QCD Theory - physics.rutgers.edu

INT David Kaplan - QCD Town Meeting - January 12-14, 2007

QCD Theory:Challenges, opportunities, & community needs

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2



Some of the exciting theoretical advances in recent years:

2


QCD Theory:

• Partons

• Hot and Dense QCD

• Effective Field Theory

• Ads/QCD

• Lattice QCD

Challenges, opportunities, & community needs

Some of the exciting theoretical advances in recent years:

2

N ∼ e#αsY , σ ∝ e#αsY∝ s#


Partons Hot/dense QCD EFT AdS/QCD Lattice

3

! <<s

1! ~s

1

BFKL

DGLAP

Q2

QCD

2"

Y = ln 1/x

Extended GeometricScaling region

Saturation region

Q (Y)s

k geom

Color Glass Condensate

BK/JIMWLK

Figure 29: The summary of our knowledge of high energy QCD interactions plotted again in the planeof rapidity Y = ln 1/xBj and ln Q2.

such that the border of extended geometric scaling region is defined by the scale

kgeom ≡ Qs0 e3.28 αs Y (188)

which, using Eq. (164) can be rewritten as [73, 62]

kgeom = Qs(Y )

(

Qs(Y )

Qs0

)0.34

. (189)

Therefore, extended geometric scaling is valid up to

Q ≤ kgeom, (190)

which is a more restrictive condition than Eq. (186). The exact value of kgeom may still be slightlydifferent from the one given by Eq. (189) [73, 74, 75]: what is important is that at large Y this scaleis much larger than the saturation scale, Qs(Y ) # kgeom, allowing for a parametrically wide region ofextended geometric scaling.

The summary of our current knowledge of high energy interactions is shown in Fig. 29. One can seethere that, on top of the saturation region Q ≤ Qs(Y ) of Fig. 27, one now has the extended geometricscaling region Qs(Y ) < Q ≤ kgeom, where the linear BFKL evolution still applies with its solutionhaving the property of geometric scaling due to the presence of saturation region.

Indeed the property of extended geometric scaling was derived here for the case of DIS where asmall projectile (qq dipole) scatters on a nucleus. Saturation effects were only present in the nuclearwave function. At extremely high energies gluon saturation may take place even in the projectile’swave function: to take this into account pomeron loop resummation needs to be performed [124]-[128].While such resummation is still an open problem, it has been argued in [163, 164] that such pomeronloop effects along with energy conservation constraints may potentially lead to a violation of geometricscaling at very high energies.

48

BFKL: parton density increases with Y

Violates Froissard bound

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4

! <<s

1! ~s

1

BFKL

DGLAP

Q2

QCD

2"

Y = ln 1/x


Saturation region

Q (Y)s

k geom


BK/JIMWLK



kgeom ≡ Qs0 e3.28 αs Y (188)


kgeom = Qs(Y )

(

Qs(Y )

Qs0

)0.34

. (189)


Q ≤ kgeom, (190)




48

Q2

s∼

αsπ2

S⊥Nc

xG(x, Q2

s)

BK/JIMWLK equations

take into account gluon fusion

Parton saturation:

∼ 1/Qs

Aµ ∼

1

gs



5

! <<s

1! ~s

1

BFKL

DGLAP

Q2

QCD

2"

Y = ln 1/x


Saturation region

Q (Y)s

k geom


BK/JIMWLK



kgeom ≡ Qs0 e3.28 αs Y (188)


kgeom = Qs(Y )

(

Qs(Y )

Qs0

)0.34

. (189)


Q ≤ kgeom, (190)




48

∼ 1/Qs

In saturation region

Strong, semi-classical field

!1

ΛQCD

INT David Kaplan - QCD Town Meeting - January 12-14, 2007 6

Color Glass Condensate (McLerran, Venugopalan)

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Saturated low-x partons = classical field generated by

random color sources in plane

Heavy ion


Geometric scaling

1

Qs! x⊥ !

1

ΛQCD

At transverse length scales

Scattering is only a function of Qsx⊥ Q/Qsor,

10-1

1

10

102

103

10-3

10-2

10-1

1 10 102

103

E665

ZEUS+H1 high Q2 94-95

H1 low Q2 95

ZEUS BPC 95

ZEUS BPT 97

x<0.01

all Q2

!

"to

t#*p [µ

b]

Figure 28: HERA data on the total DIS γ∗p cross section plotted in [71] as a function of the scalingvariable τ = Q2/Q2

s(xBj).

of the scaling variable τ = Q2/Q2s(xBj). One can see that, amazingly enough, all the data falls on the

same curve, indicating that σγ∗ptot is a function of a single variable Q2/Q2

s(xBj)! This gives us the bestto date experimental proof of geometric scaling. (For a similar analysis of DIS data on nuclear targetssee [162] and the first reference of [81].)

The fact that geometric scaling is a property of the solution of the BK equation has been laterdemonstrated in [72, 73]. In the next Section we will also show that such scaling is also valid outside ofthe Q < Qs(Y ) saturation region.

2.4.3 Extended Geometric Scaling

In [73] Iancu, Itakura and McLerran noticed that the geometric scaling of [72], which was originallyderived as a solution of the BK equation inside the saturation region, also applies in an area outsideof that region. To see this let us first remember that outside of saturation region (xT < 1/Qs(Y )) thenonlinear BK equation (135) reduces to the linear BFKL evolution (140). Therefore, the dipole-nucleusamplitude N is still given by Eq. (158), which we rewrite here as

N(xT , Y ) =∫ ∞

−∞dν eP (ν) Cν (176)

withP (ν) = 2 αs χ(0, ν) Y + (2 i ν + 1) ln(xT Qs0). (177)

46

αs

(Qs ∝ A1/3)



8

HERA data: evidence for geometric scaling, saturation?

Extracted Qs yields large

Would like to see in eA scattering

Q2/Qs2


! <<s

1! ~s

1

BFKL

DGLAP

Q2

QCD

2"

Y = ln 1/x


Saturation region

Q (Y)s

k geom


BK/JIMWLK



kgeom ≡ Qs0 e3.28 αs Y (188)


kgeom = Qs(Y )

(

Qs(Y )

Qs0

)0.34

. (189)


Q ≤ kgeom, (190)




48


Outstanding issues: Theoretical connection between CGC & DGLAP? Detailed phenomenological tests?



10

z (beam axis)

t

strong fields classical EOMs

gluons & quarks out of eq. kinetic theory

gluons & quarks in eq.hydrodynamics

hadrons in eq.

freeze out

from: F. Gelis, R. Venugopalan, hep-ph/0611157

On to heavy ion collisions

Working toward a comprehensive theory: a huge challenge with some progress made

0.0

0.2

0.4

0.6

0.8

1.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

T/Tc

p/pSB

3 flavor2 flavor

pure gauge

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

p/T4

HTL

T/Tc

(1x1) (1x2)

RG

Fig. 4. The pressure in a SU(3) gauge theory and QCD with 2 and 3 light flavordegrees of freedom (left). The right hand part of the figure shows a comparison ofa HTL-resummed perturbative calculation with lattice calculations of the pressurein a SU(3) gauge theory performed with different gauge actions.

ready the early calculations in quenched QCD have shown that up to a fewtimes Tc ε and p show large deviations from ideal gas behavior. E.g. one hasfor the pressure in QCD with massless quarks

p

T 4=

8π2

45+

∑

f=u,d,..

[

7π2

60+

1

2

(

µf

T

)2

+1

4π2

(

µf

T

)4]

fp(g2(T ), T, µf) , (5)

with fp ≡ 1 and ε = 3p in the infinite temperature limit. Deviations fromideal gas behavior are parametrized here by the function fp. Its structure isapparently dominated by non-perturbative contributions arising already inthe gluonic sector of QCD. This is apparent from Fig. 4(left), which showsthe pressure in quenched as well as 2 and 3 flavor QCD with (moderately)light quarks at vanishing quark chemical potential [16] and normalized to thecorresponding ideal gas value given by the prefactor in Eq. 5. The temperaturedependence of this ratio shows only little flavor dependence. Recent studies ofε/T 4 and p/T 4 with smaller quark masses and closer to the continuum limit[17] as well as the (isentropic) equation of state for non-zero quark chemicalpotential [18] (Fig. 5(left)) show that this pattern is a generic feature of QCDthermodynamics. In the temperature interval Tc ≤ T<∼3Tc thermodynamicsthus is characterized by large deviations from the conformal ideal gas limit,which also results in large deviations of the velocity of sound, v2

s = dp/dε,from the asymptotic infinite temperature value, v2

s → 1/3 (Fig. 5(right)).

The QCD pressure for µq ≥ 0 has been analyzed to all orders that are cal-culable in perturbation theory [19]. Non-perturbative contributions at O(g6)have been analyzed [20] and the screening of electric modes has also been im-plemented in self-consistent calculations [21]. We show in Fig. 4(right) resultsfrom an analysis of the pressure that uses HTL-resummed gluon self energiesin the gluon propagator [21]. This suggests that the structure of the pressure,

7

Lattice results, various actions

Ideal gas



11

Pressure of hot SU(3) gauge theory

Theory calculation

from F. Karsch



12

!"#

$

µ%&'!()*

+),

-./

012

3450

'678)'9:,9)*

%6%!012

M. Alford, hep-ph/0610046

The QCD phase diagram:

Untitled-1 1Untitled-1 1



13

Effective Field theory: implementing the symmetries of QCD in phenomenological Lagrangians

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• Chiral perturbation theory


13


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• SCET (Soft Collinear Effective Theory)


13


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• Nuclear Effective Theory (Extending chiral Lagrangians to include multi-nucleon interactions)


13


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• Nuclear Effective Theory (Extending chiral Lagrangians to include multi-nucleon interactions)

• EFT for the lattice


13


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Chiral perturbation theory

A remarkable new & rigorous result from an old theory:

Mσ −

i

2Γσ = 441

+16−8 − i272

+9−12.5 MeV

The pole of the elusive - meson determined with great accuracy from dispersion relations & chiral perturbation theory:

σ

Caprini, Colangelo, Leutwyler (2006)


• Allows one to separate perturbative from nonperturbative QCD in processes with energetic hadrons with nearly collinear constituents (e.g., B decays, hard scattering)

• all-orders factorization arguments, corrections to factorization

• RG resummation of large logs (eg, Sudakov factors)

• High precision extractions of Vub, heavy-light form factors

• Event generation for LHC (SCET interpolates between PQCD for hard events and parton shower for soft events

• Jets, event shapes, etc.


15

SCET: Soft Collinear Effective TheoryBauer Fleming LukePirjolsStewart

BauerSchwarz



16

Nuclear effective theory

Extension of chiral perturbation theory to multi-nucleon (few-body) systems at low energy

• Weinberg (1990), many subsequent authors

• High precision, model independent description of low energy few-body processes

• A key component for extracting few-nucleon physics from lattice QCD simulations



17

Deuteron breakup @ N4LO (1% accuracy, 2 free phenomenological constants)

2 4 6 8 10

0.5

1

1.5

2

2.5

E! (MeV)

"!(mb)

G. Rupak, Nucl. Phys. A (2000)

100

200

300

400d!/d" NLO d!/d" NNLO, full

0

0.02

0.04

0.06 Ay

Ay

-0.02

-0.01

0

0.01

0.02T

20T

20

0

0.01

0.02

0.03T

21T

21

0 60 120 180

# [deg]

-0.04

-0.03

-0.02

-0.01

0

T22

0 60 120 180

# [deg]

T22

Figure 4: nd elastic scattering observables at 3 MeV at NLO (left column) andNNLO (right column). The filled circles are nd pseudo data based on [61, 62] whilethe filled triangles are true nd data [63]. The bands correspond to the cut–offvariation between 500 and 600 MeV. The unit of the cross section is mb/sr.

20

100

200

300

400d!/d" NLO d!/d" NNLO, full

0

0.02

0.04

0.06 Ay

Ay

-0.02

-0.01

0

0.01

0.02T

20T

20

0

0.01

0.02

0.03T

21T

21

0 60 120 180

# [deg]

-0.04

-0.03

-0.02

-0.01

0

T22

0 60 120 180

# [deg]

T22

Figure 4: nd elastic scattering observables at 3 MeV at NLO (left column) andNNLO (right column). The filled circles are nd pseudo data based on [61, 62] whilethe filled triangles are true nd data [63]. The bands correspond to the cut–offvariation between 500 and 600 MeV. The unit of the cross section is mb/sr.

20INT David Kaplan - QCD Town Meeting - January 12-14, 2007


18

Epelbaum et al., Phys. Rev. C (2004)

nd elastic scattering, 3 MeV

Triton binding energy: BENNLO = 8.54 MeV BEEXP = 8.48 MeV

(3-body input = nd scattering length)Platter, Phys. Rev. C (2006)



19

Ongoing EFT developments are critical for lattice QCD:


• Extrapolation to infinite volume


19




• Extrapolation to zero lattice spacing


19





• Extrapolation to physical quark mass


19






• Exploitation of mixed fermion actions to extend computational power


19







• Extraction of S-matrix elements from Euclidean correlation functions


19







• Extraction of S-matrix elements from Euclidean correlation functions

• Treatment of multi-baryon systems


19




20

AdS/CFT: a startling development from string theory

N=4 supersymmetric Yang-Mills theory* in the limit of infinite colors is equivalent to a classical supergravity theory in 5-dimensional anti-deSitter space, and can be exactly solved.

* Gluons, octet fermions, octet scalars (for Nc=3)

• Partons and BFKL

• Energy loss in a plasma

• Universal viscosity bound

Can this theory be used to learn about the real world?

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21

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BrowerPolchinskiStrasslerTan

Derived interpolation between soft pomeron (glueball) exchange, and hard pomeron exchange (BFKL behavior)

PolchinskiStrassler

Showed how glueball-glueball scattering exhibits hard scattering behavior (power law momentum scaling)

Liu, Rajagopal, Wiedemann

Jet quenching, energy loss of heavy quark in hot nonabelian plasmaHerzog et al.

2006

2006

2001

η

s≥

1

4π



22

1 10 100 1000T, K

0

50

100

150

200

Helium 0.1MPaNitrogen 10MPa

Water 100MPa

Viscosity bound

4! "

sh

Figure 2: The viscosity-entropy ratio for some common substances: helium, nitrogen and

water. The ratio is always substantially larger than its value in theories with gravity duals,

represented by the horizontal line marked “viscosity bound.”

experimentally whether the shear viscosity of these gases satisfies the conjectured bound.

This work was supported by DOE grant DE-FG02-00ER41132, the National Science

Foundation and the Alfred P. Sloan Foundation.

References

[1] S.W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43, 199 (1975).

[2] J.D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).

[3] G.T. Horowitz and A. Strominger, “Black strings and p-branes,” Nucl. Phys. B 360,

197 (1991).

[4] L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1987).

[5] G. ’t Hooft, “Dimensional reduction in quantum gravity,” gr-qc/9310026.

7

Conjectured viscosity bound:

Kovtun, Son, Starinets (2004)

η

s≥

1

4π



22

1 10 100 1000T, K

0

50

100

150

200

Helium 0.1MPaNitrogen 10MPa

Water 100MPa

Viscosity bound

4! "

sh

Figure 2: The viscosity-entropy ratio for some common substances: helium, nitrogen and

water. The ratio is always substantially larger than its value in theories with gravity duals,

represented by the horizontal line marked “viscosity bound.”

experimentally whether the shear viscosity of these gases satisfies the conjectured bound.

This work was supported by DOE grant DE-FG02-00ER41132, the National Science

Foundation and the Alfred P. Sloan Foundation.

References

[1] S.W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43, 199 (1975).

[2] J.D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973).

[3] G.T. Horowitz and A. Strominger, “Black strings and p-branes,” Nucl. Phys. B 360,

197 (1991).

[4] L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, New York, 1987).

[5] G. ’t Hooft, “Dimensional reduction in quantum gravity,” gr-qc/9310026.

7

Conjectured viscosity bound:

Kovtun, Son, Starinets (2004)

Does QGP

go lower? The

closer to

saturation, the

more likely a simple

gravitational dual to

QCD exists.



23

Improved technology + intense theoretical effort= a new era in lattice QCD

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• High precision calculations of hadronic properties (1% for some quantities)


23


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• Exploration of the QCD phase diagram


23


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• Advancing frontier:


23


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• nucleon properties


23


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• structure functions


23


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• resonance and glueball spectra


23


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• resonance and glueball spectra

• two - baryon systems


23


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24

1% precision from the lattice in the meson sector:

fπ/fK 1.210(4)(13) MILC

Exp

=

= 1.223(12)



25

Operated by the Jefferson Science Associates, LLC for the U.S. Department of Energy

!"#$%&'()**)+&#,'-%./#,%0'122)0)+%.#+'3%2/0/.4

S and T 2006: Lattice overview

!"#$%&'()$*+)*$,'

• !-.$/#'0%12*)")/%& %3'!"#$%&'()$*+)*$,'*4/&5'6780'"49)"# :"))/+,4

"&#'#%1"/&;<"::;3,$1/%&'=":,&+,'9*"$>4

• !"4',&".:,#'+%12*)")/%&4')%'.,'2,$3%$1,#'/&'3*::'?0@'")'1!

"22$%"+A/&5'BCD'6,E

Nucleon’s axial-vector

charge gA: benchmark

of lattice QCD

LHPC (Edwards et al.),

PRL 96 (2006) 052001

Operated by the Jefferson Science Associates, LLC for the U.S. Department of Energy

!"#$%&'()**)+&#,'-%./#,%0'122)0)+%.#+'3%2/0/.4

S and T 2006: Lattice overview

!"#$%&'()$*+)*$,'

• !-.$/#'0%12*)")/%& %3'!"#$%&'()$*+)*$,'*4/&5'6780'"49)"# :"))/+,4

"&#'#%1"/&;<"::;3,$1/%&'=":,&+,'9*"$>4

• !"4',&".:,#'+%12*)")/%&4')%'.,'2,$3%$1,#'/&'3*::'?0@'")'1!

"22$%"+A/&5'BCD'6,E

Nucleon’s axial-vector

charge gA: benchmark

of lattice QCD

LHPC (Edwards et al.),

PRL 96 (2006) 052001

One nucleon properties: gA

144

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

a!

ENucleon Mass Spectrum

G1gHg G2g G1u

Hu G2u

Figure 8.9: The low-lying I=1/2, I3=+1/2 nucleon spectrum extracted from 200 quenchedconfigurations on a 123 × 48 anisotropic lattice using the Wilson action with as ∼ 0.1 fmand as/aτ ∼ 3.0. The vertical height of each box indicates the statistical uncertainty in thatestimate. Our pion mass for this study was aτMπ = 0.1125(26), or approximately 700 MeV.A different color was chosen for each level in a symmetry channel to help the reader discernamong the different levels.

mπ = 700 MeV

145

0

0.4

0.8

1.2

1.6

2

2.4

2.8

M (

Me

V)

P11

(939)

P11

(1440)

P11

(1710)

F17

(1990)

P11

(2100)

H19

(2220)

K1,13

(2700)

F15

(1680)

P13

(1720)

P13

(1900)

F17

(1990)

F15

(2000)

H19

(2220) (x2)

K1,13

(2700)

F15

(1680)

F17

(1990)

F15

(2000)

K1,13

(2700)

S11

(1535)

S11

(1650)

S11

(2090)

G17

(2190)

G19

(2250)

I1,11

(2600)

D13

(1520)

D15

(1675)

D13

(1700)

D13

(2080)

G17

(2190)

D15

(2200)G

19(2250) (x2)

I1,11

(2600)

D15

(1675)

G17

(2190)

D15

(2200)

I1,11

(2600)(x2) (x2)

(x2)

Nucleon Mass Spectrum (Exp)

G1gHg G2g G1u

Hu G2u

Figure 8.10: The I=1/2, I3=+1/2 nucleon spectrum as determined by experiment [Y+06]and projected into the space of lattice spin-parity states. Black denotes a four-star state,blue denotes a three-star state, tan denotes a two-star state, and gray denotes a one-starstate.



26

LHPC collaboration, from Lichtl (2006)

I=1/2, I3=1/2 baryons

corrections to the Luscher formula can be computed in chiral perturbation theory, as shownin the ππ case in [41] and for two nucleons in [42]. These effects are particularly small inthe NΛ system, as the long-range part of the interaction is dominated by two-pion exchangeand one-kaon exchange, and not one-pion exchange.

100 150 200 250 300 350 400m! (MeV)

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

"(

|k| =

255 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n# ( 1S0 )

100 150 200 250 300 350 400m! (MeV)

-50

-40

-30

-20

-10

0

10

20

30

40

"(

|k| =

168 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n# ( 3S1 )

100 150 200 250 300 350 400 450 500 550m! (MeV)

-40

-30

-20

-10

0

10

20

30

40

50

"(

|k| =

179 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n$% ( 1S0 )

100 150 200 250 300 350 400 450 500 550m! (MeV)

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

"(

|k| =

261 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n$% ( 3S1 )

FIG. 5: Comparison of the lowest-pion-mass lattice results in each channel with a recently developedYN EFT [20] (squares), and several potential models: Nijmegen [11] (triangles) and Julich [15]

(diamonds). The dark error bars on the lattice data are statistical and the light error bars arestatistical and systematic errors added in quadrature.

D. Discussion

We have presented results of the first fully-dynamical lattice QCD calculation of YN inter-actions. The scattering amplitudes for s-wave nΛ and nΣ−, in both the 1S0-channel and the3S1−3D1 coupled-channels, have been determined at one value of momentum for pion massesof ∼ 350 MeV, ∼ 490 MeV and 590 MeV. Unfortunately, the lightest pion mass at whichwe have been able to extract a signal is at the upper limits of the regime of applicabilityof the effective field theories that have been constructed, thus precluding a chiral extrap-olation. However, this work does provide new rigorous theoretical constraints on effective

7



27

Two baryon properties:

NPLQCD hep-lat/0612026

corrections to the Luscher formula can be computed in chiral perturbation theory, as shownin the ππ case in [41] and for two nucleons in [42]. These effects are particularly small inthe NΛ system, as the long-range part of the interaction is dominated by two-pion exchangeand one-kaon exchange, and not one-pion exchange.

100 150 200 250 300 350 400m! (MeV)

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

"(

|k| =

255 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n# ( 1S0 )

100 150 200 250 300 350 400m! (MeV)

-50

-40

-30

-20

-10

0

10

20

30

40

"(

|k| =

168 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n# ( 3S1 )

100 150 200 250 300 350 400 450 500 550m! (MeV)

-40

-30

-20

-10

0

10

20

30

40

50

"(

|k| =

179 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n$% ( 1S0 )

100 150 200 250 300 350 400 450 500 550m! (MeV)

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

"(

|k| =

261 M

eV )

(

deg

rees

)

EFT ’06

Juelich ’04

Nijmegen NSC97f

This Work

n$% ( 3S1 )

FIG. 5: Comparison of the lowest-pion-mass lattice results in each channel with a recently developedYN EFT [20] (squares), and several potential models: Nijmegen [11] (triangles) and Julich [15]

(diamonds). The dark error bars on the lattice data are statistical and the light error bars arestatistical and systematic errors added in quadrature.

D. Discussion

We have presented results of the first fully-dynamical lattice QCD calculation of YN inter-actions. The scattering amplitudes for s-wave nΛ and nΣ−, in both the 1S0-channel and the3S1−3D1 coupled-channels, have been determined at one value of momentum for pion massesof ∼ 350 MeV, ∼ 490 MeV and 590 MeV. Unfortunately, the lightest pion mass at whichwe have been able to extract a signal is at the upper limits of the regime of applicabilityof the effective field theories that have been constructed, thus precluding a chiral extrap-olation. However, this work does provide new rigorous theoretical constraints on effective

7

Multi-nucleon physics

gets real interesting

in the Petaflops era



27

Two baryon properties:

NPLQCD hep-lat/0612026

Locating the QCD critical point

CO94

NJL01

NJLb89

NJLinst98

CJT02

NJLa89

LR04

RM98

LSM01

HB02 LTE03

LR01

LTE04130

9

5

2

17

µB

T

RHICscan

0

50

150

0 200 600 800 1000 1200 1400 1600

100

400

200

Experiments can scan the phase diagram by changing√

s: RHIC.

Signatures: event-by-event fluctuations.

Susceptibilities diverge⇒ fluctuations grow towards the critical point.

QCD Phase Diagram: Overview – p. 5/11



28

From M. Stephanov, Lattice 2006


Lattice

TheoryExperiment

OR:

Theory

LatticeExperiment

?

Scientific Computing


✦ Multi-institution, long-term collaborations

✦ Infrastructure

• Dell cluster, 10 Tflops peak/2 Tflops sustained = $1M

• Significant power & cooling requirements

✦ Operating costs

• Above cluster: 0.5 MW power ~ $200K/yr

• Technical staff: Scientific computing software developers

30

Lattice QCD is very theory intensive, but also shares many similarities with experimental physics



• Lattice QCD

• Hydro simulations for RHIC physics

• Nuclear astrophysics

• Nuclear structure

31

More generally, advanced scientific computing will play an ever-increasing role in all aspects

of nuclear physics:


Scientific computing

TheoryExperiment


• Lattice QCD

• Hydro simulations for RHIC physics

• Nuclear astrophysics

• Nuclear structure

31

More generally, advanced scientific computing will play an ever-increasing role in all aspects

of nuclear physics:

To keep up with scientific computing needs & opportunities will be a challenge. Specifically addressed in LRP at the same level as experiment and theory?


Scientific computing

TheoryExperiment


End of theory survey

32



32

Topics neglected:

Generalized parton distributions

Advances in understanding form factors

Spin physics

QGP properties, hydrodynamics...



32

Topics neglected:

Generalized parton distributions

Advances in understanding form factors

Spin physics

QGP properties, hydrodynamics...

But hopefully clear: QCD is an

extremely vital and active field


How do we move nuclear theory forward, and kick it up a notch?

33



33

Ideas!

ManpowerData(Computational

power)



33

Ideas!


power)


Data

A vigorous experimental program is vital for a healthy theory program


Data

A vigorous experimental program is vital for a healthy theory program

But how closely should theory initiatives be tied to particular experimental efforts?


Leon Lederman’s view of the experimentalist and the theorist




...But there also has to be room for theorists to play around with ideas not directly applicable to experimental phenomenology



1954:



1954:

• First 4” prototype liquid hydrogen bubble chamber installed in Bevatron



1954:

• First 4” prototype liquid hydrogen bubble chamber installed in Bevatron

• Yang & Mills invent nonabelian gauge theory


Ideas!


power)

?INT David Kaplan - QCD Town Meeting - January 12-14, 2007 38

Ideas!


power)


Ideas!


power)

97 98 99 00 01 02 03 04 05 06

25

50

75

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150

Out[90]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

40

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Out[91]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

40

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100

Untitled-1 1


DOE supported permanent PhD staff (theory)

39

2005: 1602006: 144 -10%

97 98 99 00 01 02 03 04 05 06

25

50

75

100

125

150

Out[90]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

40

60

80

Out[91]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

40

60

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100

Untitled-1 1


DOE supported non-permanent PhD staff (theory)

40

2005: 932006: 78 -16%

97 98 99 00 01 02 03 04 05 06

25

50

75

100

125

150

Out[90]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

40

60

80

Out[91]= (17:29:45 on 1/12/07)

Ü Graphics Ü

97 98 99 00 01 02 03 04 05 06

20

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60

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100

Untitled-1 1


DOE supported graduate students (theory)

41

2005: 1152006: 111 -3%


Manpower

42

2006, people supported by DOE:

• # of permanent theory PhDs: -10%

• # non-permanent theory PhDs: -16%

• # theory grad students: -3%


Manpower

• If 2006 is a trend rather than an aberration, nuclear theory is in trouble.

42






Manpower

• If 2006 is a trend rather than an aberration, nuclear theory is in trouble.

• The reduction of post-doc positions is particularly alarming, and should be a focus for remediation

42






Ideas!


power)

Competitive programs to assist the collaborations and individuals with

great ideas


Collaborations

44


Collaborations

44

Seconds103 105 106104 107 108

(Collaboration rapidity)-1


Collaborations

44

Telephone

Seconds103 105 106104 107 108



Collaborations

44

Telephone Workshop

Seconds103 105 106104 107 108



Collaborations

44

Telephone Workshop INT Program

Seconds103 105 106104 107 108


Topical CentersNew:


Collaborations

44


Seconds103 105 106104 107 108


Topical CentersNew:


Collaborations

44


• A virtual center of collaborators organized around a physics problem

Seconds103 105 106104 107 108


Topical CentersNew:


Collaborations

44



• Competitive

Seconds103 105 106104 107 108


Topical CentersNew:


Collaborations

44



• Competitive

• ~3+3 years duration?

Seconds103 105 106104 107 108



Individuals

45


Individuals

• Graduate students: Nuclear Theory Graduate Fellowships (as in 2003 Mueller report)

45


Individuals


• Post-doc level: Post-doctoral prize fellowships (Mueller report)

45


Individuals



• Assistant professor level: existing OJI program is great

45


Individuals




• Tenured professor level: one-time ~$30K awards to allow senior researchers to buy out of teaching for proposed project (like a Guggenheim award)

45


Individuals




• Tenured professor level: one-time ~$30K awards to allow senior researchers to buy out of teaching for proposed project (like a Guggenheim award)

• Analogous opportunities for those at National Labs

45


Competitive awards for the theorists with the ideas


Graduate, Postdoctoral

Prize Fellowships



OJI award

s

(Assist. Profs.)Graduate, Postdoctoral

Prize Fellowships



OJI award

s

(Assist. Profs.)Graduate, Postdoctoral

Prize Fellowships

Competitive “duty relief” 1-yr fellowships

(tenured)



OUTREACH


Main Conclusions:


• QCD theory is a vital field with innovation on many fronts & many opportunities

• Lattice QCD plays an increasingly important role in nuclear physics, and its combination of intensive theory + extensive infrastructure = neither “experiment” nor “theory”

• Manpower is a serious concern in light of the 2006 budget, especially the 16% cut in theory post-docs

• Fund virtual topical centers for theorists to spend several years attacking particular vital problems

• Competitive fellowships for the most productive theorists at all stages of career

48

Main Conclusions:

Documents

QCD Theory - physics.rutgers.edu