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0002014v1 | 2 | teresting to verify this [the existence of a KT transition for $$X Y$$ models
on a fractal lattice]”. Yet we do not see the relevance of such an obvious
claim.
We disagree however with the authors of [1] when they say “our ar-
gument does not depend on the existence of such a transition on that
particular percolating cluster”. Instead, after the conclusions of Ref. [2],
we think that the non–rigorous proof proposed in [3] for the case when
the equatorial cluster does percolate, heavily lies on whether or not such
a transition is realized.
# References
[1] A. Patrascioiu and E. Seiler, unpublished report hep–lat/9912014 (v1).
[2] B. All´es, J.J. Alonso, C. Criado and M. Pepe, Phys. Rev. Lett. 83 (1999)
3669.
[3] A. Patrascioiu and E. Seiler, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 184.
[4] Yu.E. Lozovik and L.M. Pomirchy, Solid State Comm. 89 (1994) 145.
[5] P. Minnhagen and H. Weber, Physica B152 (1988) 50.
| <p>teresting to verify this [the existence of a KT transition for $$X Y$$ models
on a fractal lattice]”. Yet we do not see the relevance of such an obvious
claim.</p>
<p>We disagree however with the authors of [1] when they say “our ar-
gument does not depend on the existence of such a transition on that
particular percolating cluster”. Instead, after the conclusions of Ref. [2],
we think that the non–rigorous proof proposed in [3] for the case when
the equatorial cluster does percolate, heavily lies on whether or not such
a transition is realized.</p>
<h1>References</h1>
<p>[1] A. Patrascioiu and E. Seiler, unpublished report hep–lat/9912014 (v1).
[2] B. All´es, J.J. Alonso, C. Criado and M. Pepe, Phys. Rev. Lett. 83 (1999)
3669.
[3] A. Patrascioiu and E. Seiler, Nucl. Phys. B (Proc. Suppl.) 30 (1993) 184.
[4] Yu.E. Lozovik and L.M. Pomirchy, Solid State Comm. 89 (1994) 145.
[5] P. Minnhagen and H. Weber, Physica B152 (1988) 50.</p>
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|
0002014v1 | 0 | # Reply to A. Patrascioiu’s and E. Seiler’s comment on our paper
# Percolation properties of the 2D Heisenberg
model
B. Allés $$\mathrm{a}$$ , J. J. Alonso $$\mathrm{b}$$ , C. Criado $$\mathrm{b}$$ , M. Pepe $$\mathrm{c}$$
$$\mathrm{a}$$ Dipartimento di Fisica, Universita di Milano-Bicocca
and INFN Sezione di Milano, Milano, Italy
$$^\mathrm{b}$$ Departamento de Fisica Aplicada I, Facultad de Ciencias, 29071 Malaga, Spain
The most of the problems raised by the authors of the comment [1] about
Ref. [2] are based on claims which have not been written in [2], for instance
almost all the introduction and the point (1) in [1] are based on such non–
existent claims.
Instead in Ref. [2] we avoid to make claims not based on well–founded
results. For instance in the abstract we write “... This result indicates how
the model can avoid a previously conjectured Kosterlitz–Thouless $$[K T]$$ phase
transition...” and in the conclusive part we notice that “Our results exclude
this massless phase for $$T\,>\,0.5$$ ”. Therefore it seems to us that the opening
sentence in the Comment [1] “In a recent letter All´es et al. claim to show
that the two dimensional classical Heisenberg model does not have a massless
phase.” is strongly inadequate.
As for the points that appear in the Comment:
• (1) The purpose of the paper [2] is to fill a gap in the research about
the critical properties of the Heisenberg model. This gap is the following
one: in Ref. [3] a scenario was proposed where the 2D Heisenberg model
should undergo a KT phase transition at a finite temperature. This sce-
nario is based mainly on three hypotheses, the third one (which states
the non–percolation of the $$\boldsymbol{S}$$ –type or equatorial clusters) being left in [3]
without a plausible justification. To back up that hypothesis a numerical
| <h1>Reply to A. Patrascioiu’s and E. Seiler’s comment on our paper</h1>
<h1>Percolation properties of the 2D Heisenberg
model</h1>
<p>B. Allés $$\mathrm{a}$$ , J. J. Alonso $$\mathrm{b}$$ , C. Criado $$\mathrm{b}$$ , M. Pepe $$\mathrm{c}$$</p>
<p>$$\mathrm{a}$$ Dipartimento di Fisica, Universita di Milano-Bicocca
and INFN Sezione di Milano, Milano, Italy</p>
<p>$$^\mathrm{b}$$ Departamento de Fisica Aplicada I, Facultad de Ciencias, 29071 Malaga, Spain</p>
<p>The most of the problems raised by the authors of the comment [1] about
Ref. [2] are based on claims which have not been written in [2], for instance
almost all the introduction and the point (1) in [1] are based on such non–
existent claims.</p>
<p>Instead in Ref. [2] we avoid to make claims not based on well–founded
results. For instance in the abstract we write “... This result indicates how
the model can avoid a previously conjectured Kosterlitz–Thouless $$[K T]$$ phase
transition...” and in the conclusive part we notice that “Our results exclude
this massless phase for $$T\,>\,0.5$$ ”. Therefore it seems to us that the opening
sentence in the Comment [1] “In a recent letter All´es et al. claim to show
that the two dimensional classical Heisenberg model does not have a massless
phase.” is strongly inadequate.</p>
<p>As for the points that appear in the Comment:</p>
<p>• (1) The purpose of the paper [2] is to fill a gap in the research about
the critical properties of the Heisenberg model. This gap is the following
one: in Ref. [3] a scenario was proposed where the 2D Heisenberg model
should undergo a KT phase transition at a finite temperature. This sce-
nario is based mainly on three hypotheses, the third one (which states
the non–percolation of the $$\boldsymbol{S}$$ –type or equatorial clusters) being left in [3]
without a plausible justification. To back up that hypothesis a numerical</p>
| [{"type": "title", "coordinates": [134, 142, 464, 157], "content": "Reply to A. Patrascioiu\u2019s and E. Seiler\u2019s comment on our paper", "block_type": "title", "index": 1}, {"type": "title", "coordinates": [110, 170, 487, 206], "content": "Percolation properties of the 2D Heisenberg\nmodel", "block_type": "title", "index": 2}, {"type": "text", "coordinates": [163, 245, 434, 261], "content": "B. All\u00e9s $$\\mathrm{a}$$ , J. J. Alonso $$\\mathrm{b}$$ , C. Criado $$\\mathrm{b}$$ , M. Pepe $$\\mathrm{c}$$", "block_type": "text", "index": 3}, {"type": "text", "coordinates": [160, 275, 437, 304], "content": "$$\\mathrm{a}$$ Dipartimento di Fisica, Universita di Milano-Bicocca\nand INFN Sezione di Milano, Milano, Italy", "block_type": "text", "index": 4}, {"type": "text", "coordinates": [87, 310, 509, 324], "content": "$$^\\mathrm{b}$$ Departamento de Fisica Aplicada I, Facultad de Ciencias, 29071 Malaga, Spain", "block_type": "text", "index": 5}, {"type": "text", "coordinates": [99, 385, 497, 443], "content": "The most of the problems raised by the authors of the comment [1] about\nRef. [2] are based on claims which have not been written in [2], for instance\nalmost all the introduction and the point (1) in [1] are based on such non\u2013\nexistent claims.", "block_type": "text", "index": 6}, {"type": "text", "coordinates": [99, 448, 498, 564], "content": "Instead in Ref. [2] we avoid to make claims not based on well\u2013founded\nresults. For instance in the abstract we write \u201c... This result indicates how\nthe model can avoid a previously conjectured Kosterlitz\u2013Thouless $$[K T]$$ phase\ntransition...\u201d and in the conclusive part we notice that \u201cOur results exclude\nthis massless phase for $$T\\,>\\,0.5$$ \u201d. Therefore it seems to us that the opening\nsentence in the Comment [1] \u201cIn a recent letter All\u00b4es et al. claim to show\nthat the two dimensional classical Heisenberg model does not have a massless\nphase.\u201d is strongly inadequate.", "block_type": "text", "index": 7}, {"type": "text", "coordinates": [117, 583, 358, 597], "content": "As for the points that appear in the Comment:", "block_type": "text", "index": 8}, {"type": "text", "coordinates": [116, 615, 497, 717], "content": "\u2022 (1) The purpose of the paper [2] is to fill a gap in the research about\nthe critical properties of the Heisenberg model. This gap is the following\none: in Ref. [3] a scenario was proposed where the 2D Heisenberg model\nshould undergo a KT phase transition at a finite temperature. This sce-\nnario is based mainly on three hypotheses, the third one (which states\nthe non\u2013percolation of the $$\\boldsymbol{S}$$ \u2013type or equatorial clusters) being left in [3]\nwithout a plausible justification. To back up that hypothesis a numerical", "block_type": "text", "index": 9}] | [{"type": "text", "coordinates": [135, 145, 463, 159], "content": "Reply to A. Patrascioiu\u2019s and E. Seiler\u2019s comment on our paper", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [109, 172, 488, 194], "content": "Percolation properties of the 2D Heisenberg", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [272, 190, 326, 208], "content": "model", "score": 1.0, "index": 3}, {"type": "text", "coordinates": [163, 249, 210, 263], "content": "B. All\u00e9s", "score": 0.9943311810493469, "index": 4}, {"type": "inline_equation", "coordinates": [210, 252, 216, 260], "content": "\\mathrm{a}", "score": 0.62, "index": 5}, {"type": "text", "coordinates": [216, 249, 294, 263], "content": ", J. J. Alonso", "score": 1.0, "index": 6}, {"type": "inline_equation", "coordinates": [294, 250, 299, 260], "content": "\\mathrm{b}", "score": 0.44, "index": 7}, {"type": "text", "coordinates": [300, 249, 365, 263], "content": ", C. Criado", "score": 1.0, "index": 8}, {"type": "inline_equation", "coordinates": [365, 250, 370, 260], "content": "\\mathrm{b}", "score": 0.5, "index": 9}, {"type": "text", "coordinates": [371, 249, 428, 263], "content": ", M. Pepe", "score": 1.0, "index": 10}, {"type": "inline_equation", "coordinates": [428, 252, 433, 260], "content": "\\mathrm{c}", "score": 0.26, "index": 11}, {"type": "inline_equation", "coordinates": [160, 280, 165, 288], "content": "\\mathrm{a}", "score": 0.48, "index": 12}, {"type": "text", "coordinates": [165, 276, 439, 293], "content": "Dipartimento di Fisica, Universita di Milano-Bicocca", "score": 0.9901946783065796, "index": 13}, {"type": "text", "coordinates": [187, 293, 410, 305], "content": "and INFN Sezione di Milano, Milano, Italy", "score": 1.0, "index": 14}, {"type": "inline_equation", "coordinates": [91, 312, 97, 323], "content": "^\\mathrm{b}", "score": 0.41, "index": 15}, {"type": "text", "coordinates": [97, 308, 508, 330], "content": "Departamento de Fisica Aplicada I, Facultad de Ciencias, 29071 Malaga, Spain", "score": 0.9878029227256775, "index": 16}, {"type": "text", "coordinates": [116, 387, 497, 403], "content": "The most of the problems raised by the authors of the comment [1] about", "score": 1.0, "index": 17}, {"type": "text", "coordinates": [99, 401, 498, 417], "content": "Ref. [2] are based on claims which have not been written in [2], for instance", "score": 1.0, "index": 18}, {"type": "text", "coordinates": [100, 417, 497, 431], "content": "almost all the introduction and the point (1) in [1] are based on such non\u2013", "score": 1.0, "index": 19}, {"type": "text", "coordinates": [100, 432, 179, 444], "content": "existent claims.", "score": 1.0, "index": 20}, {"type": "text", "coordinates": [117, 451, 497, 464], "content": "Instead in Ref. [2] we avoid to make claims not based on well\u2013founded", "score": 1.0, "index": 21}, {"type": "text", "coordinates": [99, 464, 497, 479], "content": "results. For instance in the abstract we write \u201c... This result indicates how", "score": 1.0, "index": 22}, {"type": "text", "coordinates": [99, 479, 440, 494], "content": "the model can avoid a previously conjectured Kosterlitz\u2013Thouless ", "score": 1.0, "index": 23}, {"type": "inline_equation", "coordinates": [440, 481, 464, 493], "content": "[K T]", "score": 0.85, "index": 24}, {"type": "text", "coordinates": [464, 479, 498, 494], "content": " phase", "score": 1.0, "index": 25}, {"type": "text", "coordinates": [99, 493, 498, 509], "content": "transition...\u201d and in the conclusive part we notice that \u201cOur results exclude", "score": 1.0, "index": 26}, {"type": "text", "coordinates": [99, 507, 221, 524], "content": "this massless phase for ", "score": 1.0, "index": 27}, {"type": "inline_equation", "coordinates": [222, 510, 263, 519], "content": "T\\,>\\,0.5", "score": 0.87, "index": 28}, {"type": "text", "coordinates": [263, 507, 498, 524], "content": "\u201d. Therefore it seems to us that the opening", "score": 1.0, "index": 29}, {"type": "text", "coordinates": [99, 523, 497, 537], "content": "sentence in the Comment [1] \u201cIn a recent letter All\u00b4es et al. claim to show", "score": 1.0, "index": 30}, {"type": "text", "coordinates": [98, 536, 497, 552], "content": "that the two dimensional classical Heisenberg model does not have a massless", "score": 1.0, "index": 31}, {"type": "text", "coordinates": [99, 552, 258, 567], "content": "phase.\u201d is strongly inadequate.", "score": 1.0, "index": 32}, {"type": "text", "coordinates": [118, 585, 359, 598], "content": "As for the points that appear in the Comment:", "score": 1.0, "index": 33}, {"type": "text", "coordinates": [118, 618, 497, 632], "content": "\u2022 (1) The purpose of the paper [2] is to fill a gap in the research about", "score": 1.0, "index": 34}, {"type": "text", "coordinates": [128, 633, 498, 647], "content": "the critical properties of the Heisenberg model. This gap is the following", "score": 1.0, "index": 35}, {"type": "text", "coordinates": [128, 648, 498, 661], "content": "one: in Ref. [3] a scenario was proposed where the 2D Heisenberg model", "score": 1.0, "index": 36}, {"type": "text", "coordinates": [128, 661, 497, 675], "content": "should undergo a KT phase transition at a finite temperature. 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Patrascioiu\u2019s and E. Seiler\u2019s comment on our paper ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "Percolation properties of the 2D Heisenberg model ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "B. All\u00e9s $\\mathrm{a}$ , J. J. Alonso $\\mathrm{b}$ , C. Criado $\\mathrm{b}$ , M. Pepe $\\mathrm{c}$ $\\mathrm{a}$ Dipartimento di Fisica, Universita di Milano-Bicocca and INFN Sezione di Milano, Milano, Italy ", "page_idx": 0}, {"type": "text", "text": "", "page_idx": 0}, {"type": "text", "text": "$^\\mathrm{b}$ Departamento de Fisica Aplicada I, Facultad de Ciencias, 29071 Malaga, Spain ", "page_idx": 0}, {"type": "text", "text": "The most of the problems raised by the authors of the comment [1] about Ref. [2] are based on claims which have not been written in [2], for instance almost all the introduction and the point (1) in [1] are based on such non\u2013 existent claims. ", "page_idx": 0}, {"type": "text", "text": "Instead in Ref. [2] we avoid to make claims not based on well\u2013founded results. For instance in the abstract we write \u201c... This result indicates how the model can avoid a previously conjectured Kosterlitz\u2013Thouless $[K T]$ phase transition...\u201d and in the conclusive part we notice that \u201cOur results exclude this massless phase for $T\\,>\\,0.5$ \u201d. Therefore it seems to us that the opening sentence in the Comment [1] \u201cIn a recent letter All\u00b4es et al. claim to show that the two dimensional classical Heisenberg model does not have a massless phase.\u201d is strongly inadequate. ", "page_idx": 0}, {"type": "text", "text": "As for the points that appear in the Comment: ", "page_idx": 0}, {"type": "text", "text": "\u2022 (1) The purpose of the paper [2] is to fill a gap in the research about the critical properties of the Heisenberg model. This gap is the following one: in Ref. [3] a scenario was proposed where the 2D Heisenberg model should undergo a KT phase transition at a finite temperature. This scenario is based mainly on three hypotheses, the third one (which states the non\u2013percolation of the $\\boldsymbol{S}$ \u2013type or equatorial clusters) being left in [3] without a plausible justification. To back up that hypothesis a numerical test was cited in [3] but the details of the numerics (temperature, size of the lattice, etc.) and several data concerning the percolation properties of the system, were completely skipped. The only quoted result was (see beginning of section 4 in [3]) \u201cWe also tested numerically for $\\epsilon=1/3$ ,... There is no indication of percolation...\u201d. On the contrary, such interesting results about the critical properties should be put forward with a thorough description of the hypotheses involved. Moreover, one would like to understand how was possible to use the small value of epsilon mentioned in Ref. [3], because that value implies a really tiny temperature $T$ and consequently it requires a huge lattice size. If \u201cEverybody agrees that at $\\beta\\:=\\:2.0$ the standard action model has a finite correlation length\u201d, see [1], also everybody would like to know details about the numerics and the computer used to simulate the model at such a small temperature. 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|
0002004v1 | 0 | # Three generation neutrino mixing is
compatible with all experiments
B. Hoeneisen and C. Marı´n
Universidad San Francisco de Quito
2 February 2000
# Abstract
We consider the minimal extension of the Standard Model with three
generations of massive neutrinos that mix. We then determine the
parameters of the model that satisfy all experimental constraints.
PACS 14.60.Pq, 12.15.Ff
Three observables in disagreement with the Standard Model of Quarks
and Leptons are: i) A deficit of electron-type solar neutrinos; ii) A deficit of
muon-type atmospheric neutrinos; and, possibly, iii) The observation of the
apearance of $$\nu_{e}$$ in a beam of $$\nu_{\mu}$$ by the LSND Collaboration. The invisible
width of the $$Z$$ implies that the number of massless, or light Dirac, or light
Majorana neutrino species is $$N_{\nu}\,=\,2.993\pm0.011.$$ .[1] To account for these
observations we consider the minimal extension of the Standard Model with
three massive neutrinos that mix. The neutrino interaction eigenstates $$\nu_{l}$$ are
superpositions of the neutrino mass eigenstates $$\nu_{m}$$ :
We consider the “standard” parametrization of the unitary matrix $$U_{l m}$$ [1]:
where $$c_{i j}~\equiv~c o s{\theta}_{i j}$$ , $$s_{i j}~\equiv~s i n\theta_{i j}$$ , $$\begin{array}{r}{0\ \leq\ \theta_{i j}\ \leq\ \frac{\pi}{2}}\end{array}$$ and $$-\pi\ \leq\ \delta\ <\ \pi$$ . The
probability that an ultrarelativistic neutrino produced as $$\nu_{l}$$ decays as $$\nu_{l^{\prime}}$$
| <h1>Three generation neutrino mixing is
compatible with all experiments</h1>
<p>B. Hoeneisen and C. Marı´n</p>
<p>Universidad San Francisco de Quito
2 February 2000</p>
<h1>Abstract</h1>
<p>We consider the minimal extension of the Standard Model with three
generations of massive neutrinos that mix. We then determine the
parameters of the model that satisfy all experimental constraints.
PACS 14.60.Pq, 12.15.Ff</p>
<p>Three observables in disagreement with the Standard Model of Quarks
and Leptons are: i) A deficit of electron-type solar neutrinos; ii) A deficit of
muon-type atmospheric neutrinos; and, possibly, iii) The observation of the
apearance of $$\nu_{e}$$ in a beam of $$\nu_{\mu}$$ by the LSND Collaboration. The invisible
width of the $$Z$$ implies that the number of massless, or light Dirac, or light
Majorana neutrino species is $$N_{\nu}\,=\,2.993\pm0.011.$$ .[1] To account for these
observations we consider the minimal extension of the Standard Model with
three massive neutrinos that mix. The neutrino interaction eigenstates $$\nu_{l}$$ are
superpositions of the neutrino mass eigenstates $$\nu_{m}$$ :</p>
<p>We consider the “standard” parametrization of the unitary matrix $$U_{l m}$$ [1]:</p>
<p>where $$c_{i j}~\equiv~c o s{\theta}_{i j}$$ , $$s_{i j}~\equiv~s i n\theta_{i j}$$ , $$\begin{array}{r}{0\ \leq\ \theta_{i j}\ \leq\ \frac{\pi}{2}}\end{array}$$ and $$-\pi\ \leq\ \delta\ <\ \pi$$ . The
probability that an ultrarelativistic neutrino produced as $$\nu_{l}$$ decays as $$\nu_{l^{\prime}}$$</p>
| [{"type": "title", "coordinates": [149, 169, 447, 217], "content": "Three generation neutrino mixing is\ncompatible with all experiments", "block_type": "title", "index": 1}, {"type": "text", "coordinates": [212, 235, 382, 251], "content": "B. Hoeneisen and C. Mar\u0131\u00b4n", "block_type": "text", "index": 2}, {"type": "text", "coordinates": [210, 262, 384, 290], "content": "Universidad San Francisco de Quito\n2 February 2000", "block_type": "text", "index": 3}, {"type": "title", "coordinates": [273, 320, 321, 333], "content": "Abstract", "block_type": "title", "index": 4}, {"type": "text", "coordinates": [131, 341, 463, 394], "content": "We consider the minimal extension of the Standard Model with three\ngenerations of massive neutrinos that mix. We then determine the\nparameters of the model that satisfy all experimental constraints.\nPACS 14.60.Pq, 12.15.Ff", "block_type": "text", "index": 5}, {"type": "text", "coordinates": [101, 407, 493, 537], "content": "Three observables in disagreement with the Standard Model of Quarks\nand Leptons are: i) A deficit of electron-type solar neutrinos; ii) A deficit of\nmuon-type atmospheric neutrinos; and, possibly, iii) The observation of the\napearance of $$\\nu_{e}$$ in a beam of $$\\nu_{\\mu}$$ by the LSND Collaboration. The invisible\nwidth of the $$Z$$ implies that the number of massless, or light Dirac, or light\nMajorana neutrino species is $$N_{\\nu}\\,=\\,2.993\\pm0.011.$$ .[1] To account for these\nobservations we consider the minimal extension of the Standard Model with\nthree massive neutrinos that mix. The neutrino interaction eigenstates $$\\nu_{l}$$ are\nsuperpositions of the neutrino mass eigenstates $$\\nu_{m}$$ :", "block_type": "text", "index": 6}, {"type": "interline_equation", "coordinates": [250, 548, 344, 578], "content": "", "block_type": "interline_equation", "index": 7}, {"type": "text", "coordinates": [101, 587, 483, 602], "content": "We consider the \u201cstandard\u201d parametrization of the unitary matrix $$U_{l m}$$ [1]:", "block_type": "text", "index": 8}, {"type": "interline_equation", "coordinates": [101, 613, 500, 661], "content": "", "block_type": "interline_equation", "index": 9}, {"type": "text", "coordinates": [101, 683, 492, 713], "content": "where $$c_{i j}~\\equiv~c o s{\\theta}_{i j}$$ , $$s_{i j}~\\equiv~s i n\\theta_{i j}$$ , $$\\begin{array}{r}{0\\ \\leq\\ \\theta_{i j}\\ \\leq\\ \\frac{\\pi}{2}}\\end{array}$$ and $$-\\pi\\ \\leq\\ \\delta\\ <\\ \\pi$$ . 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Mar\u0131\u00b4n", "score": 1.0, "index": 3}, {"type": "text", "coordinates": [210, 264, 383, 278], "content": "Universidad San Francisco de Quito", "score": 1.0, "index": 4}, {"type": "text", "coordinates": [257, 280, 336, 290], "content": "2 February 2000", "score": 1.0, "index": 5}, {"type": "text", "coordinates": [272, 322, 322, 334], "content": "Abstract", "score": 1.0, "index": 6}, {"type": "text", "coordinates": [132, 344, 463, 355], "content": "We consider the minimal extension of the Standard Model with three", "score": 1.0, "index": 7}, {"type": "text", "coordinates": [131, 357, 463, 369], "content": "generations of massive neutrinos that mix. We then determine the", "score": 1.0, "index": 8}, {"type": "text", "coordinates": [130, 371, 446, 383], "content": "parameters of the model that satisfy all experimental constraints.", "score": 1.0, "index": 9}, {"type": "text", "coordinates": [131, 384, 251, 397], "content": "PACS 14.60.Pq, 12.15.Ff", "score": 1.0, "index": 10}, {"type": "text", "coordinates": [119, 409, 492, 424], "content": "Three observables in disagreement with the Standard Model of Quarks", "score": 1.0, "index": 11}, {"type": "text", "coordinates": [101, 425, 493, 438], "content": "and Leptons are: i) A deficit of electron-type solar neutrinos; ii) A deficit of", "score": 1.0, "index": 12}, {"type": "text", "coordinates": [101, 439, 492, 452], "content": "muon-type atmospheric neutrinos; and, possibly, iii) The observation of the", "score": 1.0, "index": 13}, {"type": "text", "coordinates": [101, 453, 171, 466], "content": "apearance of ", "score": 1.0, "index": 14}, {"type": "inline_equation", "coordinates": [172, 456, 182, 465], "content": "\\nu_{e}", "score": 0.91, "index": 15}, {"type": "text", "coordinates": [182, 453, 256, 466], "content": " in a beam of ", "score": 1.0, "index": 16}, {"type": "inline_equation", "coordinates": [256, 456, 267, 466], "content": "\\nu_{\\mu}", "score": 0.92, "index": 17}, {"type": "text", "coordinates": [268, 453, 492, 466], "content": " by the LSND Collaboration. The invisible", "score": 1.0, "index": 18}, {"type": "text", "coordinates": [102, 468, 169, 481], "content": "width of the ", "score": 1.0, "index": 19}, {"type": "inline_equation", "coordinates": [170, 469, 179, 478], "content": "Z", "score": 0.9, "index": 20}, {"type": "text", "coordinates": [179, 468, 491, 481], "content": " implies that the number of massless, or light Dirac, or light", "score": 1.0, "index": 21}, {"type": "text", "coordinates": [102, 482, 257, 496], "content": "Majorana neutrino species is ", "score": 1.0, "index": 22}, {"type": "inline_equation", "coordinates": [258, 483, 363, 494], "content": "N_{\\nu}\\,=\\,2.993\\pm0.011.", "score": 0.8, "index": 23}, {"type": "text", "coordinates": [364, 482, 492, 496], "content": ".[1] To account for these", "score": 1.0, "index": 24}, {"type": "text", "coordinates": [102, 496, 492, 509], "content": "observations we consider the minimal extension of the Standard Model with", "score": 1.0, "index": 25}, {"type": "text", "coordinates": [101, 511, 462, 524], "content": "three massive neutrinos that mix. The neutrino interaction eigenstates ", "score": 1.0, "index": 26}, {"type": "inline_equation", "coordinates": [463, 515, 472, 523], "content": "\\nu_{l}", "score": 0.9, "index": 27}, {"type": "text", "coordinates": [472, 511, 492, 524], "content": " are", "score": 1.0, "index": 28}, {"type": "text", "coordinates": [101, 525, 347, 540], "content": "superpositions of the neutrino mass eigenstates ", "score": 1.0, "index": 29}, {"type": "inline_equation", "coordinates": [348, 530, 362, 537], "content": "\\nu_{m}", "score": 0.89, "index": 30}, {"type": "text", "coordinates": [362, 525, 366, 540], "content": ":", "score": 1.0, "index": 31}, {"type": "interline_equation", "coordinates": [250, 548, 344, 578], "content": "|\\nu_{l}\\rangle=\\sum_{m}U_{l m}|\\nu_{m}\\rangle", "score": 0.94, "index": 32}, {"type": "text", "coordinates": [101, 588, 446, 604], "content": "We consider the \u201cstandard\u201d parametrization of the unitary matrix ", "score": 1.0, "index": 33}, {"type": "inline_equation", "coordinates": [446, 591, 465, 603], "content": "U_{l m}", "score": 0.83, "index": 34}, {"type": "text", "coordinates": [466, 588, 481, 604], "content": "[1]:", "score": 1.0, "index": 35}, {"type": "interline_equation", "coordinates": [101, 613, 500, 661], "content": "\\left(\\begin{array}{c}{{\\nu_{e}}}\\\\ {{\\nu_{\\mu}}}\\\\ {{\\nu_{\\tau}}}\\end{array}\\right)=\\left(\\begin{array}{c c c}{{c_{12}c_{13}}}&{{s_{12}c_{13}}}&{{s_{13}e^{-i\\delta}}}\\\\ {{-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\\delta}}}&{{c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\\delta}}}&{{s_{23}c_{13}}}\\\\ {{s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\\delta}}}&{{-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\\delta}}}&{{c_{23}c_{13}}}\\end{array}\\right)\\left(\\begin{array}{c}{{\\nu_{1}}}\\\\ {{\\nu_{2}}}\\\\ {{\\nu_{3}}}\\end{array}\\right)", "score": 0.92, "index": 36}, {"type": "text", "coordinates": [101, 685, 137, 701], "content": "where ", "score": 1.0, "index": 37}, {"type": "inline_equation", "coordinates": [137, 687, 201, 700], "content": "c_{i j}~\\equiv~c o s{\\theta}_{i j}", "score": 0.91, "index": 38}, {"type": "text", "coordinates": [201, 685, 210, 701], "content": ", ", "score": 1.0, "index": 39}, {"type": "inline_equation", "coordinates": [210, 687, 275, 700], "content": "s_{i j}~\\equiv~s i n\\theta_{i j}", "score": 0.89, "index": 40}, {"type": "text", "coordinates": [275, 685, 283, 701], "content": ", ", "score": 1.0, "index": 41}, {"type": "inline_equation", "coordinates": [283, 687, 354, 700], "content": "\\begin{array}{r}{0\\ \\leq\\ \\theta_{i j}\\ \\leq\\ \\frac{\\pi}{2}}\\end{array}", "score": 0.89, "index": 42}, {"type": "text", "coordinates": [354, 685, 383, 701], "content": " and ", "score": 1.0, "index": 43}, {"type": "inline_equation", "coordinates": [384, 687, 457, 698], "content": "-\\pi\\ \\leq\\ \\delta\\ <\\ \\pi", "score": 0.9, "index": 44}, {"type": "text", "coordinates": [457, 685, 493, 701], "content": ". The", "score": 1.0, "index": 45}, {"type": "text", "coordinates": [102, 700, 410, 714], "content": "probability that an ultrarelativistic neutrino produced as ", "score": 1.0, "index": 46}, {"type": "inline_equation", "coordinates": [410, 705, 419, 712], "content": "\\nu_{l}", "score": 0.88, "index": 47}, {"type": "text", "coordinates": [419, 700, 479, 714], "content": " decays as ", "score": 1.0, "index": 48}, {"type": "inline_equation", "coordinates": [479, 705, 490, 712], "content": "\\nu_{l^{\\prime}}", "score": 0.83, "index": 49}] | [] | [{"type": "block", "coordinates": [250, 548, 344, 578], "content": "", "caption": ""}, {"type": "block", "coordinates": [101, 613, 500, 661], "content": "", "caption": ""}, {"type": "inline", "coordinates": [172, 456, 182, 465], "content": "\\nu_{e}", "caption": ""}, {"type": "inline", "coordinates": [256, 456, 267, 466], "content": "\\nu_{\\mu}", "caption": ""}, {"type": "inline", "coordinates": [170, 469, 179, 478], "content": "Z", "caption": ""}, {"type": "inline", "coordinates": [258, 483, 363, 494], "content": "N_{\\nu}\\,=\\,2.993\\pm0.011.", "caption": ""}, {"type": "inline", "coordinates": [463, 515, 472, 523], "content": "\\nu_{l}", "caption": ""}, {"type": "inline", "coordinates": [348, 530, 362, 537], "content": "\\nu_{m}", "caption": ""}, {"type": "inline", "coordinates": [446, 591, 465, 603], "content": "U_{l m}", "caption": ""}, {"type": "inline", "coordinates": [137, 687, 201, 700], "content": "c_{i j}~\\equiv~c o s{\\theta}_{i j}", "caption": ""}, {"type": "inline", "coordinates": [210, 687, 275, 700], "content": "s_{i j}~\\equiv~s i n\\theta_{i j}", "caption": ""}, {"type": "inline", "coordinates": [283, 687, 354, 700], "content": "\\begin{array}{r}{0\\ \\leq\\ \\theta_{i j}\\ \\leq\\ \\frac{\\pi}{2}}\\end{array}", "caption": ""}, {"type": "inline", "coordinates": [384, 687, 457, 698], "content": "-\\pi\\ \\leq\\ \\delta\\ <\\ \\pi", "caption": ""}, {"type": "inline", "coordinates": [410, 705, 419, 712], "content": "\\nu_{l}", "caption": ""}, {"type": "inline", "coordinates": [479, 705, 490, 712], "content": "\\nu_{l^{\\prime}}", "caption": ""}] | [] | [612.0, 792.0] | [{"type": "text", "text": "Three generation neutrino mixing is compatible with all experiments ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "B. Hoeneisen and C. Mar\u0131\u00b4n ", "page_idx": 0}, {"type": "text", "text": "Universidad San Francisco de Quito 2 February 2000 ", "page_idx": 0}, {"type": "text", "text": "Abstract ", "text_level": 1, "page_idx": 0}, {"type": "text", "text": "We consider the minimal extension of the Standard Model with three generations of massive neutrinos that mix. We then determine the parameters of the model that satisfy all experimental constraints. PACS 14.60.Pq, 12.15.Ff ", "page_idx": 0}, {"type": "text", "text": "Three observables in disagreement with the Standard Model of Quarks and Leptons are: i) A deficit of electron-type solar neutrinos; ii) A deficit of muon-type atmospheric neutrinos; and, possibly, iii) The observation of the apearance of $\\nu_{e}$ in a beam of $\\nu_{\\mu}$ by the LSND Collaboration. The invisible width of the $Z$ implies that the number of massless, or light Dirac, or light Majorana neutrino species is $N_{\\nu}\\,=\\,2.993\\pm0.011.$ .[1] To account for these observations we consider the minimal extension of the Standard Model with three massive neutrinos that mix. The neutrino interaction eigenstates $\\nu_{l}$ are superpositions of the neutrino mass eigenstates $\\nu_{m}$ : ", "page_idx": 0}, {"type": "equation", "text": "$$\n|\\nu_{l}\\rangle=\\sum_{m}U_{l m}|\\nu_{m}\\rangle\n$$", "text_format": "latex", "page_idx": 0}, {"type": "text", "text": "We consider the \u201cstandard\u201d parametrization of the unitary matrix $U_{l m}$ [1]: ", "page_idx": 0}, {"type": "equation", "text": "$$\n\\left(\\begin{array}{c}{{\\nu_{e}}}\\\\ {{\\nu_{\\mu}}}\\\\ {{\\nu_{\\tau}}}\\end{array}\\right)=\\left(\\begin{array}{c c c}{{c_{12}c_{13}}}&{{s_{12}c_{13}}}&{{s_{13}e^{-i\\delta}}}\\\\ {{-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\\delta}}}&{{c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\\delta}}}&{{s_{23}c_{13}}}\\\\ {{s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\\delta}}}&{{-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\\delta}}}&{{c_{23}c_{13}}}\\end{array}\\right)\\left(\\begin{array}{c}{{\\nu_{1}}}\\\\ {{\\nu_{2}}}\\\\ {{\\nu_{3}}}\\end{array}\\right)\n$$", "text_format": "latex", "page_idx": 0}, {"type": "text", "text": "where $c_{i j}~\\equiv~c o s{\\theta}_{i j}$ , $s_{i j}~\\equiv~s i n\\theta_{i j}$ , $\\begin{array}{r}{0\\ \\leq\\ \\theta_{i j}\\ \\leq\\ \\frac{\\pi}{2}}\\end{array}$ and $-\\pi\\ \\leq\\ \\delta\\ <\\ \\pi$ . 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The neutrino interaction eigenstates ", "type": "text"}, {"bbox": [463, 515, 472, 523], "score": 0.9, "content": "\\nu_{l}", "type": "inline_equation", "height": 8, "width": 9}, {"bbox": [472, 511, 492, 524], "score": 1.0, "content": " are", "type": "text"}], "index": 17}, {"bbox": [101, 525, 366, 540], "spans": [{"bbox": [101, 525, 347, 540], "score": 1.0, "content": "superpositions of the neutrino mass eigenstates ", "type": "text"}, {"bbox": [348, 530, 362, 537], "score": 0.89, "content": "\\nu_{m}", "type": "inline_equation", "height": 7, "width": 14}, {"bbox": [362, 525, 366, 540], "score": 1.0, "content": ":", "type": "text"}], "index": 18}], "index": 14, "page_num": "page_0", "page_size": [612.0, 792.0], "bbox_fs": [101, 409, 493, 540]}, {"type": "interline_equation", "bbox": [250, 548, 344, 578], "lines": [{"bbox": [250, 548, 344, 578], "spans": [{"bbox": [250, 548, 344, 578], "score": 0.94, "content": "|\\nu_{l}\\rangle=\\sum_{m}U_{l m}|\\nu_{m}\\rangle", "type": "interline_equation"}], "index": 19}], "index": 19, "page_num": "page_0", "page_size": [612.0, 792.0]}, {"type": "text", "bbox": [101, 587, 483, 602], "lines": [{"bbox": [101, 588, 481, 604], "spans": [{"bbox": [101, 588, 446, 604], "score": 1.0, "content": "We consider the \u201cstandard\u201d parametrization of the unitary matrix ", "type": "text"}, {"bbox": [446, 591, 465, 603], "score": 0.83, "content": "U_{l m}", "type": "inline_equation", "height": 12, "width": 19}, {"bbox": [466, 588, 481, 604], "score": 1.0, "content": "[1]:", "type": "text"}], "index": 20}], "index": 20, "page_num": "page_0", "page_size": [612.0, 792.0], "bbox_fs": [101, 588, 481, 604]}, {"type": "interline_equation", "bbox": [101, 613, 500, 661], "lines": [{"bbox": [101, 613, 500, 661], "spans": [{"bbox": [101, 613, 500, 661], "score": 0.92, "content": "\\left(\\begin{array}{c}{{\\nu_{e}}}\\\\ {{\\nu_{\\mu}}}\\\\ {{\\nu_{\\tau}}}\\end{array}\\right)=\\left(\\begin{array}{c c c}{{c_{12}c_{13}}}&{{s_{12}c_{13}}}&{{s_{13}e^{-i\\delta}}}\\\\ {{-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\\delta}}}&{{c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\\delta}}}&{{s_{23}c_{13}}}\\\\ {{s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\\delta}}}&{{-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\\delta}}}&{{c_{23}c_{13}}}\\end{array}\\right)\\left(\\begin{array}{c}{{\\nu_{1}}}\\\\ {{\\nu_{2}}}\\\\ {{\\nu_{3}}}\\end{array}\\right)", "type": "interline_equation"}], "index": 21}], "index": 21, "page_num": "page_0", "page_size": [612.0, 792.0]}, {"type": "text", "bbox": [101, 683, 492, 713], "lines": [{"bbox": [101, 685, 493, 701], "spans": [{"bbox": [101, 685, 137, 701], "score": 1.0, "content": "where ", "type": "text"}, {"bbox": [137, 687, 201, 700], "score": 0.91, "content": "c_{i j}~\\equiv~c o s{\\theta}_{i j}", "type": "inline_equation", "height": 13, "width": 64}, {"bbox": [201, 685, 210, 701], "score": 1.0, "content": ", ", "type": "text"}, {"bbox": [210, 687, 275, 700], "score": 0.89, "content": "s_{i j}~\\equiv~s i n\\theta_{i j}", "type": "inline_equation", "height": 13, "width": 65}, {"bbox": [275, 685, 283, 701], "score": 1.0, "content": ", ", "type": "text"}, {"bbox": [283, 687, 354, 700], "score": 0.89, "content": "\\begin{array}{r}{0\\ \\leq\\ \\theta_{i j}\\ \\leq\\ \\frac{\\pi}{2}}\\end{array}", "type": "inline_equation", "height": 13, "width": 71}, {"bbox": [354, 685, 383, 701], "score": 1.0, "content": " and ", "type": "text"}, {"bbox": [384, 687, 457, 698], "score": 0.9, "content": "-\\pi\\ \\leq\\ \\delta\\ <\\ \\pi", "type": "inline_equation", "height": 11, "width": 73}, {"bbox": [457, 685, 493, 701], "score": 1.0, "content": ". The", "type": "text"}], "index": 22}, {"bbox": [102, 700, 490, 714], "spans": [{"bbox": [102, 700, 410, 714], "score": 1.0, "content": "probability that an ultrarelativistic neutrino produced as ", "type": "text"}, {"bbox": [410, 705, 419, 712], "score": 0.88, "content": "\\nu_{l}", "type": "inline_equation", "height": 7, "width": 9}, {"bbox": [419, 700, 479, 714], "score": 1.0, "content": " decays as ", "type": "text"}, {"bbox": [479, 705, 490, 712], "score": 0.83, "content": "\\nu_{l^{\\prime}}", "type": "inline_equation", "height": 7, "width": 11}], "index": 23}], "index": 22.5, "page_num": "page_0", "page_size": [612.0, 792.0], "bbox_fs": [101, 685, 493, 714]}]} |
|
0002004v1 | 4 | with 116 degrees of freedom, including the 8 discussed earlier plus the 108
measurements by the Homestake Collaboration from 1970.281 to 1994.388[12]
we obtain the allowed region shown in Figure 2.
The reliability of $$M_{2}^{2}\mathrm{~-~}M_{1}^{2}$$ depends on the correctness of the error as-
signed to the Homestake observed-to-predicted flux ratio. For example, if the
Homestake error listed in Table 1 is doubled we obtain the solutions shown
in Figure 3.
In view of the preceeding results let us assume that neutrinos indeed
have mass. The question then arizes wether neutrinos are distinct from an-
tineutrinos (Dirac neutrinos) or wether neutrinos are their own antiparticles
(Majorana neutrinos). This latter possibility arizes because neutrinos have
no electric charge.
Let us consider Big-Bang nucleosynthesis that determines the abundances
of the light elements $$D$$ , $$^{3}H e$$ , $$^4H e$$ and $$^7L i$$ . These abundances are determined
by the temperatures of freezout $$T_{f}\approx1M e V$$ when the reaction rates $$\propto T_{f}^{5}$$
become comparable to the expansion rate $$\propto T_{f}^{2}\times(5.5+\textstyle{\frac{7}{4}}{N_{\nu}})^{1/2}$$ . Here $$N_{\nu}$$ is
the equivalent number of massless neutrino flavors that are ultrarelativistic
at $$T_{f}$$ and are still in thermal equilibrium with photons and electrons at
that temperature. The calculated abundances of the light elements are in
agreement with observations if $$1.6\,\leq\,N_{\nu}\,\leq\,4.0$$ at $$95\%$$ confidence level.[1]
For three generations of Majorana neutrinos, $$N_{\nu}=3$$ . For three generations
of Dirac neutrinos, $$N_{\nu}\,=\,6$$ while in thermal equilibrium. However, in the
Standard Model only the left-handed component of neutrinos couple to $$Z$$ ,
$$W^{+}$$ and $$W^{-}$$ . Right-handed neutrinos are not in thermal equilibrium at
| <p>with 116 degrees of freedom, including the 8 discussed earlier plus the 108
measurements by the Homestake Collaboration from 1970.281 to 1994.388[12]
we obtain the allowed region shown in Figure 2.</p>
<p>The reliability of $$M_{2}^{2}\mathrm{~-~}M_{1}^{2}$$ depends on the correctness of the error as-
signed to the Homestake observed-to-predicted flux ratio. For example, if the
Homestake error listed in Table 1 is doubled we obtain the solutions shown
in Figure 3.</p>
<p>In view of the preceeding results let us assume that neutrinos indeed
have mass. The question then arizes wether neutrinos are distinct from an-
tineutrinos (Dirac neutrinos) or wether neutrinos are their own antiparticles
(Majorana neutrinos). This latter possibility arizes because neutrinos have
no electric charge.</p>
<p>Let us consider Big-Bang nucleosynthesis that determines the abundances
of the light elements $$D$$ , $$^{3}H e$$ , $$^4H e$$ and $$^7L i$$ . These abundances are determined
by the temperatures of freezout $$T_{f}\approx1M e V$$ when the reaction rates $$\propto T_{f}^{5}$$
become comparable to the expansion rate $$\propto T_{f}^{2}\times(5.5+\textstyle{\frac{7}{4}}{N_{\nu}})^{1/2}$$ . Here $$N_{\nu}$$ is
the equivalent number of massless neutrino flavors that are ultrarelativistic
at $$T_{f}$$ and are still in thermal equilibrium with photons and electrons at
that temperature. The calculated abundances of the light elements are in
agreement with observations if $$1.6\,\leq\,N_{\nu}\,\leq\,4.0$$ at $$95\%$$ confidence level.[1]
For three generations of Majorana neutrinos, $$N_{\nu}=3$$ . For three generations
of Dirac neutrinos, $$N_{\nu}\,=\,6$$ while in thermal equilibrium. However, in the
Standard Model only the left-handed component of neutrinos couple to $$Z$$ ,
$$W^{+}$$ and $$W^{-}$$ . Right-handed neutrinos are not in thermal equilibrium at</p>
| [{"type": "image", "coordinates": [179, 119, 407, 273], "content": "", "block_type": "image", "index": 1}, {"type": "text", "coordinates": [102, 366, 491, 409], "content": "with 116 degrees of freedom, including the 8 discussed earlier plus the 108\nmeasurements by the Homestake Collaboration from 1970.281 to 1994.388[12]\nwe obtain the allowed region shown in Figure 2.", "block_type": "text", "index": 2}, {"type": "text", "coordinates": [101, 410, 492, 467], "content": "The reliability of $$M_{2}^{2}\\mathrm{~-~}M_{1}^{2}$$ depends on the correctness of the error as-\nsigned to the Homestake observed-to-predicted flux ratio. For example, if the\nHomestake error listed in Table 1 is doubled we obtain the solutions shown\nin Figure 3.", "block_type": "text", "index": 3}, {"type": "text", "coordinates": [101, 468, 492, 539], "content": "In view of the preceeding results let us assume that neutrinos indeed\nhave mass. The question then arizes wether neutrinos are distinct from an-\ntineutrinos (Dirac neutrinos) or wether neutrinos are their own antiparticles\n(Majorana neutrinos). This latter possibility arizes because neutrinos have\nno electric charge.", "block_type": "text", "index": 4}, {"type": "text", "coordinates": [101, 540, 493, 715], "content": "Let us consider Big-Bang nucleosynthesis that determines the abundances\nof the light elements $$D$$ , $$^{3}H e$$ , $$^4H e$$ and $$^7L i$$ . These abundances are determined\nby the temperatures of freezout $$T_{f}\\approx1M e V$$ when the reaction rates $$\\propto T_{f}^{5}$$\nbecome comparable to the expansion rate $$\\propto T_{f}^{2}\\times(5.5+\\textstyle{\\frac{7}{4}}{N_{\\nu}})^{1/2}$$ . Here $$N_{\\nu}$$ is\nthe equivalent number of massless neutrino flavors that are ultrarelativistic\nat $$T_{f}$$ and are still in thermal equilibrium with photons and electrons at\nthat temperature. The calculated abundances of the light elements are in\nagreement with observations if $$1.6\\,\\leq\\,N_{\\nu}\\,\\leq\\,4.0$$ at $$95\\%$$ confidence level.[1]\nFor three generations of Majorana neutrinos, $$N_{\\nu}=3$$ . For three generations\nof Dirac neutrinos, $$N_{\\nu}\\,=\\,6$$ while in thermal equilibrium. However, in the\nStandard Model only the left-handed component of neutrinos couple to $$Z$$ ,\n$$W^{+}$$ and $$W^{-}$$ . Right-handed neutrinos are not in thermal equilibrium at", "block_type": "text", "index": 5}] | [{"type": "text", "coordinates": [103, 369, 492, 383], "content": "with 116 degrees of freedom, including the 8 discussed earlier plus the 108", "score": 1.0, "index": 1}, {"type": "text", "coordinates": [101, 383, 490, 396], "content": "measurements by the Homestake Collaboration from 1970.281 to 1994.388[12]", "score": 1.0, "index": 2}, {"type": "text", "coordinates": [102, 397, 348, 411], "content": "we obtain the allowed region shown in Figure 2.", "score": 1.0, "index": 3}, {"type": "text", "coordinates": [119, 411, 212, 426], "content": "The reliability of ", "score": 1.0, "index": 4}, {"type": "inline_equation", "coordinates": [212, 412, 262, 425], "content": "M_{2}^{2}\\mathrm{~-~}M_{1}^{2}", "score": 0.95, "index": 5}, {"type": "text", "coordinates": [263, 411, 492, 426], "content": " depends on the correctness of the error as-", "score": 1.0, "index": 6}, {"type": "text", "coordinates": [102, 427, 491, 439], "content": "signed to the Homestake observed-to-predicted flux ratio. For example, if the", "score": 1.0, "index": 7}, {"type": "text", "coordinates": [102, 441, 492, 453], "content": "Homestake error listed in Table 1 is doubled we obtain the solutions shown", "score": 1.0, "index": 8}, {"type": "text", "coordinates": [101, 455, 163, 468], "content": "in Figure 3.", "score": 1.0, "index": 9}, {"type": "text", "coordinates": [118, 470, 492, 483], "content": "In view of the preceeding results let us assume that neutrinos indeed", "score": 1.0, "index": 10}, {"type": "text", "coordinates": [100, 483, 492, 497], "content": "have mass. The question then arizes wether neutrinos are distinct from an-", "score": 1.0, "index": 11}, {"type": "text", "coordinates": [102, 499, 492, 512], "content": "tineutrinos (Dirac neutrinos) or wether neutrinos are their own antiparticles", "score": 1.0, "index": 12}, {"type": "text", "coordinates": [103, 513, 492, 527], "content": "(Majorana neutrinos). This latter possibility arizes because neutrinos have", "score": 1.0, "index": 13}, {"type": "text", "coordinates": [102, 529, 195, 541], "content": "no electric charge.", "score": 1.0, "index": 14}, {"type": "text", "coordinates": [118, 540, 493, 556], "content": "Let us consider Big-Bang nucleosynthesis that determines the abundances", "score": 1.0, "index": 15}, {"type": "text", "coordinates": [101, 556, 206, 569], "content": "of the light elements ", "score": 1.0, "index": 16}, {"type": "inline_equation", "coordinates": [207, 558, 217, 567], "content": "D", "score": 0.83, "index": 17}, {"type": "text", "coordinates": [217, 556, 222, 569], "content": ", ", "score": 1.0, "index": 18}, {"type": "inline_equation", "coordinates": [222, 557, 244, 567], "content": "^{3}H e", "score": 0.78, "index": 19}, {"type": "text", "coordinates": [244, 556, 249, 569], "content": ",", "score": 1.0, "index": 20}, {"type": "inline_equation", "coordinates": [249, 557, 271, 567], "content": "^4H e", "score": 0.63, "index": 21}, {"type": "text", "coordinates": [271, 556, 294, 569], "content": " and", "score": 1.0, "index": 22}, {"type": "inline_equation", "coordinates": [295, 557, 312, 567], "content": "^7L i", "score": 0.71, "index": 23}, {"type": "text", "coordinates": [312, 556, 492, 569], "content": ". 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Here ", "score": 1.0, "index": 31}, {"type": "inline_equation", "coordinates": [465, 588, 479, 599], "content": "N_{\\nu}", "score": 0.93, "index": 32}, {"type": "text", "coordinates": [480, 584, 495, 605], "content": " is", "score": 1.0, "index": 33}, {"type": "text", "coordinates": [101, 601, 492, 615], "content": "the equivalent number of massless neutrino flavors that are ultrarelativistic", "score": 1.0, "index": 34}, {"type": "text", "coordinates": [101, 616, 118, 629], "content": "at ", "score": 1.0, "index": 35}, {"type": "inline_equation", "coordinates": [118, 618, 131, 630], "content": "T_{f}", "score": 0.92, "index": 36}, {"type": "text", "coordinates": [131, 616, 493, 629], "content": " and are still in thermal equilibrium with photons and electrons at", "score": 1.0, "index": 37}, {"type": "text", "coordinates": [101, 631, 492, 644], "content": "that temperature. 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The \u201clower island\u201d is symmetrical. The vertical bands correspond, from left to right, to 2.5, 3.5, 4.5, 6.5 and 7.5 oscillations from Sun to Earth of the $^7B e$ line. "], "img_footnote": [], "page_idx": 4}, {"type": "text", "text": "with 116 degrees of freedom, including the 8 discussed earlier plus the 108 measurements by the Homestake Collaboration from 1970.281 to 1994.388[12] we obtain the allowed region shown in Figure 2. ", "page_idx": 4}, {"type": "text", "text": "The reliability of $M_{2}^{2}\\mathrm{~-~}M_{1}^{2}$ depends on the correctness of the error assigned to the Homestake observed-to-predicted flux ratio. For example, if the Homestake error listed in Table 1 is doubled we obtain the solutions shown in Figure 3. ", "page_idx": 4}, {"type": "text", "text": "In view of the preceeding results let us assume that neutrinos indeed have mass. The question then arizes wether neutrinos are distinct from antineutrinos (Dirac neutrinos) or wether neutrinos are their own antiparticles (Majorana neutrinos). This latter possibility arizes because neutrinos have no electric charge. ", "page_idx": 4}, {"type": "text", "text": "Let us consider Big-Bang nucleosynthesis that determines the abundances of the light elements $D$ , $^{3}H e$ , $^4H e$ and $^7L i$ . These abundances are determined by the temperatures of freezout $T_{f}\\approx1M e V$ when the reaction rates $\\propto T_{f}^{5}$ become comparable to the expansion rate $\\propto T_{f}^{2}\\times(5.5+\\textstyle{\\frac{7}{4}}{N_{\\nu}})^{1/2}$ . Here $N_{\\nu}$ is the equivalent number of massless neutrino flavors that are ultrarelativistic at $T_{f}$ and are still in thermal equilibrium with photons and electrons at that temperature. The calculated abundances of the light elements are in agreement with observations if $1.6\\,\\leq\\,N_{\\nu}\\,\\leq\\,4.0$ at $95\\%$ confidence level.[1] For three generations of Majorana neutrinos, $N_{\\nu}=3$ . For three generations of Dirac neutrinos, $N_{\\nu}\\,=\\,6$ while in thermal equilibrium. However, in the Standard Model only the left-handed component of neutrinos couple to $Z$ , $W^{+}$ and $W^{-}$ . 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0002004v1 | 3 | "Table 3: Limits on the mixing probabilities from astrophysical, accelerator\nand reactor experiment(...TRUNCATED) | "<p>Table 3: Limits on the mixing probabilities from astrophysical, accelerator\nand reactor experim(...TRUNCATED) | "[{\"type\": \"table\", \"coordinates\": [162, 141, 432, 290], \"content\": \"\", \"block_type\": \"(...TRUNCATED) | "[{\"type\": \"text\", \"coordinates\": [101, 311, 492, 325], \"content\": \"Table 3: Limits on the (...TRUNCATED) | "[{\"coordinates\": [178, 503, 406, 659], \"index\": 18.0, \"caption\": \" confidence.\", \"caption_(...TRUNCATED) | [] | "[{\"coordinates\": [162, 141, 432, 290], \"content\": \"\", \"caption\": \"\", \"footnote\": \"\"},(...TRUNCATED) | [612.0, 792.0] | "[{\"type\": \"table\", \"img_path\": \"images/e34693f6a4630b6d50b7fea14902eda53eacb639273a3b7d28541(...TRUNCATED) | "[{\"category_id\": 5, \"poly\": [450, 393, 1201, 393, 1201, 806, 450, 806], \"score\": 0.969, \"htm(...TRUNCATED) | "{\"preproc_blocks\": [{\"type\": \"table\", \"bbox\": [162, 141, 432, 290], \"blocks\": [{\"type\":(...TRUNCATED) |
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0002004v1 | 1 | "Table 1: Observed solar electron-type neutrino flux, compared to the Stan-\ndard Solar Model (SSM) (...TRUNCATED) | "<p>Table 1: Observed solar electron-type neutrino flux, compared to the Stan-\ndard Solar Model (SS(...TRUNCATED) | "[{\"type\": \"table\", \"coordinates\": [112, 125, 481, 231], \"content\": \"\", \"block_type\": \"(...TRUNCATED) | "[{\"type\": \"text\", \"coordinates\": [101, 252, 492, 268], \"content\": \"Table 1: Observed solar(...TRUNCATED) | [] | "[{\"type\": \"block\", \"coordinates\": [142, 366, 451, 397], \"content\": \"\", \"caption\": \"\"}(...TRUNCATED) | "[{\"coordinates\": [112, 125, 481, 231], \"content\": \"\", \"caption\": \"\", \"footnote\": \"\"}](...TRUNCATED) | [612.0, 792.0] | "[{\"type\": \"table\", \"img_path\": \"images/58f4e515357520a89a5c257eeb2486ac2b1e29825cfbe284d732c(...TRUNCATED) | "[{\"category_id\": 1, \"poly\": [282, 1118, 1368, 1118, 1368, 1721, 282, 1721], \"score\": 0.981}, (...TRUNCATED) | "{\"preproc_blocks\": [{\"type\": \"table\", \"bbox\": [112, 125, 481, 231], \"blocks\": [{\"type\":(...TRUNCATED) |
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0002004v1 | 2 | "Table 2: Ratio of the numbers of observed and predicted electron-type and\nmuon-type neutrinos as a(...TRUNCATED) | "<p>Table 2: Ratio of the numbers of observed and predicted electron-type and\nmuon-type neutrinos a(...TRUNCATED) | "[{\"type\": \"table\", \"coordinates\": [181, 125, 412, 202], \"content\": \"\", \"block_type\": \"(...TRUNCATED) | "[{\"type\": \"text\", \"coordinates\": [101, 224, 492, 238], \"content\": \"Table 2: Ratio of the n(...TRUNCATED) | [] | "[{\"type\": \"inline\", \"coordinates\": [321, 270, 334, 280], \"content\": \"R_{e}\", \"caption\":(...TRUNCATED) | "[{\"coordinates\": [181, 125, 412, 202], \"content\": \"\", \"caption\": \"\", \"footnote\": \"\"}](...TRUNCATED) | [612.0, 792.0] | "[{\"type\": \"table\", \"img_path\": \"images/77d9acb6b86f9c9a84ea1fbf27649993b710e71540165032c1de6(...TRUNCATED) | "[{\"category_id\": 1, \"poly\": [280, 957, 1369, 957, 1369, 1515, 280, 1515], \"score\": 0.982}, {\(...TRUNCATED) | "{\"preproc_blocks\": [{\"type\": \"table\", \"bbox\": [181, 125, 412, 202], \"blocks\": [{\"type\":(...TRUNCATED) |
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0002004v1 | 6 | "[5] KAMIOKANDE Collab., Y. Fukuda et al., Phys. Rev. Lett. 77 (1996)\n1683\n[6] Super-Kamiokande Co(...TRUNCATED) | "<p>[5] KAMIOKANDE Collab., Y. Fukuda et al., Phys. Rev. Lett. 77 (1996)\n1683\n[6] Super-Kamiokande(...TRUNCATED) | "[{\"type\": \"text\", \"coordinates\": [99, 126, 495, 390], \"content\": \"[5] KAMIOKANDE Collab., (...TRUNCATED) | "[{\"type\": \"text\", \"coordinates\": [101, 130, 491, 146], \"content\": \"[5] KAMIOKANDE Collab.,(...TRUNCATED) | [] | [] | [] | [612.0, 792.0] | [{"type": "text", "text": "", "page_idx": 6}] | "[{\"category_id\": 1, \"poly\": [277, 350, 1376, 350, 1376, 1086, 277, 1086], \"score\": 0.75}, {\"(...TRUNCATED) | "{\"preproc_blocks\": [{\"type\": \"text\", \"bbox\": [99, 126, 495, 390], \"lines\": [{\"bbox\": [1(...TRUNCATED) |
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0002004v1 | 5 | "$$T_{f}$$ : their temperature has lagged below the temperature of photons due to\nthe anihilation o(...TRUNCATED) | "<p>$$T_{f}$$ : their temperature has lagged below the temperature of photons due to\nthe anihilatio(...TRUNCATED) | "[{\"type\": \"image\", \"coordinates\": [179, 119, 407, 273], \"content\": \"\", \"block_type\": \"(...TRUNCATED) | "[{\"type\": \"inline_equation\", \"coordinates\": [102, 343, 115, 356], \"content\": \"T_{f}\", \"s(...TRUNCATED) | "[{\"coordinates\": [179, 119, 407, 273], \"index\": 9.0, \"caption\": \".\", \"caption_coordinates\(...TRUNCATED) | "[{\"type\": \"inline\", \"coordinates\": [102, 343, 115, 356], \"content\": \"T_{f}\", \"caption\":(...TRUNCATED) | [] | [612.0, 792.0] | "[{\"type\": \"image\", \"img_path\": \"images/2ce2465af6c296f9c4eea471476bfc3a9c2bf97bb24d3b8eb832c(...TRUNCATED) | "[{\"category_id\": 1, \"poly\": [283, 1146, 1368, 1146, 1368, 1386, 283, 1386], \"score\": 0.979}, (...TRUNCATED) | "{\"preproc_blocks\": [{\"type\": \"image\", \"bbox\": [179, 119, 407, 273], \"blocks\": [{\"type\":(...TRUNCATED) |
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