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Mu-e scattering: Measuring the leading hadronic contribution to (g-2) μ Massimo Passera INFN Padova KEK 9 February 2018

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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 3

Status of the muon g-2

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

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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

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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

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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

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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

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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

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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

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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>

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A new approach to aμHLO

C. Carloni Calame, MP, L. Trentadue, G. Venanzoni

PLB 2015 - arXiv:1504.02228

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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

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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

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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

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Muon-electron scattering

Abbiendi, Carloni Calame, Marconi, Matteuzzi, Montagna,

Nicrosini, MP, Piccinini, Tenchini, Trentadue, Venanzoni

EPJC 2017 - arXiv:1609.08987

e e

Hadronst

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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

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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

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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!

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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

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Systematic effects must be known at the level of ≲ 10ppm!

aμHLO via muon-electron scattering (3) μe

G. Venanzoni, Fermilab, June 5th 2017

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μeTest Beam at CERN — Sep 2017

Data analysis under way.

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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!

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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.

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Theory workshop in Padova — Sep 2017 μe

h"ps://agenda.infn.it/internalPage.py?pageId=0&confId=13774

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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

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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.

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μe

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

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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…

JOIN US!

M. Passera KEK Feb 09 2018

The End

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M. Passera KEK Feb 09 2018 32

1

10

100

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

L = 1.5⇥ 107 nb�1

�LO = 245.04 µb

Efe

> 1 GeV

dN/dx

(101

1)

x

1

10

100

1000

10000

�0.14 �0.12 �0.1 �0.08 �0.06 �0.04 �0.02 0

L = 1.5⇥ 107 nb�1

�LO = 245.04 µb

Efe

> 1 GeV

dN/dt

(101

1G

eV�2)

t (GeV2)