Two-loop fermionic contributions to polarized Moller scattering asymmetries Yong Du In collaboration with Ayres Freitas, Hiren Patel, Michael J. Ramsey-Musolf LoopFest XVIII, August 13, 2019 FermiLab, IL
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 Yong Du UMass-Amherst ACFI 2
Motivations Standard Model (SM) for particle physics was completed in the 1960s by Glashow, Salam and Weinberg. The chiral structure of SM implies parity violation for all electroweak processes. Low energy precision measurements of weak neutral current provide a rigorous way to test the SM. Also complementary to high energy searches. Yong Du UMass-Amherst ACFI 3
Motivations Standard Model (SM) for particle physics was completed in the 1960s by Glashow, Salam and Weinberg. The chiral structure of SM implies parity violation for all electroweak processes. Low energy precision measurements of weak neutral current provide a rigorous way to test the SM. Also complementary to high energy searches. One example is: longitudinally polarized electrons scattering from unpolarized targets. A LR = d σ L − d σ R d σ L + d σ R Yong Du UMass-Amherst ACFI 3
Motivations y = Q 2 s = G µ Q 2 1 − 4 sin 2 θ W 1 − y A LR ( e − e − → e − e − ) � � Derman and Marciano, 1979 √ 1+ y 4 +(1 − y ) 4 2 πα One-loop EW radiative corrections reduce SM prediction by 40+-3%, making it more sensitive to the weak mixing angle. Czarnecki and Marciano, 1996 Yong Du UMass-Amherst ACFI 4
Czarnecki, Marciano, 2000 Motivations J. Erler, M.J. Ramsey-Musolf, 2005 arXiv:hep-ex/0509008 Yong Du UMass-Amherst ACFI 5
Czarnecki, Marciano, 2000 Motivations J. Erler, M.J. Ramsey-Musolf, 2005 arXiv:hep-ex/0509008 3 σ Marciano, 2006 Yong Du UMass-Amherst ACFI 5
Czarnecki, Marciano, 2000 Motivations J. Erler, M.J. Ramsey-Musolf, 2005 arXiv:hep-ex/0509008 3 σ Marciano, 2006 Yong Du UMass-Amherst ACFI 6
Motivations Moller looks directly into this discrepancy, and the projected Moller uncertainty is: A PV = 35 ppb , δ A PV = 0 . 73 ppb δ Q e W = ± 2 . 1%(stat . ) ± 1 . 1%(syst . ) δ (sin 2 θ W ) = ± 0 . 00024(stat . ) ± 0 . 00013(syst . ) Q 2 ' 0 . 005GeV 2 The MOLLER collaboration, arXiv:1411.4088 K. Kumar, MOLLER workshop at UMass-Amherst, 2014 Yong Du UMass-Amherst ACFI 7
Motivations The MOLLER collaboration, arXiv:1411.4088 In an EFT approach, four-fermion contact interaction ! g 2 Λ ij X L e 1 e 2 = e i γ µ e i e j γ µ e j ' 7 . 5TeV p | g 2 RR � g 2 2 Λ 2 LL | i , j=L , R q Λ ' 50TeV | g 2 RR − g 2 LL | = 2 π Yong Du UMass-Amherst ACFI 8
Motivations The MOLLER collaboration, arXiv:1411.4088 In an EFT approach, four-fermion contact interaction ! g 2 Λ ij X L e 1 e 2 = e i γ µ e i e j γ µ e j ' 7 . 5TeV p | g 2 RR � g 2 2 Λ 2 LL | i , j=L , R q Λ ' 50TeV | g 2 RR − g 2 LL | = 2 π Complementary to collider searches ∆ −− YD, A. Dunbrack, M.J. Ramsey-Musolf, J.-H. Yu, 2018 Yong Du UMass-Amherst ACFI 8
Motivations The MOLLER collaboration, arXiv:1411.4088 In an EFT approach, four-fermion contact interaction ! g 2 Λ ij X L e 1 e 2 = e i γ µ e i e j γ µ e j ' 7 . 5TeV p | g 2 RR � g 2 2 Λ 2 LL | i , j=L , R q Λ ' 50TeV | g 2 RR − g 2 LL | = 2 π Complementary to collider searches ∆ −− YD, A. Dunbrack, M.J. Ramsey-Musolf, J.-H. Yu, 2018 Kurylov, Ramsey-Musolf, Su, 2002, 2003, 2004 Other scenarios: Dark photon/Z, SUSY Davoudiasl, Lee, Marciano, 2012 Yong Du UMass-Amherst ACFI 8
Theoretical calculation symmetry Yong Du UMass-Amherst ACFI 9
Theoretical calculation symmetry Derman and Marciano, 1979 LO: 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 Aleksejevs et al, 2011, 2012, 2015 NNLO: Yong Du UMass-Amherst ACFI 9
Theoretical calculation symmetry Derman and Marciano, 1979 LO: 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 Aleksejevs et al, 2011, 2012, 2015 NNLO: Conclusion: need a full NNLO calculation to match experimental precision at JLab. Yong Du UMass-Amherst ACFI 9
NNLO contributions with a closed Fermion loop lightening introduction of expansion by regions using the gamma-Z box For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday p ex << m Z Z µ 2 ✏ d d q 1 F [0] = q 2 ( q + k 1 ) 2 ( q − p 1 ) 2 h Γ (2 π ) d i ( q + k 1 − k 2 ) 2 − m 2 Z Yong Du UMass-Amherst ACFI 10
NNLO contributions with a closed Fermion loop lightening introduction of expansion by regions using the gamma-Z box For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday p ex << m Z Z µ 2 ✏ d d q 1 F [0] = q 2 ( q + k 1 ) 2 ( q − p 1 ) 2 h Γ (2 π ) d i ( q + k 1 − k 2 ) 2 − m 2 Z Z µ 2 ✏ d d q Z µ 2 ✏ d d q 1 1 1 F [0] = ( q 2 ) 3 ( q 2 − m 2 q 2 ( q + k 1 ) 2 ( q − p 1 ) 2 − m 2 Γ (2 π ) d (2 π ) d Z ) Z Yong Du UMass-Amherst ACFI 10
NNLO contributions with a closed Fermion loop lightening introduction of expansion by regions using the gamma-Z box For a more comprehensive review, see Jort Sinninghe Damsté's talk from yesterday p ex << m Z Z µ 2 ✏ d d q 1 F [0] = q 2 ( q + k 1 ) 2 ( q − p 1 ) 2 h Γ (2 π ) d i ( q + k 1 − k 2 ) 2 − m 2 Z Z µ 2 ✏ d d q Z µ 2 ✏ d d q 1 1 1 F [0] = ( q 2 ) 3 ( q 2 − m 2 q 2 ( q + k 1 ) 2 ( q − p 1 ) 2 − m 2 Γ (2 π ) d (2 π ) d Z ) Z Yong Du UMass-Amherst ACFI 10
NNLO contributions with a closed Fermion loop 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 { Yong Du UMass-Amherst ACFI 11
NNLO contributions with a closed Fermion loop 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 T. Hahn, 2001 Package-X for the tensor algebra. H.H. Patel, 2015, 2016 Own Mathematica code to do the expansion by regions. FIRE for reduction. A.V. Smirnov, 2008 Yong Du UMass-Amherst ACFI 11
NNLO contributions with a closed Fermion loop Finished topologies X X X Yong Du UMass-Amherst ACFI 12
NNLO contributions with a closed Fermion loop Finished topologies X Yong Du UMass-Amherst ACFI 13
NNLO contributions with a closed Fermion loop Finished topologies X Remaining topology: Plan to finish cross-checking by the end of August. Yong Du UMass-Amherst ACFI 13
NNLO contributions with a closed Fermion loop 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. Yong Du UMass-Amherst ACFI 14
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. Yong Du UMass-Amherst ACFI 15
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. Yong Du UMass-Amherst ACFI 16
Back up slides
L i τ 2 ∆ L j L s.s. = h ij L ic L + h.c. � ρ parameter EXCLUSION region from above � ATLAS, JHEP03, 041(2015) ATLAS, Eur. Phys. J C78 (2018) H ++ H -- → W + W + W - W - - � W ± W ± hW ∓ ��� � = ����� ��������� ������ ∆ � λ 5 ��� [ ��� � Δ ] [ ��� ] m 2 H ±± ' m 2 2 v 2 ��� � = ���� ��������� ������ Φ - � m ∆ ≥ 0 GeV S ⇔ m H ±± ≥ 54 . 78 GeV - � √ S + B ≥ 5 LEP constraints - � automatically satisfied OPAL (1992, 2002) ℓ ± ℓ ± hW ∓ - � H ++ H -- →ℓ + ℓ + ℓ ' - ℓ ' - - � � ���� ���� ���� ���� � Δ [ ��� ]
Credit to: Michael J. Ramsey-Musolf
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