The Proton Gerald A

The Proton Gerald A. Miller University of Washington The Proton Gerald A. Miller University of Washington

“Everything that rises”, Martin Puryear The Proton Gerald A. Miller University of Washington

“Everything that rises”, Martin Puryear The Proton Outline

• General information about quark, gluons, QCD Motivation for study of proton How does the proton spin? • Phenomenological considerations proton is not round.

• How large is the proton: precision <1%? Cool Facts about Quarks, Gluons (QCD) and Did you know that … ? Nuclei

• If an atom was the size of a football field, the (atomic) nucleus would be about the size of a marble. • Despite its tiny dimensions, the nucleus accounts for 99.9% of an atom’s mass. Neutrons and protons account for 99.2% of the mass of nucleus • Protons and neutrons swirl in a heavy atomic nucleus. Average speed is some ¼ the speed of light. They are “strong-forced” to reside in a small space. • Quarks (and gluons) are “confined” to the even smaller space inside protons and neutrons. Because of this, they swirl around with the speed of light. Cool Facts about QCD=strong force Did you know that … ?

• The strong force is so strong, that you can never find one quark alone (this is called “confinement”). •When pried even a little apart, quarks experience ten tons of force pulling them together again. • Quarks and gluons jiggle around at nearly light- speed, and extra gluons and quark/anti-quark pairs pop into existence one moment to disappear the next. • It is this flurry of activity, fueled by the energy of the gluons, that generates nearly all the mass of protons and neutrons, and thus ultimately of all the matter we see. • 99% of your mass is due to this stored energy. QCD the fundamental theory of the strong interaction

QCD Lagrangian: quarks and gluons

We know that QCD works, but theory is difficult to evaluate. Lattice QCD makes big progress now. Exciting prospect: comparing experiment with correctly evaluated fundamental theory. Why study the nucleon?

• Neutrons protons made of quarks, gluons • Quantum Chromodynamics QCD • CONFINEMENT, test QCD lattice • Size influences atomic physics tests of QED • How does the nucleon stick together when struck by photon? • Where is charge and magnetization density located? Origin of angular momentum= spin? • What is the shape of the proton? Naive Quark Model of Proton, Neutron (nucleon)

Proton 2 u(2/3 ), 1 d Neutron 2 d(-1/3) 1 u

Confined quarks move with zero orbital angular momentum

This idea has great success - magnetic moments, spectra of particles, etc 1.6 fm =1.6 * 10-15 m Proton has size

Proton has spin

8 “Spin Crisis”

Proton spin is 1/2 ~ Experiment shows that the spin of the quark carry only 30 % of 1/2 ~ Possibilities: u, d quarks surrounded by strange quark pairs ss¯ -RULED OUT gluons carry spin and orbital angular momentum quarks carry orbital angular momentum STATUS? “Spin Crisis”

We are still trying to ﬁgure out how much of each Study proton: How to tell how big something is? Proton

• Look P+q

e’

Non rel form factor -old

P e Proton

Structure factor Electron-nucleon scattering

jµ=

Deep inelastic scattering Nucleon vertex: 1990 Nobel Prize

Cross section for scattering from a point-like object

Form factors describing 1961 Nobel Prize nucleon shape/structure Shape of proton

Random spin -direction -means no direction proton is spherical

Fix spin direction -three vectors:spin (up) , quark position, direction of quark spin

12 θ s r Shapes of the proton- momentum space n parallel to S n anti-parallel to S

S three vectors n, K, S n is quark spin S is proton spin

Phys.Rev. C68 (2003) 022201 Shapes of the proton- momentum space n parallel to S n anti-parallel to S

S three vectors n, K, S n is quark spin S is proton spin

Phys.Rev. C68 (2003) 022201

MODEL , HOW TO MEASURE? How to compute fundamentally? Measure h? : e + p( ) e0⇡X 1T " !

3 vectors: Spin direction, photon direction, hadron direction

e’

γ e

Cross section has term proportional to cos 3φ Βoer Mulders 1998 Measure h? : e + p( ) e0⇡X 1T " !

3 vectors: Spin direction, photon direction, hadron direction

e’

γ e

Cross section has term proportional to cos 3φ Βoer Mulders 1998 Summary • Proton is not round- Theory lattice QCD spin- dependent-density is not zero • Experiment can whether or not proton is round by measuring still waiting, some indications have been found

Summary • Proton is not round- Theory lattice QCD spin- dependent-density is not zero • Experiment can whether or not proton is round by measuring still waiting, some indications have been found

The Proton Electrophobic scalar boson and muonic puzzles Gerald A. Miller, University of Washington

Pohl et al Nature 466, 213 (8 July 2010)

Feb. 2014 Pohl, Gilman, Miller, Pachucki muon H rp =0.84184 (67) fm (ARNPS63, 2013) electron H rp =0.8768 (69)fm 2 2 dGE(Q ) electron-p scattering rp =0.875 (10)fm rp 6 ⌘ dQ2 Q2=0 PRad at JLab- lower Q2 4 % Difference RESEARCH ARTICLES

Figure 3 shows the two measured mp res- The uncertainties result from quadratically This rE value is compatible with our pre- onances. Details of the data analysis are given adding the statistical and systematic uncertain- vious mp result (6), but 1.7 times more precise, in (12). The laser frequency was changed every ties of ns and nt. and is now independent of the theoretical pre- few hours, and we accumulated data for up to The charge radius. The theory (14, 16–22) diction of the 2S-HFS. Although an order of 13 hours per laser frequency. The laser frequen- relating the Lamb shift to rE yields (13): magnitude more precise, the mp-derived proton cy was calibrated [supplement in (6)] by using radius is at 7s variance with the CODATA-2010 th 2 well-known water absorption lines. The reso- DE 206:0336(15 − 5:2275(10 r DETPE (7)valueofr =0.8775(51)fmbasedonHspec- L ¼ Þ Þ E þ E nance positions corrected for laser intensity ef- 7 troscopy and electron-proton scattering. fects using the line shape model (12)are ð Þ Magnetic and Zemach radii. The theoretical stat sys where E is in meV and rE is the root mean prediction (17, 18, 27–29)ofthe2S-HFSis(13) ns 54611:16(1:00) (30) GHz 2 ¼ ð Þ square (RMS) charge radius given in fm and 2 3 2 th pol stat sys defined as rE = ∫d rr rE(r) with rE being the DE 22:9763(15 − 0:1621(10)rZ DE nt 49881:35(57) (30) GHz 3 HFS ¼ Þ þ HFS ¼ ð Þ normalized proton charge distribution. The first 9 where “stat” and “sys” indicate statistical and sys- term on the right side of Eq. 7 accounts for ð Þ tematic uncertainties, giving total experimental un- radiative, relativistic, and recoil effects. Fine and where E is in meV and rZ is in fm. The first term is certainties of 1.05 and 0.65 GHz, respectively. hyperfine corrections are absent here as a con- the Fermi energy arising from the interaction Although extracted from the same data, the fre- sequence of Eqs. 4. The other terms arise from between the muon and the proton magnetic mo- quency value of the triplet resonance, nt,isslightly the proton structure. The leading finite size effect ments, corrected for radiative and recoil con- 2 more accurate than in (6)owingtoseveralimprove- −5.2275(10)rE meV is approximately given by tributions, and includes a small dependence of 2 ments in the data analysis. The fitted line widths Eq. 1 with corrections given in (13, 17, 18). −0.0022rE meV = −0.0016 meV on the charge are 20.0(3.6) and 15.9(2.4) GHz, respectively, com- Two-photon exchange (TPE) effects, including the radius (13). patible with the expected 19.0 GHz resulting from proton polarizability, are covered by the term The leading proton structure term depends the laser bandwidth (1.75 GHz at full width at half DETPE =0.0332(20)meV(19, 24–26). Issues on rZ,definedas maximum) and the Doppler broadening (1 GHz) related with TPE are discussed in (12, 13). th exp of the 18.6-GHz natural line width. The comparison of DEL (Eq. 7) with DEL 3 3 ′ ′ ′ rZ d r d r r r (r)r (r − r ) 10 The systematic uncertainty of each measure- (Eq. 5) yields ¼ ∫ ∫ E M ð Þ ment is 300 MHz, given by the frequency cal- exp th ibration uncertainty arising from pulse-to-pulse rE 0:84087(26) (29) fm with rM being the normalized proton mag- fluctuations in the laser and from broadening ¼ 0:84087(39) fm 8 netic moment distribution. The HFS polariz- effects occurring in the Raman process. Other ¼ ð Þ systematic corrections we have considered are Muonic Hydrogen Experiment the Zeeman shift in the 5-T field (<60 MHz), AC and DC Stark shifts (<1 MHz), Doppler shift (<1 MHz), pressure shift (<2 MHz), and black-body radiation shift (<<1 MHz). All these typically important atomic spectroscopy system- atics are small because of the small size of mp. The Lamb shift and the hyperfine splitting. From these two transition measurements, we can independently deduce both the Lamb shift

(DEL = DE2P1/2−2S1/2) and the 2S-HFS splitting (DEHFS) by the linear combinations (13)

1 3 hns hnt DEL 8:8123 2 meV 4 þ 4 ¼ þ ð Þ hns − hnt DEHFS − 3:2480 2 meV 4 ¼ ð Þ ð Þ

Finite size effects are included in DEL and DEHFS. The numerical terms include the cal- From 2013 culated values of the 2P fine structure, the 2P3/2 hyperfine splitting, and the mixing of the 2P states (14–18). The finite proton size effects on Science paper the 2P fine and hyperfine structure are smaller than 1 × 10−4 meV because of the small overlap between the 2P wave functions and the nucleus. Thus, their uncertainties arising from the proton structure are negligible. By using the measured transition frequencies ns and nt in Eqs. 4, we obtain (1 meV corresponds to 241.79893 GHz) Fig. 1. (A)Formationofmpinhighlyexcitedstatesandsubsequentcascadewithemissionof“prompt” DEexp 202:3706(23) meV 5 L ¼ ð Þ Ka, b, g.(B)Laserexcitationofthe2S-2Ptransitionwith subsequent decay to the ground state with Ka emission. (C)2Sand2Penergylevels.Themeasuredtransitionsns and nt are indicated together with DEexp 22:8089(51) meV 6 HFS ¼ ð Þ the Lamb shift, 2S-HFS, and 2P-fine and hyperfine splitting. EMBARGOED UNTIL 2PM U.S. EASTERN TIME ON THE THURSDAY BEFORE THIS DATE: 418 25 JANUARY 2013 VOL 339 SCIENCE www.sciencemag.org university of melbourne cssm, university of adelaide The Experimentmuonic hydrogen experiment Muonic Hydrogen

2P1/2 The Lamb shift is the splitting of the degenerate 2S1/2 and 2P1/2 eigenstates The Lamb shift is the splitting ∆ 2S−2P ELamb of the degenerate 2S1/2 and 2P1/2 eigenstates,Dominant due to in vacuum μH polar- vacuum polarization 205 of 206 meV ization

2S1/2 Dominant in eH electron self-energy ∞ 2 Zα α d(q ) −meqr 4 2 VVP(r)=− 2 e 1 − 2 1+ 2 r 3π 4 q q q Proton radius in! " # $ ? Lamb shift J. Carroll — Proton Radius Puzzle — Slide 8 pt 2 2 E = V V = ⇡↵ (0) ( 6G0 (0)) h S| C C | Si 3 | S | E • Muon/electron mass ratio 205! 8 million times larger for muon

1 university of melbourne cssm, university of adelaide The Experimentmuonic hydrogen experiment Muonic Hydrogen

1 4 % in radius: why care?

• Can’t be calculated to that accuracy • 1/2 cm in radius of a basketball Is the muon-proton interaction the same as the electron-proton interaction? - many possible ramiﬁcations 4 % in radius: why care?

116 DAVIER ! MARCIANO

1. INTRODUCTION

One of the great successes of the Dirac equation (1) was its prediction that the magnetic dipole moment, µ,ofaspin s 1/2 particle such as the electron (or muon) is given by ⃗ |⃗|= e µl gl s, l e,µ..., 1. ⃗ = 2ml ⃗ = with gyromagnetic ratio gl 2, a value already implied by early atomic spectroscopy. Later it was realized= that a relativistic quantum ﬁeld theory such as quantum electrodynamics (QED) can give rise via quantum ﬂuctuations to a shift in gl ,

gl 2 al − , 2. ≡ 2 called the magnetic anomaly. In a now classic QED calculation, Schwinger (2) found the leading (one-loop) effect (Figure 1), α al 0.00116 = 2π ≃ e2 α 1/137.036. 3. ≡ 4π ≃ This agreed beautifully with experiment (3), thereby providing strong confidence in the validity of perturbative QED. Today, we continue the tradition of testing QED and its SU(3)C SU(2)L U(1)Y standard-model (SM) extension (which includes × × exp strong and electroweak interactions) by measuring al for the electron and muon SM ever more precisely and comparing these measurements with al expectations, calculated to muchAnother higher order in perturbation muon theory. Such comparisons opp testortunity-anomalous moment by University of Washington on 01/27/13. For personal use only. 3.6 st. dev anomaly now Annu. Rev. Nucl. Part. Sci. 2004.54:115-140. Downloaded from www.annualreviews.org + fix: add new scalar boson interacts preferentially with muon µ ? Figure 1 The first-order µ Muon data is g-2 - BNL exp’t, QED correction to g-2 of the muon. Lamb shift Hertzog... Maybe dark p e p matter, µ energy particles show up as mediator in e muon µ p p physics!

1 Possible resolutions

• QED bound-state calculations not accurate-very unlikely- this includes recoil effects • Electron experiments not so accurate -new ones ongoing • other stuff -unlikely

• Muon interacts differently than electron!- scalar boson Notation

Couplings of to standard model fermions, f:

e✏ ff,¯ ✏ g /e L f f ⌘ f e = electric charge of the proton, f is particle label. One scalar boson exchange potential between ﬂavor 1 and 2:

m r V (r)= ✏ ✏ ↵e /r f1 f2 Others pursued this idea, using further assumptions:

TuckerSmith (2010) uses ✏p = ✏µ, ✏n =0 Izaguirre (2014), assume mass-weighted couplings & ✏n =0 Here: NO assumptions re signs or magnitudes of coupling constants. Lamb shift ✏ ✏ > 0 take ✏ , ✏ > 0. Then ✏ , ✏ : either sign ! µ p µ p e,µ n NT@UW-16-06

Electrophobic Scalar Boson and Muonic Puzzles

Yu-Sheng Liu,⇤ David McKeen,† and Gerald A. Miller‡ Department of Physics, University of Washington, Seattle, Washington 98195-1560, U.S.A. (Dated: May 17, 2016)

A new scalar boson which couples to the muon and proton can simultaneously solve the proton NT@UW-16-06 radius puzzle and the muon anomalous magnetic moment discrepancy. Using a variety of measurements, we constrain the mass of thisElectrophobic scalar and its couplings Scalar to Boson the electron, and Muonic muon, neutron, Puzzles and proton. Making no assumptions about the underlying model, these constraints and the requirement that it solve both problems limit the mass of the scalar to between about 100 keV and 100 MeV. We Yu-Sheng Liu,⇤ David McKeen,† and Gerald A.NT@UW-16-06 Miller‡ identify two unexplored regionsDepartment in the of coupling Physics, constant-massUniversity of Washington, plane. Potential Seattle, Washington future experiments 98195-1560, U.S.A. and their implications for theories with mass-weighted lepton(Dated: couplings May 17, 2016)are discussed. Electrophobic Scalar Boson and Muonic Puzzles A new scalar boson which couples to the muon and proton can simultaneously solve the proton radius puzzle and the muon anomalous magnetic moment discrepancy. Using a variety of measure- The recent measurementYu-Sheng of the Liu, protonments,⇤ David we charge constrain McKeen, radius the† massand of Geraldmuon’s this scalar A. magnetic Miller and its‡ couplings moment to due the electron, to one-loop muon, neutron,exchange and is using the LambDepartment shift of in Physics, muonic University hydrogenproton. of Making is Washington, troublingly no assumptions Seattle,given about Washington the by underlying [11] 98195-1560, model, theseU.S.A. constraints and the requirement (Dated: May 17, 2016) discrepant with values extracted fromthat standard it solve both hydrogen problems limit the mass of the scalar to between about 100 keV and 100 MeV. We identify two unexplored regions in the coupling constant-mass plane. Potential future experiments A new scalar boson which couples to the muon and proton can simultaneously2 solve1 the proton 2 spectroscopy and electron-proton scattering.and their implications Presently, for theories with mass-weighted↵✏ lepton couplings(1 arez) discussed.(1 + z) radius puzzle and the muon anomalous magnetic moment discrepancy. Usinga = a variety` ofdz measure- . (1) the value from muonic hydrogen is 0.84087(39) fm [1, 2] ` 2 2 ments, we constrain the mass of this scalar and its couplings to the electron, muon,2⇡ 0 neutron,(1 andz) +(m/m`) z while the CODATA average of data from hydrogen spec- Z proton. Making no assumptionsThe recent about measurement the underlying of the model, proton these charge constraints radius andmuon’s the requirement magnetic moment due to one-loop exchange is troscopythat and ite solve-p scattering both problemsusing yields the limit Lamb0.8751(61) the shift mass in of fm muonic the [3]; scalar these hydrogen to betweenAdditionally, is troublingly about 100 keV scalargiven and exchange 100 by [11] MeV. We between fermions f1 and f2 di↵er atidentify more than two unexplored 5. Although regions the in the discrepancy coupling constant-mass may plane. Potential future experiments mr discrepant with values extracted from standardleads hydrogen to a Yukawa potential, V (r)= ✏f1 ✏f2 ↵e /r. arise dueand to their subtle implications lepton-nucleonspectroscopy for theories non-perturbative and with electron-proton mass-weighted ef- scattering. leptonIn couplings atomic Presently, are systems, discussed. this leads↵✏ to2 an1 additional (1 z)2 contribu-(1 + z) a = ` dz . (1) the value from muonic hydrogen is 0.84087(39) fm [1, 2] ` 2 2 fects within the standard model or experimental uncer- tion to the Lamb shift in the2⇡ 2S-2P0 transition.(1 z) +(m For/m` an) z while the CODATA average of data from hydrogen spec- Z Thetainties recent [4, measurement 5], it could of also the proton be a signal charge of radius new physicsmuon’s magnetic(electronic moment or muonic) due to atom, one-loop N, ofexchange atomic mass is and num- troscopy and e-p scattering yields 0.8751(61) fm [3]; these usingcaused the Lamb by a shift violation in muonic of lepton hydrogen universality. is troublingly givenmuonic byber [11] g-2A and Z LambthisAdditionally, shiftshift is given scalar by exchange [12] between fermions f1 and f2 di↵er at more than 5. Although• the discrepancy may mr leads to a Yukawa potential, V (r)= ✏f1 ✏f2 ↵e /r. discrepantAnother with values potential extracted signalarise from of due new standard to physicssubtle hydrogen lepton-nucleon is the muon non-perturbative ef- 2 1 In↵ atomic2 systems, this leads to an additional contribu- spectroscopyanomalous and magnetic electron-proton moment.fects scattering. within The BNL the standard Presently, [6] measurement model or experimental↵✏ uncer-``N (1 z) (1 + z) a =E = dz tion✏ to`[Z the✏p +( LambA shiftZ).✏ inn] thef((1)a 2S-2P`Nm) transition. (2) For an the value from muonic hydrogen is 0.84087(39) fm [1, 2] ` L 2 2 di↵ers from the standardtainties model [4, prediction 5], it could by also at be least a signal of new2 physics⇡ 0 2(1a(electronic`N z) +( orm muonic)/m`) z atom, N, of atomic mass and num- while the CODATA average of data from hydrogenexp th spec- Z three standard deviations,causedaµ by= aaµ violationaµ of= lepton 287(80) universality. ber A and Z this shift is given by [12] troscopy11 and e-p scattering yieldsAnother 0.8751(61) potential fm [3]; signal these of newAdditionally,⇥ physics is thescalar muon exchange2 between4 fermions f and f 1 10 [7, 8]. where f(x)=x /(1+x) [9, 13], with1 a`N =(2 Z↵ m`N) di↵er at more than 5. Althoughanomalous the discrepancy magnetic moment. may The BNL [6] measurement `N ↵ mr leads to athe Yukawa Bohr potential, radius andV (rm)= is✏f1 the✏f2 ↵ reducede /r. mass of the A new scalar boson, which we denote , that couples Lamb Shift EL `=N ✏`[Z✏p +(A Z)✏n]f(a`Nm) (2) arise due to subtle lepton-nucleondi↵ers non-perturbative from the standard ef- modelIn prediction atomic systems, by at least this leads to an additional2a`N contribu- to the muon and proton could explain both the protonexp lepton-nucleusth system. Throughout this paper we set f(x)=x2/(1 + x)4 fects within the standard modelthree or standard experimental deviations, uncer-aµ =tionaµ to theaµ = Lamb 287(80) shift in the 2S-2P transition. For an ⇥ 2 4 1 taintiesradius [4, and5], it (g could2)µ alsopuzzles be10 a11 [9].signal[7, We 8]. of investigate new physics the cou- where f(x)=x /(1+x) [9, 13], with a`N =(Z↵ m`N) (electronic or muonic) atom, N, of atomic11 µ massH and num- causedplings by a of violation this boson of lepton to standard universality.A new model scalar fermions, boson, whichf,which weber denoteA and,Z thatathisµ couples= shift 287(80) is giventhe10 Bohr by [12] radius, EL and= m0`N.307(56)is the reduced meV (3) mass of the lepton-nucleus⇥ system. Throughout this paper we set Anotherappear potential as terms signal in the of Lagrangian,to new the physics muon and is the protone✏ muonf ff could¯ ,where explain both the proton radius and (g L 2) puzzles [9]. We investigate the↵ cou- µH anomalous✏ = g magnetic/e and moment.e is the The electric BNL [6] charge measurementµ of the proton. `Nwithin two standard deviations. This valueµH of E ,is f f E = ✏`[Z✏p +(A Z)✏n]f(a`Nm11) (2) L plings of this boson to standard model fermions,L f,which aµ = 287(80) 10 , EL = 0.307(56) meV (3) di↵ersOther from authors the standard have pursued model prediction the basic byidea at but least have gen- the same2a`N as the energy shift caused⇥ by using the di↵erent appearexp as termsth in the Lagrangian, e✏f ff¯ ,where three standard deviations, aµ = aµ aµ = 287(80) erally made further assumptions✏ = g /e relatingand e is the the⇥ electric couplings chargeL ofvalues the2 proton. of the4 protonwithin radius two standard [1–3, 14] deviations. to explain1 This the value two of EµH,is 10 11 [7, 8]. f f where f(x)=x /(1+x) [9, 13], with a`N =(Z↵ m`N) L to di↵erent species; e.g.Other in [9], authors✏p is have taken pursued equal the to basic✏µ ideadiscrepancies. but have gen- Thisthe same allows as the us energy to determine shift caused both by using✏p and the di↵erent A new scalar boson, which we denote , that couples the Bohr radius and m`N is the reduced mass of the and in [10], mass-weightederally couplings made further are assumed. assumptions Ref- relating✏ theµ as couplings functions ofvaluesm. of The the proton unshaded radius regions [1–3, 14] in to Figs. explain 1 the two to the muon and proton could explain both the proton lepton-nucleus system. Throughout this paper we set erences [9] and [10] both neglectto di↵erent✏n (due species; in e.g.part in to [9], strong✏p is takenand equal 3 show to ✏µ thediscrepancies. values of ✏p Thisandallowed allows✏µ, respectively, us to determine as both a ✏p and radius and (g 2)µ puzzles [9]. We investigate the cou- constraints on this couplingand inthat [10], we mass-weighted will outline couplings below). are assumed.function Ref- of the11 ✏ scalar’sµ asµH functions mass of thatm. lead The to unshaded the values regions of in Figs. 1 plings of this boson to standard model fermions, f,which aµ = 287(80) 10 , EL = 0.307(56) meV (3) erences [9] and [10] both neglect ✏n (due in part to strong⇥ µH and 3 show the values of ✏p and ✏µ, respectively, as a We make no aprioriassumptions regarding¯ signs or mag-allowedaµ and E in Eq. (3). appear as terms in the Lagrangian,constraints one✏f thisff coupling,where that we will outline below).L function of the scalar’s mass that lead to the values of L µH µH arXiv:1605.04612v1 [hep-ph] 15 May 2016 nitudes of the coupling constants. The Lamb shift in We next study several observables sensitive to the cou- ✏f = gf /e and e is the electricWe make charge no ofapriori the proton.assumptionswithin regarding two signs standard or mag- deviations.aµ and ThisEL valuein Eq. of (3).EL ,is muonic hydrogen fixes ✏µ and ✏p to have the same sign plings of the scalar to neutrons, ✏ , and protons, ✏ .This Other authors have pursuedarXiv:1605.04612v1 [hep-ph] 15 May 2016 thenitudes basic idea of the but coupling have gen- constants.the same The Lambas the shift energy in shift causedWe next by study using several then di observables↵erent sensitivep to the cou- erallywhich, made without further assumptionsloss of generality,muonic relating hydrogen we the take couplings fixes to✏ beµ and positive.✏pvaluesto have ofallows the same proton us sign to radius obtainplings [1–3, new of 14] the bounds to scalar explain onto neutrons,m the. two✏n, and protons, ✏p.This to di✏↵e erentand ✏ species;n are allowed e.g. in to [9],which, have✏p is either without taken sign. equal loss of toYavin-&Tucker-Smith generality,✏µ discrepancies. we take to be positive. This allows assumeallows us to us determine to coupling obtain both new bounds✏p toand onneutronm. = proton ✏ and ✏ are allowed to have either sign. and inIn [10], the mass-weighted following, we couplings describee are an host assumed. of e↵ects Ref- and✏ pro-µ as functionsLow of m energy. The unshaded scattering regions of neutrons in Figs. 1on 208Pb has erences [9] and [10] both neglect ✏In(due the following, in part to we strong describe aand host 3 of show e↵ects the• and values pro- of ✏ andLow✏ energy, respectively, scattering as of a neutrons on 208Pb has cesses that could be sensitiven to the scalar boson.n- Pb(208) Our imposebeen used severe top • constrain µrestriction, light force carriers but why coupled =? constraints on this coupling thatcesses we that will outline could be below). sensitive tofunction the scalar of boson. the scalar’s Our mass thatbeen lead used to to the constrain values light of force carriers coupled analysis starts by assuming that scalar boson exchange µH to nucleons [15] assuming a universal coupling of a We make no aprioriassumptionsanalysis regarding starts signs by assuming or mag- that scalara and bosonE exchangein Eq. (3). to nucleons [15] assuming a universal coupling of a can account for both the proton radius puzzle and theµ L can account for both the proton radius puzzle andscalar the to nucleonsscalar of togN nucleons. Using of thegN . replacement Using the replacement arXiv:1605.04612v1 [hep-ph] 15 May 2016 nitudes of the coupling constants. The Lamb shift in We next study several observables sensitive to the cou- (g 2)µ discrepancy. The(g shift2)µ discrepancy. of the lepton The (` shift= µ, of e the) lepton (` = µ, e) muonic hydrogen fixes ✏µ and ✏pto have the same sign plings of the scalar to neutrons, ✏n, and protons, ✏p.This 2 g2 A Z Z gN A Z 2N Z 2 which, without loss of generality, we take to be positive. allows us to obtain new bounds on m. ✏n + ✏p✏n (4) 2 ✏en2 +! ✏Ap✏n A (4) ✏e and ✏n are allowed to have either sign. e ! A A In the following, we describe a host of e↵ects and pro- 208 ⇤ [email protected] Low energy scattering offor neutrons scattering on on a nucleusPb has with atomic mass A and [email protected] • for scattering on a nucleus with atomic mass A and cesses⇤ that could be sensitive to† [email protected] the scalar boson. Our been used to constrain lightatomic force number carriersZ, coupled we can separately constrain the analysis† [email protected] starts by assuming that‡ [email protected] scalar boson exchange to nucleonsatomic [15] assuming numbercoupling aZ universal, we can of a coupling separately scalar to of protons a constrain and neutrons. the [email protected] can‡ account for both the proton radius puzzle and the scalar to nucleonscoupling of ofgN a. scalar Using to the protons replacement and neutrons. (g 2) discrepancy. The shift of the lepton (` = µ, e) µ g2 A Z Z N ✏2 + ✏ ✏ (4) e2 ! A n A p n

⇤ [email protected] for scattering on a nucleus with atomic mass A and † [email protected] atomic number Z, we can separately constrain the ‡ [email protected] coupling of a scalar to protons and neutrons. Nuclear Physics Constraints

Low energy n Pb scattering constrains gN

Charge independence breaking of nucleon-nucleon scattering

1/2(Vnn+Vpp)- Vnp is constrained to be small via scattering length difference <1.6 fm

3 3 Binding energy difference between He and H: Vpp-Vnn change in binding energy difference < 30 keV Binding energy in inﬁnite nuclear matter: change in binding energy <1 MeV Constrain coupling to electron (analysis similar to dark photon) • anomalous magnetic moment of electron- used to determine ↵ , needs value obtained free of possible scalar boson effects- ratio of Planck constant to mass of Rb: Bouchendira et al PRL 106 080801

+ - m • Bhabha (e e ) scattering sensitive to resonance at cm energy = Bhabha scattering in the MeV range Tsertos et al PRD40, 1397 • Beam dump experiments- phi decays to e+e- or pairs. We provide exact evaluation of phase space integral • Lamb shift in hydrogen <14 kHz (Eides reviews) • Stellar cooling limits see An et al PLB725,190 (we have same limits for masses less than 200 keV). Supernova cooling -gp large enough to keep scalar trapped mu D and mu He constraints EµD = 0.368 (78) meV • L (Preliminary) from talk, 3 st. dev. EµHe = 1.4(1.5) meV • L (Preliminary) from talk, 3 st. dev

Combining nuclear and muonic atom results Shaded regions excluded

Allowing opposite sign widens allowed region Possible new experiments • Publish muon D and muon 4He results (big impact on soft proton) • proton and or muon beam dump experiments for large mass region • low mass region Izaguirre et al underground nuclear decays • pp to pp phi detect protons • improve neutron-nucleus experiments • If scalar boson solves proton radius problem, MUSE will detect same `large radius’ for positively and negatively charge electrons and muons • muon beam dump (COMPASS) • new muon anomalous moment measurement • Goudelis et al PRL 116, 211303 particle of mass 1.6 to 20 MeV may provide solution to understanding cosmological abundance of 7Li Summary of proton size

• If all of the experiments relevant to rp, and their analyses, are correct some unusual or BSM physics occurs • new scalar boson • Searching over a wide range of experiments a new scalar boson could account for both muonic puzzles and exist in the allowed parameter space.

Liu McKeen Miller 1605.04612