PHYSICS OF THE NEUTRINO FACTORY (AND FRIENDS) J.J. Gmez Cadenas - PowerPoint PPT Presentation

PHYSICS OF THE NEUTRINO FACTORY (AND FRIENDS) J.J. Gómez Cadenas IFIC (CSIC-UV) Lecture II viernes 17 de julio de 2009

LECTURE II • Matter matters • Degenerate physics • Design your experiment viernes 17 de julio de 2009

TRAVEL IN MATTER • In a NuF, rates grow with muon energy (flux & cross sections increase with E) • To work at the oscillation peak one needs long baselines (~5000 km at 10 GeV) • This implies that the neutrino beam travels through Earth. • But Earth is less transparent to ν e than to ν μ , ν τ viernes 17 de julio de 2009

THE MATTER PARAMETER A • The fact that ν e (both neutrinos and antineutrinos) have charged current elastic scattering interactions on the Earth electrons introduce effective “masses” for the electron neutrinos m= ± 2EA, where A is the matter parameter viernes 17 de julio de 2009

MATTER IMPORTANT AT LARGE L A = 2 G F n e � n e is electron number density eV 2 GeV km A increases with L � Matter effects important at large L viernes 17 de julio de 2009

� � 2 L � � atm = sin 2 � 23 sin 2 2 � 13 sin 2 1.267 � m atm 2 sin 2 2 � 13 sin 2 � 23 L � 23 = 2.534 � m atm 2 � � s 23 � � � , P � � � � E 2 E � 2 L � � � sun = cos 2 � 23 sin 2 2 � 12 sin 2 1.267 � m sol 2 sin 2 2 � 12 sin 2 � 12 L � 12 = 2.534 � m sol 2 � � c 23 � � � , P � � � � E 2 E � 2 L � � 2 L � � 2 L � � � � � � � int = J cos ± � � 1.267 � m atm � 1.267 � m sol � sin 1.267 � m atm � � J � 12 L � sin � 23 L � cos ± � � � 23 L � � � � � � � P � � � � � � � � � � � � E E E 2 2 2 Matter : � B � = A � � 23 A � 0 � B � = � 23 A � � 23 � B � is different for � and � : "Fake CP violation effect" Matter effects can be described by the following (golden) formula: A � � 12 : Effective neutrino mass shorten solar oscillation B � � � 23 :Matter distinguishes between � and � � � 2 � � � 23 sin 2 B � L 2 sin 2 2 � 13 atm = s 23 � � P atm is now different for � and � � � � P � � � � B � 2 � � � � 2 � 12 sin 2 AL 2 sin 2 2 � 12 sun = c 23 � � P sol amplitude controlled by A not by � 12 � � � P � � � � A 2 � � � � � � � � � � int = J � 12 � � 23 � cos ± � � � 23 L � sin AL � sin B � L � � Extra "fake" CP violation in P � � � � � P � � � � � � � � int � � A B � 2 2 2 viernes 17 de julio de 2009

L=300 KM, NEGLIGIBLE EFFECT --- P sol � in matter --- P atm � --- P sol � in vacuum --- P atm � --- P int � --- P tot � --- P int � --- P tot � viernes 17 de julio de 2009

L=1000 KM, ATM TERM SEES EFFECT viernes 17 de julio de 2009

L=3000 KM STRONG ATM EFFECT viernes 17 de julio de 2009

L=10,000 KM ALL IS MATTER • At L=10000 Km (E=30GeV) matter effects are also important for solar term and will mask completely any oscillation effect viernes 17 de julio de 2009

L=300 KM NO FAKE CP --- P tot � , � = 0 in matter --- P tot � , � = 90 in vacuum --- P tot � , � = 0 in matter --- P tot � , � = 90 in vacuum --- P tot � , � = 90 in matter --- P tot � , � = 90 in matter viernes 17 de julio de 2009

L=1000 KM, TRUE CP LARGER THAN MATTER CP viernes 17 de julio de 2009

L=3500 KM, TRUE CP SAME ORDER THAN MATTER CP viernes 17 de julio de 2009

L=10,000 KM, TRUE CP MUCH SMALLER THAN MATTER CP viernes 17 de julio de 2009

MEASURING THE SIGN OF MATTER Matter : � B � = A � � 23 • The bad news: Matter effects are large at large distances. For a high energy neutrino factory one is prevented to go to the oscillation peak and has to work in the “lineal region” where one is less sensitive to ACP. • The good news: Because matter effects are large, one can use them to find out the mass hierarchy, that is the so-called, “sign of matter”. • Notice that B changes sign depending on whether the sign of matter is “positive” or negative”. viernes 17 de julio de 2009

MEASURING THE SIGN OF MATTER L = 300 Km � m atm > 0 2 � m atm < 0 2 L = 300 Km L = 800 Km L = 800 Km � m atm > 0 � m atm < 0 2 2 viernes 17 de julio de 2009

MEASURING THE SIGN OF MATTER � m atm < 0 2 � m atm > 0 2 L = 3500 Km L = 3500 Km � m atm > 0 � m atm < 0 2 2 L = 10000 Km L = 10000 Km viernes 17 de julio de 2009

HOMEWORK • You are the owner of a tunable beta-beam facility. • Choose a neutrino beam energy • Choose baseline • Choose detector technology (explain your reasons) • Explain your physics program • Repeat the game for a tunable neutrino-factory. • Compare both facilities • Since matter matters. What is your criteria now to choose a baseline? viernes 17 de julio de 2009