Milind Diwan's site


Address: Bldg 510e, Brookhaven National Laboratory, Upton, NY 11973
Address for Fedex: Department of Physics, Bldg 510, Brookhaven National Laboratory, Upton, NY 11973
Phone: 631-344-3327, fax: 631-344-4741
email: diwan at or milind.diwan at
Title: Senior Physicist

Curriculum Vitae CV


I initiated, proposed, and organized the ambitious long-baseline neutrino program in the US based on the high intensity Fermilab Main Injector and a massive underground detector (LBNF/DUNE) at the Sanford Underground Research Facility at the former Homestake gold-mine in South Dakota. The plan I developed and promoted is now the highest priority fundamental science project in the US (named Long-baseline Neutrino Facility and Deep Underground Neutrino Experiment(LBNF/DUNE)). It is also likely to be the largest international project in the US.

Here is my first talk promoting a project to measure CP violation with neutrinos with a wide band accelerator beam.

Paper that provides details of the analysis Phys.Rev.D68:012002

This is the preprint that provides justification for the configuration of LBNF/DUNE with Fermilab as the source. The Case for a Super Neutrino Beam

This is the link to the national study that I co-led and authored; this report formed the basis for the LBNF/DUNE project approval.

I have made many innovations in particle physics experiments including important measurements of neutrino electron elastic scattering and rare kaon decays. My contributions span development of analysis, software, and hardware techniques as well as leadership of key scientific projects. I am known for orgnizing ambitious science and engineering projects with high efficiency and setting achievable short term milestones.
Jump Directly to Seminars

Recent Papers

Parton distribution function uncertainties in theoretical predictions for far-forward tau neutrinos at the Large Hadron Collider

The Large Hadron Collider at CERN collides protons with center of mass energy of 14 tera-electron-volts (7 TeV on 7 TeV). These collisions produce a large number of particles that decay as they fly away from the collision point. It turns out that the decays in forward direction of the LHC produce a big flux of neutrinos. We have investigated this flux and energy spectrum and possible applications for fundamental physics.

Article on neutrinos for children. This was reviewed by children.

Detecting Ghostlike Neutrinos: Tiny Messengers From the Universe

It was a wonderful experience to do this project with Karen McNulty Walsh.

Annual reviews article on neutrino physics with focus on experimental evolution on oscillations

Annual Reviews Long Baseline Neutrinos

Another link to same review

Experiments with solar, atmospheric, reactor, and accelerator neutrinos have resulted in a coherent picture of neutrino masses and mixings of the three known flavor states. We summarize the current best knowledge of neutrino parameters and phenomenology, with a focus on the evolution of the experimental technique.

Recent Seminars

Liquid Scintillators Review at TIPP2023 Cape Town

Liquid Scintillators (Technology and Challenges)

Link to the conference indico site: TIPP2023

Milind Diwan (BNL)
September 7, 2023
Local Links

Wine and Cheese at Fermilab

Liquid Argon Detector for Far-Forward Physics at the LHC
Milind Diwan (BNL)
March 2, 2023
Local Links

Particle Physics Seminar at INFN/Frascati

Neutrinos and Far-Forward Physics at the LHC
Milind Diwan (BNL)
October 5, 2022
Local Links

Physics/Theory Colloquium at the Los Alamos National Laboratory

Neutrinos and Far-Forward Physics at the LHC
Jonathan Lee Feng (UCI) and Milind Diwan (BNL)
August 11, 2022
Local Links
Part 1 (Jonathan Feng) Slides
Part 2 (Milind Diwan) Slides
Pat 2 (Milind Diwan) keynote with animation

Particle Physics Seminar at the Saha Institute of Nuclear Physics

Far forward neutrino detectors at the high luminosity LHC
Local Link
August 8, 2022 Slides

Particle Physics Seminar at the University of Pennsylvania

Far forward neutrino detectors at the high luminosity LHC
Local Link

Particle Physics Seminar at Stony Brook University

Overview of Light Sterile Neutrino Search Video and Slides
Link to SBU site
Local Link to Video and slides
Video of Seminar

Physics Colloquium at Brown University

Sterile Neutrino Searches, November 13, 2021 Local Link to slides
Slides PDF
Slides KEY

Nuclear Engineering and Nuclear Non-proliferation Seminar

Development of Water based liquid scintillator for Detection of Neutrinos from Nuclear Reactors, January 19, 2022 Local Link to slides
Slides PDF

Physics Department Summer Lectures 2021

Basic Statistics of Charge and Time Measurements from Photo-sensors Video and Slides
Link to BNL Physics indico site

Table of contents for pedagogical material

  1. Introduction
  2. Neutrino Physics
    1. Sources of Neutrinos
    2. Neutrino Interactions
    3. Oscillations (including mathematica notebook)
    4. Aside on Index of Refraction
    5. Reactor calculations
    6. Solar calculations
  3. Detector Techniques
    1. Basics of Neutrino Detectors
    2. Special section on photomultiplier tubes
      1. Photomultiplier tubes and coaxial cables
      2. Photomultipliers with AC coupling
      3. Photomultiplier charge spectrum and absolute calibration
      4. Paper Describing the Charge Spectrum Derivation
      5. Statistics of the time resolution
      6. Comprehensive summary of charge and time statistics
    3. Liquid Scintillators
    4. Liquid argon properties
    5. Energy Loss calculations
    6. Notes on preamp, signal, and noise requirements for a liquid argon TPC
  4. Probability, Statistics, Analysis Techniques
    1. Signals and Noise
      1. Basic Mathematics of Random Noise Part 1
      2. Basic Mathematics of Random Noise Part 2
    2. Detector Spectra and the Compound Poisson
    3. Derivation of Polya from Binomial law and basics of Urn models
    4. Exponentially modified Gaussian and the Log-normal
    5. Gamma modified Gaussian
    6. Application of logistic PDF to pulse fitting
    7. Covariance and Spectrum Analysis
    8. Vibration analysis
  5. Mathematica


Here you will find a variety of notes on physics, detectors, and analysis techniques. My emphasis is on particle and nuclear physics with a special focus on neutrino physics. Some of the notes and lectures are specialized, but others can be used for classroom instruction.

You will find that I attempt to be as general as possible when discussing experimental techniques. The lectures are academic and will contain original work that connects textbook material to actual application. I have also supplied notebooks and spreadsheets to make realistic calculations.

Please feel free to use these, but I will certainly appreciate any acknowledgement.

Neutrino Physics

These set of lectures are at a level of senior undergraduate to graduate students. They are 1) a brief introduction to natural and man-made neutrino sources, 2) a survey of neutrino interactions, basic formulas for calculating event rates, and cross sections, 3) a summary of physics of oscillations and results from leading experiments. and a brief aside on the index of refraction of neutrinos Nov. 29, 2018. 4) (Feb 16, 2023) I have added a Mathematica notebook for calculating oscillation probabilities following Ohlsson and Snellman (J. Math Phys. 41, No 5 May 2000)

Neutrino Sources KEY
Neutrino Sources PDF
Neutrino Interactions KEY
Neutrino Interactions PDF
Neutrino Oscillations KEY
Neutrino Oscillations PDF
Neutrino Oscillation Calculator Math-notebook NB
Neutrino Index of Refraction PDF

Reactor Neutrino Calculations

I will provide some introductory material and mathematica notebooks for performing reactor neutrino calculations. The idea here is not to perform extremely precise calculations, but to provide enough tools to understand the physics. The notebooks should be very useful for a graduate level course. If you use them, I will certainly appreciate acknowledgement.

Some basics of reactor neutrinos. These slides were for undergraduate students.
Reactor Basics PDF

Mathematica notebooks
Inverse Beta Decay Cross Section
Reactor Spectrum Parameterization
Event Rates and Oscillations

Some data files that need to be read into above notebooks. Please note the XCCreactor.dat cross section tabulation is not very good at low energies, but it is included for comparison with the correct one from Vogel and Beacom.
Reactor Neutrino Spectrum
IBD crosssection
Daya Bay based detected spectrum (not normalized)

Notebooks in PDF form
Inverse Beta Decay Cross Section
Reactor Spectrum Parameterization
Event Rates and Oscillations

Solar Calculations

Not done yet.

Detector Techniques

In this section, I will provide materials to understand basics of radiation detectors. This includes notes in the format of slides, spreadsheets for calculations, and mathematica notebooks.

Basics of Neutrino Detectors

Neutrino Detectors 1
Neutrino Detectors 1 PDF

Neutrino Detectors 2
Neutrino Detectors 2 PDF

Special section on photomultiplier tubes

In the three lectures and associated materials below, I provide the basic tools for understanding photomultiplier tubes and their applications for particle physics. The slides are focused on what is needed for scientific analysis of experimental data. The manuals and guides from the photomultiplier vendors such as Hamamatsu and Electron-tubes are excellent and should be consulted on various technical details.

Photomultiplier Tubes and Coaxial cables

A thorough analysis is provided on how to calculate the gain, high voltage dependence, and pulse shape from a PMT. Many of the pathologies that are encountered due to poor choices are provided along with techniques for understanding the pulses. An introduction to cable transmission is provided with techniques that could be used for simulation of the effects of the cable.

Photomultiplier tubes and coaxial cables PDF

Photomultiplier tubes and coaxial cables KEY

Notebook to make the plots in the above slides NB

Notebook for calculation of cable dispersion/attenuation NB

Photomultiplier divider calculation example XLSM

Photomultipliers with AC coupling readout

Often photomultipliers (as well as other detectors) are utilized with capacitive coupling. Primary motivation for this it to provide the bias voltage for the detector on the same cable that carries the signal. The capacitive coupling is needed to separate the fast signal from the high voltage. This however leads to some complications which includes a bipolar pulse. The treatment of all this is well known in the community, nevertheless here I have performed a rather detailed analysis of the pulse shape and its consequences.

Photomultiplier with AC coupling PDF

Photomultiplier with AC coupling KEY

Notebook to make some of the plots for AC coupling

Photomultiplier charge spectrum and absolute calibration

In these set of slides, I have derived a complete, with very few assumptions or approximations, description of the expected charge spectrum from a typical photomultiplier tube. The resulting formula can be used for fitting the charge spectrum from a phototube subjected to a constant low intensity light source. If the source is sufficiently low intensity, it is possible to separate the mean intensity of photons from the gain and the variance on the gain. This subject has been treated in the literature in the past, but I found the treatment incomplete.

Photomultiplier spectrum analysis PDF

Photomultiplier spectrum analysis KEY paper on PMT charge spectrum

I have written a paper describing the PMT spectrum. This should be used together with the slides above. The mathematica code that generates the plots in the paper along with the data is provided in a link below.

Photomultiplier PAPER PDF Also see 1909.05373

PMT spectrum code and data TAR-file

Limitations on time resolution from Photomultipliers

In this subsection we will explore the time resolution. The first limitation is from the statistics of photon detection and the time distribution of scintillation photons. In these set of notes, we calculate the expected resolution if we measure the time of the first photon from a light pulse. We then calculate the effect of Poisson fluctuations on the number of detected photons. Interestingly, we end up with a time resolution that has long tails, reminiscent of data from scintillation counters.

PMT first photon resolution PDF

PMT first photon resolution KEY

Comprehensive summary of charge and time statistics

A summary of the charge and time statistics is provided. A brief comment on counting statistics is also made. For detailed derivations, please check the material above. A recorded video of a seminar is also here.

PMT charge, time, counting statistics PDF

Seminar direct link to video MP4

Liquid Scintillators

In this section, I will cover the basics of organic liquid scintillators. I will also contrast them with noble liquids. The first section of the talk will be pedagogical on the mechanics of light production in such materials, second section will provide a review of applications for particle and nuclear physics, and last will be current R and D as well as some speculations on future directions that might be fruitful. (This is based on a seminar that I gave at TIPP2023 conference in South Africa)


Liquid Argon Properties

Our group has been assembling an extensive library of properties for liquid argon as detector material. The link is provided here. The webpage is interactive.

Liquid argon properties LINK

Energy Loss Calculations

This is a link to a Mathematica notebook that has a library of common detector materials, and modules for calculating basics of energy loss in those materials. The notebook covers 1) average dEdx, 2) restricted energy loss, 3) calculations with or without density correction, 4) basic kinematic quantities in energy loss, 4) most probable energy loss, 5) energy loss distribution in thin material, 6) simulation of energy loss in thin material, 7) Particle range in materials.

At the start of the notebook, you have to select one of the many materials. If you want to add a material, please follow the format and add it. In the future, I intend to add several items: range straggling calculation, simple simulation of low energy scattering, calculation for showering particles. Further to do list: simple formulas for muon enery loss including showering at high energies. Basic simulation of electromagnetic showers.

Notebook for Energy Loss NB

Notes on preamp, signal, and noise requirements for a liquid argon TPC

I performed a conceptual evaluation of the science requirements for signal detection with low noise preamplifiers used for liquid argon time projection chambers. Many of the slides are conceoptual and quite applicable for many situations. Generally the same chain of logic has to be applied to any detector, amplification, and noise situation. I have posted them here.

Science requirements for signal and noise in liquid argon TPC

Probability, Statistics and Experimental analysis techniques

This covers topics in analysis of linear systems. It should be a basic reference for a unified treatment of noise and Fourier analysis. Some of my derivations are unusual.

Detectors Signals and Noise

Detectors Signals and Noise PDF

The subject of random noise is very important and deep; In these two lectures I present some of the mathematical tools.

Basic Mathematics of Random Noise 1 PDF

Basic Mathematics of Random Noise 2 PDF

The subject of probability and statistics is vast and varied. There are also connections between subtopics that are not obvious and sometimes mysterious because of the long history. My own interest is not the mathematics but its application to detector analysis. In the following, I will build a library of material for such purpose.


This is an example of using characteristics functions to obtain combined probability density functions. This example corresponds to detector pulses that are composed of a finite number of counts.

Detector Pulses and Compound Poisson PDF


Binomal, Urn models are fundamental to any analysis for detectors. There is a lot of confusion in the detector physics literature; mainly because of inconsistent nomenclature. This is an attempt to produce notes that are useful for the practicing experimental physicists.

Binomial, Urn models, and Polya distribution


In the following we examine the exponentially modified Gaussian and the Log-normal distributions. We will derive these distributions, and compare their various properties. We show that in most practical situations either of these can be used. We also provide references.

Exponentially modified Gaussian and the log-normal distributions PDF

Exponentially modified Gaussian and the log-normal distributions KEY


Detector pulses have similarities to the Gamma PDF (for good reasons), and so it seems natural to try convoluting it with the normal for use in modeling and fits. While I was doing this, I found a very nice solution on stack-exchange (by Mr. Huber). I will add to this over time. Gamma Modified Gaussian PDF


We examine the logistic PDF and show an application in pulse fitting to obtain the precise time and total charge in the presence of noise. The logistic PDF is an extraordinarily useful tool which appears to be underutilized. This PDF is fundamental to schemes of classification. I will discuss this separately (still in the works).

Logistic distribution and application to pulse fitting

A random sequence in time is a fundamental entity in physics (and all of science and even the stock market.). A random process is a collection of random variables indexed by time. The simplest example is an indicator function or just 1 or 0. The random number can also be a real number such as temperature. The time index can be continuous or discrete. A random process is also known as a random function of time. A particular outcome of an experiment is called a "sample function" or "sample path". This is a vast subject. We will collect some useful items from the literature here.

counting statistics PDF

counting statistics key


Here basic tools for analysis of spectra are developed.

Covariance and Spectrum analysis

Covariance and Spectrum analysis PDF

Here are some basics for mechanical vibration analysis. I wrote this lecture to provide basic understanding for physicists who needed to move large objects. These have many common features with the mathematics of noise and similar tools from electrical analysis. .

Mechanical Vibration Analysis KEY

Mechanical Vibration Analysis PDF

Notebook on 2 body vibration simulation NB


E949: Rare decays of kaons; Kplus to piplus neutrino and anti-neutrino click here

MINOS: Main Injector Neutrino Oscillations click here

The Joint FNAL-BNL study on long baseline neutrinos click here

The Daya Bay project click here

Sanford Underground Research Facility click here

The Long Baseline Neutrino Experiment LBNE which has been transformed into DUNE

PROSPECT project prospect

ICARUS experiment at Fermilab ICARUS

AIT/NEO project in Boulby AIT/NEO


click here

Technical Notes

Search under OSTI


Transparencies of talks that I gave: click here.


Computing at BNL physics and on SDCC cluster


SSH and tunnels etc.

For Summer Students


Amazing Books.

Field Guide to Continuous PDFs by G. E. Crooks

Bateman Manuscripts on Integral Transforms

Introduction to using Mathematica for simple physics calculations

Some of this material was produced for the African School of Physics in 2018. It was presented in Namibia to a group of 60 high school teachers using Raspberry PIs. Each unit has a Mathematica notebook and a PDF. Some of the units have multiple files.

Introduction to PI

Notebook to learn basics

How to do basic mechanics (high school level)

Electricity and Magnetism (high school level)

Basics of probability and statistics

Fractals, Marcov chains, and a puzzle

I keep developing new stuff all the time. I will eventually collect it into a separate section on this webpage.

This is a way to visualize Fourier transforms as projections of circles added together. It is well known idea and there are many You Tube videos on this. Here I have provided a basic Mathematica structure for those who want to play with this.

Fourier Transform Visualization NB

This material was created for the DOE Renew Program 2023. All materials for DOE Renew Program 2023

Milind Diwan

Last modified: (2023-11-02 10:56:05 EDT)