Sensitivity potential to a light flavor-changing scalar boson with DUNE and NA64 μ

Eu . Phys. J. C (2023) 83:775 h ps://doi.o g/10.1140/epjc/s10052-023-11891-3 Regula A icle - Expe imen al Physics Sensi i i y po en ial o a ligh la o -changing scala boson wi h DUNE and NA64µ B. Radics1,a, L. Molina-Bueno2, L. Fields3, H. Siebe 4, P. C i elli4 1Depa men o Physics and As onomy, Yo k Uni e si y, To on o, ON, Canada 2Ins i u o de Física Co puscula , Uni e sidad de Valencia and CSIC, Ca e del Ca ed á ic José Bel án Ma inez, 2, 46980 Pa e na, Valencia, Spain 3Depa men o Physics and As onomy, Uni e si y o No e Dame, No e Dame, IN 46556, USA 4ETH Zü ich, Ins i u e o Pa icle Physics and As ophysics, 8093 Zu ich, Swi ze land Recei ed: 12 June 2023 / Accep ed: 31 July 2023 / Published online: 4 Sep embe 2023 © The Au ho (s) 2023 Abs ac In his wo k, we epo on he sensi i i y po en- ial o complemen a y muon-on- a ge expe imen s o new physics using a scala boson benchma k model associa ed wi h cha ged lep on la o iola ion. The NA64μexpe i- men a CERN uses a 160-GeV ene gy muon beam wi h an ac i e a ge o sea ch o excess e en s wi h missing ene gy and momen um as a p obe o new physics. A he same ime, he p o on beam a Fe milab, which is used o p oduce he neu ino beam o he Deep Unde g ound Neu- ino Expe imen (DUNE), will also p oduce a high-in ensi y muon beam dumped in an abso be . Combined wi h he liq- uid a gon nea de ec o , he sys em could be used o sea ch o simila scala boson pa icles wi h a lowe -ene gy bu highe -in ensi y beam. We ind ha bo h NA64μand DUNE could co e new, unexplo ed pa s o he pa ame e space o he same benchma k model, p o iding a complemen a y way o sea ch o new physics. 1 In oduc ion Obse a ions in cosmology and as ophysics imply he exis- ence o a da k sec o po en ially con aining new pa icles ha could weakly couple o S anda d Model (SM) pa i- cles [1]. Neu ino oscilla ions coupled wi h nonze o neu ino masses p o ide expe imen al e idence o lep on la o io- la ion. Fu he mo e, he exis ing disc epancy be ween he measu ed [2] and expec ed [3,4] alue o he muon anoma- lous magne ic momen p o ides s ong mo i a ion o new physics sea ches wi h muons [5]. Inspi ed by hese de elop- men s, a ce ain class o new heo ies p oposes he sea ch o cha ged lep on la o iola ion (CLFV), which is hea ily ae-mail: [email p o ec ed] (co esponding au ho ) supp essed in he SM. In he coming decades, a new gene - a ion o expe imen s will be conduc ed o sea ch o CLFV [6–11]. In pa allel, nex -gene a ion long-baseline neu ino oscilla ion expe imen s [12,13] will s udy neu ino oscilla- ions while a he same ime p oducing an in ense muon beam dump wi h i s beam line. In his wo k, we s udy he sensi i i y po en ial o muon-on- a ge expe imen s o new physics using a CLFV benchma k model in oduced in a ecen wo k [14], which uses a ligh , scala boson associa ed wi h μ−τcon e sion. While he p e- ious wo k de i ed cons ain s om da a in exis ing beam- dump expe imen s (LSND [15], NuTeV [16], CHARM [17]) and o he u u e SHiP expe imen [18], he e we ocus on wo u he expe imen s: he coming neu ino expe imen , DUNE [12] deploying a high-in ensi y beam om he Long-Baseline Neu ino Facili y (LBNF) [19], and a ixed- a ge expe i- men , NA64μ[20,21], which sea ches o new physics wi h he high-ene gy muon beam om he CERN Supe P o on Synch o on (SPS) accele a o . Hence, we s udy new physics sea ches using wo complemen a y muon beam se ups. E en hough we ocus on one pa icula benchma k model sce- na io, he e a e also o he possibili ies o p obe hidden sec- o s wi h muon beams and using simila echniques [22–26]. We also no e ha o he g oups ha e also pe o med s udies o (cha ged) lep on la o physics, including he ole o mesons o bosons wi h di e en spin-pa i y assignmen s [27–32]. 2 Fla o -changing scala wi h long li e ime The model p oposed by [14] conside s a new complex scala ield, φ, wi h a mass window [mτ−mμ,mτ+mμ] ha cou- ples o (μ, τ ). Wi h such a mass ange, long li e imes can 123 775 Page 2 o 7 Eu . Phys. J. C (2023) 83 :775 be achie ed wi h p opaga ion dis ances on he o de o ens o kilome e s. The e ec i e Lag angian in e ac ion e ms desc ibe he coupling o he new scala ield wi h lep ons, LI=φ¯μ(gV+gAγ5)l+φ∗¯ l(g∗ V−g∗ Aγ5)μ (1) wi h ec o and axial ec o coupling gV,gA, espec i ely. This model p oduces a benchma k pa ame e egion explain- ing he muon g−2 anomaly wi h a ypical alue o |gV|≃ 3×10−3, also used in his wo k. The e a e mul iple p oduc- ion modes o p oduce φa beam dump expe imen s: di ec elec oweak p ocess, hea y meson decay, and high-ene gy muons hi ing a ixed a ge . In his wo k, we ocus on he hi d case ( he so-called μ-on- a ge scena io). In his mode, muons pass h ough dense ma e ial and can p oduce he φ boson ia he exchange o a i ual pho on wi h he nuclei o he a ge , μ(p)N(Pi)→τ(p)φ(k)N(P ). Once c ea ed, he bosons p oduce a missing ene gy signa u e o p opaga e long dis ances and may be de ec ed in a de ec o downs eam om he a ge . When he incoming beam ene gy is much highe han he pa icle mass, he double-di e en ial c oss sec ion o he 2 →3 p oduc ion p ocess can be es ima ed using he equi alen pho on app oxima ion [33], d2σ(p+Pi→p+k+P ) dEφd cos θφ =αχ π Eμxβφ 1−x dσ(p+q→p+k) d(p·k) = min ,(2) whe e Eμis he ini ial muon ene gy, Eφis he ene gy and θφ he sca e ing angle o φwi h espec o he ini ial muon in he lab ame, x=Eφ/Eμ,q=Pi−P , =−q2is he momen um ans e , α=1/137 is he ine s uc u e cons an , βφis he ela i is ic ac o o φ, and χis he e ec i e pho on lux, de ined as χ= max min d − min 2F2( ), (3) whe e F( )=Z2/(1+ /d)2is he o m ac o , wi h d= 0.164 GeV2A−2/3, and he limi s a e gi en in he appendix o [14]. We calcula e he analy ical exp ession o χusing Ma hema ica [34] and ob ain χ=Z2 min +d+ min d+ +(d+2 min) d ln ln (d+ ) max min . (4) In Eq. (2), σ(p+q→p+k)is he c oss sec ion o he 2→2 sca e ing p ocess, μ(p)γ (q)→τ(p)φ(k), dσ(p+q→p+k) d(p·k)=|¯ A2→2|2 8πs2,(5) whe e |¯ A|2is he ampli ude squa ed, which we calcula e using he FeynCalc ools [35] o Ma hema ica. We ob ain he ollowing exp ession o he (μ, τ) case |¯ A2→2|2=−e2mμmτ(gAg∗ A−gVg∗ V) (m2 μ−s)2(m2 τ−u)2 ×m4 μ(m2 φ+u)+2m3 μ(m3 τ−mτu) +m2 μm4 τ−2m2 φs−2m2 τu+u(u−2s) +2mμmτs(u−m2 τ)+sm2 φs+m4 τ−2m2 τu+u(s+u), (6) whe e e=√4πα,mφ,mτ, and mμa e he masses o he boson φ,τ, and μ, espec i ely, and s,ua e he Mandels am a iables, which can be e alua ed in he labo a o y ame, s=(p+q)2≃m2 μ−u−m2 τ 1−x u=(p−k)2≃−Eμxθ2 φ−1−x xm2 φ+(1−x)m2 μ.(7) To calcula e he li e ime o he φboson, τφ, we use Equa- ions 3.2−3.5 in [14] adap ed o he (μ, τ ) case. We calcula e he c oss sec ion and decay wid h using he GNU Scien i ic Lib a y [36]. The p oduc ion c oss sec ion o he φboson as a unc ion o he incoming lep on ene gy is shown in Fig. 1. Assuming mφ≃mτ, he h eshold o he p oduc ion is gi en by Eμ>[(2mτ+mN)2−m2 μ−m2 N]/2mN≃3.8GeV o Pb, abo e which he c oss sec ion s eeply ises. In he ol- lowing, we use he co esponding muon beam lux o each expe imen (NA64μand DUNE) o e alua e he exp essions o he φp oduc ion ia he a iables de ined in Eq. (7). 3µ-on- a ge expe imen s We es ima e he p ojec ed sensi i i y o an expe imen by inding he pai o pa ame e alues (gV,mφ), whe e Nφ app op ia e signal e en s a e p oduced ei he di ec ly in he a ge (NA64μ) o in he de ec o (DUNE), as explained la e , a e a gi en exposu e. In his wo k we exploi he φboson p oduc ion p ocess using di e en and complemen a y μ- on- a ge expe imen s: NA64μwi h he ac i e dump ech- nique (using missing ene gy as a signal) compa ed o p o on beam-dump expe imen s such as he DUNE neu ino expe i- men using he LBNF p o on beam (di ec de ec ion h ough in e ac ion as a signal). Al hough he unde lying p oduc ion mechanism is he same, he wo echniques di e in he lux o he muon beam, μ(E), and he a ge hickness and ma e- ials. In a gene al case, φbosons a e gene a ed by he μ-on- a ge p ocess, and a e p oduc ion, a ac ion o hem decay 123 Eu . Phys. J. C (2023) 83 :775 Page 3 o 7 775 Fig. 1 P oduc ion c oss sec ion o he φboson, wi h mass mφ=mτ and coupling cons an |gV|=3×10−3, as a unc ion o he incoming muon ene gy inside a de ec o olume and can be de ec ed. The numbe o such signal e en s is Nφ=dEφφ(Eφ)×lde γβcτφ ,(8) whe e γis he ela i is ic Lo en z ac o , lde is he leng h wi hin which bosons decay, lde /γβcτφis he ac ion o bosons decaying in ligh o p oduce a signal in he de ec o , and φ(Eφ)is he lux o φbosons a he de ec o , es ima ed as φ(Eφ)=dEμ(E)E Emin dEl nA −dE/dl ×θde 0 dθφsin θφ d2σ(El,Eφ) dEφd cos θφ .(9) He e, μ(E)is he lux o he muon beam as a unc ion o ene gy, nAis he numbe o a ge a oms pe olume, El is he muon ene gy a e a eling a leng h lin he a ge and losing ene gy acco ding o he s opping powe −dE/dl, Emin is he ene gy o he muon a he end o he a ge , and θde is he angula accep ance o he de ec o . In he ollowing subsec ions, we sepa a ely desc ibe he wo expe imen al scena ios and he assump ions in he de i ed sensi i i y limi s. 3.1 NA64μscena io NA64μis a ixed- a ge expe imen a CERN looking o new pa icles o da k ma e and po al in e ac ions p oduced in elec omagne ic showe s and coupled o muons. The expe - imen uses he seconda y 160-GeV muons om he in e ac- ions o 400-GeV p o ons om he CERN SPS wi h a a ge . A se o beam scin illa o s and e o coun e s, low-ma e ial- budge acke s, and dipole magne s allow us o p ecisely cons ain he momen um o he incoming 160-GeV muons impinging on an ac i e a ge . The main de ec o , whe e φ may be p oduced, consis s o an elec omagne ic calo ime- e wi h 40 X0 adia ion leng h. Downs eam, he de ec o is u he equipped wi h e o coun e s and a ∼30-in e ac ion- leng h had onic calo ime e . New pa icles could be p oduced by he muon beam sca e ing in he a ge and la e decay o isible SM pa icles ha could be seen by hei signa u es in a downs eam de ec o . The cu en wo k is based on he de ec ion o missing ene gy and momen um ca ied away by he p oduced hypo he ical, long-li ed φboson, lea ing a sca e ed muon as expe imen al signa u e (wi h he momen- um o he sca e ed muon in he ange o 10–80 GeV/c). The sensi i i y in he sea ch o he φboson is highe wi h espec o he beam-dump app oach due o he lowe powe in he coupling s eng h wi hou a decay e ex. Thus, in NA64μ, only he numbe o e en s a he p oduc ion a ge needs o be es ima ed. The e o e, he numbe o e en s is gi en by Nφ=dEφφ(Eφ). Fu he mo e, he p oduc ion a ge hickness is small, and he muon ene gy loss can be neglec ed. As a esul , we use he ollowing exp ession o es ima e he φboson lux φ(Eφ)=l a ge nAdEμ(E) ×θde 0 dθφsin θφ d2σ(E,Eφ) dEφd cos θφ ,(10) whe e l a ge is he hickness o he a ge . The e has been ex ensi e s udy o simula ing and e alua - ing he p oduc ion o da k ma e pa icles wi h a muon beam a NA64 [26,37,38]. We use he same me hod in his wo k o es ima e he sensi i i y each o he expe imen . We assume a muon beam wi h a mean o 160 GeV ene gy and a wid h o 4.3 GeV hi ing a lead a ge wi h o al da a o ∼3×1013 muons-on- a ge (MOT). 3.2 DUNE/LBNF scena io The Deep Unde g ound Neu ino Expe imen is a nex - gene a ion, wide-ene gy-beam long-baseline neu ino expe - imen a Fe milab. I will use an in ense (an i)neu ino beam ha passes h ough a nea de ec o a Fe milab and a a de ec- o 1300km away in Sou h Dako a. The neu ino beam line 123 775 Page 4 o 7 Eu . Phys. J. C (2023) 83 :775 o DUNE is a esul o exhaus i e design and op imiza ion wo k [19]. The beam is p oduced by a 60–120-GeV p o on beam hi ing a g aphi e a ge , a e which he p oduced pions and kaons decay o lep ons and neu inos in a ∼220-m-long decay pipe. A he end o he pipe, a dedica ed ∼30-m- long s ainless-s eel s uc u e ac s as a beam dump o s op all muons 300 m ups eam om he nea de ec o . We use he simula ion o he neu ino beam p oduc ion o ace pa icles along he beam axis. The muon lux used in he calcula ion is es ima ed om a dedica ed acking plane, which is loca ed a he end o he decay pipe in he simula ion. An example o he ob ained muon ene gy spec um is illus a ed in Fig. 2. The peak o he spec um is a Eμ≃2.5 GeV; howe e , he long high-ene gy ail is esponsible o he majo i y o φ boson p oduc ion due o he apid inc ease in he c oss sec ion wi h he incoming lep on ene gy (see Fig. 1). A he lowe - ene gy egion, he p oduc ion a e is much smalle . F om he neu ino lux simula ion we es ima e an in eg a ed muon lux o μ≃5×1019 muons o 1.1×1021 p o ons on a ge (POT), co esponding o 1 yea o da a- aking. In DUNE, a signal could be de ec ed in he nea de ec- o om he decay o he φboson ha was p oduced by he muons hi ing he s ainless-s eel dump. We conside he decay channel φ→μ+μ−νμντwi h a b anching a io o 17% [14], mo i a ed by he dimuon esul s om NuTeV [16]. Possible backg ounds leading o a dimuon signa u e include deep inelas ic sca e ing (DIS) and esonance p oduc ion o mesons in cha ged-cu en (CC) muon–neu ino (νμ) in e - ac ions wi h a a ge nucleus. The mesons could decay in semi-lep onic mode, p oducing an ex a muon. In o de o analyze such po en ial backg ound p ocesses, we pe o med simula ions wi h he GENIE [39] Mon e Ca lo (MC) e en gene a o ha p o ides a comp ehensi e neu ino in e ac ion modeling in he Eν∼100 MeV − ew-hund ed GeV neu- ino ene gy egion, including quasi-elas ic, esonance, and DIS p ocesses. Unlike he φboson decay, e en s wi h DIS o esonan meson p oduc ion a e accompanied by addi ional ac i i y in he inal s a e. Simila ly o p e ious indings o NuTeV, a e disc imina ing o low-mul iplici y e en s wi h wo muons, we ound ha hese backg ounds could be com- ple ely supp essed in an MC simula ion o 400 million e en s o neu ino in e ac ions on an a gon a ge (co esponding o ∼5 yea s o ope a ion o DUNE a he nominal in en- si y). Howe e , u he s udies a e planned wi h a ull de ec- o simula ion o gain a de ailed unde s anding o he possible bounds on he backg ound ejec ion. 4 Resul s We illus a e he sensi i i y po en ial o he benchma k CLFV scena io wi h he complemen a y muon beams a NA64μand DUNE in Fig 3. Fo bo h expe imen s, he Fig. 2 Ene gy spec um o muons a he end o he decay pipe om he ull DUNE neu ino beam line simula ion [19], see explana ion in he ex double-di e en ial c oss sec ion in Eqs. (9)o (10) is e al- ua ed gi en he ene gy spec a o each expe imen , μ(E), and he kinema ic limi s on he inal-s a e φ-boson ac ional ene gy, x, which is cons ained by he masses o he boson φ and he τ. In he case o he NA64μexpe imen , a o al in eg a ed muon lux o ∼3×1013 MOT is achie able [20]. The ime needed o accumula e he assumed o al MOT is es ima ed o be ∼100 days. This conse a i e es ima ion is based on he CERN SPS deli e ing on a e age 3500 spills pe day and 2 ×108muons pe spill. Bene i ing om he unique combina ion o a 160-GeV muon beam wi h missing-ene gy and momen um sea ch, NA64μwould be able o pe o m a compe i i e sea ch o such a CLFV signal. Fu he mo e, he sensi i i y each c i ically depends on he leng h o he ac i e a ge . We ind ha a 1-m-long a ge would al eady be able o explo e a la ge pa o he pa ame e space, gV≥6×10−3. Howe e , he expe imen is highly modula , and a possible op imiza ion o he se up could u he enhance i s po en ial: a easible op ion is o inc ease he a ge leng h o 5m which would make i possible o comple ely co e he (gμ−2) p e e ed egion and o p obe a a ie y o o he new physics scena ios in ol ing muons. We also ind ha , al eady wi h a10 12 MOT and a ∼3-m-long a ge , he gV≥×10−2 pa ame e egion can be co e ed. A de ailed Mon e Ca lo simula ion o an op imized se up will ollow as a nex s ep. Fo he DUNE expe imen , he φ-boson p oduc ion is d i en by he high-end ail o he muon lux. Compa ed o 123 Eu . Phys. J. C (2023) 83 :775 Page 5 o 7 775 NA64μ, he lowe muon ene gies a DUNE and hus lowe p oduc ion c oss sec ion a e compensa ed by he mo e in ense muon lux. Assuming 10–20 yea s o ope a ion a nominal in ensi y, DUNE would be able o explo e a signi ican pa o he pa ame e space, eaching in o he gV≃10−2 egion and po en ially imp o ing he cons ain s om NuTeV. How- e e , an op imiza ion o he neu ino beam line could u - he enhance he con ibu ion o high-ene gy muons in he lux and subsequen ly app oach he gV≤10−2benchma k egion. This scena io is pa ially mo i a ed by a ecen wo k explo ing an al e na i e beam-dump ope a ion mode o p obe new physics wi h DUNE [40]. Fo compa ison, we also show he p ojec ed sensi i i y o he same μ-on- a ge mode calcula ed by [14] o CHARM, NuTeV, and SHiP. He e, we do no show he cons ain s o p ojec ed sensi i i y limi s de i ed o he di ec elec oweak and hea y meson decay p ocess, which was included in he p e ious wo k [14], since we only ocus on he μ-on- a ge scena io. In he case o SHiP, he assumed o al da a co - esponds o 2 ×1020 p o ons on a ge (POT). The wo se sensi i i y in DUNE ela i e o SHiP s ems om he lowe muon ene gies in he lux [41]. I is also no ed ha he e a e di e ences in he beam in ensi y be ween NA64μand SHiP. We assume 1012 POT pe spill in ensi y a he CERN SPS in he case o he muon beam line used by NA64μ, while o SHiP he p o on beam in ensi y is gene ally expec ed o be an o de o magni ude highe . We no e ha a simila se up o NA64μis capable o sea ching o o he new scala pa icle candida es using he same muon beam [26]. In addi ion, he p oposed Muon Miss- ing Momen um (M3) expe imen a Fe milab [42] plans o p obe new physics wi h a dedica ed muon beam. Finally, a numbe o expe imen s also ha e he po en ial o sea ch o hidden-sec o scala pa icles, such as SHADOWS [43], HIKE [44], and ATLAS [45]. 5 Conclusions In summa y, we p esen he sensi i i y po en ial o wo μ-on- a ge expe imen s, NA64μand DUNE, as complemen a y modes o sea ching o new physics wi h muon beams. We ind ha bo h NA64μand DUNE ha e he po en ial o co e a signi ican po ion o he benchma k model pa ame e space, (mφ,gV). NA64μwi h an op imized se up could p obe he coupling pa ame e down o gV≃3×10−3, comple ely co e ing he muon gμ−2 p e e ed egion and hus p o id- ing a simila p ojec ed each as SHiP. DUNE will also be able o co e unexplo ed pa s o he pa ame e space, po en- ially imp o ing on he ob ained cons ain s om NuTeV. An op imiza ion o he neu ino beam line, inc easing he con- ibu ion om he high-ene gy ail, could allow us o u he enhance he sensi i i y o DUNE. Fig. 3 Cons ain s om CHARM, NuTeV [16,17], and p ojec ed sen- si i i y cu es o SHiP [14,18] (dash-do ed, magen a line), DUNE (solid b own and blue lines o 10 and 20 yea s o ope a ion, espec- i ely), and NA64μ(dashed b own and black lines) in he μ-on- a ge p oduc ion mode (excep o CHARM). In he case o NA64μ, he op i- mized se up wi h 1-m-long (b own dashed line) and 5-m-long (black dashed line) a ge s a e also shown sepa a ely. The ligh blue egion shows he benchma k pa ame e ange explaining he muon gμ−2 anomaly Al hough we use a gi en CLFV model as a benchma k in his wo k, we no e ha simila echniques can be used o s udy he sensi i i y po en ial o expe imen s wi h muon beams o o he physics scena ios. Beyond he gμ−2 disc ep- ancy and neu ino la o oscilla ions, sea ches o da k sec o pa icles a e also mo i a ed by he ma e –an ima e asym- me y, he known da k ma e abundance om as ophysical and cosmological obse a ions, o by heo e ical mo i a ions s ongly sugges ing he exis ence o addi ional gauge g oups weakly coupling o SM ields [1,46]. Acknowledgemen s We g a e ully acknowledge con e sa ions wi h D. Ha is. The wo k o LMB is suppo ed by SNSF G an no. 186158 (Swi ze land), RyC-030551-I, and PID2021-123955NA-100 unded by MCIN/AEI/ 10.13039/501100011033/FEDER, UE (Spain). Da a A ailabili y S a emen This manusc ip has no associa ed da a o he da a will no be deposi ed. [Au ho s’ commen : The simula ions and calcula ions ha suppo he indings o his s udy a e a ailable om he au ho s upon eques ]. Open Access This a icle is licensed unde a C ea i e Commons A i- bu ion 4.0 In e na ional License, which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o- ide a link o he C ea i e Commons licence, and indica e i changes 123 775 Page 6 o 7 Eu . Phys. J. C (2023) 83 :775 we e made. The images o o he hi d pa y ma e ial in his a icle a e included in he a icle’s C ea i e Commons licence, unless indi- ca ed o he wise in a c edi line o he ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no pe mi ed by s a u o y egula ion o exceeds he pe mi - ed use, you will need o ob ain pe mission di ec ly om he copy- igh holde . To iew a copy o his licence, isi h p://c ea i ecomm ons.o g/licenses/by/4.0/. Funded by SCOAP3.SCOAP 3suppo s he goals o he In e na ional Yea o Basic Sciences o Sus ainable De elopmen . Re e ences 1. G. 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