Restricted Scope: Theory of Light Hydrogenlike Bound States: High Order Corrections to Lamb Shift, Hyperfine Splitting, and g-Factors

Recent years witnessed a steady pro!!;ress in th(' field of hil!;h precision quantum (']Pctrodynamics of hydrol!;enlik(' bound stat('s. Roth th(' eXPNinwntal errors and th(' accuracy of theory were sil!;niticantly improved. ,c\s oft('n happens this rapid pro!!;r('ss leads to new probkms. In th(' fi('ld of hil!;h pr('cision qua nt um ('I('ctrodyna mic t h('ory of bou nd sta tes t Ilf' Ion!!; tNm problrms a n' as follows: .1'11(' theorC'tical Nror of th(' IS Lamb shift in hydrol!;en should be reduced sil!;nificantl,v below tlH' Irvel of 1 kHz (and. resprctively. of th(' 2S' Lamb shift sil!;nificantly below tenth of kHz), • The throretical error of the hyperfine splittin!!; in 111uoniu111should be reduced to about 10 Hz. • Th(' theorC'tical ('ITor of the 2.', - 2P Lamb shift in Tl1uonic hydrol!;('n should be reduced below 0.001 meV. :\11 main theor('tical problrms of th(' theory of lil!;ht hydrol!;('nlike atoll1(,s will b(' addr('ssed in the proposed research. Its main objectiv('s include: • Complete calculation of all three-loop non recoil corrections of order o:'(7o)'im to the Lall1b shift in hydrol!;('n. These an' th(' lar!!;est sti\lunknown contributions to the Lamb shift. Respective thn'('-Ioop nonn'coil corrections to hyperfinc splittin!!; in hydro!!;en and muonium also will be calculated. • ('om plete ca Iculation of all three-loop radia tivp-recoil corrections of order 0:' (m Ii'vl) EF to hYPNfin(' splittinl!; in muonium. • Calculation of nonlo!!;arithmic corrections of order n2(7o)4 III to the Lamh shift in muonic hydro- !!;('n. Calculation of li!!;ht hy 1i~ht electron-loop contrihution of order o2(7n ):1m to the Lamb shift in muonic hydro~en. • Resolution of th(' discr('pancy in the theory of bound state .rJ factors in syst('ms includinl!; particl('s with spins j -# 1/2. In the proposed r('search quantum d('ctrodynamics will he applied to 100s('ly bound two-partick systems. The calculations will b(' done in th(' franwwork of perturbation theory and nOIH('lativistic quantum ekctrodynamics. and combined expansions in the small parameters n. 7n. and m/AI will be perfornH'd. 1'hre('-loop non recoil corr('ctions of order o:'(7o)'im to th(' Lamb shift in hydrol!;('n and of ord('r n:' (7' 0) E F to hyp('rfi ne splittinl!; in muon ium will b(' ca Icula t('d in t h(' fra 111('\VOl'k of the s kelcton int('l!;ral approach devdoped earlier. NOIllol!;arithmic recoil corrections of order (7nr'(m/AI)f"F' and oU;;n)2(mj,\l)EF to hyperfine splittin~ in muoniuTn will be considNed in tl1(' nOl1r('lativistic quantum plectrodynamics approach. Methods of non relativistic quantull1 pkctrodynamics will be us('d also to obtain nonlol!;arithmic contribution of order o2(;/,o)4m and lil!;ht by lil!;ht scatterinl!; contribution of order (i2(7o)' to the Lamb shift in muonic hydrol!;en. In the framework of the bound g-factor physics th(' probkms connected with application of th(' Rarl!;mann-l'vlichel-Telel!;di equation for partich; with hil!;her spins will b(' r('solved. Theoretica I results of t he proposed resea rch tOl!;ether wit h the t heoretica I results of ot her aut hors a nd wit h existinl!; a nd pia nned ('x peri m('nts would a \low to deterllli ne much mon' pr('cise va lues for many fundamental physical constants: the Rydb('rl!; constant. electron-muon and electron-proton mass ratios. ekctron mass in atomic units. proton charl!;(' radius. deuteron structure radius. etc. The proposf'd research will hav(' hroadf'r impacts. beyond the fi('ld of theor('tical physics. The research will result in more precise valuf's of the fundamental physical constants. These values play an important rok in metrolol!;'y which is a natural consumer of th('se results. Precise values of the physical constants and therefore results of this resf'arch are widely used in ~Iohal positioninl!; systems. for precise ti me detf'rm ina tion. in f'very scienn' classroom. etc. Rot h I!;raduate and underl!;rad uate st udents wi \I participate in this resf'arch and hesides learnin~ physics will acquirf' computer and problem solvin~ skills. Studf'nts will make presentations at APS meetin~s. This project will promote deV!'lopment of international collahoration. an active participation of a Russian theorist is planned. 1'11