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Mu-e scattering:
Measuring the leading hadronic contribution to (g-2)μ
Massimo Passera INFN Padova
KEK 9 February 2018
M. Passera KEK Feb 09 2018 2
Outline
Status of the muon g-2
Hadronic corrections to the muon g-2: a new approach
Muon-electron scattering: proposal for a new experiment
M. Passera KEK Feb 09 2018 4
The muon g-2: experimental status
BNL E821: aμEXP = (116592089 ± 54stat ± 33sys)x10-11 [0.5ppm].
Future: new muon g-2 experiments at:
Fermilab E989: aims at ± 16x10-11, ie 0.14ppm. Started taking data at the end of 2017. First result expected in late 2018 with a precision comparable to BNL E821. J-PARC proposal: phase-1 start with 0.46ppm (TDR 2017).
Are theorists ready for this (amazing) precision? Not yet!
Jan 04 ?July 02
μ
SM
M. Passera KEK Feb 09 2018
aμQED = (1/2)(α/π) Schwinger 1948
+ 0.765857426 (16) (α/π)2
Sommerfield; Petermann; Suura&Wichmann ’57; Elend ’66; MP ’04
+ 24.05050988 (28) (α/π)3
Remiddi, Laporta, Barbieri … ; Czarnecki, Skrzypek; MP ’04; Friot, Greynat & de Rafael ’05, Mohr, Taylor & Newell 2012
+ 130.8780 (60) (α/π)4 Kinoshita & Lindquist ’81, … , Kinoshita & Nio ’04, ’05; Aoyama, Hayakawa,Kinoshita & Nio, 2007, Kinoshita et al. 2012 & 2015;Steinhauser et al. 2013, 2015 & 2016 (all electron & τ loops, analytic);S. Laporta, arXiv:1704.06996 (mass independent term). COMPLETED2!
+ 750.80 (89) (α/π)5 COMPLETED! Kinoshita et al. ‘90, Yelkhovsky, Milstein, Starshenko, Laporta,…Aoyama, Hayakawa, Kinoshita, Nio 2012 & 2015 & 2017
The muon g-2: the QED contribution
…
Adding up, I get:
aμQED = 116584718.976 (20)(73) x 10-11 from coeffs, mainly from 4-loop unc from δα(Rb)
with α=1/137.035998995(85) [0.62 ppb]
5
μ
M. Passera KEK Feb 09 2018
The muon g-2: the electroweak contribution
One-loop term:
1972: Jackiv, Weinberg; Bars, Yoshimura; Altarelli, Cabibbo, Maiani; Bardeen, Gastmans, Lautrup; Fujikawa, Lee, Sanda; Studenikin et al. ’80s
One-loop plus higher-order terms:
aμEW = 153.6 (1) x 10-11
Hadronic loop uncertaintiesand 3-loop nonleading logs.
Kukhto et al. ’92; Czarnecki, Krause, Marciano ’95; Knecht, Peris, Perrottet, de Rafael ’02; Czarnecki, Marciano and Vainshtein ’02; Degrassi and Giudice ’98; Heinemeyer, Stockinger, Weiglein ’04; Gribouk and Czarnecki ’05; Vainshtein ’03; Gnendiger, Stockinger, Stockinger-Kim 2013.
6
with MHiggs = 125.6 (1.5) GeV
μ
M. Passera KEK Feb 09 2018
The muon g-2: the Hadronic LO contribution (HLO)
7
F. Jegerlehner and A. Nyffeler, Phys. Rept. 477 (2009) 1
Central Error
F. Jegerlehner, arXiv:1711.06089
Davier, Hoecker, Malaescu, Zhang, arXiv:1706.09436
Keshavarzi, Nomura, Teubner, arXiv:1802.02995
aμHLO = 6894.6 (32.5) x 10-11
= 6931 (34) x 10-11
= 6932.7 (24.6) x 10-11
K(s) =
Z 1
0dx
x2(1� x)
x2 + (1� x)(s/m2)aHLOµ =
1
4⇡3
Z 1
4m2⇡
dsK(s)�(0)(s) =↵2
3⇡2
Z 1
4m2⇡
ds
sK(s)R(s)
Radiative Corrections are crucial. S. Actis et al, Eur. Phys. J. C66 (2010) 585
Lots of progress in lattice calculations. FNAL - Muon g-2 workshop - June 2017
μ
Capri - FCCP 2017 workshop - Sep 2017
M. Passera KEK Feb 09 2018
The muon g-2: the Hadronic NLO contributions (HNLO) - VP
8
HNLO: Vacuum Polarization
O(α3) contributions of diagrams containing hadronic vacuum polarization insertions:
Krause ’96, Alemany et al. ’98, Hagiwara et al. 2011, Jegerlehner 2017
aμHNLO(vp) = -99.27 (67) x 10-11
Already included in aμHLO
μ
M. Passera KEK Feb 09 2018
The muon g-2: the Hadronic NLO contributions (HNLO) - LBL
9
HNLO: Light-by-light contribution
aμHNLO(lbl) = + 80 (40) x 10-11 Knecht & Nyffeler ’02
aμHNLO(lbl) = +136 (25) x 10-11 Melnikov & Vainshtein ’03
aμHNLO(lbl) = +105 (26) x 10-11 Prades, de Rafael, Vainshtein ’09
aμHNLO(lbl) = + 100 (29) x 10-11 Jegerlehner, arXiv:1705.00263
Results based also on Hayakawa, Kinoshita ’98 & ’02; Bijnens, Pallante, Prades ’96 & ’02
Unlike the HLO term, the hadronic l-b-l term relies at present on theoretical approaches.
This term had a troubled life! Latest values:
Improvements expected in the π0 transition form factor A. Nyffeler 1602.03398 The HLbL contribution can be expressed in terms of observables in a
dispersive approach. Colangelo et al, 2014, 15 & 17; Pauk & Vanderhaeghen 2014.
Progress on the lattice: +53.5(13.5)x10-11. Statistical error only, finite-volume and finite lattice-spacing errors being studied. Omitted subleading disconnected graphs still need to be computed.
μ
Blum, Christ, Hayakawa, Izubuchi, Jin, Jung, Lehner, arXiv:1610.04603
M. Passera KEK Feb 09 2018
The muon g-2: the Hadronic NNLO contributions (HNNLO)
10
HNNLO: Vacuum Polarization
O(α4) contributions of diagrams containing hadronic vacuum polarization insertions:
Kurz, Liu, Marquard, Steinhauser 2014
aμHNNLO(vp) = 12.4 (1) x 10-11
HNNLO: Light-by-light
Colangelo, Hoferichter, Nyffeler, MP, Stoffer 2014
aμHNNLO(lbl) = 3 (2) x 10-11
μ
M. Passera KEK Feb 09 2018 11
The muon g-2: SM vs. Experiment
[1] F. Jegerlehner, arXiv:1711.06089. [2] Davier, Hoecker, Malaescu, Zhang, arXiv:1706.09436. [3] Keshavarzi, Nomura, Teubner, arXiv:1802.02995.
with the hadronic light-by-light aμHNLO(lbl) = 100 (29) x 10-11 of F. Jegerlehner arXiv:1705.00263, and the hadronic leading-order of:
Comparisons of the SM predictions with the measured g-2 value:
aμEXP = 116592091 (63) x 10-11 E821 – Final Report: PRD73 (2006) 072 with latest value of λ=μμ/μp from CODATA’10
μ
aSMµ ⇥ 1011 �aµ = aEXP
µ � aSMµ �
116 591 783 (44) 308 (77) ⇥ 10�11 4.0 [1]
116 591 820 (45) 271 (77) ⇥ 10�11 3.5 [2]
116 591 821 (38) 270 (74) ⇥ 10�11 3.7 [3]<latexit sha1_base64="Ip+Q1udC+rbvEk/aY3taHOmvELY=">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</latexit><latexit sha1_base64="Ip+Q1udC+rbvEk/aY3taHOmvELY=">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</latexit><latexit sha1_base64="Ip+Q1udC+rbvEk/aY3taHOmvELY=">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</latexit>
M. Passera KEK Feb 09 2018 12
A new approach to aμHLO
C. Carloni Calame, MP, L. Trentadue, G. Venanzoni
PLB 2015 - arXiv:1504.02228
M. Passera KEK Feb 09 2018 13
New space-like proposal for HLO
which involves Δαhad(t), the hadronic contribution to the running of α in the space-like region. It can be extracted from scattering data!
At present, the leading hadronic contribution aμHLO is computed via the time-like formula:
aHLOµ =
1
4⇡3
Z 1
4m2⇡
dsK(s)�0had(s)
K(s) =
Z 1
0dx
x2 (1� x)
x2 + (1� x)�s/m2
µ
�
Alternatively, exchanging the x and s integrations in aμHLO
aHLOµ =
↵
⇡
Z 1
0dx (1� x)�↵had[t(x)]
t(x) =x2m2
µ
x� 1< 0
Hadronst
M. Passera KEK Feb 09 2018 14
Carloni Calame, MP, Trentadue, Venanzoni, PLB 2015
smooth integrand
New space-like proposal for HLO (2)
Time-like Space-like
F. Jegerlehner, arXiv:1511.04473
M. Passera KEK Feb 09 2018 15
New space-like proposal for HLO: which experiment?
Δαhad(t) can be measured via Bhabha scattering:
The peak occurs at xpeak = 0.914, tpeak = −0.108 GeV2 ≃ −(330 MeV)2
Bhabha scattering: x vs the electron scattering angle θ
Carloni Calame, MP, Trentadue, Venanzoni, PLB 2015
M. Passera KEK Feb 09 2018 16
Muon-electron scattering
Abbiendi, Carloni Calame, Marconi, Matteuzzi, Montagna,
Nicrosini, MP, Piccinini, Tenchini, Trentadue, Venanzoni
EPJC 2017 - arXiv:1609.08987
e e
Hadronst
M. Passera KEK Feb 09 2018 17
Muon-electron scattering
Δαhad(t) can also be measured via the elastic scattering μ e ➞ μ e.
We propose to scatter a 150 GeV muon beam, available at CERN’s North Area, on a fixed electron target. Modular apparatus, several layers of low Z material (Be) paired to Si strip planes.
μe
e
μ
targetn targetn+1
(a)
e
μ
(b)
≈
ECAL MUON
modulen
~1m
M. Passera KEK Feb 09 2018 18
μe
With CERN’s 150 GeV muon beam M2, which has an average of ~ 1.3 × 107 μ/s, incident on Be layers for a total thickness of 60cm, and 2 years of data taking with a running time of 2 × 107 s/yr, one can reach an int. luminosity of 𝓛int ~ 1.5 × 107 nb-1.
Muon-electron scattering (2)
e-out
μ-out
μ-inθe
θμ
M. Passera KEK Feb 09 2018 19
For a 150 GeV muon beam, the scan region extends up to x=0.932, ie beyond the peak! (the peak is at x=0.914)
The integrand in the remaining region x ∈ [0.932,1] accounts for ~13% of the aμHLO integral. It cannot be reached by our experiment but it can be determined using pQCD & time-like data, and/or lattice QCD results.
Same detector for signal and normalization (x ≲ 0.3, Δαhad(t) ≲ 10-5) leads to cancellation of detector effects at first order.
aμHLO via muon-electron scattering μe
normalization
signal
It looks like an ideal process!
M. Passera KEK Feb 09 2018 20
aμHLO via muon-electron scattering (2) μe
Modular apparatus: one Beryllium target (~1cm thick) coupled to three Silicon planes (thickness: 300μm).
State-of-the-art Silicon strip detectors with hit resolution ~10 μm will provide an expected angular resolution of ~10 μm / 0.5 m = 0.02 mrad
ECAL and μ detector located downstream will solve PID ambiguity below 5 mrad (above that, the angular measurements provide PID).
With 𝓛int ~ 1.5 × 107 nb-1 we estimate that we can reach a statistical sensitivity of ~ 0.3% on aμHLO, ie ~ 20 × 10-11!
Be
M. Passera KEK Feb 09 2018 21
Systematic effects must be known at the level of ≲ 10ppm!
aμHLO via muon-electron scattering (3) μe
G. Venanzoni, Fermilab, June 5th 2017
M. Passera KEK Feb 09 2018 23
To extract Δαhad(t) from the measured cross section, the SM prediction must be known at NNLO!
Muon-electron scattering: theory μe
e
µ
e
e,µ
e
µ
e
µ
e
µ
e
µ
e
µ
e
µ
e
µ
e
µ
e e
Hadronst
NLO QED corrections known & checked. Pavia group: MC ready!
NNLO QED corrections unknown.
NLO hadronic contributions unknown. NB: the hadronic light-by-light contributions are of higher order!! 😀
Dedicated high-precision MC tools needed.
Possible interplay with lattice calculations.
Explore the new physics sensitivity of this experiment!
M. Passera KEK Feb 09 2018 24
Muon-electron scattering: theory (2) μe State-of-the-art methods required to calculate the 2-loop diagrams. Two-loop box diagrams:
Mastrolia, MP, Primo & Schubert, arXiv:1709.07435.
Missing Master Integrals for the planar 2-loop box diagrams computed.
M. Passera KEK Feb 09 2018 25
Theory workshop in Padova — Sep 2017 μe
h"ps://agenda.infn.it/internalPage.py?pageId=0&confId=13774
M. Passera KEK Feb 09 2018 26
MITP 2018 workshop in Mainz μe
Mainz Institute for Theoretical Physics
SCIENTIFIC PROGRAMS
ACT
IVIT
IES
2018 The Evaluation of the Leading Hadronic Contribution
to the muon anomalous magnetic momentMassimo Passera INFN Padua, Luca Trentadue U Parma, Carlo Carloni Calame INFN Pavia Graziano Venanzoni INFN Frascati
February 19-23, 2018
Challenges in Semileptonic B DecaysPaolo Gambino U Turin, Andreas Kronfeld Fermilab, Marcello Rotondo INFN-LNF Frascati, Christof Schwanda OEWA Vienna
April 16-20, 2018
Tension in LCDM ParadigmCora Dvorkin U Harvard, Silvia Galli IAP Paris, Fabio Iocco ICTP-SAIFR, Federico Marinacci MIT
May 14-18, 2018
The Proton Radius Puzzle and BeyondGil Paz Wayne State U, Richard Hill Perimeter Inst., Randolf Pohl JGU
July 23-27, 2018
Scattering Amplitudes and Resonance Properties from Lattice QCDMaxwell T. Hansen CERN, Sasa Prelovsek U Ljubljana, Steve Sharpe U Washington, Georg von Hippel, Hartmut Wittig JGU
August 27-31, 2018
Quantum Fields – From Fundamental Concepts to Phenomenological QuestionsAstrid Eichhorn U Heidelberg, Roberto Percacci SISSA Trieste, Frank Saueressig U Nijmegen
September 26-28, 2018
Probing Physics Beyond SM with Precision Ansgar Denner U Würzburg, Stefan Dittmaier U Freiburg, Tilman Plehn U Heidelberg February 26-March 9, 2018
Bridging the Standard Model to New Physics with the Parity Violation Program at MESAJens Erler UNAM, Mikhail Gorshteyn, Hubert Spiesberger JGU
April 23-May 4, 2018
Modern Techniques for CFT and AdSBartlomiej Czech IAS Princeton, Michal P. Heller MPI for Gravitational Physics, Alessandro Vichi EPFL
May 28-June 8, 2018
The Dawn of Gravitational Wave ScienceRafael A. Porto ICTP-SAIFR, Riccardo Sturani IIP Natal, Salvatore Vitale MIT, Luis Lehner Perimeter Inst.
June 4-15, 2018
The Future of BSM PhysicsGiulia Ricciardi U Naples Federico II, Gian Giudice CERN
Tobias Hurth, Joachim Kopp, Matthias Neubert JGU June 4-15, 2018, Capri, Italy
Probing Baryogenesis via LHC and Gravitational Wave SignaturesGermano Nardini U. Bern, Carlos E.M. Wagner U Chicago /
Argonne NatLab., Pedro Schwaller JGU June 18-29, 2018
From Amplitudes to PhenomenologyFabrizio Caola IPPP Durham, Bernhard Mistlberger, Giulia Zanderighi CERN August 13-24, 2018
String Theory, Geometry and String Model BuildingPhilip Candelas, Xenia de la Ossa, Andre Lukas U Oxford, Daniel Waldram Imperial College London, Gabriele Honecker, Duco van Straten JGU September 10-21, 2018
Johannes Henn, Matthias Neubert, Stefan Weinzierl, Felix Yu JGU
Juli 2018
MITP SUMMER SCHOOL 2018
© S
abrin
a Ho
pp
© C
arlo
Mül
ler
© S
abrin
a Ho
pp
TOPICAL WORKSHOPS
For more details: http://www.mitp.uni-mainz.de
Mainz Institute for Theoretical PhysicsPRISMA Cluster of Excellence Johannes Gutenberg-Universität Mainz, Germany
M. Passera KEK Feb 09 2018 27
μeExperimental plans for 2018
Build & test a full-scale prototype (2 modules) on a muon beam at Cern:
We have been allocated 1 week (22-29 August 2018) of high-energy muon beam (160 GeV) in H8 (A138).
We will also run on the M2 line behind COMPASS (start-up in April).
This proposal is part of the Physics Beyond Colliders activities @ Cern
Proposal presented in 2017 to INFN’s Committee 1. Funds have been allocated for a full-scale test of a detector prototype in 2018. Letter of Intent planned for 2018-19.
M. Passera KEK Feb 09 2018
Conclusions
Muon g-2: Δaμ ~ 3.5 - 4 σ. New upcoming measurement: QED & EW ready. Lots of progress in the hadronic sector, but not yet ready!
New proposal for an experiment at CERN to measure the leading hadronic contribution to the muon g-2 via μ-e elastic scattering.
μ-e exp: first μ-e testbeam completed at CERN in October. Data analysis under way. One more week of testbeam allocated next August. Test run planned also on CERN's M2 line in April. INFN funds allocated for a test of a detector prototype in 2018.
μ-e th: NLO MC generator ready. Lots of theoretical work needed! NNLO QED & NLO hadronic corrections unknown. First results obtained for the NNLO planar box diagrams contributing to μ-e scattering in QED. Dedicated high-precision MC tools needed. The new physics sensitivity of this experiment must be explored!
29
M. Passera KEK Feb 09 2018 30
G. Abbiendi, M. Alacevich, M. Bonomi, A. Broggio, C. Carloni Calame, E. Conti, D. Galli, M. Fael, A. Ferroglia, F.V. Ignatov, M. Incagli, U. Marconi, M.K. Marinković, P. Mastrolia, C. Matteuzzi, G. Montagna, O. Nicrosini, G.Ossola, L.Pagani, M. Passera, P. Paradisi, C. Patrignani, F. Piccinini, F. Pisani, M. Prest, A. Primo, A. Principe, M. Pruna, M. Rocco, U. Schubert, L. Tancredi, R. Tenchini, L. Trentadue, E. Vallazza, G. Venanzoni, A. Vicini, E. Del Nobile…
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