Assumpta Parreño
NPLQCD Collaboration
HYP-XInternational conference of hypernuclear physics,
JPARC, Ibaraki, JAPAN
Sep. 14- Sep. 18 2009
Former member:
Paulo F. Bedaque
(Maryland)
Silas R. Beane
New Hampshire
William Detmold
William & Mary
Former member:
Ellisabetta Pallante
(Groningen)
Huey-Wen Lin
U of Washington
Kostas Orginos Assumpta Parreño Martin J. Savage
William & Mary
Barcelona
U of Washington
Tom Luu
Livermore
Aaron Torok André Walker-Loud
William & Mary
Indiana
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)
3
NPLQCD, Nucl. Phys. A 794 (2007) 62-72
PANIC 2008, 9-14/11/08, Eilat
4
4
Study of the baryonic interactions in the strange sector
with LQCD
provide complementary information to experiment (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
5
Study of the baryonic interactions in the strange sector
with LQCD
provide complementary information to experiment (LN, SN, LL, SS, XX, …)
In general, the analysis of data presents:
Poor statistics
Effective range parameters fit to data highly correlated
LN: What is safe to say?
There is not L-hyperdeuteron
(S-hyperdeuteron?)
Consistency of potential models with
hypertriton data (b.e., spin)
a
(1So )
 0,
a
(1So )
a
(3S1 )
a
0
(3S1 )
The theoretical study of YN interactions is hindered by the lack
of experimental guidance.
6
PANDA at FAIR
SPHERE at JINR
• Anti-proton beam
• Double L-hypernuclei
• g-ray spectroscopy
• Heavy ion beams
• Single L-hypernuclei
MAMI C
HypHI at GSI/FAIR
• Electro-production
• Single L-hypernuclei
• L-wavefunction
• Heavy ion beams
• Single L-hypernuclei at
extreme isospins
• Magnetic moments
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
BNL
• Heavy ion beams
• Anti-hypernuclei
• Single L-hypernuclei
• Double L-hypernuclei
J. Pochodzalla, Int. Journal Modern Physics E, Vol 16, no. 3 (2007) 925-936
7
p p  K+ L p
(COSY, Jülich)
g d  K+ L n
Balewski et al. EPJA 2 (1998)
Hinterberger, Sibirtsev, EPJA 21 (2004)
Gasparyan, Haidenbauer, Hanhart, Speth, PRC69 (2004)
Gasparyan, Haidenbauer, Hanhart, PRC72 (2005)
Gasparyan, Haidenbauer, Hanhart, K. Miyagawa
(CEBAF, ELSA, JLAB, MAMI-C)
Reconstruct the elastic two-body amplitude via
the invariant mass dependence of the production amplitude
in the region where the YN momentum is small.
K - d  nL g
Gall et al., PRC42 (1990)
Gibson et al. BNL report No. 18335(1973)
Gibbs, Coon, Han, Gibson ,PRC61 (2000)
a(1S0 )  -0.15  -5.0
a(3S1 )  -1.3  -2.65
Our (NPLQCD) first study of hyperon-nucleon interactions:
Ref: “hyperon-nucleon interactions from Lattice QCD” Nucl. Phys. A794 (2007) 62-72
Idea: write down the effective theory for the hyperon-nucleon interaction at
low energies (below the pion production threshold)
9
a ( S0   1

 LN 
LL C0

2 
 1 S 
 0
 1 S 
 0
SL
C0
-
3
4
3 g SL g A  LN
2 f 2
2


 SL C0   LN 


 2   m  m2
  m
 1 S 
 0
2
3 g SL
g A2  LN 2 3  4 2 m  6m2  3m3
2
4 f 4
2(  m 
Extract LECs

2
2


 1 S 
0 


 LN
2

3

 
r ( S0   C


SL 0
 1 S 
 
 0 
 LN  
8  

 LL C0 
 1 S 
2
2
 0  3g
SL g A  LN 3  9 m  8m
 SL C0
3
2 f 2
6(  m 
1
Result of the LQCD
simulation
1
2
3g SL
g A2  LN 6 3  23 2 m  28m2  7m3
4
4 f 4
12(  m 
10

LQCD is a non-perturbative implementation of Field Theory, which uses the
Feynman path-integral approach to evaluate transition matrix elements
The starting point is the partition
function in EUCLIDEAN space-time
Imaginary time: t  i τ
-Sgluon
nonlocal term which contains the fermionic contributions
11
Quarks
Discrete space-time
Use a discrete action
Gluons
Evaluate a path ordered
exponential between
neighbour sites
space-time lattice
b 0

continuum
action
{U }

 1

Sg (U)   1- Re(Tr(P (x)))

 3

x,
ˆ )U  (x  
ˆ )U (x)
P (x)  U  (x)U (x  
12
The starting point is he partition
function in EUCLIDEAN space-time
Z
  dU (x)  dd e
 ,x

-S g (U )-S f (, ,U )
x
  dU (x) det(D(U)

D(U))e
-Sg (U )
 ,x
S f  D(U)
Correlation functions:
1
O 
Z

1
-S g (U )

dU
(x)
O(
,U)
det(D(U)
D(U))
e



D(U)
 ,x

(main numerical task)
(huge integration: 8x4x6x12x6x12 x # space points)
Montecarlo Integration
1
-S (U )
det(D(U) D(U)) e g P(U)
Z
Euclidean action
for real and
positive actions
e-S
weighting factor
≈ Probability
(positive definite quantity)
13
Basic algorithm:
1.
Produce N gauge field configurations {U} with probability
distribution P(U)
2. Evaluate:
N

1
1 
O  lim  OU i ,

N  N
 D(U i ) 
i1
Solve a linear system of equations:

Present
L ≈ 2.5 fm
b ≈ 0.1 fm
mq ≈ ms/2
Procedure
D (U)[m] D(U)[m]   
Condition number ≈ 1/m
Aproaching
 nature
EFT
Configurations
(MILC)
L
b
mq
Compute
propagator
s
∞
0
mu,dphys
Compute
correlators
Sets of configurations used in our MIXED simulations
b (fm)
L (fm)
m (MeV)
mK (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 24
b (fm)
L (fm)
m (MeV)
mK (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 3
LS3
LS3
Dimensions
x LT
(L5 = 16)
Dimensions
x LT
(L5 = 12)
403 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
2+1 flavors
Domain-Wall valence quarks on staggered sea quark configurations
15
Extracting masses
Lattice simulations  Evaluation of vacuum correlation functions:
1 (t )2 (0)  0 1 (t )2 (0) 0
1 (t )2 (0)  0 1 (0) e
- Hˆ t
at large t
2 (0) 0   0 1 (0) En e - Ent En 2 (0) 0
n
0 1 (0) E0 E0 2 (0) 0 e - E0t ,

as
t
lowest energy eigenstate
from the exponential decay  energies
Ensure that the (asymptotic) exponential dominates the correlation function
Ex:
C  (t )  

x
  
 (t, x ) (0,0) ,
-



 (t , x )  u (t , x )g 5d (t , x )





a
bT
c
pi (t , x)   abc di (t , x ) ( d (t , x ) C g 5 u (t , x ) )
mass
One-baryon correlator:
C A (t )  

x
n
 † 
n - EA
A(t , x ) A (0,0)   C A e t  C A e - M At
n
2-baryon correlator:
n

 †  † 
- E AB
n
C AB (t )   A(t , x ) B(t, x ) B (0,0) A (0,0)   C AB e t  C AB e - E ABt
 
x,y
Energy shift:
n
DE = EAB – MA -MB
C AB (t )
n - DE n t
G AB (t ) 
 C e
 Ce - DE t
C A (t ) C B (t ) n
17
generalized effective mass plots
M eff ,t J
 C(t) 
1
 log 
 M 0
tJ
C(t  t J ) 
(statistical average over measurements on an ensemble of configurations)

proton
clover on clover, 203x128, antiperiodic BC in t direction
smeared-point, 1194 conf
18
DE 
p 2  M A2 
p 2  M B2 - M A - M B
below inelastic
thresholds
obtained from the simulation
 2 p 2 L2 

S  
2 
4 


j L


j
1
- 4 L
2
j - 2
u.v. regulator
1 1 2
-  r0 p 
a 2
1  p 2 L2 

p cot  ( p)  S 
2 
 L  4 
19
channel
isospin
isospin
projection
quark
content
strangeness
Ln
1/2
-1/2
uuddds
-1
S -n
3/2
-3/2
udddds
-1
LL
0
0
uuddss
-2
S S 
2
2
uuuuss
-2
X0X0
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
20
NPLQCD, Nucl. Phys. A794 (2007) 62-72
Ln
MILC 203x32 L = 2.5 fm b ~ 0.125 fm
G AB (t )
 DE
G AB (t  1)
- ( M N  M L - 2 m - mK ) t
signal-to-noise ratio ~ N conf e
1S
1S
0
0
1S
0
contamination from excited states
m = 350 MeV
m = 490 MeV
3S
1
m = 590 MeV
3S
1
3S
21
1
NPLQCD, Nucl. Phys. A 794 (2007) 62-72
PANIC 2008, 9-14/11/08, Eilat
22
22
Anisotropic (bs > bt) clover lattices
higher resolution in the time direction
i.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
ADVANTAGES
• Mπ ≈ 390 MeV
No mixed-action calculation: we used the same fermion
action 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?
23
Mπ = 390.3(0.7)(0.3) MeV
MN = 1163.9(1.8)(0.6) MeV
MS = 1283.7(1.6)(1.0) MeV
MK = 546.0(0.6)(0.2) MeV
ML = 1252.4(1.6)(0.3) MeV
MX = 1356.1(1.4)(0.2) MeV
EN(1/2-) = 1610(06)(11) MeV
ES(1/2-) = 1727(06)(06) MeV
EL(1/2-) = 1679(05)(02) MeV
EX(1/2-) = 1825(6)(5) MeV
NPLQCD, Phys. Rev. D79 (2009) 114502
24
Prof. T. Hatsuda- HAL QCD Coll
talk at Chiral Dynamics 2009 (Bern)
(Note different scale)
clover on clover
m2≈ 0.15 GeV2
ongoing work
25

(no anihilation diagrams)
CB (t)  Pij 
r
r
r
r
 (t, x )Bi (t, y)(0,0)B j (0,0)
eff
 ,B
 C (t) 
1
 ,B
 log



nJ
C ,B (t  nJ ) 
r r
x ,y
E

C(SS) - aC(SP)
 X0
NPLQCD, arXiv:0803.2728v1 [hep-lat]
26
# 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 clear
due to the difference in Ns
(Note that the triton, with Nu=4 and Nd=5 requires 2880)
27
energy splitting
GX 0X 0 n (t) 
CX 0X 0 n (t)
CX20 (t)Cn (t)
-E
 A0 e
X 0X0n
t

28
1. How does the noise-to-signal scale in hadron correlators?
2. How to distinguish between scattering states and bound
states?
29
Fermilab
Jlab
Franklin - Cray XT4
LBNL
INT
U Washington
U Illinois
NSF-LLNL
30
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