YN AND YY INTERACTIONS FROM LATTICE QCD

SIMULATIONSAssumpta Parreño

NPLQCD Collaboration

HYP-XInternational conference of hypernuclear physics, JPARC, Ibaraki, JAPANSep. 14- Sep. 18 2009

NPLQCD Collaboration

André Walker-LoudWilliam & Mary

Silas R. BeaneNew Hampshire

William DetmoldWilliam & Mary

Huey-Wen LinU of Washington

Tom LuuLivermore

Kostas OrginosWilliam & Mary

Assumpta ParreñoBarcelona

Martin J. SavageU of Washington

Aaron TorokIndiana

Former member:Paulo F. Bedaque

(Maryland)

Former member:Ellisabetta Pallante

(Groningen)

interaction among hadrons: why lattice?

3

First principle QCD calculation

Quantifiable uncertainties

Possibility of study processes which are not accessible experimentally

Examples of the impact of few body lattice simulations:• Evolution of a supernova (NEOS)• Nuclear structure calculations• Hadronic parity-violation

Hypernuclear physics(structure and decay)

PANIC 2008, 9-14/11/08, Eilat 4

NPLQCD, Nucl. Phys. A 794 (2007) 62-72

4

5

provide complementary information to experiment

Study of the baryonic interactions in the strange sector

with LQCD(LN, SN, LL, SS, XX, …)

In the low energy regime, around half of the pion production theshold…

In general, YN data show large error bars and absence of true low-energy cross sections

6

provide complementary information to experiment

Study of the baryonic interactions in the strange sector

with LQCD(LN, SN, LL, SS, XX, …)

In general, the analysis of data presents:Poor statisticsEffective range parameters fit to data highly

correlatedLN: What is safe to say?

There is not L-hyperdeuteron(S-hyperdeuteron?)

Consistency of potential models withhypertriton data (b.e., spin)

0,0 )()( 131

SS aa o

)()( 131 SS aa o

The theoretical study of YN interactions is hindered by the lack of experimental guidance.

7

PANDA at FAIR• Anti-proton beam• Double L-hypernuclei• g-ray spectroscopy

MAMI C• Electro-production• Single L-hypernuclei• L-wavefunction

Jlab• Electro-production• Single L-hypernuclei• L-wavefunction

FINUDA at DAFNE• e+e- collider• Stopped-K- reaction• Single L-hypernuclei• g-ray spectroscopy

J-PARC• Intense K- beam• Single and double L-hypernuclei• g-ray spectroscopy for single L

HypHI at GSI/FAIR• Heavy ion beams• Single L-hypernuclei at

extreme isospins• Magnetic moments

SPHERE at JINR• Heavy ion beams• Single L-hypernuclei

BNL• Heavy ion beams• Anti-hypernuclei • Single -hypernuclei• Double L-hypernuclei

Experimental program

J. Pochodzalla, Int. Journal Modern Physics E, Vol 16, no. 3 (2007) 925-936

p p K+ p

g d K+ n

(COSY, Jülich)

Reconstruct the elastic two-body amplitude via the invariant mass dependence of the production amplitude

in the region where the YN momentum is small.

Balewski et al. EPJA 2 (1998)Hinterberger, Sibirtsev, EPJA 21 (2004)

Gasparyan, Haidenbauer, Hanhart, Speth, PRC69 (2004)

Gasparyan, Haidenbauer, Hanhart, PRC72 (2005)

alternatives…Gasparyan, Haidenbauer, Hanhart, K. Miyagawa

(CEBAF, ELSA, JLAB, MAMI-C)

ndKGibson et al. BNL report No. 18335(1973)Gibbs, Coon, Han, Gibson ,PRC61 (2000)

Gall et al., PRC42 (1990)65.23.1)(

0.515.0)(

13

01

Sa

Sa

The LN interaction

9

Idea: write down the effective theory for the hyperon-nucleon interaction at low energies (below the pion production threshold)

Our (NPLQCD) first study of hyperon-nucleon interactions:Ref: “hyperon-nucleon interactions from Lattice QCD” Nucl. Phys. A794 (2007) 62-72

Beane, Bedaque, Parreño, Savage, Nucl. Phys. A747, 55-74 (2005); nucl-th/0311027

2

3223

4

22

22

20

2

00

2

3642

4

3

2

3

4

3

2

01

01

01

01

m

mmm

f

gg

m

mm

f

ggC

CCa

NA

NA

NNS

S

SS

4

3223

4

22

3

22

20

2

0

2

0

12

728236

4

3

6

893

2

3

8

321

01

01

01

01

m

mmm

f

gg

m

mm

f

ggC

CC

r

NA

NA

N

N

S

S

S

S

10

Extract LECs

Result of the LQCDsimulation

What is Lattice QCD ?

11

LQCD is a non-perturbative implementation of Field Theory, which uses the Feynman path-integral approach to evaluate transition matrix

elementsThe starting point is the partition

function in EUCLIDEAN space-timeImaginary time: t i τ

-Sgluonnonlocal term which contains the fermionic

contributions

HARD

12

space-time lattice

Quarks

Gluons

Discrete space-time

Use a discrete action

Evaluate a path ordered

exponential between

neighbour sites

€

b → 0

€

{U}

∑continuum

action

€

Sg (U) = β 1−1

3Re(Tr(Pνμ (x)))

⎛

⎝ ⎜

⎞

⎠ ⎟

x,νμ

∑

Pνμ (x) = Uμ (x)Uν (x + ˆ μ )Uμ+(x + ˆ ν )Uν

+(x)

13

The starting point is he partition function in EUCLIDEAN space-

time

Euclidean action

for real andpositive actions

e-S

weighting factor

€

S f =ψ D(U)ψ

€

Z = dUμ (x) dψ dψ e−Sg (U )−S f (ψ ,ψ ,U )

x

∏μ ,x

∏∫

= dUμ (x)μ ,x

∏ det(D(U)+ D(U))e−Sg (U )∫

Correlation functions:

€

O =1

ZdUμ (x) O(

1

D(U),U) det(D(U)+ D(U)) e−Sg (U )

μ ,x

∏∫

(main numerical task)(huge integration: 8x4x6x12x6x12 x # space

points)

Montecarlo Integration

≈ Probability

€

1

Zdet(D(U)+ D(U)) e−Sg (U ) →P(U)

(positive definite quantity)

important sampling

Basic algorithm:1. Produce N gauge field configurations {U} with probability distribution P(U)2. Evaluate:

€

O = limN →∞

1

NO U i,

1

D(U i)

⎛

⎝ ⎜

⎞

⎠ ⎟

i=1

N

∑

€

D+(U)[m] D(U)[m] χ = φSolve a linear system of equations:

Condition number ≈ 1/mPresent

L ≈ 2.5 fmb ≈ 0.1 fmmq ≈ ms/2

L ∞b 0mq mu,d

phys

Aproaching nature

EFT

Configurations(MILC)

Compute propagator

s

Compute correlators

Procedure

Sets of configurations used in our MIXED simulations

Dimensions LS

3 x LT (L5 = 16)b (fm) L (fm) m p

(MeV)m K

(MeV)no. conf x no.

src

203 x 32 ml=0.030 ms=0.050

0.125 2.5 591 675 564 x 24

203 x 32 ml=0.020 ms=0.050

0.125 2.5 491 640 486 x 24

203 x 32 ml=0.010 ms=0.050

0.125 2.5 352 595 769 x 24

203 x 32 ml=0.007 ms=0.050

0.125 2.5 291 580 1039 x 24Dimensions

LS3 x LT (L5 = 12)

b (fm) L (fm) m p

(MeV)m K

(MeV)no. conf x no.

src

283 x 96 ml=0.0062 ms=0.031

0.09 2.5 320 560 1001 x 7

283 x 96 ml=0.0124 ms=0.031

0.09 2.5 446 578 513 x 3403 x 96 ml=0.0062 ms=0.031 (L5 =

40)0.09 2.5 230 539 109 x 1

403 x 96 ml=0.0062 ms=0.031 (L5 = 12)

0.09 2.5 234 540 109 x 1

152+1 flavors

Domain-Wall valence quarks on staggered sea quark configurations

One hadron in a box

0)0()(0)0()( 2121 tt

teEE

EeEet

tE

ntE

nn

tH n

as ,0)0()0(0

0)0()0(00)0()0(0)0()(

02001

212

ˆ

121

Lattice simulations Evaluation of vacuum correlation functions:

at large t

lowest energy eigenstate

from the exponential decay energies

Ensure that the (asymptotic) exponential dominates the correlation function

,)0,0(),()(

x

xttC

),(),(),( 5 xtdxtuxt

Ex:

Extracting masses

Extracting masses and energy shifts

17

One-baryon correlator:

2-baryon correlator:

Energy shift: DE = EAB – MA -MB

tE

n

tEn

BA

ABAB CeeC

tCtC

tCtG

n )()(

)()(

x n

tMA

tEnAA

AnA eCeCAxtAtC

)0,0(),()(

†

yx n

tEAB

tEnABAB

ABnAB eCeCABxtBxtAtC

,

)0,0()0,0(),(),()(† †

mass

)),(),((),(),( 5 xtuCxtdxtdxtp cbTaiabci

18

One hadron in a box

generalized effective mass plots

(statistical average over measurements on an ensemble of configurations)

clover on clover, 203x128, antiperiodic BC in t directionsmeared-point, 1194 conf

proton€

Meff ,t J=

1

tJ

logC(t)

C(t + tJ )

⎛

⎝ ⎜

⎞

⎠ ⎟→ M0

19

2

22

4

1)(cot

Lp

SL

pp

BABA MMMpMpE 2222

41

4 222

222

j

j j

LpS

u.v. regulator

below inelastic thresholds

obtained from the simulation

€

−1

a+

1

2r0 p2 =

studied BB channels in the strange sector

20

channel isospin

isospin projection

quark content

strangeness

Ln 1/2 -1/2 uuddds -1

S-n 3/2 -3/2 udddds -1LL 0 0 uuddss -2

S+S+ 2 2 uuuuss -2X0X0 1 1 uussss -4

not considered in the present work

channel isospin isospin projection

quark content

strangeness

mixing

X0n 0 0 uuddss -2 LL

X0n 1 0 uuddss -2 S0L

X0p 1 1 uuudss -2 S+L

X-n 1 -1 udddss -2 S-L

21

Ln

contamination from excited states

mp = 350 MeV mp = 490 MeV mp = 590 MeV

NPLQCD, Nucl. Phys. A794 (2007) 62-72

tmmMMconf

KNeN )2( signal-to-noise ratio ~

203x32MILC L = 2.5 fm b ~ 0.125 fm

1S01S0

1S0

3S1 3S1

3S1

EtG

tG

AB

AB )1(

)(

PANIC 2008, 9-14/11/08, Eilat 22

NPLQCD, Nucl. Phys. A 794 (2007) 62-72

22

23

more recently: no MIXING: high statistics simulations

Anisotropic (bs > bt) clover lattices higher resolution in the time directioni.e. better study of noisy states

• 292500 sets of measurements

• 1194 gauge configurations of size 203 x 128

produced by the Hadron Spectrum Collaboration

• anisotropy parameter ξ=bs/bt=3.5

• spatial lattice spacing of bs=0.1227 ± 0.0008 fm

• Mπ ≈ 390 MeV

No mixed-action calculation: we used the same fermionaction used in the gauge-field generation to compute the quark propagators clover on clover

Faster than our previous MA simulations DW on staggered(4-D clover compared to 5-D DW fermions)

Clover discretization keeps corrections O(b)

Clover discretization does not have a lattice chiral symmetry… systematic uncertainties in the properties/interaction of baryons?

AD

VA

NTA

GES

One hadron simulations

24NPLQCD, Phys. Rev. D79 (2009) 114502

MK = 546.0(0.6)(0.2) MeVML = 1252.4(1.6)(0.3) MeVMX = 1356.1(1.4)(0.2) MeV

Mπ = 390.3(0.7)(0.3) MeVMN = 1163.9(1.8)(0.6) MeVMS = 1283.7(1.6)(1.0) MeV

EN(1/2-) = 1610(06)(11)

MeVES(1/2

-) = 1727(06)(06) MeV

EL(1/2-) = 1679(05)(02) MeV

EX(1/2-) = 1825(6)(5) MeV

25

clover on clover

mp2 ≈ 0.15

GeV2

Prelimina

ry(Note different scale)

Prof. T. Hatsuda- HAL QCD Coll talk at Chiral Dynamics 2009 (Bern)

ongoing work

meson-baryon

26

€

CφB (t) = Pij φ+(t,r x )B i(t,

r y )φ(0,

r 0 )B j (0,

r 0 )

r x ,

r y

∑

NPLQCD, arXiv:0803.2728v1 [hep-lat]

(no anihilation diagrams)

p+ X0€

Eφ,Beff =

1

nJ

logCφ,B (t)

Cφ,B (t + nJ )

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

C(SS) - a C(SP)

Three Baryons

27

# Wick contractions to form the correlation function is naively Nu! Nd! Ns!

the cheapest 3-baryon system would be X0 X0 n, with 3! 2! 4! = 288 Wick

contractions

The LLS0 requires 63 contractions but the signal is less cleardue to the difference in Ns

(Note that the triton, with Nu=4 and Nd=5 requires 2880)

28

energy splitting

€

G Ξ 0Ξ 0n

(t) =C

Ξ 0Ξ 0n(t)

C Ξ 02 (t)C n (t)

→A0 e−δE

Ξ0Ξ0nt

Three Baryons

I did not cover...

29

1. How does the noise-to-signal scale in hadron correlators?

2. How to distinguish between scattering states and bound states?

acknowledgents…computational resources

30

Fermilab Jlab

Franklin - Cray XT4LBNL

NSF-LLNL

INTU Washington

U Illinois

in memory of Prof. Cornelius Bennhold

Over the years, Cornelius' thorough vision of the field, together with his open minded attitude and generosity in offering advise, has guided scientists through unexplored and imaginative research paths, leading to the present impressive knowledge and understanding of the mechanisms governing the decay of hypernuclei.

31