Pion condensation with neutrinos
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- Magnus Barker
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1 Pion condnsation with nutrinos Or how dos QCD bhav undr high dnsitis of lctron/muon nutrinos Harmn Warringa, Goth Univrsität, Frankfurt Basd on work don with Hiroaki Abuki and Tomas Braunr arxiv:
2 Pion condnsat = BEC of pions Bos & Einstin: At low T bosons can all go in th groundstat (zro momntum). Bos Einstin Wiman and Cornll Particls loos individuality BEC of Rubidium atoms. Plottd: vlocity distribution for diffrnt T
3 Pion condnsation in nuclar mattr Migdal (1972): In dns nuclar mattr pions might condns n n p n n - Kaplan and Nlson (1986): K mor likly to condns. - Rason: mass K drops blow pion mass du to intractions with nuclons
4 Pion condnsation in QCD Son and Stphanov (2001) Chiral condnsat: = ordr paramtr chiral symmtry braking Pion condnsat: i 5 2 = ordr paramtr pion condnsation Pion cond.: isospin chmical potntial should xcd pion mass I m Continous rotation of chiral condnsat into pion condnsat (2nd ordr transition) = =0 cos I i 5 2 = =0 sin I m cos = 2 2 I
5 Pion condnsation with Lattic QCD B=0 No sign problm at finit isospin chmical potntial i 5 2 dt D I 3 0 m 0, ral! Pictur of a computr usd for Lattic calculations QCDOC@Brookhavn National Laboratory Kogut and Sinclair (2002) I s also Kogut and Sinclair (2004), Nishida (2004), d Forcrand t al. (2007), Dtmold t al. (2008)
6 Pion condnsation in th NJL modl down quark chm. pot Nambu I m Jona-Lasinio Low nrgy modl for QCD. I m Has sam global symmtris. L= i 0 Lq q m Up quark chm. pot 2 2 L q q=g[ 2 2 ] i 5 i 5 Barducci, Casalbuoni, Pttini & Ravagli (2004) s also Toublan and Kogut (2003)
7 QCD: Onst of condnsation Q = I m Could such a thing rally xist in natur? Pion condnsat is chargd. Furthrmor pions dcay wakly Naturally unstabl. + + How to mak stabl pion condnsat in lctrically nutral systm?
8 How to mak a stabl pion condnsat in an lctrically nutral systm? + + Nutraliz pion condnsat with lctrons and muons Block dcay by high nutrino dnsity
9 Why nutrinos can crat pion condnsat Nutrinos ar frmions: In dns nutrino gas it is nrgtically favord to convrt som of thm on Frmi-sphr into pions and lctrons/muons Assum wak quilibrium: up quarks u = B /32/3Q down quarks d = B /3 1/3Q = L Q lctrons = L lctron nutrinos = L Q = L muons muon nutrinos
10 Why nutrinos can crat pion condnsat up quarks u = B /32/3Q down quarks d = B /3 1/3Q = L Q lctrons = L Q = L = L lctron nutrinos muons muon nutrinos Onst pion condnsation Q = I =m If T = 0 and Q m (no pions) and B m p Q no (baryons=protons) Hnc at onst pion condnsation: nutralization with lptons only Phas boundary to pion condnsd phas dtrmind by n = L m n = L m =0 Solvabl analytically Abuki, Braunr and HJW (arxiv: )
11 Phas diagram of lctrically nutral QCD B m p 2 m /3 (Muon nutrino chm. pot.) Lngth vrtical lin = twic muon mass Rqurd lctron nutrino zro muon numbr dnsity (black dot) : fm (Elctron nutrino chm. pot.) Abuki, Braunr and HJW (arxiv: ) n = L m n = L m =0
12 Phas diagram of m 2 m /3 lctrically nutral QCD B p T = 0: xact (Muon nutrino chm. pot.) T=25, 50: stimats. Assumptions: low T pion mass not much changd. T = 0 MV Pion condnsation still at T m T = 50 MV Q =m still almost no hadronic stats around nutraliz with lptons only T = 25 MV (Elctron nutrino chm. pot.) Abuki, Braunr and HJW (arxiv: ) n = L m n = L m =0
13 Us NJL modl to invstigat largr T and B Dscribs QCD qualitativly howvr no nuclar mattr First two phas diagrams should also com out of NJL modl Nambu Jona-Lasinio Low nrgy modl for QCD. W can find out up to which tmpratur thy ar good Has sam global symmtris. L= i 0 L q q m 2 2 L q q= 1 G [ 2 2 ] i 5 i G[ 2 2 ] i 5 i 5 Axial U(1) braking
14 Valus of various quantitis n L =0 T=0 B =0 Pion condnsation L =163 MV lctron nutrino numbr dnsity fm 3 Kaon condnsation L =1040 MV lctron nutrino numbr dnsity 2.5fm (Elctron nutrino chm. pot.) Abuki, Braunr and HJW (arxiv: ) 3
15 NJL modl phas diagram (Muon nutrino chm. pot.) Prfct agrmnt with low tmpratur stimat and zro tmpratur xact rsult. Black dots n L =0 (Elctron nutrino chm. pot.) Abuki, Braunr and HJW (arxiv: )
16 Phas diagrams NJL modl T = 0 n L =0 L =0 L =231 MV L =163MV Blu lin: zro axial U(1) braking. Rd lin: strong axial U(1) braking. B /3= M u 2 m /3 232 MV Abuki, Braunr and HJW (arxiv: )
17 First ordr transition at n L =0 Abuki, Braunr and HJW (arxiv: ) L =400 MV
18 Nutral NJL phas diagram at largr baryon chmical potntial L =0 Abuki, Braunr and HJW (arxiv: ) Rüstr, Wrth, Buballa, Shovkovy and Rischk (2006) S also: Sandin and Blaschk (2007)
19 Pion dcay rat in nutrino gas L =0 Lorntz gamma factor L = Pion vlocity Abuki, Braunr and HJW (arxiv: )
20 Conclusions Pion condnsation taks plac in a larg part of th phas diagram of lctrically nutral QCD at high lctron/muon nutrino dnsitis. A pion condnsat will b formd in a dns nutrino gas at small baryon chmical potntials Is this situation ralizd in somwhr in our univrs? Protonutron star has high nutrino dnsitis but also high baryon dnsitis. Mayb in atmosphr but that is highly spculativ.
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