Neutrino mass in tritium and rhenium single beta decay

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1 Nutino mass in titium and hnium singl bta dcay Rastislav Dvonicky Comnius Univsity, Batislava Slovakia in collaboation with.simkovic, K. Muto & R. Hodak Nutinos in Cosmology, in Asto-, Paticl- and Nucla Physics, ic, Sicily, St. 6-4, 009

2 Outlook Intoduction Titium bta dcay within standad aoach xact lativistic tatmnt of H dcay ist uniqu fobiddn dcay of 87 R Comaison of Kui lots fo H & 87 R dcays Rlic nutinos Summay

3 Nutino Nutino was suggstd in y. 90 by Pauli to xlain th continuity of β sctum as a sin / aticl obying mi-diac statistics I hav don a tibl thing I invntd a aticl that cannot b dtctd W. Pauli Tübingn

4 Nutino oscillations Pontcovo -Maki-Nakagawa-Sakata matix Zh.ks.To.iz.,957 Maki,Nakagawa,Sakata. Pog.Tho.Phys oscillations massiv nutinos lavo ignstats Mass ignstats m P ν ν µ = sin ϑ sin 4t

5 Absolut mass scal of nutinos? 0νββ-dcay H dcay Cosmology W nd mass ignstats To xlain diffnt m m -m = m sol.0-5 V Sola nutinos m -m = m atm.0 - V Atmoshic nutinos 968 Homstak 998 SuKamiokand

6 Titium bta dcay H H ~ ν 94 mi ointd out that sha of lcton sctum in bta dcay na th ndoint is snsitiv to nutino mass. mi, Z. Phys. 88, 94 ndoint bta sctum ist masud by G. Hanna, B. Pontcovo: Phys. Rv. 75, with stimation m ν ~ kv

7 Titium bta dcay low ndoint Q=8.6 kv su-allowd nucla tansition mi, Gamow-Tll M.. shot half-liv T / =. y KATRIN ximnt U limit on nu mass Masuing last 0 V ndoint.w. Ottn, C. Winhim: Rt. Pog. Phys. 7: Adquat lcton ngy dscition na th ndoint is ncssay

8 Standad aoach Nglcting th coil and intgating ov nutino momntum consving th ngy in dcay. W oby th lcton ngy sctum. NM within sin-isosin symmty a givn M = & M GT = M = g M V g A M GT,, T momntum, ngy and kintic ngy of lcton Q maximal kintic ngy of lcton in zo nutino mass cas mi function taking into account th Coulomb intaction btwn th lcton and daught nuclus

9 Standad aoach Kui function Th advantag of Kui lot is that nonlinaity imlis nonzo nutino mass. Hyd, Basic idas & concts in nucla hysics

10 Rlativistic aoach to H dcay Rlativistic dscition of body dcay within lmntay Paticl Tatmnt PT - Kim & Pimakoff, Phys.Rv. 9, B PT sin & isosin otis of titium dcay a idntical with th dcay of f nuton H n H ν ~ ~ ν Sin & aity of H n and H / /

11 Rlativistic aoach to H dcay W consid coil momntum in th has sac xact avagd amlitud of 4 f sin ½ aticls within th mi V-A contact intaction = Γ f f f i sins d d P P P P M d 4 ν ν ν δ i d Z M 5, 6 π

12 Rlativistic aoach to H dcay Pfoming th intgation ov nutino and coil momntum w gt th xact lativistic lcton ngy sctum fo th H bta dcay y = max m = M i M i m max = M f [ M m M ] i f m ν Maximal - ngy about.4 V low than standad valu max = M i M f m ν S. S. Masood t al.: PRC 76, Šimkovic, Dvonický, äßl: PRC 77,

13 Rlativistic aoach to H dcay In od to vify th sult w can fom non-lativistic limit of th lcton ngy sctum. King only dominant tms na th ndoint w gt: Rmind: No NM, no. & aa natually. Assuming g V = th axial couling can b fixd fom known half-liv x T / =.y g A =.47 ba Ba nuclon valu =. 695 g A PDG W.M. Yao t al.: J. Phys. G, 006

14 W dfin a Rlativistic aoach to H dcay / Kui function K y = BT y y mν y mν with GVud B T = g V g π A Th atio Ky/B T is f of couling constants y y m y m / K y / BT = ν ν Stuctu in agmnt with f.: Šimkovic, Dvonický, ässl: PRC 77, S. S. Masood t al.: PRC 76,

15 Rlativistic aoach to H dcay Whn lacing y = 0 m ν W gt fom l. Kui function th standad Kui function assuming M = and M GT = y y m y m / K y / BT = ν ν GVud B T = g V g π A Standad non-lativistic Kui function PT l. aoach vifis th standad Kui fom na th ndoint

16 xotic intactions in H dcay Assum th gnal fom of th wak bta dcay Hamiltonian Th tms a givn T P S A V H H H H =,, β.. ' ' , h c n C C n C C H A A V V A V = γ γ ν γ γ γ γ ν γ γ µ µ µ µ.. ' ' , h c n C C n C C H P P S S P S = γ ν γ γ ν γ.. ' 5 c h n C C H T T T = λµ λµ σ ν γ σ N. Svijns t al.: Rv. Mod. Phys. 78:

17 xotic intactions in H dcay PT is a tool fo studis of nw intactions in titium bta dcay Standad V-A lus tnso focs Standad V-A lus sudo/scala focs calculations in ogss

18 Rhnium bta dcay Bta mitt of g.s. g.s. tansition with lowst known Q valu.47 kv Rlativ high half-liv T / =4.5 x 0 0 y ~ ag of th univs cosmo chonomt Natual abundanc 6% R Os ~ ν Good candidat fo th nutino mass study

19 Rhnium bta dcay MAR ximnt T / = y low adioactivity bolomt souc=dtcto Th nti ngy is masud in th dtcto xct th nutino including th molcula & atomic xcitations ß i, R-87 Os87 o mo dtails s talk of.ioini

20 Rhnium bta dcay Th chang of th angula momntum and aity btwn moth and daught nucli g.s. fist uniqu fobiddn dcay 87 5/ 87 R Os ~ ν π / J = Non-vanishing M w will oby whn considing th -wavs of th mittd ltons in th bta dcay of 87 R Gβ µ H β = ψ x γ γ 5 ψν x jµ x h. c. Ψ ltons = Ψ S Ψ P K

21 Rhnium bta dcay ist uniqu fobiddn tansition Plan wav xansion fo ν ψ ν J π = = ik. v k Th lcton is mittd in th snc of th Coulombic fild of th daught nuclus thfo th wav function is xssd in tms of shical wavs J=/ L=0 s=/ J=/ L= s=/ J=/ L= s=/ S wav P wav

22 Rhnium bta dcay = Ψ s s S f g χ σ χ ~ ˆ. ~ = Ψ s s P f g i χ σ χ σ σ.ˆ ~ ˆ..ˆ ~ / = Ψ s s P f g i χ σ σ χ σ σ.ˆ] ˆ. ˆ [ˆ. ~ ˆ..ˆ ˆ [ ˆ. ~ / / / / P P S Ψ Ψ = Ψ Ψ W nglct high wavs du to cntifugal sussion Doi, Kotani, Takasugi, PTPS No. 8,985 J=/ L=0 s=/ J=/ L= s=/ J=/ L= s=/..., / i Z u P γ γ ψ = Z i Z u P.ˆ, 0 0 / γ γ α ψ =, 0 / Z u S = ψ k a mi functions fo th shical wavs of lcton

23 Rhnium bta dcay J π = mittd ltons hav to ca th angula momntum L= Thfo th constuction of amlitud fo th bta dcay ocss of 87 R Amlitud = s / & ν / / & νs /

24 Rhnium bta dcay Aft foming th calculation w finally oby fo th lcton ngy sctum dγ = d GVud π lcton in th / stat M 0 0 m Z, k Z, R 0 ν lcton in th s / stat dγ d = dγ d P dγs d k = 0 mν Rmind: no intfnc tms du to hysically diffnt final stats of mittd ltons

25 Rhnium bta dcay Th is only on NM du to th fact of fist uniqu fobiddn dcay M g 4π A 87 = < Os τ n Ji n n R { σ Y } 87 R > Within th tatmnt of l. lcton wav function th momntum and osition dcoul and M is indndnt of ngy om th known ximntal half-liv w can dduc M valu T x 0 4 / = y M =.57 0

26 Rhnium bta dcay With bta stngth fixd to th ximntal valu of half-liv w can lot th lcton ngy sctum 0 0 ν π m M G V d d ud = Γ,, 0 Z k Z R Nom. to unity Nom. to T / x

27 Rhnium bta dcay Th contibution of th atial ats to th total at is not qual Γ S = 0 m d dγs d Γ P = 0 m d dγ d P Γ S / Γ P = W dfin atio of ths two tms R dγ S dγ = / d d P Th lcton P / dcay at channl is dominant imotant! This is cntly confimd by MAR ximntal sults: Anaboldi t al.: PRL 96,

28 Rhnium bta dcay Nglcting th Coulomb intaction w st k and fom additiv tm oiginating fom P wavs of ltons w hav only ~ k k max =. 47kV Th kinmatics is nhancing th contibution of th lcton P wav to th total dcay at max 50kV o th nhancmnt within th mi function s talk of K. Muto

29 Rhnium bta dcay 0 0 0, ν π m Z M G V d d ud = Γ 0,, k Z Z R Dcay at could b factoizd th way to s connction with allowd bta dcay at Allowd tansition. Th sam fomula in titium cas Tm oiginating fom th high shical wavs of ltons

30 Rhnium bta dcay Nutino momntum tm could b nglctd na th ndoint Du to th small Q valu comad to th lcton st mass is th maining tm in backts actically indndnt on lcton kintic ngy 0,, k Z Z R,, 0 m m Z Z

31 Rhnium bta dcay As a consqunc is th goal that w can dfin th Kui function simila to on fo th titium dcay cas,, 0 Z Z R { } > < = n n n i A ud R Y R Os J g V G B R 4 σ τ π π R / m B K ν with Pactically constant

32 Rhnium bta dcay vn if th 87 R is a fist uniqu fobiddn bta dcay th Kui lot fo zo nutino mass is lina in a vy good aoximation Thoy ximnt Th M = is assumd fom th ximntal valu of half-liv T / = y Anaboldi t al.: PRL 96,

33 Kui lots fo hnium and titium bta dcay W now intoduc th vaiabl y= max - instad of and call th bta stngths fo th hnium and titium A V ud T g g V G B = π { } > < = n n n i A ud R Y R Os J g V G B R 4 σ τ π π,, 0 Z Z R R / m B K ν Poly nomalizd Kui functions bcom idntical / / ν ν m y m y y B y K T = K/B R Ky/B T KATRIN MAR

34 Rlic nutinos Th a lnty of nutinos in ou Univs ~ 0 87 flavo idlman t al.: PLB 59, 004 Th analog of CMB is Cosmic Nutino Backgound Abundant but challnging dtction

35 Rlic nutinos Th nutino catu via th bta dcaying nuclus is a uniqu tool to dtct cosmological nutinos Th is a ga of width m ν to distinguish btwn th bta dcay and lic low ngy nutino catu

36 Rlic nutinos Th dnsity of nutinos <η>=56 cm - Psnt nutino tmatu Psnt man momntum Rf.: C.Giunti, C.W. Kim, undamntals of nutino hysics and astohysics, Oxfod 007

37 Rlic nutinos Th CNB nutinos a non-lativistic and wakly clustd If th CNB nutinos a havy nough vlocitis a small than sca vlocity and thy a clustd tad within otntial wlls till snt tims Th xctd ov-dnsitis η ν /<η ν > with sct to th avag CNB nutinos dnsity ~ Rf.: R. Lazauskas, P. Vogl, C. Vol: JPG: Nucl. Pat. Phys. 5, 008

38 Rlic nutinos Nutino catu by titium nuclus Assuming M =, M GT = and η ν =<η ν > th catu at T / =. y KATRIN will us ~50 µg of H numb of vnts vn considing clusting η ν /<η ν > ~ th ffct is ngligibl

39 Rlic nutinos Nutino catu by hnium nuclus Th catu at Th bta stngth T / = y Assuming η ν =<η ν > th catu at and th atio of cat./mission 760 g of AgRO 4 bolomts >00 lag as H

40 Summay Th xact lativistic tatmnt of H bta dcay within th PT mthod confims that viously considd non-lativistic Kui function is adquat and th coil ffct is small Analysis of th fist uniqu fobiddn bta dcay of 87 R showd that th - is fably mittd in th P-wav stat in agmnt with ximnt In a good accuacy th Kui lot is a lina function fo mass-lss nutino in fist fobiddn bta dcay of 87 R In th cas of o nomalization of Kui lots of H & 87 R thy a actically idntical clos to th ndoint Unfotunatly th lic nutinos cannot b obsvd in KATRIN & MAR ximnts vn in th cas of clusting of CNB, but th is a chanc to ut fist constaint on dnsity of nutinos

Hydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals

Hydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas