A new experiment to measure the hadronic contribution to g-2

Luca TrentadueUniversità di Parma

and INFN Milano-Bicocca

on behalf of the proponents of the project

June 27th 2018

1

C. M. Carloni Calame, M. Passera, L. Trentadue. and G. Venanzoni,”A new approach to evaluate the leading hadronic corrections to the muon g-2”, Phys. Lett. B 746 (2015) 325

G. Abbiendi, C.M. Carloni Calame, U. Marconi, C. Matteuzzi, G. Montagna, O. Nicrosini M. Passera, F. Piccinini, R. Tenchini, L.Trentadue and G. Venanzoni,“Measuring the leading hadronic contribution to the muon g-2 via mu-e scattering”, Eur. Phys. J. C77 (2017) 3, 139. arXiv:1609.08987 [hep-ex].

work based on:

is a new experiment to measure the Hadronic Leading Order ( HLO) contribution to the muon g-2 by using

elastic scattering

3 L. Trentadue - QCD@Work 27 June 2018 Univ. Parma and INFN Milano Bicocca

µ+ e ! µ+ e

Outlook:- Physics Motivations- Tools to perform the measurement- The first testbeam (CERN)- Future plans and developments

This talk is about how to measure the Vacuum ( the hadronic contribution to )

Vacuum, since a long time ( 2500 years ), constitutes an always present issue in Physics or, better, in Natural Sciences

PhilosophyParmenides, Democritos, Leucippos,…..Torricelli, von

Guericke, Casimir, Schwinger, ….. to mention only a few until nowadays

In Quantum Field Theory, in the perturbative phase, Vacuum is naturally represented by the vacuum polarization contribution

Historical Aside

e2 ! e2 (q2 ) = e2

1+ ("(q2 )#"(0))!(q2 ) = !(0)

1#$!; $! = #%e "(q2 )#"(0)( )

Vacuum Polarization makes αem runningassuming a well defined “effective” value at any

scalevacuum polarization and the “effective charge” are

defined by:

α

Δα takes contributions from leptonic and hadronic and gauge bosons elementary states

Among these the non-perturbative Δαhad

Δα = Δαleptonic + Δαgb + Δαhad + Δα top

The physics motivations

6

aSMµ = 116591783(35)⇥ 10�11

F. Jegerlehner, MITP Workshop, 19-23 February 2018 Mainz

aexpµ = 116592089(63)⇥ 10�11

G.W. Bennet et al., Phys. Rev. D73(2006_072003

aµ =g � 2

2The muon g-2 has been measured with high precision

The Standard Model prediction gives:

�aµ(exp� SM) = 306± 72

Systematics of the measurement ?Systematics of the theoretical prediction ?

New Physics ?

from M. Passera

The muon g-2 - The Hadronic contribution

from M. Passera

.From T. Blum et. al., “The Muon g-2 Theory Value: Present and Future” arXiv:1311.2198 [hep-ph]

Comparison between the SM predictions and the experimental determinations

Theory parametrizations DHMZ ( M.Davier et al. ) , HLMNT ( K. Hagiwara et al. )SMXX is the average of the two previous values

BNL-E821 04 average is the current experimental value of aμ

New (g-2) exp. is the same central value with a fourfold improved precision of future g-2 experiments at Fermilab and J-PARC.

will this possibly change in the next few years ?The present experimental error as from the BNL E821 is

�aExpµ ' 6.3 · 10�10[0.54 ppm]

The new experiments in preparation at Fermilab and J-PARCare aiming to a precision of *

(*assuming the same central value as today’s one)

�aExp�FL/J�PARCµ ' 1.6 · 10�10[0.14 ppm]

a fo

urfo

ld g

ain

The question is how to cope with such an improvement from the theoretical side

The physics motivations

discrepancy between the experimental value of the muon anomalous magnetic moment and the Standard Model prediction

aµ =g � 2

2

Within the framework of low-energy high precision measurementsthe long-standing (~ )

�aµ(Exp� SM) ' 28± 8 · 10�10

The accuracy of the SM prediction 5 · 10�10

is limited by strong interactions effects

The present error on the leading order hadronic contribution to muon g � 2

It constitutes the main uncertainty of the SM predictions

�aHLOµ ' 4 · 10�10

The physics motivations

�

4�

The physics motivations

The largest contribution to the theoretical uncertainty comes from the term which can be measured experimentally

In order to understand the discrepancy between the experimental measurement and the Standard Model prediction it is needed to reduce the theoretical uncertainty to have a more precise determination

�↵had

12

More theoretical work is necessary: Radiative corrections, Lattice evaluations, etc…

The Standard Dispersive Approachto the evaluation of the HLO contribution to the muon anomalous magnetic moment goes

back to the ‘60

The Standard Dispersive Approach

from F. Jegerlehner talk in Frascati March 23, 2016

aHLOµ = (

↵mµ

3⇡)2

Z 1

4m2⇡

dsK(s)Rhad(s)

s2

Optical Theorem

K(s) =

Z 1

0dx

x2(1� x)

x2 + (1� x) sm2

µ

aHLOµ = (

↵

⇡2)

Z 1

0

ds

sK(s) Im⇧had(s+ i✏)

Rhad(s) =�(e+e� ! hadrons)

�(e+e� ! µ+µ�)

Im ⇧had(s) ! �hadtot (s)

from F. Jegerlehner talk in Frascati March 23, 2016

�aµ (��aµ)2

Measurement of the running of αemA direct measurement of αem(s/t) in space/

time-like regions can show the running of αem(s/t)

It can provide a test of “duality” (far away from resonances)

It has been done in past by few experiments at e+e- colliders by comparing a “well-known” QED process with some reference (obtained from data or MC)

!(q2 )!(q0

2 )!

"#

$

%&

2

~Nsignal (q

2 )Nnorm (q0

2 )

Nsignal can be any QED process, muon pairs, etc…Nnorm can be Bhabha process, pure QED as γγ pair production, a well as theory, or any other reference process.

We propose an alternative approach

aHLOµ = (

↵

⇡)

Z 0

�1

dt

�t(1� �

1 + �)2⇧had(t) = �(

↵

⇡)

Z 0

�1

dt

�t(1� �

1 + �)2�↵had(t(x))

t(x) = �x2m2

µ

1� x� =

r1�

4m2µ

t↵(t) =

↵(0)

1��↵(t)

�↵had(t) is the hadronic contribution to the running of ↵

t = �|q|2 �↵had(t) = �↵(t)��↵lep(t)

This may be obtained by using Bhabha scattering

aHLOµ =

↵

⇡

Z 1

0dx (1� x)⇧had(t(x)) =

↵

⇡

Z 1

0dx (1� x) �↵had(t(x))

The alternative approach of using a space-like formula for the vacuum polarization

�↵lep(t)

�↵had(t)

�↵i(t(x))

xpeak = 0.914 tpeak = �0.108 GeV 2is given by the total area under the curve

↵had

The smooth integrand function

The space-like kinematics allows a direct comparison with the lattice

evaluations

[22] C. Aubin, T. Blum, Phys. Rev. D 75 (2007) 114502; P. Boyle et al., Phys. Rev. D 85 (2012) 074504; X. Feng et al.,Phys. Rev. Lett. 107 (2011) 081802; M. Della Morte et al. ,J. High Energy Phys. 1203 (2012) 055. [23] T. Blum et al., PoS LATTICE 2012 (2012) 022.

aµ=(g-2)/2

aµHLO = !

!"

(1! x)0

1

" #had (!x2

1! xmµ2 )dx

t =x2mµ

2

x !10 " !t < +#

x = t2mµ

2 (1! 1!4mµ

2

t); 0 " x <1;

t = !ssin2(!2)

!!had (t) = "#had (t) for t < 0

aµHLO = !

!"

(1! x)0

1

" #!had (!x2

1! xmµ2 )dx

To summarize

with the “t” kernel

A.Arbuzov, D.Haidt, C.Matteuzzi,M.Paganoni, L.T. Eur. Phys. J. C 34 (2004) 267

AN EXAMPLE OF A SPACE-LIKE APPROACH

A. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L.T., Eur. Phys. J. C 34 (2004) 267

each one of them known with an accuracy of at least 0.1% 1st factor

The Born cross section contains all the soft and

virtual corrections

Bhabha is a pure QED processQuarks enter only in loops

2nd factor Vacuum polarization effectsgives the running of alpha

3rd factor

with all the real and virtual effects not incorporated in the running of alpha

↵(0) is the Sommerfeld fine structure constant

measured with a precision of

O(10�9)

from loop contributions to the photon propagator�↵(q2)

A couple of years later….

!

"#had(5) (MZ

2 ) = $#MZ

2

3%Re ds

4m%2

&

' R(s)s(s$MZ

2 $ i()

time-like

Running of αem

space-like

A new possibilityvia

scatteringµe ! µe

32

µe ! µe

s ' 0.16 GeV 2 � 0.14 t 0 GeV 2 0 x 0.93

• High intensity muon beam available in the CERN North Area E =150 GeV • pure t-channel process d�

dt=

d�0

dt|↵(t)↵(0)

|2

Same process can be used for signal and normalization

1.3⇥ 107µ/s

Muon and electron scattering angles are correlatedThis very important constraint may be used to select elastic events, reject

background from radiative events and minimize systematics

Electron scattering angle (mrad)0 10 20 30 40 50

Muo

n sc

atte

ring

angl

e (m

rad)

0

1

2

3

4

5 Muon beam momentum = 150 GeV

= 0.1 GeV

e

x = 0.1, E = 0.5 GeV

e

x = 0.2, E = 1.4 GeV

e

x = 0.3, E = 2.9 GeV

e

x = 0.4, E = 5.5 GeV

e

x = 0.5, E = 9.8 GeV

e

x = 0.6, E

= 17.8 GeV

e

x = 0.7, E

= 35.0 GeV

e

x = 0.8, E

= 88.5 GeVex = 0.9, E

= 130.7 GeVex = 0.928, E

x = 0.932 = 139.5 GeVe E

U. Marconi at the CSN1 May 2017

i) Initial muons have to be tagged with their direction and momentumii) 60 Be (C) layers interfaced with Si planes spaced by 1m air gap modularly spacediii) The use of a low Z material in order to reduce multiple scattering and background

iv) A final EM calorimeter to discriminate e/mu at small angles ( 2-3 mrad )

The Detector

Statistics

Systematics

Theory

µ beam 1.3⇥ 107µ/s for 2⇥ 107s/yr

2⇥ 1012 events/yr statistical precision 0.3% in 2 yrs running

many effects have to be under control:efficiencies (uniformity, acceptance, tracking, trigger, PID) alignment of the Si planes, uncertainties in vertex location, incoming muon momentum, effect of multiple scattering (different in “control” and “signal” regions) ……………………(many others, can be studied with data themselves).

Electroweak radiative corrections ( including subleading logaritmic and mass contributions) have to be under control at the NNLO accuracy

This idea has been proposed in 2016 at the “Physics Beyond Collider Workshop” at CERN• The idea has been presented in 2016 to the “Physics Beyond Collider Study Group”

• C. Matteuzzi and G. Venanzoni are members of the board as the experiment representatives.

• Physics Beyond Collider Study Group will select in fall 2018 experiments aiming to:

• Enrich and diversify the CERN scientific program: Exploit the unique opportunities offered by CERN’s accelerator complex and scientific infrastructure Complement the laboratory’s collider programme (LHC, HL-LHC and possible future colliders). The scientific findings will be collected in a report to be delivered by the end of 2018.

This document will also serve as input to the next update of the European Strategy for Particle Physics.

Also proposed to the INFN NSCI in 2017 and 2018

from U. Marconi

Prepared for submission to JHEP

Master integrals for the NNLO virtual corrections to

µe scattering in QED: the non-planar graphs

Stefano Di Vita,aStefano Laporta,

b,cPierpaolo Mastrolia,

b,cAmedeo Primo,

dUlrich

Schuberte

aINFN, Sezione di Milano, Via Celoria 16, 20133 Milano, ItalybDipartimento di Fisica ed Astronomia, Universita di Padova, Via Marzolo 8, 35131 Padova, ItalycINFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, ItalydDepartment of Physics, University of Zurich, CH-8057 Zurich, SwitzerlandeHigh Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA

E-mail: stefano.divita@mi.infn.it, stefano.laporta@pd.infn.it,

pierpaolo.mastrolia@pd.infn.it, aprimo@physik.uzh.ch,

schubertmielnik@anl.gov

Abstract: We evaluate the master integrals for the two-loop non-planar box-diagrams

contributing to the elastic scattering of muons and electrons at next-to-next-to-leading

order in QED.We adopt the method of di↵erential equations and the Magnus exponential to

determine a canonical set of integrals, finally expressed as a Taylor series around four space-

time dimensions, with coe�cients written as combination of generalised polylogarithms.

The electron is treated as massless, while we retain full dependence on the muon mass.

The considered integrals are also relevant for crossing-related processes, such as di-muon

production at e+e� colliders, as well as for the QCD corrections to top-pair production

at hadron colliders. In particular our results, together with the planar master integrals

recentely computed, represent the complete set of functions needed for the evaluation

of the two-loop virtual next-to-next-to-leading order QED corrections to eµ ! eµ and

e+e�! µ

+µ�.

Just a few days ago !

TEST Beams 2017/2018 at CERN

from U. Marconi

from U. Marconi

from U. Marconi

from U. Marconi

from U. Marconi

from U. Marconi

from U. Marconi

Setup located in the North Areabehind COMPASS detector

52from U. Marconi

Tentative timeline of the project

• Studies with Geant4 ( underway )

• Detector geometry, number of planes, thickness, calorimeter for pid,…

• Test beam 2018 ( muons ) 2019 ( electrons )

• Assemble the detector -> 2020

• Start to collect data 2021

• We propose to measure muon electron scattering by using the muon beam in the CERN North Area ( 150 GeV ) to extract the space-like quark vacuum polarization

• This measurement will allow to obtain the leading hadronic contribution to the g-2 in a new independent way and will constitute a crosscheck with previous time-like determinations and with the lattice results

• The goal is to determine the origin of the presently observed discrepancy between experiments and Standard Model predictions of the g-2 and the origin if within SM or if it could be attributed to BSM physics

Conclusions

The End