Nuclear Effective Field Theories - the crux of the matter
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2 Wht s owe coutg? P coutg owes of soft sces fo eozed cotbutos to obsevbes Eg hpt: >> Howeve evutg the oo teg wth cutoff Λ πfπ oe fds: y fte subtctg the U dvegeces Λ d ogλ/μ the esut s geeet wth P Wht s W s och? Let s stt wth se cse of oess EFT
3 c c [ ]HB GW PWAthe otet 9 W: defe [ ]HB KH PWA Λ [ ]covt dt 75 9 c c d d d d 5 d d 5 e e U cutoff toduce π sove Schödge e d tue 58 Λ 99 to d Λ d 8the Fo sh cutoff oe fds t L: hve toduced: eg 5 whee 5 d d f 8 eg eg 8 8 eg h h cty eozed 8 8 fo exesso the vese tude: eg f eg d d d d8 d d h h feg eg 8 8 et 8 h h 8 d d h T H eg E h h d d h h feg hghe-ode tes esut E eg we-defed d coect oduo H d d f eg e fo ; thgs y d geey w go wog H E Wge coex fo boud etzto eg e H d E h h d h h feg d d feg
4 We But D ED hpt oe oy tes the t Λ Why? Becuse t sfes ccutos syetes d etes fte-λ tfcts EFT t s suffcet to te Λ Λb s t justfed to te ths t? Yes but oy fte bsobg ostve owes d Log s of Λ to ct Ths s ot wys ossbe: χeft wth oetubtve π ftey y ct s e eeded; t s uow how to eet subtctve eozto ctce fo S ches Whch owe coutg does W och coesod to? The swe deeds o the choce of eozto codtos Defe: ece: Subtctve eozto: d { } otoy Te the t:
5 } { { } { } { 5 { } 5 } 5 5 Soe ossbe choces of eozto codtos: { } ost DA fo { gee 5 5 bty et } et cotbe wth 8 usefu et fe tug but est ccetos { } Fo : et 8 et 5 et 8 d et et 5 Secfyg : the sce d et et : DA fo LEs descbes both the tu d 8 utu cses e both 8 8 et 8 cses: d 8 d d the ot ecooc ost schee fo 8 8 et d 8 8 Exso of exso of T fo but 8 8 et 8 sef-cosstet och systetc st d & et d d d 8 et et : DA fo the tu cse; scg descbes LEs KSW fo the 8 of LEs utu cse 8 8 et
6 otce: whe both oches e euvet the π-ess cse they yed dffeet edctos whe geezed to χeft oetubtve vs etubtve π Wht does the G yss of e te us? t detees the scg of fo fo syste e the tv o o-tv fxed ot eozto codtos s e KSW Do the fdgs of the G yss y tht the DA scg of o Dffeet choces of eo codtos ossbe eg s wog? oe use ct eozto wthout secfyg eo codtos W? Yes Tvy thee s : g betwee π-ess EFT d EE Does W s och coesod to exso oud tv fxed ot? o t s desged to tch the EE egdess of the sze of s the G yss oe edctve? Eg t sees to suggest tht the ge coecto s etubtvey s o e hs to secfy the sttg codtos fo the G euto - tht s whee oe eeds dt A stoge fe tug cot be excuded o
7 π-ess cse s tv How to geeze to EFT wth og-ge tectos? f og s ow excty geezto s stghtfowd ety og s oy ow wth the ch exso oo och: tes be cot og e ogzed ccodg to the stdd χ coutg e DA Ths coesods to the set of cotct tes d s the coect ssget wey-tectg cse Wht exso of the tude does ths coesod to? EE fo og EE fo the cse of excty ow og Geey o goous swe s ow to e But c be tested by oog t the covegece tte of cty eozed edcted obsevbes G yss he oe to detee the exso? Pehs eve though ot covced t c ctce Ae thee tetve suggestos to ogze the exso of? Yes tycy suggestg to oote soe tes cot to owe odes these oches be tested? Yes eg by cog edctos fo few- obsevbes t hghe odes
8 Hve such tests bee efoed? o the oy och whch hs so f bee ushed to hgh odes L s bsed o the stdd DA ssget W Do these ccutos gve y dcto of the eed to det fo DA W? o fct the ooste s tue h exso of obsevbe sees gee to gee esoby we wth the DA tte Exso ete fo obsevbe : x b b Λb estted fo eo ots: Λb e [fo ot h too soft cutoffs] h exso of the tot coss secto [ 9 f] Eb 5 e [ 5 e]: σtot b 5/ exect: 8 5 Eb 9 e [ e]: σtot b / 5 exect: 5 Eb e [ 7 e]: σtot b 7 / 5 exect: 9 5
9 Descto of exeet dt: Eegy b L L L L L L euto-oto dt e 79 o ew 8 LE 8 8 e e oto-oto dt LEs e o ew 8 8 e e LEs 7 B LEs 5 LEs B LE 5 LE S LEs e evdece of the ete-fee ch π-exchge f shot-ge tectos hd to be ooted etve to og oe woud t exect substt educto χ t L d L Sy tetve schees suggest tht the cotbutos to eg the S d S - D ches e ehced etve to DA Howeve we fd these ches to be ey efecty descbed t L d L W s schee The eo χ s doted by dffeet wves
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11 d # T G T G G G # f ex SF SF { # } d # # SF d ex f d ex f ex f ex SF # # # { } d f Tex f G ex G T G G the f A dffcut se och bsed o ccuted edctos fo ts Poosed ex # d How e the tucto eos estted? obsevbe t ow odes the ch exso [EE Kebs eße EPJA 5 5 5] f ex the coesodg deotg Let be soe obsevbe wth oetu sce d SF 5 edcto t ode 5 the ch exso: d # f # 5 5 ex 5 ccuted the ch exso # ex 8 f 7 # ex # 8 7 f x wth Exect bsed o DA: 7 ex 8 ex f 8 7 f 7 b b L 5 # L # x 87 # sze of 5 of the theoetc L ucetty hghe-ode tes: egected Estto x 8 8 ex ex L f 7 L ex 8 f f 8 L L 5 L L L x x L et L L L L 8 L L L 9 9 x L L L L L L 5 L 5 L 5 L L L L L L x 8 9 x # x L L L L L L L L L L x ex 8 f 9 9 L L PWA j PWA L j ed9 PWA PWA L x L L j PWA PWA j ed9 PWA L L L LPWA j PWA L L PWA PWA j j PWA PWA ed9 ed9 PWA > x L x L 5 ded: x x x PWA j PWA j PWA ed9 PWA L L b obsevbes x b PWA ed9 Esy to eet wos eby we fo cosdeed sof vdto j PWA PWA j PWA b b j j PWA ed9 PWA PWA PWA x
12 oe do bette eg oe ebote G-bsed eo yss? ybe Woud e to see covcg evdece Suy The te-wy essge Do t te t too seousy whe you he ext te t s we ow tht W s wog :- As fo dets guets d deftos Futue esectves fo W och osstecy checs e d we ectos foce ecso few- hyscs og wth othe owe-coutg schees Loog fowd to see esuts fo the coetto Thee e ety of ossbtes to test the edctve owe of the theoy
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