(Superluminal Neutrinos)

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Sapporo Winter School 8-10 March, 2012
????????? (Superluminal Neutrinos)
?? ?? (???????)
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1. Superluminal OPERA neutrinos
???????????

• 1930???????????????????????????1950?????????????
• ??????????(??????)???????????????
• ??????3??????
• 3??????????????????????(????????)?
• ???????????????????
• ??????????????????100???1?????????
• ?????????????????????
• 1987?????SN1987A???????11?????????????????????????
  ?????????????????????????

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OPERA???
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??????????????OPERA????????? (Oscillation Project
with Emulsion-tRacking Apparatus)
??????????????????????????????(???????????)?
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OPERA???????????????????????????????????10????????
????20?????????????????????????? ???????????????60
???10????????????????????????????????????? ??????
??????????????????????????????????????????????????
????????????? ????????????????????????????????????
???????????????????????? ???????????????????????GP
S? ?????????????????????GPS???????
??????????????????????????????????10??????????????
?????????????? ??? GPS ???????????????????GPS
??????????????????????????????????????????????????
?????????????????????? ?????????????????GPS
??????100200??????????? ????????????????????????
?????????????????????????????????????????????????G
PS????????????????????????????????????????????????
?? ???????????T2K????????????????????????????? ??
??????????????????????????????????????????????????
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?????????????????????????????????????? ?????
??
GPS??????????????!
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From a slide of seminar at CERN
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Before OPERA, MINOS (2007) 1 sigma
SN1987A??? (1987)
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????????????60??? (60??10???1)????!
?????????????????
????????????????????!
?????????????????????????????(????????)?
?????????(????)????????????????
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???????????????????????????????! ????????????????
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??????
(1) ????????????????
(2) ????????????????(3km)
10??????
10
????? (18 November, 2011)
20 ???????? ????62.1 ????? ???????????????
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(3) ????????? (23 Februay, 2012)
Timing Oscillator Miscalibration Tens of ns ??
GPS??
??
60 ns
Sensitive Fiber Angle As Much as 100 ns ??
0 ns
September, 2011
February, 2012
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??????
?????????????????????? ????????????
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20GeV
40GeV
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OPERA group
ICARUS group
17 October, 2011
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• ??????????
• OPERA??????????????????(?)
• ?????????
• ??????SN1987A?????????????????????????????OPERA??
  ??????4??????????!
• ??????????????????????????????????????????!

CG??????????
???????????????????????????????
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????????????
v
c
E
???????OPERA?SN1987A????????????????? ????????
??????????????(CG effects)??????! ????????????????
???????ultra-high energy! ????????????????????????
??????!
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???idea
H. Taira and I. O., arXiv1110.6571 hep-ph, I.
O., arXiv1112.5793 hep-ph
???????????????????!
??????????????????????? ????????? ??????????????
CG effects?????? ???????? ?????????????OPERA?SN19
87A???? ???????????????
????????????????????????? ?????????????!
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??????????????OPERA?????????????????????
??????????!
??????????????????
?.??????????????????3/4
???????
?????????
???????
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1. ??????????????????????? ?

?.??????
???????????????? ????????
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(2) ???? ? ????? ????????????
?????????
????
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(3) ????????????? ?
???????
???????????
J.-M. Frere et al., P.R. D77 (2008) 083005
???????????????????????? ?????????
??????????????????? ???????
??????????????!
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????????
???????????!
?????????????????2???????????8??????(???????)?????
??
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???
???
2006????????? 2?????????????????(???)?????(???)???
?????
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?????
(1) ??????????????????
2?????????????
No! ???????????????????
cf. S.L. Glashow, Madrid conference, Dec.
2011 One possibility could have been that the
speed of a photon is a descreasing function of
its energy.
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?????
(2) ?????????????????????????
2?????? ???????? ????????????????????? ?????????
????????????????????
??????????????? ???????????????? ??????????????
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?????????
?????????? ?????????????????????????
W.V. Ignatowsky, Arch. Math. Phys. Lpz. 17 (1910)
1 P. Frank et al., Ann. Phys. Lpz. 34 (1911)
825 N.D. Mermin, Boojums All The Way.,
Cambridge Univ. Press, 1990(??????????????? ?)
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????. ???????????????????????????
????????????
????????D?????????????
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??????(????v?-v???????)
?????????????t?x?????????
???I???V??????????I???? ??????V?
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???????????????????????? ?????
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??????????????

• ?????????????????
• CG effects?????????????????
• OPERA???????????SN1987A???
• ??????????????????????
• OPERA(17GeV), SN1987A(10MeV)??????
• ???????????????ultra-high?
• ????????????????????
• ???????????
• ???????????????????
• ???????????

?????????????????????????
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2. Subluminal OPERA neutrinos
Our key idea
SN1987A??????
???????????????????????? ???????(??????)????
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OPERA??????
?????????????????????????
??????????????????????????????
Subluminal
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2-1. Scalar dark matter
Non-renormalizable term
This effective theory is defined only for
We set
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Here an effective metric, along which photon
propagates, is
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Eq. of motion for scalar field
At the linearized approximation,
Otherwise 0
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Linearized eq. of motion
A solution to this eq.
We postulate that Compton wave-length of the
scalar is the order of planetary distance
, so we can set m 0. Then, we have
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The effective space-time on which photon
propagates
Here
and
By using the coordinate transf.,
Here
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The effective velocity of photon
At the last step, is recovered.
Beyond Standard Model
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3. Conclusion
If OPERA result is correct, we can explain it
by using dark matter without violating special
relativity. Then, OPERA neutrinos are not
superluminal but subluminal whereas the velocity
of light is reduced by the refraction index
coming from dark matter as a medium.