N - PAVI 14

Partonic charge symmetry violation
on the lattice
Ross D. Young
CSSM & CoEPP, University of Adelaide
PAVI 14: From parity violation to hadron structure and more...
Skaneateles, NY, 14–18 July, 2014
Partonic charge symmetry violation
on the lattice
Ross D. Young
CSSM & CoEPP, University of Adelaide
PAVI 14: From parity violation to hadron structure and more...
Skaneateles, NY, 14–18 July, 2014
Outline
From parity violation to hadron structure and more...
Outline
From parity violation to hadron structure and more...
From hadron structure to parity violation and more...
Outline
From parity violation to hadron structure and more...
From hadron structure to parity violation and more...
From hadron structure to parity violation and nothing more...
Outline
From parity violation to hadron structure and more...
From hadron structure to parity violation and more...
From hadron structure to parity violation and nothing more...
From hadron structure to parity violation and nothing more... so far
Hadron Structure
Dynamics of the strong force comes from QCD
Hadron Structure
Dynamics of the strong force comes from QCD
Almost all of the structure of the proton is governed by QCD
Hadron Structure
Dynamics of the strong force comes from QCD
Almost all of the structure of the proton is governed by QCD
Nonperturbative QFT
Lattice QCD
2400
H
*
H
Hs
*
Hs
Bc
*
Bc
© 2012 Andreas Kronfeld/Fermi Natl Accelerator Lab.
2200
2000
m
1800
4000 MeV
(MeV)
1600
1400
1200
1000
800
600
400
Kronfeld
200
0
π
ρ
K
∗
K
η
η+
ω
φ
N
Λ
Σ
Ξ
Δ
∗
Σ
Ξ
∗
Hadron spectrum in lattice QCD
Excellent description of low-lying hadron masses
Ω
Shanahan et al., PRD(2014)
Shanahan et al., 1403.1965[hep-lat]
Structure: Isovector Nucleon Form Factors
Red curves: Kelly parameterisation of data
Form Factors: Details for another talk
Lattice Dirac form factors
Form Factors: Details for another talk
Lattice Dirac form factors
Lattice Pauli form factors
Form Factors: Details for another talk
Lattice Dirac form factors
Lattice Pauli form factors
(Partially quenched) SU(3)
Chiral EFT-inspired...
Form Factors: Details for another talk
Lattice Dirac form factors
Lattice Pauli form factors
(Partially quenched) SU(3)
Chiral EFT-inspired...
2
Q ⇠ 0.26 GeV
2
Q2 ⇠ 1.35 GeV2
Chiral extrapolation
Form Factors: Details for another talk
Lattice Dirac form factors
Lattice Pauli form factors
(Partially quenched) SU(3)
Chiral EFT-inspired...
2
Q ⇠ 0.26 GeV
2
Q2 ⇠ 1.35 GeV2
Chiral extrapolation
Phiala Shanahan,
U. Adelaide
Shanahan et al., PRD(2014)
Shanahan et al., 1403.1965[hep-lat]
Isovector Nucleon Form Factors
Red curves: Kelly parameterisation of data
Shanahan et al., PRD(2014)
Shanahan et al., 1403.1965[hep-lat]
Some items still to address:
* Finite “a” extrapolation
* Excited state contamination
Isovector Nucleon Form Factors
Red curves: Kelly parameterisation of data
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge symmetry is broken by:
Quark masses
md mu
⇠ 0.5%
Mp
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge symmetry is broken by:
Quark masses
md mu
⇠ 0.5%
Mp
Electromagnetism
Qu 6= Qd
O(↵) ⇠ 1%
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge symmetry is broken by:
Quark masses
md mu
⇠ 0.5%
Mp
Electromagnetism
Qu 6= Qd
O(↵) ⇠ 1%
Strong physics:
Straightforward for lattice
Charge Symmetry Violation
Nature doesn’t exhibit exact charge symmetry invariance
Charge symmetry is broken by:
Quark masses
md mu
⇠ 0.5%
Mp
Electromagnetism
Qu 6= Qd
O(↵) ⇠ 1%
Strong physics:
Straightforward for lattice
“Long” physics:
New for lattice simulations
Proton–neutron mass splitting
Electromagnetic effects: Cottingham sum rule
Subtracted dispersive analysis:
Walker-Loud, Carlson & Miller, PRL(2012)
(Mp
Mn )
EM
= 1.30(03)(47) MeV
Proton–neutron mass splitting
Electromagnetic effects: Cottingham sum rule
Subtracted dispersive analysis:
Walker-Loud, Carlson & Miller, PRL(2012)
(Mp
Mn )
EM
Strong contribution
= 1.30(03)(47) MeV
Lattice QCD
Proton–neutron mass splitting
Electromagnetic effects: Cottingham sum rule
Subtracted dispersive analysis:
Walker-Loud, Carlson & Miller, PRL(2012)
(Mp
Mn )
EM
= 1.30(03)(47) MeV
Strong contribution
Lattice QCD
NPLQCD H2007L
RBC H2010L
WLCM
RM123 H2012L
QCDSF-UKQCD H2012L
Shanahan et al. H2013L
BMW H2013L
-6
-4
-2
HM p-MnLstrong @MeVD
0
Current Status
4
BMW (2013)
HM p-MnLEM @MeVD
3
WLCM
2
1
0
R
PE
EX
-2
T
EN
IM
-1
-5
-4
-3
-2
-1
HM p-MnLStrong @MeVD
0
1
Current Status
4
BMW (2013)
HM p-MnLEM @MeVD
3
WLCM
2
1
0
R
PE
EX
-2
T
EN
IM
-1
-5
-4
-3
-2
-1
HM p-MnLStrong @MeVD
0
1
Current Status
4
BMW (2013)
HM p-MnLEM @MeVD
3
WLCM
2
1
0
R
PE
EX
-2
T
EN
IM
-1
-5
-4
-3
-2
-1
HM p-MnLStrong @MeVD
0
1
Charge symmetry violations in
nucleon parton distributions
Partons
Fast-moving bike: Distribution of momenta carried by components
Partons
0.6
u(x)
u
¯(x)
0.5
0.4
0.3
0.2
0.1
0.0
0.0
d(x)
¯
d(x)
MSTW@4 GeV2
0.2
0.4
0.6
0.8
1.0
x
Fast-moving bike: Distribution of momenta carried by components
Fast-moving proton: distribution of momenta carried by quarks
Charge symmetry violation in partons
Partonic charge symmetry relations
p
n
p
n
u (x) = d (x)
d (x) = u (x)
Charge symmetry violation in partons
Partonic charge symmetry relations
p
n
p
n
u (x) = d (x)
d (x) = u (x)
Let’s appeal to lattice to determine the breaking
p
u(x) ⌘ u (x)
d(x) ⌘ dp (x)
n
d (x)
un (x)
Charge symmetry violation in partons
Partonic charge symmetry relations
p
n
p
n
u (x) = d (x)
d (x) = u (x)
Let’s appeal to lattice to determine the breaking
p
u(x) ⌘ u (x)
d(x) ⌘ dp (x)
n
d (x)
un (x)
Lattice can only make contact with moments
Z 1
m 1
m 1
m
hx
i=
dx x
[q(x) + ( 1) q¯(x)]
0
Parton CSV (quark mass)
For small breaking in the u-d quark masses m ⌘ (md
hxi
u
m
'
2
✓
@hxipu
@mu
+
@hxipu
@md
◆
✓
@hxind
@mu
+
@hxind
@md
mu )
◆
Parton CSV (quark mass)
For small breaking in the u-d quark masses m ⌘ (md
hxi
u
m
'
2
✓
@hxipu
@mu
+
@hxipu
@md
◆
✓
@hxind
@mu
Charge symmetry
+
@hxind
@md
mu )
◆
Parton CSV (quark mass)
For small breaking in the u-d quark masses m ⌘ (md
hxi
hxi
u
u
m
'
2
✓
@hxipu
@mu
+
@hxipu
@md
◆
✓
@hxind
@mu
Charge symmetry

@hxipu
@hxipu
'm
+
@mu
@md
+
@hxind
@md
mu )
◆
Parton CSV (quark mass)
For small breaking in the u-d quark masses m ⌘ (md
hxi
hxi
u
u
m
'
2
✓
@hxipu
@mu
+
@hxipu
@md
◆
✓
@hxind
@mu
Charge symmetry

@hxipu
@hxipu
'm
+
@mu
@md
How does much does the
up quark momentum
fraction change if I make the
up quark a bit lighter?
+
@hxind
@md
mu )
◆
Parton CSV (quark mass)
For small breaking in the u-d quark masses m ⌘ (md
hxi
hxi
u
u
m
'
2
✓
@hxipu
@mu
+
@hxipu
@md
◆
✓
@hxind
@mu
+
@hxind
@md
mu )
◆
Charge symmetry

@hxipu
@hxipu
'm
+
@mu
@md
How does much does the
up quark momentum
fraction change if I make the
up quark a bit lighter?
How does much does the
up quark momentum
fraction change if I make the
down quark a bit heavier?
QCDSF-UKQCD Lattices
Bietenholtz et al. PRD(2011)
Strange quark mass
Tune lattice parameters such to have exact SU(3) symmetry at
the physical average (light) quark mass
lat
phys
mq = (mu + md + ms )
/3
Physical point
Symmetric Line
ms = mu = md
Lines of constant 3-flavour
average quark mass
Starting point
Light quark mass
Hyperon PDF moments
Start from exact SU(3) symmetric point
hxipu
=
⌃+
hxiu
=
⌅0
hxis
Hence we can estimate relevant derivatives
p
@hxiu
@mu
) hxi
u
'
⌅0
hxis
'm
ms

p
hxiu
ml
@hxipu
@mu
+
,
p
@hxiu
@md
@hxipu
@md
'
'm
⌃+
hxiu
ms
⌃+
hxiu
ms
p
hxiu
ml
⌅0
hxis
ml
Just need to determine hyperon moments about SU(3)
symmetric point
Charge Symmetry Violation
In units of the proton
isovector momentum fraction
Lattice results for quark-mass dependence of hyperon
momentum fractions
Horsley et al. (2011)
Slopes determine
CSV at SU(3)
symmetric point
Charge Symmetry Violation
In units of the proton
isovector momentum fraction
Lattice results for quark-mass dependence of hyperon
momentum fractions
Horsley et al. (2011)
Using phenomenological
momentum fraction and
dispersive estimate of
quark mass ratio:
hxi
hxi
u
=
0.0012(3)
d
= 0.0010(2)
Slopes determine
CSV at SU(3)
symmetric point
Improved estimate: Chiral extrapolation
Tree-level operators
h
↵(n) (BB
q) +
(n)
(B
q B) +
O(mq ) counterterms
n
⇥
(n)
b1 Tr B
⇤
(n)
(BB)Tr(
i
{µ1
µn }
)
p
.
.
.
p
q
⇥
⇤
(n)
b2 Tr B{[ q , B] , M }
[[ q , B] , M ] +
⇥
⇤
⇥
⇤
(n)
(n)
+ b3 Tr B [{ q , B}, M ] + b4 Tr B{{ q , B}, M }
⇥
⇤
⇥
⇤
(n)
(n)
+ b5 Tr BB Tr [ q M ] + b6 Tr BB q Tr [M ]
⇥
⇤
⇥
⇤
(n)
(n)
+ b7 Tr B q B Tr [M ] + b8 Tr BM B Tr [ q ]
⇥
⇤
(n)
+ b9 Tr BBM Tr [ q ]
o
⇥
⇤
(n)
+ b10 Tr B q Tr [M B] p{µ1 . . . pµn } Tr
Shanahan, Thomas & RDY, PRD(2013)114515
Tr
Improved estimate: Chiral extrapolation
Loops
Tree-level operators
h
↵(n) (BB
q) +
(n)
(B
q B) +
O(mq ) counterterms
n
⇥
(n)
b1 Tr B
⇤
(n)
(BB)Tr(
i
{µ1
µn }
)
p
.
.
.
p
q
⇥
⇤
(n)
b2 Tr B{[ q , B] , M }
[[ q , B] , M ] +
⇥
⇤
⇥
⇤
(n)
(n)
+ b3 Tr B [{ q , B}, M ] + b4 Tr B{{ q , B}, M }
⇥
⇤
⇥
⇤
(n)
(n)
+ b5 Tr BB Tr [ q M ] + b6 Tr BB q Tr [M ]
⇥
⇤
⇥
⇤
(n)
(n)
+ b7 Tr B q B Tr [M ] + b8 Tr BM B Tr [ q ]
⇥
⇤
(n)
+ b9 Tr BBM Tr [ q ]
o
⇥
⇤
(n)
+ b10 Tr B q Tr [M B] p{µ1 . . . pµn } Tr
Shanahan, Thomas & RDY, PRD(2013)114515
Tr
Improved estimate: Chiral extrapolation
Loops
Tree-level operators
h
↵(n) (BB
q) +
(n)
(B
q B) +
O(mq ) counterterms
n
⇥
(n)
b1 Tr B
⇤
(n)
(BB)Tr(
i
{µ1
µn }
)
p
.
.
.
p
q
Tr
⇥
⇤
(n)
b2 Tr B{[ q , B] , M }
[[ q , B] , M ] +
⇥
⇤
⇥
⇤
(n)
(n)
+ b3 Tr B [{ q , B}, M ] + b4 Tr B{{ q , B}, M }
⇥
⇤
⇥
⇤
(n)
(n)
+ b5 Tr BB Tr [ q M ] + b6 Tr BB q Tr [M ]
⇥
⇤
⇥
⇤
(n)
(n)
+ b7 Tr B q B Tr [M ] + b8 Tr BM B Tr [ q ]
⇥
⇤
(n)
+ b9 Tr BBM Tr [ q ]
o
⇥
⇤
(n)
+ b10 Tr B q Tr [M B] p{µ1 . . . pµn } Tr
Shanahan, Thomas & RDY, PRD(2013)114515
Phiala Shanahan,
U. Adelaide
Chiral extrapolation of CSV
Using SU(3) symmetry, we can fit isospin symmetric lattice
results for hyperons
No new parameters in EFT to determine CSV
Shanahan, Thomas & RDY, PRD(2013)094515
Chiral extrapolation of CSV
Using SU(3) symmetry, we can fit isospin symmetric lattice
results for hyperons
No new parameters in EFT to determine CSV
Our result
hxi
hxi
Shanahan, Thomas & RDY, PRD(2013)094515
u
=
0.0023(7)
d
= 0.0017(4)
CSV Distributions
We only get one moment from the lattice
Simple parameterisation: MRST
hxi
q
= q x
1/2
(1
x)4 (x
1/11)
Constrained with lattice CSV moments
RY, Shanahan & Thomas, 1312.4990[nucl-th]
NuTeV Experiment
NuTeV Experiment
Paschos-Wolfenstein ratio
RPW =
⌫A
NC
⌫A
CC
⌫
¯A
NC
⌫
¯A
CC
⌫
⌫¯ &
neutral current
charged current
NuTeV: indirect measure of this ratio
With
Exact charge symmetry
Vanishing partonic strangeness s(x)
s¯(x)
Isoscalar nucleus
PW ratio direct measure of weak mixing angle
RPW
1
!
2
sin2 ✓W
2
NuTeV & sin ✓W
Reported discrepancy from the Standard Model
Relies on assumption that CSV is negligible
Back to NuTeV
Correction to the Paschos-Wolfenstein ratio from CSV
✓
◆
1
7
hxi u
hxi d
2
CSV
RPW =
1
sin ✓W
2
3
hxiu + hxid
Our result + CSV from QED parton evolution
Reduce NuTeV Standard Model discrepancy by ~1-sigma
Back to NuTeV
Correction to the Paschos-Wolfenstein ratio from CSV
✓
◆
1
7
hxi u
hxi d
2
CSV
RPW =
1
sin ✓W
2
3
hxiu + hxid
Our result + CSV from QED parton evolution
Reduce NuTeV Standard Model discrepancy by ~1-sigma
Further corrections: Non-isoscalar nucleus, strangeness
see Bentz, Cloet, Londergan & Thomas PLB(2010)
PVDIS@6GeV
PVDIS@6GeV
See X. Zheng yesterday
PVDIS: CSV?
Stolen from P. Souder (JLab gamma-Z boxing, Dec’13)
PVDIS: CSV?
Stolen from P. Souder (JLab gamma-Z boxing, Dec’13)
x = 0.295, Q2 = 1.9 GeV2
AP V
'
AP V
0.003
PVDIS: CSV?
Stolen from P. Souder (JLab gamma-Z boxing, Dec’13)
x = 0.295, Q2 = 1.9 GeV2
AP V
'
AP V
0.003
Don’t worry about it!
Melnitchouk & Hobbs PRD(2008)
PVDIS: CSV
Lattice: (u
d )/2 '
0.20 ± 0.06
Summary
Effects of charge symmetry violation are becoming increasingly
significant in precision studies
Great progress in nucleon structure from lattice QCD
Unambiguously resolved CSV parton moments in lattice QCD
Reduces the NuTeV anomaly
Could improve sensitivity of future SM tests: eg. SoLID
Didn’t show: strange ffs, spin-dep. parton CSV
Future
Improved systematic control of things I’ve discussed
Electromagnetic corrections in parton distributions
Lattice calculations of “disconnected” terms: eg. strangeness
Feynman–Hellmann technique
Thanks
Phiala Shanahan, Tony Thomas, James Zanotti
& QCDSF-UKQCD Collaboration
Spin-dependent CSV
~1% correction to the
Bjorken sum rule
Cloet et al., PLB(2012)
Linear
Chiral
Shanahan, Thomas & RDY, PRD(2013)094515
Connected Spin Contributions
• Energy shift v
Linear terms give:
ulatt
conn =
0.990(20)
dlatt
conn =
0.313(14)
Recall 3-point results:
• Rough agreement
• Possible excited state contamination in 3-point function results?
ulatt
conn =
0.911(29)
dlatt
conn =
0.290(16)
Connected Spin Contributions
• Energy shift v
Linear terms give:
ulatt
conn =
0.990(20)
dlatt
conn =
0.313(14)
Recall 3-point results:
• Rough agreement
Alex Chambers,
• Possible excited state contamination in 3-point
function results?
U. Adelaide
ulatt
conn =
0.911(29)
dlatt
conn =
0.290(16)
Disconnected Spin Contributions
SU(3) symmetric point, m⇡ ⇡ 470 MeV
3 dlatt
disc =
3 ulatt
disc =
ZA = 0.867(4)
0.061(122)
0.030(126)
ulatt
disc =
dlatt
disc =
slatt
disc =
0.015(41)
udisc =
ddisc =
sdisc =
0.013(36)
Tensor Charge - Disconnected
SU(3) symmetric point, m⇡ ⇡ 470 MeV
latt
3 qdisc
= 0.009(79)
ZTMS (µ = 2 GeV) = 0.995(1)
qdisc = 0.003(26)
BMW QCD+QED Lattice calculation
BMW QCD+QED Lattice calculation
BMW QCD+QED Lattice calculation
Some lattice specs:

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