doubly-charged scalars at high-energy and high-precision ... · to be " 0.2 ppb, smaller than...

Doubly-charged scalars at high-energy andhigh-precision experiments

BHUPAL DEV

Washington University in St. Louis

with M. J. Ramsey-Musolf (UMass) and Y. Zhang (WashU), arXiv:1805.0xxxx

PHENO 2018University of Pittsburgh

May 8, 2018

Outline

Introduction: Energy versus Precision Frontier

Example: LHC versus MOLLER

A case study: Doubly charged scalar

Conclusion

Two Frontiers: Energy versus Precision

[Le Dall, Pospelov, Ritz (PRD ’15)]

Two Frontiers: Energy versus Precision

Complementary and intertwined. Need input from both to probe new physics.

Two Frontiers: Energy versus Precision8

28 m

liqui

d hy

drog

enta

rget

upst

ream

toro

id

hybr

idto

roid

dete

ctor

syst

ems

elec

tron

beam

FIG

.7:

MO

LLE

RE

xper

imen

tO

ver

vie

w:

Lay

out

ofth

eta

rget

,sp

ectr

om

eter

and

det

ecto

rs.

Com

pto

n-s

catt

ered

phot

onor

elec

tron

mea

sure

men

ts.

Inor

der

toac

hie

veth

enec

essa

ryra

te,th

eliquid

hydro

gen

targ

et

ispla

nned

tobe

150

cmlo

ng.

This

requir

esa

cryo

genic

targ

etsy

stem

capab

leof

han

dling

ahea

tlo

adof

⇠5

kW

from

the

bea

m.

This

wou

ldbe

the

hig

hes

tpow

erliquid

hydro

gen

targ

etco

nst

ruct

ed,but

itw

ould

be

bas

edon

succ

essf

ulex

per

ience

wit

hth

eop

erat

ion

ofth

eQ

wea

kta

rget

whic

hsu

cces

sfully

oper

ated

up

to18

0µA

wit

ha

tota

lpow

erof

2.9

kW

[29]

.T

he

final

des

ign

ofth

eM

OLLE

Rta

rget

willm

ake

use

ofco

mputa

tion

alfluid

dynam

ics

(CFD

),a

key

rece

nt

dev

elop

men

tw

hic

hhas

bee

nva

lidat

edby

the

succ

essf

ulop

erat

ion

ofth

eQ

wea

kta

rget

.Fro

mth

ephysi

cspoi

ntof

vie

w,th

em

ostim

por

tantdes

ign

consi

der

atio

nis

suppre

ssio

nof

den

sity

fluct

uat

ionsat

the

tim

esca

leof

the

hel

icity

flip

rate

,w

hic

hca

nru

inth

est

atis

tica

lre

ach

ofth

eflux

inte

grat

ion

tech

niq

ue.

Pre

lim

inar

yes

tim

ates

bas

edon

oper

atio

nal

exper

ience

wit

hth

eQ

wea

kta

rget

[29]

sugg

est

that

den

sity

vari

atio

nca

nbe

mai

nta

ined

at.

26ppm

at1.

92kH

z(c

ompar

edto

the

expec

ted

counti

ng

stat

isti

csw

idth

of⇠

83ppm

/pai

rat

75µA

),co

rres

pon

din

gto

acce

pat

able

5%ex

cess

noi

se.

Apre

cis

ion

collim

ati

on

syst

em

care

fully

des

igned

tom

inim

ize

bac

kgr

ounds

will

acce

pt

all

Møl

ler

scat

tere

del

ectr

ons

inth

epol

aran

gle

range

⇥C

OM

=60

��

120�

(cor

resp

ondin

gto

ala

bpol

arsc

atte

ring

angl

era

nge

of5

mra

d<✓ l

ab

<17

mra

d).

The

spectr

om

ete

rsy

stem

that

focu

sses

thes

esc

atte

red

par

ticl

esis

des

igned

toac

hie

vetw

ogo

als:

100%

azim

uth

alac

cepta

nce

and

the

ability

tofo

cus

the

scat

tere

dM

ølle

rflux

over

ala

rge

frac

tion

alm

omen

tum

bit

ew

ith

adeq

uat

ese

par

atio

nfr

ombac

kgr

ounds.

Thes

eco

nsi

der

atio

ns

hav

ele

dto

auniq

ue

solu

tion

invo

lvin

gtw

obac

k-t

o-bac

kse

tsof

toro

idal

coils,

one

ofth

emof

conve

nti

onal

geom

etry

(alb

eitlo

ng

and

quit

esk

inny)w

hile

the

other

isof

quite

nov

elge

omet

ry.

Due

toth

esp

ecia

lnat

ure

ofid

enti

calpar

ticl

esc

atte

ring,

itis

pos

sible

toac

hie

ve10

0%az

imuth

alac

cepta

nce

insu

cha

syst

emby

choos

ing

anodd

num

ber

ofco

ils.

The

idea

isto

acce

pt

bot

hfo

rwar

dan

dbac

kw

ard

(in

cente

rof

mas

san

gle)

Møl

lers

inea

ch�

bit

e.Sin

ceth

ese

are

iden

tica

lpar

ticl

es,th

ose

that

are

acce

pte

din

one�

bit

eal

sore

pre

sent

allth

est

atis

tics

avai

lable

inth

e�

bit

eth

atis

dia

met

rica

lly

oppos

ed(1

80�+�),

whic

his

the

sect

orth

atis

blo

cked

due

toth

epre

sence

ofa

toro

idal

coil.

An

even

tw

ith

afo

rwar

dan

gle

scat

tere

dM

ølle

rel

ectr

onth

ataz

imuth

ally

scat

ters

into

ablo

cked

sect

oris

det

ecte

dvia

its

bac

kw

ard

angl

esc

atte

red

par

tner

inth

eop

ense

ctor

dia

met

rica

lly

oppos

ed,an

dvic

eve

rsa.

The

focu

ssin

gan

dse

par

atio

nof

the

scat

tere

dM

ølle

rel

ectr

ons

isch

alle

ngi

ng

due

toth

eir

larg

esc

atte

red

ener

gyra

nge

E0 la

b=

1.7�

8.5

GeV

and

the

nee

dto

separ

ate

them

from

the

pri

mar

ybac

kgr

ound

ofel

asti

can

din

elas

tic

elec

tron

-pro

ton

scat

teri

ng.

The

solu

tion

isa

com

bin

atio

nof

two

toro

idal

mag

net

sw

hic

hto

geth

erac

tin

anon

-lin

ear

way

onth

ech

arge

dpar

ticl

etr

aje

ctor

ies.

The

firs

tis

aco

nve

nti

onal

toro

idpla

ced

6m

dow

nst

ream

ofth

eta

rget

and

the

seco

nd,a

nov

el“h

ybri

d”

toro

idpla

ced

bet

wee

n10

and

16m

dow

nst

ream

ofth

eta

rget

.E

ach

ofth

etw

oto

roid

alfiel

ds

isco

nst

ruct

edou

tof

seve

nid

enti

calco

ils

unifor

mly

spac

edin

the

azim

uth

.T

he

“hybri

d”

toro

idhas

seve

ralnov

elfe

ature

sto

pro

vid

eth

ere

quir

edfiel

dto

focu

sth

ela

rge

range

ofel

ectr

onsc

atte

ring

angl

esan

dm

omen

ta.

Ithas

four

curr

ent

retu

rnpat

hs,

assh

own

inFig

.8

and

som

enov

elben

ds

that

min

imiz

eth

efiel

din

cert

ain

crit

ical

regi

ons.

Apre

lim

inar

yen

ginee

ring

des

ign

ofth

ishybri

dto

roid

wit

hre

alis

tic

conduct

or,w

ater

Example: LHC versus MOLLER

MOLLER Experiment

Measurement Of a Lepton Lepton Electroweak Reaction 8

28 m

liquid hydrogentarget

upstreamtoroid

hybridtoroid

detectorsystems

electronbeam

FIG. 7: MOLLER Experiment Overview: Layout of the target, spectrometer and detectors.

Compton-scattered photon or electron measurements.In order to achieve the necessary rate, the liquid hydrogen target is planned to be 150 cm long. This requires a

cryogenic target system capable of handling a heat load of ⇠ 5 kW from the beam. This would be the highest powerliquid hydrogen target constructed, but it would be based on successful experience with the operation of the Qweaktarget which successfully operated up to 180 µA with a total power of 2.9 kW [29]. The final design of the MOLLERtarget will make use of computational fluid dynamics (CFD), a key recent development which has been validated bythe successful operation of the Qweak target. From the physics point of view, the most important design considerationis suppression of density fluctuations at the timescale of the helicity flip rate, which can ruin the statistical reach of theflux integration technique. Preliminary estimates based on operational experience with the Qweak target [29] suggestthat density variation can be maintained at . 26 ppm at 1.92 kHz (compared to the expected counting statisticswidth of ⇠ 83 ppm/pair at 75 µA), corresponding to accepatable 5% excess noise.

A precision collimation system carefully designed to minimize backgrounds will accept all Møller scatteredelectrons in the polar angle range ⇥COM = 60� � 120� (corresponding to a lab polar scattering angle range of 5 mrad< ✓lab < 17 mrad). The spectrometer system that focusses these scattered particles is designed to achieve twogoals: 100% azimuthal acceptance and the ability to focus the scattered Møller flux over a large fractional momentumbite with adequate separation from backgrounds. These considerations have led to a unique solution involving twoback-to-back sets of toroidal coils, one of them of conventional geometry (albeit long and quite skinny) while the otheris of quite novel geometry. Due to the special nature of identical particle scattering, it is possible to achieve 100%azimuthal acceptance in such a system by choosing an odd number of coils. The idea is to accept both forward andbackward (in center of mass angle) Møllers in each � bite. Since these are identical particles, those that are accepted inone � bite also represent all the statistics available in the � bite that is diametrically opposed (180� +�), which is thesector that is blocked due to the presence of a toroidal coil. An event with a forward angle scattered Møller electronthat azimuthally scatters into a blocked sector is detected via its backward angle scattered partner in the open sectordiametrically opposed, and vice versa. The focussing and separation of the scattered Møller electrons is challengingdue to their large scattered energy range E0

lab = 1.7 � 8.5 GeV and the need to separate them from the primarybackground of elastic and inelastic electron-proton scattering. The solution is a combination of two toroidal magnetswhich together act in a non-linear way on the charged particle trajectories. The first is a conventional toroid placed 6m downstream of the target and the second, a novel “hybrid” toroid placed between 10 and 16 m downstream of thetarget. Each of the two toroidal fields is constructed out of seven identical coils uniformly spaced in the azimuth. The“hybrid” toroid has several novel features to provide the required field to focus the large range of electron scatteringangles and momenta. It has four current return paths, as shown in Fig. 8 and some novel bends that minimize thefield in certain critical regions. A preliminary engineering design of this hybrid toroid with realistic conductor, water

Scattering of longitudinally polarized electrons off unpolarized electrons.Upgraded 11 GeV electron beam in Hall A at JLab.

Parity-Violating Asymmetry

APV =σR − σL

σR + σL

3

electroweak theory prediction at tree level in terms of the weak mixing angle is QeW = 1�4 sin2 ✓W ; this is modified at

the 1-loop level [4–6] and becomes dependent on the energy scale at which the measurement is carried out, i.e. sin2 ✓W

“runs”. It increases by approximately 3% compared to its value at the scale of the Z0 boson mass, MZ ; this and otherradiative corrections reduce Qe

W to 0.0435, a ⇠ 42% change of its tree level value of ⇠ 0.075 (when evaluated at MZ).The dominant e↵ect comes from the “� � Z mixing” diagrams depicted in Fig. 2 [5]. The prediction for APV for theproposed experimental design is ⇡ 33 parts per billion (ppb) and the goal is to measure this quantity with an overallprecision of 0.7 ppb and thus achieve a 2.4% measurement of Qe

W . The reduction in the numerical value of QeW due

to radiative corrections leads to increased fractional accuracy in the determination of the weak mixing angle, ⇠ 0.1%,matching the precision of the single best such determination from measurements of asymmetries in Z0 decays in thee+e� colliders LEP and SLC. An important point to note is that, at the proposed level of measurement accuracy ofAPV , the Standard Model (SM) prediction must be carried out with full treatment of one-loop radiative correctionsand leading two-loop corrections. The current error associated with radiative corrections for MOLLER is estimatedto be ⇠ 0.2 ppb, smaller than the expected 0.7 ppb overall precision. There is an ongoing e↵ort to investigate severalclasses of diagrams beyond one-loop [31–33], and a plan has been formulated to evaluate the complete set of two-loopcorrections at MOLLER kinematics by 2016; such corrections are estimated to be already smaller than the MOLLERstatistical error. The existing work makes it clear that the theoretical uncertainties for the purely leptonic Møller PVare well under control, and the planned future work will reinforce that conclusion.

e- e-p1

p2

p1�

p2�e- e-�

p1

p2

e-

e-

p1�

p2�� Z

e- e-

e- e-Z

e- e-

e- e-

FIG. 1: Feynman diagrams for Møller scattering at tree level (reproduced from Ref. [5])

Z

�f

Z

�W W

Z

�W

W W�

�e

FIG. 2: Significant 1-loop radiative corrections: � � Z mixing diagrams and W -loop contribution to the anapole moment(reproduced from Ref. [5])

The proposed MOLLER measurement will make a precision (2.4% relative) measurement of a suppressed StandardModel observable (Qe

W ⇠ 0.0435) resulting in sensitivity to new neutral current amplitudes as weak as ⇠ 10�3 · GF

from as yet undiscovered dynamics beyond the Standard Model. The fact that the proposed measurement providessuch a sensitive probe of TeV-scale dynamics beyond the SM (BSM) is a consequence of a very precise experimentalgoal (⇠ 10�3 · GF ), the energy scale of the reaction (Q2 ⌧ M2

Z), and the ability within the electroweak theory toprovide quantitative predictions with negligible theoretical uncertainty. The proposed measurement is likely the onlypractical way, using a purely leptonic scattering amplitude at Q2 ⌧ M2

Z , to make discoveries in important regions ofBSM space in the foreseeable future at any existing or planned facility worldwide.

The weak mixing angle sin2 ✓W has played a central role in the development and validation of the electroweaktheory, especially testing it at the quantum loop level, which has been the central focus of precision electroweakphysics over the past couple of decades. To develop the framework, one starts with three fundamental experimentalinputs characterizing, respectively, the strength of electroweak interactions, the scale of the weak interactions, and thelevel of photon-Z0 boson mixing. The three fundamental inputs are chosen to be ↵ (from the Rydberg constant), GF

(from the muon lifetime) and MZ (from the LEP Z0 line-shape). Precise theoretical predictions for other experimentalobservables at the quantum-loop level can be made if experimental constraints on the strong coupling constant andheavy particle masses, such as mH and the top quark mass, mt, are also included.

Precision measurements of the derived parameters such as the W boson mass MW , and the weak mixing anglesin2 ✓W are then used to test the theory at the level of electroweak radiative corrections. Consistency (or lack thereof)of various precision measurements can then be used to search for indications of BSM physics. One important new

ASMPV = mE

GF√2πα

2y(1− y)

1 + y4 + (1− y)4 QeW

For the MOLLER design, ASMPV ≈ 33 ppb (including 1-loop effect).

Goal: δAPV = 0.7 ppb. [J. Benesch et al. [MOLLER Collaboration], arXiv:1411.4088 [nucl-ex]]

Achieve a 2.4% precision in the measurement of QeW .

Sensitive to New Physics

e�

e�

e�

e�

e�

e�

fee feeH��

e�

e�

1

Λ√|g2

RR − g2LL|

=1√√

2GF|∆QeW |' 7.5 TeV

Case Study: Doubly Charged Scalar

e�

e�

e�

e�

e�

e�

fee feeH��

e�

e�

1

MPV ∼|(fL)ee|2

2(M±±L )2(eLγ

µeL)(eLγµeL) + (L↔ R) .

MOLLER Sensitivity :MH±±

L,R

|(fL,R)ee|& 5.3 TeV .

Why Doubly Charged Scalar?

Neutrino Mass via Type-II Seesaw

LY = − (fL)ij ψTL, iCiσ2∆LψL, j + H.c.

mν =√

2 fLv∆ = UmνUT .

[Schechter, Valle (PRD ’80); Mohapatra, Senjanovic (PRD ’81); Lazarides, Shafi, Wetterich (NPB ’81)]

Fixes the elements of fL (up to an overall scale)

LFV Constraints

ProcessExperimental limit

on BRConstraint on Bound ×

(MHL

100 GeV

)2

µ→ eγ < 4.2× 10−13 |(f †L fL)eµ| < 2.4× 10−6

µ→ 3e < 1.0× 10−12 |(fL)µe||(fL)ee| < 2.3× 10−7

τ → eγ < 3.3× 10−8 |(f †L fL)eτ | < 1.6× 10−3

τ → µγ < 4.4× 10−8 |(f †L fL)µτ | < 1.9× 10−3

τ → e+e−e− < 2.7× 10−8 |(fL)τe||(fL)ee| < 9.2× 10−5

τ → µ+µ−e− < 2.7× 10−8 |(fL)τµ||(fL)µe| < 6.5× 10−5

τ → e+µ−µ− < 1.7× 10−8 |(fL)τe||(fL)µµ| < 7.3× 10−5

τ → e+e−µ− < 1.8× 10−8 |(fL)τe||(fL)µe| < 5.3× 10−5

τ → µ+e−e− < 1.5× 10−8 |(fL)τµ||(fL)ee| < 6.9× 10−5

τ → µ+µ−µ− < 2.1× 10−8 |(fL)τµ||(fL)µµ| < 8.1× 10−5

[BD, Rodejohann, Vila (NPB ’17)]

MOLLER versus LFV

10-2 0.1 1 1010-3

10-2

0.1

1

10

vΔ [eV]

|(f L) ee|

NH, MHL±± = 1 TeV

excluded by μ→eee

excluded by μ→eγ

MOLLER prospect


MOLLER versus LFV

10-2 0.1 1 10

10-2

0.1

1

10

vΔ [eV]

|(f L) ee|

IH, MHL±± = 1 TeV

excluded byμ→eee

excluded byμ→eγ

MOLLERprospect


Parity-Violating Left-Right Model

LY ⊃ − (fR)ij ψTR, iCiσ2∆RψR, j + H.c..

Could have fR 6= fL at low scale. [Chang, Mohapatra, Parida (PRL ’84)]

fR is not related to the neutrino oscillation data.

LFV constraints do not restrict (fR)ee anymore.Other relevant constraints:

Neutrinoless double beta decayBhabha scattering at LEP: e+e− → e+e−.Drell-Yan process at LHC: pp → γ∗/Z∗ → H++H−−.

Future prospects at ILC/CLIC: e+e− → e±e±H∓∓R and e±γ → e∓H±±R .[BD, Mohapatra, Zhang ’18]

Parity-Violating Left-Right Model

0.5 1 5 10

10-3

10-2

0.1

1

10

MHR

±± [TeV]

|(f R) ee|

parity-violating case

ee→ee

MOLLER

dileptonlimits

0νββ [NH

]

[IH]

ILCCLIC

perturbative limit


Conclusion

Complementarity between the high-energy and high-precisionexperiments.

We considered a case study of doubly-charged scalars.

Can be probed at the MOLLER experiment up to ∼ 20 TeV.

For the parity-violating left-right scenario, goes well beyond the currentconstraints, as well as the future collider sensitivities.

doubly-charged scalars at high-energy and high-precision ... · to be " 0.2 ppb, smaller than...

Documents