis Leinweber, Young et al.

31 uσ valence

32 Check: Octet Magnetic Moments

33 Input Calculated Ratios Calculate l R s d ) u p /u Σ = u n /u Ξ = ve G M s in steps of ve

34 Summary: G s M New QQCD data to very low m π now available Chiral corrections from QQCD to Full QCD under control Magnetic moments of Octet Baryons in good agreement with data G Ms = µ N : from CS constraints Environment independence broken by 7% for u in p (Σ + ) and 35% for u in n (Ξ 0 )

35 SAMPLE measurement Initial results: Latest ) Spayde et al., nucl-ex/ : µ N Theory ahead of experiment for a long time! Or is it??

36 B. Can QCD Shed Light on How Nuclear Physics Works? Choose saturation as classic nuclear phenomenon Classic treatment as non-relativistic 2- and 3-body force problem is successful/complicated QHD ) Relativity matters Certainly true at high ρ! (N.B. v/c > 0.3 even at ρ 0 ) Vector repulsion " linearly with ρ Scalar attraction " less fast (Ψ N Ψ N ) BUT huge scalar fields..

37 Quark-Meson Coupling Model: QMC * Intermediate step to full quark-gluon theory of nuclear matter Use successful model of hadron structure : MIT Bag Couple scalar (σ: 0 + ) and vector (ω: 1 - ) mesons to confined quarks Confined quarks generate mean scalar and vector fields Scalar field changes confined quark wave function This changes source * Guichon, Phys. Lett. B200 (1988) 235; Saito & Thomas, Phys. Lett. B327 (1994) 9

38 QMC-2 Source changes: and hence mean scalar field changes SELF-CONSISTENCY and hence quark wave function changes. THIS PROVIDES A NATURAL SATURATION MECHANISM (VERY EFFICIENT BECAUSE QUARKS ARE ALMOST MASSLESS) source is suppressed as mean scalar field increases (i.e. as density increases) N.B. Vector field is trivial: just rises linearly with density.

39 QMC-3

40 QMC-4 ; ONLY CHANGE FROM INTERNAL NUCLEON STRUCTURE IS THAT σ-nucleon COUPLING NOW DECREASES (approximately linearly) WITH INCREASING DENSITY

41 QMC-5 Scalar mean-field less than 50% of QHD Decrease of g σ (σ) as density g σ σ _ (MeV) C ρ Β / ρ 0 g σ σ _ (MeV)

42 Scalar Polarizability Simple Model suggests many problems of QHD solved and nuclear saturation understood if nucleon scalar polarizability of nucleon is negative i.e. it opposes applied scalar field i.e. M N* = M N free g σ σ + g σσ σ 2 M N free g σ (σ) σ where g σ (σ) = g σ [ 1 g σσ σ ] g σ Does N behave this way in QCD?

43 Variation of M N under Chiral Invariant Scalar Field i.e. Change m q BUT not mass of pionic fluctations BUT Part A ) study of chiral extrapolation of M N and M in QQCD and full QCD ) can do this now! M N* = a 0 + a 2 m π2 + a 4 m π4 + self-energy(m π phys,λ) χ PT ) m π2 ¼ 4 m q + 20 m 2 q and in mean field m q! m q g σq σ positive HENCE: M N* = M N (4 a 2 g σq ) σ + (20 a a 4 ) g q2 σ σ 2 ¼ M N g σ (1 g σ σ) σ Coefficient» unity if units GeV ) 10-20% + at ρ 0 as in QMC!

44 QMC: Generalization to Finite Nuclei * Use Born-Oppenheimer approximation i.e. assume internal nucleon structure adjusts to local mean-field assuming time to adjust ~ 1 fm/c ) 3% accuracy in typical nuclei I KNOW OF NO OTHER WAY TO DERIVE EXISTENCE OF NUCLEI WITHIN QCD ) MAJOR CHANGE IN OUR UNDERSTANDING everyone has heard of shell model (Nobel Prize 50 years ago) BUT: what occupies shell model orbits are NOT free nucleons * Guichon, Saito, Rodionov & Thomas: Nucl. Phys. A601 (1996) 349

45 Application of QMC to Nuclear Density Guichon, Saito, Rodionov & Thomas, Nucl. Phys. A601 (1996) 349

46 QMC: Finite Nuclei - 2 MAJOR CONCEPTUAL CHANGE: What occupies shell model orbits are nucleon-like quasi-particles Have: new mass, M N* ; new form factors, etc. EXPERIMENTAL EVIDENCE? He First have to ask the question! Changes are subtle: G E,M /G E,M(free) G E (1s 1/2 ) G M (1s 1/2 ) Lu et al., Phys. Lett. B417 (1998) Q 2 (GeV 2 )

47 Recent Advance at Mainz & JLab * Capacity to measure polarization in coincidence: e e' 4 He T L p σ T / σ L» G E /G M : Compare ratio in 4 He and in free space S. Dieterich et al., Phys. Lett. B500 (2001) 47; and JLab report 2002

48 Jefferson Lab & Mainz: HINT Full theoretical analysis: Udias et al.

49 C. Implications for Cosmology & Physics Beyond the Standard Model Unified theories applied to cosmology suffer generically from a problem of predicting time-dependent coupling constants Fujii, Omote & Nishakoa, Prog. Th. Phys. 92 (1994) 3...in cosmology with extra dimensions people try to find solutions with external dimensions expanding while extra dimensions remain static. But at present no mechanism for keeping internal spatial scale static has been found. Li & Gott, Phys. Rev. D58 (1998) d R KK / dt 0 could give rise to observable time variation in the fundamental constants of our 4D world and thereby provide a window to the extra dimensions Marciano, PRL 52 (1984) 489

50 Recent Evidence for dα d /dt Quasar (QSO) absorption spectra ) α/ α = for z>1 Webb, Flambaum, Churchill, Drinkwater, Barrow, PRL 82 (1999) 884 But if α varies so do other constants e.g. Langacker et al., Phys Lett B528 (2002) 121; Calmet & Fritsch, Eur. P. J. C24 (2002) 639; Marciano, PRL 52 (1984) 489 δλ QCD / Λ QCD ¼ 34 δα/ α ; δ m / m ¼ 70 δα/ α ) δ(m/λ QCD ) / (m/λ QCD ) ¼ 35 δα/ α N.B. values are highly model dependent BUT large coefficients are generic for GUTS!

51 Hyperfine Structure in Absorption lines of QSO s Murphy, Webb & Flambaum, Mon. Not. R. Astron. Soc., astro-ph/

52 Fits to Variation of α Best is linear in look-back time

53

54 Limits on Variation of m q /Λ QCD Big Bang Nuclear-Synthesis Oklo Natural Reactor Quasar absortion spectra Laboratory clock experiments! N.B. Precision of possible c.f in 10 9 years! e.g. Karshenboim, Can. J. Phys. 78 (2000) 639 ) Ratios of hyperfine structure levels in different atoms very Sensitive to changes in magnetic moments

55 Limits from Atomic Hyperfine Structure 1 st limits: Flambaum & Shuryak, PR D65 (2002) Using H, Cs, Hg + ) δ ln (m q /Λ QCD ) < More recently: Flambaum, Leinweber, Thomas & Young, hep-ph/ Updated F&S and derived new limits for hyperfine transitions in: H, Rb, Cs, Yb +, Hg + and optical transition in Hg

56 Relation to Chiral Extrapolation Proton mass & magnetic moment dominated by chiral symmetry breaking Hence changes of quark mass may seem unimportant : BUT with mass generation comes π cloud and non-analytic behaviour e.g. 1/3 rd of µ n is a purely non-analytic contribution from the pion cloud ) there is sensitivity!

57 Controlled Study of δ m q Lattice extrapolation studies involve δ m q / m q» 1-50 and we only need 10-3 ) under very good control Main Results * : M N» m s etc. Flambaum, Leinweber, Thomas, Young, hep-ph/

58 Cs clock, frequency standard: Sample Results Use ratio of hyperfine frequencies:» α 8 under quoted GUT scenario Current best experimental determination: ) δα/ α < /year under GUT scenario

59 Conclusions Study of hadron properties as function of m q using data from lattice QCD is extremely valuable.. has given major qualitative advance in understanding! Inclusion of model independent constraints of χ PT to get to physical quark mass is essential But radius of convergence of traditional (not FRR) χ P T is too small

60 Conclusions....2 Precisely where divergence occurs, new, simple degree of freedom appears : constituent quark Scale for this transition is set by clear physics : whether π -Compton wavelength is larger or smaller than size of pion source i.e. m π < or > GeV Insight enables: accurate, controlled extrapolation of all hadronic observables. ( e.g. m H, µ H, <r 2 > ch, G E,G M, G Ms, <x n >..)

61 Conclusions.3 Progress in calculation of Nucleon and Delta masses in lattice QCD ) allows estimate of scalar polarizability of the nucleon. It is negative opposes applied scalar field and this naturally leads to saturation of nuclear matter in relativistic mean-field theory NEW conceptual view of nuclear structure : Bound nucleons are quasi-particles There is an experimental hint of this in quasi-elastic electron scattering precursor to quark-gluon transition

62 Conclusions 4 GUTS with compactified dimensions suggest fundamental constants must change with time There is evidence that such changes may occur! Important to seek further experimental evidence ideally laboratory based. Understanding of M N, µ p, µ n etc. as functions of m u,d and m s, makes interpretation of such experiments extremely reliable!

63 Special Mentions

64 Title

65 Title

66 Title

67 Original Mainz Result (2001): Q2=0.1 GeV2

68 Formal expansion of µ p in powers of m π ( Young et al., to be published )

69 Baryon Masses in Quenched QCD: An Extreme Test of Our Understanding! Chiral behaviour in QQCD quite different from full QCD η is an additional Goldstone Boson, so that: m N = m 0 +c 1 m π + c 2 m π2 + c LNA m π3 + c 4 m π4 + c NLNA m π4 ln m π +.. LNA term now ~ m q 1/2 origin is η double pole Contribution from η and π N N N

70 Extrapolation Procedure for Nucleon in QQCD Coefficients of non-analytic terms again model independent (Given by: Labrenz & Sharpe, Phys. Rev., D64 (1996) 4595) Let: m N = α + β m π2 +σ QQCD with same Λ as full QCD

71 in QQCD LNA term linear in m π! N π contribution has opposite sign in QQCD (repulsive) Overall σ QQCD is repulsive!

72 Suggests Connection Between QQCD & QCD IF lattice scale is set using static quark potential (e.g. Sommer scale) (insensitive to chiral physics) Suppression of Goldstone loops for m π > Λ implies: can determine linear term ( α + β m π2 ) representing hadronic core : very similar in QQCD & QCD Can then correct QQCD results by replacing LNA & NLNA behaviour in QQCD by corresponding terms in full QCD Quenched QCD would then no longer be an uncontrolled approximation!

73 1 Very Weak Dependence on Mass Parameter of FRR Extrapolated mn GeV DIP GeV

74 Early Lattice Work on µ p and µ n µ p(n) = µ 0 / (1 ± α / µ 0 m π + β m π 2 ) : fit µ 0 and β to lattice data. Thus: µ p = µ 0 α m π + ; α = 4.4 µ N -GeV -1 (from χ PT) p At physical quark mass: ~ 1 / M (~ 1 / m π2 ) µ p = 2.85 ± 0.22 µ N µ n = ± 0.15 µ N n (purely statistical errors) (Leinweber et al., Phys. Rev. D60 (1999) ; /// result: Hemmert & Weise: nucl-th/ )

75 Strong Evidence for QQCD Chiral Behaviour proton + New data Zanotti et al. (CSSM), 1 Teraflop FLIC action (nucl-th/ )

76 Extrapolation of lattice data for µ to pole Data: Lopez-Castro, Mariano (2002) & Bosshard et al. (1991) Lattice data from Leinweber et al. (~1991!) Recent measurement (Mainz) Kotulla et al., PRL 89 (2002) µ + = (stat) 1.5 (syst.) 3 (theory) From Cloet et al., hep-lat/

77 Chiral Extrapolation of G p E Lattice data: Göckeler et al. (QCDSF), hep-lat/ Wilson fermions Chiral Extrapolation: Ashley et al. (CSSM), Nucl. Phys. A721 (2003) 915

78 Chiral Extrapolation of G p M Finest lattice a» 0.05 fm

79 Direct Calculation of G s M q 2 = n (π / 10 a) 2 n=1,2,3 a» 0.1 fm hep-ph/ : Lewis, Wilcox & Woloshyn

80 Evaluation of G s M by Linear Chiral Extrapolation Lewis, Wilcox & Woloshyn, hep-ph/ G Ms (0.1 GeV 2 ) = c.f. Hasty et al., Science 290 p.2117 = G Es (0.4 GeV 2 ) G Ms (0.4) = c.f. Aniol et al., Phys. Lett. B509 p.211 =

81 unvalence

82 u in valence Ξ 0

83 A GAME : HOW MODEL DEPENDENT? Quantitative comparison of 6 different regulator schemes Ask over what range in m π2 is there consistency at 1% level? Use new CP-PACS data from >1 year dedicated running: - Iwasaki gluon action - perturbatively improved clover fermions - use data on two finest lattices (largest β): a = 0.09 & 0.13 fm - follow UKQCD (Phys. Rev. D60 ( 99) ) in setting physical scale with Sommer scale, r 0 = 0.5 fm (because static quark potential insensitive to χ al physics) - restricted to m π2 > 0.3 GeV 2 Also use measured nucleon mass in study of model dependence Young, Leinweber & Thomas, hep-lat/

84 Constraint Curves MN GeV All 4 FRR curves indistinguishable Physical m 2 Π GeV 2 CP-PACS nucleon mass data BP DR Dim-Reg curves wrong above last data point

85 Best fit (bare) parameters Regulator a 0 a 2 a 4 a 6 Λ (GeV) DR BP SC MON DIP GAU N.B. Improved convergence of residual series is dramatic!

86 Low Energy Parameters are Model Independent for FRR Regulator DR BP SC c c c } Inaccurate higher order coefficients with DR & BP SC not as good as other FRR MON DIP GAU } Note consistency of low energy parameters! Note terrible convergence properties of conventional series.. (c 6» 60)

87 Lattice data (from MILC Collaboration) : red triangles Green boxes: fit evaluating σ s on same finite grid as lattice Lines are exact, continuum results (QQCD) Bullet points N (QQCD) N α N + β N m π2 + self-energies (LNA+NLNA) α N β N α β FULL 1.24 (2) 0.92 (5) 1.43 (3) 0.75 (8) QQCD 1.23 (2) 0.85 (8) 1.45 (4) 0.71 (11) From: Young et al., hep-lat/ ; Phys. Rev. D66 (2002)

88 Conclusions.3 Insight enables: accurate, controlled extrapolation of all hadronic observables. ( e.g. m H, µ H, <r 2 > ch, G E,G M, G Ms, <x n >..) Suggests new connection between QQCD and QCD (chiral loops seem to explain whole difference!) Findings suggest development of new CQM in region where it has a chance to be valid & tests of all quark models!

89 Title

90 Title

91 Octet Masses Fit quenched data with : α + β m π2 + σ QQCD ; then let σ QQCD! σ QCD Errors for: Stats a! 0 finite L NOT SHOWN (Preliminary results from CSSM group: Young, Zanotti et al.)

92 Title

93 η = #B /# γ Shift of ε d and BBN D He CMB -WMAP data BBN with current ε d 7 He Present ε d New Dmitriev, Flambaum & Webb, astro-ph/