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Transcript of Assumpta Parreño NPLQCD Collaboration HYP-XInternational conference of hypernuclear physics, JPARC,...
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?
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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
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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
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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.
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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)(
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01
Sa
Sa
The LN interaction
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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
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00
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3642
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4
3
2
01
01
01
01
m
mmm
f
gg
m
mm
f
ggC
CCa
NA
NA
NNS
S
SS
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0
2
0
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728236
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321
01
01
01
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m
mmm
f
gg
m
mm
f
ggC
CC
r
NA
NA
N
N
S
S
S
S
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Extract LECs
Result of the LQCDsimulation
What is Lattice QCD ?
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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# 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)
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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...
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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.
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