Two-loop fermionic contributions to polarized Moller scattering - - PowerPoint PPT Presentation

LoopFest XVIII, August 13, 2019 FermiLab, IL

Yong Du

Two-loop fermionic contributions to polarized Moller scattering asymmetries

In collaboration with Ayres Freitas, Hiren Patel, Michael J. Ramsey-Musolf

Two-loop fermionic contributions to polarized Moller scattering asymmetries (status report)

Yong Du

In collaboration with Ayres Freitas, Hiren Patel, Michael J. Ramsey-Musolf LoopFest XVIII, August 13, 2019 FermiLab, IL

Outline

• Motivations for the polarized Moller scattering at JLab
• Theoretical calculation summary
• Status of NNLO calculations with a closed fermion loop
• Summary

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Yong Du UMass-Amherst ACFI

Motivations

Standard Model (SM) for particle physics was completed in the 1960s by Glashow, Salam and Weinberg. Low energy precision measurements of weak neutral current provide a rigorous way to test the SM. Also complementary to high energy searches. The chiral structure of SM implies parity violation for all electroweak processes.

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Yong Du UMass-Amherst ACFI

Motivations

Standard Model (SM) for particle physics was completed in the 1960s by Glashow, Salam and Weinberg. Low energy precision measurements of weak neutral current provide a rigorous way to test the SM. Also complementary to high energy searches. The chiral structure of SM implies parity violation for all electroweak processes. One example is: longitudinally polarized electrons scattering from unpolarized targets.

ALR = dσL − dσR dσL + dσR

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ALR (e−e− → e−e−) = GµQ2

√ 2πα 1−y 1+y4+(1−y)4

• 1 − 4 sin2 θW
• Derman and Marciano, 1979

One-loop EW radiative corrections reduce SM prediction by 40+-3%, making it more sensitive to the weak mixing angle. Czarnecki and Marciano, 1996

Motivations

y = Q2 s

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• J. Erler, M.J. Ramsey-Musolf, 2005

arXiv:hep-ex/0509008

Motivations

Czarnecki, Marciano, 2000

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• J. Erler, M.J. Ramsey-Musolf, 2005

arXiv:hep-ex/0509008

Motivations

Czarnecki, Marciano, 2000

3σ

Marciano, 2006

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Motivations

• J. Erler, M.J. Ramsey-Musolf, 2005

arXiv:hep-ex/0509008 Czarnecki, Marciano, 2000

3σ

Marciano, 2006

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δQe

W = ±2.1%(stat.) ± 1.1%(syst.) Moller looks directly into this discrepancy, and the projected Moller uncertainty is:

The MOLLER collaboration, arXiv:1411.4088

APV = 35 ppb, δAPV = 0.73 ppb δ(sin2 θW ) = ±0.00024(stat.) ± 0.00013(syst.)

• K. Kumar, MOLLER workshop at UMass-Amherst, 2014

Q2 ' 0.005GeV2

Motivations

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In an EFT approach, four-fermion contact interaction

Le1e2 = X

i,j=L,R

g2

ij

2Λ2 ! eiγµeiejγµej

Λ p |g2

RR g2 LL|

' 7.5TeV

q |g2

RR − g2 LL| = 2π

Λ ' 50TeV

Motivations

The MOLLER collaboration, arXiv:1411.4088

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Yong Du UMass-Amherst ACFI

In an EFT approach, four-fermion contact interaction

Le1e2 = X

i,j=L,R

g2

ij

2Λ2 ! eiγµeiejγµej

Λ p |g2

RR g2 LL|

' 7.5TeV

q |g2

RR − g2 LL| = 2π

Λ ' 50TeV

Motivations

∆−−

YD, A. Dunbrack, M.J. Ramsey-Musolf, J.-H. Yu, 2018

Complementary to collider searches

The MOLLER collaboration, arXiv:1411.4088

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In an EFT approach, four-fermion contact interaction

Other scenarios: Dark photon/Z, SUSY

Kurylov, Ramsey-Musolf, Su, 2002, 2003, 2004 Davoudiasl, Lee, Marciano, 2012

Le1e2 = X

i,j=L,R

g2

ij

2Λ2 ! eiγµeiejγµej

Λ p |g2

RR g2 LL|

' 7.5TeV

q |g2

RR − g2 LL| = 2π

Λ ' 50TeV

Motivations

∆−−

YD, A. Dunbrack, M.J. Ramsey-Musolf, J.-H. Yu, 2018

Complementary to collider searches

The MOLLER collaboration, arXiv:1411.4088

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Theoretical calculation symmetry

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Theoretical calculation symmetry

LO:

Derman and Marciano, 1979

NLO:

Czarnecki and Marciano, 1996; Denner and Pozzorini, 1998; Petriello, 2003; Zykunov, 2004; Kolomensky et al, 2005; Zykunov et al, 2005; Zykunov, 2009; Aleksejevs et al, 2010, 2011, 2012

NNLO:

Aleksejevs et al, 2011, 2012, 2015

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Yong Du UMass-Amherst ACFI

Theoretical calculation symmetry

LO:

Derman and Marciano, 1979

NLO:

Czarnecki and Marciano, 1996; Denner and Pozzorini, 1998; Petriello, 2003; Zykunov, 2004; Kolomensky et al, 2005; Zykunov et al, 2005; Zykunov, 2009; Aleksejevs et al, 2010, 2011, 2012

NNLO:

Aleksejevs et al, 2011, 2012, 2015

Conclusion: need a full NNLO calculation to match experimental precision at JLab.

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lightening introduction of expansion by regions using the gamma-Z box

F [0]

Γ

= Z µ2✏ddq (2π)d 1 q2 (q + k1)2 (q − p1)2 h (q + k1 − k2)2 − m2

Z

i

For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday

NNLO contributions with a closed Fermion loop

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pex << mZ

lightening introduction of expansion by regions using the gamma-Z box

F [0]

Γ

= Z µ2✏ddq (2π)d 1 q2 (q + k1)2 (q − p1)2 h (q + k1 − k2)2 − m2

Z

i

F [0]

Γ

= Z µ2✏ddq (2π)d 1 (q2)3 (q2 − m2

Z)

− 1 m2

Z

Z µ2✏ddq (2π)d 1 q2 (q + k1)2 (q − p1)2

For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday

NNLO contributions with a closed Fermion loop

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Yong Du UMass-Amherst ACFI

pex << mZ

lightening introduction of expansion by regions using the gamma-Z box

F [0]

Γ

= Z µ2✏ddq (2π)d 1 q2 (q + k1)2 (q − p1)2 h (q + k1 − k2)2 − m2

Z

i

F [0]

Γ

= Z µ2✏ddq (2π)d 1 (q2)3 (q2 − m2

Z)

− 1 m2

Z

Z µ2✏ddq (2π)d 1 q2 (q + k1)2 (q − p1)2

For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday

NNLO contributions with a closed Fermion loop

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pex << mZ

{

LO+NLO: two years hand written note Lorentz contraction, Dirac trace all done by hand All scalar/vector/tensor integrals evaluated by hand in two schemes: dim reg and mass regularization

NNLO contributions with a closed Fermion loop

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Yong Du UMass-Amherst ACFI

{

LO+NLO: two years hand written note Lorentz contraction, Dirac trace all done by hand All scalar/vector/tensor integrals evaluated by hand in two schemes: dim reg and mass regularization FeynArts to generate the amplitudes Package-X for the tensor algebra. Own Mathematica code to do the expansion by regions. FIRE for reduction.

H.H. Patel, 2015, 2016

• T. Hahn, 2001

A.V. Smirnov, 2008

{

NNLO contributions with a closed Fermion loop

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Finished topologies

X X X

NNLO contributions with a closed Fermion loop

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X

NNLO contributions with a closed Fermion loop

Finished topologies

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Remaining topology:

Plan to finish cross-checking by the end of August.

X

NNLO contributions with a closed Fermion loop

Finished topologies

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MOLLER status (private communication with K. Kumar):

• 1. Project is funded and facilities under construction.
• 2. Expect theoretical result in early 2021 (We are on track).
• 3. Finish construction around 2023.
• 4. 3 years data taking starting from 2024.

NNLO contributions with a closed Fermion loop

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Summary

APV is sensitive to the weak mixing angle, current most precise measurements differ by 3sigma, using one or the other predicts very different dynamics. MOLLER project at JLab looks into this discrepancy with comparable precision and will be sensitive to TeV or 10's of TeV scale BSM physics. Previous work found that theoretical uncertainty from NNLO is less or about the same as MOLLER at JLab, and a full NNLO calculation is needed. We calculated the NNLO contributions of SM to APV with a closed fermion loop. Each topology is cross-checked by at least two of us. The remaining topology is 2-loop box diagrams, expect to finish by the end of this August.

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Thanks

Special thanks to K. Kumar for supporting this travel. Tons of thanks to Hiren and Ayres for teaching me how to automate 2-loop calculation.

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Back up slides

• =
• =
• Δ []

[Δ] []

ρ parameter EXCLUSION region from above

H++H--→ℓ+ℓ+ℓ'-ℓ'- ℓ±ℓ±hW∓ W±W±hW∓ H++H--→W+W+W-W-

ATLAS, JHEP03, 041(2015) ATLAS, Eur. Phys. J C78 (2018)

S √ S + B ≥ 5

m∆ ≥ 0 GeV ⇔ mH±± ≥ 54.78 GeV

LEP constraints automatically satisfied

OPAL (1992, 2002)

m2

H±± ' m2 ∆ λ5

2 v2

Φ

Ls.s. = hijLic

Liτ2∆Lj L + h.c.

Credit to: Michael J. Ramsey-Musolf