Probing TeV scale physics in precision UCN decays Rajan Gupta Theoretical Division Los Alamos...

Probing TeV scale physics in precision UCN decays

Rajan Gupta

Theoretical Division

Los Alamos National Lab

Lattice 2013 Mainz, 30 July 2013

Superconducting Spectrometer

Neutron Polarizing/Spin-flipper Magnet

1LAUR-12-20208

Theory and Experimental effort centered at LANL

• Tanmoy Bhattacharya (LANL)

• Vincenzo Cirigliano (LANL)

• Saul Cohen (U of Washington)

• Alberto Filipuzzi (Valencia, Spain)

• Martin Gonzalez-Alonso (Madison, Wisconsin)

• Michael Graesser (LANL)

• Rajan Gupta (LANL)

• Anosh Joseph (LANL)

• Huey-Wen Lin (U of Washington)

Theory and Lattice QCD Collaboration (PNDME)

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PRD85:5 (2012) 054512 arXiv:1110.6448 arXiv:1306.5435

Precision calculations of gS, gT

using Lattice QCD

gT ~

gS ~

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Goal: 10-20% accuracy

XBSM

T. Bhattacharya, S. Cohen, R. Gupta, H-W Lin, A. Joseph

Impact of reducing errors in gS and gT from 50→10%

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|B1-b| < 10-3

|b| < 10-3

b0+ = 2.6 (4.3)∗10-3

Allowed region in [εS , εT ] (90% contours)

gT ~

gS ~

Expt. input

Limited by precision of ME

• Achieving 10-20% uncertainty is a realistic goal but requires:

– High Statistics: computer resources from USQCD, XSEDE, LANL

– Controlling all Systematic Errors:

• Finite volume effects

• Contamination from excited states

• Chiral Extrapolations to physical u and d quark masses

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

• Non-perturbative renormalization of bilinears using the RIsmom scheme

Lattice QCD calculation of <p|u Γd|n>Oi

q

n p×

Isolate the neutron e-

Mnτ

Project on the proton e-

Mpτ

ud

uud d

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Lattice setup: Choices we made• Gauge configurations with 2+1+1 flavor of dynamical quarks

– HISQ lattices generated by the MILC collaboration (short-term)

• Analysis using clover fermions (Clover on HISQ)

– Issue of exceptional Configurations – extensive tests

• Improving Signal in Baryon Correlators

– Large smearing of source used in matrix inversion (p = 0)

– HYP smearing of gauge configurations

• Study multiple time separations between the source (neutron) and sink (proton) to study & reduce excited state contribution

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n p×tsep

Sequential propagators with

nucleon insertion at p=0

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p pu

d

uO(p,t)

Initial inversion of Dirac operator with smeared source

Sequential inversion with (n,p) insertion at p=0

2+1+1 flavor HISQ lattices: goal 1000 configs

• ms set to its physical value using Mss

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a(fm) ml/ms LatticeVolume

Mπ L Mπ (MeV) Configs. Analyzed

0.12 0.2 243 × 64 4.54 305 1013/1013

0.12 0.1 323 × 64 4.29 217 958/958

0.09 0.2 323 × 96 4.5 313 881/1000

0.09 0.1 483 × 96 4.73 220 890/1000

0.06 0.2 483 × 144 4.53 320 800/1000

0.06 0.1 643 × 144 4.28 229 0/1000

Issues in Analysis

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Signal in 2-point baryon correlators

a = 0.12 fm lattices with Mπ = 310 MeV

(Total of 1013 Configurations, each with 4 sources)10

SS

: E

ffec

tive

Mas

s P

lot M

eff

507 Conf 506 Conf 1013 conf

2-point function → MN

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Findings at a=0.12 fm with Mπ=310, 220 MeV

• Statistical analysis of ~1000 configurations and

as 2 subsets of ~500 configurations

– All three estimates consistent within 1–2 σ

– Errors of the 2 subsets ~√2 larger than the full set

– Variation in gΓ between 2 subsets ≈ Δt dependence

– Signal improves as a → 0

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Need > 4x1000 configurations before tsep dependence, chiral and continuum extrapolations

can be resolved & estimated to give gS to 10%

Excited States

• Statistics & better interpolating operators

– Improve overlap with ground state of (p,n) operators

• Simulations at many Δt

– Needed to eliminate excited state contribution

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n p×

n nΔt =tf - ti =tp - tn

Γ(t)

Signal in the ratio

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The calculation of gS will dictate the statistics needed

One-state versus two-state fit

Scalar channel gS: Signal versus Δt, t

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Δt = 8 9 10 11 12

Δt=10 (~1.2 fm) is the best compromise

1013 conf

Tensor channel gT: Signal versus Δt

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Δt = 8 9 10 11 12

No significant Δt dependence

Reducing excited state contamination

Simultaneous fit to all Δt =tf - ti

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Assuming 1 excited state, the 3-point function behaves as

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

n p×

ti t tf

Simultaneous fit to all Δt

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Δt=8 Δt=10 Δt=12

Data for gS on the Mπ=220 MeV ensemble at a=0.12fm

Term

Excluding

Simultaneous fit to all Δt

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Δt=10 Δt=12 Δt=14

Data for gS on the Mπ=220 MeV ensemble at a=0.09fm

Term

Excluding

Uncertainty in the chiral extrapolation

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Do chiral logs dominate at lower Mπ

2 ?

What Mπ2

interval should be used in the extrapolation?

Reducing uncertainty in the chiral extrapolation

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Ongoing simulations

Renormalization of bilinear operators

• Non-perturbative renormalization ZΓ

using the RI-sMOM scheme

– Need quark propagator

in momentum space

• Results

– 101 lattices at a=0.12 fm Mπ=310

– 60 lattices at a=0.12 fm Mπ=220

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×

Γ

> >

ZA

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Mπ = 310 MeV 220 MeV

ZS (in MS scheme at 2 GeV )

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Mπ = 310 MeV 220 MeV

ZT (in MS scheme at 2 GeV)

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Mπ = 310 MeV 220 MeV

Renormalization constants ZΓ • Largest uncertainty:

– O(a) errors due to full rotational symmetry → cubic symmetry

– Examine p4 versus (p2)2 behavior

• Data show (~0.05) variation at fixed p2

• ZA, ZS and ZT are all between 0.95–1.0 with < 1% error

– HYP smearing brings the ZΓ close to unity

• ZΓ → 1 as a → 0

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ResultsPNDME Collaboration

• gA = 1.214(40)

• gS = 0.66(24)

• gT = 1.094(48)

LHPC

• gA = 1.0-1.2

• gS = 1.08(28)(16)

• gT = 1.038(11)(12)

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gS and gT

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Continuum extrapolation

• Need estimates at a = 0.12, 0.09, 0.06 fm

to perform a continuum extrapolation of

renormalized charges (gR = gbare × Z)

• Will need >1000 configurations at a=0.12, 0.09

and 0.06 fm to quantify if gS and gT have

significant a dependence and get estimates with

10% uncertainty

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Summary

• GOAL: To use experimental measurements of b and b-bν

at the 10-3 level to bound εS and εT requires calculation of

gT and gS at the 10-20% level

• 2011: Lattice QCD estimates of gS and gT improved the

bounds on εS and εT compared to previous estimates based

on phenomenological models

• 2013: Lattice calculations are on track to providing

gT and gS with 10-20% uncertainty

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β-decay versus

LHC constraints

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LHC @ 14TeV and 300fb-1, will provide comparable constraints to low-energy ones with δgS/gS ~15%

Acknowledgements

• Computing resources from

– USQCD

– XSEDE

– LANL

• 2+1+1 HISQ lattices generated by the MILC

collaboration

• Computer code uses CHROMA library

• Supported by DOE and LANL-LDRD

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