Probing TeV Physics in the Nucleon using large scale simulations of Lattice QCD

Rajan Gupta Laboratory Fellow

Theoretical Division Los Alamos National Laboratory, USA

LA-UR 15-25075 Oak Ridge: May 24, 2016

Collaboration of Collaborations

•  Tanmoy Bhattacharya •  Vincenzo Cirigliano •  Huey-Wen Lin •  Boram Yoon •  E. Mereghetti •  S. Cohen •  A. Joseph

Bhattacharya et al, PRD85 (2012) 054512 Bhattacharya et al, PRD89 (2014) 094502 Bhattacharya et al, PRD92 (2015) 114026 Bhattacharya et al, PRL 115 (2015) 212002 Bhattacharya et al, PRD92 (2015) 094511

PNDME collaboration Jlab and W&M collaboration •  Balint Joo •  Kostas Orginos •  David Richards •  Frank Winter

Yoon et al, arXiv:1601.07737

•  Michael Engelhardt •  Jeremy Green •  John Negele •  Andrew Pochinsky •  Sergey Syritsyn

LHPC collaboration

Outline •  Physics Motivation

–  gA

– Novel Scalar and Tensor Interactions (~10-3 GF) – Novel Sources of CP violation

•  Lattice QCD •  Status of control over systematic errors •  gA, gS, gT

•  Neutron Electric Dipole Moment

Why are these calculations interesting and exciting

•  Nucleons charges –  Provide the strength with which nucleons interact

•  Form factors –  How probes at different q2 couple & see the neutron –  Size of the nucleon: charge radii

•  Neutron Electric Dipole Moment –  A very sensitive probe of CP violation –  The universe is observed to be mainly matter –  Need additional CP violation to explain baryogenesis

Lattice QCD •  Non-perturbative

field theory •  Simulations provide

properties of hadrons in terms of quarks and gluons.

•  QCD corrections to matrix elements of weak operators

Feynman Path Integral Formulation of QCD

M is the discretized Dirac Action: a (3x4xLxLxLxT)2 sparse matrix SF = d 4x∫ ψ(x)(i /D+m)ψ(x) lattice" →"" ψiMijψ ji, j∑

The contribution of the “sea” of each fermion flavor is given by the non-local weight det(M) after integration of ψ. It depends only on the gauge field Uµ=exp{iaAµ} and the quark mass m.

Ω = DA∫ Ωe−SG + Tr LnMPhysics is extracted from expectation values given by

ZQCD = dψ dψ dA e−SG−SF∫= dA∫ det(M ) e−SG

= DA∫ e−SG + Tr LnM

What hogs the computer time? Inversion of the Dirac matrix

SF(x,y) is the non-perturbative Feynman propagator: Amplitude of a quark to go from source x to sink y

SF (x, y) =1

M (x, y)where the DiracAction =ψ(x)M (x, y)ψ(y)

A very useful identity:

€

SF (x,y) = γ 5SF+ (y,x)γ 5

y x

Smeared sink Smeared source

Pion

Baryons

Propagation of stable states in Euclidean time

τ

€

π(τ ) e−Lτ π(0) = Ane−mnτ

n∑

€

SF (x,y)γ 5 SF (y,x)γ 5 = SF (x,y)SF+ (x,y)

Mesons

9

Calculate nucleon 3-point functions matrix element <N|Hint |N> in nucleon ground state

Full quantum state at time τ

Hint

Hint is made up of quark bilinears

10

Connected Disconnected

Need to calculate two types of Feynman diagrams: “connected” and “disconnected”

uγµd(!q)

A number of matrix elements within nucleon states become accessible

•  Iso-vector charges gA, gS, gT

•  Axial vector form factors

•  Vector form factors

•  Flavor diagonal matrix elements

•  Quark EDM and quark chromo EDM

•  Generalized Parton Distribution Functions

11

€

p q q p€

p u Γd np(!q) uγµγ5d(

!q) n(0)

p(!q) uγµd(!q) n(0)

I will focus on two quantities •  Iso-vector scalar and tensor charges

needed to probe novel scalar and tensor interactions at the TeV scale.

•  gA is the benchmark charge

•  The contributions of the * Θ-term, * quark EDM * quark chromo EDM to the neutron electric dipole moment

~10-13 fm

⇥0.0010 ⇥0.0005 0.0000 0.0005 0.0010

⇥0.004

⇥0.002

0.000

0.002

0.004

0.006

0.008

�T

� S LHC ⇧ 14 TeV, 300 fb⇥1

Low⇥energy future, ⌅gS�gS ⇤ 50�

LHC ⇧ 14 TeV, 10 fb⇥1

Low⇥energy future, ⌅gS�gS ⇤ 20�

Status of numerical simulations being done

on Titan at OLCF As Titan hums we shake off slumber sharping our tools dive into the frigid neutron in the outpour of numbers hides the cosmic structure

•  Reached 10% uncertainty in nuclear charges. It required: –  High Statistics (O(50,000) – O(128,000) measurements)

–  Demonstrating control over all Systematic Errors: •  Contamination from excited states

•  Non-perturbative renormalization of bilinear operators (RIsmom scheme) Ø  Finite volume effects

Ø  Chiral extrapolation to physical mu and md (simulate at physical point)

Ø  Extrapolation to the continuum limit (lattice spacing a → 0)

n p ×

n p ×

n p ×

Achieving <10% uncertainty in nuclear charges <p|u Γd|n>

14

Oiq

n p ×

Isolate the neutron e-Mnτ Project on the proton e-Mpτ

u d

u u d d

2+1 flavor (u, d, s) clover lattices

ms “tuned” to its physical value using Mss

Md = mu is lowered to its physical value displaying the dependence of physical quantities on the quark mass

15

a(fm) Lattice Volume

Mπ L Mπ

(MeV) # of Configs

HP Measure

Low-precision Measure

0.114 323 × 96 5.55 316 1000 4x1000 128x1000

0.081 323 × 64 4.08 312 1005 3x1005 96x1005

0.080 483 × 96 4.09 210 629 4x629 128x629

0.080 643 x 128 5.46 210 350 5x350 160x350

AMA analysis on 4 ensembles

•  LP=Low precision; HP=high-precision •  Cost: 64 LP measurements ≈ 4(HP-LP) bias correction •  128 well-separated source points on 4 time slices.

(use random source points for smaller correlations compared to fixed source locations)

•  A low cost way to improve statistics (≈16x)

16

Next level of precision requires: O(2000) configurations with O(100) AMA measurements on each.

Blum, Izubuchi, Shintani, PRD88, 094503 (2013)

CAMA =1NLP

C LP∑ +1NHP

(C HP∑ −C LP )

Reducing excited state contamination: 3-pt fn.

17

Assuming 1 excited state, the 3-point function is given by

Where M0 and M1 are the masses of the ground & excited state and A0 and A1 are the corresponding amplitudes.

Γ3(t f , t, ti ) = A02 0 O 0 e−M0 Δt + A1

2 1O 1 e−M0Δte−ΔM Δt +

A0A1* 0 O 1 e−M0 Δte−ΔM (Δt−t ) + A0

*A1 1O 0 e−ΔM te−M0Δt

n p×

ti Δt = tsep = tf - ti tf

O(t)

Make a simultaneous fit to data at multiple Δt = tsep =tf - ti

Manifestation of excited state contamination

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

-6 -4 -2 0 2 4 6

g Au-d

, con

τ - tsep/2

a09m220 Extraptsep=10tsep=12tsep=14

Signal for the charges C13, 1000 confs D5, 1005 confs D6, 629 confs D7, 350 confs

1.15

1.20

1.25

1.30

1.35

1.40

1.45

-8 -6 -4 -2 0 2 4 6 8

g A

τ - tsep/2

Extraptsep=8

tsep=10

tsep=12tsep=14

1.15

1.20

1.25

1.30

1.35

1.40

1.45

-8 -6 -4 -2 0 2 4 6 8

g A

τ - tsep/2

Extraptsep=10tsep=12

tsep=14tsep=16

1.15

1.20

1.25

1.30

1.35

1.40

1.45

-8 -6 -4 -2 0 2 4 6 8

g A

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

1.15

1.20

1.25

1.30

1.35

1.40

1.45

-8 -6 -4 -2 0 2 4 6 8

g A

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-8 -6 -4 -2 0 2 4 6 8

g S

τ - tsep/2

Extraptsep=8

tsep=10

tsep=12tsep=14

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-8 -6 -4 -2 0 2 4 6 8

g S

τ - tsep/2

Extraptsep=10tsep=12

tsep=14tsep=16

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-8 -6 -4 -2 0 2 4 6 8

g S

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

0.40

0.60

0.80

1.00

1.20

1.40

1.60

-8 -6 -4 -2 0 2 4 6 8

g S

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

1.05

1.10

1.15

1.20

1.25

1.30

1.35

-8 -6 -4 -2 0 2 4 6 8

g T

τ - tsep/2

Extraptsep=8

tsep=10

tsep=12tsep=14

1.05

1.10

1.15

1.20

1.25

1.30

1.35

-8 -6 -4 -2 0 2 4 6 8

g T

τ - tsep/2

Extraptsep=10tsep=12

tsep=14tsep=16

1.05

1.10

1.15

1.20

1.25

1.30

1.35

-8 -6 -4 -2 0 2 4 6 8

g T

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

1.05

1.10

1.15

1.20

1.25

1.30

1.35

-8 -6 -4 -2 0 2 4 6 8

g T

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

1.23

1.24

1.25

1.26

1.27

1.28

-8 -6 -4 -2 0 2 4 6 8

g V

τ - tsep/2

Extraptsep=8

tsep=10

tsep=12tsep=14

1.19

1.20

1.21

1.22

1.23

1.24

-8 -6 -4 -2 0 2 4 6 8

g V

τ - tsep/2

Extraptsep=10tsep=12

tsep=14tsep=16

1.19

1.20

1.21

1.22

1.23

1.24

-8 -6 -4 -2 0 2 4 6 8

g V

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

1.19

1.20

1.21

1.22

1.23

1.24

-8 -6 -4 -2 0 2 4 6 8

g V

τ - tsep/2

Extraptsep=08tsep=10

tsep=12tsep=14tsep=16

Renormalization of bilinear operators

•  Non-perturbative renormalization factors ZΓ using the RI-sMOM scheme (p1

2 = p22 = q2)

–  Need quark propagator in momentum space

•  Need to demonstrate: there exists a window ΛQCD << p << π/a

•  Smearing introduces artifacts –  Gluon momentum above (~1/a) are averaged out

–  May shrink the ΛQCD << p << π/a window

•  Renormalized results presented in MS@2 GeV: –  2-loop matching

–  3-loop running to 2 GeV

20

× Γ

p1 p2

Martinelli et al, (1995) hep-lat/9411010 Strum et al, (2009) hep-ph 0901.2599

Analyzing lattice data Ω(a, Mπ, Mπ L): Extrapolations in a, Mπ

2, Mπ L

21

€

g(a,Mπ ,L) = g + A a + B Mπ2 + C e−M π L +…

We use lowest order corrections when fitting lattice data w.r.t.

•  Lattice spacing: a

•  Dependence on light quark mass: mq ~ Mπ2

•  Finite volume: Mπ L

AMA: Simultaneous extrapolation in a, Mπ2, MπL

22

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Status of results on iso-vector charges (preliminary– to appear June, 2016)

23

** gA = 1.23 ** gS = 1.02 *** gT = 1.01

Expt. gA = 1.276(3)

Vector and Axial form-factors

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

GEv (Q

2)

Q2 (GeV2)

C13D5D6D7

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

GEv (Q

2)

Q2 (GeV2)

Alberico, et al., 2009, Fit I Alberico, et al., 2009, Fit II

Kelly, 2004

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0

GMv (Q

2)

Q2 (GeV2)

C13D5D6D7

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0

GMv (Q

2)

Q2 (GeV2)

Alberico, et al., 2009, Fit I Alberico, et al., 2009, Fit II

Kelly, 2004

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

GA (

Q2)

/ G

A (

0)

Q2 (GeV2)

C13D5D6D7

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.2 0.4 0.6 0.8 1.0

GA (

Q2)

/ G

A (

0)

Q2 (GeV2)

Dipole:mA = 1.10 GeVmA = 1.29 GeVmA = 1.35 GeV

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 0.2 0.4 0.6 0.8 1.0

GP (

Q2)

/ G

A (

0)

Q2 (GeV2)

Pheno. (mA = 1.29 GeV)C13

D5D6D7

What is needed for obtaining isovector charges with 2% total errors?

This is attainable by 2020

2000 lattices (10–15K trajectories) with

large volume Mπ L ≥ 4

a = 0.1, 0.075, 0.05 fm Mπ = 300, 200, 140 MeV

O(200,000) measurements

What is needed for obtaining isovector charges with 2% total errors?

This is attainable by 2020

2000 lattices (10–15K trajectories) with

large volume Mπ L ≥ 4

a = 0.1, 0.08, 0.05 fm Mπ = 300, 200, 140 MeV

O(200,000) measurements

Constraints on [εS ,εT]: β-decay versus LHC

•  LHC can provide constraints comparable to low-energy ones with δgS/gS ~10% and b, bν ~ 10-3

•  LHC @ 14 TeV and 300 fb-1: look for events with an electron and missing energy at high transverse mass

27

d u

e ν W

,HB

SM

LHC

Neutron Electric Dipole Moment

•  New (larger) CP violation needed to explain weak scale Baryogenesis

•  All CPV interactions contribute to the nEDM

•  nEDM provides stringent constraints on BSM theories

•  Need precise values of matrix elements of CP violating effective operators to convert bounds on nEDM into bounds on BSM parameters.

28

~10-13 fm

nEDM: History & Promise

29

•  ORNL •  Sussex •  ILL •  PSI •  Munich •  TRIUMF •  LANL •  …

Future: UCN experimental sensitivity: S∝E N τ

dn ≤ 2.9 × 10-26 e cm

B E

ν

For E = 50kV/cm dn= 4x10-27e·cm Δν = 0.2 µHz (~60 days for 2π rotation)

ν = −[2µnB± 2dnE] / hΔν = −4dnE / h

dn = hΔν4E

Principle of the Measurement

For B ~ 10mG ν = 30 Hz

S∝E N τSensitivity of Ramsey Method

Novel CP violation: operators in EFT

31

€

q σµν γ 5 q F µν

€

q σµν γ 5 q λaGaµν

×

γ5σµν

n n ×

n n •  4-pt function as γ can attach to any quark line •  Gluon free end can attach to any quark line

γ attaches to the vertex

Quark-EDM Chromo-EDM

> > > >

γ5σµν

Quark Chromo EDM: 4-pt functions

32

Connected Contribution

33

u"

d"

d"

u"

d"

d"Pε"

Pε"P"

P"seq"

u"

d"

d"

u"

d"

d"P"

P"

P)ε"seq"

Pε"

u"

d"

d"

u"

d"

d"

P"

Pε"

Pε"

P)ε"seq"

u"

d"

d"

u"

d"

d"

P"

P"

P"seq"

Pε"

Disconnected Contribution

34

u"

d"

d"

u"

d"

d"Pε"

Pε"P"

u"

d"

d"

u"

d"

d"P"

P"Pε"

u"

d"

d"

u"

d"

d"

P"

Pε"

Pε"

u"

d"

d"

u"

d"

d"

P"

P"

Pε"

P" Pε"

Pε" P"

Reweight by the ratio of determinants

35

eiεu"

d"

d"

u"

d"

d"Pε"

Pε"P"

P"seq"

u"

d"

d"

u"

d"

d"P"

P"

P)ε"seq"

Pε"

u"

d"

d"

u"

d"

d"

P"

Pε"

Pε"

P)ε"seq"

u"

d"

d"

u"

d"

d"

P"

P"

P"seq"

Pε"

u"

d"

d"

u"

d"

d"Pε"

Pε"P"

u"

d"

d"

u"

d"

d"P"

P"Pε"

u"

d"

d"

u"

d"

d"

P"

Pε"

Pε"

u"

d"

d"

u"

d"

d"

P"

P"

Pε"

P" Pε"

Pε" P"+

Det[ /D+m− r2D2 +Σµν (cSWGµν + iε !Gµν )]

Det[ /D+m− r2D2 + cSWΣ

µνGµν ]

= exp{Tr Ln[1+ iεΣµν !Gµν ( /D+m−r2D2 + cSWΣ

µνGµν )−1]}

≈ exp{Tr iεΣµν !Gµν ( /D+m−r2D2 + cSWΣ

µνGµν )−1}

Does the method work?

36

0.08

0.10

0.12

0.14

0.16

0.18

2 4 6 8 10 12

α

t

Clover-on-HISQa≈0.12 fm, m

π≈310 MeV

60 meas × 125 confs

ε = 0.010.0

0.1

0.2

0.3

0.4

0 0.01 0.02 0.03

α

ε

Clover-on-HISQ

a≈0.12 fm, mπ≈310 MeV

60 meas × 25 confs

t ≈ 1.2 fm

With CP violation uN (p)N u(p) = eiαNγ5 (i/p+MN )e

iαNγ5

2-pt function: The phase α should be linear in ε for small ε

Connected part of F3 with the chromo EDM operator

37

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7 8

F3D

, d

-u

t

Clover-on-HISQa≈0.12 fm, m

π≈310 MeV

60 meas × 212 confs

ε = 0.01, Q2=1

tsep= 8tsep=10

Preliminary!!-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7 8

F3U

, d-u

t

Clover-on-HISQa≈0.12 fm, m

π≈310 MeV

60 meas × 212 confs

ε = 0.01, Q2=1

tsep= 8tsep=10

Preliminary!!

What Next •  Write up all the results obtained this year •  Develop and demonstrate signal (10% error) in

all the pieces of the chromo EDM operator •  Resources for generating the lattices to do a

credible study versus a, Mπ and the lattice volume